Dmitry G Eskin Physical Metallurgy of Direct Ch

Physical Metallurgy

of Direct Chill Casting

of Aluminum Alloys

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Copyright 2008 by Taylor and Francis Group, LLC

Advances in Metallic Alloys

A series edited by J.N. Fridlyander, All-RussianInstitute of Aviation Materials, Moscow, Russia andD.G. Eskin, Netherlands Institute for Metals Research,Delft, The Netherlands

Volume 1Liquid Metal Processing: Applications to Aluminum Alloy ProductionI.G. Brodova, P.S. Popel and G.I. Eskin

Volume 2Iron in Aluminum Alloys: Impurity and Alloying ElmentN.W. Belov, A.A. Aksenov and D.G. Eskin

Volume 3Magnesium Alloy Containing Rare Earth Metals: Structure and PropertiesL.L. Rokhlin

Volume 4Phase Transformations of Elements Under High PressureE.Yu Tonkov and E.G. Ponyatovsky

Volume 5Titanium Alloys: Russian Aircraft and Aerospace ApplicationsValentin N. Moiseyev

Volume 6Physical Metallurgy of Direct Chill Casting of Aluminum AlloysDmitry G. Eskin

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CRC Press is an imprint of theTaylor & Francis Group, an informa business

Boca Raton London New York

Physical Metallurgy

of Direct Chill Casting

of Aluminum Alloys

DMITRY G. ESKIN

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CRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742

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To my mama and papa

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vii

Contents

List of Symbols and Abbreviations ............................................................xiPreface .........................................................................................................xvAuthor ........................................................................................................xix

1 Direct Chill Casting: Development of the Technology ................. 1References ..................................................................................................... 17

2 Solidification of Aluminum Alloys ............................................... 192.1 Effect of Cooling Rate and Melt Temperature

on Solidifi cation of Aluminum Alloys ............................................ 192.2 Microsegregation in Aluminum Alloys ..........................................282.3 Solidifi cation Reactions and Phase Composition...........................43

2.3.1 Commercial Aluminum ........................................................432.3.2 Wrought Alloys with Manganese (3XXX Series) ................462.3.3 Al–Mg–Si Wrought Alloys (6XXX Series) ............................472.3.4 Al–Mg–Si–Cu Wrought Alloys

(6XXX and 2XXX Series) ........................................................502.3.5 Al–Mg–Mn Wrought Alloys (5XXX Series) ......................... 512.3.6 Al–Cu–Mn (Mg, Si, Ni) Wrought Alloys

(2XXX Series) ...........................................................................542.3.7 Al–Mg–Zn–(Cu) Wrought Alloys (7XXX Series) ...............552.3.8 Wrought Alloys Containing Lithium ..................................56

2.3.8.1 Al–Cu–Li Commercial Alloys ...............................562.3.8.2 Al–Li–Mg Commercial Alloys .............................. 572.3.8.3 Al–Li–Cu–Mg Commercial Alloys ...................... 57

2.4 Effect of Alloy Composition on Structure Formation: Grain Refi nement ................................................................................ 592.4.1 Mechanisms of Grain Refi nement ........................................ 592.4.2 Al–Sc–Zr Phase Diagram ......................................................682.4.3 Al–Ti–B Phase Diagram ........................................................ 702.4.4 Al–Ti–C Phase Diagram ....................................................... 71

References .....................................................................................................75

3 Solidification Patterns and Structure Formation during Direct Chill Casting ............................................................ 793.1 Shape and Dimensions of the Billet Sump ...................................... 793.2 Solidifi cation Rate and Cooling Rate

during DC Casting ............................................................................. 913.3 Effects of Process Parameters on the Formation

of Grain Structure ............................................................................. 101

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viii Contents

3.4 Effect of Process Parameters on the Amount of Nonequilibrium Eutectics ............................................................... 111

3.5 Effect of Process Parameters and Alloy Composition on the Occurrence of Some Casting Defects ................................ 115

References ................................................................................................... 122

4 Macrosegregation ........................................................................... 1254.1 Mechanisms of Macrosegregation ................................................. 125

4.1.1 Historic Overview ................................................................ 1254.1.2 Permeability........................................................................... 1324.1.3 Convection-Driven Macrosegregation .............................. 1364.1.4 Shrinkage-Driven Macrosegregation ................................ 1414.1.5 Floating Grains and Macrosegregation ............................. 1454.1.6 Deformation-Driven Macrosegregation ............................ 151

4.2 Effects of Process Parameters on Macrosegregation during DC Casting ........................................................................... 1524.2.1 Effect of Casting Speed on Macrosegregation

during DC Casting ............................................................... 1524.2.2 Effect of Melt Temperature on Macrosegregation

during DC Casting ............................................................... 1594.2.3 Dimensions of the Billet: Scaling Rule of

Macrosegregation ................................................................. 1594.2.4 Effect of Forced Convection on Macrosegregation

during DC Casting ............................................................... 1694.3 Effect of Composition on Macrosegregation:

Macrosegregation in Commercial Aluminum Alloys ................ 170References ................................................................................................... 179

5 Hot Tearing ...................................................................................... 1835.1 Thermal Contraction during Solidifi cation .................................. 1855.2 Mechanical Properties of Semi-Solid Alloys ................................200

5.2.1 Testing Techniques ...............................................................2005.2.2 Strength Properties of Aluminum Alloys

in the Semi-Solid State .........................................................2055.2.3 Ductility of Aluminum Alloys

in the Semi-Solid State .........................................................2085.3 Mechanisms and Criteria for Hot Tearing .................................... 216

5.3.1 Historic Overview of Hot Tearing Research and Suggested Mechanisms ................................................ 216

5.3.2 Hot Tearing Criteria .............................................................2255.3.2.1 Stress-Based Criteria .............................................2255.3.2.2 Strain-Based Criteria .............................................2295.3.2.3 Strain Rate-Based Criteria .................................... 2315.3.2.4 Criteria Based on Other Principles ......................234

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Contents ix

5.3.3 Application of Hot Tearing Criteria to DC Casting of Aluminum Alloys ..................................236

5.3.4 Quest for a New Hot Tearing Criterion ............................. 2405.4. Effects of Process Parameters on Hot Tearing

during DC Casting ........................................................................... 2455.4.1 Thermo-Mechanical Behavior of a DC-Cast

Billet (Ingot) ........................................................................... 2465.4.2 Effects of Composition and Casting Speed

on Hot Tearing during DC Casting ................................... 2515.4.3 Effect of Melt Temperature on Hot Tearing

during DC Casting ............................................................... 2595.4.4 Structural Features Associated with Hot

Tearing in DC Casting ......................................................... 262References ................................................................................................... 269

Concluding Remarks ...............................................................................275

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xi

List of Symbols and Abbreviations

1D one-dimensional2D two-dimensional3D three-dimensionalA a constantBi Biot numberC0 nominal alloy compositionCE eutectic compositionCL; CL solute concentration in the liquid at the solid/liquid interfaceClimit limit solubility of a solute in aluminumCS; CS solute concentration in the solid at the solid/liquid interface C SS

L solute concentration in the supersaturated liquid at the solid/liquid interface

D billet diameterDgr grain sizeDS diffusion coeffi cient of a solute in the solid phaseE Young’s modulusEq, eq equilibriumFz separation forceG shear modulusG thermal gradient, temperature gradientH depth of the sumpK partition coeffi cientK permeabilityL liquidus isothermLm vertical dimension of the mushy zoneN amount (density) of particles in the meltNi principal quantum number of the i electron shell

(Ai for aluminum)NEq, neq nonequilibriumP undercooling parameterPe Peclet numberQ fl ow rateQ growth restriction factorQw water fl ow rateR billet radius; regression coeffi cientS solidus isothermSe interfacial area concentration of the grain envelopeSv specifi c surface area of the solid phaseT temperatureTcoh coherency temperatureTm melting temperature

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xii List of Symbols and Abbreviations

Tsurf surface temperatureTth temperature of thermal contraction onset (rigidity)T· cooling rate

Vc cooling rateVcast casting speedVgrowth interfacial growth velocityVL volume of liquidVs solidifi cation rate (linear velocity of the solidifi cation front)Vshr shrinkage-fl ow velocityV volume elementacr critical defect sizeb liquid fi lm thickness; coeffi cientc specifi c heatc tortuosity constant of dendrite networkd (secondary) dendrite arm spacingf fraction of nucleating particles fe feeding ratefe volume fraction of grain envelopefl liquid fractionfr shrinkage (contraction) ratefs solid fractiong gravity accelerationh melt levelkD permeability coeffi cientkKC Kozeny–Carman constantm microstructure parameterm liquidus slopen coarsening exponent, material parameter, coeffi cientna number of atoms in a stable nucleusni number of electrons on the i level (Ai for aluminum)pr reserve of plasticityPs effective feeding pressureq heat transfer coeffi cientq/A heat fl ux through surface At running (solidifi cation) timetf local solidifi cation timetR time available for stress relieftV vulnerable time periodv average (superfi cial) fl ow velocityε thermal strain rate∆Hf enthalpy (latent heat) of fusion∆Hv enthalpy (latent heat) of evaporation∆lexp pre-shrinkage expansion∆P pressure drop∆Pcr critical pressure drop∆Pmech pressure drop due to the deformation-induced fl uid fl ow

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List of Symbols and Abbreviations xiii

∆Psh pressure drop due to the solidifi cation shrinkage∆sf volumetric entropy of fusion∆T0 solidifi cation range∆Tbr brittle temperature range∆Tc constitutional undercooling∆Tn undercooling required for nucleationΓ Gibbs–Thompson coeffi cientΞ solutal supersaturationΩ grain-refi ning criterionα angle between the tangent to the coherency isotherm

and the horizon; coeffi cientαn angle between the billet axis and the normal to the

solidifi cation front α′ Fourier numberβ volumetric shrinkage; coeffi cientβd intradendritic permeability βl extradendritic permeabilityβT volumetric thermal expansion coeffi cientε total solidifi cation shrinkage; strain; deformationεapp actual (apparent) strainεfree free thermal contraction strainεint internal strainεp elongation to failureεth linear thermal contractionφ porosityγ surface tension; effective fracture surface energy λ thermal conductivityλ1 primary dendrite arm spacingλ2 secondary dendrite arm spacingµ dynamic viscosity of the liquidν Poisson’s ratioθ dihedral angleρ densityσfr fracture stressσ ls solid/liquid interfacial energyψ shape factorψ( fs) function discriminating the mechanical behavior of a

semi-solid sampleζcr critical feeding rate∆εres reserve of technological strain (plasticity)CET columnar-to-equiaxed transitionDAS dendrite arm spacingDC casting direct chill castingEl tensile elongationEMC electromagnetic castingEPMA electron probe microanalysis

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xiv List of Symbols and Abbreviations

FEM fi nite element methodGR grain refi nedHCS hot cracking susceptibilityLTEC linear thermal expansion coeffi cientNES nonequilibrium solidusNGR not grain refi nedPFT pseudo front tracking modelSC similarity criterionSEM scanning electron microscopeSPV maximum volumetric fl ow rate per unit volume

(feeding term)SRG rate of volumetric solidifi cation shrinkageTCC thermal contraction coeffi cientUTS ultimate tensile strength

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xv

Preface

Direct chill (DC) casting is not a new technology; it has been known for more than 70 years. Despite important developments in this casting technique over the years, the core features have remained the same, and the prototypes invented in the 1930s are still evident in modern DC casting machines. For more than 60 years, this casting technology has been the primary means for producing extrusion billets and rolling ingots from a wide range of alumi-num wrought alloys. There is no other technology on the horizon that could replace DC casting. This book is not about the technology of casting, though some principles and milestones are discussed in Chapter 1.

The principles of solidifi cation and structure formation are very important for understanding the quality and performance of billets and ingots pro-duced by DC casting. This book is not about the fundamentals of solidifi ca-tion, but Chapter 2 gives all necessary information for understanding the formation of structure and defects during casting of aluminum alloys.

Today most efforts in the fi eld of solidifi cation and practical casting are concentrated on computer modeling and process simulation. Physicists and mathematicians are replacing materials scientists at the forefront of research. This book is not about modeling and simulation, but the results obtained using these methods are widely used throughout the book as tools for inter-preting experimental results and for studying the physical mechanisms involved.

At this point, the reader might ask: What is this book about? The answer is in the book title: the book is about physical metallurgy of DC casting. This means that the formations of structure, properties, and defects in the as-cast material are considered in close correlation with the physical phenomena that are involved in the solidifi cation and with the process parameters. There is a serious lack of such information in the Western literature.

The formation of structure in relation to the peculiarities of heat and mass fl ow during DC casting is the main subject of Chapter 3, while the forma-tion of major defects—macrosegregation and hot cracking—is the topic of Chapters 4 and 5. Throughout the book, the formation of structure and defects is considered in relation to the main process parameters: casting speed, melt temperature, water-fl ow rate, and grain refi nement.

In this book, I have tried to present a logical system of structure and defect formation based on the specifi c features of the DC casting process. The basis of this system is, on the one hand, melt fl ow and heat fl ow (cooling) in dif-ferent parts of the solidifying domain and, on the other hand, kinetics of solidifi cation and the solidifi cation path of the alloy. The complexity of the mechanisms involved in the structure and defect formation is the main problem that frequently hinders clear understanding of the experimentally observed patterns. In this book, I try to single out these mechanisms and

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xvi Preface

demonstrate that the seemingly controversial results reported in the litera-ture are, in fact, caused by different ratios of the same mechanisms.

This book is inspired by and based on results that have been obtained in the last 8 years from the extensive scientifi c program on solidifi cation and casting of the Netherlands Institute for Metals Research. The scientifi c foundation for understanding DC casting was established long before that, by extraordinary scientists and visionaries such as W. Roth, W. Patterson, V. Kondic, S.M. Voronov, V.I. Dobatkin, and V.A. Livanov. Among these names, Roth, Dobatkin, and Livanov should be distinguished as three indi-viduals who successfully combined the practical development of DC casting technology with fundamental studies. Dobatkin and Livanov have also writ-ten monographs (V.I. Dobatkin, Direct Chill Casting and Casting Properties of Alloy, 1948; Ingots of Aluminum Alloys, 1960; V.I. Livanov et al., Direct Chill Cast-ing of Aluminum Alloys, 1977) that were published in the former Soviet Union and remain to date the only scientifi c books on DC casting. I frequently refer to these books because they are still very valuable in many respects. Two other important books provide a background for scientifi c understanding of structure and defect formation during solidifi cation: Solidifi cation Process-ing by M.C. Flemings (1974) and Hot Tearing of Non-Ferrous Metals and Alloys by I.I. Novikov (1966).

The current book is based on the important achievements of previous gen-erations of scientists. We realize that we are building on an already exist-ing foundation, and that we can only move forward if we have taken into account what has been achieved before us. Chapters 1, 4, and 5 include his-toric overviews of technologies, theories, and hypotheses that demonstrate the brilliant heritage we can utilize in our work.

The original data that are presented in this book result from a team effort. I would like to acknowledge the contribution of post- doctoral researchers Dr. Q. Du and Dr. R. Nadella and Ph.D. students Suyitno, J. Zuidema, A. Stangeland, V. Savran, A. Turchin, and D. Ruvalcaba, who actively par-ticipated in the solidifi cation research. Our joint papers are extensively cited in the book. Technical assistance in setting up and performing experiments was provided by J.J. Jansen and J.J.H. van Etten, whose help and expertise are gratefully acknowledged.

I am a metals scientist who graduated from the distinguished Depart-ment of Metals Science of the Moscow Institute of Steel and Alloys. I am greatly indebted to my teachers, Professor V.S. Zolotorevsky and Professor I.I. Novikov, for the knowledge they imparted to me and for the passion and critical approach to the research they fostered in me. DC casting has been a familiar subject for me since childhood. My father, Professor G.I. Eskin, is a well-known scientist in solidifi cation processing who worked with the renowned Professor V.I. Dobatkin for many years. It was, however, not until 1999 when I became involved in solidifi cation science. Two professors gave me this opportunity: Professor S. Radelaar, then the scientifi c director and general manager of the Netherlands Institute for Metals Research, who hired me as a senior researcher and always supported me, and Professor L. Katgerman,

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Preface xvii

who heads the light-metals processing research at Delft University of Technology. I would like to express my profound gratitude to Professor Katgerman, who gave me many opportunities, supported me in my work, and shared with me his vast expertise. Many of the results presented in this book were obtained within the framework of the research program of the Netherlands Institute for Metals Research (www.nimr.nl), and I would like to thank Dr. S. Hoekstra for the opportunity to carry on our solidifi ca-tion research. Constant help and support from Corus Aluminium are also gratefully acknowledged.

Over the years I have met many individuals involved in solidifi cation research all over the world who have impressed me with their knowledge, attitude, and experience, including Professors A. Mo, L. Arnberg, M. Rap-paz, C. Beckermann, and Drs. R. Mathiesen, Ø. Nielsen, R. Kieft, W. Boender, A.L. Dons, G.-U. Grün, J. Grandfi eld, and J.-M. Drezet.

And fi nally, I would like to thank my father and mother for their love and encouragement. Special thanks go to my wife, Natasha, who courageously and critically read the drafts of this book.

I hope that this book will fi ll the gap in the literature on solidifi cation pro-cessing and provide new insight and perspective for DC casting research. The book is written for a wide audience that includes scientists, engineers, postgraduate and graduate students, and hopefully can be easily understood by readers without a special background in the subject.

Dmitry G. Eskin

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www.nimr.nl

xix

Author

Dmitry G. Eskin, Ph.D., received his M.Sc. and Ph.D. in physical metal-lurgy in 1985 and 1988, respectively, from the Moscow Institute of Steel and Alloys (Technical University). He worked at the Baikov Institute of Metal-lurgy (Russian Academy of Sciences) until 1999, researching precipitation hardening, alloy development, and phase composition of aluminum alloys. Since 1999, he has worked at the Netherlands Institute for Metals Research in Delft, the Netherlands. As a senior scientist and fellow, Dr. Eskin is involved in an extensive research program on solidifi cation phenomena in light alloys, including industrial applications. The focus of this research is the interconnection among solidifi cation parameters, as-cast structure, and casting defects. A well-known specialist in the fi eld of aluminum alloys, Dr. Eskin has published more than 90 scientifi c papers and co-authored three monographs.

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1

1Direct Chill Casting: Development of the Technology

Direct chill casting of aluminum alloys, commonly known as DC casting, is an example of a technology that appeared just in time to serve the needs of the industry. Before discussing the history of DC casting, we will briefl y consider the history of aluminum.

Aluminum is a “young” metal whose existence was established only 200 years ago. However, Pliny the Elder mentions a strange, light, and silvery metal in his Historia Naturalis, which might indicate that aluminum may have been discovered accidentally and then forgotten almost 2000 years ago:

One day a goldsmith in Rome was allowed to show the Emperor Tiberius a dinner plate of a new metal. The plate was very light, and almost as bright as silver. The goldsmith told the Emperor that he had made the metal from plain clay. He also assured the Emperor that only he, himself, and the Gods knew how to produce this metal from clay. The Emperor became very interested, and as a fi nancial expert he was also a little con-cerned. The Emperor felt immediately, however, that all his treasures of gold and silver would decline in value if people started to produce this bright metal of clay. Therefore, instead of giving the goldsmith the regard expected, he ordered him to be beheaded.

Modern scientists and inventors were more fortunate and, as a result of their efforts, we now have a variety of aluminum alloys that are used in a wide range of applications.

In 1808 the Englishman H. Davy established the existence of a new metal that he called alumium. This name later was changed to aluminum (U.S.A.) and aluminium (U.K.). It was not until 1825 that minute amounts of pure aluminum were extracted by the Dane N.C. Oersted. Between 1827 and 1845, the German F. Wöhler developed the fi rst process to produce aluminum powder by reacting potassium with anhydrous aluminum chloride. He also determined some physical properties of aluminum, including density, which appeared to be the most remarkable characteristic of the new metal. Jules Verne wrote in his “From the Earth to the Moon” in 1865 about the material of his fi ctitious space capsule:

This valuable metal possesses the whiteness of silver, the indestructibil-ity of gold, the tenacity of iron, the fusibility of copper, the lightness of glass. It is easily wrought, is very widely distributed, forming the base

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2 Physical Metallurgy of Direct Chill Casting of Aluminum Alloys

of most of the rocks, is three times lighter than iron, and seems to have been created for the express purpose of furnishing us with the material for our projectile.

The era of light metals would have begun if not for one vital problem—the price. Despite some improvement to Wöhler’s process in 1854 by the Frenchman H.E.S.-C. Deville, aluminum remained very expensive, infact it cost more than platinum and gold. An ingot of aluminum was presented at the Paris World Exhibition in 1855 as a new precious metal. During the next 30 years alumi-num remained an exotic, expensive material used in jewelry, royal cutlery, plates, and parade decorations. “Silver from clay” was an unoffi cial name of the metal. Napoleon III allowed only the most honored guests to eat from aluminum plates; the others were forced to settle for silver and gold ones. In 1889 the British Royal Society presented a set of scales made from gold and aluminum to the Russian scientist D.I. Mendeleev to honor his achievements in chemistry. In 1886, two 22-year-old scientists, Paul-Louis Toussaint Héroult of France and Charles Martin Hall of the United States, independent of each other and in different countries, invented a commercial process of produc-ing pure aluminum by electrolysis of alumina dissolved in molten cryolite. Their process, the Hall–Héroult process, is still used today. In 1888, together with A.E. Hunt, C.M. Hall founded the Pittsburgh Reduction Company, now known as the Aluminum Company of America (ALCOA). By 1914, the cost of a kilogram of aluminum was down from $40 in 1860 to 40¢, and aluminum was no longer considered a precious metal. The annual production went from 15 tons in 1885 to 65,000 tons in 1913. Simultaneous or almost simultaneous discoveries and inventions occur frequently in the history of aluminum. This is an unmistakable sign of the need for such discoveries and inventions and the research that is under way throughout the industrial world.

Remarkably, Jules Verne foresaw the most promising application for aluminum—airspace vehicles. The fi rst aircraft that took to the air on December 17, 1903 at Kitty Hawk was designed and built by the Wright Brothers. Their biplane was made from wood and fabric and powered by a 12- horsepower, 4-cylinder engine. And yet, even in this fi rst successful attempt to fl y with a heavier-than-air machine, aluminum had a vital role as a one-piece cast crankcase of the engine.

One more discovery was needed to fully implement the potential of alu-minum in construction. Although castings from aluminum alloys were occasionally used in manufacturing some details, the strength of deformed aluminum was not suffi cient for its use as a structural material. The break-through came in 1908–1909 when A. Wilm of Germany found that the strength of an Al–Cu alloy would increase after several days of so-called “natural aging” after quenching. He patented the alloy and the technology of its heat treatment as “duralumin.” Now aluminum alloys could acquire the mechanical properties that would make them suitable for use in structures. The true era of aluminum had begun. It is interesting to note that the nature of hardening zones that cause room-temperature aging was discovered in



Direct Chill Casting: Development of the Technology 3

1938 simultaneously and independently by A. Guinier in France and G.D. Preston in Great Britain.

Not surprisingly, the demand for wrought aluminum alloys came from the aircraft industry, fueled by World War I and later by increased requirements for speedy delivery of mail. The fi rst all-metal (mainly duralumin) airplanes were built by the German designer H. Junkers in 1915–1916. Junkers started from steel (J1) and then shifted to duralumin in the J7 and J9. The fuselage was made from plane and corrugated sheets. In 1919 Junkers together with O. Reuter designed the fi rst all-metal passenger plane, the F13 (J13). This design served as a benchmark for several aircrafts made in different countries [1]. The Soviet Union was quick to follow. After World War I, Germany was not allowed to manufacture military aircraft, so the U.S.S.R. provided con-cessions for Junkers to build his aircraft in Moscow from 1923 to 1927. The designer A.N. Tupolev made his fi rst aluminum plane, the ANT-2, in 1924 using Russian-made duralumin. Just a year later the United States followed with the passenger Stout Air Sedan and Ford 3-AT. Tupolev made a very large, all-metal heavy bomber, the ANT-4 (TB1), in 1925. This plane was 18 m long, with a 28.7-m wing span, and was powered by two engines. In the late 1920s, Ford produced several passenger planes, including the famous 4-AT “Tin Goose.” Despite all these efforts, only 5% of all aircraft in production by 1930 were of all-metal construction. In the 1930s the corrosion resistance of duralumin had been improved by cladding with pure aluminum, and a wide variety of airplanes were manufactured from aluminum alloys. The U.S.S.R. continued to design and build record-size heavy bombers and passenger air-liners including the ANT25 in 1933 that fl ew 11,500 km nonstop in record time, in 1937 from the U.S.S.R. to the United States; the 8-engine ANT20 “Maxim Gorky” made in 1934 that was the largest aircraft of its time (33 m long with a 63-m wing span, and a passenger capacity of 48); and the ANT37 (DB2), a long-range bomber put in service in 1936. Junkers in Germany designed and produced midsize and practical passenger planes such as the Ju60 in 1932 and the Ju160 in 1934. In the United States Boeing started to produce passenger planes, the Boeing 200 in 1930 and the Boeing 247 in 1933, and was joined by Douglas with the DC1–DC3 in 1933–1935. The DC3 was the fi rst aircraft that actually enabled airlines to make money from passenger rather than mail transport. In addition to the “main players”—Germany, the United States, and U.S.S.R.—other countries made their efforts as well. France manufactured the Devoitine D332 in 1933, and the United Kingdom produced the Ensign-1 in 1934 and the de Havilland DH95 in 1938. Some of the benchmark planes are shown in Figure 1.1 [1]. Throughout the industrialized world all-metal, mainly aluminum aircraft were dominant by the late 1930s. It became obvious that mass fabrication of wrought aluminum products was necessary to sustain the development of military and civil airplanes. Let us now consider the manufacturing technology for large-scale wrought alumi-num ingots and billets required for rolling, extrusion, or forging.

From 1924 to 1939 the average weight of an aluminum fl at ingot cast in a permanent mold increased from 20 to 500 kg [2]. By the mid-1930s most




bulk ingots and billets were made by permanent-mold casting, while the increased volume and cross-section resulted in exponential deterioration of the structure and properties of the cast metal. Three main problems were intrinsically present in permanent-mold casting: turbulence during pour-ing; air-gap formation during cooling; and variable low cooling rate across the ingot. Several innovations were proposed to deal with these drawbacks. In the Züblin method the mold was fi lled gradually from the bottom to the top by moving the feeding nozzle upward and corresponding closure of the sidewall [3, 4]. This technique helped avoid large temperature gradients

FIGURE 1.1Examples of all-metal airplanes designed and built in the 1920s and 1930s: (a) the Junkers F13 (1919, Germany); (b) the ANT-4 (1925, U.S.S.R.); (c) the Ford 4-AT (1926, U.S.A.); (d) the Junkers Ju60 (1932, Germany); (e) the Boeing 247 (1933, U.S.A.); (f) the ANT-20 (1934, U.S.S.R.); (g) the Douglas DC-3 (1935, U.S.A.); and (h) the ANT-37 (DB2) (1936, U.S.S.R.) [1].

(a) (b)

(c) (d)

(e) (f)

(g) (h)




and decreased chemical and structure inhomogeneity of the ingot. Another widely used technique was the so-called tipping mold, the main purpose of which was to avoid turbulence while fi lling the large volume. The idea was the same as the process of fi lling a glass with beer in order to avoid too much foaming: one starts to fi ll the tilted glass by pouring the beer along the glass wall and gradually straightens the glass until it is completely full without foam. Another casting technology that was a transition stage to the direct chill casting was casting by dipping the fi lled mold gradually into the water [5]. With this technique, solidifi cation was almost directional from the bottom to the top and the solidifi cation front was fl at. As a result, the thermal gradients were low, and large ingots of 800 × 1300 mm2 could be cast. Fig ure 1.2 illus-trates schematically these methods of casting. However, the problems of air-gap and low cooling rates, and thus the problems of uniform structure and properties, remained unsolved and required revolutionary change in tech-nology. It was absolutely clear that there was no further room for improve-ment in the permanent-mold casting of large ingots and billets.

In response to these demands, German and American engineers devised a solution that addressed two problems successfully and simultaneously: con-trol of solidifi cation and production of large ingots and billets. The solution was in the modifi cation of a so-called continuous casting process that had been proposed and sluggishly developed for almost 80 years but never used in mass production.* Henry Bessemer, the inventor of modern steelmaking, suggested in 1856 the fi rst method of steel strip casting by pouring the melt in the opening between two rotating wheels [6]. In 1886 B. Atha of the United States suggested casting molten steel into a high, water-cooled, bottom-less mold and extracting the resulting billet with withdrawal rolls [6]. This method was used for semi-commercial production of 100 × 100 mm steel bars in the early twentieth century. However, these inventions had limited, if any, application, and the continuous casting of steel was not in high demand until the 1950s. A similar technique was developed by Siegfried Junghans in the early 1930s [7]. His machine was initially used at Wieland-Werke in Ger-many for casting brass [4]. The mold consisted of a copper tube open at both sides and surrounded by a water jacket. The melt was fed into the mold from the top and the solid part was withdrawn by rolls from the bottom. The melt feeding was adjusted to the withdrawal speed by a special system in such a way that a constant melt level was maintained in the mold. The mold was lubricated and given an up-and-down oscillating movement to prevent the sticking of the solid metal to the mold walls. Flying saws were positioned in the pit below the installation for continuous cutting of the billet into required lengths. This successful scheme was widely used for casting copper and aluminum alloys in Germany, the United States, and the U.S.S.R. Figure 1.3 depicts the Junghans method of continuous casting. Junghans later added

* The vertical DC casting of aluminum alloys is the main subject of this book. Other types of continuous casting are mentioned here only as predecessors or analogs of vertical DC casting.



6 Physical M

etallurgy of Direct C

hill Casting of A

luminum

Alloys

FIGURE 1.2Some typical methods used for casting large ingots and billets in permanent molds: (a) the Züblin mold with a feeding trough and a built-up wall [4]; (b) a tipping mold in two positions [4]; and (c) a mold with a melt before being dipped in a water tank [5].

Built-up wall

(a)

Ladle with melt

Mold in an intermediate positionduring casting

Mold in the starting position

(b) (c)

Melt

Dippingmechanism Water

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water spraying directly on the billet and made several innovations to the proper melt feeding/distribution system. Dobatkin [8] mentions that the maximum casting speed achieved for aluminum alloys with the Junghans machine was 300 mm/min for relatively small rods.

Compared with permanent-mold casting, the Junghans method offered the following advantages [9]:

A truly continuous process with the possibility of advanced automa-tion that increased productivity with less manpowerReproducible casting regimes that allowed the reproducible quality of billetsImproved feeding of the central portions of billets with a corre-spondingly increased soundness of billetsMore uniform structure across the billetBetter removal of gases during casting through the liquid portion of the billetLess scraped material

•

•

•

••

•

FIGURE 1.3A diagram of Junghans method of continuous casting [8].

Holding furnace

MeltFeeding channel

Mold

Water

Solid billet

Withdrawalrolls




At the same time, this method did not solve all problems. The following drawbacks remained, most of which were related to the fact that the heat was still extracted through the walls of the mold [9]:

Air gap formation, deep sump, and high thermal gradientsMacrosegregation and inhomogeneous structure in large billets 300–500 mm in diameterLow casting speedsNeed for a long mold with high surface quality requirements

To eliminate these shortcomings, it was necessary to develop a technology where the heat would be extracted mainly through the solid part of the casting. As a result, the sump of the casting would be shallower and the solidifi cation profi le would be fl atter. The macrosegregation, structure inho-mogeneity, and radial stresses would be much less pronounced. These needs were met by a new casting technology developed, again almost simultane-ously and independently, in Germany and the United States. The technology was given the German name “Wasserguß” or “water-casting,” and was later called “direct chill casting.” Berthold Zunkel in 1935 [10], Walter Roth in 1936 [11], and William T. Ennor in 1938 [12] fi led and subsequently received patents for the casting technology with several common features. Melt was poured from the top in an opened, relatively short, water-cooled mold that at the beginning is closed from the bottom by a dummy block connected with a hydraulic or mechanical lowering system. After the melt level in the mold reaches a certain level, the ram is lowered and the solid part of the billet or the ingot is extracted downward. The melt fl ow rate and the casting speed are adjusted in such a way that the melt level in the mold remains con-stant. As soon as the solid shell emerges from the bottom part of the mold, water is applied to the surface in the form of spray or water fi lm. Cooling of the solid billet (or ingot) is further intensifi ed by lowering it into a pit fi lled with water. The process is semi-continuous. As soon as the ram reaches its lowest position in the pit, the casting is stopped and the billet (or ingot) is removed from the pit. Figure 1.4 shows schematic drawings of these three inventions, clearly demonstrating that their similarities are more important than any differences. The new casting technology provided fl exibility in casting applications. Trials started immediately with round billets, rectan-gular ingots (or rolling slabs), and hollow billets (pipes). In addition, mul-tiple casting was possible with several molds positioned on a single casting table. DC- casting inventions were commercialized in Germany at Vereinigte Leichtmetall-Werke beginning in 1936 [4] and in the United States at ALCOA from 1934 [13]. The water cooling or direct chill in these fi rst patents was done either by dipping the billet directly into the water bath or by spraying water onto the surface using separate sprinklers located along the billet length. Already in his 1937 patent application in Great Britain (GB Patent 492216) Roth suggested using openings in the lower part of the water-cooled mold for spraying the coolant onto the billet surface. Roth, Patterson, and Kondic

••

••




were also among the fi rst to publish scientifi c papers based on extensive research of this new technology [14–18]. In 1939, the U.S.S.R. began exten-sive work on the development and use of DC casting of aluminum alloys, building mainly on the German inventions as shown in Figure 1.4d [8]. This rapid advance was facilitated by close economical links between the U.S.S.R. and Germany with many Russian and German engineers exchang-ing ideas and technological knowledge. Well-known names in Russian DC casting include S.M. Voronov, V.A. Livanov, R.I. Barbanel, and V.I. Dobatkin. Extensive reports on the Russian experience in DC casting and physical metallurgy of the process were published immediately after World War II [8, 9, 19]. Roth, Livanov, and Dobatkin recognized the important role of heat transfer, thermal contraction, and the dimensions of the semi-solid region in the billet and made the fi rst attempts to explain the formation of hot and cold cracks, macrosegregation, and the homogeneity of structure and properties distribution.

The early reports on the application and mastering of the new technology highlight the great diffi culties that engineers had to overcome on the casting fl oor. In addition to mechanical diffi culties, one of the main problems reported was splitting and fracture of ingots, especially from high-strength alloys such as duralumin and emerging Zn-containing aluminum alloys [13]. Today we still face these problems, known as cold cracks and hot tearing. It was soon acknowledged that the main drawback of DC casting that caused cracking problems was the high thermal gradient between the surface and the inte-rior of the billet (ingot) that resulted from direct cooling with water. Kondic put it this way: “The problem of continuous casting is essentially a matter of heat exchange between the metal cast and the cooling medium” [17]. Another problem was bleed-out, when the solid shell was fractured below the mold and the melt went through it. On the other hand, high cooling (and solidi-fi cation) rates achieved during DC casting, especially in short molds, were advantageous for structure formation, producing fi ne and homogeneous structure across the billet (ingot). Livanov wrote in 1945: “The essence of direct chill casting is the possibility to sharply increase the cooling rate” [19].

Kastner suggested two ways of decreasing the danger of cracking and bleed-outs: either increase the distance between the point where direct cool-ing was applied and the bottom of the mold or decrease the casting speed in such a way that the billet was solidifi ed completely over the whole cross-section before it reached the region of direct cooling [4]. Later, it was shown that sound billets and ingots could be obtained under a variety of conditions, provided the casting processes were well understood.

Direct chill casting had a unique feature that distinguished it from other casting techniques. The solidifi cation occurred in a narrow layer of the cast-ing inside and below the mold. During the steady-state stage of casting, the shape and the dimensions of this region remained constant and reproducible from one heat to another. By regulating the melt distribution during feeding the mold, cooling conditions inside the mold, direct cooling below the mold, and the casting speed, the shape and dimensions of the solidifi cation region



10 Physical M


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Alloys

FIGURE 1.4DC casting methods patented by Zunkel [10] (a), Roth [11] (b), and Ennor [12] (c), and a scheme of a working DC casting machine used in the 1940s [8] (d).

Melt

Water-cooledmold

Billet

Water

Withdrawal ram

Ladle with melt

(a)

MeltMelt

Mold

Water

Water

Withdrawal ram

Water Billet

(b)

Billet

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Direct C

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evelopment of the Technology

11FIGURE 1.4 (Continued)

Melt levelcontrol

MoldMelt

Water

Billet

Withdrawal ram

(c)

Distribution box

Melt

Mold

Billet

Water

20°

Withdrawal ram

(d)

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could be controlled. Because shape and dimensions determined the thermal gradient and were responsible for cracking, macrosegregation, and structure homogeneity, the occurrence of these defects could also be controlled.

Determination of a correct casting recipe for each alloy and size was essential. The main rules were formulated as follows [8, 19]. The melt level in the mold should be minimum; the water should be applied onto the bil-let surface as close to the bottom part of the mold as possible and at the minimum angle to the billet axis; and the melt should be evenly fed into the sump using special distribution boxes or bags. Maintaining these rules, Dobatkin reported that the optimal casting speed for 400-mm billets from high-strength aluminum alloys ranged between 40 and 85 mm/min [8]. The interrelation between the casting speed and the shape and dimensions of the sump and the transition region (between liquidus and solidus isotherms) was quickly recognized and main relationships were established between the physical properties of the alloy, the dimensions of the billet, and the process parameters [8, 15, 19]. Roth showed that the depth of the billet sump (H) is directly proportional to the casting speed (Vcast) and to the squared radius (R) [15, 16]: H = AVcastR2 (1.1)

This dependence was confi rmed by Livanov [19] and Dobatkin [8].Livanov found out that the solidifi cation rate (the velocity of the solidifi ca-

tion front) depends on the casting speed as

Vs = Vcastcos αn, (1.2)

where αn is the angle between the billet axis and the normal to the solidifi ca-tion front [19]. As a result, the solidifi cation rate is a function of the shape of the solidifi cation front and is usually maximum in the center and at the periphery of the billet. It was also shown that the ratio between the sump depth and the billet diameter can be maintained constant if VcastR = const [8]. However, for each billet size and alloy there exists a maximum solidifi cation rate that can-not be exceeded by further increasing the casting speed [8]. This maximum solidifi cation rate is lower for larger billet diameters. These fundamental rela-tionships provided the basis for scaling up the technology to very large cast-ings. Today round billets more than 1000 mm in diameter and 4700 mm long and ingots over 2400 × 1000 mm2 in cross-section and 4400 mm long can be successfully cast from high-strength aluminum alloys [20].

Extensive research undertaken in close connection with industrial DC casting produced outstanding results. By the end of World War II all high-strength aluminum alloys in the United States and the U.S.S.R. were cast using this new technique.

The comparison of DC casting and Junghans’ method showed the follow-ing advantages of the former [9]:

Considerably reduced centerline segregationIncreased density of the central portion of a billet

••




Finer and more homogeneous structure with correspondingly improved mechanical propertiesBetter surface qualityLower operation costs

The fi rst three features were attributed to the shallower sump and fl atter solidifi cation front. It was shown that, for the same casting speed and billet diameter, the sump depth would be four times greater for the Junghans’ method than for DC casting [9]. Therefore, using the scaling rules, one can say that the billet with the same sump depth can be cast four times faster with DC casting than with Junghans’ technique. The DC-cast billet would also have four times higher solidifi cation rate and, hence, better structure and properties, as demonstrated by Dobatkin [8]; see Figure 1.5.

The economical benefi ts of the new casting process were summarized as a decrease of 1.5 times in workplace occupied; scrap reduction from 25 to 10%; and a 50% reduction in workforce [9]. The working conditions became so much easier that Voronov [9] noted that women could be employed in the cast house, which was very important in wartime.

Despite the great and obvious success of DC casting as a major technique for producing billets and ingots for further deformation, there remained some intrinsic drawbacks that inspired inventive people to suggest numer-ous improvements to the technology. Some of these inventions were short-lived and some were minor, but others were milestone achievements.

•

••

FIGURE 1.5Dependence of dendrite arm spacing on the solidifi cation rate in DC casting [8].

1.70.50.20

50

100

150

200

250238

183

100

52

207 6

3.1 8.0Solidification rate, m/h

35 55

× 200

× 200

× 200

× 200

× 200

× 200

Ave

rage

den

drite

arm

spa

cing

, µm




The necessity to maintain low melt level in the mold became a more serious problem as the cross-sections of billet and ingots became larger and larger. But there was no other option—the melt level had to be low in order to avoid large thermal stresses, a wide transition region, and a large zone of air-gap within the mold. Due to thermal contraction of the just solidifi ed shell, this shell with-draws from the mold surface, reheats, and may remelt. Because the metallo-static head is large, the melt can penetrate through the remelted crust and cause periodic segregation bands at the billet surface or bleed-out, resulting in dete-rioration of the quality of the casting or abandonent of the casting altogether. The shape of the sump and the distribution of cooling rates for the cases of high and low melt levels are demonstrated in Figure 1.6a and b [21]. Note that the region of very low cooling rates is present inside the mold when casting with a high melt level and is absent when casting with a low melt level.

In 1958, Gunther E. Moritz of Reynolds Metals proposed a solution for the problem of the low melt level by simply isolating the upper part of the mold with a heat-insulating material [22]. The effective mold length (similar to the former melt level) could be controlled by the sizes of this insert. As a result, the effective mold length or the effective melt level decreased while the real melt level could be maintained as high as suitable for the casting control. The level of the melt above the insert was no longer important. What mattered was the distance between the lower edge of the refractory insert and the lower edge of the water-cooled mold. Figure 1.7a shows the schematic of this invention. As the next step, Moritz suggested making the heat insulating insert composite with the internal graphite ring for better surface quality [23]. This was the beginning of the “hot top” era in DC casting. Later, the refractory part was extended above the mold and became a part of the top melt container con-nected to the feeding system patented by Furness and Harvey (Great Britain, British Aluminium) in 1973 [24], hence the name “hot top”; see Figure 1.7b. The control of heat transfer in the mold was further improved by constant feeding of gas/lubricant mixture into the mold. This process was invented by Ryota Mitamura and Tadanao Itoh at Showa Denko in Japan in 1977 [25] and later refi ned by Wagstaff Engineering as the “air-slip” mold where the gas/ lubricant mixture was supplied to the inner surface of the mold through a fi neporous graphite ring [26]. The main improvement was in the surface qual-ity. The introduction of hot-top mold was an important and popular develop-ment that spread through casting houses around the world in the 1970s.

Despite all these efforts air-gap formation could not be avoided. An area of coarser structure was formed inside the casting at some distance from the surface because of the lower cooling rate at which the billet was solidifi ed while traveling from the point of the air-gap formation to the point of water impingement below the mold. An elaborate attempt to overcome this prob-lem was the invention of a so-called “dual-jet” mold by Wagstaff Engineering [27]. In this mold design two water jets exited the mold and hit the billet sur-face at two different angles, 22° and 45°, as shown in Figure 1.7c. The region of slower cooling was thus considerably reduced. Wagstaff Engineering also produced a combination of air-slip and dual-jet molds.



Direct C

hill Casting: D

evelopment of the Technology

15

FIGURE 1.6Shape of the sump, transition region (gray zone) and isolines of cooling rates (K/min) upon casting in the normal mold with low (a) and high (b) melt levels and upon casting in the electromagnetic mold (c) [21].

MoldMelt levelMelt level

Melt level

50

0

50

100

150

200

250

300

350

400

450

500

550

Inductor

Dis

tanc

e fr

om th

e bo

ttom

of t

he in

duct

or, m

m

150

100

5060

60

130160

200

280 645°

645°

645°

505°

100

60

60

740340

240 200160

130

130

100

200

160

615°505°

130150

100

60

160

160

100

150130

160

180350

280

615°

505°

120

3601180

0

50

100

150

200

250

300

350

400

Dis

tanc

e fr

om th

e bo

ttom

of t

he m

old,

mm

115100

1520

60

3530

600380

1000°/min

(a) (b) (c)

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16 Physical M


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Alloys

FIGURE 1.7Development of DC casting molds in the 1960s–1990s: (a) refractory insert, 1958 [22]; (b) hot top, 1973 [24]; (c) dual-jet mold, 1996 [27]; and (d) electromag-netic casting, 1969 [28].

Refractory insert

Melt

Billet

Actualmelt level

Effectivemelt level

Sumpdepth

Water Water

(a)

Refractory hot top

Melt

Mold

Water

Billet

Water

(b)

Graphite insertWaterchamber

Mold

Waterchamber

Water jets

Billet

Solidshell

(c)

Distribution system

Electro-magneticinductor

Melt

Billet

(d)

Coolingwater

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The revolutionary invention was electromagnetic casting (EMC) or mold-less casting. The idea of DC casting included the mold with primary cooling of the melt where the solid shell was formed and the direct cooling of this shell with water outside the mold. The existence of the mold created some diffi culties: premature solidifi cation with potential hanging of the billet or ingot, freezing of liquid meniscus and formation of a banded surface with cold shuts, air-gap formation and corresponding change of solidifi cation conditions, requirements for lubrication, etc. Engineer Zinovy N. Getselev, who worked at Kuibyshev Aluminum Works in the U.S.S.R., came up with an astonishingly simple and controversial idea: to abandon the mold alto-gether. The molten metal is shaped and held in the required position by an alternating electromagnetic fi eld that induced electromotive forces and eddy currents in the melt. The interaction of these eddy currents with the exter-nal magnetic fi eld creates electrodynamic forces that compress the melt. The cooling water is applied onto the surface of this molded melt and the solidi-fi ed part is withdrawn downward as in the normal DC casting [28]. A suc-cessful start-up is, however, diffi cult and requires very accurate maintenance of several parameters such as the pouring rate, water fl ow rate, initial casting speed, and strength of the magnetic fi eld. Figure 1.7d depicts the principle of the proposed method. The most important features of this method of cast-ing are the absence of the air gap between zones of primary and secondary cooling typical of traditional DC casting and stirring of the melt in the sump by electromagnetic forces. This technology and its variations were patented in most industrialized countries between 1969 and 1977. The advantages of EMC include very good surface that does not require scalping, less mac-rosegregation due to the melt stirring during casting; and more uniform and generally fi ner structure [21]. The sump during electromagnetic casting is shallower and the thermal gradients are less, as shown in Figure 1.6c. The disadvantage of this method that limits its wider application is the relative complexity of the casting machine.

The history of DC casting shows that engineering ingenuity has always matched the demands of the industry and met the challenge for new products and new materials. DC casting is a relatively new technology that is rapidly developing. In many cases this advancement is limited by the lack of under-standing of mechanisms of structure and defect formation. It is essential that physical metallurgy catch up with the technology and provide the scientifi c basis for even better technology.

References

1. http://www.airwar.ru/main.html. 2. V.A. Livanov. In: Belov A.F., Agarkov G.D. (ed.), Aluminum Alloys, Collection of

Papers, Moscow: Oborongiz, 1955, pp. 128–168.



www.airwar.ru


3. J. Züblin. Apparatus for Casting Metals, 1929, US Patent 1734786. 4. H. Kastner. Metal Industry, 1947, vol. 71, August, pp. 83–85; 106–108; 131–132. 5. V.I. Dobatkin, E.G. Safonova. In Aluminum Alloys, Collection of Papers, Moscow:

Oborongiz, 1955, pp. 188–215. 6. M. Wolf. Rev. Metall.–CIT, 2001, no. 1, pp. 63–73. 7. S. Junghans. Apparatus for Continuous Casting of Metal Rods, 1938, US Patent

2135184, fi led 1936; German Patent 750301, fi led 1933. 8. V.I. Dobatkin. Continuous Casting and Casting Properties of Alloys, Moscow:

Oborongiz, 1948. 9. S.M. Voronov. Continuous Casting of Round Billets from Light Alloys, Selected Works

on Light Alloys (1946), Moscow: Oborongiz, 1957, pp. 336–362. 10. B. Zunkel. Gießvorrichtung zum ununterbrochenen Geißen von Blöcken und

ähnlichen Werkstücken aus Lichtmetall oder Leichmetallegierungen, 1939, DR Patent 678534, fi led 1935.

11. W. Roth. Verfahren zum Gießen von Metallblöcken mit Ausnahme solcher aus Leichtmetallen, 1960, BRD Patent 974203, fi led 1936.

12. W.T. Ennor. Method of Casting, 1942, US Patent 2301027, fi led 1938. 13. M.B.W. Graham, B.H. Pruitt. R&D for Industry. A Century of Technical Innovation

at Alcoa, Cambridge: Cambridge University Press, 1990, pp. 251–262. 14. P. Brenner, W. Roth. Metallwirtschaft, Metallwissenschaft, Metalltechnik, 1942,

vol. 21, pp. 695–699. 15. W. Roth. Aluminium, 1943, vol. 25, pp. 283–291. 16. W. Roth. Z. Metallkde., 1949, vol. 40, pp. 445–456. 17. V. Kondic. Metal Industry, 1944, vol. 65, pp. 56–58. 18. W. Patterson. Aluminium, 1943, vol. 25, pp. 75–78. 19. V.A. Livanov. In Proceedings of the First Technological Conference of Metallurgical

Plants of Peoples’ Commissariat of Aviation Industry, Moscow: Oborongiz, 1945, pp. 5–58.

20. Light Metal Age, 2003, no. 1, pp. 47–49; 2005, no. 4, pp. 32–33. 21. V.A. Livanov, R.M. Gabidullin, V.S. Shipilov. Continuous Casting of Aluminum

Alloys, Moscow: Metallurgiya, 1977. 22. G.E. Moritz. Metal Casting System, 1961, US Patent 2983972, fi led 1958. 23. G.E. Moritz. Continuous Casting System, 1965, US Patent 3212142, fi led 1962. 24. A.G. Furness, J.D. Harvey. Mould Assembly and Method for Continuous or

Semi-continuous Casting, 1975, GB Patent 1389784, fi led 1973. 25. R. Mitamura, T. Itoh. Process for Direct Chill Casting of Metals, 1979, US Patent

4157728, fi led 1977. 26. F.E. Wagstaff, W.G. Wagstaff, R.J. Collins. Direct Chill Metal Casting Apparatus

and Technique, 1983, UK Patent Application 2129344A; 1986, US Patent 4598763, fi led 1985.

27. R.B. Wagstaff, D.A. Salee. Direct Cooled Metal Casting Process and Apparatus, 1996, US Patent 5582230, fi led 1994.

28. Z.N. Getselev, G.A. Balakhontsev, V.K. Zinoviev, et al. Method of Continuous and Semicontinuous Casting of Metals and a Plant for the Same, 1969, US Patent 3467166, fi led 1967. Z.N. Getselev. Continuous Casting Apparatus with Electro-magnetic Screen, 1971, US Patent 3605865, fi led 1969.



19

2Solidifi cation of Aluminum Alloys

2.1 Effect of Cooling Rate and Melt Temperature on Solidifi cation of Aluminum Alloys

There are two vital factors to consider regarding the formation of struc-ture and the quality of any casting—cooling rate and melt temperature. The cooling rate refl ects the heat extraction rate and is measured in K/s. Cooling rate is closely connected to the solidifi cation rate, which can be defi ned either as the velocity of the solidifi cation front or as the liquid–solid phase transformation rate, measured in units of m/s or s−1, respectively.

The solidifi cation rate and cooling rate affect the structure formed during solidifi cation in a manner that was demonstrated in Figure 1.5. Generally, the structure is refi ned by increasing the heat extraction and corresponding increase in the solidifi cation rate. Let us look at these relationships in some detail.

In fundamental and theoretical studies casting structure is often repre-sented as unidirectional and columnar, with the grains or their branches represented by cylinders with rounded tips. In reality the structure of com-mercial alloy castings consists of dendritic equiaxed grains. The structure is therefore conventionally considered on two levels: grain size and dendrite arm spacing, as illustrated in Figure 2.1a.

The grain usually has a rather complex, branched shape, hence the name— dendrite. Its branches are called dendrite arms. Dendrite grains are formed in alloys solidifi ed in the presence of thermal gradient at the solid–liquid interface and their shape is a result of chemical inhomogeneity and corre-sponding instability at this interface, as shown in Figure 2.2.

The grain size is obviously a function of several parameters, the most important of which are the nucleation rate and the growth rate. The nucle-ation rate depends on the amount of energy required for the creation of a new phase structure and new surface area. Therefore, the nucleation rate can be affected by the melt undercooling below the liquidus (which gives a direct thermodynamic stimulus for nucleation, decreasing the critical size of the solidifi cation nucleus) and/or by the presence of solidifi cation sites for heterogeneous nucleation (that provide the suitable surface for nucle-ation, decreasing the amount of required energy). The latter mechanism can be facilitated by special additions called grain refi ners. The growth rate is




a function of the crystallography (growth kinetics is different at different crystal planes), heat extraction, and mass transfer. The liquid undercooling is higher at higher cooling rates. As a result, grains generally nucleate and grow faster at higher cooling rates, with corresponding grain refi nement; see Figure 2.1b.

FIGURE 2.1The structure of an Al–1.8% Cu alloy solidifi ed at a cooling rate of 0.4 K/s (a) and 13 K/s (b). Grain size D and dendrite arm spacing d are shown in (a).

1 mm

1 mm

(a)

(b)



Solidifi cation of Aluminum Alloys 21

FIGURE 2.2Instabilities (branches shown by arrows) at the dendrite tip interface caused by an abrupt change of thermal gradient as a result of quenching in the semi-solid state (an Al–3% Si alloy).

200 µm

The dependence of the grain size (Dgr) on the important kinetic parameters of solidifi cation can be written as [1]

Dgr = A∆ T 0 0.25 V s –0.25 G–0.5, (2.1)

where ∆T0 is the alloy solidifi cation range, Vs is the velocity of the solid–liquid interface (solidifi cation rate), G is the interfacial temperature gradient, and A is the alloy-dependent coeffi cient that takes into account the interface surface energy, solute diffusion, distribution coeffi cient, and latent heat of fusion. For the same alloy, the most decisive factor for the grain size is the temperature gradient. Under identical cooling conditions, the equilibrium solidifi cation range is one of the important parameters that govern the grain size [2]. This explains the experimentally observed fact that the increased amount of solute in alloys results in grain refi nement [2, 3], as demonstrated in Figure 2.3a for binary Al–Cu alloys. The effect of the alloy composition on grain refi nement is considered in more detail in Section 2.4.

The internal fi neness of the grain structure is characterized by the size and spacing of dendrite branches. The analysis of dendrite branching usu-ally involves the phenomenon of so-called constitutional undercooling [1, 4]. During solidifi cation of a hypoeutectic alloy (with the partition coeffi cient K = CS/CL < 1), the solute concentration in the liquid very close to the solid–liquid interface is higher than the bulk liquid concentration because of the




solute rejection from the solute-lean solid phase. This situation is shown in Figure 2.4. As a result of this liquid enrichment, the equilibrium liquidus at the interface may lower signifi cantly. Local equilibrium that usually exists at the interface under normal solidifi cation conditions dictates that the actual temperature of the melt at the interface should be equal to the liquidus tem-perature corresponding to the local composition. The existing melt tempera-ture gradient creates the situation that the melt temperature in the vicinity of the interface is lower than the actual liquidus, forming the region of consti-tutional (in contrast to thermal) undercooling. In this case, any protrusion at the solid–liquid interface happens to be in the constitutionally undercooled region and has a possibility to become stable and grow. This effect is more pronounced in the case of columnar growth when there is no thermal under-cooling (marked b in Figure 2.4). For equiaxed grains, the thermal under-cooling is always present so it seems that contribution of the constitutional undercooling is not so important (marked c in Figure 2.4). In real conditions, however, the thermal undercooling in liquid regions between equiaxed grains is to a great extent compensated for by the latent heat evolution and the very low ratio between the solute and heat diffusion, which makes the impact of constitutional undercooling much more pronounced.

It is important to note that the region of the maximum constitutional undercooling occurs at some distance from the solid–liquid interface, which has profound implications for the columnar–equiaxed transition and grain refi nement.

Dendrite branches are initially formed as periodic disturbances of the fl at interface. The average distance between the interface protrusions refl ects the minimum segregation distance when the diffusion fi elds of the neighboring branches do not overlap yet [1, 5]. As soon as the diffusion fi elds overlap, the branches stop growing and the process of their ripening (coarsening) starts,

FIGURE 2.3Effect of cooling rate and composition on the grain size (a) and dendrite arm spacing (b) in binary Al–Cu alloys [3]. (Reproduced with kind permission of Elsevier.)

4.3% Cu3.24% Cu2.12% Cu

12

Cooling rate, K/s

4 800

1

2

3

4

Gra

in s

ize,

mm

5

0.98% Cu

100

Den

drite

arm

spa

cing

, µm

100.1 1.0

Cooling rate, K/s

10.0

4.3% Cu3.24% Cu2.12% Cu0.98% Cu

(a) (b)




when fi ner branches disappear and coarser ones dominate [1, 4]. Eventually, the spacing between branches becomes wider. This process is considered in more detail in the next section. The distance between these branches is called the secondary dendrite arm spacing because these branches appear on the primary trunks of the dendrite.

FIGURE 2.4Concentration and temperature fi elds around a dendritic grain showing the concept of constitu-tional undercooling [1]: (a) section of a hypoeutectic region of a binary eutectic phase diagram; (b) columnar grain growth; and (c) equiaxed grain growth. C0, C x S , and C x L are the compositions of the alloy, solid, and liquid phases at a particular melt temperature Tx, respectively. C i

S is the initial solid concentration at the liquidus temperature of the alloy C0. Tinteface is the equilibrium liquidus temperature corresponding to the solute concentration in the melt. Tmelt is the melt temperature far from the solid–liquid interface (or solidifi cation front) corresponding to the nominal alloy composition C0. Regions of constitutional undercooling are shown in (b) and (c).

Liquid

Solid

Tx

TC0Ci

S

CxS C0 CCx

L

CxL

CxL

CxsCx

s

CisCi

s

C0C0

Tc0Tc0

Tmelt

Tinterface=TxTinterface=Tx

Tmelt

Heat flow

Hea

t flo

w

Liquid Liquid

Heat flow

Region ofconstitutional undercooling

Region ofconstitutional undercoolingSolid Solid

(a)

(b) (c)




It has been shown that the secondary dendrite arm spacing (d) is a unique function of the local solidifi cation time (tf) [4]:

d = B t f n . (2.2)

As tf = ∆T0/GVs and GVs is the cooling rate (Vc) in the solidifi cation range, we can write the same expression in a well-known form,

d = C V c –n , (2.3)

where n, a so-called coarsening exponent, varies between 0.4 and 0.2 for various aluminum alloys. Figure 2.3b illustrates this relationship for binary Al–Cu alloys. This unique correspondence between the secondary den-drite arm spacing and the cooling rate (which is an important technologi-cal parameter) has paramount importance and allows us in many cases to estimate the cooling rate based on metallographic examination of the as-cast structure. However, it is virtually impossible to single out secondary den-drite arms on cross-sections of real as-cast samples, like those shown in Fig-ure 2.1. Instead, the average thickness of all dendrite branches is measured. Numerous experimental studies confi rm that Equation 2.3 is also valid for the average dendrite arms’ thickness or spacing.

The relationships for the grain size and the dendrite arms spacing can look similar (as Equation 2.3) providing that the solidifi cation conditions are all the same, except for the cooling rate. Our results for Al–Cu alloys show that the exponent n is close to 0.3 for the grain size and to 0.4 for the dendrite arms spacing, and the coeffi cient C decreases with the increasing copper concentration [3].

It is important to note here that the cooling rate Vc and the solidifi cation rate Vs are, in general, proportional to each other but not always directly. In the case of DC casting, the solidifi cation rate is equal to the velocity of the solidifi cation front and depends on the casting speed as shown by Equation 1.2. The cooling rate for a structure found in a particular section of the billet is a function of its solidifi cation history, as will be discussed in more detail in Chapter 3.

In addition to the cooling rate, the superheating of a melt over the liquidus temperature is an important process parameter when preparing and casting alloys. The melts of commercial aluminum alloys are seldom heated over 800°C because a higher superheating can result in structure coarsening, development of columnar grain structure, and increased saturation of the melt with gas. In the 1950s some scientists and engineers involved in the production of foundry aluminum alloys observed interesting effects from melt superheating. They found out that after a stage of structure coarsening upon increasing the melt temperature, the structure tends to refi ne.

Later, there were many studies and attempts to explain this phenomenon. First, some anomalies in the temperature dependences of viscosity and density were observed upon heating and cooling of the melt [6, 7]. Then, with the devel-opment of new techniques of X-ray and neutron diffraction, the short-range




order in aluminum melts was revealed and interpreted [6, 8]. Some scientists explain the phenomenon of structure refi nement at high superheating from the viewpoint of changes in the melt structure. There are hypotheses about the melt structure, phase transformations in the liquid phase, and even about quasicrystalline or polycrystalline constitution of melts [6–8]. Other specialists explain these anomalies in terms of impurities in aluminum and insuffi ciently correct experiments [9]. There is also a viewpoint that the spontaneous solidi-fi cation of homogeneous melt can occur, showing the direct dependence of the grain size on melt undercooling [10, 11].

Most commercial aluminum alloys belong to the eutectic type with respect to main alloying components. The solidifi cation of such aluminum alloys (except for purely eutectic alloys) starts with the formation of primary phases. In this case, the primary phase is considered to be a phase of the main alloy-ing system that is the fi rst to crystallize. In hypoeutectic aluminum alloys, this phase is the aluminum-based solid solution. In most cases the so-called primary solidifi cation occurs heterogeneously. The main primary phase can nucleate onto intermetallic particles formed by specially added grain refi n-ers (Ti, Zr, Sc, Mn, etc.), on active or activated impurities (alumina particles with remains of the solid phase in surface defects), and on clusters of the melt with the short-range order similar to the crystal structure of the main primary phase. We should not overlook the possibility that physico-chemi-cal properties of some inert impurities can change with temperature, and these impurities can become active with respect to the melt, which is what happens with alumina that undergoes polymorphic transformation at high temperatures and becomes wettable [12].

Figure 2.5 shows the experimental results on the structure change with an increasing pouring temperature. In pure aluminum, the equiaxed grain coars-ens in the temperature range up to 950°C, then its size stabilizes and somewhat decreases upon heating above 1000–1050°C; see Figure 2.5a. The columnar zone narrows while casting from temperatures above 950°C. Apparently, the pecu-liar temperatures of these effects depend on the purity of the aluminum and the cooling rate. This behavior can be explained by the effect of alumina fi ne particles that are inert with respect to liquid aluminum at temperatures below 950°C and then become wet from aluminum and act as solidifi cation nuclei at higher temperatures [12]. These processes affect the re-coarsening of the struc-ture in a 2024 alloy cast from very high temperatures; see Figure 2.5b.

The 2024-type alloy is the most common of the widely used wrought aluminum alloys. Its structure is predominantly equiaxed due to the small additions of Ti and Zr; see Figure 2.5c. The grains of aluminum solid solution grow markedly (from 63 to 622 µm) as the pouring temperature increases from 700 to 980°C, then the size of equiaxed grains essentially decreases (to 332 µm at 1030°C) and coarsens again on further heating; see Figure 2.5b,c. An exami-nation of the microstructure shows that the growth of the grain size is accom-panied by the development of dendritic branching with relevant refi nement of the average section of dendritic arms. The grain refi nement achieved during high-temperature pouring results in the decreased dendritic branching.




We can say that there is a characteristic melt temperature typical of each alloy starting from which the grain structure or primary intermetallics start to refi ne. This temperature depends on the cooling rate: the higher cooling rate, the lower the temperature [13]. The occurrence of an additional high- temperature heterogeneity factor can delay or even suppress the refi nement [14].

The observed phenomena can be explained, in our opinion, based on the following ideas [13, 14]:

The melt is a heterogeneous liquid in the particular temperature range above the liquidus: in other words, the melt contains vari-ous ready-to-solidify sites that become nuclei at small undercool-ing (these are the remains of solid phase in defects of nonmetallic particles and remains of intermetallics that need some time and thermodynamic stimulus to dissolve).

•

FIGURE 2.5Effect of melt superheating on the structure of pure aluminum (a) and a 2024 alloy (b, c) [14]. Cooling rate during solidifi cation 5.5 K/s. (Reproduced with kind permission of Carl Hanser Verlag.)

1.4

1.2

1.0

1.8

0.6600 700 800 900 1000 11001200 650

10

100

14

12

10

8

6

100086

4

2

86

4

2

750 850 950 1050 1150

Size of dendritic cells

Temperature of pouring, °CTemperature of pouring, °C

Size of grains

Siz

e of

gra

ins

and

dend

ritic

cel

ls, µ

m

: Siz

e of

equ

iaxe

d gr

ains

, mm

: wid

th fo

col

umna

r zo

ne, m

m

200 µm

(a)

(c)

(b)




Upon increasing the melt temperatures these structural and compo-sitional heterogeneities dissolve: this process requires melt super-heating about 200–250°C.At higher temperatures the melt can be considered as homogeneous liquid.The formation of new solidifi cation nuclei upon undercooling occurs in a way similar to the decomposition of supersaturated solution. These new nuclei are represented mainly by aluminides of transition metals in hypoeutectic aluminum alloys. The fi nal structure depends on the composition (undercooling and corresponding supersatura-tion) and sequence of phase precipitation (solidifi cation).

All processes determining the structure formation upon solidifi cation from different melt temperatures are summarized in Figure 2.6.

Generally, the primary structure constituents coarsen due to the gradual decrease in the amount of ready nuclei. Starting from a certain temperature, the liquid becomes homogeneous and tends to undercool before solidifi ca-tion. The higher the melt temperature and the cooling rate, the greater the undercooling and the supersaturation of the liquid solution. The greater the undercooling, the larger the amount of new nuclei and the fi ner the grain or primary intermetallics.

The increased amount of solidifi cation nuclei, the narrowed two-phase zone, the increased temperature gradient in the melt, and the decreased

•

•

•

FIGURE 2.6Processes occurring during melt superheating and relevant structure changes [13, 14]. ( Reproduced with kind permission of Carl Hanser Verlag.)

Overheatingof the melt

Dissolution ofintermetallic

remains

Deactivationof impurities

Increased temperaturegradient in the melt

Increased diffusioncoefficient

Decreased constitutionalundercooling

Arresteddendriticbranching

Increased content ofalloying elements

in the melt

Increasedthermal

undercooling

Grain growth

Columnarstructure

Narrowedsolidification

zone

Increased amount ofactive solidification

sites

Increased supersaturationof the liquid solution (melt)

Higher fineness and precipitationdensity of products of decompositionof the supersaturated liquid solution

Formation of fineequiaxed grains

with slight dendriticbranching

Refinement ofprimary structure

constituents(grains)




constitutional undercooling result in the formation of equiaxed grain struc-ture with only slight dendritic branching.

This occurs when the homogeneous state of the liquid can be achieved. Active inhomogeneities, such as wet alumina particles, prevent large under-cooling and promote nucleation of few grains at high temperatures, effec-tively coarsening the structure; see Figure 2.5b.

The commercial application of melt superheating as a means of structure refi nement in conventional ingot and shape casting is impractical because of the temperature limitation of furnaces and increased gas absorption and porosity. In conventional casting practice only the coarsening stage is usually observed.

2.2 Microsegregation in Aluminum Alloys

The occurrence of additional solidifi cation reactions and the formation or retention of additional phases during nonequilibrium solidifi cation upon direct chill casting are caused, in most cases, by the phenomenon called microsegregation.* Microsegregation means the inhomogeneity of the chemical composition on the scale of a single grain (dendrite). The origins of microsegregation are well known. All phase transformations during solidi-fi cation occur by diffusion, and therefore require some time to be accom-plished. The degree of this accomplishment is controlled by the following three diffusion processes:

Diffusion of alloying elements in the bulk liquid toward and from the solid–liquid interface in order to create the equilibrium differ-ence of concentrations according to the difference in concentrations in the liquid and solid phases refl ected by the liquidus and solidus lines in the equilibrium phase diagram (see Figure 2.4).Diffusion in the liquid close to the solid–liquid interface in order to dissipate the solute (partition coeffi cient K < 1) or solvent (K > 1) pile-up at the solidifi cation front (Figure 2.4).Diffusion in the solid phase in order to equilibrate the solute concen-tration within the solid grain.

If all three diffusion processes proceed fully during solidifi cation, then the solidifi cation occurs according to the equilibrium phase diagram, with the average compositions of solid and liquid changing according to the solidus and liquids lines, respectively. In most cases, even at relatively low cooling rates, these diffusion processes are to some extent incomplete, which results

* Incomplete peritectic reactions and corresponding retention of high-temperature phases in the as-cast structure are usually not considered as microsegregation, but are also a result of hindered diffusion.

•

•

•




in the incomplete peritectic reactions, change of the average compositions of the liquid and solid phases, appearance of excess phases, and inhomoge-neous distribution of alloying elements in the volume of the grain.

One of the main approaches to treat microsegregation was suggested by Gulliver in 1913–1922 and developed by Scheil in 1942. These scientists assumed that the diffusion in the liquid phase was complete whereas the diffusion in the solid phase was fully suppressed, and the conditions of local equilibrium were preserved at the solid–liquid interface. For the cooling-rate range of commercial shape and direct chill casting, these assumptions are frequently believed to be valid. For the sake of simplicity, we consider in this section mainly cases of binary alloys, though the same mechanisms act in more complex and commercial alloys.

The Gulliver–Scheil approximation can be written in the following form for the one-dimensional case:

CL = C0(1 – fs)(K–1), (2.4)

where CL is the composition of the liquid phase, C0 is the nominal alloy compo-sition, fs is the fraction of solid, and K is the partition coeffi cient (K = CS/CL).

It is important to note that the Gulliver–Scheil model presents the limited case when no diffusion occurs in the solid phase, and it does not take into account either morphology of real structure or phase transformations occur-ring during solidifi cation. In principle, the solidifi cation occurs within this approximation as follows (Figure 2.7):

The liquid phase changes its composition during primary solidifi ca-tion according to the liquidus line, from C0L to CFL and eventually to CE (which is the eutectic concentration).The composition of the solid phase at the interface with the liq-uid is according to the equilibrium solidus at each temperature in the primary solidifi cation range and is locally preserved at lower temperatures.Therefore, the solute distribution in the solid phase changes from C0S in the center of the grain (dendrite) to CFseq and, eventually, to Climit (which is the limit solubility of the solute in the matrix) at the periphery of the grain (dendrite).The average composition of the solid phase CSav changes with the decreasing temperature from C0S to CFsneq.

As a result of this nonequilibrium solidifi cation, the solid phase at the moment when the alloy reaches the equilibrium solidus contains less sol-ute than the nominal alloy composition C0. Therefore, there is still liquid existing in the system to accommodate the remaining solute. This liquid continues to solidify according to the equilibrium liquidus. It may happen that the difference between the alloy composition and the actual average

•

•

•

•




composition of the solid phase will be so large that the solidifi cation pro-cess will continue until the eutectic temperature is reached. At this moment, the Gulliver–Scheil equation just shows the amount of the remaining liquid phase of the eutectic composition (Figure 2.8). This liquid will solidify as the eutectic, forming the “nonequilibrium eutectic” or “nonequilibrium phase” (Al2Cu in the case of Al–Cu alloys), which will be discussed in the next sec-tion of this chapter.

The reality of solidifi cation is obviously much more complicated than the Gulliver–Scheil approximation. Measurable diffusion of solute occurs in the solid phase during and after solidifi cation, diffusion in the liquid phase may be hindered at high cooling rates, dendritic grains evolve during solidifi cation with dissolution of some fi ner arms, thermo-solutal convec-tion may cause local changes in the composition with correspondingly

660

620

580

540

0 10 20

Cu, wt%

30

CETE

TS; CFL

TL; C0L

C0

C0s

CFSeq

CFSneq

TSneq

CSav

Tem

pera

ture

, °C

FIGURE 2.7A scheme of nonequilibrium solidifi cation as applicable to binary Al–Cu alloys. C0 is the Al–4% Cu alloy; TL is the equilibrium liquidus temperature; TS is the equilibrium solidus temperature; TE is the equilibrium eutectic temperature; C0S is the initial concentration of solid (C0S = KC0L); CFL and CFSeq are the equilibrium liquid and solid concentrations at the end of the equilibrium solidifi cation and the liquid and solid concentrations at the interface at TS; CFSneq is the average concentration of the solid phase at the eutectic temperature TE; CSav is the line of the average solid concentration; and TSneq is the experimental nonequilibrium solidus [17].




accelerated or slowed-down local solidifi cation, and the temperatures of liquidus and solidus (eutectic reaction) may be lower than the equilibrium ones as a result of undercooling during solidifi cation. All these phenom-ena occurring simultaneously and in different proportions can dramati-cally change the distribution of the solute in the solid grain and the ratio of phase fractions. One of the most important external parameters that affects microsegregation is the cooling rate during solidifi cation.

Experimental results on the infl uence of the cooling rate on the extent of microsegregation are seemingly controversial, as illustrated in Table 2.1 by the variation in the amount of nonequilibrium eutectics.

The most frequently cited explanation of dependence is the one pub-lished by Sarrial and Abbaschian [15], shown in Figure 2.9a, which agrees in the range of moderate cooling rates with much earlier results by Michael and Bever [16]. The ascending shoulder of the dependence is convention-ally explained by an increasing degree of microsegregation due to the limited diffusion in the solid; and the descending shoulder is explained by the limited diffusion in the liquid at very high cooling rates. It is inter-esting to note, however, that in this dependence the range of cooling rates below 1 K/s has not been well researched. Novikov and Zolotorevsky [17] performed thorough experiments by cooling the samples at different rates

FIGURE 2.8Variation of the volume fraction of solid during nonequilibrium solidifi cation of an Al–4% Cu alloy. About 8 vol.% of liquid remaining at the eutectic temperature will form the eutectic.

100

90

80

70

60

50

40

Fra

ctio

n so

lid, %

30

20

10

0

540 560 580 600 620 640 660

Temperature, °C

Eutectic reaction




and quenching them at the eutectic temperature to reduce the effect of struc-ture homogenization. They showed for aluminum- and copper-based binary and commercial alloys that the dependence of the nonequilibrium eutectics on the cooling rate is quite special in the range of low cooling rates, the one that had not been thoroughly examined by other researchers. An example is given in Figure 2.9b for an Al–5% Cu alloy, showing the distinct peak at a low cooling rate. This dependence cannot be easily explained without taking into account the complexity of the microsegregation phenomenon.

Recent results obtained on Al–Cu alloys confi rm the dependence reported by Novikov and Zolotorevsky, as shown in Figure 2.10 [3, 18]. Several mecha-nisms mentioned previously can contribute to this phenomenon.

An attempt to reproduce the observed behavior using one of the known models of microsegregation failed. The Brody–Flemings, Alstruc, and Pseudo Front Tracking (PFT) models predict the increase of the nonequilib-rium eutectic fraction with the increasing cooling rate.

TABLE 2.1

Dependence of the Amount of Nonequilibrium Eutectics on the Cooling Rate Reported in Different Sources (as compiled in [3])

Alloy Composition, wt%

Cooling Rate Range, K/s

Variation in the Amount of Nonequilibrium Eutectics

with Cooling Rate Comments*

2Cu; 3Cu; 4Cu; 4.8Cu 0.01; 0.8; 5; 50 Increase RT1Cu; 3Cu; 4.5Cu 1–38 Increase End-chill

casting2.8Cu; 4.9Cu; 1Si 0.1–37000 Increase to 190 K/s, then

decreaseDS

2Cu; 5Cu; 6Mg; 1.4Mn; alloy 2024

0.001–4 Initial increase to 0.002–1 K/s followed by decrease

Q

5Cu 1; 3 Increase Calculated7Mg; 11Mg 0.5–10000 Increase RT5Mg (alloy 5182) 0.5–2 Decrease** RT7.5Si–0.45Mg (alloy 356) 0.25–1.5 Increase** RT0.94Mg–4.11Cu 1.3–21.3 Initial increase followed by

decreaseQ

0.87Mg–5.07Cu 0.9–18.7 Increase QAl–Cu–Mg (alloy 2024); Al–Mn–Mg (alloy 3004)

0.05–8.5 Decrease DS

Steel (1.25C. 1.06Si, 6.6Mn, 1.06Al, etc.)

Growth rate during directional solidifi cation 7–450 µm/s

Initial increase followed by slight decrease

Q

* RT = cooling was not interrupted until the room temperature is reached, DS = directional solidifi cation, and Q = alloy was quenched after the end of solidifi cation.

** Estimated from the fraction of solid at which the eutectic reaction starts.




The Brody–Flemings model correlates the composition of the liquid at the solid–liquid interface to the solid fraction and the so-called Fourier number that is defi ned as

α′ = 4DStf/d2, (2.5)

where DS is the diffusion coeffi cient of the solute in the solid phase, tf is the local solidifi cation time, and d is the dendrite arm spacing. It is assumed that the contribution of the solid diffusion (so-called back diffusion) to the microsegregation will be appreciable if the dimensionless parameter α′K ≥ 0.1. For the cooling rates ranging from 0.1 to 10 K/s, the calculated solid-state Fourier numbers are at the order of 10–2 and decrease very slowly as the cooling rate increases [3]. It is not surprising that the Brody–Flemings model cannot produce the trend observed experimentally.

The Alstruc model is a 1D model of solidifi cation and homogenization that takes into account phase transformations during solidifi cation and considers

FIGURE 2.9Effect of cooling rate on the degree of microsegregation in an Al–5% Cu alloy expressed by the amount of nonequilibrium eutectics: (a) after [15]; (b) after [17].

1

0.8

0.6

0.4

Rel

ativ

e eu

tect

ic fr

actio

n

0.2

0−3 −2 −1 0 1 2

Log of the cooling rate, K/s3 4 5 6

3.31.71.31.0

Cooling rate, K/s

0.70.3

6

7

Vol

ume

frac

tion

of e

utec

tics,

%

8

(b)

(a)




the structure as a cylindrical dendrite arm, as described in detail elsewhere [19]. This model also cannot reproduce the experimentally observed trend.

The Pseudo Front Tracking model solves the diffusion equations both in the solid and the liquid numerically and allows one to use a temperature- dependent diffusion coeffi cient and a non-linear phase diagram as the input parameters [20]. In a 1D model of the PFT model, calculations performed with the domain size equal to the half of the dendrite arm spacing show that, for

FIGURE 2.10Effect of cooling rate on the amount of nonequilibrium eutectic in Al–Cu alloys: (a) Al–1.8% Cu and (b) Al–2.5% Cu, grain refi ned. Samples were quenched at the temperature of nonequilib-rium solidus (eutectic).

0 1

Cooling rate, K/s

Non

-equ

ilibr

ium

eut

ectic

frac

tion,

%

10

0

1

2

3

4

3.5

3

2.5

2

1.5

1

0.5

00.1 1 10 100

Cooling rate, K/s

Non

-equ

ilibr

ium

eut

ectic

frac

tion,

%

(a)

(b)




cooling rates of 0.4 and 13 K/s, the calculated eutectic fraction still increases with the cooling rate (2.72 and 3.22 wt%, respectively). However, if the calcula-tion domain size is artifi cially decreased (13 µm instead of experimentally meas-ured 20 µm), then the calculated eutectic fraction (2.68 wt%) is indeed less than the calculated result for a cooling rate of 0.4 K/s (2.72 wt%). This artifi cial cal-culation supports the explanation of Novikov and Zolotorevsky [17] as shown in Figure 2.11a: more solute remained in the primary phase at a higher cooling rate as a result of effi cient diffusion in the solid contributed by a higher solid concentration gradient. That means that if microstructure is fi ne enough and the corresponding solute gradients are high, the solid-state (back) diffusion is so effi cient that it decreases the degree of microsegregation. Upon slow cool-ing the degree of microsegregation is also low because of a longer solidifi ca-tion time and correspondingly more time that is available for diffusion. In both cases, the fraction of nonequilibrium eutectics can be lower than at some inter-mediate cooling rates. Although this artifi cial calculation reveals the impor-tant effect of the fi ner microstructure on the fi nal eutectic fraction, it cannot be directly used to explain the observed trend due to the deliberately decreased calculation domain size.

Yet another indication of the role of dendrite fi neness on the degree of microsegregation is a simple exercise in normalizing the experimentally measured fraction of nonequilibrium eutectic to the experimentally deter-mined dendrite arm spacing, as shown in Figure 2.11b. The dependences appear to be linear and the normalized value of the eutectic fraction increases with the increasing cooling rate.

These results show that the tested 1D models cannot adequately reproduce experimentally observed dependence. It should be noted that none of the exist-ing models of microsegregation includes all the known effects that may occur during solidifi cation, namely, limited diffusion in the solid phase, back diffu-sion in the solid during solidifi cation, temperature dependences of diffusion coeffi cients in the solid and liquid, structure refi nement with increasing cool-ing rate, dendrite coarsening with dissolution of fi ner branches, undercooling of the eutectic reaction with the shift of the eutectic point, thermodynamics of alloy solidifi cation, and solute accumulation in the liquid with mixing depen-dent on the diffusion rate. In addition, these models do not include the geom-etry of the dendritic structure. The scale of the structure is usually taken into account only as the secondary dendrite arm spacing or the grain size.

Three factors may be quite important in the understanding of the experi-mentally observed phenomenon. First, the coarsening of the dendritic arms, which means that fi ne branches formed at higher temperatures and contain-ing less solute dissolve and coarser branches thicken by “attaching” the solid phase containing more solute. As a result, the surrounding liquid is diluted of the solute, and the amount of nonequilibrium eutectic eventually decreases. This process should be active in the medium range of cooling rates (at very low cooling rates the branches are too thick to be dissolved) and the effect has to increase with the increasing cooling rate. Second, the undercooling of the eutectic reaction with the shift of the eutectic point to a higher solute




FIGURE 2.11(a) Accumulation of copper in the primary (Al) phase during solidifi cation of an Al–1.8% Cu alloy calculated using a 1D PFT model and (b) dependence of the nonequilibrium eutectic frac-tion (NEqE) normalized to the dendrite arm spacing (d) on the cooling rate during solidifi ca-tion of Al– Cu alloys (experimental data, see symbols in Figure 2.3) [3]. (Reproduced with kind permission of Elsevier.)

Concentration profiles in 1D PFT calculations

0.04

0.035

0.03

0.025

0.02

0.015

0.01

0.005

00 0.1 0.23 0.46 0.69 0.77

Solid fraction

0.84 0.92 0.95 1

Cu

atom

ic fr

actio

nSlow cooling (0.4 K/s)Fast cooling (13 K/s)

0.16

0.12

0.08

NE

qE/d

, %/µ

m

0.04

0.00

0 4 8 12 16

Cooling rate, K/s

(a)

(b)




concentration and the increased concentration of the solute in the solid phase at the solid–liquid interface under conditions of the hindered diffusion in the solid should result in the decreased amount of nonequilibrium eutectics. Third, the structure refi nement with increasing cooling rate may result in more active back diffusion with the corresponding decrease in the amount of nonequilibrium eutectics, as has been shown by the 1D PFT model.

A recently developed 2D PFT microsegregation model can predict the grain morphology of the primary phase and its effect on secondary phase forma-tion [20]. Rather complex and time-consuming 2D PFT calculations that use the measured grain sizes as input parameters of calculation domain size to reproduce the dendrite arm spacing observed in the measurements are, in our opinion, required for taking into account the effect of grain morphology on the formation of eutectic fraction.

Before discussing the outcome of the 2D PFT simulation results, let us con-sider separately the possible contribution of dendrite coarsening to the eutec-tic volume fraction. A model suggested by Voller and Beckermann [21] is able to predict the fi nal eutectic fraction as a function of the coarsening exponent. This model assumes that the dendrite arm spacing is not constant during solidifi cation, but is a function of solidifi cation time in the following form:

d(t) = d0(t/tf)n, (2.6)

in which d(t) is the dendrite arm spacing during solidifi cation, d0 is the fi nal dendrite arm spacing, t is the running solidifi cation time, tf is the total local solidifi cation time, and n is the coarsening exponent. The details of the cal-culation can be found elsewhere [18]. The results are shown in Figure 2.12.

FIGURE 2.12The mass eutectic fraction in an Al–2.5% Cu alloy as a function of the coarsening exponent as predicted by the approximate microsegregation model [21] for two given cooling rates [18]. (Reproduced with kind permission of Elsevier/Pergamon.)

0.80.70.60.4 0.50.30.2

Coarsening exponent, n

0.100

0.01

0.02

0.03

Eut

ectic

frac

tion

0.04

0.05Fast cooling (16 K/s)Slow cooling (0.8 K/s)




It is interesting to note that when coarsening is absent, i.e., n = 0, the calculated eutectic fraction is almost double the one calculated with n = 0.33, which is regarded as a default value for aluminum alloys [1]. According to this model, coarsening indeed makes a difference in the fi nal eutectic fraction formed. For the same coarsening exponent, the eutectic fraction predicted for a faster cooling is always higher than the one obtained for a slower cool-ing. This result seemingly contradicts experimental observations in Figure 2.10. But should the coarsening exponent be held as the same value for fast and cooling solidifi cation conditions? In other words, does the coarsening exponent depend on cooling rate? Diepers et al. [22] showed numerically that the change of coarsening conditions from diffusion to convection controlled increased the coarsening exponent from 0.33 to 0.5.

Recently, it has been demonstrated experimentally that the coarsening exponent indeed increases for a Al–4.5% Cu alloy from 0.3 to 0.5 in the pres-ence of forced fl ow [23]. In other in situ experiments on an Al–30 wt% Cu alloy, the analysis of dendrite coarsening shows that the coarsening behavior dur-ing solidifi cation is affected by natural fl uctuations in the solidifi cation front velocity that occur due to accumulation and settlement of solute-rich liquid [24]. The coarsening exponent is found to be equal to 0.4 during front deceler-ation and to vary between 0.28 and 0.5 upon acceleration of the solidifi cation front. It is argued that solute accumulation and drainage within the mushy zone may have a signifi cant effect on the kinetics of solidifi cation, being the function of the dendrite geometry. A greater coarsening is associated with a higher solute accumulation caused by a lower mush permeability.

Given the complex circumstances in which coarsening may occur during solidifi cation and different coarsening mechanisms (local melting, ripening, coalescence, and fragmentation), it seems there is no reason to restrict the coarsening exponent to a constant value. If in the fast cooling case the coars-ening exponent is slightly higher than the one at a slower cooling rate, then the experimentally observed tendency could be explained, as illustrated in Figure 2.12. But certainly this explanation is not complete without a physi-cally based reason to adjust the coarsening exponent.

Since the 2D PFT model can release the grain morphology restriction made in the 1D PFT model and track the grain morphology evolution and dendrite arm coarsening, the corresponding simulation results can shed the light on the development of the structure and local composition during solidifi ca-tion. Two cooling rates were taken according to Figure 2.10b, i.e., 0.8 and 16 K/s. Indeed, the application of the 2D PFT model indicates the trend in the cooling-rate dependence of the eutectic fraction that agrees well with that observed in the experiments; see Figure 2.13a. Although the amount of non-equilibrium eutectic is overestimated, the difference can be due to two fac-tors: (1) the model does not take into account the undercooling of the eutectic reaction and (2) the real structure develops in the 3D space rather than in two dimensions. What is even more important is that the computational results allow us to follow the evolution of the structure, which can be instrumental in understanding the observed phenomena.




Fast cooling leads to more dendritic grain morphology compared to slow cooling. The direct consequence of such a structure refi nement in the fast cooling case is the higher interfacial concentration value (solid–liquid inter-face area per unit volume, or solid–liquid interface length per unit area); see Figure 2.13b. An immediate result of this could be the reduced extent of microsegregation in the faster cooled structure by the means of back dif-fusion. The comparison of Fourier numbers calculated by setting charac-teristic solidifi cation length to the dendrite arm spacing obtained from the completely solidifi ed microstructure for both cases (0.009 and 0.0165 for the

FIGURE 2.13(a) Volume fraction of nonequilibrium eutectic predicted by PFT modeling (1D, 2D) and observed experimentally (E) in an Al–2.5% Cu alloy and (b) development of interfacial con-centration (Sv) and dendrite arm spacing (DAS) during solidifi cation of an Al–2.5% Cu alloy as calculated by the 2D PFT model for two cooling rates [18]. (Reproduced with kind permission of Elsevier/Pergamon.)

Fast cooling (16 K/s)Slow cooling (0.8 K/s)0

0.5

1

1.5

2

2.5

3

3.5

4.5

4

Vol

ume

frac

tion

of e

utec

tic (

%)

E 2D 1D E 2D 1D

0.400.200.001.0E+02

9.1E+03

1.8E+04

2.7E+04

3.6E+04

4.5E+04

5.4E+04

6.3E+04

7.2E+04

0.60

Solid fraction

0.80 1.000

15

30D

AS

(µm

)

Sv

(1/µ

m)

45

60

75

90

105

120

16 K/s0.8 K/s

(a)

(b)




fast and slow cooling, respectively) tells us, however, that the fi nal struc-ture refi nement is less effective in infl uencing the microsegregation than the decreased solidifi cation time. Therefore, the structure refi nement due to the increased cooling rate cannot be the main contributor to the observed trend in the eutectic fraction variation.

Another phenomenon that occurs at later stages of solidifi cation, approxi-mately at volume fraction solid above 70%, is the coalescence of dendrite arms. At the beginning of solidifi cation when the solid fraction is low, den-drite arm spacings are quite large, refl ecting the fact that side branching has not yet started. The dendrite arm spacing decreases as the solidifi cation progresses, which indicates that dendrite multiplication is dominant over the ripening. With the further increase of the solid fraction, dendrites begin to impinge onto one another, and ripening and coalescence take over the side branching. As a result, the dendrite arm spacing starts to increase; see Figure 2.13b. This process works more effi ciently for the fi ner structure, i.e., at a higher cooling rate, as demonstrated by the variation of the interfacial concentration. This can be readily observed on simulated microstructures shown in Figure 2.14. In the fast cooling case, tertiary arms are formed and they experience quick and severe remelting and re-solidifi cation (ripening). The surviving tertiary arms fi nally coalesce. In the slow cooling case, only secondary arms are induced, and all of them survive.

The fi nal volume fraction of eutectic is, of course, a measure of the amount of liquid that is retained, due to the nonequilibrium regime of solidifi cation, at the temperature of the eutectic reaction. It is interesting that coarsening starts to affect the volume fraction of liquid at rather high temperatures, at the liquid fraction of about 0.46 [18].

Compared to the slow cooling rate, the severe coarsening in the fast cooling case implies that fast cooling must be accompanied by a higher coarsening exponent, as defi ned in Equation 2.6. This implication is sup-ported by tracing how the dendrite arm spacing evolves in later stages of solidifi cation in Figure 2.13b, where ripening occurs and Equation 2.6 can be applied. As solid fraction increases, the difference between dendrite arm spacings in the two given cases decreases, which means that in the fast cooling case dendrite branches coarsen faster than in the slow cooling case. Therefore, the difference in coarsening kinetics at different cooling rates can produce the results that are observed experimentally, as suggested by Voller’s model.

Another important factor that can be estimated using the 2D PFT modeling is the enrichment in solute of tertiary arms as compared to secondary arms. The enrichment is logical because the n-order arms are generated at lower temperatures. What is more interesting is that the solute concentration on the tertiary arms keeps increasing during solidifi cation because of the back diffusion while that in the secondary arms remains virtually unchanged due to a longer diffusion distance [18]. This enrichment in the core of tertiary arms results in general enrichment of the solid phase in the solute and, as a result, in a lesser nonequilibrium eutectic fraction.




FIGURE 2.14Structure development during solidifi cation of an Al–2.5% Cu alloy as modeled by the 2D PFT model [18] (a, b, d, e) and observed experimentally (c, f). a–c, 16 K/s; d–f, 0.8 K/s. a, d, 50% solid phase; b, e, 94% solid phase; c, f, 100% solid phase. The domain size is 330 × 330 µm in (a–c) and 524 × 524 µm in (d–f). Black fi eld in (a, b, d, e) is the solid phase; black fi eld in (c, f) is the nonequilibrium eutectic. (Reproduced with kind permission of Elsevier/Pergamon.)




The correct trend in the dependence of the eutectic fraction in the range of moderate cooling rates predicted by 2D PFT calculations is indicative of the important role played by the structure morphology. It is clear that 3D model-ing could provide even better correspondence with the reality, though such a simulation would be very computer demanding.

In situ observations of the structure evolution during solidifi cation provide valuable insight into coarsening kinetics. Recently, such experimental results started to emerge thanks to the new technique of X-ray microscopy and tomography. Figure 2.15a demonstrates signifi cant coarsening of secondary dendrite arms accompanied by dissolution and fragmentation during pri-mary solidifi cation in Al–Cu alloys [25]. A similar process of coarsening, but in 3D, is shown in Figure 2.15b for an Al–Si–Cu alloy [26]. It will be quite exciting to further employ this technique for studying the coarsening kinet-ics, since the conventional solidify-and-quench technique can only produce the fi nal microstructure, and cannot show the solidifi cation process.

FIGURE 2.15In situ observation of structure evolution during solidifi cation. (a) 2D columnar growth in an Al–30% Cu alloy [25]. The sequence is courtesy of Dr. R. Mathiesen (SINTEF, Norway) and Prof. L. Arnberg (NTNU, Norway). (b) 3D images of coarsening by dendrite-arm coalescence in an Al–Si–Cu alloy [26]. The images are courtesy of Prof. M. Suéry (INPG, France). Growth occurs from the bottom to the top; three sequential stages are shown. Note the coarsening of dendrite arms in frames.

50 µm

1200

1000

800

600

0 100 200 300 400 500 600 700µm

µm

(a)

(b)




There is one more phenomenon that occurs in real solidifi cation of multi-component alloys: local change of composition and solidifi cation path [27, 28]. The local liquid enrichment as compared to the local equilibrium conditions results in remelting of the solid phase, and the local liquid depletion causes accelerated freezing. The consequence of this process is the formation of less primary phase in the former case and more primary phase in the latter case. Hence, the local depletion of the liquid of the solute may result in the forma-tion of less eutectic phase.

2.3 Solidification Reactions and Phase Composition

The structure and, ultimately, the mechanical and technological proper-ties of the as-cast material depend to a considerable extent on the solidifi ca-tion reactions and the selection of phases that occur during casting. Most commercial alloys contain several alloying elements and impurities, which makes their phase composition rather complex. In addition, solidifi cation during real casting does not follow the path of equilibrium solidifi cation that can be derived from the phase diagram. Additional reactions proceed and excess phases are formed under conditions of nonequilibrium solidifi cation. In this section we briefl y consider the solidifi cation and phase composition of main groups of commercial wrought alloys. For more detailed treatises of this subject the reader is referred to more complete accounts such as Refs. [29–32].

2.3.1 Commercial Aluminum

Low alloyed aluminum, often called commercial aluminum or 1XXX-series alloys, belongs to the Al–Fe–Si phase diagram. This phase diagram is very complex, as shown in Figure 2.16a. The ternary phases in the solid state exist mainly outside the fi elds of their primary crystallization; therefore, numerous peritectic reactions should be completed for the equilibrium to be achieved. As a result, real alloys produced at commercial cooling rates can have the Al3Fe, Al6Fe, α(Al5FeSi), β(Al8Fe2Si) and δ(Al4FeSi2) phases co- existing in their structure [29]. Identifi cation of the phases based only on their morphology can often lead to a mistake because the same phase can have different mor-phologies depending on its origin: primary crystals or products of peritec-tic and eutectic reactions. In addition, silicon and other stable, metastable, and nonequilibrium binary and ternary phases can precipitate during the decomposition of supersaturated solid solutions in the process of homogeni-zation or upon cooling of ingots or billets. Some of the phases are also known to undergo transformations during heat treatment.

The Al–Fe–Si system is among the most important for the analysis of as-cast structure of aluminum alloys, and there are quite a few works suggest-ing its nonequilibrium variants. For example, the phase-fi eld distribution in




the as-cast state given by Philips [33] shows 4- and 5-phase regions (Fig-ure 2.16b), which is the most evident feature of the nonequilibrium struc-ture. A shift in the primary solidifi cation fi elds of the Al3Fe, Al8Fe2Si, and Al5FeSi phases depending on the cooling rate during solidifi cation (Vc) is reported by Langsrud [34], who shows that these fi elds drift toward a lower Si concentration with the increasing Vc. As a consequence, the Al3Fe forma-tion is less probable at high cooling rates, even in alloys containing 2–3% Fe at 2–3% Si.

At low cooling rates (Vc1 = 10–2 – 10–1 K/c), the onset of solidifi cation can be analyzed with suffi cient accuracy by the equilibrium phase diagram; see Fig-ure 2.16a. Binary eutectic reactions with participation of Fe- and Si- containing phases take place after the primary crystals are formed. However, due to the

FIGURE 2.16Projection of the solidifi cation surface under conditions of nonequilibrium solidifi cation (a) and distribution of phase fi elds in the solid state after casting at a cooling rate 10–1 K/s (b) and 10 K/s (c) in Al–Fe–Si alloys [32]. (Reproduced with kind permission of Elsevier.)

Si,%0 1

1

2

3

4

2 3 4

Al3 - Al3Fe; Al8 - Al8Fe2Si; Al5 - Al5FeSi

(Al)+Al8+ (Si)

(Al)+Al3

(Al)+(Si)

(Al)+Al3+ Al8+(Si)

Al 3

Fe,

%

(Al)+Al3+ Al8

(c)

10 12Si,%

Fe,

%

e2

e1

140

1

2

3

650

640

630

620

610

600

600

640

680

720710

690

670

650

630

680710

740

590

576

2 4 6 8

Al3 - Al3Fe; Al5 - Al5FeSi;Al8 - Al8Fe2Si; Al4 - Al4FeSi2

Al3

Al8

(Al)

(Si)E

Al5

P2

P1

Al4

Si,%0 0.5

0.5

1.0

1.5

2.0

1.0 1.5 2.0

Al3 - Al3Fe; Al8 - Al8Fe2Si;Al5 - Al5FeSi

(Al)+Al3+Al8+Al5+(Si)

(Al)+Al3+Al8

(Al)+Al3

(Al)+

Al 3

+A

l 8+

Al 5

Al 3

Fe,

%

(Al)+Al5+(Si)(Al)+Al5

(Al)+Al8+ Al5+(Si)

(Al)+Al8+ Al5

(a) (b)

(Al)+Al5+(Si)

(Al)+Al8+ Al5+(Si)




inhibition of peritectic transformations, some alloys can simultaneously form all three binary eutectics with participation of the Fe-containing phases. The nonequilibrium solidus of most alloys is equal to 576°C and corresponds to the ternary eutectics L → (Al) + (Si) + Al5FeSi (point E in Figure 2.16a), and only the alloys whose compositions are within a narrow region close to the binary systems complete solidifi cation by the binary eutectic reac-tions. The inhibition of the peritectic transformations L + Al8Fe2Si → (Al) + Al5FeSi (P2 in Figure 2.16a) and L + Al3Fe → (Al) + Al8Fe2Si (P1 in Figure 2.16a) leads to the following result. With the Si concentration increasing, the sequence of phase regions (not taking (Al) into account) in slowly solidifi ed alloys containing more than 0.5% iron will be Al3Fe, Al3Fe + Al8Fe2Si, Al3Fe + Al8Fe2Si + Al5FeSi, Al3Fe + Al8Fe2Si + Al5FeSi + (Si), Al8Fe2Si + Al5FeSi + (Si); Al5FeSi + (Si). This is in very good agreement with the distributions of the phase regions proposed by Philips and shown in Figure 2.16b.

At higher cooling rates, more relevant to DC casting (Vc2 = 100–102 K/c), a noticeable swing of the liquidus surface (Figure 2.16c) shifts the boundaries of intermediate reactions and phase regions in the as-cast state as compared with slower solidifi cation. Apart from these changes, the eutectic reactions L → (Al) + Al3Fe, L → (Al) + Al5FeSi and L → (Al) + (Si) + Al5FeSi are hin-dered at certain concentrations of Fe and Si. As a consequence, the Al8Fe2Si and (Si) phases are present and the Al3Fe and Al5FeSi phases are absent in the as-cast structure.

Literature data indicate that, besides the stable phases, various metastable phases are formed in commercially pure aluminum and low-alloyed materi-als containing up to 0.5% Fe and 0.5% Si, at cooling rates typical of indus-trial casting; see, e.g., [35–37]. In the chemical composition, these metastable phases are close to the stable phases but differ in crystal structure (Table 2.2).

TABLE 2.2

Metastable Phases Occurring in Cast Al–Fe–Si Alloys [31]

Phase Structure

Lattice Parameters

a, nm b, nm c, nm β

α(Al12.7–12.9Fe3Si1–1.5) (27–35% Fe, 4–8% Si)

Primitive cubic or bcc

1.256 — — —

α′(Al12–12.6Fe3Si1.6–2) Hexagonal 1.23 — 2.62 —α″, q1 Tetragonal or

orthorhombic1.26–1.3 — 3.70 —

β′, β* Monoclinic 0.89 0.49 4.16 92°αv(Al14.8–12.4Fe3Si1–2.1) Monoclinic 0.847–0.869 0.635 0.610–0.632 93.4°αγ(29% Fe, 5.5% Si) Monoclinic 2.795 3.062 2.073 97.74°q2 Monoclinic 1.250 1.230 1.970 111°19–27% Fe, 0–3% Si Rhombohedral 0.89 — — 111.8°

2.082 — — 95.2°29.2% Fe; 11.3% Si Hexagonal 0.836 — 1.458 —19% Fe; 1% Si Hexagonal 1.776 — 1.088 —




The complete account of metastable phases occurring in Al–Fe–Si alloys can be found elsewhere [31].

Metastable phases can also precipitate from the aluminum solid solu-tion during homogenization of ingots. Among these phases, metastable modifi cations of the equilibrium Al8Fe2Si (α, α′, α″) phase are well docu-mented (Table 2.2). If the homogenization temperature is suffi ciently high, these metastable phases are, as a rule, transformed into respective equi-librium phases. One should bear in mind that, due to the low solubility of iron in (Al) (under typical casting conditions), the maximum amount of Fe- containing phases of secondary origin cannot exceed 0.1–0.2 vol.%.

Free (Si) is rare as the Fe:Si ratio is usually maintained above unity in order to prevent hot tearing during casting, by avoiding the low-temperature eutec-tic reaction L → (Al) + Al5FeSi + (Si) (E in Figure 2.16a). The phase selec-tion in as-cast commercial aluminum is a function of the Fe:Si ratio and the cooling rate. Table 2.3 shows experimentally observed temperatures during solidifi cation of a 1050 alloy containing 0.37% Fe and 0.05% Si [5]. The solidus temperature decreases with increasing the cooling rate reaching 630°C (close to point P1 in Figure 2.16a) at which the invariant peritectic reaction specifi ed by Bäckerud et al. in Table 2.3 should occur under equilibrium conditions. The formation of the metastable Al6Fe phase is possible in a 1050 alloy cast at cooling rates above 1 K/s [5].

2.3.2 Wrought Alloys with Manganese (3XXX Series)

Analysis of Mn-containing alloys is quite complex and depends on the amount of alloying elements and impurities. For example, an 8006 alloy with a low content of Si impurity may contain Al6(FeMn) and Al3Fe phases formed upon secondary reactions during casting. Primary crystals of these phases are likely to be formed only at low cooling rates and high concentrations of iron. Silicon-containing 3009 and 3003 alloys contain the ternary Al15Mn3Si2 com-pound at a low Fe concentration in these alloys, by 60°C, Silicon dramatically, decreases the solidus of Al–Mn alloys. Typically, however, commercial alloys contain Mn, Fe, and Si together. As a result, in addition to binary phases, the

TABLE 2.3

Solidifi cation Reactions under Nonequilibrium Conditions in Commercial Aluminum Containing 0.37% Fe and 0.05% Si [5]

Reaction

Temperatures (°C) at a Cooling Rate

0.4 K/s 1.2 K/s 18 K/s

L ⇒ (Al) 659 659 659L ⇒ (Al) + Al3Fe 650 649 647L+Al3Fe ⇒ (Al) + Al8Fe2Si

— 642–638 630

Solidus 642 638 630




complex Al15(FeMn)3Si2 phase is formed as a result on bi- and monovariant eutectic and invariant peritectic transformations during solidifi cation.

Nonequilibrium solidifi cation further complicates the phase composition, which is due to the inhibition of invariant and monovariant peritectic reac-tions. Bäckerud et al. [5] experimentally observed the solidifi cation reactions given in Table 2.4 during nonequilibrium solidifi cation of a 3003 alloy. Note the considerable decrease in the solidus temperature with increasing the cooling rate. The as-cast structure contains Al6(FeMn) and Al15(FeMn)3Si2 phases. The amount of the latter phase increases with the silicon concentra-tion. If the concentration of silicon is at the upper level (0.6%) and that of iron is at the lower level, the formation of free (Si) is possible with corresponding decrease of the solidus to 573°C (temperature of the monovariant eutectic reaction L → (Al) + (Si) + Al15(FeMn)3Si2).

2.3.3 Al–Mg–Si Wrought Alloys (6XXX Series)

Alloys of the 6XXX series would be easy to analyze if they did not contain other elements, apart from magnesium and silicon, capable of affecting the phase composition. However, this is not always the case, as these alloys usu-ally contain Mn, Fe, and Si, and sometimes Cu. Nevertheless, the Al–Mg–Si phase diagram gives important information and it is appropriate to start the analysis of commercial 6XXX alloys with this diagram. Figure 2.17a shows the equilibrium phase composition (solidus surface) in the as-cast state. In the compositional range of 6XXX series alloys all phases that form during solidifi cation are of eutectic origin and are, generally, a result of nonequilib-rium solidifi cation. If the ternary eutectics (Al) + (Si) + Mg2Si is present, the solidus is as low as 555°C.

The presence of iron in 6XXX alloys results in the formation of different Fe-containing phases, i.e., α(Al8Fe2Si), β(Al5FeSi), Al3Fe, and π(Al8FeMg3Si6). In a 6003 alloy (0.8–1.5% Mg, 0.35–1% Si, up to 0.6% Fe, 0.8% Mn) the selection of phases depends on the ratio between alloying elements; see Figure 2.17b. At a high Mg:Si ratio, all iron should be bound to the Al3Fe

TABLE 2.4

Solidifi cation Reactions under Nonequilibrium Conditions in a 3003 Alloy Containing 1.19% Mn, 0.55% Fe, and 0.18% Si [5]

Reaction


0.5 K/s 17 K/s

L ⇒ (Al) 655 655L ⇒ (Al) + Al6(FeMn) 653 646–615L + Al6(FeMn) ⇒ (Al) + Al15(FeMn)3Si2 and/or L ⇒ (Al) + Al15(FeMn)3Si2

641–634 589

Solidus 634 589




phase, at the inverse ratio of these elements phases β(Al5FeSi) and π become dominant in the equilibrium state. The compositional range where iron is completely bound in the α(Al8Fe2Si) phase, which has the most favorable morphology among all Fe-containing phases, is quite narrow.

The concentration of alloying elements can considerably affect the extent of the solidifi cation range. Figure 2.17c shows that even a small increase in Si concentration can strongly lower the solidus temperature (TS). For example, in a 6162 alloy containing 0.9% Mg, the change of TS within the grade compositional limits (0.4–0.8% for Si) can be as large as 25°C. The effect of magnesium is less strong. The effect of iron on TS depends on the formation of α(Al8Fe2Si) and β(Al5FeSi). These phases bound silicon and, therefore decrease

FIGURE 2.17Solidus surface of the Al–Mg–Si system (a) and isopleths at 0.5% Si and 0.2% Fe (b) and 0.9% Mg (c) [32]. F denotes Al3Fe. (Reproduced with kind permission of Elsevier.)

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

0.0 0.5 1.0 1.5 2.0 2.5

570

570

570

590

(Al)+

Mg 2

Si58

0

560

580

590

Qua

si-b

inar

y se

ctio

n [5

95°C

]

580

590

600610

620

560 (Al)+(Si)

(Al)+Mg2Si+(Si) [555°C]

Si, %

Mg,

%

3.0 3.5 4.0

(Al)+F+Mg2Si

(Al)+F+α+Mg2Si

(Al)+α+Mg2Si

(Al)+α+β+Mg2Si

(Al)+β+π+

Mg

2 Si

(Al)+β+

(Si)

(Al)+β+π

(Al)+β+π+

(Si)

(Al)+β+Mg2Si

(Al)+β

(Al)+β+α

(Al)+α

(Al)+F+αL+(Al)+F+Mg2Si

L+(Al)+F

(Al)+F

L+(Al)+Mg2Si

L+(Al)

L

643

657654635

T°C

612606

555545

435

500

300

700

6311.9

533

0.74

518

500

0.88

0.8

Al−0.5%Si−0.2%Fe 1

0.89

0.880.7

0.80.680.23

0.12 0.342

Mg,%

1

1.1 1.2 1.3

200

300

400

500

600

700

Al−0.9% MgSi, %

(Al)+Mg2Si

(Al)

6162

(Al)+Mg2Si+(Si)

L+(Al)+(Si)

L+(Al)+Mg2Si

(Al)+

Mg 2

Si

(Al)+Mg2Si+(Si)

L+(Al)+(Si)1.241.12

555

L+(Al)

L+(Al)

L

T°C

2 3

(a) (b)

(c)




its free amount, resulting in a higher solidus temperature. According to Belov et al. [32], up to 0.1% Si can be bound in the Fe-containing phases in 6XXX alloys containing 0.2% Fe.

Nonequilibrium solidifi cation causes deviation from the equilibrium phase composition. For example, in an alloy containing 0.5% Mg, 0.5% Si, and 0.2% Fe, the Al3Fe phase is formed during equilibrium solidifi cation as follows from the isopleth shown in Figure 2.17b. However, as the formation of this phase requires larger undercooling as compared to the α(Al8Fe2Si) phase, the latter usually forms under real casting condition (at this alloy composition). High-temperature peritectic reactions are hindered during solidifi cation at real cooling rates and, as a result, the phases that should disappear upon these reactions are retained in the structure.

Experimental studies of nonequilibrium solidifi cation of a 6063 alloy were performed by Bäckerud et al. [5]. The results given in Table 2.5 show the simultaneous presence of α(AlFeSi) and β(Al5FeSi) phases in the as-cast struc-ture. This agrees well with the casting practice. The amount of Mg2Si formed at the end of solidifi cation is small. Frequently, particles of Mg2Si form con-glomerates with iron-containing particles that testifi es for the occurrence of the last, peritectic reaction in Table 2.5.

On increasing the concentration of Mg and Fe in 6XXX series alloys, the probability of Al3Fe formation increases, especially at moderate cooling rates. Hsu et al. [38] examined the phase composition of an Al–0.8% Mg–0.6% Si–0.3% Fe alloy (6063 type, high-alloyed) after nonequilibrium solidifi cation at ~0.1 K/s and revealed the eutectic formation of the Al3Fe phase at 625°C and of the metastable α(AlFeSi) phase at 593°C.

On further increasing concentration of silicon (and low iron), the forma-tion of Al3Fe is unlikely even upon slow cooling, and the probability of the quaternary π phase formation increases. For example, simultaneous pres-ence of Mg2Si, (Si), β, and π crystals within one conglomerate is observed in an Al–0.86% Mg–1.61 Si–0.072% Fe alloy cast at 0.03 K/s [39].

TABLE 2.5

Solidifi cation Reactions under Nonequilibrium Conditions in a 6063 Alloy (0.43% Mg, 0.39% Si, and 0.2% Fe) [5]

Reaction


0.5 K/s 15 K/s

L ⇒ (Al) 655–653 654L ⇒ (Al) + α(AlFeSi)* 618–615 617L + α(AlFeSi)* ⇒ (Al) + Al5FeSi 613 610L + α(AlFeSi)* ⇒ (Al) + Al5FeSi + Mg2Si 576** 576**Solidus 576** 576**

* The crystal structure of α(AlFeSi) is cubic, hence this is a metastable phase (see Table 2.2).** Estimated value from [29].




2.3.4 Al–Mg–Si–Cu Wrought Alloys (6XXX and 2XXX Series)

Several widely used commercial alloys of the 6XXX series contain copper that is added to improve strength. In most cases, the solidifi cation of 6XXX series alloys containing copper can be described using the Al–Mg–Si phase diagram (Figure 2.17). With taking into account typical additions of transi-tion metals, the as-cast structure exhibits the aluminum solid solution with Mn, Ti, and Cr-containing particles formed during high-temperature eutec-tic (Mn) and peritectic (Ti, Cr) reactions.

Only at the concentrations of alloying elements close to the upper limits do the alloys fall at different phase fi elds (containing Si and Mg2Si) at the end of equilibrium solidifi cation as shown in the isothermal section at 500°C (close to the solidus) for alloys containing 1% Si (Figure 2.18). Impurity of Fe reacts with Si and Mn to form (AlFeMnSi) particles of eutectic origin. Under real casting conditions nonequilibrium eutectics containing Mg2Si and Si are formed, decreasing the solidus of the alloy. The main implication of copper addition to Al–Mg–Si alloys is the formation of the quaternary Al5Cu2Mg8Si6 (Q) phase through peritectic reactions with Mg2Si and Si occurring at 529 and 512–514°C or by a multi-phase eutectic reaction at 505–507°C. This phase

FIGURE 2.18Isothermal section of the Al–Cu–Mg–Si phase diagram at 500°C and 1% Si [32]. (Reproduced with kind permission of Elsevier.)

321.1

[1.1;1.03][0.5;1.04]

[0.6;1.52]

[0.29;3.9]

[0.56;4.05]

[1.35;4.2]

[1.72;3.74]

1.340.580.28 1.72

1−0.5

2

4

6

4.05

(Si)+Mg2Si

Mg2Si+Al2CuAl2Cu+Q

Q+

(Si)

(Si)+

Al 2

Cu

Q+M

g 2S

i

Mg, %

Cu,

%

Al − 1% Si




is very stable and can be found in Al–Mg–Si alloys with an excess of Si even at additions of copper as small as 0.25% [40]. According to Mondolfo this phase forms upon solidifi cation and is in equilibrium with aluminum under the following conditions: Mg:Si < 1.73, [Mg] > 2 [Cu], and [Cu] > 1% [29]. Depending on the ratio of copper, magnesium, and silicon, the Q phase can coexist with Al2Cu (θ) (that appears in Al–Cu–Mg–Si alloys with the suffi -cient amount of copper, > 4%), Mg2Si and Si.

The phase composition of cast alloys signifi cantly differs, as a rule, from the equilibrium selection of phases, which is due to incomplete peritectic reac-tions and hindered diffusion of copper, magnesium, and silicon in (Al) during solidifi cation. Almost all phases from the aluminum corner of the Al–Cu–Mg–Si system—(Si), Mg2Si, Al2Cu, Al2CuMg and Q—can be found simultane-ously in as-cast ingots and billets of wrought alloys of the 2XXX series.

2.3.5 Al–Mg–Mn Wrought Alloys (5XXX Series)

Let us fi rst look at the general effect of magnesium and manganese on the sol-idus and liquidus of commercial alloys with minor silicon content (< 0.5%). Plots in Figure 2.19a and b are obtained by interpolation of data from [41]. Obviously, magnesium has much stronger infl uence on both characteristic temperatures than manganese. These charts can serve as a directory on the correct choice of casting and annealing temperatures.

The polythermal section of the ternary Al–Mg–Mn phase diagram shown in Figure 2.19c gives us the fi rst approximation of phase transformation his-tory for alloys like 5083, 5182, and 5456 containing 4–7% Mg and 0.3–0.8% Mn. Solidifi cation starts at 635–640°C with the formation of (Al) grains. After that, providing that the concentration of Mn is suffi cient, the (Al) + Al6Mn eutectics is formed in the range of temperatures from 627 to 617°C [5]. Other phases that may be present in the solid state are formed by precipitation from the aluminum solid solution. These reactions usually seldom occur during cooling after the end of solidifi cation because, due to a relatively low diffusion coeffi cient, manganese usually remains in a supersaturated solid solution. During annealing of cast material, Mn-containing phases precipi-tate from the solid solution supersaturated during solidifi cation and form dispersoids. The fi nal equilibrium phase composition of alloys containing more than 4% Mg and 0.1% Mn is (Al) + Al8Mg5 + Al10(MgMn)3. If the con-centration of Mg is less than 2–3%, the equilibrium phase composition at room temperature would be (Al) + Al6Mn + (traces) Al10(MgMn)3.

The presence of silicon, as an impurity or an alloying element, in Al–Mg–Mn alloys results in the formation of Mg2Si in addition to other phases that we have already considered. After formation of primary aluminum grains, the binary eutectics (Al) + Al6Mn is solidifi ed. During further cooling, Al15Mn3Si2 is formed. This phase then reacts with liquid to produce Al10(MgMn)3 and Mg2Si phases, and these phases remain in equilibrium with aluminum down to the room temperature. The Al8Mg5 phase is formed by precipitation from the aluminum solid solution upon cooling in the solid state.




Most commercial alloys contain iron as an impurity. As a result, the (Al) + Al6(FeMn) eutectics is formed in the temperature range from 600 to 570°C, and the solidifi cation ends at approximately 570°C with the formation of the (Al) + Al6(FeMn) + Al3Fe eutectics. Under equilibrium, other phases that are frequently observed in Al–Mg–Mn–Fe alloys, e.g., Al8Mg5 and Al10(MgMn)3, are formed only by precipitation from the aluminum solid solution upon cool-ing in the solid state. Under real, nonequilibrium conditions, these phases can form during solidifi cation as a result of eutectic reactions.

In the case of simultaneous presence of iron and silicon in a 5XXX series alloy containing 5% Mg (e.g., the 5182 alloy), the solidifi cation will end at 576–578°C with the formation of Mg2Si by a eutectic reaction.

FIGURE 2.19Isotherms of liquidus (a) and solidus (b) for commercial Al–Mg–Mn alloys containing silicon and iron on the impurity level; and (c) isopleth of the Al–Mn–Mn phase diagram at 5% Mg. Compositional range of some 5XXX series alloys is marked by dashed lines [32]. (Reproduced with kind permission of Elsevier.)

2

0.2

0.4

0.6

0.8

1.0

1.2M

n, %

645

635

625

610

590

570

550

510

530

4 6 8 10Mg, %

20

0.0

0.5

1.0

1.5

Mn,

%

4 6 8 10Mg, %(a) (b)

1100

200

264

2.75

2.73

300

400

500

600

700615 649

627

205

0.1

0.37

2 3

L+(Al)

(Al) (Al)+Al6

Al10: Al10(MgMn)3

Al8: Al8Mg5

Al6: Al6Mn

(Al)+Al8Al−5% Mg

Mn,%

T°C

(Al)+Al10+Al8

(Al)+Al10+Al6

L+(Al)+Al6

L+Al6L

(c)




The solidifi cation paths that we considered above describe the phase equi-librium and can hardly be accomplished under real casting conditions when cooling rates are high and the diffusion processes, especially in the solid phase, cannot be completed to such an extent that the compositions of the phases change with temperature in accordance with the equilibrium phase diagram. Local deviations from equilibrium result in microsegregation and eventually in the shift of local equilibrium to the concentrations where new phases are formed. In addition, some high-temperature peritectic reactions remain uncompleted, and high-temperature phases—that have to disappear as a result of these reactions—are retained at lower temperature and can be found in the solid sample.

The consequences of nonequilibrium solidifi cation for the phase transfor-mations and phase selection are demonstrated below for a 5182 alloy that has been tested upon solidifi cation at different cooling rates, from 0.3 to 11 K/s, these cooling rates being characteristic of direct-chill and die casting [5]. The equilibrium phase diagram gives a solidus temperature of 576–578°C. However, thermal and phase analyses performed during and after solidi-fi cation clearly demonstrate that solidifi cation continues at lower tempera-tures. Table 2.6 gives solidifi cation reactions and corresponding temperature ranges at different cooling rates for this alloy [5]. The solidifi cation starts with the formation of aluminum grains. The solidifi cation temperature slightly decreases with increasing cooling rate due to increased undercooling. Then two concurrent reactions may occur at 620°C. After that the eutectics con-taining Mg2Si and Al3(FeMn) is formed at about 580°C. The equilibrium solidifi cation ends at this point. However, experimental results show that, after reaching the equilibrium solidus, the alloy still contains a liquid phase that undergoes a complex eutectic reaction and completely vanishes only at 470°C, thereby extending the solidifi cation range by almost 100°C. Thompson et al. studied the nonequilibrium solidifi cation of a 5182 alloy cast at different cooling rates [42]. They observed that the temperature of (Al) + Al6(FeMn) eutectics decreases from 588 to 575°C and the solidus decreases from 510 to 461°C on increasing the cooling rate from 0.5 to 2 K/s. The resultant phase

TABLE 2.6

Solidifi cation Reactions under Nonequilibrium Conditions in a 5182 Alloy (4.74% Mg, 0.34% Mn, 0.28% Fe, 0.1% Si) [5]

Reaction


0.3 K/s 11 K/s

L ⇒ (Al) 632 632–623L ⇒ (Al) + Al6(FeMn) and/or L ⇒ (Al) + Al3(FeMn) 621–617 620L ⇒ (Al) + Al3Fe + Mg2Si 586 583L ⇒ (Al) + Al3Fe + Mg2Si + Al8Mg5 557–470 543–470Solidus 470 470




composition of a 5182 alloy is (Al), Al3Fe, Mg2Si, Al8Mg5, and Al6(FeMn), the last phase frequently replaced by Al4(FeMn) due to the incomplete high-tem-perature peritectic reaction and enrichment of liquid in Mg and Mn [43].

2.3.6 Al–Cu–Mn (Mg, Si, Ni) Wrought Alloys (2XXX Series)

The combined presence of Mn, Fe, and Si in these alloys mainly results in the formation of the Al15(FeMn)3Si2 phase through different eutectic reactions.

The number of phases in the as-cast (nonequilibrium) state can be larger than the number under equilibrium conditions, but the sequence of solid-ifi cation reactions is in general agreement with the corresponding phase diagrams. Table 2.7 gives as an example the solidifi cation reactions identi-fi ed during nonequilibrium solidifi cation of a 2024 alloy [5, 30]. This alloy belongs to the Al–Cu–Mg–Mn system but the presence of Fe and Si impuri-ties complicates the situation and causes the formation of phases containing these elements (Table 2.7). The as-cast structure of a 2024 alloy exhibits par-ticles of the Al15(MnCuFe)3Si2 phase that is formed after primary (Al) grains. As iron is completely bound in this phase, the early solidifi cation reactions can be analyzed using the Al–Cu–Mn–Si phase diagram. Therefore, the binary eutectic reaction L → (Al) + Al15Mn3Si2 transforms to the ternary one L → (Al) + Al20Cu2Mn3 + Al15Mn3Si2. Then, Al20Cu2Mn3 must disap-pear through the peritectic reaction L + Al20Cu2Mn3 → (Al) + Al15Mn3Si2 + Al2Cu. The next reactions can be analyzed using the Al–Cu–Mg–Si phase diagram because manganese and iron have already been consumed by the earlier formed phases.

A stringent analysis of 2618-type alloys requires the fi ve-component Al–Cu–Fe–Mg–Ni phase diagram because these alloys contain enough copper and magnesium to produce the Al2CuMg phase. As this phase diagram is yet to be constructed, only a simplifi ed analysis of the phase composition of this type of alloys is possible using constitutive phase diagrams and considerable experimental data on the structure of 2618-type alloys [32]. According to

TABLE 2.7

Solidifi cation Reactions under Nonequilibrium Conditions in a 2024 Alloy (4.44% Cu, 1.56% Mg, 0.55% Mn, 0.21% Si and 0.23% Fe) [5]


Reaction 0.8 K/s 13 K/s

L ⇒ (Al) 637–633 637–627L ⇒ (Al) + Al15(MnCuFe)3Si2 633–613 613L ⇒ (Al) + Al15(MnCuFe) 3Si2 + Al20Cu2Mn3

L + Al20Cu2Mn3 ⇒ (Al) + Al15(MnCuFe)3Si2 + Al2Cu551–538 544

L ⇒ (Al) + Al2Cu + Mg2Si 486 480L ⇒ (Al) + Al2Cu + Al2CuMg + Mg2SiSolidus 486 480




these data, the microstructure of these alloys in the as-cast state contains particles of the Al9FeNi and Al2CuMg phases. The former probably forms through the binary eutectic reaction L → (Al) + Al9FeNi which, due to the presence of copper and magnesium in an alloy, occurs over a wide tempera-ture range, from approximately 640–645°C down to 505–515°C. The Al9FeNi phase is then preserved in the fi nal structure of deformed semifi nished items. A subsequent treatment can only change the morphology of particles that, as a rule, is rather compact. The appearance of the Al2CuMg phase in the as-cast structure is a consequence of nonequilibrium solidifi cation. During homogenizing annealing, it completely dissolves in solid (Al). The nonequilibrium solidus of 2618-type alloys corresponds to the temperature of the quasi-ternary L → (Al) + Al9FeNi + Al2CuMg eutectics and is about 515°C. At a maximum copper concentration (within the alloy nominal com-position), the Al2Cu phase can form, in this case the solidifi cation completes at a lower temperature, ~505°C according to the Al–Cu–Mg phase diagram. The formation of Al9FeNi primary particles is unlikely in the entire compo-sitional range of a 2618 alloy.

2.3.7 Al–Mg–Zn–(Cu) Wrought Alloys (7XXX Series)

Copper-less 7XXX-series alloys, e.g., 7004 and 7005, contain, as a rule, less than 6–7% (Zn + Mg) because higher concentrations facilitate stress corro-sion. In the as-cast condition, the structure of these alloys consists mainly of (Al) grains. The presence of iron and silicon impurities causes the formation of Al3Fe and Mg2Si phases as has been shown experimentally by Bäckerud et al. for a 7005 alloy [5] (Table 2.8). However, the Al8Fe2Si phase should form in this type of alloy at Si:Fe > 3 [29]. The probability of Al8Fe2Si formation increases at high cooling rates [32]. Slow cooling favors the formation of Al3Fe because magnesium in 7XXX alloys is in excess of Mg2Si. Additions of Mn in some commercial 7XXX alloys promote the formation of Al15(FeMn)3Si2 particles that can hardly be dissolved during heat treatment and are retained in the structure of the fi nal product. Small additions of Cr and Zr do not

TABLE 2.8

Solidifi cation Reactions under Nonequilibrium Conditions in a 7005 Alloy Containing 5.14% Zn, 1.12% Mg, 0.18% Mn, 0.19% Fe, and 0.08% Si [5]

Reaction

Temperatures (°C)* at a Cooling Rate

0.3 K/s 15 K/s

L ⇒ (Al) 641 638L ⇒ (Al) + Al3Fe 632–596 610L ⇒ (Al) + Mg2Si 596 560L ⇒ (Al) + Al2Mg3Zn3 470 470Solidus 470 470

* Start of reaction.




affect the as-cast phase composition much because these elements enter the aluminum solid solution during solidifi cation.

High-strength wrought aluminum alloys have a complex chemical compo-sition, i.e., they contain at least fi ve or six components. With certain assump-tions, these alloys can be assigned to the Al–Cu–Mg–Zn system.

According to Bäckerud et al. the nonequilibrium solidifi cation of a 7075 alloy ends at 466–469°C with the invariant eutectic reaction L → (Al) + Al2Cu* + MgZn2 + Al2Mg3Zn3 [5]. In our opinion, the reaction with the par-ticipation of the Al2CuMg (S) phase is more likely (see Table 2.9).

Inclusions of the η (MgZn2) and T (Al2Mg3Zn3) phases formed during non-equilibrium solidifi cation are completely dissolved in (Al) during homogeni-zation in the temperature range 435°C–445°C.

2.3.8 Wrought Alloys Containing Lithium

Commercial Al–Li alloys can be tentatively divided into three groups: Al–Li–Cu (2090, 2020, VAD23rus); Al–Li–Mg (1420rus), and Al–Li–Cu–Mg (2091, 8090, Weldalite049, CP276, 1441rus, 1464rus). Most Al–Li alloys contain Zr; some contain other small additions such as Ag (Weldalite049), Sc (1421rus, 1424rus, 1464rus), Cd (VAD23rus). The implications of these additions for the phase composition are discussed in this section.

2.3.8.1 Al–Cu–Li Commercial Alloys

Commercial alloys that belong to this system contain 1–2.5% Li, 2.5–5.5% Cu and small additions of Zr (2090) or Mn and Cd (VAD23rus).

The solidifi cation of a VAD23-type alloy (1.15% Li, 5.15% Cu) starts with the formation primary (Al) grains, then a small amount of binary (Al) + Al2Cu eutectics precipitates. The remaining liquid reacts with Al2Cu according to the transition reaction L + Al2Cu → (Al) + Al7.5Cu4Li (TB). During that reaction (under equilibrium conditions) Al2Cu disappears and T1 (Al2CuLi) and TB

TABLE 2.9

Solidifi cation Reactions under Nonequilibrium Conditions in a 7075 Alloy (5.72% Zn, 2.49% Mg, 1.36% Cu, 0.19% Cr, 0.28% Fe, and 0.11% Si) [5]

Reaction

Temperatures (°C)* at a Cooling Rate

0.3 K/s 2.3K/s

L ⇒ (Al) 630–623 628L ⇒ (Al) + Al3Fe 618–615 —L ⇒ (Al) + Mg2Si 568–563 558–550L ⇒ (Al) + Al2Cu**+MgZn2+ Al2Mg3Zn3 469 466Solidus 469 466

* Start of reaction.** Al2CuMg




phases are formed. The solidifi cation is likely to end with the formation of (Al) + TB binary eutectics. During cooling in the solid state, TB and T1 phases precipitate from the aluminum solid solution as a result of decreasing solubil-ity of Cu and Li in (Al). The resultant phase composition of a VAD23-type alloy is (Al) + T1 + TB, the ternary phases forming different structure constituents.

In the case of a 2090-type alloy with a higher concentration of Li (2.25%) and a lower concentration of copper (2.7%), after primary formation of (Al) grains the (Al) + AlLi binary eutectics solidifi es. The alloy then undergoes transition reactions with the formation of T1 and T2 (Al6CuLi3) phases. Hence, the fi nal equilibrium phase composition at room temperature of a 2090-type alloy is (Al) + T1 + T2.

Under nonequilibrium solidifi cation conditions, the amount of the binary eutectics in both alloys increases. Transition (peritectic) reactions may not complete, hence some particles of Al2Cu and AlLi, respectively, remain in the fully solidifi ed structure. The formation of the ternary eutectics (Al) + T1 + TB becomes possible, and the solidus temperature may decrease to 518–528°C. The structure of all eutectics in wrought Al–Cu–Li alloys is divorced and appears as individual particles at grain and dendritic cell boundaries. Nonequilibrium phases Al2Cu and AlLi will dissolve during homogeniza-tion annealing of commercial alloys.

2.3.8.2 Al–Li–Mg Commercial Alloys

Commercial Al–Li–Mg alloys (without copper) were developed and used in Russia. All alloys of this group (142Xrus) contain small additions of transi-tion metals such as Zr, Mn, and Sc.

The equilibrium phase composition and the solidifi cation path of 142X-type alloys can be evaluated from ternary and quaternary phase diagrams, e.g., an isopleth shown in Figure 2.20a. The equilibrium structure (at 4–6% Mg, 1.5–3% Li) consists of (Al) grains with secondary particles of AlLi and Al2LiMg phases formed during cooling in the solid state.

Additional alloying with Zr and Sc results in more complex solidifi ca-tion behavior with primary solidifi cation of Al3Zr and Al3Sc phases. There are indications that the Al2LiMg phase may form peritectically at higher Li concentrations [44]. The (nonequilibrium) solidus of Al–Li–Mg–Zr alloys is 530°C. At cooling rates realized during real casting, scandium and zirconium enter the aluminum solid solution during solidifi cation and then precipitate upon high-temperature annealing to form coherent particles of stable Al3Sc and metastable Al3Zr phases.

2.3.8.3 Al–Li–Cu–Mg Commercial Alloys

The majority of commercial Al–Li alloys contain copper and magnesium within the compositional ranges 0.3%–6% Mg, 1–5.5% Cu, and 1–3% Li. All three elements contribute to the formation of phases and structure during solidifi cation, deformation, and aging. The as-cast and annealed alloys may contain the following phases: (Al), T1 (Al2CuLi), T2 (Al6CuLi3), Al2Cu,




and S (Al2CuMg). Figure 2.20b demonstrates the polythermal section of the quaternary phase diagram at 3% Cu and 2.5% Li, which is relevant for the analysis of such commercial alloys as CP276, 2091, 8091 (up to 3% Mg). One can easily see that the solidifi cation for these alloys starts with the formation of the aluminum solid solution, then T2 and S phases are formed through eutectic reactions. The T1 phase is formed by precipitation from the solid

FIGURE 2.20Isopleths of Al–Li–Mg–Zr (a) and Al–Cu–Li–Mg (b) phase diagrams. (Reproduced with kind permission of Elsevier.)

700

T°C

T°C

650

600

550

400

600

2090,CP276 8091

2091,

200

2 4 6 8 10

5001.0 2.0 3.0 4.0 5.0

(Al)+Al2Zr

(Al)+T1+T2

(Al)+T1+T2+S

(Al)+T2+S+Al2LiMg

L+(Al)+T2+S

L+(Al)+T2L+(Al) L

(Al)+T2+S

(Al)+T2

Al − 4.5% Mg − 0.2% Zr

Al − 3% Cu − 2.5% Li

Li, %

Mg, %

(Al)+Al3Zr +Al3LiMg

L+(Al)+Al3Zr+Al2LiMg

(Al)+

Al 3

Zr+

Al 2

LiM

g+A

lLiL+(Al)+Al3Zr

L+Al3Zr

(a)

(b)

484°C




solution. The lowest possible eutectic reaction in this system is L → (Al) + S + T2 + Al2LiMg at 484°C.

The effects of alloying elements on the solidus temperature of Weldalite-type alloys (4–6.3% Cu, 0–2% Li, 0–0.8% Mg) were studied by Montoya et al. [45]. The variation in copper concentration above 4% has virtually no effect on the solidus temperature of the base alloy Al–1.3% Li–0.4% Mg, the soli-dus being at 512–513°C. Increasing the concentration of magnesium in the Al–(5–6)% Cu–1.3% Li alloys results in the continuously decreasing solidus temperature, from 521 to 507°C. A minimum solidus temperature of 507–513°C suggests the occurrence of a eutectic reaction at this temperature. The temperature is, however, about 10°C lower than that of the eutectic reaction L → (Al) + T1 + TB of the Al–Li–Cu system. Mukhopadhyay et al. suggest that the eutectic reaction L → (Al) + Al2Cu + Al2CuMg (S) that takes place at 507°C is responsible for the lowest melting temperature in Weldalite-type alloys [46]. They also observed the melting of the ternary eutectics (Al) + T1 + TB at 521°C. The phase composition of as-cast Weldalite-type alloys is (Al) + T1 + TB + Al2Cu + Al2CuMg (S), with the last phase being present only in small quantities [46]. It should be noted that the possibility of the invariant eutectic reaction L → (Al) + T1 + S that occurs at 505 ± 10°C can-not be excluded under nonequilibrium solidifi cation conditions [40]. The existence of low-melting eutectics in Weldalite-type alloys should be taken into account while choosing the correct regime of solution treatment.

2.4 Effect of Alloy Composition on Structure Formation: Grain Refinement*

2.4.1 Mechanisms of Grain Refinement

It is well known that that the fi nal structure formed in a casting depends on both the alloy composition and the casting conditions. Figure 2.3 illustrates this fact for binary Al–Cu alloys and Figure 2.4 explains the principle of con-stitutional undercooling, the phenomenon driven by the alloy composition and phase diagram constitution. In this section we look at the interrelation between the alloy composition and the as-cast structure in more detail.

The ranking of solute effects on the grain size in hypoeutectic aluminum alloys can be done simply by comparison of their equilibrium solidifi cation ranges [2].

Two parameters have been suggested for quantifying the effect of alloy composition on grain size, both parameters being proportional to the solidi-fi cation range. These are the undercooling parameter [47]:

P = mC0(K – 1)/K = ∆T0 (2.7)

* Fruitful discussions with Dr. R. Mathiesen of SINTEF (Norway) and Dr. M. Easton of CAST CRC (Australia) on the issues of solute effects in grain refi nement are greatly appreciated.




and the growth restriction factor [48]:

Q = mC0(K – 1) = K∆T0, (2.8)

where m is the liquidus slope at the alloy composition C0, K is the partition coeffi cient, and ∆T0 is the equilibrium solidifi cation range, i.e., the difference between equilibrium liquidus and solidus temperatures.

The undercooling parameter represents the potentially possible under-cooling and is equal to the solidifi cation range of an alloy with composi-tion C0, while the growth restriction factor refl ects the solute rejection at the solid–liquid interface.

The constitutional undercooling at the solid–liquid interface is propor-tional to the growth restriction factor:

∆Tc = ΞQ, (2.9)

where Ξ = ( C ss L – C0)/( C ss L (1 – K)) is the solutal supersaturation [1]. C ss L rep-resents the liquid constitution at the interface, which is different from the equilibrium C0, when undercooling is present (see Figure 2.22).

Generally the constitutional undercooling at the solid–liquid interface will drive the growth according to the general formulation for the maximum growth velocity [1, 49]:

Vgrowth = Ds∆ T c 2 /QΓ, (2.10)

where Ds is the diffusion coeffi cient of the solute in the melt, ∆Tc is the under-cooling, Q is the growth-restriction factor, and Γ is the Gibbs–Thompson coef-fi cient refl ecting the effect of the dendrite tip curvature on the tip growth velocity. (Γ = σ ls/∆sf, where σls is the solid–liquid interfacial energy and ∆sf is the volumetric entropy of fusion, which corresponds to the latent heat of solidifi cation.) We can see, at least qualitatively, that slow solute diffusion (Ds), small undercooling (∆Tc), large solidifi cation range and partitioning (Q), and large interfacial energy (σ ls) would result in limited growth of the solid phase into the liquid.

It might seem awkward that the growth-restriction factor is proportional to solute-caused* undercooling (compare Equations 2.8 and 2.9) and, at the same time, determines the hindering of solid-phase growth in the presence of solute in the melt. This apparent dilemma can be resolved if we accept the following.

1. Growth of the interface requires the local equilibrium between solid and liquid concentrations that is easily shifted under real solidifi cation conditions from the global equilibrium according to the equilibrium phase diagram for the alloy composition C0. In the case of hypoeutectic aluminum alloys, the liquid becomes supersaturated with the solute.

* Here and below we mainly consider hypoeutectic alloys where the constitutional undercool-ing is a result of solute enrichment. In the case of peritectic systems and hypereutectic alloys, the constitutional undercooling is caused by the solvent (aluminum).




2. The so-called growth restriction can be caused not only by the sol-ute rejected from the advancing front (“parent” interface) but also by the solute that is brought to the front from elsewhere, e.g., by convection.

The solute supersaturation at the interface should be dissipated either by diffusion (convection) or by remelting of the solid phase. Figure 2.21 [25] brilliantly illustrates how the uneven accumulation of Cu in the melt at the columnar front (frame 2) hinders the growth of a grain marked by an arrow. As soon as this accumulation is dissipated by diffusion and convection (frame 3), the grain resumes its growth (frame 4).

The reasons for the solute accumulation or the solute infl ux to the solid/liquid interface can be many. Most frequently, the growth restriction is con-sidered in relation to grain refi nement by inoculants and to the columnar-to-equiaxed transition (CET) [50–52]. In the course of grain refi nement, the solute rejected by the growing grain slows down its growth and, at the same

FIGURE 2.21A sequence of X-ray micrographs (from 1 to 4) taken in the European Synchrotron Radiation Facility from an Al–30 wt% Cu alloy solidifying in a Bridgeman-type furnace with the cooling at the bottom. Gray shade in the liquid area changes from black to light gray on decreasing the concentration of copper from 33 to 30 wt% Cu. An arrow points at the columnar dendrite tip, the growth of which depends on the Cu concentration ahead. (The sequence is courtesy of Dr. R. Mathiesen (SINTEF, Norway) and Prof. L. Arnberg (NTNU, Norway).)

1 2

3 4




time, may create the constitutional undercooling suffi cient for the nucleation of a new grain at the substrate that pre-exists in the melt [52].

In the case of CET, the “added” solute is the solute rejected by the colum-nar grain tip, but it also can come from the neighboring columnar grain or the solid phase nucleated ahead of the columnar front. The constitutional undercooling due to the solute rejection at the solid–liquid interface creates favorable conditions for heterogeneous nucleation at some distance ahead of the solidifi cation front (see Figures 2.4 and 2.22b). The nucleated grains start to grow and reject solute as well as generate the latent heat. As a result, the growth of the “parent” interface stops. The greater the solidifi cation rate (solid fraction evolution per unit time), the more effective this growth restriction.

FIGURE 2.22Diagram of solute effects on the advance of the solidifi cation front: (a) a scheme of a binary diagram with characteristic temperatures and compositions; (b) change in the constitu-tional undercooling at the “parent” interface in the case of nucleation ahead of this interface (solid lines and arrows = no or weak nucleation ahead; dashed lines and arrows = intensive nucleation ahead [53]); and (c) the remelting of the “parent” interface due to the excess solute accumulation.

Liquid

Solid

Tx

Tss

TC0

TC0

TC0

Tmelt

T

CiS

CxS C0 CCx

L CssL

CssL

CxL

C0

Cxs

Cis

Tinterface=Tx

Tss

Solid Region ofconstitutional superheating


(a)

CxL

Cxs

Cis

C0

Tinterface=Tx

Tmelt


Solid LiquidLiquid

(b)(c)




Martorano et al. showed that the rejection of solute by newly formed grains with a high grain density will, in fact, effec-tively decrease the constitutional under-cooling initially created at the “parent” interface and stop its advance, as shown in Fig ure 2.22b [53].

The solute also can be brought to the int-erface by thermo-solutal and shrinkage-driven fl ows during solidifi cation (see (2) above), as well as be caused by nonequi-librium solidifi cation conditions (see (1) above). In both cases the volume around the interface cannot be considered a closed system. The volume becomes open. The extent of this solute accumulation depends on the effective diffusivity of the solute in the melt (see Equation 2.10). In order to maintain the local equilibrium at the interface and obtain the momentum for further growth (solidifi cation) the interface should fi rst remelt and absorb the excess of the solute. This situation is shown in Figure 2.22c and is often a case upon fragmentation of dendrite branches [54, 55]. It is worth mentioning here that fragmentation or “grain multiplication” is considered to be one of the mecha-nisms of grain refi nement in castings. An example of fragmentation observed in situ during solidifi cation of an Al–20% Cu alloy is demonstrated in Figure 2.23 [56]. It is quite obvious that the accumula-tion of the solute copper at the root of the dendrite branch causes its remelting and, eventually, detachment from the parent branch, as shown in Figure 2.24 [55]. In this particular case the accumulation of the solute is a result of solute transport from the solidifi cation front (far from the fragmentation site), from the tip of the fragment-to-be, and due to the local solid-ifi cation in the place of detachment [55].

It is also suggested that the solute accumulated at the interface hinders the growth only until some values of Q, when the solid–liquid interface is relatively smooth (which is the case for globular and little-branched grains)

FIGURE 2.23Fragmentation during columnar growth of an Al–20% Cu alloy observed in situ by X-ray microscopy [56] (images are cour-tesy of R. Mathiesen of SINTEF, Norway.)




[52, 57]. In the case of high Q, and hence high constitutional undercooling, grains start to grow faster and in a very branched manner. As a consequence, the solute is rejected from the sharp and elongated dendrite-branch tips not only to the front but also sideways. This solute is accumulated in the mush between the dendrite branches and is, upon decreasing the temperature, absorbed by the solid phase. In such a way, the effective growth restriction is decreased and the dendrite grains have the opportunity to grow faster, even if the average concentration of solute in the melt is high.

The concept of growth restriction is rather popular nowadays for the expla-nation of the effect of different solute levels on the effi ciency of grain refi ne-ment in aluminum alloys [50–52, 58]. There are, however, some problems that are still exist with this concept.

First of all, the idea that the growth restriction factor Q of an alloy can be estimated by summation of growth restriction factors of its individual alloy-ing elements can be argued for two main reasons: (1) the interaction between different alloying elements can dramatically change not only the slope of the liquidus but also the amount of solute in the melt at different stages of solidi-fi cation [58] and (2) the effects of hypoeutectic, e.g., Cu, and “hypoperitectic,” e.g., Ti, elements on the composition of liquid in equilibrium with solid (Al) during solidifi cation are different; the former add solute into the melt while the latter add solvent. At the same time, this “summation” approach works

FIGURE 2.24Fragmentation of a tertiary branch (gray in fi gure) during columnar solidifi cation of an Al–20% Cu alloy, similar to that shown in Figure 2.23. Images are quantifi ed in terms of copper concen-tration in the liquid as shown in the insert scale [55]. The accumulation of copper at the root of the fragment-to-be is demonstrated. (The frame sequence is courtesy of Dr. R. Mathiesen (SINTEF, Norway).)

20

22

24

26

Cu

wt%

0 0

40

80

120

0

50

100

150

0

20

20 0 20 0 20 400

50

100

150

0 20 40

40

60




in practice quite well, and is explained by the fact that, though different ele-ments affect the solute distribution ahead of the interface differently, their individual effects on the constitutional undercooling are similar [59].

The second problem is that the growth restriction factor is usually used in order to explain why Ti is so powerful as a grain refi ner. Indeed, the growth restriction factor of Ti is Q ≈ 35 for the region of (Al) primary solidifi cation and at C0 = 0.15% Ti. This value is well above the typical values of the usual solutes in aluminum alloys [51]. However, there is no explanation as to why the most powerful grain refi ner in aluminum alloys—scandium—has a relatively low growth restriction factor, Q = 2.5 for C0 = 0.6% Sc, and yet remains very effi cient [60]. It is noteworthy that the undercooling factors P of both elements are quite close: 5 for Sc versus 4.4 for Ti. It is also very important to realize that the typical concentrations of Ti that are added to commercial aluminum alloys in the form of Al–Ti–B master alloys are in the range 0.001%–0.005% (C0 in Equation 2.8), and hence the growth restriction caused by titanium effectively decreases. It is, however, possible that the local enrichment of aluminum melt in Ti due to nonequilibrium segregation in the vicinity of grain-refi ning par-ticles of TiB2 compensates for the otherwise very low bulk Ti concentration.

In any case, the growth-restriction theory helps rank commercial alumi-num alloys with regard to their susceptibility to grain refi ning. The grain refi ning criterion (grain size) can be determined as

Ω = 1 _____ 3 √

____ Nf

+ b∆Tn _____ Q

, (2.11)

where N is the amount (density) of particles in the melt, f is the fraction of these particles that can act as nucleants, ∆Tn is the undercooling required for nucleation, and Q is the growth restriction factor [61]. The fi rst term is related to the availability of solidifi cation sites, while the second term shows the pos-sibility for nucleation (see Figure 2.28).

Another theory of grain refi nement links the formation of solidifi cation nuclei to compositional and structural fl uctuations in liquid. Atoms of the matrix metal and the addition are able to form stable confi gurations. Sam-sonov and Lamikhov [62] suggested that the incompleteness of d electron shells in transition metals was the main factor determining their refi ning ability. Then the grain-refi ning criterion looked as

Ω = 1/Ndnd, (2.12)

where Nd is the principal quantum number of the d electron shell and nd is the number of electrons on the d level. The greater the Ω, the larger the grain refi ning effi ciency. The following values can be obtained for Sc, Ti, Mn, Fe, and Zr: 0.333, 0.167, 0.067, 0.055, and 0.125. The combined effi ciency of several transition elements can be estimated from the electron exchange between s and d electron shells. This theory explains the high refi ning ability of Sc and Ti from the statistically stable confi guration of atomic clusters that can act as solidifi cation nuclei.




Further development of this theory included the interaction of valence electrons of both transition metal and aluminum [63]. Collective behavior of these electrons on s – p electron shells determines the stability of the nucleus. The following criterion has been suggested [63]:

Ω = 1 _________________________ Nsns + Npnp + Asas + Apap , (2.13)

where Ns, Np are the principal quantum numbers of and ns, np are the num-ber of electrons on the s- and p-levels of the addition atom, whereas As, Ap, as, and ap are the same for the aluminum atom.

Figure 2.25a illustrates the application of this criterion to two groups of additions to aluminum alloys. The fi rst group consists of typical grain refi n-ers that act through the nucleation mechanism, facilitating the nucleation of solid aluminum by providing a better structural match between the sub-strate and aluminum. The second group represents so-called surface-active additions that can refi ne grain by changing surface properties of substrates, e.g., facilitating nucleation by lowering the interfacial surface energy. The results show the obvious advantage of Ti and Sc for the fi rst group and Ca for the second group of additions.

The potency for grain refi nement is also a function of the size of an atomic cluster that can become a nucleus. The number of atoms in such a stable nucleus is a function of the ratio between enthalpy (latent heat) of evaporation ∆Hv and enthalpy (latent heat) of fusion ∆Hf of an Al–Addition compound:

na = J ( ∆Hv ____ ∆Hf ) ,

,

(2.14)

where J is the coeffi cient equal to 1/4 for hexagonal closed packed and fcc lattices and to 9/16 for bcc lattices [63]. Using the number n, it is possible to determine the size of the cluster, as shown in Figure 2.25b. The larger the size, the lower the undercooling required for stable nucleation, and the smaller the grain size. Note, however, that the data shown in Figure 2.25b refl ect only the stability of the nucleus and do not consider its further growth, and therefore do not fully agree with the casting practice.

Let us now look at some of the mechanisms of grain refi nement in alumi-num alloys. Generally, the idea behind grain refi nement is the sharp increase in the number of solidifi cation sites for heterogeneous nucleation of the pri-mary aluminum phase. This is usually done by special additions to an alloy, which are called grain refi ners. However, it is possible to achieve grain refi n-ing by multiplication of solidifi cation sites either by fragmentation of exist-ing solid grains or by activation of usually inert submicron solid particles that are always present in melts (e.g., oxides and carbides).

The grain refi nement by special additions is by far the most common method of producing castings with small, equiaxed, and uniformly distrib-uted grains. Particles that act as substrates for primary (Al) are usually rep-resented by high-temperature phases with crystal lattices that have a small




FIGURE 2.25(a) Variation of grain size with respect to the interaction criterion (Equation 2.13) for nucle-ation-type (solid line) and surface-active-type (dashed line) grain refi ners and (b) the size of a stable cluster [63].

Mn

Cr

ZrB

Cu

Fe

Mg

Zn

Ni

Ti Ca

Si

V

Sc

12

8

4

Gra

in s

ize,

mm

0

0.03 0.04 0.05 0.06Interaction parameter Ω

0.07 0.08

YHf

Zr

NbTi

Ta MoW

V

Sc

B

CrCoNi

Fe

Mn

0

0.5

Clu

ster

siz

e, n

m

1

1.5

2

2.5

(a)

(b)




mismatch with the crystal lattice of (Al), at least along some crystal planes. The demand for their formation in the alloy prior to the (Al) phase is obvi-ous: they should act as a substrate and be stable in the melt from which (Al) is formed. In addition, (Al) will “choose” these phases as substrates only if the heterogeneous nucleation on them will reduce the energetic barrier for the “ critical” nuclei [1]. Hence, these solidifi cation sites should present at least one of the surfaces with low interfacial (nucleation) energy, which is pos-sible if the crystal planes of the substrate and (Al) have as little a mismatch as possible. The similarity of chemical composition can also be helpful in nucleation of a primary phase, but it usually acts in the case of fragmenta-tion or, sometimes, activation of solid impurities, but not when special grain refi ners are added.

Among the most potent grain refi ners are Ti (Al3Ti) with the peritectic-type phase diagram with Al and Sc (Al3Sc) with the eutectic-type phase dia-gram with Al. The Al3Ti phase has a tetragonal crystal lattice and has a small mismatch with (111)Al at (112)Al3Ti plane [64]. The Al3Sc phase is cubic with a = 0.4104 nm, which is very close to the lattice parameter of (Al), a = 0.404 nm [60]. But, of course, the grain-refi ning effect in binary Al–Ti or Al–Sc alloys can be obtained only at concentrations where the corresponding primary phases are formed, >0.15% Ti and >0.6% Sc, respectively. In commercial practice, much less Ti or Sc is added, but then in combination with other elements such as B, C, and Zr. The question of how effi cient grain refi nement can be achieved at low concentrations of active elements is a problem in modern solidifi cation theory [52, 65].

As a fi rst approach to solving this problem, we need to look at what is known about the sequence and nature of solidifi cation in complex systems that are used as grain refi ners, i.e., Al–Sc–Zr, Al–Ti–B, and Al–Ti–C [32].

2.4.2 Al–Sc–Zr Phase Diagram

In the aluminum corner of this system only binary Al3Sc and Al3Zr phases are in the equilibrium with (Al). The Al3Sc phase is formed at 1320°C during a peritectic reaction, has a cubic ordered structure of L12 type with a = 0.4104 nm, and can dissolve Zr up to the composition Al3Sc0.6Zr0.4 (35% Zr) [60]. The Al3Zr phase melts congruently at 1577°C, has a tetragonal structure of D023 type with a = 0.4006–0.4014 nm and c = 1.727–1.732 nm, and dissolves Sc up to the composition Al3Zr0.8Sc0.2 (5% Sc) [60, 66]. These phases participate in the invariant reaction L + Al3Zr ⇒ (Al) + Al3Sc at 659°C. Mutual equilib-rium solubility of Zr and Sc in solid (Al) is 0.06% Zr, 0.03% Sc and 0.09% Zr, 0.06% Sc at 550 and 600°C, respectively [60].

The typical concentration of scandium and zirconium in commercial alu-minum alloys is lower than 0.3% Sc and 0.15% Zr or <0.45% in total [67]. Fig ure 2.26 shows the polythermal and isothermal sections of the Al–Sc–Zr phase diagram [60, 68]. Depending on the Zr:Sc ratio, either Al3Sc (Zr:Sc < 1) or Al3Zr (Zr:Sc > 1) solidifi es as the primary phase. The effi ciency of Sc as a grain refi ner is much improved in the presence of Zr. In this case usually 0.15%




FIGURE 2.26Al–Sc–Zr phase diagram: (a) projection of liquidus [68]; (b) isothermal sections at 450°C (dashed line) and 600°C (solid line) [32, 60]; and (c) isolpleth [60]. (Reproduced with kind permission of Elsevier.)

Al3Zr

Al3Sc

900

850

800

750

0.2

0.4

659

0.6

0.8

Sc,

wt.%

700

661 0.2Al

(Al)

0.4 0.6 0.8Zr, wt. %(a)

(c)

L+Al3Zr

L+(Al)+Al3Zr

L+(Al)+Al3Sc (Al)+Al3Zr

Al−0.8% ZrAl−0.4% Sc0.4% Zr

Zr, %Sc, %

0.2% Sc

(Al)+Al3Sc

L+(Al)

L

630

650

670

~850T°C

(Al)+Al3Zr+Al3Sc

(b)

(Al)+Al3Sc

(Al)+Al3Zr(Al)

0.2Al 0.4 0.6 0.8Zr, wt. %

0.2

0.4

0.6

Sc,

wt.%

(Al)+Al3Sc+(Al)+Al3Zr




FIGURE 2.27Precipitation of Al3Sc onto primary Al3Zr phase during Solidifi cation, SEM, secondary electrons, arrows show the Sc-rich layer [69].

Sc and 0.15% Zr are added to an alloy. The reason why is under discussion. Some authors suggest the formation of a ternary Al3(ScZr) phase with the crys-tal structure similar to that of stable Al3Sc and metastable Al3Zr. However, there is no evidence in favor of the formation of a new phase in the Al–Sc–Zr system. Metallographic examination of primary particles in Al–Sc–Zr alloys show that the Al3Sc phase (as a result of the peritectic reaction) forms a rim on primary Al3Zr particles (Figure 2.27). This surface layer possesses very good refi ning ability of Al3Sc and “activates” Al3Zr, allowing strong grain refi ne-ment at relatively low Sc concentrations [69].

2.4.3 Al–Ti–B Phase Diagram

The Al–Ti–B phase diagram has been a subject of investigation since the early 1970s. Under equilibrium solidifi cation conditions, the following phases can be found together with aluminum in the solid state: Al3Ti, AlB2, and TiB2. The Al3Ti phase has a tetragonal crystal structure (space group I4/mmm) with a = 0.385 nm and c = 0.86 nm [29]. The open question is the existence of continuous solid solution between AlB2 and TiB2. Both compounds have a hexagonal crystal structure (space group P6/mmm) with close lattice parameters: a = 0.3003 nm and c = 0.3251 nm for AlB2 and a = 0.3032 nm and c = 0.3231 nm for TiB2 [70]. Thermodynamical calculations show the




possible formation of (AlTi)B2 solid solution. However, numerous experimen-tal results attest to the formation of separate, well-distinguished borides.

The liquid–solid equilibria in Al-rich Al–Ti–B alloys have been studied in detail [71]. The invariant and monovariant solidifi cation reactions are shown in Table 2.10, and the schematic projection of the solidifi cation surface is given in Figure 2.28.

2.4.4 Al–Ti–C Phase Diagram

Another system that is important for grain refi ning is Al–Ti–C. In the alumi-num corner of this system three phases are in equilibrium with (Al): Al3Ti, Al4C3, and TiCx (0.48 < x < 0.98). The Al4C3 carbide (25.3% C) has a rhombo-hedral structure with a = 0.855 nm and β = 22o28′ [29] or a hexagonal struc-ture with a = 0.33328 nm and c = 2.5026 nm [66]. TiCx has a cubic structure (space group Fm3m) with a = 0.43176 [66].

TABLE 2.10

Invariant and Monovariant Reactions in the Aluminum-Rich Al–Ti–B Alloys [71]

Reaction T, °C Point in Figure 2.28

L + Al3Ti ⇒ (Al) 665 p1–P1

L + Al3Ti ⇒ (Al) + TiB2 ~665 P1

L ⇒ (Al) + AlB2 659 e1

L + TiB2 ⇒ (Al) + AlB2 ~659 P2

L ⇒ TiB2 + Al3Ti > 665 S–P1

L ⇒ TiB2 + AlB2 > 659 F–P2

L ⇒ (Al) + AlB2 — P2–e1

L + TiB2 + (Al) either peritectic or eutectic

659 < T < 665 P1–P2

FIGURE 2.28Scheme of the Al–Ti–B phase diagram [32, 71]. (Reproduced with kind permission of Elsevier.)

52

6

4

3F

AIB2

TiB 2

e1 P2

P1

p1 p Al3TiAI

eJ

h

D

1

S

Liquid(Al)




The invariant equilibrium L + TiC ⇒ Al3Ti + Al4C3 occurs in the aluminum corner of the phase diagram at 693°C (0.53 at.% Ti, 7 × 10–6 at.% C) [72]; other tem-peratures of 700 or 812°C also have been reported for the same equilibrium.

In the structure of solidifi ed samples, the association of Al3Ti with TiC and TiC with Al4C3 is frequently observed, suggesting complex character of solidifi -cation reactions in this system [73]. However, the full sequence of solidifi cation is not clear yet. A schematic isothermal cross-section is shown in Figure 2.29. Line 1 connects Al with the stoichiometric composition of TiC, whereas line 2 refl ects the equilibrium with the nonstoichiometric titanium carbide. The latter line does not cross phase fi elds with Al4C3 present and, therefore, the Al–TiCx (off-stoichiometric) system can be considered as quasi-binary [72].

As the reader can see, the mechanism of grain refi ning in Al–Sc–Zr alloys is more or less clear—a peritectic reaction stimulates the formation of Al3Sc layer onto primary Al3Zr particles with subsequent effi cient nucleation of (Al).

The situation is somewhat more complicated in Ti-containing alloys. It is obvious that Al3Ti is a very powerful grain refi ner for (Al), when present at “hyperperitectic” concentrations, i.e., when Al3Ti is formed as a primary phase. In practice, the grain refi ning additions of Ti in the form of Al–Ti–B and Al–Ti–C master alloys are seldom above 0.05% Ti and, in many cases, much less. Yet the result they produce is remarkable.

One set of theories is based on the assumption that there is a peritectic reac-tion that can produce (Al) from Al3Ti at very low concentrations of Ti, much less than in the binary Al–Ti system. An analysis of solidifi cation reactions in the Al–Ti–B system yields the following. Alloys in compositional ranges 1 and 2 (Figure 2.28) start solidifi cation with the formation of TiB2, then Al3Ti and TiB2 are formed through the eutectic reaction (S–P1). Small TiB2 particles are observed inside bulk Al3Ti crystals [64, 71, 74]. The equilibrium crystal-lization fi nishes with the invariant reaction P1 when the aluminum solid

FIGURE 2.29Scheme of the Al–Ti–C phase diagram [32, 72]. (Reproduced with kind permission of Elsevier.)

Al4C3

L+TiCx1+Al4C3

L+TiCx2+Al3Ti

L+Al3Ti

L

21

TiCx2

TiC0.48

TiCx1

TiC0.98

C

L+TiC

x

L+Al4C3

Al3TiAl Ti




solution is formed. Under nonequilibrium conditions, the peritectic reac-tion P1 is unfi nished and the remained liquid solidifi es as divorced eutectics along line P1–P2. The described solidifi cation path is typical of titanium and boron concentrations in Al–Ti–B master alloys, i.e., 3–5% Ti, 1–3% B.

In compositional ranges 3 and 4, the primary phase is TiB2. The solidifi ca-tion continues along line F–P2 (formation of TiB2 + AlB2 eutectics) to point P2, where the invariant peritectic reaction occurs with the formation of AlB2 and (Al). Under real casting conditions, some liquid may remain at tempera-tures below the temperature of the peritectic reaction. This liquid solidifi es according to line P2–e1, forming the (Al) + AlB2 eutectics.

Alloys with intermediate compositions 5 and 6 also start to solidify with the formation of TiB2 as the primary phase. Then the aluminum solid solu-tion is formed as a result of the peritectic reaction L + TiB2 ⇒ (Al) (P1–P2), and this reaction may transform to the eutectic reaction L ⇒ (Al) + TiB2 until all liquid vanishes at point P2. In compositional range 6, the peritectic reac-tion L + TiB2 ⇒ (Al) + AlB2 is likely to occur.

As we can see, the analysis of the phase diagram does not give any evi-dence as to the existence of a peritectic reaction with participation of Al3Ti at low Ti concentrations.

In a real casting situation the total amount of Ti is less than 0.05% and there is an excess of Ti with respect to TiB2. In this case, rims of Al3Ti onto TiB2 and rims of TiB2 onto AlB2 are frequently observed, suggesting complex incomplete solidifi cation reactions and possible mechanisms of grain refi ne-ment [64, 70]. The peritectic reaction may not be necessary if it were possible to have Al3Ti present in some form at these small Ti concentrations. There is a possibility that Al3Ti survives in the surface defects of boride particles and then acts as a nucleant for (Al) [75]. A more feasible mechanism is, however, as follows. During dissolution of Al–Ti–B master alloys in aluminum-alloy melt, the borides remain virtually unaffected while Al3Ti particles dissolve, creating the excess of solute Ti in the melt. This Ti can then segregate to the surface of boride particles and form there a very thin layer of Al3Ti phase. This layer is metastable and can be preserved for some time at tempera-tures above the melting point of the main alloy, creating the substrate for (Al) nucleation [74]. The sequence of habitus crystal planes is suggested as (0001)TiB2 || (112)Al3Ti || (111)Al [64]. Therefore, the aluminum solid solution nucleates on Al3Ti that is dispersed in the melt by primary solidifi ed borides (or pre-existing borides from the master alloy), and much less titanium is required for the same refi ning effect. Hence, there is a similarity in the ulti-mate mechanism of activation in Al–Ti–B and Al–Sc–Zr alloys: less effi cient solidifi cation sites are covered with the layer of more potent nucleant, effec-tively decreasing the required amount of the latter.

Recently, very interesting results have been produced by in situ X-ray diffraction measurements using a synchrotron radiation [76]. It has been demonstrated that in Ti-rich liquid aluminum inoculated by TiB2 the (meta-stable) Al3Ti phase is indeed formed prior to the solidifi cation of primary aluminum and then vanishes (is consumed) in the process of aluminum




nucleation, as shown in Figure 2.30 [76]. The nucleation process of primary aluminum is limited to the upper part of the solidifi cation range and is almost complete when about 20% of the solid phase is formed. Further nucleation is hindered by the latent heat released by previously formed grains. It also has been found that the presence of solute titanium in the melt indeed enhances the nucleation of new grains, not by a growth-restriction mechanism but rather by improved wetting of TiB2 particles by the melt.

Al–Ti–C master alloys contain about 3% Ti and 0.15% C with the phase composition (Al) + TiC + Al3Ti. Titanium carbide can act as a solidifi cation sites for (Al) by itself as having a suffi ciently good structural match with aluminum. It was suggested by Cibula in the 1950s that even upon adding Ti to aluminum alloys, the actual nuclei for (Al) are represented by carbides formed by the reaction of Ti and Al with carbon impurities in the melt [77]. Later it was confi rmed that TiC indeed acts as a powerful grain refi ner in aluminum alloys [78]. However, in this system there is a possible peritectic reaction that produces Al3Ti from TiC, which may facilitate the formation of an Al3Ti envelope onto TiC particles and increase their nucleation potential by the same mechanism as in the case of the systems discussed earlier.

The research interest has shifted lately from the search for the nucleation sites to the understanding why the nucleated grains do not grow big. The growth restriction caused by highly segregated Ti is the basis of this school of thought [50–52]. In this case, the “center of gravity” is shifted from the number of nucleation centers as a condition of effi cient grain refi nement to

FIGURE 2.30Growth of an aluminum grains (Al) and metastable Al3Ti phase in an Al–0.1% Ti–0.1% TiB2 alloy as a function of temperature during continuous cooling at a rate of 1 K/min [76]. Note that the Al3Ti phase appears at about 10 K above the onset of (Al) nucleation and is consumed during (Al) growth. (Reproduced with kind permission of Elsevier/Pergamon.)

930

0

50

(AI)

AI3Ti ×10

100

940 950Temperature, K

Gra

in s

ize,

µm




the amount of growth restriction that is necessary to suppress their growth. Excess titanium that is brought to the melt during dissolution of master alloy then hinders the growth of (Al) grains that are nucleated on either borides or carbides. As we mentioned in the beginning of this section, the growth-restriction theory is not fl awless, but then there are drawbacks to each hypothesis of grain refi ning with complex master alloys. It is quite possible that the initial formation of aluminum grains is controlled by the constitu-tional and thermal undercooling that drives the heterogeneous nucleation onto active envelopes of high-temperature particles. The accumulation of sol-ute (solvent) that assists the nucleation simultaneously prevents the growth of the parent particles. The latent heat released during solidifi cation acts in the same direction. The greater the nucleation density of the primary grains, the sooner their thermo–solutal fi elds start to interact and the less their den-dritic development. As a result, the fi ne and not well-developed dendritic equiaxed structure is formed. Sometimes the branching is so negligible that the grains are called globular or nondendritic.

Another way to produce very fi ne grains is the activation of impurities that are always present as “plankton” in aluminum melts. These impurities could be oxides and carbides that are usually not wettable by liquid aluminum and, therefore, are excluded from the process of solidifi cation. If, however, they could be wet with liquid aluminum and form substrates for either alu-minides or aluminum, then they would become a means for very effi cient refi nement. It has been suggested that cavitation melt treatment can facilitate the activation process and produce very fi ne, nondendritic structure in com-mercial-size billets and ingots of aluminum alloys [79]. The activation of non-metallic impurities facilitates and refi nes the primary phases that solidify in alloys prior to (Al) [80]. The cavitation treatment can also disperse boride and carbide agglomerates that are frequently formed during introduction of master alloys into the melt and thereby involve more substrate particles into the solidifi cation process [81].

References

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pp. 306–312.



79

3Solidifi cation Patterns and Structure Formation during Direct Chill Casting

3.1 Shape and Dimensions of the Billet Sump

The billet (ingot) during casting can be subdivided into several stages with distinctly different characteristics. We mentioned in Chapter 1 (Figure 1.6) the sump and the transition region. Other terms can be found in the litera-ture, e.g., liquid pool, slurry zone, and mushy zone. There is also the solid part of the billet (ingot). We have to defi ne these terms because there are discrepancies in the literature about what is actually what. Figure 3.1a shows a schematic cross-section of a billet with isotherms of liquidus, coherency,* [1] and solidus, and the defi nition of the different zones of the billet. The real sump profi le is shown in Figure 3.1b.

The dimensions and geometry of these regions are determined by tem-perature distribution that is the product of heat transport in and out of the system. Heat input is the energy introduced into the system by the melt (tem-perature and specifi c heat of the liquid) and generated during solidifi cation (latent heat of solidifi cation and the specifi c heat of the solid). Heat extraction occurs by convection of the melt in the sump; by conduction of heat through liquid, semi-solid, and solid part of the billet; and by convection of cooling water inside the mold and at the billet surface. The heat transport is usually characterized by the following two dimensionless numbers.

The thermal Peclet number is

Pe = ρcVcR/λ, (3.1)

where ρ is the density, c is the specifi c heat, Vc is the casting speed, R is the billet radius, and λ is the thermal conductivity. The Peclet number shows the ratio between heat convection (advection) and heat conduction.

The Biot number is

Bi = qR/λ, (3.2)

* Coherency is a conditional term denoting the change in the slurry behavior, e.g., the change in the viscosity or heat conductivity related to the beginning of interaction between solid grains. The coherency isotherm can be also called the “solidifi cation front,” marking the macroscopically continuous front of the growing solid phase (see Section 3.2). A detailed discussion of the coherency phenomenon can be found elsewhere [1].




where q is the heat transfer coeffi cient. The Biot number refl ects the ratio between heat convection (advection) at the surface and heat conduction inside the sample. Typical values for direct chill casting of aluminum alloys are 1.8 < Pe < 4.5 and 1 < Bi < 25 [2].

The temperature distribution in the billet sump depends on the melt tem-perature, melt fl ow, and cooling conditions in the mold and at the billet sur-face and, therefore, is the function of process parameters such as casting speed, water fl ow rate, melt temperature, and the melt distribution system. On the other hand, the dimensions and geometry of these regions deter-mine to a great extent the formation of structure and casting defects during solidifi cation.

It became clear early on in DC casting practice that there was a direct link between the casting speed and the depth of the sump as well as between the casting speed and the solidifi cation rate. These relationships were briefl y mentioned in Chapter 1, Equations 1.1 and 1.2, and they remain valid despite later advances in the analysis of DC casting.

Roth [3] and Dobatkin [4] showed that the sump depth (H) depends on the casting speed (Vcast) and billet radius as

H = AVcastR2/4λs(Tm − Tsurf), (3.3)

Reference point at thebottom of hot top

3

2

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30%

S

L

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Melt temperature 707 deg.CWater rate 200 l/minWater temperature 28.5 deg.CAlloy Al−3.7% CuCasting speed 7 cm/min

(a) (b)

FIGURE 3.1(a) Defi nition of billet portions during casting (L = liquidus; S = solidus, and 30% = coherency isotherm): 1 = molten pool; 2 = transition region; (1 + 2) = sump; (2–3) = slurry zone; and 3 = mushy zone; and (b) real sump profi le revealed by adding liquid Zn during casting: the lighter part shows the solid part of the billet at the moment of Zn addition and the darker part shows the sump.



Solidifi cation Patterns and Structure Formation during Direct Chill Casting 81

where Tm is the melting temperature, Tsurf is the temperature of the billet sur-face or the temperature of the cooling medium, R is the billet radius, λs is the thermal conductivity of solid, and A is determined as follows:

A = ∆Hf ρs + 1/2cs ρs(Tm – Tsurf), (3.4)

where ∆Hf is the latent heat of fusion, ρs is the density of solid, and cs is the specifi c heat of solid.

Similar relationships can be written for sheet ingots using the ingot thick-ness instead of billet radius in Equation 3.3.

These formulations, though derived based on the assumption of the con-stant surface temperature, have proved to be valid in practice. Figure 3.2a shows that the experimentally measured sump depth depends linearly on the

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FIGURE 3.2Dependence of the sump depth in the center of the billet on the casting speed: (a) experimen-tal data for 200-mm billets from three binary Al–Cu alloys [4]; (b) experimental sump depth (1 + 2)’ and calculated molten pool depth (1), transition region (2), and sump depth (1 + 2) for a 200-mm Al–4.3% Cu billet cast at two casting speeds (numbers are as in Figure 3.1a) [5]; and (c) the variation of the transition region vertical dimension along the billet radius for two casting speeds [5]. (Parts (b) and (c) reproduced with kind permission of Elsevier.)




casting speed for different alloy compositions [4]. Figure 3.2b confi rms this dependence by numerical simulations [5].

The sump depth normalized to the billet radius is also shown to increase linearly with the increasing Peclet number, which means that the sump depth is inversely proportional to the alloy thermal conductivity [2].

The direct consequence of Equation 3.3 is the rule that the ratio between the sump depth and the billet radius is constant if the following condition is valid:

VcastR = const. (3.5)

The dimensions of the transition region, however, do not change uniformly along the billet cross-section. The effect of casting speed is mostly felt in the central part of the billet, as demonstrated in Figure 3.2c.

It is important to note that Equation 3.3 is derived and valid only for the steady-state regime of casting. If the casting speed is ramped up or down the sump does not change its shape and depth instantly, but rather with some thermal inertia as has been shown experimentally [8] and by numeri-cal simulations [9]. Similar phenomena occur during the start-up phase of casting [6, 7, 10]. Let us look at this phenomenon in more detail.

The typical beginning of DC casting involves either ramping of the cast-ing speed from some low value (or zero) to the run speed according to the recipe, or starting the casting directly with the run casting speed. During this transient stage, the cooling from the direct water jet is felt in the center of the billet with a delay. As a result, the sump depth increases to an extent greater than in steady-state casting, and only after some time does the sump become shallower, approaching the steady-state depth. The “overshot” of the sump depth is a function of the run casting speed, as shown in Figure 3.3.

The evolution of the sump depth at the beginning of casting depends on the start-up regime and on the geometry of the starting block [7, 11].

0

20

40

60

80

100

400300200100Billet length, mm

Sum

p de

pth,

mm 110 mm/min

90 mm/min

75 mm/min

FIGURE 3.3Experimentally measured sump depth in the start-up phase of DC casting of a 228-mm billet from a 6061 alloy as a function of the billet length and the run casting speed [6, 7]. The starting casting speed was equal to the run speed.




Suggestions have been made to raise the central part of the starting block or make the starting casting speed higher than the run speed to diminish the initial deepening of the sump [7]. Figure 3.4 illustrates how the starting regime affects the sump depth. Gentle ramping of the casting speed to the run speed (regimes 2 and 4) decreases the “overshot” [11]. It is interesting to note that the length of the mushy zone changes in a manner similar to the total sump depth [7, 11], although the response of the mushy zone to the casting speed is stronger than that of the sump depth.

During DC casting, the casting speed may change either stepwise or in the form of ramping, especially when experiments are performed. Several cast-ing regimes have been simulated using the numerical model of DC casting and different casting regimes, as shown in Figure 3.5a [9].

Figure 3.6 demonstrates velocity vectors with superimposed solid fraction contours upon casting with regimes 1 and 2 denoted in Figure 3.5a. All of these vector fi elds characterize four distinct fl ow zones: the bulk liquid zone (solid fraction 0.0), the slurry region (between solid fractions 0.0 and 0.3),

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3

3

4

4

2

2

Time, s0 50 100 150 200 250 300

Time, s

Sum

p de

pth,

mm

80

70

60

50

40

30

20

10

0

Leng

th o

f the

mus

hy z

one,

mm

1

34

2

FIGURE 3.4Effect of the start-up regime (a) on the sump depth (b) and the length of the mushy zone (c) during casting of a 200-mm billet from an Al–4.5% Cu alloy (computer simulations) [11]. (Reproduced with kind permission of Springer Science and Business Media.)



84

Physical Metallurgy of D

irect Chill C

asting of Alum

inum A

lloys

FIGURE 3.5Calculated dependences of the sump depth in the center of the billet on the casting speed and ramping rate upon casting of a 200-mm Al–4% Cu billet: (a) casting regimes at a casting temperature of 675°C with 1 = steady state casting at 200 mm/min, 2 = ramping at 113.2 mm/min2, 3 = ramping at 113.2 mm/min2 then casting at 200 mm/min, 4 = ramping at 56.6 mm/min2, 5 = ramping at 34.9 mm/min2, and 6 = ramping at 11.32 mm/min2; (b) evolution of the sump depth in a transient regime 2 with experimentally measured values shown by triangles; (c) evolution of the sump depth in regimes 1 (steady state) and 3; and (d) evolution of the sump depth at different ramping rates [9]. Vertical lines in (b) and (d) show the position of the maximum casting speed. (Reproduced with kind permission of Elsevier.)

0.17

0.16

0.15

0.14

0.13

0.12

0.11

0.1

0.09

0.08

0.07

200

190

180

170

160

150

140

130

120

110

1000 10 20 30 40 50 60 70 80 90 100 110

Time, s

Cas

ting

spee

d, m

m/m

in

Ramping Depth (m)Steady Depth (m)Measured DepthCasting Speed

Sum

p D

epth

, m

(b)

0.17

0.16

0.15

0.14

0.13

0.12

0.11

0.1

0.09

0.08

0.07100 119 138 157 175 200

Casting speed, mm/min

Sum

p D

epth

, m

(d)

4

6 5

2

187 168 149 130 111 100

250

200

2, 3

150

100

50

00 200 400 600 800 1000

Time, s

Cas

ting

spee

d, m

m/m

in

(a)

1

2

4 56

1,3

0.170.160.150.140.130.120.110.1

0.090.080.07

0 20 40 60 80 100 120 140 160

Time, s

Regime 3

Regime 1steady state

Sum

p D

epth

, m

(c)

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(a) (b)

FIGURE 3.6Computer-simulated fl ow patterns together with the contours of solid fraction at values of 0.0, 0.3, and 1.0, for regimes 1 (a) and 2 (b) after 53.5 s of casting as shown in Figure 3.5a,b. Only half of the 200-mm Al–4% Cu billet is shown: the left-hand side of the fi gures is the billet center and the right-hand side is the surface.

the mushy zone (between solid fractions 0.3 and 1.0), and the solid zone (solid fraction 1.0). Below the solidus contour is the solid zone, in which solid moves uniformly at the casting speed.

The thermal inertia in the transient state is obvious from the comparison of the steady-state situation shown in Figure 3.6a with the transient state shown in Figure 3.6b. This thermal inertia is quantifi ed by calculating the evolution of the sump depth, as shown in Figure 3.5b. After 53 sec of casting when the peak casting speed is reached during ramping, the depth of the sump is about 4 cm lower than the steady-state depth, shown as a horizontal dashed line in Figure 3.5b. It is interesting to note that although casting speed begins to decrease after this peaking point, the depth of the sump keeps increasing up to 14.2 cm, still below the steady-state value. These calculation results are qualitatively similar to the experimental results reported by Commet et al. [8], though the quantitative differences in the sump depth response to the changing casting speed is, obviously, a function of the particular casting conditions.

To answer the question as to how long it would take for this transient state to reach steady state, calculation 3 was performed. In this regime, the casting




speed is maintained constant and equal to 200 mm/min after the transient stage of ramping. All other calculation parameters are the same as in regime 2. The evolution of the sump depth is shown in Figure 3.5c. After 45 sec of simulated casting time (or 150 mm of the casting length) in calculation 3, the same sump depth as in steady-state calculation 1 is reached.

Ramping rate is an obvious controlling parameter that determines the magnitude of the thermal inertia. Calculations 4, 5, and 6 (corresponding casting regimes shown in Figure 3.5a) were made to fi nd the critical ramp-ing rate at which no thermal inertia exists. The sump depths as a function of casting speed in these calculations are shown in Figure 3.5d. Almost real-time response of the sump depth to the ramping casting speed is achieved in casting regime 6 at a ramping rate of 11.32 mm/min2, while regime 2 shows a very big lag.

Two more casting parameters may affect the sump depth, i.e., cooling water fl ow rate and melt temperature. Both parameters may potentially infl uence the thermal conditions inside the mold. The water fl ow promotes heat extrac-tion from the melt whereas the melt temperature adds heat to the system.

The dimensions of the sump and transition region as functions of cooling intensity characterized by the Biot number (Equation 3.2) have been assessed by numerical and physical modeling [12]. The sump depth varies, depend-ing on the cooling intensity, as shown in Figure 3.7a. For Bi < 4, increased cooling results in a signifi cantly decreased sump depth, whereas further intensifi ed cooling has only slight consequences for the depth of the sump and other characteristic dimensions. The temperature of the cooling liquid can also affect the sump depth and the thickness of the transition region, as demonstrated in Figure 3.7b. This infl uence becomes considerable, however, only at coolant temperatures above 70°C [12]. The dependences shown in Fig-ure 3.7 demonstrate that it is not possible to increase heat extraction beyond a certain limit that is a function of thermal properties of the alloy and the cooling medium.

Few data are available in the literature on the effect of water fl ow rate on sump geometry. Most of the research has been done on the interrelation between water fl ow rate, water temperature, heat transfer coeffi cient, and the so-called Leidenfrost temperature that corresponds to the point at the billet surface where the evaporation of water takes the longest time and the heat fl ux density is minimum [13]. It is important to understand that actual water fl ow rate in DC casting can be safely decreased only to a certain value because otherwise the solid shell will not be formed inside the mold and the melt will bleed out, which is dangerous. On the other hand, the increase of the water fl ow rate above a certain value is useless because the water cannot extract more heat than its heat capacity and heat conductivity allows (see Figure 3.7a). Therefore, the actual range of water fl ow variation is rather nar-row. The Leidenfrost temperature can be shifted to higher surface tempera-tures by increasing water fl ow rate [13]. The best conditions of heat extraction are created when so-called nucleate boiling occurs during direct water chill of the billet surface. In this case the heat transfer coeffi cient can be on the




order of 40 kW/m2 K with corresponding heat fl axes up to 6000 kW/m2 [2]. The conditions of nucleate boiling are maintained during steady-state cast-ing because the surface temperature stays below 300°C. Under these condi-tions the infl uence of the water fl ow rate is considered negligible because of very small effects of water fl ow rate on the heat fl ux density and heat transfer coeffi cient [13]. However, during the start-up phase of DC casting when the water fl ow rate is kept lower than during steady-state casting in order to decrease thermal gradients and thermal stresses, partial or even stable fi lm boiling may occur, and the water fl ow rate does have an effect [13].

1.2

1

0.8

0.6

0.6

0.5

0.4

0.3

0.2

0.1

0.4

0.2

00 5 10 15 20 25 30

Bi

Nor

mal

ized

sum

p pa

ram

eter

Nor

mal

ized

sum

p pa

ram

eter

1+2

1+2−3

1

00 50 100 150 200

Cooling water temperaure, °C

(a)

(b)

1+2

2

FIGURE 3.7Effect of cooling intensity (a) and cooling media temperature (b) on the sump parameters nor-malized to (VcR2) in the center of a round 2024 billet [12]. (1) Molten pool depth, (2) transition region, (1 + 2) sump depth, (1 + 2 – 3) slurry zone. Numbers are as in Figure 3.1a.




Typically, experimental studies are performed under laboratory conditions, using a hot slab with thermocouples at various positions at the surface and inside the slab, and a water source moving along the slab at a certain speed. However, Wells et al. [14] note that laboratory-based studies cannot directly reproduce heat transfer behavior in the industrial DC casting process.

Prasso et al. have shown that the water fl ow rate has only a small effect on the sump depth, i.e., the decrease of the water fl ow rate by 20% causes the deepening of the sump by only 4% [15]. At the same time, the relative infl u-ence of the water fl ow rate on temperature distribution in the sump is more pronounced at the periphery of the billet [15].

Our results shown in Figure 3.8a,b demonstrate that the water fl ow rate can infl uence the parameters of the sump, but only at low casting speeds.

The infl uence of melt temperature on the geometry of the sump during DC casting has been studied using computer simulations, model experiments, and pilot-scale experiments but only within narrow margins of temperature variation. The golden rule of the cast shop is “melt hot, cast cold” because high melt temperatures are known to produce coarser structure (see Chap-ter 2, Figure 2.5) with greater porosity and to increase the probability of bleed-outs. Tarapore [16] reported experimental and computer-simulation results on DC casting of a 2024 alloy. The melt temperature varied from 660 to 715°C in the trough (the resultant melt temperature in the hot top changed from 642 to 696°C). The increased depth of the sump, higher tem-perature gradients in the liquid bath, and a thinner surface liquation layer corresponded to a higher melt temperature.

Some results are available for computer simulation of DC casting under different process conditions, including the melt temperature. Reese [17] tested an analytical model for liquid aluminum fl ow in the sump of a DC-cast round billet at different superheats, from 30 to 70 K. The increase in melt superheat was shown to increase the depth of the sump and the melt fl ow velocity along the mushy zone. At the same time, the thickness of the mushy zone and the upward melt fl ow velocity (in the central part of the sump) remained virtually unaffected. A conclusion was made that the deep sump resulted from high melt superheat. Shestakov [18, 19] modeled the effect of melt superheat (∆T = 0–300 K) on the kinetics of progressive solidi-fi cation and the parameters of the transition region (between liquidus and solidus isotherms) of an aluminum alloy. The increase in melt temperature was shown to narrow the transition region in the billet and to accelerate the solidifi cation (local solidifi cation time is shortened). The optimum super-heating for aluminum alloys was recommended as 150–200 K in contrast to the usual 60–80 K. However, this effect was only pronounced in alloys with low solidifi cation rate (when the solid phase was formed evenly throughout the solidifi cation range).

We studied the effects of melt temperature on the temperature distribu-tion in the liquid pool and on the sump geometry in DC casting of a binary Al–2.8% Cu alloy [20]. Both experiments and computer simulations were performed. The melt temperature in the furnace varied between 700 and



Solidifi cation Patterns and Structure Formation during D

irect Chill C

asting 89

160

140

120

100

80

60

40

20

0140 180

Water flow, l/min

Melt temperature, °C

220 260 140 180

Water flow, l/min

220 260

Par

amet

er o

f liq

uid

pool

and

sum

p, m

m

160

120

80

40

0

Par

amet

er o

f liq

uid

pool

and

sum

p, m

m

160

120

80

40

0

Par

amet

er o

f liq

uid

pool

and

sum

p, m

m

160

140

120

100

80

60

40

20

0

Par

amet

er o

f liq

uid

pool

and

sum

p, m

m

700 725 750 775Melt temperature, °C

700 725 750 775

1+2

1+2

1+2

1+2

2

2

1

1

Exp

Exp

2

2

11

3 3

(a) (b)

(c) (d)

FIGURE 3.8Effect of water fl ow (a,b) and melt temperature (c,d) on the parameters of the liquid pool and sump at the casting speed 120 mm/min (a), 100 mm/min (c) and 200 mm/min (b,d) for the central portion of 200-mm billets from an Al–4.3% Cu alloy (a,b) and an Al–2.8% Cu alloy (c,d) [5, 20]. (1) Molten pool depth, (2) transition region, (1 + 2) sump depth, (3) mushy zone. The numbers are as in Figure 3.1a. These results were obtained from computer simulations of DC casting validated by experiments. “Exp” designates the experimentally measured sump depth. (Reproduced with kind permission of Elsevier (a,b) and Springer Science and Business Media (c,d).)

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760°C, which corresponded to the range of 660°C and 740°C at the inlet to the hot top. The results are given in Figures 3.8c,d and 3.9. These data are taken from the computer-simulated patterns and are validated by temperature and sump depth measurements [20].

The dimensions and the position of the transition region in the billet (in rela-tion to the hot top or to the mold) show the following trends. Increasing the melt temperature shifts the positions of liquidus and solidus isotherms in the center of the billet downward; however, the liquidus position is affected to a greater extent than the solidus position. This effect is understandable if one takes into account that the incoming hot melt introduces more heat into the system and extends the liquid part of the billet, whereas the cooling in the mold is effi cient enough to form the solid shell within the limits of the mold. The transition region narrows in the center of the billet and at the periphery with increasing melt temperature. The dimensions of the mushy zone remain virtually independent of the melt temperature. In addition, the simulation of melt fl ow patterns (Figure 3.9) shows that higher melt tempera-tures produce more severe melt fl ow toward the surface and deeper penetra-tion of the fl ow into the mushy zone compared to lower melt temperatures.

(a) (b)

FIGURE 3.9Computer-simulated fl ow patterns and positions of liquidus, coherency and solidus isotherms in 200-mm Al–4% Cu billets cast at 200 mm/min with the melt temperature at the inlet to hot top 675°C (a) and 725°C (b) [9]. Only half of the billet is shown: the left-hand side of the fi gures is the billet center and the right-hand side is the surface. (Reproduced with kind permission of Elsevier.)




0.5

0.4

0.3

0.2

0.1

00 25 50 75 100 125 150

Solidification range, °C

Bi=2.4

Bi=4.3

Bi=6.9

Bi=24.3

Nor

mal

ized

tran

sitio

n re

gion

FIGURE 3.10Effect of the alloy solidifi cation range and the intensity of cooling on the thickness of the transition region in the center of the billet normalized to (VcR2) [12].

The fi nal factor that affects the shape and the dimensions of the sump is alloy composition. It is obvious that different alloys have different thermal properties and different solidifi cation ranges that determine the positions of the liquidus and solidus isotherms in the billet. The structure of the solidify-ing alloy, e.g., columnar or equiaxed grains, coarse or fi ne grains, may have a considerable effect on the position of the coherency isotherm and, therefore, the dimensions of the mushy zone. Figure 3.10 demonstrates that the greater the solidifi cation range, the wider the transition region in the billet. In the range of smaller solidifi cation ranges this dependence is almost linear. For alloys with a greater solidifi cation range, the transition region widens more quickly. The increased intensity of cooling, characterized by the Biot num-ber, can narrow the transition region.

3.2 Solidification Rate and Cooling Rate during DC Casting

One of the most prominent features of the DC casting process is that the sump does not change shape and position during steady-stage DC casting. The stability of the sump shape can be expressed by Equation 1.2, which we repeat here:

Vs = Vcastcos αn,

where αn is the angle between the billet axis and the normal to the solidifi cation front. The steadiness of the sump during progression of the solidifi cation




front with the velocity Vs can be compensated for by the withdrawal of the solid part of the billet with the casting speed Vcast only if this relationship holds. The relationship between the shape of the sump and the solidifi cation rate Vs is schematically illustrated in Figure 3.11a. The solidifi cation rates cal-culated based on the computer simulation of two billets cast at two casting speeds are shown in Figure 3.11b [5]. The maximum solidifi cation rates are, therefore, reached at the periphery and in the center of the billet, where the solidifi cation front is fl at. The minimum solidifi cation rate occurs at about midradial position, where the solidifi cation front is the steepest [12]. The increase in casting speed affects mostly the solidifi cation rate at the periph-ery and in the center of the billet [5, 12].

It has been shown that the average solidifi cation rate of the entire solidifi -cation front across the billet has limits beyond which it cannot be increased any more [4, 21]. This maximum average solidifi cation rate is a function of the billet radius and the thermophysical properties of the alloy [4]:

V s max = 4λ(Tm – Tsurf)/∆HρR, (3.6)

where λ is the thermal conductivity of the solid, ρ is the density of the solid, ∆H is the difference in the enthalpies of the liquid at the melting point Tm and the solid at a temperature (Tm − Tsurf)/2, Tsurf is the surface temperature,

250

200

150

100

50

00 20 40 60 80

200 mm/min

120 mm/min

100Distance from billet center, mm

Sol

idifi

catio

n ra

te, m

m/m

in

(a) (b)

FIGURE 3.11(a) Scheme explaining the interrelation between the casting speed (Vcast), solidifi cation rate (Vs) and sump profi le (αn) [53] and (b) the change of the solidifi cation rate along the billet radius for the two billets described in Figure 3.2b,c [5].




and R is the billet radius. This relationship, which is shown in Figure 3.12, is derived with the assumption that the sump has a conical shape.

The concept of solidifi cation rate is based on the idea that the solidifi cation front is formed by solid grains that grow continuously from and in normal direction to the solidus; hence, the solidifi cation front is continuous. Only in this case, the solidifi cation rate can be taken as a parameter that deter-mines the formation of structure, as we discussed in Chapter 2. The real-ity is, however, more complicated. Commercial alloys form mostly equiaxed grain structures. This means that the small equiaxed grains fl oat freely in the upper part of the transition region (the slurry zone). With the increas-ing fraction of solid and with decreasing temperature, these grains start to “feel” and touch one another, being still quite loose. Eventually, the grains start to tangle and bridge, forming a weak but macroscopically (and statisti-cally) coherent network. At this temperature and in this portion of the billet, a macroscopically continuous solidifi cation front is formed. This network is, however, still microscopically quite discontinuous, with grain detachment and fragmentation occurring. Finally, at rather high fractions of solid, a rigid skeleton of the solid phase is formed. Then the solid phase is continuous on both macroscopic and microscopic levels. Therefore, the concept of solidifi -cation rate can be applied to the formation of structure in the mushy zone, i.e., between the coherency and solidus isotherms, rather than to the general description of structure formation upon DC casting.

The other parameter that is often used in practice and that can be seem-ingly easily measured is the cooling rate. We discussed in Chapter 2 the importance of the cooling rate for structure formation during solidifi cation. The typical set-up for measuring cooling rate during DC casting consists of

100

80

60

40

20

00 50 100 150 200 250

R = 185 mmVs max = 54 mm/min


Sol

idifi

catio

n ra

te, m

m/m

in

R = 97.5 mmVs max = 103 mm/min

FIGURE 3.12Scheme illustrating the concept of the maximum average solidifi cation rate for two billets of a 2024 alloy [4].




a rack of long thermocouples arranged in a regular manner along the bil-let diameter. These thermocouples are dipped into the liquid pool at a rate equal to the casting speed. Eventually, the tips of the thermocouples reach the slurry zone, then the mushy zone and, fi nally, are frozen into the solid part of the billet. Temperature readings from these thermocouples can be used to locate the isotherms of liquidus and solidus. If we know the time of passing the transition region, we can calculate the cooling rate. A scheme for such a set-up is shown in Figure 3.13, along with the actual rack used in our experiments.

The cooling rate measured in this way should correspond well to the dimensions of the transition region, which in turn refl ects the cooling con-ditions of the billet. Previously, we assumed that the cooling of the billet occurs uniformly at the surface. In reality, there are several distinct cooling zones with different heat transfer conditions and different cooling rates, as illustrated in Figure 3.14a,b. Melt starts to cool and solidify inside the water-cooled mold (primary cooling). The solid shell that is formed contracts as a result of the temperature-dependent density of the solid phase. This contrac-tion is almost free as the interior of the billet is still liquid and does not offer much resistance. Consequently, the surface of the billet pulls away from the mold with the formation of so-called air gap. The heat transfer coeffi cient immediately drops several times, e.g., from 1–2.5 to 0.5 kW/m2K, and the billet undergoes reheating from the incoming hot melt and the latent heat of solidifi cation. In the worst scenario, this reheating can reach the point of

Rack withthermocouples

Hot top

Inlet

Mold

Billet

Casting direction, Vc

(a) (b)

FIGURE 3.13Scheme (a) of a rack for measuring temperatures during DC casting and a photo (b) of a similar set-up used for measuring temperatures in the sump and billet during DC casting.




MENISCUS BASE

MOLD COOLING

AIR-GAP

SECONDARY

COOLING

MUSH

REHEATINGZONE

SOLID

(b)

2.5

0.25

1.0

1.5

0.25

1.0

1.7

6.0

11.7

14.016.0

2.7

2.2

505 °C

615 °C

645 °C

Dow

nstr

eam

Impi

ngem

ent

Air

gap

Prim

ary

cool

ing

19.0

(a) (c)

0.4300350400450500550600650700750

0.5 0.6Billet length, m

Tem

pera

ture

, °C

0.7 0.8 0.9

4 3 21

43

21

L

Tcoh

S

Bill

et le

ngth

(d)

FIGURE 3.14Different cooling zones in DC casting [2] (a); experimental data on cooling rates (K/s) meas-ured during DC casting of a 2024-alloy 330-mm billet, casting speed 75 mm/min [12] (b); cool-ing curves obtained upon computer simulation of DC casting of an Al–4% Cu 200-mm billet, casting speed 200 mm/min (c); and the corresponding sections of the same billet with liquidus (L), coherency (Tcoh), and solidus (S) isotherms, with billet surface on the right (d).




TABLE 3.1

Coeffi cients α and β for Different Surface Temperature Ranges in Aluminum DC Casting [22]

Temperature Range,°C α, 104 m2/W°C β, 106°C

<120 2.73 –1.27120 < T < 150 9.43 –9.24>150 1.23 3.06

remelting with subsequent bleed-out of the melt through the remelted shell. The shell eventually goes out of the mold and at some point the cooling water impinges onto the billet surface (direct chill, secondary cooling), increasing the heat transfer by one or two orders of magnitude, e.g., to 48 kW/m2K. Finally, the surface of the billet is cooled by free-falling water with the heat transfer coeffi cient ranging from 30 to 40 kW/m2K. The heat transfer coeffi -cients in the regions of water impingement and downstream cooling are the functions of the surface and water temperatures and the cooling-water rate as shown by Equations 3.7 and 3.8 for the case of aluminum DC casting [22].

Heat fl ux in the zone of impingement can be described as

q/A = αT – β, (3.7)

where q is the heat transferred through the surface A, and the coeffi cients α and β are shown in Table 3.1.

Heat fl ux in the downstream cooling region can be fi tted by the following formula:

q/A = (–1.67 × 105 + cT*)Qw1/3∆T + 100∆Tx

3, (3.8)

where c = −4.01 × 106 Q w 2 + 6.9 × 104Qw + 628; T* is the average of the water and the surface temperatures in K; ∆T is the difference between these temperatures; ∆Tx is the difference between the surface temperature and the saturation temperature of water (taken as 90°C); and Qw is the water fl ow rate in m3/m s.

As a result of such uneven cooling, different sections of the transition region solidify under different cooling conditions, as refl ected in structure formation. The consequences for structure formation will be considered in the next section of this chapter.

Direct measurement [12, 23] and computer simulation of the cooling-rate distribution [9] in cross-sections of fl at ingots and round billets yield consistent results, as illustrated in Figure 3.14c,d. High cooling rates close to the billet surface gradually decrease toward the central portion of the billet (ingot). On approaching the central part, however, the cooling curve exhib-its two distinct regions. Very slow cooling in the upper part of the transi-tion region, appearing as an almost horizontal plateau on the cooling curve




( Figure 3.14c, curves 3 and 4), gives way to a much faster cooling in the mushy zone. The remarkable feature of this transition is that the cooling curve in the mushy zone is steeper in the center (curve 4) than at midradius (curve 3). Hence, there are two features to be addressed. The fi rst is the appearance and extent of the plateau at temperatures close to the liquidus, and the second is the “faster” cooling in the central part of the mushy zone versus intermediate radial (thickness) location.

There are several reasons for these observations. First, the overall shape of the cooling curve can be explained by the extension of the slurry region. The temperature variation within the slurry region is rather small whereas its width increases toward the billet center (Figures 3.1a, 3.2c). The rate of solid-phase formation in aluminum alloys is, however, very high, which means that more than 50% of the solid phase can be formed within a few degrees below the liquidus (see Figure 2.8). The formation of the solid phase produces latent heat of solidifi cation and pumps additional thermal energy into the slurry zone, effectively slowing down the cooling. As a result, a nearly isothermal plateau appears in the fi rst portion of the cooling curve and lengthens on approaching the billet center. Second, the central part of a casting is formed in the last stage of solidifi cation. This means that the amount of latent heat that is released in a particular horizontal cross-section of the billet decreases toward the bottom of the sump, as most of the lower cross-section already has been solidifi ed and no longer releases latent heat. Therefore, the cooling in the central–bottom part of the mushy zone (second portion of the cooling curve) is more effi cient than in the slurry zone. Four factors may further enhance the acceleration of cooling in the central part of the billet compared to an intermediate radial (thickness) position. (1) The lower part of the sump (central portion of a billet) is formed, in most cases, in the range of secondary and downstream cooling (Figure 3.14a,b), where the heat transfer is the highest. (2) In addition, the heat is extracted from this part of the billet mostly through the solid phase, which has a higher heat conductivity than the liquid. (3) Some infl uence can be imposed by melt fl ow in the liquid/slurry part of the billet (see, e.g., Figure 3.9). Hotter melt pen-etrates the slurry region about the midradius, possibly impeding the cooling effi ciency, whereas in the central–bottom part of the slurry zone, the colder melt is driven upward, additionally cooling the melt in this section of the billet. (4) And, fi nally, the high solidifi cation-front velocity in the center of the billet (Figure 3.11) may narrow the mushy zone as a result of a higher upward velocity of the solidus isotherm compared to the liquidus velocity.

We should, however be very careful in attributing the measured cooling curve to the actual cooling rate in the solidifi cation range. It is true that if we take the temperature versus casting length and assume the constant casting speed, we can recalculate the data in terms of temperature versus time. This “cooling rate” can be related to the structure formation only if the solid phase follows the tip of a thermocouple, in other words, travels from the liquidus to the solidus at the casting speed. The actual situation in the sump of the billet (ingot) is more complicated with thermo-solutal convection and gravity




involved and with the resultant complex fl ow patterns that exist in the liquid and slurry zones of the billet (see Figures 3.6 and 3.9). This situation is refl ected in the real structure observed in different sections of the billet (ingot).

As we know, the cooling rate during solidifi cation can be also estimated by examination of the as-cast structure. The measured dendrite arm spac-ing can be recalculated to the cooling rate using Equation 2.3 with the pre-liminary determined coeffi cients. In this case we assume that the structure refl ects its solidifi cation history.

Let us look at the distributions of cooling rate estimated by different meth-ods in DC-cast billets 200 mm in diameter from an Al–4.3% Cu alloy produced at 120 and 200 mm/min. The variation of the transition region size for these billets is shown in Figure 3.2c, and the estimated solidifi cation rate is shown in Figure 3.11b. Figure 3.15a,b shows the cooling rates recalculated from the distance between liquidus and solidus isotherms (dashed lines) and from the measured dendrite arm spacing (solid lines). The former rates refl ect the expected measurements from thermocouples, and the latter refl ect the solidi-fi cation history. Although the “thermocouple” results fall in the same range as the “structural” cooling rates, they fail to reproduce the effect of the cast-ing speed on cooling rates in the central part of a billet. The larger distance between liquidus and solidus isotherms (Figure 3.2c) is fully compensated for by the increased casting speed, which is in direct contradiction with experi-mentally observed difference in structure (see next section of this chapter).

Computer simulation shows that a fl ow pattern that exists in the transition region may drag solid crystals nucleated at the periphery of the billet to its center. As a result, at least some of the grains found in the central part of the billet are solidifi ed during a longer time (and have coarser internal structure) than might be presumed based only on their fi nal position in the billet. Examples of streamlines showing simulated paths of “particles-tracers”in different parts of the billet during solidifi cation are shown in Figure 3.16 for the two given casting speeds. Cooling rates calculated using these, quan-tifi ed in time streamlines, are given in Figure 3.15b. Obviously, the fl ow pat-terns existing in the slurry zone cause scatter in the solidifi cation times and, as a result, scatter in structure parameters related to the cooling rate. The cooling rate calculated using the streamlines shows that closer to the surface of the billet the cooling rates agree well with the “ thermocouple” cooling rate, whereas closer to the center of the billet the cooling rates range from “thermocouple” to “structural,” refl ecting the mixed history of structure evolution in the central portion of the billet. The grains that travel from the periphery to the central portion of the billet do not have a fi ne-cell structure, as has been assumed by Chu and Jacoby [24]. The fact that they originate from the region with a higher cooling rate seems to be completely overruled by the longer total solidifi cation time. Some of these grains can actually go upward into the hotter region of the sump and partially remelt and consider-ably coarsen while being suspended in the slurry region.

Generally, the thermal history of solid phase that fl oats within the tran-sition region causes the formation of grains with different dendrite arm




spacing (cell size), depending on the overall solidifi cation time and the transition region where these grains spent more time. Coarse-cell struc-tures can be expected in grains that grow in the upper part of the transi-tion region and then settle to the bottom of the sump, whereas much fi ner cell structures refl ect grains that grow in the lower part of the sump where the cooling rates are higher. This may result even in the formation of a duplex internal structure of grains with coarse core and fi ne periphery, as shown in Figure 3.17a. In this case, one can imagine that the grain spent

FIGURE 3.15Cooling rate along the billet radius (billet center on the left) estimated using (a) the transition region size (dashed lines) and the dendrite arm spacing (solid lines) and (b) streamlines shown in Figure 3.16. Billets 200 mm in diameter from an Al–4.3% Cu alloy produced by DC casting at casting speeds 120 and 200 mm/min, with water fl ow rate 150 l/min [5]. (Reproduced with kind permission of Elsevier.)

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considerable time in the slurry region and then settled down and fi nished solidifi cation at a much higher rate.

Another phenomenon can also infl uence the fi nal dendrite arms spacing in grains. We have discussed in detail the development of dendrite structures

FIGURE 3.16Streamlines illustrating “tracer” paths during DC casting of the billet described in Figure 3.15 with casting speed (a) 120 mm/min and (b) 200 mm/min [5]. (Reproduced with kind permis-sion of Elsevier.)

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FIGURE 3.17Typical duplex structure found in the center of a 200-mm billet from an Al–4.3% Cu alloy cast at a casting speed of 200 mm/min: (a) fi ne periphery of some coarse-cell grains, shown by arrows; (b) a mixture of coarse-cell and fi ne-cell grains.




in Chapter 2. It has been shown that the dendrite arm spacing actually decreases in the upper part of solidifi cation range due to intensive branch-ing of grains (Figure 2.13b). Only at high fractions of solid, when the struc-ture becomes coherent, do coarsening and coalescence of dendrite branches take over [25]. Considered from the perspective of the cooling curves in Fig ure 3.14c, one can argue that dendrite cells in the billet center are fi ner because they have had less time to coarsen in the lower part of the solidifi ca-tion range where the cooling rate was higher. This logic holds, however, only if the grain in question has passed the transition region at a uniform speed without delays. Only in this case does the cooling curve refl ect the cooling rate. This ideal scenario, however, is apparently seldom realized in reality.

We can conclude that the structure found in the central part of a solidi-fi ed billet has characteristics refl ecting its solidifi cation history. In particular, the dendrite arm spacing corresponds to the solidifi cation time required for a particular section of the grain to form. Therefore, attributing the cooling rates experimentally measured by a thermocouple moving with a billet to the structure found in the position of this thermocouple in the solid bil-let is not always correct. Flow patterns, transport of the solid phase within the slurry region, and the shape of the cooling curve should be taken into account. Ultimately, this explains the refi nement of dendrite arm spacing and the occurrence of “coarse-cell” grains (Figure 3.17) that are frequently found in the central part billets and ingots. This will be discussed in more detail later in this chapter.

3.3 Effects of Process Parameters on the Formation of Grain Structure

The distribution of structure parameters in the cross-section of DC-cast billets and ingots is very important for the occurrence of defects and per-formance of as-cast metal during subsequent deformation. Despite that, relatively little is known about structure formation under different process conditions during DC casting. In this section we will examine how the main process parameters that we have considered in previous sections, i.e., cast-ing speed, water fl ow rate and melt temperature, infl uence the grain size and dendrite arm spacing in billets. We already showed in Sections 2.1 and 2.2 of Chapter 2 and 3.2 of this chapter that the structure is mainly controlled by nucleation and growth conditions, which, in turn, are governed by com-position and cooling conditions. In the previous section we discussed two parameters— solidifi cation rate and cooling rate—that could be the main fac-tors in the structure formation, provided that the alloy composition is not changed. A simple comparison of solidifi cation rate (Figure 3.11b) and cool-ing rate (Figures 3.14 and 3.15) distributions suggests that the dendrite arm spacing, according to Equati ons 2.2 and 2.3, should change differently along




the billet radius. A zone of fi ne grains with fi ne dendrite branches is formed at the surface of the billet in the region of direct contact with the mold, and then a zone of coarser structure appears in the billet section when the transi-tion region passes the air gap region. Further inside the billet, another zone of fi ner grains appears when solidifi cation occurs in the region of second-ary cooling (direct chill). There is a general structure coarsening toward the center of the billet, though there are experimental observations showing the dendrite cell refi nement in the very center, which is not surprising if we take into account our analysis of cooling rate variation in the previous section of this chapter. One should note that this refi nement is usually observed when careful separation is made between fi ne-cell grains and coarse-cell grains, otherwise the average dendrite cell size (or dendrite arm spacing) always coarsens toward the center of a billet. Grain size in equiaxed structures typi-cally increases toward the center of a billet. If the structure changes from fi ne grained at the periphery through a zone of columnar grains to equiaxed in the center (which is a common case for high-pure and not grain-refi ned alloys), then one can consider the columnar-to-equiaxed transition as the decrease in grain size in the central portion of a billet.

A typical example of different structure zones in a DC-cast billet is given in Figure 3.18. Note the duplex structure in the center of the billet (see also Figure 3.17).

Figure 3.19 demonstrates the distribution of grain size and dendrite arm spacing for different casting speeds and water fl ow rates for a binary

FIGURE 3.18Different structure zones refl ecting different cooling conditions: (a) macrostructure of a 200-mm billet from an Al–2.8% Cu alloy cast at 200 mm/min and casting temperature 740°C with the photos taken at equal distances along the billet radius; (b–d) microstructures of a 200-mm bil-let from an Al–4.3% Cu alloy cast at 120 mm/min and casting temperature of 715°C taken at 10 mm from the surface (b), 55 mm from the surface (c) and 100 mm from the surface (d).

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FIGURE 3.19Effect of casting speed (a,c) and water fl ow rate (b,d) on distribution of grain size (a,b) and dendrite arm spacing (c,d) in DC-cast, 200-mm billets of an Al–4.3% Cu alloy [5]. DAS-dendrite arm spacing.

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FIGURE 3.20Effect of copper concentration on distribution of grain sizes in the cross-section of 200-mm billets from Al–Cu alloys cast at 160 mm/min, water fl ow rate 150 l/min, and melt temperature 715°C [28]. (Reproduced with kind permission of Springer Science and Business Media.)

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Al–Cu alloy. These observations are in good agreement with previously reported data [12, 26, 27]. The dendrite arm spacing is more responsive to the increasing casting speed and water fl ow rate than the grain size, which can be expected, taking into account the basics of solidifi cation theory dis-cussed in Section 2.1.

It is important to mention here that the structure in general and the grain size in particular are infl uenced by the composition, as we already discussed in Section 2.4. Low-alloyed alloys frequently exhibit coarser grain structure with the tendency of columnar grain growth at the periphery of the billet, as shown in Figures 3.18 and 3.20 [28].

The general pattern of grain size and dendrite arm spacing distribution along the billet diameter corresponds well to the change of cooling condition as has been described earlier in this chapter; see, e.g., Figures 3.14 and 3.15. An interesting conclusion can be drawn comparing structure data in Figure 3.19 with the results of computer simulations of the same billets shown in Figures 3.2c and 3.16. The zone of fi ner structures (both grain size and dendrite arm spacing, Figure 3.19) correlates well with the region where the liquidus line shows defl ection (Figure 3.16) and the slurry region starts to widen toward the center of a billet (Figure 3.2c). Movement of solid and liquid phases is also most intense in this region (Figure 3.16). As a result, in addition to the faster cooling because of the water impingement onto the billet surface, the condi-tions for solid phase fragmentation (multiplication of solidifi cation sites) and rapid growth are created, and smaller grains with fi ner internal constitution are formed. General coarsening of the structure in the central portion of the billet can be associated with a longer total solidifi cation time and cor-respondingly slower total cooling rate in this region (Figures 3.14c and 3.15)




and with a wider region of relatively stagnant fl ow where grains have ample opportunity to grow and coarsen (see Figure 3.6).

There is experimental evidence, however, that the dendrite arm spacing can refi ne in the center of the billet because of the reasons already discussed in Section 3.2. Figure 3.21 shows the variation in grain size and dendrite arm spacing in 200-mm billets of two commercial alloys cast with and without grain refi ning [29]. In all cases, the grain structure coarsens from the surface to the center of the billet. The dendrite arm spacing, in contrast, exhibits some refi nement in the central portion of the billet, mostly in grain-refi ned alloys. The structure of billets from a 7075 alloy is shown in Figure 3.22.

Similar results have been reported elsewhere. Nagaumi [30] reported a slight refi nement in the central portion of an Al–Mg slab that was correlated to the local increase of the solidifi cation and cooling rates. Chu and Jacoby [24] described the general increase of the average dendrite cell size from the periphery to the center of a 7XXX-series rolling ingot. However, the dendrite arm spacing in their measurements would actually decrease from 55 µm at the midthickness to 40 µm in the center (instead of increasing to 80 µm) if one measured only fi ne-cell grains in the duplex structure of the central portion of the ingot.

We may conclude that the casting speed and the water fl ow rate do not change the overall distribution of grain size and dendrite arm spacing across the billet section with the general tendency of structure coarsening toward

FIGURE 3.21Variation of grain size and dendrite arm spacing along the diameter of 200-mm billets from 2024 (a,c) and 7075 (b,d) alloys: = not grain refi ned, casting speed 80 mm/min; = grain refi ned, 80 mm/min; = grain refi ned, 120 mm/min; and = additionally grain refi ned, 120 mm/min [29]. The billet surface is on the left and the billet center is on the right of the fi gures.

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the center of the billet and some structure refi nement with the increasing casting speed. There is a region of local structure refi nement at some dis-tance from the surface that is formed because this section of the billet is solidifi ed under conditions of accelerated cooling by water impingement onto the billet surface and intense fl ow motion at the border of the mushy zone. There is also some dendrite-cell refi nement in the central portion of the billet, which is more pronounced for grain-refi ned structure and when duplex grain structures are formed. The possible reason for this local den-drite-arm refi ning is in the local decrease of the solidifi cation time in the central part of the billet, as we discussed in Section 3.2.

Let us now look at how the melt temperature may affect the grain structure of the billet. Figure 3.23 shows the distribution of grain size and dendrite arm spacing in cross-sections of billets cast at different melt temperatures and at two casting speeds.

The grain size (Figure 3.23a,b) coarsens with increasing melt temperature, decreasing casting speed, and toward the center of the billet. The main cause of these phenomena is the decreasing cooling rate that affects the nucle-ation and growth of grains. In addition, the increased melt temperature deactivates available solidifi cation sites, decreasing the frequency of grain

FIGURE 3.22Microstructure of a 7075 billet: (a) not grain refi ned, close to the surface; (b) not grain refi ned, in the center; and (c) grain refi ned, in the center.




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FIGURE 3.23Effect of melt temperature (in the furnace) and casting speed on distribution of grain size (a,b) and dendrite arm spacing (c,d) in 200-mm billets of an Al–2.8% Cu alloy cast at a speed of 100 mm/min (a,c) and 200 mm/min (b,d) [20]. DAS-dendrite arm spacing.

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nucleation. The appearance of a fi ne-structured zone at some distance from the billet surface refl ects the region formed under secondary (direct chill) cooling. A subsurface zone of coarser dendrites corresponds to the air gap. The general pattern of grain size distribution, therefore does not depend on the melt temperature.

The melt temperature mostly infl uences the dendrite internal structure in the center of the billet, causing its coarsening (Figure 3.23c,d). The increase in casting speed results in the general refi nement of the dendrite internal structure across the billet. In the range of lower melt temperatures and at low casting speeds, one can see that dendrite cells refi ne in the central part of the billet (Figure 3.23c). This structure refi nement is not observed at a higher casting speed (Figure 3.23d) and at higher melt temperatures (Figure 3.23c,d). The acceleration of the solidifi cation front in the center of the bil-let and a shallower sump with faster cooling of its bottom part through the mechanisms discussed earlier (Section 3.2) may be responsible for this phe-nomenon. The fact that this effect is not observed at a higher casting speed (Figure 3.23d) may be because the faster solidifi cation rate is completely overrun by the increasing casting speed and corresponding change in the shape of the solidifi cation front, the latter becoming less shallow with less fl attening in the center of the billet.

The peripheral regions of the billet are affected mainly by the increased casting speed, with fi ner structures (and higher cooling rates) occurring in the regions of primary cooling and secondary cooling.

We already discussed that the structure found in the central part of a solidifi ed billet has characteristics refl ecting its solidifi cation history (see Figures 3.15–3.17). The dendrite arm spacing refl ects not only the total solidi-fi cation time required for a particular grain to form but also the particular cooling schedule. This is witnessed by the presence of so-called “coarse,” “coarse-cell” grains, or “daisies” in the central part of the billet (Figures 3.17 and 3.18). Therefore, attributing the cooling rates experimentally measured by a thermocouple moving with a billet to the structure found in the posi-tion of this thermocouple in the solid billet should be done cautiously. The solidifi cation rate also cannot be used directly to explain structure forma-tion, otherwise the structure in the center of the billet would always be fi ner than, for example, at the midradius. Obviously, fl ow patterns and transport of the solid phase within the slurry region along with the shape of the cool-ing curve should be taken into account and may explain the appearance of “coarse” grains.

The origin of these grains is disputed. The literature discusses several hypotheses [24, 27, 31] that can be generally summarized as follows: (1) for-mation of these grains on the open surface of the melt, on a distribution bag, or on a hot top with subsequent separation and transporting by melt fl ow or due to gravity and (2) fragmentation or separation of dendrites at the solidi-fi cation front as a result of local remelting or mechanical forces with detach-ment of fragments or dendrites and transport of them by melt fl ow toward the center of the billet. Both mechanisms are possible. Note, however, coarse




grains that appear as a result of the fi rst mechanism are usually not only coarser internally but also much larger than the surrounding grains [31, 32]. The occurrence of these grains can be avoided by using proper technology. The second mechanism is more generic for solidifi cation processing and requires more attention.

A fl ow pattern existing in round billets during DC casting involves quite strong currents close to the liquidus isotherm in the direction from the periphery to the center of a billet (see Figures 3.6 and 3.16). The maximum of these currents is at approximately two thirds of billet radius, measuring from the center. These current transform further develop into a vortex in the central part of the billet, with part of the melt going upward and part going downward. As a result, dendrite fragments or even entire dendritic grains growing at the border between slurry and mushy regions in the billet section with strong melt currents can be detached easily. The further path of these solid-phase particles can be very different. Some of them will go along the fl ow direction upward and vanish in the liquid part of the sump. Some will “roll” down along the coherency isotherm and end up in the center of the sump without much coarsening. Other grains will grow in the melt volume ahead of the solidifi cation front under very small undercooling and then drop to the central part of the billet, having large dendrite arm spacings. Some of these grains are captured earlier by the solidifi cation front, forced down by currents or sedimenting under gravity, and fi nish solidifi cation at a higher undercooling or cooling (solidifi cation) rate (that results in a fi ner dendrite arm spacing frequently observed at the grain periphery; see Figure 3.17a). Yet another grain trajectory that can result in grain-cell coarsening can be illus-trated by streamlines shown in Figure 3.16. The corresponding cooling rates in Figure 3.15b demonstrate that at least some grains found in the central part of the billet could be nucleated at the liquidus (not separated from the mushy zone!) at the billet periphery and then transported to the center, growing as they travel. Therefore, the third mechanism of fl oating grain formation is a longer growth due to the grain trajectory within the slurry zone. All these variations of grains should be more correctly called “fl oating” grains.

In addition, there is always an area of relatively slow melt fl ow in the cen-tral part of the sump where fl oating grains may grow before settling down. As a result, the structure of the central part of the billet shows a scatter in cooling rates and, hence, in dendrite arm spacing. These grains are poor in solute concentration and are frequently cited as a cause of negative centerline segregation [12, 24, 31, 33]. This concept will be considered in more detail in Chapter 4.

The process parameters affect the distribution of fl oating grains in the following manner. Figure 3.24 shows how the distribution of “coarse-cell” grains depends on casting speed, water fl ow rate, and melt temperature. The increase in the casting speed obviously produces more fl oating grains though their distribution in the billet cross-section remains the same (see Figure 3.24a). This agrees well with the distribution of cooling rates estimated from streamlines, as shown in Figure 3.15b. The increase in the casting speed




results in a deeper sump with more severe fl ows at the boundary between the slurry and the mushy zone and a larger zone of relatively stagnant fl ow in the central part of the billet [5]. As a result, the amount of fl oating grains that is generated and grows increases with the casting speed. Water fl ow rate has virtually no effect either on the amount or the distribution of “coarse-cell” grains (see Figure 3.24b).

Melt temperature infl uences the distribution and amount of fl oating grains depending on the casting speed. At a low casting speed, grains with coarse dendrite arms occupy most of the billet cross-section at low melt tempera-tures. With the increase in melt temperature their amount decreases and they are confi ned to the area around the billet centerline (Figure 3.24c). In this casting regime the area of the stagnant fl ow in the central part of the sump (growth area) shrinks with increasing melt temperature, and a larger fraction of fl oating grains may go upward and remelt, as suggested by the fl ow patterns in Figure 3.25. At high casting speeds, the amount of “coarse” grains increases with the increasing melt temperature but their distribu-tion remains typical, i.e., they appear only in the central part of the billet (see Figure 3.24d). The reasons for this pattern are the same as in the case of casting speed: deepening of the sump, more severe fl ows along the coher-ency isotherm, and a larger stagnant region (see Figure 3.9 [9]).

FIGURE 3.24Effect of process parameters on the distribution of fl oating grains along the diameter of a 200-mm billet: (a) Al–4.3% Cu alloy, water fl ow 150 l/min, melt temperature 715°C; (b) Al–4.3% Cu, casting speed 200 mm/min, melt temperature 715°C; (c) Al–2.8% Cu, water fl ow rate 150 l/min, casting speed 100 mm/min; and (d) Al–2.8% Cu, water fl ow rate 150 l/min; casting speed 200 mm/min [5, 20]. (Parts (c) and (d) reproduced with kind permission of Springer Science and Business Media.)

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3.4 Effect of Process Parameters on the Amount of Nonequilibrium Eutectics

The appearance of eutectics in most commercial wrought alloys is the con-sequence of nonequilibrium solidifi cation, as we discussed in Section 2.2 of Chapter 2. Under equilibrium conditions most wrought alloys should solidify as single-phase aluminum solid solution. That is why this eutectic is called nonequilibrium and does not usually attract much attention because during proper homogenization of billet and ingots it is dissolved anyway.

The eutectic, by defi nition, represents the last liquid that solidifi es and, therefore, its occurrence in the as-cast structure is an indication of the solidi-fi cation conditions that have led to the appearance of this last liquid and of the availability of the liquid phase at late stages of solidifi cation. The pres-ence of liquid at high volume fractions of solid in combination with the abil-ity of this liquid to penetrate through the solid network is very important for the occurrence of such casting defects as pores and hot tears, as will be discussed in Chapter 5.

The microstructure of different sections of a 200-mm billet from a binary Al–Cu alloy is shown in Figure 3.26. This alloy should be single-phase under equilibrium solidifi cation conditions but the structure unambiguously

FIGURE 3.25Melt fl ow pattern in the liquid and slurry zones of a 200-mm billet (Al–2.8% Cu) cast at a cast-ing speed 100 mm/min, at a melt temperature of 700°C (a) and 760°C (b) [20]. Only half of the billet is shown, the centerline on the left and the surface on the right. (Reproduced with kind permission of Springer Science and Business Media.)

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exhibits the veins of excess phase at dendrite boundaries. The typical pattern is a mixture of eutectic areas, where one can distinguish the coupled eutectic structure, and individual phase particles that represent so-called divorced eutectic. In the latter case, the solid solution that should constitute the part of the eutectic mixture has joined the (Al) primary solid phase and only the excess phase from the eutectic remains visible. The quantifi cation of such a structure presents some diffi culties. There are three ways of dealing with this problem. First, it is possible to accurately measure only the amount of the secondary phase and then, knowing the composition of the eutectics, to recalculate the measured fraction of the second phase to the total amount of the eutectics. Second, one can separately measure the fraction of the divorced eutectic particles and the fraction of eutectic areas, and then make a recalcu-lation for the former only. And third, the general fraction of the mixture of divorced and coupled eutectics can be assessed. The last approach is used in this work. Taking into account that the variation of cooling rates in the cross-section of the billet is noticeable but not dramatic (see Figure 3.15), the effect of the cooling rate on the ratio between the divorced and coupled eutectic can be neglected, and the mixed fraction should be representative of the total amount of nonequilibrium eutectics.

FIGURE 3.26Microstructures of a 200-mm billet from an Al–4.3% Cu alloy cast at 120 mm/min, casting temperature 715°C, water fl ow rate 150 l/min taken at 10 mm (a), 55 mm (b) and 80 mm (c) from the billet surface. Arrows point to the areas of coupled eutectics.




An important and quite persistent feature of nonequilibrium-eutectic dis-tribution in the billet is the minimum in the central portion of the billet cross-section. This means that the amount of last available liquid is always lower in the center of the billet than at its periphery. The effect of the cooling rate on the eutectic fraction was discussed in detail in Section 2.2 of Chapter 2. There are controversial reports in the literature about this dependence, as illustrated in Table 2.1. The general consensus is that the increase in the cool-ing rate would increase the amount of eutectics, which seemingly explains the increase of the eutectic fraction toward the billet surface. On the other hand, in the range of low cooling rates the dependence can be opposite, as was shown in Section 2.2 of Chapter 2. In a commercial extrusion billet of 200 mm in diameter the cooling rates in the center and periphery of the bil-let are approximately 3–5 K/s and 15–20 K/s, respectively (see Figure 3.15). It is unlikely that this difference in cooling rates between the center and the periphery of the billet can cause the experimentally observed change in the eutectic amount. Several other phenomena can infl uence the volume fraction of eutectics. We can suggest the following line of logic for the case of DC cast-ing. First, in this cooling range, the eutectic fraction does not show signifi -cant response to the cooling rate (see Figure 2.10). Second, the solidifi cation during DC casting occurs under convection conditions that are rather active in the transition region of the billet (see Figure 3.6). According to Diepers et al. [34], convection can signifi cantly increase the coarsening exponent, affecting the coarsening kinetics, as shown in Figure 2.12. The width of the transition region is maximum in the center of the billet, and the area of stag-nant fl ow where grains can ripen is always present there. As a result, the coarsening and back diffusion may occur in the center of the billet much more effi ciently than at the periphery, decreasing the amount of eutectics. On the other hand, structure coarsening may facilitate liquid penetration into the mushy zone by increasing the permeability of the solid network [35]. In this case, depending on the direction of this fl ow, the amount of eutectic formed by the solute-rich liquid increases or decreases in certain sections of the billet. And fi nally, the negative macrosegregation in the center of the billet can further contribute to the decreased amount of eutectics. As we will show in Chapter 4, the actual macrosegregation in an Al–4.25% Cu billet can be responsible for as much as 0.3 vol.% of variation in eutectic volume frac-tion along the billet diameter. There are also some kinetic effects of negative macrosegregation that may cause locally accelerated solidifi cation and, as a result, less eutectics [36–38]. The contribution of these effects is, however, not likely to be appreciable.

At the present level of knowledge it is diffi cult to rank the mechanisms that may be responsible for the formation of nonequilibrium eutectics and single out the most signifi cant one. Obviously, the scale and shape of the casting (fl at ingot or round billet) and structure formed during solidifi cation can fundamentally affect the amount and distribution of nonequilibrium eutectic. Here we consider the effect of process parameters on the formation of eutectic in an average-size extrusion billet, as shown in Figure 3.27.



114 Physical M


hill Casting of A

luminum

Alloys

FIGURE 3.27Effect of process parameters on the amount and distribution of nonequilibrium eutectic in binary Al–Cu alloys: (a) Al–4.3% Cu, water fl ow rate 150 l/min, melt temperature 715°C; (b) Al–4.3% Cu, casting speed 200 mm/min, melt temperature 715°C; (c) Al–2.8% Cu, water fl ow rate 150 l/min, casting speed 100 mm/min; (d) Al–2.8% Cu, water fl ow rate 150 l/min, casting speed 200 mm/min; and (e) water fl ow rate 150 l/min, casting speed 200 mm/min; melt temperature 715°C [5, 20, 28]. (Parts (d) and (e) reproduced with kind permission of Springer Science and Business Media.)

4.8

4.4

4.012

14

16

18

20 160

150170

190

210

230

250 160120

8040

0

12080

400





Casting speed, cm/min

Water flow rate, l/min

Eut

ectic

s, %

3.0

2.82.62.4

140

100

60

20

140

100

60

20700

720740

760

Eut

ectic

s, % 3.0

2.82.6

2.4

Eut

ectic

s, %

4.8

4.4

4.0Eut

ectic

s, %

(a)

(c)

(b)

(d)

Temperature, °C

700720

740760

Temperature, °C

5.04.03.02.01.0

200

160

120

80

400 1.0

2.03.0

4.05.0

Cu, %

Eut

ectic

s, %

(e)


CR

C_62816_C

h003.indd 114C

RC

_62816_Ch003.indd 114

2/27/2008 4:58:31 PM

2/27/2008 4:58:31 PM



At usual and high casting temperatures, the casting speed and water fl ow rate slightly affect the amount of eutectic in the central portion of the billet, as shown in Figure 3.27a–d. The eutectic fraction increases with the casting speed, with the water fl ow rate having an opposite effect. Interestingly enough, at very low casting temperatures, the amount of nonequilibrium eutectic decreases with increasing the casting speed, as illustrated in Figure 3.27c,d. The interrelation between cooling rate, solidifi cation rate, sump dimensions, and the fi neness of structure can be responsible for such behavior.

The casting temperature has a strong effect on the volume fraction and distribution of nonequilibrium eutectic, especially at high casting speeds, as illustrated in Figure 3.27d. More eutectic is concentrated in the center of the billet upon casting from high melt temperatures. In this case, the coarseness of the structure in combination with more active melt fl ows (see Figures 3.9 and 3.22) may facilitate a deeper penetration of the solute-rich melt into the mushy zone in the center of the billet, effectively increasing the amount of eutectic [9, 20].

More eutectic is formed in more alloyed billets. This obvious fact is dem-onstrated in Figure 3.27e. It is interesting, though, that the degree of eutec-tic decline in the center of the billet seems to be more pronounced in less alloyed billets.

The experimental and computer-simulation results shown in this chapter constitute a background for the discussion in Chapters 4 and 5. The solidi-fi cation and structure formation during DC casting are intricate phenom-ena that are not yet fully understood and described. It is, however, obvious that the process parameters infl uence the structure formation through their effect on the geometry and dimensions of the billet sump and on the fl ow patterns that exist in the liquid and slurry part of the sump. A complex interplay between cooling rate, solidifi cation rate, and the dimensions of the sump sometimes results in seemingly controversial effects of process condi-tions on structure parameters. All in all, the material and discussion given in this chapter do not present the fi nal solution to the problems but rather provide broad information and offer some possible mechanisms involved in the structure formation during DC casting.

This chapter would not be complete without a discussion of the effect of process parameters on the occurrence of some casting defects that can either result in the rejection of the casting or in the increased amount of removed (scalped) material.

3.5 Effect of Process Parameters and Alloy Composition on the Occurrence of Some Casting Defects

Many things may go wrong during DC casting if the casting recipe does not address the requirements of the alloy and particular mold design. Mod-ern molds are designed in such a way that they help produce better surface




quality and more uniform temperature distribution across the casting, but at the same time these molds have a narrower allowed variation range of cast-ing parameters and demand fi ner tuning of casting recipes.

One of the problems that became a hot topic of discussion in the 1980s and 1990s was the formation of a so-called “fi r-tree” zone in ingots and billets of diluted aluminum alloys. For example, the macrostructure of billets and ingots of 1XXX- and 5XXX-series alloys is inhomogeneous and demonstrates regions with different etching ability, e.g., in hot NaOH (see Figure 3.28a). After high-temperature annealing, the regions with different etching ability are no longer detected. Westengen [39] attributes the formation of this zone to the phase selection of iron-containing phases formed at different cooling rates in different zones of the ingot. This point of view was supported by a number of researchers; see [40–42]. It should be noted that the segregation of iron in the subsurface region is virtually unavoidable under real casting conditions (for further discussion on macrosegregation, see Chapter 4).

The main reason for the formation of the fi r-tree zone is the competition in nucleation and growth between different metastable and stable modifi ca-tion of Fe-containing phases [41] under variable cooling conditions in the subsurface layer of DC casting [43] (see Figure 3.14a,b). It is important to note that the fi r-tree structure is caused not by the formation of metastable phases proper but rather by formation of a specifi c mixture of these phases due to uneven cooling conditions and nucleation-and-growth pattern. High cooling rate at the surface of the casting promotes the formation of metastable phases such as body-centered tetragonal or monoclinic AlmFe (Al9Fe2) and tetrag-onal α″(AlFeSi) that require about 20 K/s for their formation [44] (see also Table 2.2). On decreasing the cooling rate, in the area of air-gap formation and generally deeper under the surface, the cooling conditions (2–5 K/s) are more favorable for the formation of a mixture of monoclinic AlxFe (Al5Fe), orthorhombic Al6Fe, and cubic α(AlFeSi) phases [44]. Phases like Al6Fe nucle-ate at a lower cooling rate in the environment where AlmFe phase dominates but, having a higher growth rate, overgrow it, forming a specifi c pattern, as shown in Figure 3.28b [41]. Different phases promote different etching ability of the alloy, which ultimately results in the appearance of the fi r-tree zone. Brusethaug et al. [41] note that the fi r-tree structure can be observed not only in subsurface layers but also in the central part of billets and small ingots, which is in line with the enhanced cooling and increased solidifi cation rate in this region, as we discussed in Section 3.2.

The phase composition of aluminum ingots, containing 0.25% Fe and 0.13% Si, in the as-cast condition and after homogenization is given in Table 3.2 after Westengen [39] and Skjerpe [40]. The equilibrium phase composition of this alloy must be (Al) + A13Fe + α(Al8Fe2Si) [44].

The main change that occurs during high-temperature annealing is the transformation of binary and ternary metastable phases at the surface to more stable phases. Such an annealing may help reduce the appearance of the fi r-tree zone but is not always effi cient (note the persistence of the meta-stable α″(AlFeSi) phase).




FIGURE 3.28Fir-tree structure in a horizontal cross-section of an aluminum ingot (a) and a scheme illustrating the formation of the fi r-tree zone (b) [41]. (Courtesy of Dr. S. Brusethaug, Hydro Aluminium, Norway.)

(a)

Al3Fe, α′′

Al6Fe, Al3Fe,α(AlFeSi)cubic

(b)




Other ways of preventing formation of the fi r-tree structure include the control of alloy composition (keep the Fe:Si ratio at about 3 [41], presence of small amounts of Cr and Mn [43]), and optimization of cooling conditions at the surface (low-head casting, reducing the air-gap zone [43]).

Yet another undesirable structure pattern that is observed in DC-cast bil-lets is formed by so-called feathery grains that appear as elongated crystals with both straight and wavy boundaries and are frequently assembled in fan-shaped agglomerates. The appearance of such grains is favored by high melt temperature [31], high temperature gradient [45, 46], forced melt fl ow [47, 48], and concentration of certain alloying elements [49–51]. Figure 3.29 shows a typical image of feathery grains, inclined toward the direction of melt fl ow.

In practice, feathery grains may appear during DC casting if the cooling rate is higher than 10 K/s (or the overheated melt comes in contact with the water-cooled mold promoting high thermal gradients), the alloy is relatively

TABLE 3.2

Phase Composition of Direct-Chill Cast Ingots in As-Cast and Annealed Conditions (600 × 1350 mm Ingots, Casting Speed 100 mm/min) [39, 40, 44]

Phase Al8Fe2Si α(AlFeSi) α″ Al3Fe Al6Fe AlmFe AlxFe β′(AlFeSi) Si

As–CastSurface – + +++ – – +++ – – –Inner region

– – – + +++ – +++ + +

Annealed (590°C, 5 h)Surface + + +++ +++ – + – – –Inner region

+ + + +++ – – + – –

FIGURE 3.29Feathery grains formed in the presence of forced fl ow (from left to right) in an Al–4% Cu alloy. (Courtesy of A.N. Turchin.)




pure (e.g., 1XXX series) or the alloy contains Cr, Zr, or Ti as growth- restricting elements or Mg, Cu, Zn, or Si as the elements that increase the solidifi cation range and strongly segregate.

A thorough study of crystallographic orientations and morphology of feathery grains shows that these grains, unlike normal columnar grains that grow in <100> direction, are made of <110> dendrites with trunks split by a 111 plane [46]. The straight boundaries in the structure shown in Figure 3.29 represent the coherent 111 planes, whereas the wavy boundaries represent incoherent twin planes between neighboring grains. It is suggested that the formation of feathery grains is a result of two mechanisms [46]. First, the anisotropic properties of the alloy, i.e., surface tension and kinetics of atom attachment, change at high growth rates facilitated by high thermal gradients and certain alloy compositions. As a result, the growth direction switches from <100> to <110>. Second, the twinning mechanism of growth is initiated by stacking faults and is promoted by convection and high ther-mal gradient. In the absence of convection or high thermal gradient normal, untwinned dendrites are expected.

Figure 3.30 demonstrates different dendrite morphologies that can be obtained under forced convection in an aluminum alloy solidifi ed in differ-ent thermal conditions.

The occurrence of feathery grains in the billet or ingot produces strong anisotropy of structure and properties of deformed products, which includes

FIGURE 3.30Effect of solidifi cation rate and thermal gradient on the morphology of dendrites formed in an Al–4% Cu alloy under forced fl ow conditions [48]. (Reproduced with kind permission of Elsevier/Pergamon.)

20

18

16

14

12

10

8

6

4

2

00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Solidification rate, mm/s

The

rmal

gra

dien

t, K

/mm

equiaxedfeathery

columnar




inhomogeneous recrystallization, formation of intermetallic segregates, and low ductility in certain directions [50].

A proper grain-refi ning practice and a lower temperature gradient in the liquid (less melt overheating and slower casting) are among common prac-tices for elimination of feathery grains [51].

Apart from the sensitivity of the as-casting structure to the casting speed and melt temperature as a natural consequence of the liquidus and solidus temperatures of the particular alloy and the corresponding extent of the characteristic regions on the billet (see Figure 3.1), there are other casting defects that originate and are controlled by the conditions of cooling, i.e., by melt temperature, casting speed, and water rate.

The fi rst problem that may occur at the beginning of the casting or during casting if some casting parameters are changed on the fl y is the melt fl ash-ing into the gap between the starting block and the mold or the bleed-out of melt through the weak solid shell and then into opening below the mold. This type of defect is shown in Figure 3.31a. Another manifestation of the same problem is the separation of the billet butt due to insuffi cient degree of its solidifi cation.

All these defects are caused by the fact that the solid shell is supposed to be strong enough to contain the semi-liquid and liquid core is ruptured either due to insuffi cient strength or as a result of remelting in the air-gap region. Butt cracking may also be a result of solid shell weakness. Most likely the

FIGURE 3.31Flashing, bleed-out, hang-up, butt separation, and cracking (a) and cold folding and liquation surface defects (b) on a DC-cast aluminum-alloy billet.




casting conditions are too hot and the cooling ability of the mold is insuf-fi cient. The usual remedy is to reduce the melt temperature and to ensure that the primary cooling and secondary cooling occur homogeneously along the perimeter of the casting. Sometimes the casting can be stopped for a short period to allow the solidifi cation and healing of the bleed-out section and then resumed. If the problem persists, the casting should be aborted. It is important to note that the position and strength of the solid shell are functions of the material structure. For example, the grain refi nement that is generally a good answer to the requirement of better properties and quality of the as-cast material can promote bleed-out. The fact of the matter is that grain-refi ned alloy has a wider slurry zone and a narrower mushy zone (we will consider this in more detail in Chapter 5). The consequence of this can be the slip of the fully solid shell beneath the mold opening during casting if the melt temperature and the casting speed are not changed accordingly.

The opposite of the bleed-out is the hang-up of the casting in the mold, also shown in Figure 3.31a. In this case, the thick section of the billet is solidifi ed inside the mold and gets stuck. This defect is especially harmful in hot-top molds when the solidifi cation spreads to the ceramic part of the mold assem-bly. In most cases the casting should be stopped immediately, and frequently the mold is damaged. Another danger of this defect is that the partial hang-up can lead to the partial separation or horizontal cracking of the billet with subsequent massive bleed-out. The increase in the melt temperature along with the proper lubrication of the mold and the correct choice of casting speed help remedy this type of defects.

The surface of the billet frequently bears the characteristic marks illustrated in Figure 3.31b. The reduction of this type of defect decreases the amount of scalping needed before further processing of billets and ingots. Cold folding is caused by the freezing of the melt meniscus inside the mold, e.g., below the ceramic ring of the hot top (see Figure 3.14a). The solid meniscus then moves down and the melt fl ashes into the opening, fi lling the cavity [2]. The process repeats with a periodicity that is a function of casting speed. Cold folds can penetrate fairly deeply inside the billet, forming special bands of fi ne structures with oxide inclusions and pores, as shown in Figure 3.32. The cold folding is caused by cold casting conditions and too high heat transfer through the mold. The increased melt temperature and casting speed and the decreased water fl ow rate may help reduce this type of surface defect. Electromagnetic casting (EMC) and air-assisted (e.g., air slip) casting are much less prone to cold folding.

The formation of the air gap (see Figure 3.14) and corresponding reheating of the solid shell up to the point of its remelting is the main reason for the appearance of liquation marks on the billet surface, as shown in Figure 3.31b. When the solid shell due to the thermal contraction pulls away from the mold surface, the solid shell starts to heat up from the latent solidifi cation heat and the heat coming from the melt. The appearance of the liquation refl ects the temperature of the thermal contraction onset [4, 12] (see Chapter 5 for details). The metallostatic pressure of the liquid metal head in the mold and




hot top together with the fl ow patterns oriented toward the billet surface (see, e.g., Figure 3.25) and the shrinkage-induced fl ow in the mushy zone drive the liquid toward the surface. Remelting of the shell opens wide channels for such a fl ow. As a result, liquid can penetrate through the shell and reach the surface. In addition, this liquid is enriched in the solute elements up to the point of the eutectic concentration, which considerably lowers its solidus temperature and delays its solidifi cation. This liquid brings the solute to the surface and creates a region of highly positive surface segregation. The peri-odicity of shell pulling-off, remelting, liquation, and resolidifi cation results in the periodic subsurface structure with the bands of enriched (liquation marks) and depleted (between liquation marks) zones. Alloys with a larger solidifi cation range are more susceptible to this defect. Ohm and Engler [52] report the role of metallostatic pressure as a main reason for the liquation. Dobatkin [4] suggests the important role of the oxide surface layer. A stron-ger oxide skin, a better surface quality, and suffi cient lubrication of the mold can help reduce the liquation marks. The general remedy for the liquation is the proper thermal balance in the mold, e.g., cooler casting conditions and the reduction of air gap.

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2. J.F. Grandfi eld, P.T. McGlade. Materials Forum, 1996, vol. 20, pp. 29–51.

FIGURE 3.32Cold folding in the cross-section of a 200-mm aluminum-alloy billet.




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125

4Macrosegregation

4.1 Mechanisms of Macrosegregation

4.1.1 Historic Overview

The fact that large-scale castings and ingots are not homogeneous in chemical composition has been known for centuries. The Italian metallurgist and foundryman V. Biringuccio described segregation in bronze gun barrels in his book De la Pirotechnia as early as 1540 [1]. In 1574 the Austro- Hungarian chemist L. Ercker published his observations of liquation in precious alloys [2]. As Pell-Wallpole notes in a brilliant review [3], most observations and studies of macrosegregation during the nineteenth century were about pre-cious metals, including works by W.C. Roberts-Austin (1875) and E. Matthey (1890) in Great Britain. In 1866–1867 Russian metallurgists A.S. Lavrov and N.V. Kalakutsky observed macrosegregation in steel ingots and noted that its degree depended on the size of the ingot [4]. Lavrov noted that macrosegre-gation was caused by the precipitation of carbon during steel solidifi cation and accumulation of low-melting components in the center of the ingot. It was not until the beginning of the twentieth century, however, that mac-rosegregation attracted real scientifi c interest, fi rst as related to steel and bronze ingots and later as related to aluminum billets and ingots. Pioneer-ing works include those of T. Turner, M.T. Murray, E.A. Smith, O. Bauer,H. Arndt, R.C. Reader, R. Kühnel, and F.W. Rowe on copper alloys and those of G. Masing, W. Claus, S.M. Voronov, and W. Roth on aluminum alloys (cita-tion information can be found in Ref. [3]).

This chemical inhomogeneity is called macrosegregation because it occurs on the scale of the grain. The main reason for it is the segregation (partition-ing) of alloying elements during solidifi cation. This partitioning is considered in greater detail in Chapter 2. Somehow the large difference (sometimes tens of percent) in the compositions of solid and liquid phases occurring during solidifi cation is translated into a relatively small difference (about or less than 1%) of chemical composition across the whole section of a casting or a billet. What makes macrosegregation a really serious problem is that it cannot be eliminated during downstream processing, unlike microsegregation, which can be removed relatively easily by high-temperature anneal, the technique known as homogenization. Diffusion lengths are measured in micrometers




for microsegregation and in centimeters for macrosegregation. This differ-ence in scales makes real difference in the severity of the problem.

The simplest way to explain macrosegregation is to imagine that the advancing solidifi cation front pushes the liquid enriched in the solute (in the case of partitioning, coeffi cient K < 1) toward the hotter part of the casting, e.g., the center. As a result, after solidifi cation, the center of the casting will contain more solute than the periphery of the casting. In reality the solute-rich liquid should be transported toward the hot spot of the casting (in the direction of solidifi cation). The driving force behind such transport is either convection or shrinkage-driven fl ow. This kind of macrosegregation, called “normal” segregation, is a direct consequence of microsegregation and can easily be predicted and estimated using the phase diagram data. The fre-quently observed macrosegregation pattern in ingots and billets is just the opposite—the periphery of the casting is solute enriched while the center remains solute lean. This type of “inverse” macrosegregation is quite typical of billets and ingots from nonferrous alloys, including DC-cast aluminum alloys. The ultimate form of “inverse” segregation is liquation or exudation at the casting surface, when the solute-rich liquid penetrates through the outer shell of a casting and solidifi es at the surface as liquates or eutectic exudates (see Figure 3.31b). Obviously, in this case the solute-rich liquid is transported in the direction opposite to the solidifi cation-front movement. The inverse segregation is quite typical of DC-cast aluminum billets when it is manifested as negative centerline segregation and positive surface segre-gation, as illustrated in Figure 4.1.

During the fi rst half of the twentieth century several theories were sug-gested to explain inverse segregation [3]. These theories attempted to explain numerous observations, some of which are summarized below. It was found

0.04

0.02

0

−0.02

−0.04

−0.06

−0.08

−0.10 40 80 120 160 200Dev

iatio

n of

Cu

conc

entr

atio

n fr

om th

eav

erag

e

Cross-section of billet, mm

Center

FIGURE 4.1A typical pattern of macrosegregation in a 200-mm billet of an Al–4.2% Cu alloy cast at120 mm/min. Note the negative segregation in the center, positive at the surface, and a heavily depleted subsurface layer.



Macrosegregation 127

experimentally that inverse segregation occurred in alloys with a consid-erable freezing range and the extent of the segregation increased with the freezing range, e.g., as reported in the works of Claus and Goederitz in 1928 and Voronov in 1927 and 1929. The presence of hydrogen was shown to promote exudations, while melt overheating increased the degree of segre-gation. As early as 1926, Masing and Dahl concluded that hydrogen in alumi-num alloys would adversely affect macrosegregation if it were trapped in the mushy zone. Therefore, this infl uence was typical only of moderate cooling rates, when hydrogen was neither quenched in solid aluminum nor escaped the solidifying metal. Early accounts, such as J.T. Smith’s in 1875, noted that the cooling rate was a determining factor in segregation. Bauer and Arndt (1921) emphasized a steep temperature gradient in the ingot as an essential condition for macrosegregation. Voronov (1929) showed that any change in casting conditions that increased the cooling rate, i.e., reduced casting tem-perature, colder mold, lower pouring rate, or increased mold conductivity, would increase the degree of inverse segregation in duralumin ingots, as demonstrated in Table 4.1 [5].

The relationship of macrosegregation to alloy properties and grain struc-ture was also examined [3]. It was shown that segregation developed during solidifi cation, not in the liquid state. The transition from normal to inverse segregation was experimentally observed by increasing the thickness of the solidifi ed shell of an ingot, as reported on Fraenkel and Gödecke in 1929. Inverse segregation was often less in fi ner equiaxed structures than in colum-nar or coarse dendritic structures because of the different mechanisms of

TABLE 4.1

Effect of Casting Parameters on Macrosegregation in a Permanent-Mold Ingotfrom Duralumin (Al–Cu–Mg alloy) [5]

Parameter Values

Difference in Cu Concentration between

the Center and the Surface of an Ingot, %

Casting temperature, °C 750 0.28730 0.37700 0.57

Mold temperature 200°C 1.3Ambient 3.3Water cooled 4.7

Thermal conductivity Sand mold 0.08Chill with the wall thickness equal to the ingot thickness

0.33

Chill three times thicker than the ingot

0.71

Ingot thickness, mm 20 0.2490 0.54




feeding the solidifi cation contraction, i.e., liquid feeding in columnar struc-tures and mass feeding in equiaxed structures [3]. As early as 1925, Masing et al. correlated inverse segregation to volume contraction during solidifi ca-tion of metallic alloys [3]. This theory was further developed by Phelps (1926) and Verö (1936) and formed a basis for modern views on macrosegregation.

Tables 4.2 and 4.3 summarize some early theories that have been offered to explain the phenomenon of inverse segregation. Some of these theories were short-lived (Table 4.2), and others were developed into the contempo-rary theory of macrosegregation [6–8] (Table 4.3).

The current understanding of macrosegregation mechanisms can be for-mulated rather simply: relative movement of liquid and solid phases dur-ing solidifi cation. On the phenomenological level, we can single out several types of such relative movement that occurs in the sump of a billet during DC casting:

Thermo-solutal convection in the liquid sump caused by temperature and concentration gradients, and the penetration of this convective fl ow into the slurry and mushy zones of a billet (see Figures 3.6, 3.9, and 3.25);Transport of solid grains within the slurry zone by gravity and buoy-ancy forces, convective or forced fl ows (see Figure 3.16; the origins of such grains are discussed in Section 3.3);Melt fl ow in the mushy zone that feeds solidifi cation shrinkage and thermal contraction during solidifi cation;Melt fl ow in the mushy zone caused by metallostatic pressure;Melt fl ow in the mushy zone caused by deformation (thermal con-traction) of the solid network;Forced melt fl ow caused by pouring, gas evolution, stirring, vibra-tion, cavitation, rotation, etc., which penetrates into the slurry and mushy zones of a billet or changes the direction of convective fl ows.

We know that commercial alloys usually solidify as dendrites, forming over-all equiaxed structure in a billet (see Section 3.3). In the slurry zone (above the coherency isotherm in the transition region) the equiaxed grains are free to move and can travel short or long distances, depending on their size and direction of melt fl ow. In the mushy zone, however, these dendrites form a continuous solid network and have a fi xed position in the billet. They move only in the direction of billet withdrawal and with the casting speed. Liquid fl ow within the mushy zone is limited to distances on an order of magnitude of several grain sizes.

Before we discuss the mechanisms of macrosegregation we need to famil-iarize ourselves with the phenomenon of permeability, which refl ects the ability of liquid to penetrate through the fi lter, e.g., formed by a continuous solid-phase network.

•

•

•

••

•




TABLE 4.2

Summary of Unsubstantiated Theories of (Inverse) Macrosegregation [3]

Theory Author(s), year Essence Comments

Mobile equilibrium

S.W. Smith, 1917–1926

System tends to lower its melting point in the region of solidifi cation by segregation of low-melting components to this region.

Based on an incorrect assumption that segregation occurs in the liquid state.

Thermo-solutal segregation

Benedicks, 1925

Temperature and solute gradients in the liquid drive the segregation.

Based on an incorrect assumption that segregation occurs in the liquid state.

Undercooling Hanson, 1917; Johnson, 1918; Masing, 1922

During initial undercooling, the solid phase is enriched in the solute; next layers will be solute lean.

Cannot explain the segregation over the cross-section in relatively large ingots and upon slow solidifi cation.

Crystal migration

Voronov, 1927; Watson, 1933

Solute-lean primary crystals are detached from the ingot’s shell and pushed by the solidifi cation front toward the center of the ingot under conditions of small thermal gradient.

Contradicts the experimental observations on inverse segregation in ingots where no primary phase movement has taken place.

Contraction pressure

Kühnel, 1922; Price and Philips, 1927; Voronov, 1929

Solid shell formed at the top of a casting exerts pressure onto the liquid and forces it through the side shell to the surface.

Contradicts calculations of pressure and experimental observations of inverse segregation in ingots with the open (liquid) surface.

Thermal contraction of an ingot shell may result in its rupture (hot cracking!). The gaps between grains are fi lled with the solute-rich liquid.

Explains the exudations and surface segregation.

Gas evolution Genders, 1927 Dissolved gas concentrates in the residual, low-melting liquid and then evolves, pushing the solute-rich liquid along the grain boundaries toward the ingot surface.

Fits many experimental observations.

Requires the continuous solid network to be formed. Cannot explain inverse segregation in gas-free alloys and upon fast cooling.



13

0 Physical M


hill Casting of A

luminum

Alloys

TABLE 4.3

Summary of Theories of (Inverse) Macrosegregation That Form the Basis of the Modern School of Thought [3]

Theory Author(s), Year Essence Comments

Interdendritic feeding Gulliver, 1920 Bauer and Arndt, 1921

Interdendritic feeding is assisted by capillary forcesInterdendritic movement of solute-rich liquid from the interior toward the surface of an ingot. Segregation depends on the ratio between the solid–liquid interfacial diffusion rate and the growth velocity of primary phase. Normal segregation occurs in equiaxed structures and the inverse in columnar structures.

Feeding of solidifi cation shrinkage occurs also through intradendritic channels.

Additional mechanism of liquid transport

Does not explain inverse segregation in equiaxed structures

Dobatkin, 1948 [7]

Volume contraction Phelps, 1926 Volume solidifi cation contraction is a driving force for the interdendritic feeding. Solidifi cation expansion results in normal segregation, while solidifi cation shrinkage occurs in inverse segregation.

Very important contribution to modern theory

Gradual segregation Brenner and Roth, 1940 [6]

Segregation in DC cast billets occurs in layers: the surface receives solute-rich liquid and does not part with it; the center expels liquid but, due to restricted feeding, does not receive the fresh one.

A basis of the modern theory of macrosegregation during DC casting

Shrinkage-driven fl ow

Verö, 1936 [8] Inverse segregation is driven by interdendritic melt fl ow caused by solidifi cation shrinkage and is not limited to columnar structures. Emphasized the role of partitioning in the extent of segregation, rather than the solidifi cation range. Showed that segregation occurs in the transition region of an ingot.

Important contribution to modern theory

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Macrosegregation

131

Importance of coherency

Dobatkin, 1948 [7] Related the occurrence of macrosegregation to the formation of a coherent solid skeleton of primary phase (mushy zone). In the slurry zone only the gravity segregation of solid (fl oating) grains is possible.

Important contribution to modern theory

Shrinkage-driven fl ow and temperature gradient

Pell-Walpole, 1949 Extended the mechanism of Brenner and Roth to equiaxed structures and linked the development of macrosegregation to the temperature gradient across the billet. Correlated the occurrence of exudations to the formation of air gap.

Important link to process parameters

Relation to the geometry of the billet sump

Brenner and Roth, 1940 [6]

The extent of macrosegregation in vertical DC casting is proportional to the vertical length of the transition region, and increases with the casting speed and the size of the ingot.

Approach to the modern theory of macrosegregation in DC casting

Dobatkin, 1948 [7] The extent of macrosegregation in vertical DC casting is proportional to the horizontal thickness of the transition region and to the inclination of the solidifi cation front to the horizon.

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4.1.2 Permeability

In order to understand segregation formation, porosity, and hot tearing dur-ing DC casting, we need information on the permeability of the transition region and, in particular, of the mushy zone. This parameter is very impor-tant during the later stages of the solidifi cation process, when the channels where liquid fl ows are very narrow. Here the interdendritic fl ow caused by solidifi cation shrinkage might not be enough to feed the solid phase, which may result in discontinuity of the solid material in the form of microporosity and hot tearing. In macrosegregation, the permeability in the entire transi-tion region is crucial because it determines the depth of liquid penetration into the mushy zone and the length of liquid transport within the mushy zone. Figure 4.2 shows a 3D image of the mushy zone at approximately70 vol.% of the solid phase [9]. Note that the solid phase (darker gray portions of the image) and liquid channels (light gray areas) are continuous.

The permeability of a porous structure (in the semisolid material such aporous structure is represented by the solid-phase network) can be determined

FIGURE 4.23D image of a semi-solid sample of an Al–13% Cu alloy at 550°C. The volume fraction of solid is 71 to 74%. Light areas correspond to the liquid phase (removed from the image for clarity) and darker gray areas correspond to the solid phase. Image is obtained by 3D tomography at the European Synchrotron Radiation Facility. (Courtesy of D. Bernard (ICMCB-CNRS).)




from the fl ow rate of a penetrating liquid at the exit of sample Q and the pres-sure drop per unit length, ∆P′/L. We use Darcy’s law [10]:

Q = kD A∆P′

_______ L (4.1)

where Q is the volume fl ow rate, A is the cross-sectional area, and kD is the permeability coeffi cient. The permeability coeffi cient depends on the liquid properties. To make the permeability dependent only on the geometry of the solid phase, a specifi c permeability, K, is introduced as:

K = µkD, (4.2)

where µ is the dynamic viscosity of the liquid. This permeability depends on the packing of dendrites, hence on the volume fraction and morphology of the solid phase.

The same law can be written in terms of the average (superfi cial) fl ow velocity v as follows [11]:

v = – K ___ µf1 ( ∆P ___

L + ρ1g ) , (4.3)

where fl is the volume fraction of liquid, ρl is the density of liquid, and g is the gravity acceleration.

The value of permeability is quite diffi cult to measure for a particular type of alloy and structure. Available experimental methods are limited to alloys with high volume fraction of liquid tested upon remelting [12–14]. Recent attempts were made to perform measurements upon solidifi cation of cast-ing aluminum alloys that naturally contain considerable amounts of liquid phase (eutectics) even at temperatures close to the solidus [15]. In fact, up to now these experimental techniques have been used mainly to validate dif-ferent analytical or numerical models.

The Kozeny–Carman relationship is one of the analytical models that describe the permeability of a coherent solid network using structure param-eters. This relationship couples the porosity and tortuosity of the structure to the permeability as follows [16, 17]:

K = B φ3

___ S v 2

, (4.4)

where φ is the porosity, Sv is the specifi c surface area of the solid phase, and B is a geometrical factor.

For solidifi cation, this relationship is frequently written in the following form:

K = (1 – fs)3

_______ kKC S v 2 f s 2

, (4.5)

where fs is the solid fraction and kKC is the Kozeny–Carman constant taken equal to 5 for equiaxed structures [14].




It should be noted that the Kozeny–Carman relationship can be written in different ways depending on which structure parameter is most important for the permeability. In Equation 4.5 this is a solid–liquid interfacial area concentration, but sometimes dendrite arm spacing or grain size is used as such a parameter:

K = d2 ____ 180

(1 – fs)3

_______ f s 2

, (4.6)

where d is the secondary dendrite arm spacing. In the case of globular equiaxed grains, the secondary dendrite arm spacing in Equation 4.6 can be substituted for Dgr, the grain size [18].

In the case of columnar structures, when the fl ow occurs parallel to the dendrite trunks, the following relationship has been suggested [19, 20]:

K = C λ 1

2 (1 – fs)3

________ fs

, (4.7)

where λ1 is the primary dendrite arm spacing and C is a coeffi cient depend-ing on the fraction solid. This expression can be substituted by a simpler one (accurate within 10% of the experimental data for aluminum alloys) [20]:

K = λ 1

2 _________________

5000(1 – fs)(2fs – 1) . (4.8)

The applicability of Equation 4.7 to solid fractions larger than 0.35 is argu-able due to the complex shape of dendrites and, hence, interdendritic chan-nels [19].

The real dendritic structures are, of course, quite complicated and the melt fl ow through their network can go both along grain boundaries (extraden-dritic fl ow) and through intradendritic channels (intradendritic fl ow), as sug-gested by Dobatkin [7]. A rather complex model that describes extradendritic and intradendritic channels in the equiaxed mushy zone has been devel-oped by Wang and Beckermann [21]. They use a concept of grain envelope that separates the inner space of the grain from the exterior. Hence, there is an interfacial area concentration of the grain envelope that characterizes the interface between the grain envelope and the interdendritic liquid. The rest of the liquid exists between dendrite branches inside the envelope. The per-meability is then a function of the ratio of extradendritic and intradendritic permeabilities characterized by a factor β and the shape factor ψ [22]:

K = 1 __ S e 2

[ 3fe ___ ψβ ] 2 , (4.9)

where Se is the interfacial area concentration of the grain envelope and fe is the volume fraction of grain envelope. The ratio β can be written as:

β = βd ______________

[ f e n + ( βd ___ β1

) 2n

] 1/2n

, (4.10)




where βd and βl are the intradendritic and extradendritic permeabilities, respectively.

In numerical simulations, e.g., the modeling of macrosegregation [23], it is convenient to use permeability depending only on the solid fraction. Thus the so-called Blake–Kozeny equation is adopted:

K = k0 (1 – fs)3

_______ f s 2

, (4.11)

where k0 is a coeffi cient that takes into account structure length scale and morphology. For simplicity this coeffi cient is usually considered constant, which is a rather rough approximation.

The comparison of different approaches in the estimation of permeabil-ity, including experimental, analytical, and numerical methods, showed that for equiaxed grain structures and in the medium range of solid fractions the Kozeny–Carman relationship (4.5) gives adequate agreement with both experimental data [24, 25] and with numerical simulations of liquid fl ow through an array of close-packed spheres [24]. The Wang–Beckermann model has good agreement with experimental data but requires a detailed knowl-edge of the real structure. A summary of the results is given in Figure 4.3.

Numerical simulation of fl ow behavior in porous structures is a good method to evaluate the permeability in cases where information about the microstructure is available. This information can be in the form of measured quantities from micrographs or in the form of a 3D digitized structure. The parameters required to calculate the permeability are the solid–liquid

−1

−2

−3

−40.1 0.3 0.40.2

f1

Log(

KS

v2 )

AlSi5

AlCu16GR

AlCu10

AlSi4

AlCu10GR

Kozeny−Carman

Experiments by Nielsen et al.

Numerical simulations

Calculations with Wang−Beckermann model

Own experiments

FIGURE 4.3Comparison of analytical (Kozeny–Carman and Wang–Beckermann) and numerical calcu-lations [24] with experimental measurements of permeability [24, 25]. Index GR = a grain-refi ned sample.




interfacial area concentration, the liquid fraction or porosity and, in the case of numerical simulations, the viscosity and density of the liquid. Having detailed and adequate information on these quantities is the most important factor in determining the permeability. If more detailed and 3D informa-tion on the structures at low liquid fractions were available it could well be possible to simulate melt fl ow in real 3D networks. Nowadays, high- brilliance X-ray radiation produced in a synchrotron provides modern researchers with a tool for studying in situ solidifi cation, including the possibility of 3D tomography. Information obtained has already been used for numerical assessment of permeability in real alloy structures [9].

When choosing the way to evaluate the permeability of the mushy zone in metallic alloys, it is important to take into account the accuracy required. For most solidifi cation models the permeability needs to be known accurate to the order of magnitude. Therefore, the simplest approximation, which is the Kozeny–Carman relationship, can be reliably used for 0.6 < fs < 0.9. How-ever, its application to solid fractions approaching unity should be further investigated because of the so-called percolation limit at which the liquid fl ow stops although solidifi cation has not yet been completed.

Now let us look at the main mechanisms of macrosegregation in more detail.

4.1.3 Convection-Driven Macrosegregation

One of the most recognized phenomena behind macrosegregation is thermo-solutal convection, or the melt fl ow driven by temperature and concentration gradients. These gradients exist in the liquid (or more correctly, the fl uid) part of a casting (billet) due to uneven cooling of the whole volume. In the case of a DC-cast billet, the sides cool faster than the bottom, and there is a noticeable temperature difference between the central part and the periph-ery of the billet sump. Temperature difference determines the difference in density for the liquid. As a result of this thermal convection, the cooler liquid sinks* at the periphery and creates the momentum that forces the liquid in the center to rise. In the liquid part of the sump only thermal convection is active (if we neglect the solutal effects brought by washing out of liquid from the slurry zone, which is discussed later). As soon as the liquidus isotherm is passed, the partitioning of alloying elements starts to produce the difference in composition and corresponding difference in density, causing the solutal convection. Figure 4.4 shows the variation of densities of liquid and solid Al–Cu alloys in dependence on the composition, which refl ects the change of temperature during solidifi cation (compare with Figure 2.7) [26]. In alu-minum alloys and during DC casting, fl ow direction that resulted from both solutal and thermal convection coincide with each other, giving the overall fl ow pattern shown in Figure 4.5 [27].

* We assume here that the liquid becomes denser (heavier) on decreasing the temperature, which is the case for most alloys. Otherwise, the direction of liquid fl ow is opposite.




3.00

2.80

2.60

2.40

0 5 10 15 20 25

Den

sity

, g/c

m3

Cu, wt%

At solidus

At liquidus

FIGURE 4.4Compositional dependence of density for Al–Cu alloys at the solidus and liquidus tempera-tures [26]. Refer to Figure 2.7 for the correspondence with the temperature changes during solidifi cation.

Hot Watercooling

Cold

(a) (b)

FIGURE 4.5General thermo-solutal convective fl ow pattern in the sump of a billet during DC casting(a) and a result of simulation of thermo-solutal convection in an Al–4.5% Cu billet (corresponds to curve 1 in Figure 4.6) superimposed on the concentration map (lighter means more copper) and isotherms of liquidus, coherency, and solidus (b). (Reproduced with kind permission of The Minerals, Metals & Materials Society (TMS).)




The main reason why this fl ow may affect the distribution of alloying ele-ments in the billet cross-section is the penetration of this fl ow into the slurry zone and the washing out of the liquid with the composition already changed by the solidifi cation process. The interaction between the liquid pool and the transition zone of the billet was noted as the main reason for convection-driven segregation by Tageev in 1949 [28]. In addition, the thermo-solutal fl ow may assist in transporting the solid phase within the slurry region and to the liquid pool (see Figure 3.16 and Section 4.1.5).

Figure 4.5 shows that the penetration of the melt fl ow into the slurry zone occurs in the outer quarter of the billet cross-section. Thus, the solute-enriched liquid from this part of the billet is mixed with the bulk liquid and the resultant mixture is brought to the center of the billet. The result is cen-terline positive segregation, as shown in Figure 4.5b and curve 1 in Figure 4.6. At the billet periphery the melt fl ow is directed toward the surface (Fig-ure 4.5b). Here the liquid of the nominal composition penetrates the mushy zone and dilutes the melt that is enriched there by solidifi cation. Hence, a negative segregation at the billet periphery is facilitated (Figure 4.5b and curve 1 in Figure 4.6). Generally, we can conclude that the natural thermo-solutal convection in DC-cast billets of aluminum alloys enhances normal (direct) macrosegregation.

A rather simple experiment clearly demonstrates the dependence of the macrosegregation pattern on the extent and direction of thermo-solutal con-vection. Figure 4.7 shows the scheme of such an experiment with a screw

0.05

−0.05

−0.1

−0.150

0

0.02 0.04 0.06 0.08 0.1

Distance from the center, m

Rel

ativ

e co

ncen

trat

ion

of C

u

1

3

2

4

FIGURE 4.6Simulated distribution of Cu (relative concentration is (Cx – C0)/C0) along the radius of a 200-mm billet of an Al–4.5% Cu alloy: 1 = only thermo-solutal convection is included in the model, linear phase diagram; 2 = thermo-solutal convection and solidifi cation shrinkage are included in the model, linear phase diagram; 3 = same as (2) but the permeability K is increased two times; 4 = same as (2) but with Scheil approximation of solidifi cation path [27]. (Reproduced with kind permission of The Minerals, Metals & Materials Society (TMS).)




pump made of a refractory alloy submerged along the central vertical axis into the crucible fi lled with liquid Al–4.5% Cu alloy. The melt fl ow forced by this pump depends on the direction of screw rotation and can be either aligned with the natural thermo-solutal fl ow or opposite it. The action of the pump was verifi ed using computer simulations. It is important that the pump creates the melt fl ow in the axial direction of the sample, thus acting along the same directions as the thermo-solutal convection. During experi-ments the temperature in the vicinity of the pump was controlled to ensure that the pump operated in the fully liquid state and only infl uenced the fl ow pattern in the liquid part of the samples with subsequent penetration of the fl ow into the transition region. The experimental results on macrosegrega-tion profi les are shown in Figure 4.8. It is clear that the enhancement of the fl ow in the direction of thermo-solutal convection facilitates the positive centerline segregation, whereas the fl ow opposite to natural convection sup-presses it and effectively eliminates macrosegregation.

Real commercial alloys are always multicomponent. Different alloying ele-ments can have opposite contributions to the density of the mixed melt and, as a result, can affect the overall contribution of solutal convection to macro-segregation [29]. Let us take as an example an Al–Cu–Mg alloy.

Two cases can be considered: the macrosegregation of Cu without (Case 1) and with (Case 2) taking into account the macrosegregation of Mg. The solutal buoyancy caused by the addition of a second alloying element, which is only present in Case 2, may make some difference in the fi nal segregation pat-tern. It is expected that due to the negative contribution of Mg to the density in the liquid phase, which is opposite to the contribution by Cu, the extent

Crucible

Screwpump

Width

Hei

ght

FIGURE 4.7An experimental scheme with controlled convection using a screw pump submerged in the melt along the central axis of a crucible. The fl ow is organized either aligned with or opposite to the natural convective fl ow.




of (positive) macrosegregation of Cu in Case 2 would be less than in Case 1. Results shown in Figure 4.9 confi rm this estimation. Both Cases 1 and 2 pre-dict positive centerline segregation and in Case 2 the relative segregation of Cu is 0.017, which is about 20% less than in Case 1 (0.020). In general, the fl ow pattern will be similar to that shown in Figure 4.5b but with the following

0.40.20.0

−0.2−0.4

3020

10−40

−30−20

−100

1020

3040

Natural convection

Crucible width, mm

Crucible width, mm

Crucible width, mm

Rel

ativ

e se

greg

atio

nR

elat

ive

segr

egat

ion

Height, mm

Height, mm

Height, mm

Rel

ativ

e se

greg

atio

n

0.4

3020

10

3020

10

0.2

−0.2−0.4

0

0.4

0.2

−0.2−0.4

0

−40−30

−20−10

010

2030

40

−40−30

−20−10

010

2030

40

Aligned withnatural convection

Opposite tonatural convection

FIGURE 4.8Experimental macrosegregation pattern obtained using the setup shown in Figure 4.7. Three experiments were performed: with idle pump (natural convection), screw pump producing fl ow aligned with the natural convection, and screw pump producing fl ow opposite to natural convection.




changes caused by Mg. The fl ow beneath and along the liquidus contour and upward fl ow in the center of the liquid sump in Case 2 is weaker than in Case 1. Figure 4.10 illustrates the contribution of solutal buoyancy to the fl ow pattern in the billet sump by the velocity difference, which is calculated by the velocity fi eld in Case 1 minus that in Case 2. This velocity difference is more detectable close to the center of the billet, where an upward relative velocity component with a magnitude of 0.8 mm/s appears, corresponding very well to the place where the maximum difference in average concentra-tion occurs. This velocity component brings Cu from the solidifying part of the billet to the liquid part, effectively decreasing the concentration of copper in the center.

We can conclude that the addition of alloying elements, in this case Mg, will infl uence the fi nal segregation pattern by its contribution to the solutal buoy-ancy. It is important to consider the contribution of every solute to the buoy-ancy force because they may have opposite contributions to the overall fl ow.

4.1.4 Shrinkage-Driven Macrosegregation

Historical accounts summarized in Table 4.2 show that the importance of shrinkage-driven fl ows for the formation of inverse segregation was realized as early as the 1930s. Inverse segregation is caused by the movement of the solute-rich liquid in the direction opposite to the movement of the solidifi ca-tion front. In the case of DC casting, that would be a melt fl ow directed from the center to the periphery of a billet (ingot).

0.10.080.06

Rel

ativ

e co

ncen

trat

ion

of C

u an

d M

g


0.04

Cal. 2: Mg

Cal. 1: MgCal. 2: Cu

Cal. 1: Cu

0.02

0

0−0.05

−0.04

−0.03

−0.02

−0.01

0.01

0.02

FIGURE 4.9Calculated segregation profi les for a 200-mm round billet from a 2024-type (Al–Cu–Mg) alloy cast at 120 mm/min for two cases. In Case 1 only macrosegregation of Cu contributes to the solutal buoyancy, hence there is no segregation of Mg; in Case 2 both Cu and Mg contribute to the solutal buoyancy, hence both elements segregate. A Gulliver–Scheil solidifi cation path is implemented with a mapping technique [29] and no solidifi cation shrinkage is taken into account. (Reproduced with kind permission of Springer Science and Business Media.)




Original experiments performed by Livanov et al. [30] and Anoshkin [31] showed unambiguously the existence of melt fl ow in the mushy zone, its dependence on casting speed, and its infl uence on macrosegregation. Dur-ing DC casting of an aluminum alloy, steel partitions were installed into the billet concentrically in two modes: (1) only to the bottom of the sump (acting only in the liquid and slurry zones) and (2) with subsequent freezing into the billet (acting all the way to the fully solid billet). After the end of the casting, the billets were sawed in the horizontal plane and the chemical composition along the diameter and the billet axis was analyzed. There were no changes in chemical composition in both directions in the case when the partitions were acting only in the liquid and slurry zones of the billet, and there were no changes in the axial directions in all cases studied. However, when the parti-tions were frozen into the billet, a rather dramatic difference was observed in the radial direction of the billet, as illustrated in Figure 4.11. One can see that there is a remarkable difference in copper concentration between the different

L

S

Z0.3fs

XY

FIGURE 4.10Relative fl ow velocities (velocity fi eld in Case 1 minus that in Case 2) calculated for a steady-state casting of a 200-mm round billet from a 2024-type alloy at a casting speed of 120 mm/min [29]. Isotherms of liquidus (L), solidus (S), and coherency (0.3fs) are also shown. (Reproduced with kind permission of Springer Science and Business Media.)




sides of the partition. The trend depends on the casting speed. When the cast-ing speed is low, there is a decrease in copper content at the internal part of the partition, indicating that the solute-rich liquid tends to move toward the center of the billet. The inverse situation occurs at a higher casting speed, when the copper concentration systematically increases at the inner side of the partition and is much lower at its external part. This can be interpreted as clear evidence of the solute-rich fl ow toward the periphery of the billet. The driving force for such a melt fl ow in the mushy zone is the solidifi cation shrinkage.

Solidifi cation shrinkage is a result of density change during solidifi cation and occurs throughout the entire solidifi cation range. In the slurry zone, however, the solidifi cation shrinkage is easily compensated for by the melt fl ow. There is no pressure difference that may result in the additional fl ows and the solidifi cation shrinkage does not play any signifi cant role in the rela-tive movement of solid and liquid in the slurry zone, the main infl uence being exerted by thermo-solutal convection. Deeper into the mushy zone when the permeability is limited and the feeding of the solid phase is restricted, the solidifi cation shrinkage (assisted closer to the solidus by thermal contraction of the solid phase) causes the pressure difference over the solidifying layer of the mushy zone that creates the driving force for the so-called “shrinkage-driven” fl ow. The fl ow in the mushy zone, despite its small magnitude (veloci-ties are around 10−4 m/s or 6 mm/min as compared to casting speeds of 100 to 200 mm/min), involves the highly enriched liquid, which determines its signifi cance for macrosegregation. It is important that this fl ow is directed perpendicular to the solidifi cation front [11, 32]. Flemings bases modern mac-rosegregation theory on the interdendritic fl ow in the mushy zone and on the ratio between the velocities of solidifi cation front and the shrinkage-driven

Half with partitions

2

Cu, % Undisturbed half

30 mm/min4.8

4.4

4.04.6

4.2

3.8Surface Center

60 mm/min

Surface

A

2

4

55

C

1

3B

4

FIGURE 4.11Experimentally measured macrosegregation in a 330-mm billet from a 2024 (Al–Cu–Mg) alloy cast at 30 (1, 2) and 60 mm/min (3, 4, 5) [30]. Profi les 1 and 3 show the macrosegregation in the undisturbed part of the billet. Profi les 2, 4, and 5 show the macrosegregation in the part of the billet with partitions A, B, and C, respectively.




fl ow [32]. If the shrinkage-driven fl ow is just enough to feed the solid phase, then no macrosegregation occurs. A fl ow faster than the solidifi cation rate results in inverse segregation, whereas a fl ow with a speed less than the solid-ifi cation rate (or in the opposite direction) results in normal segregation.

In DC casting, shrinkage-driven fl ow is generally directed from a hotter part of the mushy zone to a colder one, and as such from the center to the periphery of a billet. There are two components to this fl ow. One is hori-zontal along the radius directed toward the billet surface, and the other is vertical, along the casting direction, as shown in Figure 4.12 [33]. Although the vertical downward fl ow will dilute the local volume element by bringing less enriched liquid into it, the negative centerline segregation will not form

Vh

Vshr

Vcast

Lm

α

α

FIGURE 4.12Schematic representation of the components of shrinkage-driven fl ow in the mushy zone of a DC-cast billet [33]. Isotherms of liquidus, coherency, and solidus are shown similar to those in Figure 4.10. Angle α characterizes the inclination of the solidifi cation front to the horizon; Lm is the thickness of the mushy zone; Vshr and Vh are the velocity of shrinkage-induced fl ow and its horizontal component. Black arrows show the direction of shrinkage-induced fl ow, whereas gray arrows show the direction of thermo-solutal convection. See Section 4.2.1 for more details. (Reproduced with kind permission of Elsevier/Pergamon.)




if only this vertical downward fl ow is present because as solidifi cation pro-ceeds the process eventually reaches the point that less and less solute is taken out and only solute accumulation occurs. It is the horizontal compo-nent that takes the solute away from the center to the surface [7, 11], though this solute transport physically occurs very slowly. Step by step, however, an overall solute transfer occurs from the center of the billet to its surface. The depletion in the center cannot be compensated for, as there is no horizontal infl ow of the solute from more enriched regions. At the surface, there is a pile-up of the solute because there is no outfl ow. Because the magnitude of the shrinkage-induced fl ow is dependent on the shrinkage ratio, one may conclude that the corresponding macrosegregation should depend on the dimensions of the mushy zone and the degree of shrinkage, as will be con-sidered in more detail in Section 4.2.1.

Computer simulations using a model that includes solidifi cation shrinkage demonstrate the high potential of the shrinkage-driven fl ow in the forma-tion of inverse segregation during DC casting [27, 29]. Figures 4.6 (curves 2–4) and 4.13 give clear evidence of this; hence, shrinkage-induced fl ow can adequately explain the occurrence of inverse segregation.

4.1.5 Floating Grains and Macrosegregation

Movement and sedimentation/growth of solid grains in the slurry zone is sometimes considered the main mechanism of centerline segregation in DC-cast billets and ingots [34, 35]. As already mentioned in Section 4.1.1, the link between the transport of solute-lean grains and inverse segregation is not a

0.06

0.04

−0.04

−0.06

−0.08

−0.10

0.02

0

−0.02

0.02 0.04 0.06 0.08 0.1


Rel

ativ

e se

greg

atio

nof

Cu

and

Mg

Case A: CuCase A: MgCase B: CuCase B: Mg

FIGURE 4.13Calculated segregation profi les for a 200-mm round billet from a 2024-type (Al–Cu–Mg) alloy cast at 120 mm/min for two cases. In Case A permeability is 6.67 × 10−11m2 and in Case B, 5 × 10−10m2. The model includes the contributions of thermo-solutal buoyancy and solidifi ca-tion shrinkage. A Gulliver–Scheil solidifi cation path is implemented with a mapping tech-nique [29]. (Reproduced with kind permission of Springer Science and Business Media.)




novelty. This idea was already rejected in the 1940s because it contradicted the cases of inverse segregation in castings where no fl oating grains had been found. However, the applicability of this mechanism of macrosegregation to DC casting was supported by numerous experimental observations of a duplex structure, characterized by a mixture of fi ne-branched dendrites and coarse-cell dendrites (see Section 3.3) near the ingot centerline (Figure 3.17), e.g., Refs. [36–39]. The occurrence of such a duplex structure is taken as an evidence of solid-phase transport (fl oating) within the transition region. Hence, the mech-anism of macrosegregation by fl oating grains was reinstated in the 1980s.

The mechanisms of fl oating-grain formation have been already discussed in Section 3.3. Let us now look at the reasons why negative segregation in the DC-cast billet/ingot center is attributed by some researchers to the pres-ence and accumulation of the fl oating dendrites at the bottom of the sump, although their presence is not a necessary condition for the centerline deple-tion to occur [40–42]. The mainstream concept assumes that if the coarse-cell dendrites are solute poor, fi ne-cell dendrites are richer in solute and close in their average composition to the nominal alloy composition [34, 43]. Quite an opposite line of argument is proposed by Chu and Jacoby [35], who sug-gested that the fi ne-cell dendrites originated from the start of the solidifi cation in the region of rapid cooling (i.e., dendrites detached and transported from the periphery to the center and frozen into the solidifi cation front without further growth) and coarse-cell grains grew in situ. Consequently in their opinion, fi ne-cell grains are solute poor and responsible for the negative cen-terline segregation, while coarse-cell dendrites are solute rich. Yet another suggestion is made by Glenn et al. [44] and Lesoult et al. [45] based on their examination of 5051-alloy DC-cast ingots. They found that the structure of a nongrain-refi ned billet contains, along with normal-size dendritic grains, fi ne grains, which allegedly represent grain fragments brought from the mold walls to the ingot center by turbulent fl ows.

If we assume that fl oating grains arrive from other parts of the billet and settle in its center, then they effectively bring there more solid phase than should be there at this point in time and space. Because the primary solid in hypoeutectic aluminum alloys is always depleted of the solute, the accu-mulation of the fl oating grains has to result in negative segregation. In addi-tion, the different solidifi cation schedule of coarse- and fi ne-cell dendrites may result in different bulk compositions of these grains. Obviously, the microsegregation pattern of fl oating grains would shed light on the extent of their potential infl uence on macrosegregation. Quantitative analysis of com-positional differences in the grain interior is, however, rarely reported, e.g., Yu and Granger [34] have observed a uniform plateau of copper depletion away from the cell boundary in a coarse dendrite.

We performed local composition electron-probe microanalysis (EPMA) measurements on several coarse and fi ne cells in the duplex structures found in the center of 200-mm billets from a 2024 alloy cast at 80 mm/min [46]. The nominal composition of this alloy was 3.6 wt% Cu and 1.4 wt% Mg. Figure 4.14 shows the line scans of Cu and Mg concentrations in



Macrosegregation

147

3.0

2.5

2.0

1.5

1.0

0.5

0.00

Con

cent

ratio

n, w

t%

Con

cent

ratio

n, w

t%

100 200 300 400 500 600 700Distance, µm Distance, µm

MgCu

3.0

2.5

2.0

1.5

0.5

0.00

1.0

100 200 300 400 500 600 700

MgCu

(a) (b)

FIGURE 4.14Measured microsegregation in coarse-cell (a) and fi ne-cell (b) grains found in the center of a 200-mm billet cast at 80 mm/min from a nongrain-refi ned 2024 alloy [40].

CR

C_62816_C

h004.indd 147C

RC

_62816_Ch004.indd 147

3/15/2008 12:22:21 PM



nongrain-refi ned (NGR) DC-cast samples, clearly demonstrating that the coarser cells are more solute depleted compared to the “regular” fi ner cells. Grain refi ning (GR) does not change the situation. From these measure-ments, the minimum Cu and Mg concentrations in the center of dendrite cells are listed in Table 4.4.

The contribution of fl oating grains seems to explain the negative cen-terline segregation alone, not invoking other mechanisms, e.g., shrink-age-induced fl ow. The latter conclusion is in direct opposition to the conclusion of the previous subsection, where we stated that shrinkage-induced fl ow can adequately explain inverse segregation. Obviously, these two mechanisms are the key factors in the formation of negative centerline segregation.

It is important to realize that shrinkage-induced fl ow is a physical phe-nomenon that is always present in the transition region of a solidifying billet, whereas the transport of solute-lean solid with its accumulation in a certain part of a casting is a conditional incident, the occurrence of which depends on a number of factors such as the design of the mold, structure evolution, temperature regime, and the direction of strong fl ows in the sump. It is clear that the only contribution that the fl oating grains can make to the segrega-tion is negative. This can be explicitly demonstrated by experiments with solidifi cation under constant fl ow, as explained below.

Figure 4.15a shows the simulated transport of solid grains in the experi-ment where the solidifi cation occurs in a chilled cavity embedded into the bottom of a trough with a constantly fl owing melt [47, 48]. The corresponding macrostructure with a clearly visible pile of equiaxed grains at the down-stream side of the cavity is given in Figure 4.15b (at low fl ow velocities, the structure appears to be uniform and columnar along the entire length of the sample). The change in the macrosegregation pattern with the increas-ing melt fl ow velocity is presented in Figure 4.15c. There is an obvious cor-relation between the negative segregation at the downstream section of the sample and the transport of solute-lean grains by the fl ow.

The correct estimation of this contribution in the case of DC casting, however, poses a diffi culty because the complexity of phenomena that should be taken into account includes, among other things, the following: (1) microsegregat-ion development as a result of different solidifi cation times and diffusion

TABLE 4.4

Minimum Concentrations of Alloying Elements in Dendrite Cells Measured by EPMA and Difference between Nongrain-Refi ned (NGR) and Grain-Refi ned (GR) Samples from 2024-Alloy Billet Cast at 80 mm/min

Element

NGR GR

Coarse Fine Difference Coarse Fine Difference

Cu, % 0.72 1.1 0.38 0.73 1.1 0.37Mg, % 0.47 0.7 0.23 0.46 0.7 0.24




distances; (2) altered solidifi cation path because of the local introduction of excess solid fraction with corresponding change of eutectic fraction; (3) changed kinetics of dendrite coarsening, recalescence, and back diffusion; and (4) competition between the settling of fl oating grains under gravity and the resistance to such settling from the solid-phase dragging by viscous liq-uid. The evaluation of the contribution of coarse-cell grains to the centerline macrosegregation based on experimental measurements will be discussed in Section 4.3.

0.10

0.05

0.00

−0.05

−0.100 20 40 60 80 100

Longitudinal section of sample, mm

Rel

ativ

e se

greg

atio

n of

cop

per

0.03 m/s

0.1 m/s

0.3 m/s

(a)

(b)

(c)

FIGURE 4.15Effect of solid transport by melt fl ow on the macrosegregation in an Al–4.5% Cu alloy:(a) computer-simulated transport of solid upon melt fl ow from the left to the right; (b) cor-responding macrostructure obtained at a fl ow velocity of 0.3 m/s; and (c) macrosegregation patterns obtained at different melt velocities showing the increasing negative segregation at the downstream part of the sample [48].




Taking into account that there is still a great deal of controversy in the reported data on the appearance of duplex structure in DC-cast billets and ingots and the corresponding macrosegregation pattern (Table 4.5), doubts were expressed as to what extent the fl oating grains could affect macroseg-regation [32]. At the present stage of our expertise, we can conclude that the fl oating grains contribute to inverse segregation but the extent of this contri-bution should be examined in every specifi c case. It is possible that the con-tradictory results are caused by the varying mobility of the fl oating grains (or fragments) in diverse amounts, sizes, and morphologies of the solid phase under different convective conditions. Lesoult [49] reported that the intense negative segregation resulted from a moderate fl ux density of the fl oating solid phase, whereas the segregation was effectively reduced when a larger density of the fl oating grains caused their early immobility. Smaller fl oating

TABLE 4.5

Summary of Reported Observations on Duplex Grain Structures and Macrosegregation in DC-Cast Ingots and Billets

Alloy

Ingot Size, Billet

Diameter, mm

Not Grain Refi ned (NGR)*

Grain Refi ned (GR)* Macrosegregation Ref.

Al 900 × 300 — D*, CF* N/A 36Al–(1–4)% Cu

∅200 D*, CF* — Inverse 37, 38

Al–3.6% Cu

∅200 Not observed D, CF Inverse in both cases

40

Al–4.5% Cu

∅533.4 Not observed D, CF Inverse for NGR 41

Normal in GR2024 ∅400 D, CF — Normal at low

casting speed43

Inverse at high casting speed

2024 Flat ingot, commercial size

— D, CF Inverse 34

2024 ∅200 D, CF D, CF Inverse in both cases

72

7075 ∅200 Not observed D, CF Inverse in both cases

42

7XXX 1270 × 406.5 D, FF* — Inverse 355182 1850 × 550 D, FF (fi ne

grains)Not observed, FF (fi ne grains)

Inverse in both cases

45

5182 1050 × 550 D, FF (fi ne grains)

FF (fi ne grains)

Inverse in both cases

44

6061 ∅200 Not observed D, CF Inverse in both cases

39

* GR = grain refi ned; NGR = not grain refi ned; CF = fl oating grains with coarse cells; FF = fl oating grains with fi ne cells; D = duplex structure.




grains in grain-refi ned billets may be also less prone to sedimentation than larger grains in nongrain-refi ned counterparts. The change in coherency temperature and permeability with grain refi nement can affect the ratio of contributions of different macrosegregation mechanisms and the resultant distribution of alloying elements.

Successful attempts to model the contribution of fl oating grains to the mac-rosegregation in DC casting include a description of the relative velocity of the solid and liquid phases by a special drag term [23]. A more physical approach includes the tracing of growing solid particles and, hence, multiphase model-ing. Application of this methodology to steel ingot casting showed its feasi-bility for modeling macrosegregation caused by fl oating grains [49].

4.1.6 Deformation-Driven Macrosegregation

Volumetric deformation of the dendritic network in the coherent mushy zone caused by thermal contraction (see Section 5.1 of Chapter 5) can cause melt fl ow [50]. Like the solidifi cation-shrinkage fl ow, it occurs in the mushy zone and its velocity is rather small. It has been shown that the contribution of this fl ow to macrosegregation can be as important as that of shrinkage-induced fl ow [50].

Deformation can be external (in the case of continuous casting of steels) or thermally induced. The latter applies to DC casting of Al alloys. Results indicate [50, 51] that even small volumetric strains (∼2%), which are associ-ated with thermally induced deformations, can lead to segregations compa-rable to those resulting from solidifi cation shrinkage. The compression will artifi cially increase the amount of the solid phase in the unit volume and squeeze the solute-enriched liquid out of this volume, effectively decreasing locally the concentration of the solute. In this case, the mechanism of nega-tive (inverse) segregation is similar to that caused by the transport of fl oat-ing grains. In the case of tension that occurs in the center of a DC-cast billet, the situation should be the reverse. The solute-rich liquid penetrates into the volume, resulting in positive segregation.

This mechanism is important for the subsurface and surface segregation [52] when exudation occurs (see Figure 3.31). Close to the surface of a billet, relatively high solidifi cation and cooling rates in a narrow shell result in large thermal gradients. Under such conditions, the rate of solidifi cation shrinkage and thermal contraction is also high compared to the inner part of the billet. This causes large shrinkage- and deformation-induced fl ows directed toward the surface of the billet. These fl ows are further assisted by the aligned convec-tion fl ow (see Figure 3.9), the metallostatic pressure of the melt, compressive strains in the billet outer shell, and weakening of the mushy zone by partial remelting in the air-gap region (Figure 3.14a). As a consequence of all these phenomena, a strong positive segregation forms at the surface of the billet (sometimes extended to liquation or penetration of the liquid melt through the shell) accompanied by a zone of negative subsurface segregation. The latter is a result of incomplete compensation of the surface segregation by the incoming melt and strong compressive strain that squeezes the liquid to the surface.




4.2 Effects of Process Parameters on Macrosegregation during DC Casting

4.2.1 Effect of Casting Speed on Macrosegregation during DC Casting

Since the early years of DC casting practice, it has been recognized that the casting speed is the main parameter that determines the extent of mac-rosegregation, and in some cases even the macrosegregation direction (see Figure 4.11). The latter issue is discussed in Section 4.3.

The effect of casting speed on macrosegregation is illustrated in Figure 4.16. The empirical rule says that the casting speed should not exceed the ratio A/D in order to minimize the macrosegregation in a round billet while maintain-ing acceptable productivity. In this ratio A is an alloy-dependent constant ranging from 25,000 to 33,300 for aluminum alloys and D is the billet diam-eter in mm [7]. Hence, for a 200-mm billet, the maximum allowable casting speed should be between 125 and 167 mm/min, which gives the maximum relative segregation of 3 to 6% of the nominal composition (Figure 4.16).

Dobatkin [53] emphasized two main geometrical parameters of the sump that affect the extent of inverse macrosegregation upon DC casting, namely, the size of the transition region and the slope of the solidifi cation front (see Figure 4.12).

We have already discussed in detail the effect of casting speed on the dimensions of the transition region (see Section 3.1). The fact that the center-line macrosegregation increases with the casting speed gives a hint that there might be a correlation between the macrosegregation and the dimensions of the transition region. Indeed, the macrosegregation profi les observed at dif-ferent casting speeds, being normalized to the vertical thickness of the tran-sition region, fall onto each other through the most of the billet cross-section, except for the subsurface region, as shown in Figure 4.17 [54]. The peculiar behavior of macrosegregation at the periphery of the billet can be explained by the additional contribution of deformation- and shrinkage-driven fl ows (see Section 4.1.6).

Why does the wider transition region facilitate inverse macrosegregation? It is important to note that the deepening of the sump and widening of the transition regions affect mostly the dimensions of the slurry zone where the main acting mechanisms of macrosegregation are thermo-solutal convec-tion and fl oating grains. These two mechanisms act in different directions as we discussed in Sections 4.1.3 and 4.1.5. They can also compensate for each other. On the one hand, the larger slurry zone creates a possibility for the convective fl ows to penetrate more deeply into the transition region and wash out more solute-rich liquid at midradius and bring it to the center of the billet. On the other hand, there are more possibilities for the transport of solid phase (fl oating grains) in a loose slurry zone and their settling in the center of the billet [38, 54]. The deepening of the sump also changes the geometry of the solidifi cation front by increasing the slope of the solidifi cation front and




affecting the shrinkage-induced fl ow in the mushy zone. This phenomenon tends to produce inverse macrosegregation (see Section 4.1.4).

A simple analytical model [33] is suggested to estimate the magnitude of the shrinkage-induced macrosegregation during DC casting in relation to the steepness of the solidifi cation front. The shrinkage-induced fl ow, which is almost perpendicular to the coherency-fraction contour, can be broken down into two components (Figure 4.12).

Let us consider a small volume in the mushy zone as shown in the Figure 4.12 insert. The shrinkage fl ow is directed normally to the coherency isotherm. The coherency isotherm in this region can be approximated by a straight line that

0.04

0.02

−0.02

−0.04

−0.06

−0.08

−0.10

0

40 80 120 160 200

0 40 80 120 160 200



Dev

iatio

n of

cop

per

conc

entr

atio

n fr

om th

e av

erag

e Center

Center

120 mm/min

160 mm/min

120 mm/min

160 mm/min

0.06

0.04

0.02

−0.02

−0.04

−0.06

−0.08

0

Dev

iatio

n of

iron

conc

entr

atio

n fr

om th

e av

erag

e

(a)

(b)

FIGURE 4.16Effect of casting speed on macrosegregation in a 200-mm billet of an Al–4.3% Cu (0.22% Fe and 0.11% Si as impurities): (a) relative segregation of copper and (b) relative segregation of iron.




is inclined with the angle α to the horizon. The total solidifi cation shrinkage in the direction normal to the coherency isotherm can be written as

ε = Lm cos α Sβfl, (4.12)

where Lm is the vertical dimension of the mushy zone, S is the surface area of the horizontal cross-section of the volume, β is the volumetric shrinkage (can be taken as 0.1 for aluminum alloys), α is the angle between the tangent to the coherency isotherm and the horizon, and fl is the liquid volume fraction.

This shrinkage has to be compensated for by the infl ow Vshr with the fol-lowing volume:

V = VshrS Lm/Vcast, (4.13)

where Vshr is the shrinkage fl ow velocity, Vcast is the casting speed, and Lm/Vcast is the average time available for the shrinkage.

By equating (4.12) and (4.13) we obtain:

Vshr = Vcast fl β cos α. (4.14)

We assume that only the horizontal component of shrinkage fl ow is respon-sible for segregation, which is

Vh = Vshr sin α = Vcast fl β(sin2α)/2. (4.15)

The solute fl ux caused by this horizontal velocity will be

F = CLVh = CLVcast fl β(sin2α)/2, (4.16)

where CL is the liquid concentration.

FIGURE 4.17Relative macrosegregation of copper normalized to the vertical thickness of the transition region (see Figure 3.2c) in a 200-mm billet from an Al–4.3% Cu alloy [54]. (Reproduced with kind permission of Elsevier.)

0.006

0.002

−0.002

−0.006

−0.010 20 40 60 80 100

Distance from the billet center, mm

Nor

mal

ized

rel

ativ

ese

greg

atio

n of

Cu

120 mm/min 200 mm/min




The integration of Equation 4.16 over time will lead to the overall amount of transferred solute. The evolution of the liquid phase concentration (CL ) and volume fraction ( fl) derived from heat transfer analysis have to be pro-vided to complete this integration. For a fi rst-order approximation, we can assume a linear evolution of liquid volume fraction during the period of time (t) required to pass the mushy zone, i.e.,

fl = 1 – (Vcast/Lm)t (4.17)

and then the liquid concentration in weight percent can be obtained based on the lever rule (for simplicity, though nonequilibrium solidifi cation path with back diffusion in the solid should be taken into account in a more thor-ough analysis):

CL = C0 ______________________

f1 ___________

1 + (1 – f1)β (1 – K) + K

100%, (4.18)

where C0 is the nominal concentration and K is the partition coeffi cient. Note that the presence of the shrinkage ratio β here is for the purpose of convert-ing the liquid volume fraction into the weight fraction.

The total amount of the transferred solute during the time period of Lm/Vcast or the horizontal solute transfer distance is as follows:

Lh = ∫ 0 Lm/Vcast

CLf1 Vcast β(sin2α)/2 dt

= Vcast β(sin2α) ∫ 0 Lm/Vcast

C0 f1 _____________________

f1 ___________

1 + (1 – f1)β (1 – K) + K

dt. (4.19)

Let us take as an example the Al–Cu system [33]. K is equal to 0.171 and the shrinkage ratio β can be set to 0.1 (though the solidifi cation shrinkage can be as large as 0.117 for an Al–4% Cu alloy). Substituting these values in Equation 4.19, we obtain

Lh = 0.78 C0Lmβ(sin2α)/2. (4.20)

The derivative of Equation 4.20 with respect to radial distance from the billet center R will lead to the net effl ux and is a measure of the macrosegregation caused by solidifi cation shrinkage, with (dLh/dR)/C0 refl ecting the relative segregation.

The application of this analytical model to DC casting at 100 and 120 mm/min of a binary Al–4% Cu alloy yielded the following results [33]. The isotherms of liquidus, coherency, and solidus are calculated upon computer simulation of DC casting using the model and software described in detail elsewhere [55] and the representation of results is given in Figure 4.18a,b. Different casting




FIGURE 4.18Evaluation of shrinkage-induced macrosegregation upon DC casting of a 200-mm billet from an Al–Cu alloy at 100 (a,c,e) and 120 mm/min (b,d,f): (a,b) solidifi cation profi les with isotherms of liquidus, coherency, and solidus; (c,d) amount of transferred solute along the billet radius; and (e,f) relative macrosegregation (net solute effl ux) [33]. (Reproduced with kind permission of Elsevier/Pergamon.)

(d)(c)

(b)(a)

0

0.1

0.2

0.3

Lh = 0.00737 + 0.1676 R − 0.0373 R2 +0.0036 R3 − 1.5627 10−4 R4

Lh = −0.00089 + 0.0832 R − 0.0128 R2 +0.0006 R3 − 1.6399 10−5 R4

Am

ount

of t

rans

ferr

ed s

olut

e (L

h), w

t% c

m

Am

ount

of t

rans

ferr

ed s

olut

e (L

h), w

t% c

m

Distance from the billet center (R), cmDistance from the center of the billet (R), cm

108642010864200

0.1

0.2

0.3




0.04

0.02

0

−0.02

−0.04

−0.06

0.04

0.02

−0.02

−0.04

−0.06

0

0

0 2 4 6 8 10

Rel

ativ

e ne

t sol

ute

efflu

xR

elat

ive

net s

olut

e ef

flux

Distance from the billet center, cm

2 4 6 8 10

Distance from the billet center, cm

(e)

(f)

FIGURE 4.18 (Continued)




speeds result in different profi les of the isotherms and different dimensions of the sump and the mushy zone. It can be expected that a shallower sump in the case of casting at 100 mm/min will produce less macrosegregation.

Figure 4.18c,d shows the distributions of the amount of transferred solute (or the horizontal solute transfer distance) along the radius of the billet. In this case, we took Lm and α at equal distances from the center to the surface of the billet from the profi les in Figure 4.18a,b, and C0 is taken as 4% Cu.

Simple analysis of the curves shows that the maximum solute transfer dis-tance corresponds to the region around midradius of the billet, where, in practice, the segregation is either negligible or positive. It seems logical if we interpret the results as follows. Solute-rich liquid is transported by the shrinkage-induced fl ow from the center to the periphery of the billet (see Figure 4.11). The greater the distance from the center, the more solute is transported. Starting from the distance corresponding to the maximum in Figure 4.18c,d, more solute arrives than goes away, so the accumulation of solute starts, producing positive segregation. The macrosegregation can then be better described by the fi rst derivative of the amount of transferred solute (with the negative sign) divided by the alloy nominal composition, which refl ects the relative segregation. Figure 4.18e,f shows the radial distribution of the fi rst derivative of the polynomial fi ts shown in Figure 4.18c,d. One can easily see a good semiquantitative agreement between the distribution in Figure 4.19d and the real macrosegregation profi le shown in Figure 4.16a. It should be noted that the suggested model adequately responds to the change of the casting conditions and corresponding change in the sump profi le. Less segregation is predicted for the shallower sump at a lower casting speed, as shown in Figure 4.18c,d.

Additional features in the real segregation profi le in Figure 4.16a, such as the fl atter region of slightly positive segregation in the midradius region and the negative subsurface segregation, can be attributed to the effects of thermo-solutal convective fl ows and surface exudation, which were not accounted for in the model shown. The fl oating grains may also contribute to the extent of the negative centerline segregation.

The proposed model links the macrosegregation to the local slope of the coherency isotherm, the thickness of the mushy zone, the shrinkage ratio, and the solidifi cation path of an alloy.

We can conclude that the main reasons for the dependency of macroseg-regation on the casting speed are the changes in the dimensions of the transition region (which affects thermo-solutal convection and transport of solid) and the slope of the solidifi cation front (which affects shrinkage-driven segregation). In practice, the macrosegregation is negligible when the slope α (Figure 4.12) is less than 30° and acceptable when it is less than 60° [53].

Another factor that may change the geometry of the sump is the water fl ow rate. But, as we already discussed in Section 3.1, its effect is insignifi cant if the amount of cooling provided is suffi cient. Our data on macrosegregation confi rm this [54].




4.2.2 Effect of Melt Temperature on Macrosegregation during DC Casting

The melt temperature is an important part of any casting recipe. We have already discussed in Sections 3.1, 3.3, and 3.4 the effects of melt temperature on the geometry of the sump, fl ow patterns during casting, and the structure of aluminum billets. The increase in the melt temperature does not greatly affect the geometry of the solidifi cation front and the dimensions of the mushy zone, but it narrows the transition region by lowering the position of the liq-uidus in the sump (see Figures 3.8c,d and 3.9). A higher melt temperature also facilitates the strong melt fl ow toward the surface of the billet and the deeper penetration of the melt fl ow into the mushy zone (Figure 3.9). The amount of fl oating grains decreases with melt temperature at low casting speeds and increases at high casting speeds (Figure 3.24c,d). What is even more important for macrosegregation is that at high melt temperatures the fl oating grains concentrate in the central part of the billet at low casting speeds and tend to spread more over the entire cross-section at high casting speeds. These observations allow us to forecast the effect of melt temperature on macrosegregation. The thermo-solutal convection in the subsurface area and a generally weaker shell of the billet will facilitate subsurface segrega-tion and, possibly, liquation and bleed-outs (see Fig ure 3.31). The thermo-solutal currents in the slurry and mushy zone that are directed toward the center of the billet bring more solute-rich and heavier liquid to the center and should promote positive centerline segregation. This tendency is opposed by an increased amount of fl oating grains in the center, which are, however, also distributed more evenly in the billet cross-section. Finally, the contribution of shrinkage-driven segregation should not depend on the melt temperature because the thickness of the mushy zone and the slope of the solidifi cation front are not affected by the melt temperature. All in all, we can expect, as the melt temperature increases, a higher macrosegregation close to the surface of the billet and no signifi cant changes in the rest of the billet. Our experimental observations fully support this conclusion, as illustrated in Figure 4.19.

Our results and arguments concur with the suggestions of Dobatkin [53], Tarapore [56], and Reese [57] that macrosegregation should decrease as cast-ing temperature increases.

4.2.3 Dimensions of the Billet: Scaling Rule of Macrosegregation

Examination of numerous data on macrosegregation indicates a distinct dependence of macrosegregation on the dimensions of the billet or ingot. Taking into account the interrelation between macrosegregation and the shape and dimensions of the sump, which are affected by the size of the bil-let and the casting speed, this dependence should be a function of these two parameters.

Livanov et al. [30] studied macrosegregation in 2024-alloy billets in a wide range of billet diameters, from 50 to 470 mm, and of casting speeds, from 30 to 350 mm/min. They showed that the extent and direction of




FIGURE 4.19Experimentally measured macrosegregation in Al–2.8% Cu billets cast at 200 mm/min and at different melt temperatures [38]. (Reproduced with kind permission of Springer Science and Business Media.)

0.3

0.2

0.1

0.0

Rel

ativ

e se

greg

atio

n of

Cu

12080

160200

Billet cross-section, mm40

0 700

720

740

760


Centerline

200

180

160

140

120

100

80

60

40

20

0700 710 720 730 740 750 760

Bill

et c

ross

-sec

tion,

mm

0.06 0.06 0.06 0.060.080.02 0.02 0.02

0.020.02

0.020.02

0.02

−0.02

−0.02

Centerline

−0.02−0.02−0.02

−0.02−0.02−0.02

0.02





macrosegregation depends on the average cooling rate in the solidifi cation range. Macrosegregation is negligible at very low cooling rates (no microseg-regation), then the normal segregation occurs. Upon further increasing the cooling rate, normal segregation starts to decrease and, eventually, turns to inverse segregation. There exists a certain cooling rate for each billet diameter when the centerline macrosegregation is negligible. For example, this threshold cooling rate is about 2.3 K/s for a billet diameter of 300 mm and almost 11 K/s for a diameter of 168 mm (see Figure 4.20a). The extent of inverse segregation increases with the cooling rate, and then decreases at very high cooling rates. This dependence resembles the cooling-rate dependence of microsegregation, as shown in Figure 2.9a. Evidently, the cooling rate cannot be a universal cri-terion for macrosegregation because its critical value depends on the casting dimensions. Livanov et al. made the remarkable conclusion that the similarity of thermal and strain fi elds should lead to a similarity in macrosegregation patterns. They suggested a similarity criterion [30]:

SC = VcastD/a, (4.21)

where Vcast is the casting speed in mm/min, D is the billet diameter in mm, and a is the constant that is about 12,000 (for normal molds without hot tops) for zero-centerline segregation. This dependence is illustrated in Figure 4.20b. If SC is less than unity, the macrosegregation is normal, hence positive in the center of the billet. If SC is larger than unity, the macroseg-regation is inverse, therefore negative in the center. The transition from positive to negative macrosegregation for a 200-mm billet should occur at a casting speed of about 60 mm/min, which is far below the optimum (and commercially applicable) speed.

Let us try to summarize the results on macrosegregation in a wider range of casting speeds, dimensions, and alloys, based on references and our own data. In this case we need a report on the billet (ingot) dimensions together with the casting speed and macrosegregation observations; the latter can be qualitative (normal vs. inverse or positive vs. negative). Tables 4.6 and 4.7 present a literature survey of the last 30 years that includes experimental and numerical (calculation) reports [7, 23, 30, 34, 35, 41, 43, 45, 54, 58–63]. All these seemingly diverse results are then plotted on billet diameter–casting speed axes, as shown in Figure 4.21. One can clearly see that it is possible to draw a line that separates the regions of positive (under the line) and nega-tive (above the line) centerline macrosegregation in aluminum-alloy billets [64]. The line for grain-refi ned alloys (VcastD = 21,774) apparently lies higher than the one for nongrain-refi ned alloys (VcastD = 12,465), indicating more possibilities for positive centerline segregation in grain-refi ned billets, which agrees well with the experimental observations of Finn et al. [41] and our own results, shown in Figure 4.22.

Our computer simulations of three billets of different dimensions produced at different casting speeds (the four cases shown in Figure 4.23) give results that fi t well onto the plot in Figure 4.21 (shown by crosses), with one regime




FIGURE 4.20Relationships between the macrosegregation pattern of Cu and (a) cooling rate for different billet diameters and (b) scaling parameter VcastD. These plots are based on experimental data for DC casting of a 2024-type alloy in conventional molds without hot top [30].

0.3

0.2

0.1

−0.1

−0.2

−0.3

−0.4

0

330 mm

168 mm

70 mm

10 100

Cooling rate, K/s

0.3

0.2

0.1

−0.1

−0.2

−0.3

−0.4

−0.5

0

Dev

iatio

n fr

om a

vera

geco

mpo

sitio

n, w

t%D

evia

tion

from

ave

rage

com

posi

tion,

wt%

5000 10000 15000 20000 25000 30000 35000

VcD, mm2/min

(a)

(b)

producing a positive centerline (normal) segregation, i.e., the 200-mm billet cast at 60 mm/min. These values are in good agreement with the experimen-tal data of Livanov et al. [30]. This is a good indication that the model we used works well and agrees with a set of experimental data.



Macrosegregation

163

TABLE 4.6

Relationship between the Size of a Billet, Casting Speed, and Positive Centerline Macrosegregation [66]

D, mm* Vcast, mm/min Grain** (perm.) Comp., wt% Comments*** Ref.

218–282calc 85–75 GR, ea 5.25 Cu — 59400calc 60 GR, ea 4.5 Cu — 60400calc 60 GR, ea 4.5 Cu Positive without FG; negative with FG 23400exp 38 NGR. ea 2024 Mold with hot top 43450exp 60 NGR/GR 6.0 Cu Positive/negative; airslip mold; in NGR only

central point is positive61

450calc 60 NGR/GR 6.0 Cu Positive overestimated/negative underestimated; airslip mold; K0 two times less than in [23]

61

533.4exp 38 GR 4.5 Cu Casting with fl oat 41533.4calc 38 GR (high) 4.5 Cu — 58

NGR (low) 4.5 Cu Negligible segregation 58Standard commercial ingot

45–60 GR, ea Al–Cu–Mg Scatter, at 45.4 mm/min—some points are positive; at 60 mm/min—more negative

34

55–330exp 30–200 N/A 2024 Mold without hot top 30

* exp. – experimental data; calc. – data from computer simulation.** GR – grain refi ned; NGR – not grain refi ned; ea – equiaxed; perm. – permeability.*** FG – fl oating grains; K0 – permeability constant.

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TABLE 4.7

Relationship between the Size of a Billet, Casting Speed, and Negative Centerline Macrosegregation* [66]

D, mmVcast,

mm/minGrain

(perm.) Comp., wt% Comments Ref.

533.4exp 38 NGR 4.5 Cu — 41533.4calc 38 GR fi ne (low) 4.5 Cu — 58195–370exp 60–190 NGR Al–Cu–Mg Mold without hot top 71800 × 550 60 NGR; GR 5182 Larger in GR; not

related to FG that are observed in NGR

45

150 54 (High) 4.5 Cu high viscosity 62253calc, exp N/A (High) 4.5 Cu — 63200exp 120–200 NGR, ea 4.5 Cu Fraction of FG

increases with Vcast

54

406 × 1270 N/A ea Al-Zn-Mg-Cu FG have fi ne DAS 35Large commercial ingot

45–60 GR, ea Al–Cu–Mg FG have coarse DAS, 30 vol.%

34

55–330exp 35–350 N/A 2024 Mold without hot top 30

* See footnotes for Table 4.6.

FIGURE 4.21Centerline segregation in relation to casting speed and billet diameter based on reference data from Tables 4.6 and 4.7 (circles and rhombs) and our computer simulations [66] (crosses). Lines represent a threshold between positive (under the line) and negative (above the line) segrega-tion for nongrained-refi ned (solid line) and grain-refi ned alloys (dashed line).

400

300

200

100

0

0 200 400 600Billet diameter, mm

Cas

ting

spee

d, m

m/m

in

Positive, GR

Positive, our simulationNegative, our simulation

Positive, NGR

Negative, NGRNegative, GR

NGR

GR




Let us now look now at the geometry of the sump in the billet and try to draw some conclusions about the reasons for the scaling dependence given in Figure 4.21. Figure 4.23 summarizes the calculated segregation profi les. One can see that not only the direction of macrosegregation but also its magnitude differs in relation to the diameter/casting speed ratio. Figure 4.24 and Table 4.8 show the sump profi les and relevant sump parameters for the test cases.

FIGURE 4.22Experimental data on macrosegregation of copper in a 200-mm grain-refi ned Al–3.8% Cu billet cast at two casting speeds [40]. Casting at 80 mm/min produces positive centerline segregation in a 200-mm billet.

0.06

0.04

0.02

−0.02

−0.04

−0.06

−0.080

0

50 100 150 200


80 mm/min

120 mm/min

Center

Rel

ativ

e se

greg

atio

n of

Cu

192

FIGURE 4.23Computer-simulated macrosegregation profi les (deviation of Cu concentration from the nomi-nal alloy composition Al–4.5% Cu) along the radius (billet center at R = 0) for four test cases [64]. Casting at 60 mm/min produces positive centerline segregation in a 200-mm billet.

0.1

0

0.05

−0.05

−0.1

−0.15

−0.2

Rel

ativ

e se

greg

atio

n of

Cu

0 0.05 0.1 0.15 0.2 0.25

Radius, m

2

3

4

1

1 - diameter 500 mm, speed 60 mm/min2 - diameter 200 mm, speed 200 mm/min3 - diameter 200 mm, speed 60 mm/min4 - diameter 100 mm, speed 300 mm/min




FIGURE 4.24Positions of liquidus (i.e., 0.05% solid) (L) and solidus (S) isotherms in 200-mm Al–4.5% Cu bil-lets cast at 200 (a, inverse segregation) and 60 mm/min (b, normal segregation). Characteristic features given in Table 4.8 are marked in (a). Typical fl ow pattern is shown in (b) with convec-tion fl ows indicated in the upper part of the transition region and the shrinkage-induced fl ow indicated closer to the solidus.

S

L

Mold regionS

um

p d

epth

Dis

tan

ce b

etw

een

liqu

idu

s an

d s

olid

us

S

(b)(a)

Angle

Regression analysis of data given in Table 4.8 shows that the strongest infl u-ence on the extent and sign of centerline macrosegregation (CS) is exerted by the thickness of the transition region normalized to the billet radius (Th) and the slope of the solidus isotherm (A):

CS = –0.06124 – 4.341 × 10–2 Th + 1.64 × 10–3A; R = 0.65, (4.22)

where R is the regression coeffi cient. Note that the thicker transition region (and the sump depth correlated with it) facilitates the negative segregation, whereas the larger angle (i.e., a smaller slope of the solidifi cation front and a fl atter sump) acts in the opposite direction. These observations correlate well with the dependences that we discussed in Section 4.2.1.

The scaling dependence in Figure 4.21 and corresponding sump param-eters in Table 4.8 show that the increased casting speed at the same billet diameter will result in a deeper sump with a steeper solidifi cation front, and in the transition from normal to inverse segregation. The analysis of the same scaling dependence tells us that for a given casting speed, a larger bil-let is more prone to negative (inverse) centerline segregation. A large billet usually means a slower cooling, a deeper sump, and a thicker transition region. The thicker transition region implies a thicker slurry zone. A higher



Macrosegregation

167

TABLE 4.8

Parameters of the Sump for the Test Cases Shown in Figure 4.23 [64]

Casting Parameters

CenterlineSegregation (S)

Sump Depth, mm/the Same Normalized

to the Billet Radius

Distance between Liquidus and Solidus in the Center of the Billet, mm/ the Same Normalized to the

Billet Radius (Th in Equation 4.22)

Angle between the Billet Axis and the Tangent to the Solidus

Isotherm at Midradius (A in Equation 4.22), degrees

Vcast, mm/min D, mm

300 100 – 0.04, negative 153/3.06 70.5/1.41 15200 200 – 0.16, strongly

negative220/2.2 117/1.17 16

60 500 – 0.02, slightly negative

383.5/1.534 82.4/0.33 23

60 200 +0.01, slightly positive

88/0.47 47/0.47 55

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ratio between the thickness of the transition region and the billet radius sug-gests a deeper sump.

Flood and Davidson performed a scaling analysis of the fl ow patterns in the sump of a DC-cast ingot and came to the conclusion that the sensitivity of macrosegregation to the ingot thickness and to the casting speed was a result of the changed sump dimensions [65]. They stated that the increase in ingot thickness in the commercially relevant range (400 to 600 mm) had a greater effect on the sump depth than the casting speed.

The interpretation of the observations summarized in Table 4.8 and by Equation 4.22 agrees with the suggestions of Anoshkin and Dobatkin [66] that the direction and extent of macrosegregation is determined by a ratio between thermo-solutal convection and shrinkage-induced fl ow, as shown by arrows in Figure 4.24b (see also Section 4.2.4). This relationship, however, is not straightforward, and the fi nal macrosegregation pattern is a result of a fragile balance between the amount and composition of liquid that is brought to the center of the billet by the convective fl ow and taken from the center by the shrinkage-induced fl ow, and the direction of relative movement of solid and liquid phases in the slurry zone.

As we already know, there are several co-related phenomena that can affect the macrosegregation. First of all, the deep sump enhances the shrinkage-induced fl ow and the negative centerline segregation, as we discussed in Section 4.2.1. At the same time, the wide slurry zone with loose solid grains suspended and fl oating in the liquid matrix provides more opportunities for the thermo-solutal convection fl ow to penetrate into the transition zone and to wash out solute-rich liquid from it (Figure 4.24b). This liquid can go up and mix with the bulk melt or can be transported toward the center along the liqui-dus isotherm, settle there because of its higher density, and effectively induce the positive segregation. This process is facilitated by grain refi ning, when the solid phase becomes coherent at lower temperatures (higher fractions of solid). Hence, the effect of the extent of the transition region is a function of the direction of thermo-solutal fl ow in the slurry zone. On the other hand, the “loose” slurry zone creates more opportunities for the fl oating grains to be generated. These grains can be brought to the central part of the billet and sediment there, contributing to the negative segregation. In this process, fi ner and thus lighter grains in a grain-refi ned billet may be less prone to settling and can be carried out more easily by the convective fl ow. This means less negative contribution from fl oating grains in the grain-refi ned billet.

It is important that the transport of solid be assisted by the convection. Floating grains generally follow the direction of liquid fl ow. At the same time, it is the relative movement of the solid and liquid (settling of the solid phase under gravity, fi ltration of the solid through the slurry) that actually affects the macrosegregation. At the end, the ratio between positive contri-bution of thermo-solutal convection and negative contribution of fl oating grains can be such that (1) each process compensates for the other and the negative centerline segregation results from the shrinkage-induced fl ow; (2) thermo-solutal convection prevails and the segregation pattern depends on




the ratio between convective and shrinkage contributions; and (3) fl oating grains intensely accumulate in the center, enhancing the negative segregation caused by solidifi cation shrinkage.

Positive centerline segregation can be achieved if the contribution of thermo-solutal convection dominates over the other mechanisms of macrosegregation. This is possible when the sump is shallow and the transition region is narrow, hence at low casting speeds and small billet diameters. Unfortunately, the actual casting speeds that may result in positive or negligible macrosegrega-tion are much lower than those that are currently used in industry.

4.2.4 Effect of Forced Convection on Macrosegregation during DC Casting

Anoshkin and Dobatkin [31, 66] suggest that the transition from negative (inverse) to positive (normal) segregation is possible during DC casting, especially in the presence of forced convection (mechanical or electromag-netic stirring). They link this transition to the ratio between the convection in the slurry part of the billet that washes solute-rich melt from the mushy zone and brings it to the center and the shrinkage-induced fl ow that takes the solute-rich liquid inside the mushy zone from the center toward the surface, and also to the solidifi cation shrinkage of the alloy. This concept is illustrated in Figure 4.25. The higher the intensity of forced convection in the sump and the smaller the solidifi cation shrinkage, the greater the possibility of normal (positive) macrosegregation.

FIGURE 4.25Effect of forced convection on the extent and type of macrosegregation upon DC casting; arrows show the tendency in the case of decreasing solidifi cation shrinkage [31].

Nor

mal

Inve

rse

Intensity of forced convection

Ext

ent o

f mac

rose

greg

atio

n




Livanov et al. [30] noted that the threshold value of VcastD (Equation 4.21) is larger for billets cast using an electromagnetic mold, when intensive melt fl ows are created by the electromagnetic fi eld. Figure 4.26 shows the experi-mental results on macrosegregation in billets of a 2024-type alloy cast by electromagnetic casting (EMC) (Figure 4.26a) and with mechanical stirring (Figure 4.26b). In both cases a suffi cient degree of forced convection results in the normal (positive) segregation. This fact indicates the potential of the liquid convection in the formation of macrosegregation patterns. Similar results were obtained upon EMC of a 7075 alloy [30, 67].

4.3 Effect of Composition on Macrosegregation: Macrosegregation in Commercial Aluminum Alloys

The fundamental reason for macrosegregation lies in the partitioning of solute elements between liquid and solid phases during solidifi cation (see Section 2.2). It is, therefore, not surprising that the extent and pattern of macrosegregation depend on the partition coeffi cient K, i.e., on its deviation from unity and on whether it is less than or greater than 1. This coeffi cient is defi ned as the ratio of the solid composition to the liquid composition. Partition coeffi cients for some alloying elements in aluminum are listed in Table 4.9. There is no partitioning and, therefore, segregation if K = 1. Most of the alloying elements and impurities (e.g., Cu, Mg, Zn, Li, Mn, Si, Fe) are present in aluminum alloys at hypoeutectic concentrations with K < 1. In this case, the lower the coeffi cient, the greater the macrosegregation. The overall macrosegregation pattern of such elements is similar to those already dis-cussed in this chapter (see, for example, Figures 4.13, 4.16). Certain elements (Ti, Zr, Cr) that have a peritectic reaction with aluminum (with K > 1) exhibit a segregating tendency that is exactly opposite, i.e., with a positive centerline segregation that increases with the size of the partition coeffi -cient. Figure 4.27 illustrates these phenomena by experimentally measured macrosegregation profi les. Iron has a much more pronounced segregation compared to manganese, and titanium has an opposite segregation pattern.

Figure 4.28 graphically illustrates the increasing tendency for segregation with decreasing partition coeffi cient of the alloying elements with K < 1. The extent of segregation of a particular alloying element depends more on the base alloy itself rather than on the absolute concentration of the alloying element [68].

Most commercial aluminum alloys are grain refi ned during casting in order to make a fi ne-grained structure favorable for downstream processing and to improve the alloy castability, including hot-tearing resistance (see Sec-tions 5.3.1 and 5.4.2 of Chapter 5). The effect of grain refi ning on macroseg-regation remains, however, unclear; relatively few reports with controversial




FIGURE 4.26Effect of electromagnetic (a) and mechanical (b) stirring on the macrosegregation of copper in 2024-alloy billets [30, 31, 53].

5.1

4.9

4.7

4.5

4.3

4.1

3.90 50 100 150 200 250


(a)

(b)

Cu,

%C

u,%

EMC

DC casting

Strong stirringModerate stirringWeak stirring

4.8

4.6

4.4

4.2

4

3.80 40 80 120


160 200 240 280




results are available on this subject [34, 39, 41, 42, 44, 45, 68–70]. Grain refi ning modifi es the resistance to fl ow through the solid network (mushy zone), affect-ing the permeability (see Section 4.1.2). According to Equations 4.5–4.8, grain refi nement should decrease the permeability of the mushy zone constructed out of fi ner grains, though the fi nal result would depend on the morphology and packing of the solid phase [24]. At the same time, grain refi nement lowers the coherency [71] and rigidity temperatures (see Section 5.1 of Chapter 5). For example, the solid fraction at coherency in an Al–4% Cu alloy increases from 0.23 to 0.45 upon addition of 0.05% Ti [71], and the solid fraction at rigid-ity in a 2024 alloy increases with grain refi nement from 0.75 to 0.82 [72] (see Figure 5.9 in Chapter 5). The lower permeability will hinder the shrinkage-induced fl ow, narrow the rigid mushy zone, and prevent the penetration of convective fl ows into the rigid mushy zone. On the other hand, the lower coherency temperature means a wider slurry zone with more possibilities of convective fl ows and transport of fl oating. In addition, the smaller size of these fl oating crystals impede their settling ability. It is not surprising that the consequences of grain refi nement can be quite different, depending on the ratio of the contributions of all these effects.

FIGURE 4.27Macrosegregation profi les of Mn (K = 0.8), Fe (K = 0.03) and Ti (K = 9) in a 200-mm billet from a 2024 alloy cast at 120 mm/min [42]. Data for Ti are divided by 10.

0.06

0.04

0.02

0

−0.02

−0.04

−0.06

−0.080 50 100 150


Rel

ativ

e se

greg

atio

n

Center

Mn

Fe

Ti

TABLE 4.9

Partition Coeffi cients for Some Alloying Elements in Aluminum

Element Fe Si Cu Mg Zn Mn Ti Cr

K 0.03 0.13 0.17 0.43 0.45 0.82 9.0 2.0




The reference data given in Tables 4.6 and 4.7 and in Figure 4.21 show that grain-refi ned alloys are more prone to positive centerline segregation. Hence, grain refi nement favors normal segregation. The published accounts are, however, very diverse.

Gariepy and Caron [68] examined the effect of grain-refi ning practices on centerline macrosegregation in sheet ingots of commercial 3104 (Al–Mn–Mg), 5182 (Al–Mg–Mn), and 6009 (Al–Si–Mg) alloys. They concluded that the extent of centerline segregation increases with the increasing Ti content, as demonstrated in Figure 4.29.

Segregation tendency is also dependent on the type of grain refi ner. For the same feeding conditions, the application of a more potent Al5Ti0.2B mas-ter alloy leads to more severe segregation as compared to a 5182 alloy refi ned with an Al–6% Ti master alloy or not grain refi ned at all [44, 68]. The detri-mental effect of grain refi ning on macrosegregation is usually ascribed to the nucleation of a larger number of free dendrites in the wider slurry region and consequent sweeping of those to the bottom and center of the sump. We already know that the fl oating-grain phenomenon cannot always explain the observed macrosegregation pattern (see, e.g., Table 4.5). It is suggested that the tendency for “grain-refi ning-aided” macrosegregation would depend on the alloy composition, following the “grain refi nability” of the various alloy systems (see Section 2.4).

FIGURE 4.28Centerline segregation of alloying elements vs. partition coeffi cient [68]. The deviation of con-centration is taken as the sum of the absolute values of the lowest (negative) deviation and the average of the high (positive) deviation points, and characterizes the overall amplitude of macrosegregation.

35

30

25

20

10

5

00.0 0.2 0.4 0.6

15

0.8 1.0

Partition coefficient, K

AA 6009

AA 3104

AA 5182

Dev

iatio

n of

con

cent

ratio

n, %

Fe Si Cu MgMn




Joly et al. [45, 69] also reported that grain refi ning caused more severe centerline segregation in a DC-cast Al–Mg sheet ingot. Their results agree well with the results of Glenn et al. [44] obtained independently on a similar ingot, as shown in Figure 4.30. Remarkably, duplex microstructures (mixture of coarse and fi ne grains) were observed only in the nongrain-refi ned ingot, where the segregation is less severe, but not in the grain-refi ned ingot. Con-sequently, the negative centerline segregation is not specifi cally associated with the presence of duplex microstructures (or “fl oating” grains). It was pointed out that grain morphology was an important factor to be consid-ered [45], which was more dendritic in the nongrain-refi ned ingot and more globular after grain refi ning. Combined effects of the changed permeabil-ity and movement of equiaxed grains were considered responsible for the experimentally observed segregation patterns shown in Figure 4.30.

Contrary to the above observations, there is a report that shows that grain refi ning induces positive centerline segregation upon casting 530-mm billets of an Al–4.5% Cu alloy [41]. A bi-level feeding system with a central spout and a fl oating diffuser was used. The nongrain-refi ned counterpart exhib-ited the usual pattern of negative centerline segregation. The most interest-ing observation was that the grain-refi ned billet exhibited positive centerline segregation despite the presence of fl oating grains in the central portion of the billet, whereas the negative centerline segregation in nongrain-refi ned

FIGURE 4.29Effect of grain refi ning and melt feeding system on centerline segregation of Mg in commercial 3104 ingots [68]. The deviation of concentration is taken as the sum of the absolute values of the lowest (negative) deviation and the average of the high (positive) deviation points, and charac-terizes the overall amplitude of macrosegregation.

20

18

16

14

12

10

8

6

4

0.000 0.001

Dev

iatio

n of

Mg

conc

entr

atio

n, %

0.002 0.003 0.004 0.005 0.006

Ti, %

COMBO bag

Channel bag

HeadscreenAA 3104




billet occurred without any fl oating grains noticed. It was suggested, in line with our previous discussion, that the different ratio between the shrink-age-driven fl ow and the advection of the solute-rich liquid caused the observed phenomena. We have observed positive segregation in a grain-refi ned Al–Cu billet cast a low casting speed in our level-pour DC casting system, which turns to negative centerline segregation at a higher casting speed (Figure 4.22).

Our studies on various commercial Al alloys showed that addition of an Al3Ti1B grain refi ner did not affect the macrosegregation in 200-mm bil-lets cast at 80 to 120 mm/min [39, 42, 70], as illustrated in Figure 4.31. At the same time, we observed duplex structures with depleted fl oating grains (see Figure 4.14 and Table 4.4). The number of these fl oating, coarse-cell grains signifi cantly increases with grain refi nement, from 35 to 65–70 vol.% [70].

The data on the composition of coarse-cell and fi ne-cell grains may help us understand the phenomena involved in the formation of the fi nal mac-rosegregation pattern in the central portion of the billet. The integration over the microsegregation profi les like those shown in Figure 4.14 allows us to estimate the composition of different grains. Let us look at the results in Table 4.10. The bulk composition of coarse-cell grain is confi rmed to be less than the nominal alloy composition. Somewhat surprisingly the composi-tion of the fi ne-cell grain areas appears to be higher than nominal, especially in the grain-refi ned alloy. This contradicts the usual view that the fi ne-cell grain structure refl ects the structure of nominal composition (without mac-rosegregation) [34]. The real situation is far from that. It seems that the bulk

FIGURE 4.30Macrosegregation in commercial ingots from a 5182 alloy. Data along the thickness (triangles) are given for a 1850 × 550 mm2 ingot cast at 60 mm/min [69] and data along the width (circles) are given for a 1050 × 550 mm2 ingot [44]. Dashed lines represent nongrain-refi ned part of the ingot and solid lines show the grain-refi ned part of the ingot (0.015% Ti in [44] and 0.003 Ti in [69]).

15

10

5

−5

−10

−150

0

Dev

iatio

n of

Mg

conc

entr

atio

nfr

om a

vera

ge, %

100 200 300 400 500 600

Distance, mm

Centerline CenterlineAlong thickness Along width




composition of fi ne-cell regions gives us an opportunity to estimate the con-tribution of different mechanisms to macrosegregation. Using the data in Table 4.10 we can separate the macrosegregation caused by fl oating grains and by other mechanisms. The results of this analysis are shown in Table 4.11. Indisputably, the coarse-cell, fl oating grains are able to produce strong nega-tive segregation, especially in the grain-refi ned alloy. In fact, the structure consisting entirely of fl oating grains would give centerline segregation about one order of magnitude larger than the observed macrosegregation.

0.06

0.04

0.02

−0.02

−0.04CuMg

CuMg

−0.06

−0.08

0.06

0.04

0.02

−0.02

−0.04

−0.06

−0.080 20 40 60 80 100 120 140 160 180 200

192

0

0 20 40 60 80 100 120 140 160 180

192

200

0

Distance, mm

Center

Center

∆C∆C

Distance, mm

(a)

(b)

FIGURE 4.31Measured relative macrosegregation in 200-mm billets cast at 80 mm/min from a nongrain-refi ned (a) and grain-refi ned (b) 2024 alloy [70].




TABLE 4.10

Measured Using EPMA Average Compositions of Grains in the Central Part of Nongrain-Refi ned and Grain-Refi ned 2024-Alloy Billets Cast at 80 and 120 mm/min

Structure Type

Nongrain Refi ned, 80 mm/min* Grain Refi ned, 80 mm/min*

Grain Refi ned, 120 mm/min*

Line Scan Area Scan** Line Scan Area Scan** Line Scan

Cu, % Mg, % Cu, % Mg, % Cu, % Mg, % Cu, % Mg, % Cu, % Mg, %

Coarse-cell grains

2.55 0.96 2.92 1.08 2.19 0.94 3.32 1.13 1.58 0.08

Fine-cell grains

3.9 1.48 3.32 1.13 4.01 1.56 4.38 1.43 3.49 1.51

* Nominal alloys composition: 3.5% Cu, 1.4% Mg. Grain-refi ned alloys additionally contain 0.006–0.008% Ti.

** Results on area scan are shown for comparison. Although the areas were chosen so as to refl ect coarse-cell or fi ne-cell grains, portions of mixed structures were inevitably measured.

TABLE 4.11

Estimated Relative Centerline Segregation in Nongrain-Refi ned and Grain-Refi ned 2024-Alloy Billets Cast at a Speed of 80 mm/min; Data from Line-Scan Analysis in Table 4.10 Are Used

Assumption

Nongrain Refi ned Grain Refi ned

∆Cu ∆Mg ∆Cu ∆Mg

100% fi ne-cell structure +0.11 +0.05 +0.15 +0.11100% coarse-cell structure –0.27 –0.32 –0.37 –0.33

In contrast, the structure consisting only of fi ne-cell grains would give positive (in the case of a grain-refi ned billet strongly positive) centerline segregation. We know that in the absence of fl oating grains the main acting mechanisms of macrosegregation are thermo-solutal convection and shrinkage-induced fl ow. Taking into account the shallow profi le of the sump at the given, low casting speed, we can conclude that the enrichment of fi ne-cell grain struc-ture is mostly due to the solute brought to this structure by convective fl ows. (As shown in Figure 4.18e, the contribution of shrinkage-induced fl ow to the relative segregation of copper should be less than |−0.02|.) Therefore, the effect of coarse-cell grains on the overall macrosegregation is always nega-tive and somewhat larger in the grain-refi ned structure. The impact of the enriched fi ne-cell grains and, hence, of thermo-solutal convection is much more pronounced in the grain-refi ned structure, where it can produce posi-tive centerline macrosegregation.

Obviously, the measured values given in Table 4.10 are rather local and, therefore, the specifi c numbers may change. But the overall trend in the vari-ation in macrosegregation induced by different grain structures is clear.




Based on our analysis of the mechanisms of macrosegregation and on the experimental evidence presented in Tables 4.4, 4.10, and 4.11 and in the refer-ence literature, we can suggest the following line of logic for explaining some seemingly controversial experimental results.

A stronger penetration of the convective fl ows into the slurry zone of the grain-refi ned billet in combination with the hindered shrinkage-induced fl ow in the dense mushy zone facilitates the normal segregation (positive seg-regation in fi ne-cell structure in Table 4.11). On the other hand, the strongly depleted fl oating grains appear on the massive scale in the grain-refi ned slurry zone and may constitute the bulk of the macrostructure (negative segregation in coarse-cell structure in Table 4.11). These processes compete with one another, depending on the scale of the casting, the casting speed, and the corresponding sump profi le. The resulting macrosegregation may then seem unaffected by the grain refi nement, simply because the convec-tive-induced enrichment and fl oating-grain-induced depletion compensate for each other (Figure 4.31b). However, if the grain refi nement effectively hampers the shrinkage-induced fl ow, while opening the possibilities for more active convective fl ows in the slurry, then the result can be positive centerline segregation, as observed by Finn et al. [41] and by us, as shown in Figure 4.22. Otherwise, grain refi nement can result in more pronounced negative macrosegregation, as has been reported elsewhere [44, 68, 69].

In the nongrain-refi ned billet (with a columnar grain structure [41] or coarser equiaxed structure in our experiments) the slurry zone turns into mush at a higher temperature, preventing effi cient convection, while the shrinkage fl ow is rather strong (less positive segregation in fi ne-cell struc-ture in Table 4.11). The amount of fl oating grains is lower than in the grain-refi ned billet, though they still contribute to the negative segregation (see the coarse-cell structure in Table 4.11). The experimentally observed macrosegre-gation will depend on the ratio between the convective and shrinkage fl ows as well as on the amount of coarse-cell grains. All the processes can damp one another, producing negligible segregation, as shown in Figure 4.31a.

In a billet with a deeper sump because of larger size [41] or higher cast-ing speed (Figure 4.22) the shrinkage-induced fl ow may prevail, shifting the pattern toward the negative centerline segregation. This is true for both grain-refi ned and nongrain-refi ned billets. The results shown in Table 4.10 (compare entries for grain-refi ned structures at 80 and 120 mm/min) confi rm that the fi ne-cell regions become less enriched in the solutes with increasing casting speed. This indicates that the shrinkage-induced fl ow is more active in taking away the enriched liquid that was brought to the center by thermo-solutal convection. The amount of fl oating grains does not change in grain-refi ned billets cast at different casting speeds. So their contribution to the negative centerline segregation can be associated only with their somewhat larger depletion of solute at a higher casting speed, as given in Table 4.10.

It is worth noting that the casting parameters (speed and size) in the experi-ments of Finn et al. [41] were close to the threshold condition for the transition from positive to negative centerline segregation described by Figure 4.21.




The choice of a feeding system is also important, as illustrated in Figure 4.29. Melt distribution through a channel- or combo-bag induces much more varia-tion in the centerline segregation with grain refi ning than when a headscreen is used [68]. At the same time, the extent of macrosegregation is considerably less in the case of the combo-bag than in other cases studied [68]. The main difference that the feeding system produces is the melt fl ow pattern in the liquid and slurry parts of the sump. The headscreen directs the fl ow along the sides of the ingot and downward, enhancing the natural convection fl ow. The combo-bag and channel-bag are designed for the change in the natural fl ow. In this case the channels or openings direct the fl ow either opposite to the natural convection or at some angle toward it (see also the effects of the screw pump in Figure 4.8 and EMC in Figure 4.26a). When the fl ow is directed downward in the central portion of the sump, then the macrosegre-gation can be minimized [68]. Similar experimental data were obtained for a 5182 alloy [68].

The experimental, analytical, and numerical data given in this chapter demonstrate unambiguously that the macrosegregation upon DC casting of aluminum alloys is a very complex phenomenon that cannot be explained by a single mechanism. The seemingly controversial and diverse results reported in the literature are the consequences of the intricate interaction between different mechanisms of macrosegregation that can eventually produce any result, from positive to negative. The analysis of macroseg-regation should be always performed taking into account all the possible mechanisms that can reveal themselves to varying extents, depending on the experimental conditions. At the present level of our understanding, we can conclude that we have the means (including experimental, analytical and numerical tools) to deal with the macrosegregation mechanisms known to us, individually or in some combination. The development of the model that would include all of the mechanisms in a coherent manner is the chal-lenge of the immediate future. In the past, the revelation of the true nature of a macrosegregation pattern observed under particular experimental con-ditions has been based largely on guesswork, but more recently, educated guesswork.

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183

5Hot Tearing

Casting practice is only too much familiar with various defects occurring in the fi nal product. One of the most severe and unrecoverable defects is hot tearing, also known as hot cracking or hot shortness. Hot tearing is the for-mation of an irreversible crack (failure) in the still semisolid casting.

The solidifi cation of alloys always occurs in some temperature range, i.e., the solidifi cation or freezing range. Unlike pure metals, which solidify at one temperature, alloys transform gradually from liquid to solid over a (wide) temperature interval. During casting there is a considerable time when the alloy consists of both solid and liquid. The semisolid state can be divided into two classes: slurry and mush. Slurry is defi ned as a liquid with suspended solid particles. Upon decreasing temperature, the solid phase nucleates, grows in a form of grain (usually dendritic in shape), and, starting from a certain point in the solidifi cation range, these solid grains begin to interact with one another, fi rst by sensing the presence of neighbors, then by coming into con-tact and bridging with them, and fi nally by forming a continuous skeleton of the solid phase. At a certain temperature, when solid grains start to interact with one another, the material fi rst changes its viscous behavior and later develops a certain strength [1]. The temperature at which the grains start to sense one another is called the coherency point, and the temperature at which the continuous solid network is formed is called the rigidity point. Below the coherency temperature, the material is called a mush. The solid fraction at which this transition occurs varies between 0.25 and 0.6, depending on the morphology of the solid grains [1]. In DC casting, the name “mushy zone” is often applied to the entire transition region between liquidus and solidus (see Figure 3.1a), which is misleading. The upper part of the transition region is actually a slurry because solid grains are suspended and can freely move in the liquid. A real mush is formed only after the temperature has dropped below the coherency temperature. Below the rigidity point, the semi-solid body acquires the main characteristics of the solid phase—retention of the shape and mechanical properties, such as strength and ductility [3].

Because of the strongly different mechanical behaviors of these different semi-solid states, slurries are usually described by viscosity-based models, and mush is usually described by deformation-based models [2]. The viscos-ity-based models start from the liquid side and are modifi ed to take into account the effect of the increasing amount of solid particles. The deforma-tion-based models are based on models for hot working, which are modifi ed to take into account the presence of liquid. The transition from a slurry to a mush remains a complicated problem to model, and a satisfactory model,




which describes the behavior for the complete solidifi cation range, is yet to be developed.

The solidifi cation process can be divided into four stages, based on the permeability of the solid network [4–7] (see also Section 4.1.2):

1. Mass feeding, in which both liquid and solid are free to move. 2. Interdendritic feeding, in which, after the dendrites have formed a

coherent skeleton, the remaining liquid has to fl ow through the den-dritic network. A pressure gradient (pressure drop) may develop across the mushy zone from solidifi cation shrinkage occurring deeper in the mushy zone. However, at this stage the permeability of the network is still large enough to prevent pore formation.

3. Interdendritic separation, in which the liquid network becomes frag-mented and pore formation or hot tearing may occur. With increas-ing solid fraction, liquid is isolated in pockets or immobilized by surface tension. When the permeability of the solid network becomes too small for the liquid to fl ow, further thermal contraction of the solid will cause pore formation or hot tearing.

4. Interdendritic bridging or solid feeding, in which the ingot has developed a considerable strength and solid-state creep compensates for fur-ther contraction. At the fi nal stage of solidifi cation ( fs > 0.9), only iso-lated liquid pockets remain and the ingot has considerable strength. Only solid-state creep can now compensate for solidifi cation shrink-age and thermal stresses.

Recently, the mushy zone was modeled with an emphasis on its coherency and feeding characteristics [8]. Its has been shown for an Al–1% Cu alloy that clusters of grains start to form at solid fractions about 0.97. This process involves more and more grains, and at about fs = 0.99 large grain clusters are formed with a few isolated liquid fi lms inside. Between solid frac-tions of 0.99 and 1.0 the solid network is continuous and the liquid phase survives only in separated pockets. This evolution of the mush structure causes the localization of feeding. Starting from the fraction of solid above 0.97 the melt fl ow begins to “prefer” some paths along grain boundaries, while other channels begin to “dry out” despite the fact that they still exist. As a result, the permeability of the mushy zone decreases at higher solid fraction more rapidly than predicted by the Kozeny–Carman relationship (see Equations 4.4–4.11 and Figure 4.3). Such a feeding localization along with solidifi cation shrinkage induces a pressure difference between metal-lostatic pressure on the hotter part of the mush and a lower pressure in forming cavities on the cooler part of the mush. This local pressure drop and insuffi cient feeding ability may result in the formation of cavities and, eventually, cracks.

From many studies [9–13] starting already in the 1950s, and reviewed by Novikov [3], Sigworth [14], and Eskin et al. [15], it appears that hot tears



Hot Tearing 185

initiate above the solidus temperature and propagate in the interdendritic liq-uid fi lm. The fracture surface is usually a smooth layer and sometimes shows solid bridges that connect or have connected both sides of the crack [7, 13, 16–21]. During solidifi cation, the liquid fl ow through the mushy zone decreases until it becomes insuffi cient to fi ll initiated cavities so that they can grow further.

In this chapter we mainly consider the last two stages of solidifi cation because in the slurry and upper mush regions the feeding is usually suffi cient to avoid any casting defects. It is mainly at the “interdendritic separation” stage when the casting is vulnerable to pore formation and hot tearing.

Industrial and fundamental studies show that hot tearing occurs in the late stages of solidifi cation when the volume fraction of solid is above 85–95% and the solid phase is organized in a continuous network of grains. How-ever, a hot crack would not appear if there were not some precondition for its formation. One of the main preconditions for hot tearing is the existence of tensile stresses in certain sections of the casting.

During DC casting of aluminum alloys, the primary and secondary cool-ing causes strong thermal gradients in the ingot and a corresponding uneven thermal contraction of different sections of the casting, which may lead to distortion of the ingot shape (e.g., butt curl, butt swell, rolling face pull-in) and/or hot tearing and cold cracking. Therefore, we may conclude that ther-mal contraction of the solid phase during solidifi cation is one of the major physical phenomena involved in the formation of hot cracks.

5.1 Thermal Contraction during Solidification

Hot tearing or hot cracking occurs in the lower part of the solidifi cation range, close to the solidus, when the solid fraction is more than 0.9 [7, 15]. At this point, the mushy zone is defi nitely coherent and consists of interconnected solid grains [1], but the liquid fi lm still exists between most of the grains.

The term coherency (or coherency temperature) should be used with cau-tion. We have also mentioned in the introductory part to this chapter that the mushy zone is formed at temperatures below the coherency point but the real interconnection of solid grain occurs at much lower temperatures. If the coher-ency is understood as a temperature at which a continuous dendritic network is formed, and the material starts to develop strength and retain its shape, then this point can be better defi ned as a rigidity point [1, 3]. At temperatures above the rigidity point, the grains are relatively free to re-arrange themselves with respect to one another and hence do not transfer any forces. Moreover, before the rigidity temperature is reached upon solidifi cation the liquid phase can still fl ow between grains and, therefore, melt feeding occurs without much diffi culty. This is the terminology that we adopt in this chapter.

The region where an alloy is most susceptible to hot tearing was dubbed in the 1940s–1950s “the effective solidifi cation range” [3, 22] or “the vulnerable




part of the solidifi cation interval” [9]. The upper boundary of this range is the point where the stresses begin to build up [3]; the lower boundary is the solidus (equilibrium or nonequilibrium, depending on the solidifi ca-tion conditions). Novikov [3] suggested determining the upper boundary of the effective solidifi cation range by measuring a so-called linear shrinkage. Hence, the upper temperature of this solidifi cation range is the temperature at which the “linear shrinkage” starts.

Let us specify the terms we are using. Solidifi cation shrinkage is the shrink-age (usually volume shrinkage) that occurs in the solidifi cation range, from 100% liquid to 100% solid, due to the phase transformation as a result of den-sity difference between the liquid and solid phases (see Figure 4.4). Solidi-fi cation shrinkage of aluminum alloys amounts to 6–8 vol.%, as illustrated in Figure 5.1. Thermal contraction is the contraction of the solid phase result-ing from the temperature dependence of the solid density. (The liquid phase also contracts according to the temperature dependence of the liquid density, but this contraction does not cause any stresses or strains due to fl uidity of the liquid.) The thermal contraction is usually described by the linear or volume thermal expansion coeffi cient. The linear contraction (or shrinkage) is the horizontal change in linear dimensions of a casting during solidifi cation and usually ranges from one hundredth to one percent [3, 23, 24]. Above the temperature of the linear contraction onset, the semi-solid alloy is “loose” because between opposite walls of the mold there is no continuous network of dendrites. In this stage of solidifi cation, the solidifi cation shrinkage of the melt and the thermal contraction of the solid phase cannot manifest them-selves as the horizontal contraction of the casting. All volumetric changes

650 700

5.3%

3.93%

0.25%

Liquidus

500 600550−7.00

Temperature, °C

−6.00

−5.00

−4.00

−3.00

−2.00

−1.00

0.00

Vol

ume

shrin

kage

, %

Solidus

Eutectic

FIGURE 5.1Development of volume solidifi cation shrinkage in an Al–4% Cu alloy [23]. (Reproduced with kind permission of Maney Publishing.)



Hot Tearing 187

appear as the decreasing level of the melt in the permanent mold (schemati-cally shown in Figure 5.2a and experimentally demonstrated in Figure 5.2b) or do not appear at all during DC casting, due to the continuous supply of melt to the mold. However, the linear contraction appears, and can be meas-ured, when the fl uidity of the alloy drops drastically, and the continuous rigid skeleton of the solid phase forms. Starting from that moment, the alloy acquires the capability of retaining its shape, and the volumetric changes display themselves as the linear contraction in the horizontal direction (Fig-ure 5.2c). The understanding of the shrinkage and contraction phenomena occurring in the solidifi cation range is very important for the analysis of stress–strain development and modeling of hot cracking. The temperature dependence of the linear contraction in the solidifi cation range is used in some hot tearing criteria, as we will discuss later in this chapter.

Below the solidus, the thermal contraction continues and frequently reveals itself as geometrical distortion of the billet shape. In DC casting practice, this phenomenon is known as butt curl (lifting of the billet shell from the start-ing block). The occurrence of butt curl can reduce the stability of the ingot standing on the starting block and is therefore a potential safety hazard. Besides that, the partial loss of contact between the ingot and bottom block will initially reduce the heat transfer with the possible danger of remelting. In the worst case scenario, butt curl can cause cracks and hot tears.

A special technique was developed to measure the linear thermal contrac-tion upon solidifi cation [3, 23–25]. Several designs of an experimental set-up were suggested, all sharing the following features suggested by Novikov [3]: graphite mold (providing low friction and high thermal conductivity) with one moving wall; water-cooled base (for high cooling rates comparable with those upon DC casting); and simultaneous temperature and displacement measurements (as shown in Figure 5.2c). Figure 5.3 shows a scheme and a photograph of the experimental set-up used in this work along with a sketch of an original set-up proposed by Novikov [3].

The experimental set-up used consists of the following parts: a T-shaped graphite mold (Figure 5.3b,c) with one moving wall; a water-cooled bronze base; and a linear displacement sensor (linear variable differential trans-former or LVDT) attached to the moving wall from outside and aligned with the longitudinal axis of the mold. The reason for the T shape, which is nar-rower than the main cavity, is to make the melt solidify faster there than in the rest of the mold, and so the solidifying sample can be fi xed on that side. To attach the solidifying metal in the cavity to the moving wall, we use a metallic rod with a thread (screw) embedded through the moving wall. The metallic rod fi xed in the moving head is frozen in the sample immediately after fi lling the mold with the melt. The cross-section of the main cavity is 25 × 25 mm with a gauge length of 100 mm.

Temperature measurement is of great importance for the reliability of results obtained in such experiments. The temperature should be prop-erly correlated with the measured displacement of the moving wall so as to capture correctly the moment of contraction onset. Therefore, the point




Liquid Liquid−solid part

Solid−liquid part in the effectivesolidification range:dendritic network

Linear contractionporosity

Decrease of melt level

Solidification

Filling the mold

200 400

Temperature, °C600 8000

0

10

20

30

40

Ver

tical

dis

plac

emen

t, m

m

50

SolidificationMoldfilling

(b)

(a)

Contraction

Expansion

Hor

izon

tal d

ispl

acem

ent,

%

0.2

02000 400 600 800

−0.2

−0.4

−0.6

−0.8

−1(c)

FIGURE 5.2Schematic representation of external signs of solidifi cation shrinkage and thermal contraction (a) and experimentally measured melt level (b) and horizontal contraction (c) of an Al–4.5% Cu alloy [24]. Experiments were performed in a mold shown in Figure 5.3b. Solidifi cation shrink-age is revealed by the decrease in melt level (measured by a laser sensor) up to the moment when the rigid solid skeleton is formed and the contraction begins (measured by a linear vari-able differential transformer). Note the difference in scales on vertical axes. (Reproduced with kind permission of Springer Science and Business Media.)



Hot Tearing 189

of temperature measurement should be in the location where the coher-ent solid structures propagating from cooled sides of the mold fi rst meet. This is the point where the lowest solid fraction of the continuous solid net-work is located. Experimental studies and heat transfer analysis of solidifi ca-tion in the experimental mold demonstrated that the coherent structures meet in the central part of the mold close to its bottom, as shown in Figure 5.4a,b [26]. Depending on the design of the experiments, the temperature should be measured as illustrated in Figure 5.4c, either near the side wall [25] or in the center of the mold [24]. In the latter case refractory paint is applied at the walls to delay locally the solidifi cation.

During the experiments the temperature and displacement are recorded simultaneously by a PC-based data acquisition system.

The linear thermal contraction is determined as follows:

εth = [(ls + ∆lexp − lf)/ls] × 100%, (5.1)

where ls is the initial length of the cavity, lf is the length of the sample at the solidus temperature and ∆lexp is the pre-shrinkage expansion.

T-shaped end

Horizontal displacement (linear thermal contraction)

Screw

Vertical displacement

(solidification shrinkage)

TC

ScrewMoving

block25

25

130

35

57

(a) (b)

(c) (d)

FIGURE 5.3Sketch of an original set-up by Novikov [3] made of graphite with sand inserts (a), photo of an experimental set-up on a water-cooled chill base used in this work (b), a scheme of the same set-up (c), and a sample after testing (d) [23, 25].




The pre-shrinkage expansion is mainly due to the evolution of gases and the pressure drop over the mushy zone, and it depends on the alloying sys-tem, melting, and solidifi cation conditions [3, 27].

In most cases, liquidus and solidus temperatures can be derived from the cooling curve. Note, however, that we determine the linear contraction in the entire solidifi cation range which, at the cooling rates (5 to 10 K/s) used, extends to the lowest possible eutectic temperature—nonequilibrium solidus (NES).

After acquiring the primary data, temperature, and displacement against time, the cooling curve is processed in order to obtain information about critical temperatures and cooling rates. After that, the data are reconstructed to fi nd the direct dependence of displacement on temperature. From this dependence the linear pre-shrinkage expansion, the linear solidifi cation contraction, the temperature of its onset, and the linear thermal contraction coeffi cient (TCC) can be extracted (see Figure 5.2c).

The measured linear thermal contraction in the solidifi cation range is affected by the friction force applied to the moving block [23] and by the melt level in the mold [24]. The gauge length, however, does not infl uence the measured values [24].

Figure 5.5 shows that thermal contraction decreases with larger friction forces (in the range 0.1 N to 0.85 N). At the same time, it has been demonstrated that the temperature of the contraction onset remains unchanged [23]. Another fac-tor indicated in Figure 5.5 is a so-called structure factor SF that is defi ned as

SF = Vc−0.33/Dgr, (5.2)

(a) (b)

(c)

FIGURE 5.4Development of solid fraction in the central symmetry plane (a) and at the bottom (b) of the experimental mold and the proper location of thermocouples (c) [26]. Parts (a) and (b) are related to the case when no refractory paint is applied. The black thick lines in (c) indicate refractory paint. The application of the paint delays the solidifi cation at the walls and makes the solidifi cation front advance in a more straight manner from short sides of the mold [24].



Hot Tearing 191

where Vc is the cooling rate characterizing the dendrite arm spacing (see Sec-tion 2.1) and Dgr is the grain size. The structure in this series of experiments was controlled by the cooling rate (7 to 18 K/s) and the melt temperature (700 to 800ºC), which allowed us to vary both DAS and Dgr. The grain size ranged from 120 µm to 220 µm [23]. Note that no grain refi nement has been used in these experiments. For such a coarse dendritic structure, the linear contrac-tion increases with the structure factor. In other words, the smaller the grain and the coarser the dendrite arms, the larger the thermal contraction in the solidifi cation range. As will be shown below, the situation changes when grain refi ner is added.

The melt level in the mold affects the measured parameters, which is evi-dently due to the combined infl uence of thermal gradients, dimensionality of the solidifying sample (unidirectional solidifi cation, fl at, or full three-dimensional casting), and the mechanical and rheological properties of the mushy zone [24].

We know from casting practice that the geometrical changes in the fi nal size of a DC-cast billet cannot be readily explained as a result of the thermal contraction of a solid sample of the same size. The observed contraction is usually considerably larger. The “real” casting contraction increases with increasing casting speed and varies from the theoretical value (calculated using the linear thermal expansion coeffi cient) at a zero speed to up to 50% larger values at high casting speeds [28]. The increase of the experimentally observed contraction with respect to the theoretical value originates from thermal gradients in the casting. Evidently, different layers of the casting

0.1

0.2

1.00.90.80.70.60.50.40.30.20.10.0

1.02.0

1.5

3.02.5

4.5

4.03.5

5.0

Structure factor (× 1000)

Friction force, N

Line

ar c

ontr

actio

n, %

FIGURE 5.5The effect of friction force and structure factor on the linear thermal contraction of an Al–4% Cu alloy [23]. (Reproduced with kind permission of Maney Publishing.)




are at different stages of solidifi cation, contain different amount of the solid phase, and contract at different rates. In addition, the internal, more liq-uid parts of the casting undergo, along with intrinsic contraction, tension imposed by the external, already solid, and more contracted shell. The dif-ference between the theoretical and observed contraction depends, appar-ently, on the mechanical properties of the mush, the thickness of the solid shell, and the volume of complete fl uid slurry and melt (the depth and profi le of the sump during DC casting). The “softness” of the liquid interior, which offers only negligible resistance to the contraction of the external shell, contributes to the experimentally observed contraction [26, 28]. Moreover, the pressure drop that appears in the mushy zone due to the solidifi cation shrinkage and the poor permeability of the mush could cause additional contraction by deforming the very weak solid network. The solidifi cation of melt in the experimental mold shown in Figure 5.3 b,c is in many aspects (although on the other scale) similar to the solidifi cation of an ingot or a billet cast from the top and cooled from the bottom (see Figure 5.4a,b). In this case the change of the melt level is similar to the decrease in the sump depth.

Let us take a closer look at the contraction behavior in the solidifi cation range of different alloys.

Figure 5.6 shows the temperatures of thermal contraction onset and the total contraction strain accumulated in the nonequilibrium solidifi cation range of binary Al–Cu and Al–Mg alloys. These data are superimposed on the binary phase diagram. It is quite obvious that the thermal contraction starts at a rather low temperature, close to or even below the equilibrium solidus. There is a maximum of the thermal deformation accumulated in the solidifi cation range, corresponding to the largest nonequilibrium solidifi ca-tion range. The thermal contraction in the solidifi cation range depends on the alloy composition in general and is greater for Al–Mg alloys than for Al–Cu alloys.

The volume fraction of solid in the mushy zone corresponding to the beginning of thermal contraction and, in our opinion, refl ecting the rigidity point, is quite high. At a cooling rate of 3–4 K/s, it ranges from 0.95 at 0.3% Cu to 0.8 at 4% Cu [25]. When the cooling rate is increased to 8–15 K/s, the solid fraction at the contraction onset reaches 0.9 at 4% Cu [23, 25].

The analysis of the contraction during solidifi cation is quite obvious and straightforward for binary alloys when the phase diagram with all tempera-tures and concentrations is known. The situation becomes more complicated in commercial, multi-component alloys, when a small shift in composition can dramatically change the solidifi cation path of an alloy, sometimes in rather unpredictable ways. Grain refi ning is an additional factor that may affect the contraction behavior of an alloy.

As an example we tested a 6061-type alloy containing different amounts of copper (within and above the compositional range of the grade). The effect of grain refi ner was also examined. The results are summarized in Figure 5.7.



Hot Tearing 193

The nonequilibrium solidus assumed was 500°C. The following conclusions can be made:

Contraction maxima in the solidifi cation range correspond to 0.2–0.3% Cu;Contraction starts at about 600–610°C and the onset temperature decreases to 585°C with increasing copper concentration from 0.2 to 3.8% in nongrain-refi ned alloys;Addition of grain refi ner decreases the temperature of contraction onset by 20 to 60°C depending on the composition of an alloy, and thereby delays the contraction to higher volume fractions of solid;

•

•

•

0.6

0.4

Con

trac

tion,

%

0.2

0

0.8

0.6

Con

trac

tion/

Exp

ansi

on, %

0.4

0.2

0

543

Cu, wt.%(a)

210

1086

Mg, wt.%

420

200

300

400

Tem

pera

ture

, °C

500

600

700

200

300

400

Tem

pera

ture

, °C

500

600

700

Contraction onset

Contraction onset

Contraction to NES

Contraction to NES

Expansion

(b)

FIGURE 5.6Compositional dependences of thermal contraction (expansion) and the temperature of contrac-tion onset superimposed on the binary phase diagrams for Al–Cu (a) and Al–Mg (b) alloys [24]. NES = “nonequilibrium solidus” shown by dashed lines. (Reproduced with kind permission of Springer Science and Business Media.)




Contrary to the observations on coarse-grained alloys (Figure 5.5), smaller and more globular grains in grain-refi ned alloys decrease 2–3 times the total amount of thermal strain upon solidifi cation; Grain-refi ned alloys exhibit much more pronounced pre- shrinkage expansion than nongrain-refi ned alloys, with the maximum between 0.7 and 1.5% Cu.

As we can see, grain refi ning considerably infl uences the contraction behav-ior of the alloy. At the same time, the pre-shrinkage expansion is much more pronounced in grain-refi ned alloys, compensating for some portion of the thermal contraction.

The much larger pre-shrinkage expansion of grain-refi ned alloys can be explained in the following way. It is known that the expansion is caused by the evolution of gas (mainly hydrogen) during solidifi cation [3] and the pressure drop across the mushy zone [27]. In the experimental set-up used in this work, the solidifi cation starts at the ends of the mold (see Figure 5.4). The temperature gradient in the longitudinal direction causes nonuniform volume shrinkage and, therefore, an uneven pressure drop in the two-phase zone. The pressure in the mushy zone near the ends of the solidifying sam-ple is lower than in the center. As a result there is a pressure-induced fl ow directed from the center toward the ends of the sample. Since the dendrites of the solid phase are mostly separated by liquid fi lms (expansion occurs above the rigidity point), they are shifted outward from the center of the sample. This movement is registered as a pre-shrinkage expansion. In the

•

•

650

600

550

Tem

pera

ture

, °C

500

450

4000 1 2

Cu, wt.%

3 40

0.2

0.4

Con

trac

tion/

expa

nsio

n, %

0.6

FIGURE 5.7Effect of copper concentration and grain refi ning on the contraction (expansion) behavior of a 6061-type alloy: , = contraction onset, °C; , = contraction to NES, %; and , = expan-sion [24]. Open symbols refer to an alloy without grain refi ning and solid symbols, to an alloy with grain refi ning. NES = denotes “nonequilibrium solidus.” (Reproduced with kind permis-sion of Springer Science and Business Media.)



Hot Tearing 195

case of grain-refi ned alloys, the structure consists of small, equiaxed grains that become bridged at relatively low temperature (contraction onset). Such a structure facilitates the relative movement of grains and, therefore, expan-sion. In addition, gas evolves from the melt more readily because fi ne grains provide more interfacial area and, in addition, allow more time before rigid-ity. The maximum of expansion frequently corresponds to the maximum of porosity [25, 27]. Therefore, alloys that show less thermal contraction in the solidifi cation range may exhibit larger interdendritic porosity.

The same tendencies are observed in commercial alloys of different alloy-ing groups. Figure 5.8 shows the development of solid fraction upon solidi-fi cation of commercial aluminum alloys with an indication of the thermal contraction onset. The corresponding values of the solid fraction at rigidity and contraction/expansion are given in Table 5.1.

Obviously, commercial alloys behave differently upon solidifi cation, depending on the alloying system. Commercial aluminum (1050) does not show thermal contraction, which is no surprise since it has a very narrow solidifi cation range. Al–Mg (5182) and Al–Mg–Si (6082) alloys also exhibit

100

90

80

70

60

50

Sol

id fr

actio

n, %

40

30

20

10

0

480 520 560

Temperature, °C

528°C/93%

515°C/87.5%

525°C/87%

Al 1050Al-Mg-Si 6082Al-Zn-Mg-Cu 7075Al-Mg-Mn 5182Al-Cu-Mg 2024

563°C/95%657°C/38%

600 640 680

FIGURE 5.8Development of the solid volume fraction upon nonequilibrium solidifi cation of some com-mercial alloys with the temperatures of thermal contraction onset and corresponding fraction solid being marked [23]. (Reproduced with kind permission of Maney Publishing.)




negligible contraction and only starting at temperatures below the equilib-rium solidus. The largest thermal contraction in the solidifi cation range is demonstrated by Al–Cu–Mg (2024) and Al–Zn–Mg–Cu (7075) alloys that are also known, as we will show later, to be prone to hot cracking. But even in these alloys the thermal contraction starts between the equilibrium and non-equilibrium solidus.

Similar investigation has been performed using commercial alloys with and without grain refi nement and with increased amounts of main alloy-ing elements [29]. The results are shown in Figure 5.9. The fact that the solid fraction at the contraction onset is lower in Figure 5.9 compared to the data

TABLE 5.1

Temperature of Thermal Contraction Onset (at Rigidity) (Tth), Fraction Solid at This Temperature ( f s th ), Expansion (∆ l exp ), and Thermal Contraction in the Solidifi cation Range (εth) of Some Commercial Alloys (Melt Temperature 720–730°C, Cooling Rate 12–18 K/s) [23]

Alloy Tth, °C f s th , % ∆lexp, % εth, %

1050 657 38 0 0.032024 515 87.5 0.035 0.25182 528 93 0.08 06082 563 95 0.025 0.027075 525 87 0.03 0.27

10.9

Frac

tion

solid

at t

he o

nset

of

cont

ract

ion

and

ther

mal

con

trac

tion

in s

olid

ifica

tion

rang

e

0.80.70.60.50.40.30.20.1

0

2024

NG

R

2024

GR

2024

+1%

Mg

6061

+1%

Mg

2024

+1%

Cu

6061

NG

R

7075

NG

R

6061

GR

7075

+1%

Zn

7075

+1%

Mg

7075

+1%

Cu

7075

+1%

Si

7075

GR

Thermal contraction, %Fraction solid

FIGURE 5.9Effect of grain refi ning (GR) and additional alloying on the fraction solid at the onset of ther-mal contraction and the total thermal contraction in the solidifi cation range of commercial alloys [29]. NGR = alloys without grain refi ning.



Hot Tearing 197

in Figure 5.8 and Table 5.1 is explained by the infl uence of the lower cooling rate in this series of experiments, 2 to 5.5 K/s as compared to 12–18 K/s in the previous series. One can see that grain refi nement increases the volume fraction at the thermal contraction onset (at rigidity) and generally decreases the overall thermal contraction, except for a 7075 alloy. This unconventional behavior of a 7075 alloy requires further investigation, especially because this alloy is very susceptible to hot tearing. Additional alloying, as a rule, decreases the solid fraction at rigidity and makes thermal contraction more pronounced.

The study of thermal contraction provides important information about two parameters, i.e., the temperature (fraction solid) at which the contraction starts and the total amount of contraction (thermal strain) accumulated in the solidifi cation range of a particular alloy. The fi rst parameter makes it possible to establish a constitutive equation for the thermal strain evolution during solidifi cation [25, 26, 29] and apply it to the modeling of hot tearing [30]. The second parameter can be used for ranking alloys with respect to their hot-tearing susceptibility [3, 24].

The constitutive equation that relates the macroscopic thermal strain rate ε∙ th to the solid fraction fs and temperature T is given by [24, 29]:

ε∙th = 1 __ 3 ψ( f s )βT T∙ I, with

(5.3)

ψ( fs) = 0

( fs − f s th _______

1 − f s th )

n

for fs ≤ f s th

fs > f s th

,

where βT is the volumetric thermal expansion coeffi cient, T∙ is the cooling

rate, I is the identity tensor, and n is a material parameter.The function ψ( fs) ensures that no thermal strain is transmitted through

the mushy zone above the rigidity temperature (temperature of thermal con-traction onset) or below the corresponding solid fraction. As soon as this critical solid fraction is reached, the macroscopic thermal strain in the mushy zone will tend toward thermal strain in a fully solid body as the solid frac-tion approaches unity.

Computer simulations of experiments on thermal contraction have been used to determine the material parameter n and the shape of ψ( fs). It is shown that the material parameter can be taken as 0 for most commercial aluminum alloys [29]. This means that the ψ( fs) function is in fact a step function and the semi-solid material behaves as completely solid as soon as the mush acquires rigidity. Equation 5.3 reduces to the classical equation for thermal strain rate in fully solid material. In the case of binary alloys, it can be demonstrated that the ψ( fs) function becomes more complex when higher cooling rates or grain refi nement are applied to an alloy. Figure 5.10 shows that the increased cooling rate and fi ner grains in an Al–4% Cu alloy delay the onset of thermal contraction upon solidifi cation and make the transition from viscous (liquid) to elasto-plastic (solid) mechanical behavior more gradual.




The same experimental technique of measuring thermal contraction can be used for assessing the linear thermal expansion (contraction) coeffi cient. The knowledge of this material property is important for the analysis of geo-metrical changes of a billet in the last stages and immediately after solidi-fi cation. The linear thermal expansion coeffi cients are not readily available in reference books for commercial alloys at high, subsolidus temperatures. Moreover, the linear thermal expansion coeffi cient is usually determined in a dilatometer on long cylindrical (1D) samples under nearly isothermal con-ditions (i.e., no thermal gradients in the sample). In addition, these samples are carefully homogenized to achieve the equilibrium state of the alloy. This situation is very different from the real contraction conditions of a just solidi-fi ed and cooling bulk sample in which the processes of excess-phase precipi-tation may well continue.

Figure 5.11 demonstrates the linear thermal expansion (contraction) coef-fi cients (LTEC) for binary Al–Cu and Al–Mg alloys with respect to the com-position. The LTECs have been obtained using curves like the one shown in Figure 5.2c. The coeffi cients were estimated in two temperature ranges: within 50°C below the nonequilibrium solidus (adopted as 550oC for Al–Cu alloys and 450°C for Al–Mg alloys) and from 300°C to the solidus. It is worth mentioning here that the results refl ect the nonequilibrium situation of cool-ing after solidifi cation.

In binary Al–Mg alloys, the LTEC decreases with an increasing concentra-tion of magnesium, the coeffi cients being very close at subsolidus and lower temperatures (see Figure 5.11b). This trend is quite distinct from the previ-ously reported results. According to the literature, the linear thermal expan-sion coeffi cient in Al–Mg alloys is believed to increase with Mg concentration and temperature [3, 31]. In the given compositional range, the linear thermal

10.9fs

0.80.70

0.2

0.4

0.6

ψ

0.8

1NGR, 4 K/s, n = 0

GR, 4 K/s, n = 0.3

NGR, 8 K/s, n = 0.1

FIGURE 5.10Function ψ ( fs) in Equation 5.3 for Al–4% Cu alloys [25]. NGR = without grain refi ning; GR = with grain refi ning; cooling rates and the material parameter n are shown.



Hot Tearing 199

expansion coeffi cient, as determined on annealed samples in a dilatometer, increases with magnesium concentration from 33.6 to 35 × 10−6 K−1 at 500°C [31] and from 29.2 to 30 × 10−6 K−1 at 400°C [3]. At the same time the average LTEC (20–500°C) slightly decreases with increasing magnesium, from 29.3 to 29 × 10−6 K−1 [31]. Our experimental results show a much more pronounced change in the TCC (300–450°C), from 29 to 25.5 × 10−6 K−1. The difference can be a result of different sample structures. In the case of reference data, homog-enized, single-phase samples were tested. In our experiments, the sample structure was far from equilibrium, consisting of depleted solid solution and nonequilibrium eutectics. Another factor may be the presence of hydrogen in just-solidifi ed Al–Mg alloys. Afanas’ev et al. [32] reported that the LTEC at 400°C of as-cast Al–Mg alloys decreased with the increasing Mg concentration

5432Cu, wt.%

1020

25

30

LTE

C, 1

0−6 K

−1

35500−550°C300−550°C

642Mg, wt.%

020

25

30

LTE

C, 1

0−6 K

−1

35500−550°C300−550°C

(a)

(b)

FIGURE 5.11Linear thermal expansion (contraction) coeffi cients (LTEC) obtained for binary Al–Cu (a) and Al–Mg (b) alloys in different temperature ranges [24]. (Reproduced with kind permission of Springer Science and Business Media.)




as opposed to the behavior of annealed alloys. These authors noted that this anomalous behavior was a function of hydrogen content in the alloy.

The contraction behavior of Al–Cu alloys in the temperature range from 300°C to 550°C complies with the previously reported data. According to Novikov [3] the LTEC at 500°C decreases from 32.4 to 31.2 × 10−6 K−1 upon increasing the copper concentration from 0 to 4.5%. The average LTEC (20–500oC) decreases from 29 to 28 × 10−6 K−1 [31] in the given range of copper concentrations. In our experiments the average TCC (300–550°C) decreases from 30 to 28.5 × 10−6 K−1. This is in good agreement with the data from Ellwood and Silcock [33] on the subsolidus linear thermal expansion coef-fi cients of binary Al–Cu alloys. They reported that the LTEC decreases from 32.4 × 10−6 K−1 at 0.95% Cu to 28.2 × 10−6 K−1 at 4.97% Cu.

Though the estimation of LTEC by using this technique may be less accu-rate than using a dilatometer, it has two main advantages. First, it gives data for nonequilibrium structure that is close to real structures occurring in prac-tice. Second, it is simple and does not require special equipment and sample preparation. As a result, the suggested technique can be used as a relatively simple means for the estimation of the real contraction coeffi cient at subsoli-dus temperatures, especially in cases when these coeffi cients are unknown.

Thermal contraction during and after solidifi cation along with uneven cooling of a casting creates thermo-mechanical conditions that may facilitate the formation of cracks. However, the mechanical properties that semi-solid material acquires at supersolidus temperatures may be suffi cient to prevent failure. Let us take a closer look at mechanical properties of semi-solid alu-minum alloys.

5.2 Mechanical Properties of Semi-Solid Alloys

In the last 60 years there have been many attempts to determine the proper-ties of metallic alloys in the semi-solid state. Most of these studies were initi-ated with the aim of examining and studying hot tearing, in other words, the failure of the semi-solid mush under external or internally induced stresses. The latter usually originated from uneven thermal contraction dur-ing solidifi cation.

Here we present a summary of the mechanical properties of semi-solid alloys. Interested readers are referred to the extensive reviews on the mechanical properties of semi-solid alloys by Novikov [3] and Eskin et al. [15] for more information.

5.2.1 Testing Techniques

For an alloy to be tested for mechanical properties it must have the ability to retain shape and to transfer load. In a lower part of the solidifi cation range, the so-called solid-liquid or semi-solid part, alloys meet these conditions and, therefore, can be mechanically tested.



Hot Tearing 201

Mechanical testing can be performed in two ways: by heating the sam-ple to a certain temperature above the solidus (remelting) or by cooling the liquid alloy to a certain temperature below the liquidus (solidifi cation). The structures thus obtained are different, and so also are the results of mechani-cal tests. Testing methods can be conditionally classifi ed as tensile, shear (including torque), and compression tests performed upon remelting or solidifi cation.

The main diffi culty during tensile tests of semi-solid samples is their very low strength and ductility due to the presence of liquid fi lms at grain bound-aries. Therefore, the conventional tensile testing machines cannot be used directly for studying the mechanical properties of mushy alloys.

The fi rst tests of the strength of semi-solid materials date from the begin-ning of the twentieth century when Norton [34] tested an aluminum alloy by suspending various weights to a solidifying sample. Tamman and Rocha [35] and Verö [36] used plane and notched cylindrical samples, respectively, to determine the tensile strength of binary and commercial alloys above soli-dus. It was shown that the ultimate tensile strength and ductility dropped at a temperature of solidus.

A reliable testing machine for tensile tests of aluminum alloys above soli-dus was designed and used by Singer and Cottrell [37] for studying Al–Si alloys. These authors decided that the sample should be short and com-pletely surrounded by machine clamps in order to prevent shape distortion. The sample was tested in the horizontal direction. The determined property was the ultimate tensile strength, the elongation being almost zero.

Researchers who studied hot cracking upon welding used mainly fl at-shaped specimens cut from sheets. Pumphrey and Jennings [38] heated a plane Al–Si specimen in a lead bath and tested it upon tension in the vertical direction at a rate of 25 mm/min. The temperature dependence of the ulti-mate tensile strength was constructed, but not for the elongation that scat-tered above solidus between 0 and 3%.

By the late 1940s the techniques for assessing the ultimate tensile strength of semi-solid aluminum alloys were well established. However, there were no reliable methods to measure the elongation or other plastic characteristics of alloys heated above their solidus. These techniques were developed in the 1950s mainly due to the efforts of Russian scientists, e.g., see Refs. [3, 39, 40].

The main diffi culties with respect to the measurement of elongation in the semi-solid state were (1) poor centering of the sample and, therefore, offset of the load and (2) low accuracy of measurements.

The simplest way to solve the fi rst problem is to use the scheme where the sample self-centers under gravity [3, 39]. Recently, Gleeble 1500 and 3500 thermo-mechanical simulators (testing machines) were used for studying mechanical properties of aluminum alloys upon remelting in the semi-solid state [41]. The signifi cant advantage of Gleeble-series testing set-ups is the use of Joule heat for rapid melting of the sample. In combina-tion with modern means of strain–stress and temperature acquisition and control, this increases the accuracy and reliability of measured results and




ensures more complete retention of the as-cast structure to the beginning of the test.

Figure 5.12a illustrates an example of a tensile curve recorded for an Al–6% Cu alloy tested at 570oC (22oC above the solidus) and at a strain rate of 1 mm/min. The typical feature of stress–strain curves for semi-solid testing is a well-pronounced branch of gradually decreasing stress, despite brittle fracture. Novikov [3] explained this phenomenon by the local deformation of solid bridges and extension of liquid intergranular fi lms existing in the semi-solid sample. As a result, the effective cross-section of the sample decreases and the stress–strain curve shows the gradual decrease of the stress. How-ever, the corresponding elongation is fi ctional because the sample is already fractured. Therefore, it is more reliable to determine the actual elongation by measuring the fractured sample with a microscope after the test.

It is worth mentioning here that plane specimens cut from rolled or extruded billets are quite useful for studying semi-solid properties and sensitivity to hot cracking of welded joints and heat-affected zones. But deformed samples should not be used for studying semi-solid properties and hot tearing of cast metals because the mechanical properties and, in fact, the structures in the melting range of cast and deformed materials are different. Figure 5.12b illustrates the typical difference in plastic behavior between cast and deformed alloys tested in the semi-solid state. The lower amount of eutectics in semi-solid deformed material decreases its elongation, whereas the fi ner grain structure in this material should increase its plasticity [3].

The examination of mechanical properties of alloys during the solidifi ca-tion is, of course, essential for studying the hot tearing phenomenon. The methods for this can be divided into two general groups, namely, tests upon

600

400

P, 1

0−2 N

200

0.2 0.4 0.6 0.8 1.0 T, °Cl, mm

21

El,

%FIGURE 5.12Typical stress–strain curve of an Al–6% Cu alloy tested at 570°C at a rate of 1 mm/min (a) and schematic temperature dependences of elongation for as-cast (1) and worked (2) samples tested upon remelting in the semi-solid state [3].



Hot Tearing 203

continuous cooling when the sample exhibits solid, mushy, and liquid zones simultaneously, and tests under isothermal conditions when the sample is cooled in a controlled fashion to a certain temperature and then tested.

Hall [42] reported perhaps the fi rst attempt of tensile tests upon continu-ous solidifi cation. Steel of different compositions is poured in sand molds with bolts on both sides connected with clamps of a tensile testing machine. When frozen into the solidifying melt the bolts transfer the tensile stress onto the casting.

Gulyaev [43] determined the tensile strength of solidifying steel by divid-ing the load at failure by the cross-section area of a ring layer (determined in special experiments by pouring out the rest of the melt). Determined values of tensile strength are ascribed to the average temperature of the ring layer.

In the 1980s and 1990s a group of scientists [44–46] developed and exten-sively used the technique of measuring tensile stresses and elongation of solidifying shells. The idea was to simulate the formation of a solid shell upon DC casting and to gain insight into its deformation behavior. The tech-nique includes the formation of a solidifying shell onto a water-cooled chill and the subsequent tensile testing of this shell.

Yet another apparatus for characterizing tensile strength development upon solidifi cation was developed by Instone et al. [47]. This testing set-up provides constraint during solidifi cation and collects information about strength development, strain accommodation, and hot cracking behavior of the mushy zone.

The characteristics of strength and plasticity obtained for solidifying sam-ples under nonisothermal conditions can only be accepted conditionally as mechanical properties of an alloy at different temperatures in the solidifi -cation range. These characteristics refl ect the averaged behavior of a cast-ing and, therefore, the corresponding tests can be classifi ed as sophisticated technological probes rather then pure mechanical tests.

To obtain real mechanical properties of an alloy in the solidifi cation range, the test should be performed under isothermal (or nearly isothermal) conditions.

In experiments by Pumphrey and Jennings in the 1940s [38] an aluminum alloy was poured into a horizontal, split, stainless steel mold, two halves of which were connected with clamps of a tensile testing machine. The working part of the sample was completely surrounded by the mold. Wedge-shaped heads of the sample (parts of the mold) were opened. Melt was poured into the preheated mold and allowed to cool slowly to the test temperature. The authors managed to determine the tensile strength of Al–Si alloys in the solidifi cation range, but failed to measure the elongation.

In the late 1950s [40] Prokhorov and Bochai used their set-up to examine the mechanical properties of aluminum alloys upon solidifi cation. A long, fl at sample was placed on the copper support in the furnace, melted, cooled to a testing temperature, kept at this temperature for a certain time, and then stretched out to failure. Some Al–Cu, Al–Si, and Al–Mn alloys were




tested this way, and their tensile strength and elongation were measured. However, this technique is not very reliable due to large corrections required to compensate for the change of specimen sizes during heating–cooling due to the expansion–contraction. Novikov [3] described a tensile machine for testing cylindrical samples in the solidifi cation range. The melt was cooled in the mold to the testing temperature and then tensile tested. This set-up was used to measure the elongation in the solidifi cation range of aluminum alloys. However, the same design can be used for studying tensile strength (it should be additionally equipped with a dynamometer or load cell), as was done by Kubota and Kitaoka [48].

Forest and Bercovici [4] developed a set-up allowing the controlled solidifi -cation of an alloy and tensile testing of it under nearly isothermal conditions. However, only ultimate tensile strength was measured. The tensile sample was a rod placed in a centrally situated graphite crucible capable of holding the metal in the liquid or mushy state. The crucible was heated by a focused induction furnace and then water-cooled to a test temperature inside the vertical tensile testing machine. The test was made perfectly uniaxial by means of balls and sockets. The sample temperature and the applied load were recorded throughout the experiment. Similar techniques was used by Suvanchai et al. [49], Suéry et al. [50], and Nagaumi et al. [51].

In situ melting and solidifi cation tensile tests were performed by Wis-niewski [52]. Samples were melted and resolidifi ed in a stainless steel mold coated with a graphite lubricant. The mold had three sections, each of which was split longitudinally. The upper and lower grip portions were attached to steel pull rods. The center section was designed to align itself with the two ends when a small compressive force was applied. The center was not attached to the end sections and was free to move longitudinally when the compressive force was removed. Stress–strain curves were recorded, allow-ing one to determine the ultimate tensile strength and the elongation at rupture.

Another way of testing mechanical properties in the semi-solid state is to deform the mush in shear [10, 53, 54]. The force–deformation curve can be recorded. One of the valuable features of this type of experiment is the pos-sibility of observing the interaction between dendritic grains as they move relative to one another.

The development of strength in solidifying alloys can also be examined by another sort of measurement, by torque upon rotating a vane in the mush [55]. A four-bladed vane is used to measure the fracture strength of the den-dritic network during solidifi cation. The shearing zone is approximated to be cylindrical, defi ned by the dimensions of the vane. The torque–time curve at a certain temperature exhibits a yield point refl ecting the moment when the interdendritic connections start to break. After network collapse the torque decreases rapidly. The yield stress can be calculated from the measured max-imum torque and the known surface area of the cylindrical yielding surface. The strength development can be evaluated by performing experiments at several points in the entire solidifi cation range.



Hot Tearing 205

5.2.2 Strength Properties of Aluminum Alloys in the Semi-Solid State

In the mid-1940s, Singer and Cottrell [37] were the fi rst to systematically study the tensile strength of aluminum. They heated samples of Al and Al–Si alloys to a certain temperature (including temperatures above the solidus) and then tested them in tension at a deformation rate of 6 mm/min. It was shown that the ultimate tensile strength gradually decreases as the testing temperature increases, and abruptly drops at the solidus temperature. This sharp drop in strength was accompanied by an almost complete loss of ductility.

Extensive studies of mechanical behavior of semi-solid binary aluminum alloys performed during remelting and solidifi cation showed the following general trends. A coarser grain structure and internal dendritic structure decrease the tensile strength. This phenomenon can be explained by the decreasing number of solid bridges between coarse grains [3]. Grain refi ne-ment shifts the beginning of the strength build-up to higher fractions of solid [3, 10, 55]. Since the dendritic grains in the nongrain-refi ned alloy are large and highly branched, they are very much entangled in one another, and the structure cannot accommodate much strain by rearrangement of the grains. Instead, strain must be adopted by deformation of the dendrites proper, and extensive dendrite fragmentation can occur. Strength therefore increases rapidly. In the grain-refi ned alloy, however, the dendrites are much smaller and almost round, which allows them to rearrange more easily by sliding during straining. Deformation is then concentrated in interdendritic areas, and strength develops more slowly. An increase in the cooling rate in the range relevant to DC casting shifts the onset of strength development to higher temperatures and increases the strength level [4]. The strength of semi-solid aluminum alloys increases with the deformation rate [3, 56]. This is interpreted as an effect of the deformation rate on the fracture resistance of solid bridges between grains. Creep and stress relaxation do not occur if the strain rate is suffi ciently high. It has been also shown that liquid remains in triple junctions at high strain rate whereas it spreads over grain boundaries at lower strain rates [41].

The effect of alloying elements on the strength of aluminum alloys is due to their effect on the structure, temperature range of solidifi cation, and liquid–solid interface. Novikov [3] showed that an addition of 0.8% Fe to an Al–0.7% Cu alloy considerably increased the strength in the semi-solid state. The study of microstructures of samples quenched from the mushy state shows that the “liquid” fi lms are much less continuous in the iron- containing alloy, and therefore it contains more solid bridges between grains. An addition of 0.2% Fe to an Al–1.5% Mn alloy shifts the entire soft-ening curve to higher temperatures although the solidus decreases some-what due to the formation of the ternary eutectics. Structure examination demonstrates that the structure with elongated Al6Mn particles at grain boundaries is substituted for the structure with small and compact Al6Mn and Al3Fe eutectic particles located at the grain boundaries, ensuring there-fore the existence of numerous solid bridges upon melting/solidifi cation.




Figure 5.13 demonstrates that the positive effect of grain refi nement in a low-copper alloy (a) can be completely superseded by the negative effect of the continuous liquid fi lms at grain boundaries in a high-copper alloy (b).

The mechanical properties of semi-solid commercial wrought alloys are particularly important because these properties determine to a great extent the hot-cracking susceptibility of these alloys, usually produced by DC casting.

Before considering the results of mechanical tests, it is important to note that the properties of semi-solid material depend not only on its chemical composition but also on the initial state. As shown experimentally, as-cast and deformed materials behave differently [3]. This was discussed briefl y above in connection with ductility in the semi-solid state (Figure 5.12b). Obvi-ously, the deformed and homogenized material has fi ner, rounder (equiaxed) grain structure with much fewer excess particles at grain boundaries. As a result, the solidus of such a material and the strength in the lower part of the solidifi cation range are higher (Figure 5.14a). However, closer to the liquidus the situation may change because the bonding (bridging) between developed dendrites is better than that between round small grains (Figure 5.14b).

The research in the tensile properties of semi-solid aluminum alloys shows the existence of two characteristic points in the solidifi cation range, i.e., zero-strength and zero-ductility temperatures. The transition from duc-tile to brittle behavior is associated with the onset of the formation of con-tinuous liquid fi lm at grain boundaries. Different alloys behave differently on approaching the solidus. For example, a 3004 alloy exhibits signifi cant hardening after the mush starts to build up strength, suggesting that it can-not fully accommodate thermally induced stresses [57]. Conversely, 2024

640T, °C

620600 580 600T, °C

560540

0.05

0.1

0.15

0.1

11

2

2

0.2

0.3

UT

S, 0

.1M

Pa

UT

S, 0

.1M

Pa

(a) (b)

FIGURE 5.13Temperature dependence of ultimate tensile strength of (a) Al–1.5% Cu and (b) Al–7% Cu alloys [3]. 1 = Without grain refi ning and 2 = with grain refi ning. Testing performed upon remelting.



Hot Tearing 207

and 7075 alloys increase the strength slowly on the decreasing temperature until several degrees above the solidus ( fs = 0.8 and 0.95, respectively) when the strength increases abruptly [57].

Small changes in the alloy composition, e.g., concentration of impurities, may considerably affect the mechanical behavior of a semi-solid alloy as shown in Figure 5.15 for a 7075 alloy with different ratios of Fe and Si. These data are

520 530 540 550 560 570

T, °C T, °C550

0.25

0.50

0.75

0.25

0.50

0.75

560 570 580 590 600

UT

S, 1

.0 M

Pa

UT

S, 1

.0 M

Pa

1

22

1

(b)(a)

FIGURE 5.14Temperature dependence of ultimate tensile strength of cast (1) and hot-rolled and annealed (2) 5456-type (Al–6% Mg) (a) and 7039-type (Al–3.3% Zn–4.2% Mg) alloys (b) [3]. Testing performed upon remelting.

440

4

8

1 2

28

36

UT

S, M

Pa

500 560T, °C

FIGURE 5.15Temperature dependence of ultimate tensile strength of a 7075 alloy with (1) 0.1% Fe and 0.1% Si (Fe:Si = 1) and (2) 0.5% Fe and 0.1% Si (Fe:Si = 5) [3]. Testing performed upon remelting.




strong proof for the well-known dependence of the hot-cracking tendency on the Fe:Si ratio in an alloy. The general recommendation is to keep the Fe:Si ratio above unity [58]. The explanation is that the concentration threshold for the occurrence of the low-melting eutectics with the β(Al5FeSi) and Si phases shifts to higher iron and silicon concentrations upon increasing the Fe:Si ratio. This prevents the formation of free silicon that tends to segregate to grain boundaries and form low-melting eutectics, thereby decreasing the strength level in the semi-solid state [59]. The results in Figure 5.15 show clearly that the increase in the Fe:Si ratio indeed signifi cantly strengthens the mush in the lower part of the solidifi cation range.

5.2.3 Ductility of Aluminum Alloys in the Semi-Solid State

Athough strength in the semi-solid state is an important property, many consider ductility of the semi-solid metal to be the property that determines the hot-tearing tendency of the material because the ductility characterizes the ability of the mush to accommodate stresses and strains occurring upon solidifi cation as a result of solidifi cation shrinkage and thermal gradients. The deformation ability of the semi-solid metal is frequently used in various criteria and models of hot tearing. However, the experimental data on the ductility of aluminum alloys in the semi-solid state are scarce. The reason is that the values are so low that there is no sense in measuring them because they frequently compare on the same scale with the accuracy of measure-ments. Most of the data are collected in the works of Novikov et al. [3] who considered ductility (tensile elongation to rupture) to be the main feature, along with linear thermal contraction, of hot cracking susceptibility of metal-lic alloys. These works are reviewed elsewhere [15].

First, let us consider the main features of the temperature dependence of the ductility in the solidifi cation range. All alloys exhibit some, albeit low, ductility at temperatures above the solidus. The temperature dependence of the ductility in the semi-solid state has a typical U-shape with an inter-mediate temperature range where the ductility is very low. In this brittle range, the ductility of alloys different in composition varies only by tenths of a percent, but even these small variations can be crucial for hot tearing susceptibility.

Several common types of ductility dependence that can be observed in the semi-solid range are demonstrated in Figure 5.16 [3]. Some alloys, e.g., Al–1.4% Mn, show a sharp drop in ductility above solidus. The ductility remains almost permanent upon heating in some temperature range, and then it sharply increases (see Figure 5.16a). Many commercial alloys, e.g., 7039 and 7075, demonstrate behavior as shown in Figure 5.16b. The type shown in Figure 5.16c is rather rare, but it can be observed in an Al–3% Zn alloy. The range of constant low ductility can be wide or very narrow, as shown by the dashed line in Figure 5.16a–c. Figure 5.16d depicts behavior typical of many binary and complex aluminum alloys with a stepwise change of ductility. Such behavior is observed in 2024, 7064, and 3XX.0-series alloys.



Hot Tearing 209

Let us look at some factors that infl uence the semi-solid ductility. Novikov [3] experimentally confi rmed the ideas of Singer and Cottrell [37] and Pum-phrey and Jennings [38] that the main deformation mechanism in the semi-solid state is the intergranular slide. Taking this into account, the role of grain size and shape becomes obvious. The elongation of a sample due to the intergranular deformation (δig) depends on the number of interfaces per unit length of deformation and equals approximately [3]:

δig = 0.6 ∆l/Dgr, (5.4)

where ∆l is the displacement of two adjacent grains and Dgr is the average grain size.

Figure 5.17a shows the effect of grain size on the tensile elongation of an Al–4% Cu alloy. The analysis of these results reveals that the grain refi ne-ment is accompanied by a decrease in the intergranular displacement ∆l. At the same time, this example shows that the semi-solid ductility increases with grain refi nement, which is the frequently observed case. However, in general, the resultant ductility depends on the ratio at which ∆l and Dgr are changing.

The transition from equiaxed structure to columnar can decrease the duc-tility considerably in the most vulnerable temperature range (see Figure 5.17b,c). This can be explained in terms of less available interfaces of inter-granular slide and fewer possibilities for deformation by grain rotation.

The grain coarsening or the equiaxed–columnar transition shift the upper boundary of brittle range to higher temperatures (see Figure 5.17). The position of the lower boundary depends on the development of intergranular defor-mation. In most cases, the development of columnar and coarse equiaxed grains shifts this boundary to higher temperatures because the intergranular deformation occurs more easily in fi ne-grained material (see Figure 5.17a,c). But in some cases, for example, when the surface of columnar grains is very smooth, the dependence is the reverse (see Figure 5.17b).

The structure as we know is strongly affected by cooling rate upon solidi-fi cation. The effect of cooling rate on the ductility of semi-solid alloys is illus-trated in Figure 5.18. The solidifi cation conditions are chosen in such a way that the grain size and the structure type remained the same.

T T T T

El El

a b c d

FIGURE 5.16Typical forms of temperature dependence of elongation (El) of semi-solid alloys [3].




Slower cooling shifts the lower boundary of the brittle range to lower temperatures. In low-alloyed materials (Al–1.5% Cu), in which the amount of nonequilibrium eutectic liquid is small and distributes as isolated inclu-sions, the lower boundary of the brittle range is well above the nonequilib-rium solidus (548oC for Al–Cu alloys) (see Figure 5.18a). At a high cooling rate when the dendritic grains are well developed and the liquid inclusions are particularly fi ne, the lower boundary of the brittle range is close to the temperature of the equilibrium solidus. Such an effect of cooling rate cor-relates well with the fact that the surface of grains becomes smoother upon decreasing the cooling rate and, hence, the transition from intergranular to transgranular fracture occurs at a lower temperature [3].

In the alloys containing more copper, the amount of remaining eutectic liq-uid is much larger and the alloys are brittle in the entire solidifi cation range, the lower boundary of the brittle range being upon slow cooling even lower

550 560 570 580 590

T, °C

T, °C T, °C

0.5

Sol

idus

1.0

1.5

2.0E

l, %

El,

%

El,

%

610 620 630 640 650 660 530 550 570 590 610 630 650

SoL

2.4

2.0

1.6

1.2

0.8

0.4

2.4

2.0

1.6

1.2

2

2

11

0.8

0.4

(a)

(b) (c)

1

2

FIGURE 5.17(a) Effect of grain size (1 = coarse structure; 2 = fi ner structure) and (b,c) structure type (1 = equiaxed; 2 = columnar) on elongation (El) of semi-solid Al–4% Cu (a), Al–1.5% Cu (b), and Al–5% Cu (c) alloys [3]. Testing performed upon remelting.



Hot Tearing 211

650640630

T, °C

T, °C(b)

620610600590

(a)

0.4

0.8

1.2

1.6

0.3 K/sE

l, %

El,

%2.7 K/s

0.17 K/sT

sol

530

0.4

0.8

1.2

1.6

0.17 K/s

550 570 590 610

2.7 K/s

FIGURE 5.18Effect of cooling rate upon solidifi cation on tensile elongation (El) of Al–1.5% Cu (a) and Al–5% Cu (b) alloys tested upon remelting [3].




than the temperature of the lowest eutectics (see Figure 5.18b). This phenom-enon can be explained by very weak Al/Al2Cu interfaces.

Although the position and span of the brittle range depend on the solidifi -cation conditions, the ductility itself remains virtually unaffected. Two fac-tors acting in opposite directions compensate for each other: upon decreasing the cooling rate the liquid layers become thicker but simultaneously less continuous.

The size, shape, and distribution of liquid phase inclusions at grain bound-aries should essentially affect the development of intergranular deforma-tion. So-called liquid-metal embrittlement is discussed in detail elsewhere [3, 46, 60–63], and we refer the reader to these sources for more information. In brief, the liquid-metal embrittlement and thus the ductility and strength are related to the dihedral angle, which, in turn, is a function of the relative surface energies of the solid grain boundaries and the liquid:

σ ls/σss = 1/2cos(θ/2), (5.5)

where σ ls and σss are the surface energies on the solid–liquid and solid–solid interfaces, respectively, and θ is the dihedral angle for liquid inclusions.

The smaller the dihedral angle, the greater the embrittlement caused by liquid inclusions. For aluminum alloys the dihedral angle is usually less than 20–25° and decreases with increasing temperature [3, 14]. At such values of the dihedral angle, 1% of liquid fraction is suffi cient to cover approximately 30% of grain boundaries with liquid, and at 10% liquid nearly 85% of grains are covered with liquid.

The amount of liquid at the last stages of solidifi cation is usually repre-sented by nonequilibrium eutectics that can be formed by the main alloying elements and/or by impurities. It is experimentally shown that impurities present in alloys in amounts of tenths of a percent can considerably affect the ductility and the brittle range proper. The change in the purity of base aluminum does not affect the position of the upper boundary of the brittle range, whereas the lower boundary shifts toward lower temperatures. This is due to the fact that the local melting temperature at grain boundaries is considerably lower in the presence of impurities (low-melting eutectics). At the same time, the ductility itself can be somewhat higher for alloys prepared on low-purity aluminum. This can be interpreted in terms of the increased amount of intergranular liquid, which helps accommodate intergranular deformation at supersolidus temperatures. These effects are illustrated in Figure 5.19.

The ductility of semi-solid materials measured upon tensile tests depends on the strain rate. Novikov and Novik [64] showed that a higher deformation rate (~0.004 s−1, ~0.04 s−1, and dynamic loading) does not affect the position of the upper and lower limits of the brittle range but decreases the amount of elongation in semi-solid alloys with suffi cient amount of liquid, e.g., Al–6.5% Cu, whereas the behavior of less alloyed alloys, e.g., Al–1.5% Cu, remains virtually unaffected. Hence, the effect of the deformation rate depends



Hot Tearing 213

mainly on the amount of liquid phase (thickness of liquid intergranular fi lms) in the alloy. Because plastic deformation of semi-solid alloys occurs mostly by grain sliding assisted by intergranular liquid layers, the accommodation of strain by liquid fi lms and grain sliding occurs more easily at lower defor-mation rates. In contrast, Qingchun et al. [56] and Wisniewski [52] reported that the failure strain increased with strain rate above 0.001 s−1. Qingchun et al. [56] mentioned that the observed phenomenon was due to the fact that creep and stress relaxation do not occur at high strain rates. Wisniewski [52] suggested that the liquid-fi lm cavitation may contribute to the increased strain-at-failure at high strain rates. It is quite possible that the different test-ing conditions produce different dependencies of the observed ductility on the strain rate. The “soft” (force control) scheme used by Novikov allowed for creep and strain accommodation by redistribution of liquid, whereas the “rigid” (strain-rate control) scheme employed by Wisniewski caused liquid-fi lm cavitation and increased apparent plasticity at high strain rates.

The data on ductility of commercial aluminum alloys are scarce. Most authors did not report data, but only mentioned that ductility was very small and could not be reliably measured.

However, some authors reported the results on ductility of commercial aluminum alloys in the semi-solid state [3, 19, 49, 65]. Figure 5.20 shows the results of tensile tests performed upon melting of commercial alloys of 7075 (Al–Zn–Mg–Cu), VAD 23 (Al–Cu–Li), and 2037 (Al–Cu–Mg–Si) alloys.

The temperature dependence of tensile elongation given in Figure 5.20c for a 2037-type alloy characterizes the effect of structure coarsening and gas concentration on the ductility of the mush. The samples for these experiments

5600

11

2

2

El,

%

580 600 620

T, °C

FIGURE 5.19Effect of impurity level on tensile elongation (El) of an Al–3.5% Mg alloy prepared using 99.7% pure Al (1) or 99.99% pure Al (2) [3]. Testing performed upon remelting.




were prepared from 200-mm-diameter ingots direct-chill cast at a speed of 130 mm/min after holding the melt in the furnace for 20 min (1) or 10 h (2). The holding time coarsens the structure and, as shown experimentally [3], decreases the amount of hydrogen in the melt from 0.30 to 0.19 cm3/100 g. These two factors (grain coarsening and decreased amount of gas) can considerably deteriorate the plastic ability of the semi-solid metal and favor hot tearing [3]. The effect of gas amount has been explained from its effect on linear thermal contraction. The higher the gas concentration in the melt, the lower the linear contraction and, therefore, the higher the “plasticity” reserve of the mush.

Experimental results for tensile properties of commercial aluminum alloys are summarized in Table 5.2 [3, 4, 19, 46, 49, 51, 57, 66–68]. There are two

440

0.4

0.8

1.2

1.6

2.0

10

30

50

460 480 500 520 540 560 580

El,

%

4

3

2

1

520

εth

540 560 590 600 620

12

El,

%T, °CT, °C

1.0

0.5

450 480 510 540

1

2

570

El,

%

T, °C

(b)(a)

(c)

FIGURE 5.20Temperature dependence of tensile elongation of (a) 7075 alloy; (b) VAD23 alloy with 5.15% Cu, 1.2% Li (1) and 6% Cu, 1.2% Li (2); and (c) 2037 alloy that was held liquid in the furnace for 20 min (1) and 10 h (2) [3]. Testing performed upon remelting.



Hot Tearing 215

TABLE 5.2

Tensile Properties of Some Commercial Wrought Aluminum Alloy According to Reference Data

Alloy UTS, MPa El, %Zero

Strength Zero Ductility Ref.

Al–Mg5456 1.0 at 550°C 570 — 3Al–Mg–Mn3004 — fs = 0.81 — 57Al–Mg–Si6061 — 623 ( fs = 0.82) — 496063 0.85–1.75 at

610°C (GR)0.075–0.18 at 610°C (GR)

620 ( fs = 0.9) GR

— 49, 46

0.6 at 610°C (NGR)

0.1 at 610°C (NGR)

630 NGR

6110 1.0 at 565°C 0.9 at 565°C fs = 0.7 fs = 0.77 660.25 at 607°C (GR)

0.6 at 607°C (GR)

HS60 3 at 607°C 0.4 at 607°C 620 ( fs = 0.69) 610 ( fs = 0.77) 51HS65 — — 623 ( fs = 0.78)

to 631 ( fs = 0.63) on incr. [Fe]

613 ( fs = 0.82) to 617 ( fs = 0.78) on incr. [Fe]

67

Al–Cu–Mg2024 0.5 – 0.6 at

560°C 2.7 at 560 fs = 0.76 — 19, 57

1 at fs = 0.9 1.8 at 500

2618 5 at 520°C — 610°C — 32.6 at 540°C

2017 0.39 at 560°C (fs = 0.9)

— 580°C — 4

1.4 at 520°C 2037 — 0.37 at 510°C — — 3

0.27 at 500°C0.22 at 490°C

Al–Zn–Mg–(Cu)7075 1.0 at 520°C 0.17 at 520°C 570°C 490–500 3, 57

3.2 at 480°C 0.1 at 490°Cfs = 0.926.5 at 470°C 40 at 480°C

35 at 470°C7475 — — 600–610 530–550 687005 — — 630 610 687039 2.5 at 575°C 0.15 at 575°C 600 570 3

3

3.3 at 570°C7064 — 0.5 at 480–500°C — —

0.1–0.15 at 450–460°C

Al–Cu–Li5–6 Cu, 0.4 at 550°C 0.7 at 550°C — — 31.2 Li 0.9 at 530°C 0.15 at 530°C




temperatures that can serve as benchmarks for characterizing the behav-ior of semi-solid material. A zero-ductility temperature marks the lowest temperature in the semi-solid range when the material acquires ductility. A zero-strength temperature corresponds to the temperatures when the semi-solid material starts to show some strength. Typically, the zero-strength temperature is higher than the zero- ductility temperature, meaning that the semi-solid alloy can start to build up some strength (and transfer stresses) while remaining absolutely brittle (ductility is zero) [51, 66, 67].

In conclusion, there are quite a few ways to measure or evaluate mechani-cal properties upon melting or solidifi cation. The strength and ductility of the semi-solid material depend on its initial structure (solidifi cation condi-tions, structure modifi cation by alloying, deformation, etc.), position of an alloy on the phase diagram (amount of eutectics), strength properties of solid bridges, and wetting conditions on the liquid–solid interface.

5.3 Mechanisms and Criteria for Hot Tearing

5.3.1 Historic Overview of Hot Tearing Research and SuggestedMechanisms

Foundrymen have been well acquainted with hot cracking for centuries. Compositions of alloys for casting large cannons and bells were empiri-cally chosen in order to decrease solidifi cation shrinkage and thermal con-traction in the solidifi cation range. In the case of early castings that date from several centuries ago, an alloy of 75–85% copper with 15–25% tin was selected for its castability without cracking (though thermal contraction in the solid state could cause cold cracking). The thermo-mechanical situation during solidifi cation was also recognized as a vital condition for producing a sound casting. It was not uncommon that solidifi cation and cooling of a casting took several days or even weeks in an attempt to prevent hot and cold cracks.

Hot cracking was a problem that faced the pioneers of DC casting, espe-cially when they tried to cast high-strength alloys and large-scale fl at ingots. Livanov [69] mentioned in 1945 that the problems of cracking in DC-cast ingots were so severe that the attempts to cast them were dis-continued in the former Soviet Union during World War II, between 1940 and 1945. Only after considerable experience was accumulated from cast-ing round billets did it become possible to return to the technology of fl at ingots for rolling. But even then, until the mid-1950s, large-scale ingots from 7075-type alloys were cast with secondary cooling by air in order to reduce thermal stress [58].

The deformation behavior of the mush that was discussed in the previ-ous section is very critical for the formation of hot tears. The link between



Hot Tearing 217

the appearance of hot tears and the mechanical properties in the semi-solid state is obvious and has been explored for decades. This link is refl ected in a number of hot tearing criteria [3, 15].

Another important correlation between the hot cracking susceptibility (HCS) and the composition of an alloy has been established on many occa-sions. The large freezing range of an alloy promotes hot tearing because such an alloy spends a longer time in the vulnerable state in which thin liquid fi lms exist between the dendrites. Two parameters are important here. First of all, as we showed in Section 5.1, the amount of thermal strain accumulated during the solidifi cation range depends on the extent of the nonequilib-rium solidifi cation range and, as such, on the alloy composition (Figure 5.6). Another important issue is the distribution of liquid at the grain boundaries. The liquid fi lm distribution is determined by wetting of grain boundaries, i.e., by the surface tension between liquid and solid phases (see Equation 5.5). When the surface tension is low and wetting is good, the liquid tends to spread out over the grain boundary surface, which strongly reduces the den-drite coherency, weakens the mush, and may promote hot tearing. Otherwise, the liquid will remain as droplets at the grain junctions so that the solid net-work maintains its strength. The surface tension of the remaining liquid can produce a Marangoni force that facilitates the removal of precipitating gas from the potential voids and thereby reduces hot tearing [70]. At relatively low fractions of solid, e.g., 80–85%, the interdendritic liquid can provide a bond between grains that creates a tensile strength of the mush [71].

The dependence of hot cracking on the composition of binary alloys is described by a typical “lambda” curve, as shown in Figure 5.21 [72]. One can see a nearly perfect correspondence between the compositional dependences of hot tearing susceptibility in Figure 5.21 and of thermal contraction upon solidifi cation in Figure 5.6. This is additional proof that thermal contraction accumulated in the solidifi cation range is a good measure of hot tearing sus-ceptibility of an alloy [24].

The composition dependence of hot cracking susceptibility has been reported for three series of wrought aluminum alloys, namely the AA2XXX (Al–Cu–Mg), AA6XXX (Al–Mg–Si), and AA7XXX (Al–Zn–Mg) series. For other alloys only few data are available. The probable reason is that the hot tear is found mostly in these three alloying systems. In commercial alloys, hot cracking susceptibility is not always related to a characteristic value but is rather represented comparatively, showing the effect of various additions on a certain alloy. Specifi c data can be found elsewhere [3, 15]. Here we men-tion only general tendencies.

Al –Cu –Mg –Si. Many commercial alloys belong to this system, e.g., AA2038, AA2017, AA2025, and AA2014. An increase in silicon concentration causes a shift of maximum hot cracking to lower copper and magnesium concen-trations and a decrease in the overall hot cracking susceptibility [3]. The addition of iron (up to 0.65%) to an AA2038 alloy increases the hot cracking susceptibility. This is subject to the silicon concentration. At 0.95% Si the




hot cracking index is very low even at high Fe concentrations. The addition of manganese to an AA2038 alloy initially reduces the hot cracking suscepti-bility, but at concentrations above 0.5% Mn the susceptibility increases. The maximum HCS an AA2017 alloy corresponds to about 0.2% Si.

Al –Cu –Mg–(Ni) –Ti. Several commercial alloys belong to this system, e.g., AA2024 and AA2618 alloys. Addition of Ti signifi cantly reduces the hot cracking susceptibility, especially at low Fe concentrations, as illustrated in Figure 5.22. The signifi cant effect of increasing magnesium content in Al–Cu–Mg alloys is in the shifting of the maximum of hot cracking from 0.5% Cu at 0.5% Mg to 1.5% Cu at 4% Mg [3].

543

Cu, wt.%

210

8 106

Mg, wt.%

420

0

1

2

3

Cra

ck le

ngth

0

1

2

3

Cra

ck le

ngth

4

5

6

7

(a)

(b)

FIGURE 5.21Compositional dependence of hot tearing susceptibility in binary Al–Cu (a) and Al–Mg (b) alloys [72].



Hot Tearing 219

2 4

Cu, %

6 80

(a)

(b)

(c)

(d)

0102030405060708090

100

HC

S, %

2% Mg

0% Ti

0.2% Ti

4% Mg

0% Ti

0% Ti

0% Ti

0.2% Ti

0.2% Ti

0.2% Ti

0.2% Fe

0.3% Fe

65432100

102030405060

HC

S, %

708090

100

00 0.1 0.2 0.3 0.4 0.5 0.6

102030405060

HC

S, %

708090

100

0102030405060

HC

S, %

708090

100

Cu, %

Si, %

0 0.1 0.2 0.3 0.4 0.5 0.6

Si, %

FIGURE 5.22Effects of composition and grain refi nement on hot tearing susceptibility in Al–Cu–Mg (a,b) and Al–4.5% Cu–1.5% Mg–0.6% Mn (b,c) alloys [3].




Al– Mg –Si– Fe– Ti. AA6XXX series alloys such as AA6060, AA6005, andAA6063 belong to this system. The maximum hot cracking susceptibil-ity is at 0.3–0.4% Fe for an alloy containing 0.5% Mg, 0.5% Si, and 0.15% Ti [3].

Al– Mg –Si –Cu– Fe– Ti. This system includes such commercial alloys as AA6151, AA6351, and AA6111. The addition of Ti has been proved to decrease the hot cracking susceptibility of such alloys. The minimum HCS of an AA6111-type alloy (0.5% Mg, 1.2% Si, and 0.2% Fe) is at 0.7–0.8% Cu [3]. These data correlate well to our measurements of thermal contraction, shown in Figure 5.7.

Al –Mg –Zn –Cu. High-strength commercial alloys, e.g., AA7039, AA7079, and AA7008, belong to this system. The hot cracking diagrams of Al–Zn–Mg alloys demonstrate that the addition of copper increases hot cracking sus-ceptibility, with the maximum HCS shifting to lower Zn concentrations upon increasing the copper content. For example, alloys without Cu have a peak at about 1% Mg and 7% Zn, and alloys with 0.5% Cu show two peaks: at about 1.5% Mg and 4% Zn, and at about 1.5% Mg and 7–10% Zn [3]. The addition of manganese typical of AA7039, AA7079, AA7075, and AA7050 alloys is quite harmful, especially in high-copper and low-zinc alloys [3]. Warrington and McCartney [73] compared the hot tearing susceptibility of AA7050 and AA7010 alloys. The effect of grain-refi ning addition on both alloys was also reported. They conclude that AA7050 is marginally more sensitive for hot cracking than AA7010. They argue that the differ-ence can be attributed to a larger volume fraction of iron-rich intermetal-lic phases in the AA7050 alloy. A grain refi ner can signifi cantly affect the hot cracking susceptibility. The effect depends on the alloy, with the hot tearing being minimum at 0.005% and 0.3% Ti for AA7010 and AA 7050, respectively.

Considerable effort has been made to understand the hot tearing phe-nomenon. Several mechanisms of hot tearing and conditions that may lead to it have been suggested in the literature [7, 9, 14, 22, 28, 36, 46, 63, 74–93]. Some of these mechanisms are outlined in Table 5.3 and summarized in Figure 5.23 [94].

We can see that, over the years, much more effort has been made to inves-tigate and understand the conditions required for hot tearing occurrence rather than the mechanisms of crack initiation and propagation. And when it comes to the nucleation and propagation of hot tears, an educated guess frequently replaces experimental proof. Figure 5.23 also shows that the con-ditions for and causes of hot tearing can be considered on different length scales, from macroscopic to microscopic, and some of these conditions are important on both mesoscopic and microscopic scales. It is important to note that most of the existing hot tearing criteria deal also with the conditions rather than with the mechanisms of hot tearing.

Different macroscopic and mesoscopic parameters, such as stress and strain, were considered critical for the development of hot tearing.



Hot Tearing 221

TABLE 5.3

Summary of Hot Tearing Mechanisms [94]

Mechanisms and Conditions Suggested and Developed by* Ref.**

Cause of hot tearingThermal contraction Heine (1935); Pellini (1952); Dobatkin

(1948)74, 9, 28

Liquid fi lm distribution Verö (1936) 36Liquid pressure drop Prokhorov (1962); Niyama (1977) 75, 76Vacancy supersaturation Fredriksson et al. (2005) 77NucleationLiquid fi lm or pore as stress concentrator

Patterson et al. (1953, 1967); Niyama (1977); Rappaz et al. (1999); Braccini et al. (2000); Suyitno et al. (2002)

78, 79, 76, 80, 81, 82

Oxide bi-fi lm entrained in the mush

Campbell (1991) 7

Vacancy clusters at a grain boundary or solid–liquid interface

Fredriksson et al. (2005) 77

PropagationThrough liquid fi lm by sliding Patterson (1953); Williams and Singer

(1960, 1966); Novikov and Novik (1963)78, 83, 84

By liquid fi lm rupture Pellini (1952); Patterson (1953); Saveiko (1961); Dickhaus (1994)

9, 78, 85, 46

By liquid metal embrittlement Novikov (1966); Sigworth (1996) 3, 14Through liquid fi lm or solid phase depending on the temperature range

Guven and Hunt (1988) 86

Diffusion of vacancies from the solid to the crack

Fredriksson et al. (2005) 77

ConditionsThermal strain cannot be accommodated by liquid fl ow and mush ductility

Pellini (1952); Prokhorov (1962); Novikov (1966); Magnin et al. (1996)

9, 75, 3, 87

Pressure drop over the mush reaches a critical value for cavity nucleation

Niyama (1977); Guven and Hunt (1988); Rappaz et al. (1999); Farup and Mo (2000)

76, 86, 80, 88

Strain rate reaches a critical value that cannot be compensated for liquid feeding and mush ductility

Pellini (1952); Prokhorov (1962); Rappaz et al. (1999); Braccini et al. (2000)

9, 75, 80, 81

Thermal stress exceeds rupture or local critical stress

Lees (1946); Langlais and Grizleski, (2000); Lahaie and Bauchard (2001); Suyitno et al. (2002)

89, 90, 63, 82

Stresses and insuffi cient feeding in the vulnerable temperature range

Bochvar (1942); Lees (1946); Pumphrey and Lyons (1948); Clyne and Davies (1975); Feurer (1977); Katgerman (1982)

22, 89, 72, 91, 92, 93

Thermal stress exceeds rupture stress of the liquid fi lm

Saveiko (1961) 85

* The list of the authors is by no means complete. The references have been chosen to represent the development of ideas.

** References are given in the same order as the authors in the second column.




Pellini [9] suggested a hot tearing theory based on the strain accumulation with the following main features: (1) cracking occurs in a hot spot region, (2) hot tearing is a strain-controlled phenomenon that occurs if the accumu-lated strain of the hot spot reaches a certain critical value, and (3) the strain accumulated at the hot spot depends on the strain rate and time required for a sample to pass through a fi lm stage. The most important factor of hot tear-ing based on this theory is the total strain on the hot spot region. The total strain is the additive of strain over a period within which the hot spot exists. Taking into account that the highest strain accumulates in the liquid fi lm, Metz and Flemings [10] explain the increase in hot tearing caused by the seg-regation of a low-melting component from the viewpoint that this addition increases the time of the liquid fi lm existence. Although Pellini mentions a critical value for the accumulated strain, it is not clear whether it is ductility or another entity. The Pellini theory is a basis for a hot tearing criterion pro-posed by Clyne and Davies, who paid more attention to the time spent by an alloy in the mushy zone [6, 91].

Novikov and Novik [84] have reported that at low strain rates the grain boundary sliding is the main mechanism of deformation of a semi-solid body. The load applied to the semi-solid body will be accommodated by a grain boundary displacement that is lubricated by liquid fi lm sur-rounding the grain. Prokhorov [40, 75] proposed a model for deforma-tion of the semi-solid body. If two tangential forces τ1 and τ2 are applied to the equilibrium semi-solid body, the response of the body manifests itself as the grain movement and at some point the grains will touch one another. The liquid covering the grain will circulate to the lowest pres-sure point. Further deformation will be possible if the surface tension and resistance to liquid fl ow are suffi cient to accommodate the stress imposed. If not, a brittle intergranular fracture or hot tearing will occur. In rela-tion to this theory, Prokhorov postulated that (1) an increase in fi lm thick-ness increases the fracture strain; (2) a decrease in grain size increases the fracture strain; and (3) any non-uniformity of grain size decreases the fracture strain. Based on this theory, the main measure for hot tearing is

Hot tearing

Mechanisms Conditions and causes

MicroscopicMesoscopicMacroscopicPropagationNucleation

Liquid film or pore;Oxide bi-films;Inclusions;Vacancy clusters

Liquid fim rupture;Liquid metal embrittlementof solid bridges;Through liquid film; Vacancy diffusion

Thermal stress;Insufficient feeding;Critical pressure dropover the mush;Thermal strain;Strain rate;Liquid film distribution

Nonuniformthermalcontraction

Thermal stress;Local pressure drop;Vacancy supersaturation

FIGURE 5.23Mechanisms and conditions of hot tearing suggested to date.



Hot Tearing 223

the ductility of the semi-solid body. A hot tear will occur if the strain of the body exceeds its ductility.

Today, the mesoscopic strain rate is believed to be the most important factor, and some modern models are based on it. The physical explanation of this approach is that semi-solid material during solidifi cation can accom-modate the imposed thermal strain by plastic deformation, diffusion-aided creep, structure re-arrangement, and fi lling of the gaps and pores with the liquid. All these processes require some time, and the lack of time will result in fracture. Therefore, there exists a maximum strain rate that the semi-solid material can endure without fracture during solidifi cation. Prokhorov [75] was the fi rst to suggest a criterion based on this approach. More recently, an elaborate, strain-rate-based hot tearing criterion was proposed by Rappaz et al. [80].

A theory of shrinkage-related brittleness divides the solidifi cation range into two parts. In the upper part the coherent solid-phase network does not exist. Cracks or defects occurring at this stage can be healed by liq-uid fl ow. As the solidifi cation progresses and the solid fraction further increases, at a certain stage or a certain solid fraction a coherent network is formed. This stage is considered to be the start of linear shrinkage. From this moment, the shrinkage stress is imposed onto the semi-solid body. Fracture or hot tearing occurs if the shrinkage stress exceeds the rupture stress [3].

On the mesoscopic and microscopic levels, the important factor is believed to be the feeding of the solid phase with the liquid. In this approach, the hot tear will not occur as long as there is no lack of feeding during solidifi ca-tion. Niyama [76] and Feurer [92] use hindered feeding as a base for their porosity and hot tearing criteria. The feeding depends on the permeability of the mush, which is largely determined by the structure. Later, a two-phase model of the semi-solid dendritic network [88], which focuses on the pres-sure depression in the mushy zone, was suggested to describe the hot tear formation. This approach treats the semi-solid material as solid and liquid phases with different levels of stress and strain. The pressure drop of the liquid phase in the mush is considered to be a cause of hot tear. An extension of the two-phase model that includes plasticity of the porous network was also reported [81].

These models do not distinguish between the pore formation and the crack initiation, the void being considered as the crack nucleus. The pores should not, however, necessarily develop into a crack. The crack may nucleate or develop from another defect and then propagate through a chain of pores. Logically, bridging and grain coalescence, which determine the transfer of stress and limit the permeability of the mush, are the other important micro-scopic factors in the development of hot tearing [95].

The hot tearing theories that operate with macroscopic mechanical behavior or mesoscopic and microscopic phenomena such as feeding and porosity formation do not take into account the mechanism of crack nucleation and propagation and, thus, are intrinsically weak. The other




approach to the description of the hot tearing phenomenon is the applica-tion of fracture mechanics that describes the initiation and propagation of cracks. The liquid fi lm surrounding the grain at late stages of solidifi cation is considered as a stress concentrator of the semi-solid body [78, 83]. In this theory, a liquid-fi lled cavity acts as a crack initiator. The propagation of the crack is determined by the critical stress [83]. The critical stress can be estimated using the Griffi th energy balance approach modifi ed by taking into account the plasticity. Recently, a theory of hot tearing as a phenom-enon related to microporosity has been proposed [96]. In this approach the porosity and the hot tearing are considered sequential events. As a result, there is a possibility of predicting simultaneously the occurrence of micro-porosity and hot tearing. The model uses the feeding diffi culties at the last stage of solidifi cation as a starting point of cavity nucleation. The nucleus then grows and becomes at the end of solidifi cation either a micro-pore or a hot tear as determined by the Griffi th model for brittle crack growth. The fracture-mechanical concept of hot tearing can be enriched with the application of a liquid-metal-embrittlement mechanism [14].

It is obvious that the actual hot tearing mechanism includes phenomena occurring on two scales: microscopic (crack nucleation and propagation, stress concentration, structure coherency, wet grain boundaries) and meso-macroscopic (lack of feeding, stress, strain, or strain rate imposed on the structure). Figure 5.24 illustrates these scales during equiaxed dendritic solidifi cation.

Free flow, no hot tears

Healed cracks

Liquid film rupture

Plastic deformation of bridges Liquid metal embrittlement

High-temperature creep

Macroscopic stress

Eutectics

Soild

Mush

Slurry

Melt flow to compensate solidification shrinkage and thermal contraction

Feeding paths

Coherency Bridging

Wet grainboundaries

FIGURE 5.24Different length scales of equiaxed solidifi cation showing hot tearing mechanisms [94].



Hot Tearing 225

5.3.2 Hot Tearing Criteria

Hot tearing criteria can be conditionally divided into two categories: mechan-ical and nonmechanical. The former type of criteria involves critical stress [46, 63, 83, 90, 96], critical strain [3, 87], or critical strain rate [75, 76, 80, 81, 88]. The latter deals with vulnerable temperature range, phase diagram, and process parameters and is represented by the criteria of Clyne and Davies [6], Feurer [92], and Katgerman [93]. Let us consider these criteria in more detail.

5.3.2.1 Stress-Based Criteria

The stress-based criteria of hot tearing consider that a semi-solid body will fracture if the applied or induced stress exceeds the strength of the body. The fi rst type of these hot tearing criteria takes into account that a material has a stress limit at which it fails. This approach can be subdivided into two sets of criteria. The fi rst set is based on the strength of a liquid fi lm trapped between grain boundaries and the second set is based on the strength of bulk material.

Within the second type of stress-based criteria, the hot tearing susceptibil-ity is based on the assumption that the material contains defects or weak points, and whether they become a fracture or not depends on such parame-ters as stress, defect dimensions, confi guration of a casting, and the like. This approach is more comprehensive in describing the hot tearing phenomena. The effects of some parameters involved in hot tearing can be incorporated in these criteria, for example, grain diameter, viscosity, and liquid fraction. Although it is rather diffi cult to obtain certain material property that is com-parable to the fracture toughness of solid materials, the idea of applying frac-ture mechanics theory is interesting, particularly within the framework of micromechanics.

A stress-based hot tearing criterion that uses the strength of liquid trapped between grain boundaries was reported by Saveiko [85], Novikov [3], and Dickhaus et al. [46]. They refer to the stress needed to pull apart two parallel plates separated by a thin liquid fi lm as the strength of semi-solid metals. The assumptions that are applied in this model are the uniform distribution of liquid and no infl uence of sliding on the fracture strength. This criterion is expressed as:

σfr = 2γ/b, (5.6)

where σfr is the fracture stress, γ is the surface tension, and b is the fi lm thickness.

The constraints of this model are the negligible viscosity and wetting angle. To overcome this constraint, Dickhaus et al. [46] promoted a model proposed by A. Healy in 1926 that involved the viscosity. The separation force of the




parallel plates of radius R separated by a liquid fi lm of thickness b is given as follows:

FZ = 3πµR4

______ 8t ( 1 __ b 1

2 − 1 __ b 2

2 ) , (5.7)

where FZ is the force required to increase the fi lm thickness from b1 to b2, µ is the dynamic viscosity, R is the radius of a plate, and t is the time required to increase the fi lm thickness from b1 to b2. The equation for the fi lm thickness can be written as:

b = (1 − fs) Dgr

__________ 2 , (5.8)

where fs is the fraction of solid and Dgr is the average thickness of a solidify-ing grain.

Lahaie and Bouchard [63] proposed a hot tearing model that was an exten-sion of Equation 5.7. This model involves solid fraction fs, strain ε and micro-structure parameter m and is written as:

σfr = 4µ

___ 3b ( 1 + ( f s m _______ 1 − f s m ) ε )

−1

. (5.9)

The equation can be applied to equiaxed and columnar grain structures by adjusting the microstructure parameter m, which is 1/3 for equiaxed and 1/2 for columnar structure. The fracture stress calculated using this model decreases with grain coarsening and sharply increases at a high volume frac-tion of solid, which agrees well with the experimental data (see Section 5.2). The calculated fracture strain, however, decreases linearly with increasing solid fraction and shows no response to the grain size variation. This trend is totally different from the experimental data that show a U-shaped depen-dence of the ductility on the solid fraction (see Section 5.2). The fracture stress calculated using this criterion could explain the low tendency of tear for a fi ne-grained structure. However, the predicted negligible effect of the grain diameter on the fracture strain is questionable.

Langlais and Gruzleski [90] defi ned the hot tearing susceptibility based on the bulk strength of the semi-solid material. The susceptibility is expressed as the inverse of the maximum tensile stress. They reported the result of this criterion for Al–Si alloys. Using this criterion a typical lambda curve is reproduced. However, the silicon concentration corresponding to the maximum point of the lambda curve is different from some experi-mental data [15].

The stress-based hot tearing criteria that apply a fracture mechanics approach was proposed by Williams and Singer [83]. They modify Griffi th cracking criteria for application as a hot tearing criterion. The original Griffi th criterion considers a defect or a small crack as a stress concentrator and, therefore, the initiator of fracture. On transition to hot tearing phenom-enon, the volume of liquid in the fi nal stage of solidifi cation substitutes the defect as the crack initiator in the Griffi th equation. Williams and Singer [83]



Hot Tearing 227

argue that the fi nal liquid is the weakest point and the stress concentrator of the semi-solid body. The modifi ed Griffi th model is written as:

σfr = √ _____________

8Gγ ____________

π(1 − ν)A V L ½ , (5.10)

where σfr is the fracture stress; G is the shear modulus; γ is the effective fracture surface energy; A is a constant dependent on the grain size and the dihedral angle; VL is the volume of liquid; and ν is Poisson’s ratio. This equation has been also modifi ed for the contribution of grain size and grain boundary sliding that facilitates the liquid crack growth.

This model predicts well the variation of fracture stress with alloy com-position but fails to adequately describe the effect of grain size, predicting higher strength for coarser structures.

Recently, a formulation of hot tearing as a phenomenon related to micro-porosity is proposed [82]. In this approach both phenomena are considered in sequence. When the coherency solid fraction is reached, liquid becomes increasingly isolated in separate locations of the mush and, eventually, as a result of solidifi cation shrinkage, thermal contraction and low permeability cavities may form at triple junctions of grain boundaries. Three stages, each possibly the fi nal stage, are possible. First, the solidifi cation shrinkage and thermal contraction are completely compensated for by liquid fl ow, shrink-age fl ow and, later, high-temperature creep. As a result, potential cavities are fi lled and a fully dense structure is formed with no porosity. In the second stage, feeding possibilities are limited and the cavities develop into pores. The interplay between feeding melt fl ow and shrinkage/contraction deter-mines the transition from the fi rst to the second stage. The feeding rate is defi ned as

fe = K Ps ____ µ L m 2

, (5.11)

where Ps is the effective feeding pressure, K is the permeability as defi ned by Equation 4.6, and Lm is the length of the mushy zone. The shrinkage/contrac-tion rate is as follows:

fr = ( ρ s __ ρ 1 − 1 ) ∂f1 ___ ∂t

+ ( ρs __ ρ1 ) ε·, (5.12)

where ρs and ρl are the densities of the solid and liquid phases, respectively, fl is the liquid fraction, and ε· is the strain rate. The pore is formed if

fr > |fe| (5.13)

and will grow if

fr − |fe| ≥ ζcr, (5.14)




where ζcr is the critical feeding rate that has the same form as Equation 5.11 only with Pcr substituting for Ps. This critical feeding rate is rather small and can be taken as zero in practical simulations.

The third stage is when the cavity reaches a critical size suffi cient for the development of a crack under particular thermo-mechanical conditions. The Griffi th criterion of brittle fracture is used in this case:

a > acr, (5.15)

where a = Cd with C is the shape factor and d is the diameter of a spherical pore, and the critical defect size is defi ned as follows:

acr = 4γ E ____ πσfr , (5.16)

where E is Young’s modulus and γ is the surface tension of the liquid phase.Hot cracking susceptibility is defi ned as

HCS = a/acr . (5.17)

As a result, it is possible to predict simultaneously the occurrence of micro-porosity and hot tearing, as shown in Figure 5.25a. This model also reacts adequately to the change in the cooling rate and in the grain size. The latter is illustrated in Figure 5.25b [97]. We can see that grain refi nement increases the critical stress, and that below a certain grain size no hot cracking is possible.

0.7010−08

10−07

10−06

10−05

. , s−1

10−04

10−03

10−02

0.75 0.80 0.85 0.90 0.95 1.00

A

BC

0.80 0.85 0.90

fsfs

0.95 1.00

2.01.8

1.6

1.4

, M

Pa 1.2

1.00.8

0.60.4

0.20.0

4

3

12

1′,2′,3′,4′

FIGURE 5.25(a) Three typical regions that can be predicted by a model by Suyitno et al. [82] with no porosity (A), only porosity (B), and hot cracks (C); and (b) sensitivity of this model to the grain size: 1’, 1, 600 µm; 2’, 2, 300 µm; 3’, 3, 100 µm; and 4’, 4, 30 µm (1’–4’ show the stress accumulated in the mush while 1–4 show the critical stress) [97].



Hot Tearing 229

5.3.2.2 Strain-Based Criteria

Drawing on his extensive studies of mechanical properties and thermal contraction in the solidifi cation range, Novikov suggested a hot shortness criterion based on the ductility of semi-solid nonferrous (including alumi-num) alloys [3] (see also Sections 5.1 and 5.2). He proposed a characteristic called a “reserve of plasticity in the solidifi cation range” pr. The “reserve of plasticity” pr is actually the difference between the average integrated value of the elongation to failure (εp) and the linear thermal contraction (called linear shrinkage by Novikov) (εth) in the brittle (or effective, or vulnerable) temperature range (∆Tbr) (Figure 5.26a). The hot tearing susceptibility is then given by:

pr = S ____ ∆Tbr , (5.18)

where S is the area between the εp and εth curves in the brittle temperature range ∆Tbr.

If the εth curve intersects the εp curve (see Figure 5.26b,c) then:

pr = S1 − S2 _______ ∆Tbr

(5.19)

Of course, the situation when the semi-solid ductility drops below the accu-mulated thermal strain (contraction) is specifi cally dangerous in terms of hot tearing, especially when the temperature range of such brittleness is high as in Figure 5.26c.

Magnin et al. [87] used a similar model to predict hot tearing in a DC-cast billet of an Al–4.5% Cu alloy. They suggest that cracking occurs when the maximum principle plastic strain at the solidus temperature exceeds the experimentally determined fracture strain at a temperature close to the solidus. It has been demonstrated that hot cracking is more likely to occur at higher casting speeds, which is in line with industrial experience.

A rather sophisticated strain-based criterion was suggested recently based on a two-phase model of hot tearing [98]. In this criterion, the devel-opment of porosity under conditions of insuffi cient feeding and thermal- contraction-induced deformation is considered a potential trigger for hot tearing. However, no hot cracking occurs if (1) the liquid pressure onto the mushy zone is suffi cient for feeding (compensating) the solidifi cation shrink-age and, hence no porosity is formed or (2) the liquid pressure is below the critical value and pores do form but do not reach the critical size, or (3) the porosity starts to form at a very high fraction of solid when there is already no continuous liquid fi lm existing between the grains and the mush is suf-fi ciently strong to withstand or suffi ciently ductile to accommodate thermal stresses and strains, respectively. Thus the effective tearing strain is a meas-ure of hot tearing possibility in the vulnerable temperature range that is lim-ited by the rigidity solid fraction at the upper end and by the “no-fracture” solid fraction at the lower end. It is important that the effective tearing strain




5000

0.4

0.8

1.2

1.6E

l, t

h, %

2

0

0.4

0.8

1.2

1.6

El,

th,

%

2

0

0.4

0.8

1.2

1.6

El,

th,

%

2

520 540 560

T, °C580 600 620

500 520 540 560

T, °C580 600 620

500 520 540 560

T, °C

580 600 620

p = El

p = El

p = El

∆Tbr

∆Tbr

∆Tbr

S

S2

S2

S1

S1

εth

εth

εth

(c)

(b)

(a)

FIGURE 5.26Illustration of Novikov’s strain-based hot tearing criterion using experimentally measured elongation (El, εp) and thermal contraction (εth) in the solidifi cation range of Al–5% Cu–2.65% Li (a), Al–3.8% Cu–0.9% Li–0.45% Mn (b), and Al–3.8% Cu–0.9% Li–1.4% Mn (c) alloys [3].



Hot Tearing 231

is the strain accumulated in the vulnerable section of the mushy zone, and its value depends on the structure parameters and mush evolution, number of pores, and distribution of liquid phase [98]. The critical pore size that may develop to a hot crack is several times larger than the average grain size in a grain-refi ned material [98]. This criterion reacts adequately to the grain refi nement and casting practice. One of the consequences of the criterion is that a large number of distributed pores may effectively decrease hot tear-ing susceptibility by relaxing applied deformation. In concept this criterion is close to the stress-based criterion of Suyitno et al. [82, 97], but it does not employ fracture mechanics for crack propagation.

5.3.2.3 Strain Rate-Based Criteria

During solidifi cation, alloys are in a two-phase state: liquid and solid phases are present though in a constantly changing proportion. The liquid–solid phase transformation leads to the solidifi cation shrinkage and the solid phase then contracts, resulting in the strain development affected by geo-metrical confi guration of the solidifying body. The more complex the shape of the casting and corresponding thermal gradients, the higher the strain. Based on this fact, hot tearing criteria that are based merely on the compari-son of the ductility of semi-solid alloys and the accumulated thermal strain (thermal contraction) cannot be used for hot tearing prediction of complex castings. Prokhorov [75] proposed a hot tearing model that includes the con-fi guration of a solidifying body.

During solidifi cation, a solidifying alloy passes through a low-ductility range that is called the brittle temperature range (∆Tbr) (see Figure 5.26). The highest temperature of the brittle temperature range is known as the upper limit of ∆Tbr (Bupper), and the lowest one is known as the lower limit of ∆Tbr (Blower). Figure 5.27 shows a diagram illustrating the concept. It is very simi-lar to the previously discussed approach of Novikov.* However, Prokhorov focuses not on the thermal strain but on the thermal strain rate, considering the latter to be a determining parameter.

The strain refl ecting the appearance of a hot tear is defi ned as the limita-tion of strain capacity in the semi-solid alloy, as indicated by the intersection of the strain curve (ε) and the ductility curve (El). The intersection is deter-mined by the slope of the strain curve (strain rate), the ∆Tbr span, the shape of the El curve within the brittle range ∆Tbr, and the minimum value of elon-gation Elmin. Because the strain in the solidifying body is determined by the thermal contraction and the geometrical confi guration (thermal gradient), the strain under balance conditions can be written as follows:

εapp = εfree + εint , (5.20)

where εapp is the actual (apparent) strain in the solidifying body; εfree is the free thermal contraction strain; and εint is the internal strain from the

* Novikov considered his criterion a simplifi ed version of Prokhorov’s criterion [3].




restricted shrinkage and thermal stresses as a result of the confi guration of the solidifying body.

The reserve of technological strain in the semi-solid state (∆εres) can be approximately written in the following form:

∆εres = Elmin − (∆εfree + ∆εapp), (5.21)

with the symbols explained in Figure 5.27.The expression is divided by ∆Tbr and written as:

∆εres _____ ∆Tbr

= Elmin − (∆εfree + ∆εapp)

____________________ ∆Tbr . (5.22)

Taking into account that

ε· = ∆εres _____ ∆Tbr

T∙, (5.23)

where T· is the cooling rate, one can write Equation (5.22) in terms of strain

rate:

ε·res = ε·min − ε·free − ε

·app. (5.24)

Prokhorov [75] postulated that hot tearing occurs when ε·res ≤ 0, and there-fore when the total strain rates of free contraction and apparent strain exceed

BupperBlower

EI

Elo

ngat

ion,

The

rmal

str

ain

EI m

in

LiquidusSolidus

∆εapp

∆εres

∆Tbr

∆εfree

Temperature

FIGURE 5.27A diagram illustrating the parameters of Prokhorov’s hot tearing criterion.



Hot Tearing 233

the strain rate that can be accommodated by the ductility of the semi-solid material:

ε·min ≤ ε·free + ε·app . (5.25)

The strain rate in Equation 5.25 varies with the solidifi ed body confi gura-tion or the design factor. The left-hand side of the equation includes factors that depend on the alloy composition, and it is the hot tearing criterion. The value of ε·app is considered a function of the solidifi ed body confi guration. The higher the difference (ε·min − ε

·free ) at which the hot cracking occurs, the

worse the solidifying body confi guration in relation to hot tearing.As already mentioned, this criterion is similar in principle to the criterion

proposed by Novikov [3]. The major differences are (1) Prokhorov’s criterion uses the strain rate as a measure for hot tearing tendency, while Novikov’s criterion uses the strain; (2) Prokhorov considers both the confi guration of the solidifying body and the thermal contraction as factors of hot tearing, while Novikov’s strain criterion uses only the thermal contraction; and (3) Prokhorov uses the difference between the lowest ductility of the semi-solid body and the actual strain as the reserve plastic strain, while Novikov’s cri-terion uses the area between the ductility curve and the strain curve in the entire effective solidifi cation range.

The most recent hot tearing criterion based on strain rate, derived by Rappaz et al. [80], is widely known as the RDG criterion from the names of the three co-authors of the original paper. This criterion is based on the criti-cal pressure drop over the mushy zone that results in the formation of a void that then necessarily develops into a crack.

The reason for the void formation is primarily a pressure drop over the mushy zone that can be written as:

∆P = ∆Psh + ∆Pmech − ρgh, (5.26)

where ∆Psh is the pressure drop due to the solidifi cation shrinkage, ∆Pmech is the pressure drop due to the deformation-induced fl uid fl ow, ρ is the liquid density, h is the melt level, and g is the gravitation acceleration. The pressure drop is given by the following expression:

∆Psh + ∆Pmech = 180 µ∆T

________ G λ 2

2 [AVcastβ + B

(1 + β)ε·∆T __________

G ] , (5.27)

where G is the thermal gradient, Vcast is the casting speed, λ2 is the second-ary dendrite arm spacing, β is the volumetric solidifi cation shrinkage, ε· is the viscoplastic strain rate, µ is liquid dynamic viscosity, and A and B are the parameters accounting for the solidifi cation path, coherency development, and mass feeding.




If the pressure locally drops below the critical value ∆Pcr (taken, for exam-ple, as 2 kPa for an Al–1.4% Cu alloy [80]), a pore is formed. In this case, the hot tearing criterion appears as

∆P > ∆Pcr. (5.28)

On the other hand, the formation of a void or pore occurs only if the mush cannot accommodate the imposed strain at a given strain rate. Hence, there exists a critical strain rate at which cavitation starts. The appearance of the fi rst pore is considered a hot tear. This model emphasizes the nucleation rather than the propagation of a hot crack. The hot cracking sensitivity (HCS) is then described as:

HCS = 1 ____ ε·max , (5.29)

where ε·max is the maximum deformation rate sustainable by the mushy zone.Grandfi eld et al. [71] extended the RDG model to equiaxed microstruc-

tures. Braccini et al. [81] complemented the model of Rappaz et al. [80] with the rheological behavior of the mushy zone.

The RDG criterion is intrinsically weak because it does not take into account the accumulation of thermal strain over the entire coherent mushy zone [88].

5.3.2.4 Criteria Based on Other Principles

A well-known and widely used hot tearing criterion proposed by Clyne and Davies [6] is based on the idea that in the last stage of freezing, the liquid cannot move freely so that the strain applied during this stage cannot be accommodated by mass feeding. This last stage of solidifi cation is consid-ered the most susceptible to hot tearing. On further decreasing the liquid fraction, however, bridging between adjacent dendrites is established so that interdendritic separation is prevented and the mush acquires some strength, e.g., at solid fractions above 0.99. The cracking susceptibility coeffi cient pro-posed by Clyne and Davies is formulated as the ratio between the vulnerable time period (hot tearing susceptibility in the range between solid fraction 0.9 and 0.99) tV and time available for stress relief (mass feeding and liq-uid feeding in the range of solid fractions between coherency, e.g., 0.4, and rigidity, e.g., 0.9) tR:

HCS = tV __ tR

= t0.99 − t0.90 _________ t0.90 − t0.40

, (5.30)

where t is the time at the solid fraction denoted by indices. If the time available for feeding the solidifying solid phase is great and the time spent by an alloy under conditions of restricted feeding is short, then the alloy is less susceptible to hot tearing. This criterion works well in predicting the infl uence of composi-tion on hot cracking, i.e., reproducing the lambda curve in Figure 5.21.



Hot Tearing 235

Adequate feeding of the forming solid phase with the liquid is essential for the continuity of the solid phase and, hence, plays an important role in hot tearing phenomenon. Feeding-based criteria consider that hot tear-ing occurs due to the lack of feeding, which is related to the diffi culties of fl uid fl ow through the mushy zone as a permeable media. Let us consider the hot tearing criteria suggested by Niyama [76] and Feurer [92]. In the Niyama derivation, a pore is nucleated if a critical strain rate is achieved at which the liquid cannot fi ll the intergrain gap formed by the deforma-tion. In this model, the formation of a cavity (gap) can be considered the mechanism of hot tearing. In fact, this model is very similar to the model that Rappaz et al. [80] used for their hot tearing criterion. Feurer’s model focuses on the infl uence of alloy composition and solidifi cation conditions on the dendrite arm spacing, feeding shrinkage, and hot tearing proper-ties of aluminum alloys. In this approach hot tearing occurs due to the lack of feeding that is a result of competition of accumulated solidifi cation shrinkage and decreasing permeability. Feurer proposes two parameters, SPV and SRG. SPV is the maximum volumetric fl ow rate per unit volume (feeding term). SRG is the rate of volumetric solidifi cation shrinkage. SPV is formulated as follows:

SPV = f 1 2 λ 2 2 Ps _________

24πc3η L m 2

(5.31)

where fl is the liquid volume fraction, Ps is the effective feeding pressure, Lm is the length of porous network, and c is the tortuosity constant of dendrite network.

SRG is given by the following expression:

SRG = ∂lnV _____ ∂t = − 1 __ ρ ∂ __ ρ ___ ∂t

(5.32)

where __

ρ is the average density and V is the volume element with the constant mass in the mushy zone. SRG depends on the cooling rate and the alloy composition. The Feurer criterion says that hot tearing is possible if:

SPV < SRG (5.33)

The comparison of SPV and SRG in graphical form is shown in Figure 5.28.A model suggested by Katgerman [93] combines the assumptions of

Clyne and Davies and Feurer. The model is specifi cally developed for hot tearing during DC casting of aluminum. In the model, the effects of casting speed, ingot diameter, and alloy composition are considered. The hot tearing index is defi ned as follows:

HCS = t0.99 − tcr ________ tcr − t0.40

,

(5.34)

where t0.99 is the time when fs = 0.99 is reached, t0.40 is the time when fs = 0.40, and tcr is the time when the afterfeeding becomes inadequate. The time tcr is




determined using Feurer’s criterion and refl ects the intersection of SPV and SRG curves in Figure 5.28.

5.3.3 Application of Hot Tearing Criteria to DC Casting ofAluminum Alloys

Different casting processes impose specifi c requirements on the application of hot tearing criteria. That is why some criteria work better for shape cast-ing whereas others are more suitable for DC casting. There is no doubt that a good hot tearing criterion for DC casting should correctly respond to the casting parameters, e.g., casting speed, ramping rate, and alloy composition, and predict the vulnerable section of a billet or an ingot, e.g., the center of a round billet. Most of the existing criteria have been tested for composi-tion sensitivity by calculating the hot tearing susceptibility of several binary alloys with an attempt to reproduce the so-called lambda curve showing the maximum susceptibility at a certain composition. Most existing criteria can do this successfully. However, dynamic parameters such as casting speed

Insufficient feeding

SPV

SRG

Suf

ficie

nt-

SP

V a

nd S

RG

, S−1

10−1

10−2

10−3

10−4

620 610 600

Temperature, °C

590 580

FIGURE 5.28Dependence of SPV and SRG parameters in Feurer’s criterion on temperature during solidifi ca-tion (an Al–5% Si alloy, cooling rate 4 K/s) [92].



Hot Tearing 237

and strain rate are usually kept constant upon such testing. Therefore, the compositional sensitivity of a hot tearing criterion does not ensure its suc-cessful application to a particular casting technology.

The basic phenomena that lead to hot cracking are well established and understood, but a generic criterion that will predict hot cracking under vary-ing process conditions does not exist. Although the earlier simple criteria based on the thermal history of the casting have been extended and improved to include shrinkage and deformation, they are still unable to give reliable pre-dictions under all process conditions. As we have shown in the previous sec-tion, most of the existing hot tearing criteria do not incorporate the nucleation and propagation of a hot tear, focusing instead more on the macro-, meso- and microscopic conditions that may result in rupture (see Figure 5.23).

The ultimate hot cracking criterion should combine aspects of thermal his-tory, shrinkage and porosity formation, and constitutive behavior together with the evolution of the semi-solid microstructure. Current research efforts are aimed, in particular, at the quantitative description of structure evolution (see Chapter 3) and its correlation with cracking [21, 82, 95, 96, 99].

Recently, several mechanical and nonmechanical hot tearing criteria were evaluated by implementing them into a thermo-mechanical model of DC casting [15, 96]. The criteria show different results in predicting hot tearing susceptibility, as shown in Table 5.4 and Figure 5.29.

The criteria of Clyne and Davies and Novikov give results that are incon-sistent with casting practice, and do not show any sensitivity to the cast-ing speed and position within the billet volume. These criteria are, however, very successful in predicting the compositional dependence of hot tearing and are frequently used for shape casting. The criteria of Feurer, Katger-man, Magnin et al., Prokhorov, Rappaz et al., Braccini et al., and Suyitno et al. respond correctly to the casting parameters, demonstrating that the increasing casting speed results in an increasing hot tearing susceptibility

TABLE 5.4

Sensitivity of Hot Tearing Criteria to the Casting Parameters and Practice upon DC Casting [94, 96]

Criterion

Hot Tearing Increases

with Casting Speed

More Hot Tears in

the Billet Center

Ramping Casting Speed during

Start-Up of the Casting Reduces

Hot Tearing

Correlation with Actual Cracking

Observed in Practice

Clyne and Davies [6] No No No N/AKatgerman [93] Yes Yes No N/AFeurer [92] Yes Yes No N/ANovikov [3] No No No N/AMagnin et al. [87] Yes No No NoProkhorov [75] Yes Yes No NoRappaz et al. [80] Yes Yes Yes NoBraccini et al. [81] Yes Yes No N/ASuyitno [97] Yes Yes Yes Yes




in the center of billet, which is in accordance with casting practice (see Section 5.4). However, most of the tested criteria, except those by Rappaz et al. [80] and Suyitno et al. [82, 97], are not sensitive to the ramping of cast-ing speed during the start-up phase of casting (which is a usual practice to prevent hot cracking). When confronted with casting practice, the criteria of Prokhorov, Magnin et al., and Rappaz et al. predict the occurrence of hot cracks whereas no cracks have been found in billets cast under given condi-tions. Only Suyitno et al.’s criterion adequately responds to all tested param-eters, i.e., casting speed, ramping rate, grain size, position in a billet, and casting practice.

This is illustrated in Figure 5.30 where the results of implementation of Suyitno et al.’s criterion in thermomechanical simulation of DC casting of an Al–4.5% Cu alloy is shown [97]. One can see that the hot tearing susceptibil-ity decreases with grain refi nement (Figure 5.30a), at a lower casting speed (Figure 5.30b) and upon slower speed ramping (Figure 5.30d), which agrees with casting practice (see Section 5.4). It is important to note that the values of HCS are well below unity, which means, according to this criterion (Equa-tion 5.17), that no hot cracks are formed in the billet, which again agrees with experimental results presented in Section 5.4. The RDG criterion calculated in terms of the pressure drop (see Equation 5.28) shows in the same case studies qualitatively similar results [97], but the pressure drop under most

100Casting speed, mm/min

200

CLCLCLCLCLCLCL

Feurer

Clyne & Davies

Katgerman

Prokhorov

Novikov

Magnin et al.

Rappaz et al.

0.00.10.20.30.40.50.60.70.80.91.0

FIGURE 5.29Comparison of some hot tearing criteria in the case study of DC casting of an Al–4.5% Cu alloy with the casting speed ramped up and down during the casting as shown in the right-hand part of the diagram [15, 96, 99]. In the left-hand part, a hot tearing susceptibility is shown in half of a 200-mm billet. CL = the centerline of the billet. Lighter gray shades correspond to a higher hot tearing probability.



Hot Tearing 239

conditions exceeds a critical value of 2 kPa. As a result the RDG criterion predicts the occurrence of hot tearing in situations when hot cracking does not occur in reality.

The sensitivity of the criterion of Suyitno et al. is, however, a function of correctly chosen values of properties such as Young’s modulus of the mush, surface tension between liquid and solid, and permeability of the mush. These parameters are rarely available and must be determined experimen-tally, while the existing experimental techniques are not yet reliable.

We can see that there are two problems. First, the application of a hot tear-ing criterion is not straightforward in DC casting. In practice, only those cri-teria that incorporate dynamic parameters such as strain rate or pressure build-up are, at least qualitatively, applicable to DC casting. Second, most of the existing criteria can forecast only the probability of hot tearing and not its actual occurrence. Hence, the quest for a new hot tearing criterion is high on the research agenda.

0.15

0.12

0.09

0.06HC

S

HC

SH

CS

0.03 100 µm

300 µm

500 µm

0.00

160

150

140

130

Cas

ting

spee

d, m

m/m

in

120

110

100

90

800 50 100 150 200 250 300 350 400 450

Distance from bottom, mm

0 100 200

1

1

2

4

3

2

4

3

300 400


0 20 40 60 80 100


0 20 40 60 80 100


0.000.050.100.150.20

0.250.30

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.400.45

180 mm/min

0.50

(a) (b)

(d)(c)

150 mm/min

120 mm/min

FIGURE 5.30Some results of implementation of Suyito et al.’s hot tearing criterion in thermomechani-cal simulation of DC casting of a 200-mm billet from an Al–4.5% Cu alloy: (a) effect of grain size on HCS in the radial direction; (b) effect of casting speed on HCS in the radial direction; (c) case studies on casting-speed ramping in the start-up phase of casting; and (d) correspond-ing distribution of HCS along the centerline of a billet [97].




5.3.4 Quest for a New Hot Tearing Criterion

To date, hot tearing has been considered as a phenomenon linked to casting and welding processes, and the existing theories, models, and criteria are biased by their applicability to solidifi cation, e.g., by direct link to the solidifi cation shrinkage and limited feeding. Hot tearing is, however, just another example of material failure. Therefore, it should be treated adequately, using the well-developed methodology of fracture mechanics. The challenge nowadays lies not in the adequate description of macroscopic and microscopic stress–strain situations and their correspondence to the parameters and properties of the mushy zone, but rather in fi nding real factors causing the nucleation and propagation of hot cracks. In fact, some existing theories and models of hot tearing describe in part these factors with the crack initiator presented as a cavity fi lled with liquid or a pore [80, 82], or an oxide bi-fi lm [7] and with the crack propagation path through the liquid fi lm covering grain boundaries [14]. What is lacking is the completeness of the model. A comprehensive model and a corresponding hot tearing criterion should include nucleation and propaga-tion of hot tears and connect these processes (1) to the microstructure evolu-tion during solidifi cation of the semi-solid material; (2) to the macroscopic and microscopic thermo-mechanical situation in the mushy zone; and (3) to the mechanical (or fracture-mechanical) properties of the mushy zone. The last two components are well covered by a large body of publications, though many mechanical properties still need to be determined and the fracture mechanics potential has not been fully exploited. The correspondence between the struc-ture evolution during solidifi cation and the crack nucleation and propagation is studied in much less detail. Let us now consider the possible mechanisms of crack nucleation and propagation (see also Table 5.3).

The nucleation of hot cracks is a virtually unexplored phenomenon. It is obvious that under any stress-strain conditions, there should be a certain critical size of a defect (fl aw, nucleus) that would enable crack growth. The problem of the crack initiation is today solved by an educated guess, as only recently experimental observations on the crack nucleation upon natural hot tearing have started to emerge, fi rst for transparent analogs [21] and then for real metals [100]. Usually, the development of a hot crack is studied on samples with a notch, hence with the artifi cial crack initiator [95, 101]. Based on these observations and “post-mortem” examination of hot tear surfaces, the follow-ing crack nuclei have been suggested: (1) liquid fi lm or liquid pool; (2) pore or series of pores; (3) grain boundary located in the place of stress concentration; and (4) inclusions that can be easily separated from the surrounding liquid or solid phase, e.g., intermetallic particle or oxide fi lm. It should be noted that pores that are frequently cited as potential hot tear nuclei can originate from gas precipitation [7], solidifi cation shrinkage [7], or vacancy supersaturation [77]. Figure 5.31 summarizes some of the possible crack initiators.

The mechanism of hot tear formation and propagation can be elucidated from observations of fractures. Unfortunately, the reports on hot crack fractures in metallic materials are rare. Most such reports describe the cracking of



Hot Tearing 241

semi-solid alloys at relatively large fractions of liquid, when grain boundar-ies are completely covered with liquid. In this case the mechanism of crack propagation—through liquid fi lm by grain separation—is obvious. An exam-ple of such alloys is the classic Al–4% Cu alloy. However, alloys with high fractions of liquid in the vulnerable solidifi cation range are in practice not susceptible to hot tearing [15, 24]. Cavities and gaps between grains, which may form in the mushy zone of such alloys due to solidifi cation shrinkage, presence of not wetted inclusions, thermal contraction, or external tension, are easily fi lled with liquid due to the adequate permeability of the mushy zone and the suffi cient amount of available liquid that is represented in the fi nal structure by nonequilibrium eutectics [24]. Much more important is the mechanism of crack formation and propagation in alloys containing little sol-ute that are most susceptible to hot tearing. But the information on semi-solid fracture in such alloys is only starting to emerge. If we summarize the fi nd-ings available to date, it would appear that the bridging of grain boundaries is an essential feature of the fracture surface. Moreover, the closer the semi-solid material gets to the temperature range of its maximum vulnerability to hot cracking, i.e., 90–95% solid, the greater the fraction of grain boundaries connected to each other or coalesced [102]. In this case, there is no chance of crack propagation through a continuous liquid fi lm because such a fi lm does not exist. Recent observations [103, 104] show that a hot tear apparently prop-agates through the liquid fi lm in more alloyed materials and through solid bridges in less alloyed materials. Although in both cases the fracture sur-face appears to be brittle, we can suggest that different cracking mechanisms are acting. In real castings, cracks appear both above and below the solidus. In the latter case, these cracks are called “cold.” There are reports, however,

Mesoscopic flawPlastic

deformation

Transgranularfracture/cleavageMicroscopic

flaw/oxide film

Intergranular fracture/separation

Local deformation

Wet boundaryPore

Low-meltingphases

FIGURE 5.31Possible initiators and propagation paths for hot cracking, as compiled in [94].




that these cracks, appearing at high temperatures in the fully solid material, can originate in areas of local remelting caused by intense local deformation [105]. The liquid thus formed also assists in crack propagation. These observa-tions make such “cold” cracks in fact similar to hot tears.

Despite a large body of literature on hot tearing, little research has been done on the mechanism of hot tear propagation. We have already discussed the application of the Griffi th criterion for brittle fracture [82, 97]. Another mecha-nism is vacancy-diffusion-controlled growth [77]. The methodology for the description of crack propagation is well developed within fracture mechanics for various situations, including those resembling hot cracking, i.e., liquid fi lm rupture, pore coalescence, high-temperature creep, and liquid-assisted frac-ture [106]. It is clear that hot crack propagation in the potential presence of liquid (above or below the solidus) should involve the following aspects: liq-uid feeding (involves permeability and, inevitably, structure evolution), pore coalescence, stress transfer by solid bridges, plastic deformation and creep of solid bridges in the absence of liquid, and brittle fracture of solid bridges in the presence of liquid. It is also obvious that hot crack, like any other crack, can develop catastrophically (which is usually assumed), have sustained growth, or stop growing. Liquid feeding plays a dual role. Firstly, adequate feeding of the shrinking material with liquid does not eliminate the causes of hot tearing but rather “patches” the consequences, which is refl ected in the term “crack healing.” We can say that a semi-solid alloy containing enough liquid at the last stage of solidifi cation, having a microstructure that enables adequate permeability of the mush, and subjected to tensile stresses, is a self-healing material. On the other hand, the development of solid bridges between grains at high solid fractions in the absence of any liquid would build up enough strength and ductility to prevent any brittle rupture. Hence, the liquid feeding should be just enough to supply some liquid to solid bridges that enables their liquid embrittlement, otherwise only the mechanisms of ductile fracture, e.g., high-temperature creep and pore coalescence will be active [7]. Evidence of plastic deformation during hot tearing has been noted in direct observations [101] and upon examination of fracture surfaces [3].

We can suggest the following approach to treating the nucleation and propagation of hot cracks. Several distinct mechanisms are operational in different temperature or compositional ranges or, in other words, at differ-ent fractions of solid. Here we consider only the decreasing temperature as the factor affecting the solid fraction, though the composition is obviously the other factor that acts in a similar manner. It is important to note that the microstructure, e.g., grain size and morphology, affects the critical tempera-tures and fractions of solid. In most cases, the local stress–strain situation is crucial. Therefore, the stress concentration in specifi c locations produces the conditions for crack nucleation. The crack initiator in all cases considered below could be represented by pore, liquid pool or fi lm, interface with an intermetallic particle, or non-metallic inclusion.

At relatively low fractions of solid below the coherency temperature, the permeability of the mushy zone enables adequate feeding of the solidifi cation



Hot Tearing 243

shrinkage, and most of the precipitating gas bubbles can fl oat to the liquid part of the sample. In this case, the tensile stresses caused by non uniform thermal contraction of the coherent dendrites may cause the formation of cavities and gaps that are immediately fi lled with liquid, or “healed.”

With further temperature decrease, the tensile stress builds up to such an extent that the liquid fi lm separating grains ruptures and the gap formed can-not be fi lled with liquid due to the increasing capillary pressures required to fi ll ever narrowing openings between grains. On further cooling, the bridging between solid grains replaces former entanglement and touching of grains, and the stress can now be transmitted over larger distances through the rigid solid skeleton, hence the semi-solid body acquires macroscopic strength. This critical “rigidity” temperature can be determined experimentally as discussed in Section 5.1. It is worthwhile to recall that the rigidity tempera-ture strongly depends on the structure. Usually the bridging is referred to as the bridging between (Al) dendrite branches. Recently, Nagaumi et al. [67] made a very interesting observation on the effects of impurities on hot tear-ing susceptibility of aluminum alloys. They showed that large intermetallic particles, e.g., α(AlFeMn), that were formed early in solidifi cation, just after the aluminum solid solution, could bridge (Al) dendrite arms. As a result, the semi-solid alloy acquires some strength at a lower solid fraction, well above the zero-ductility temperature (see Table 5.2, entry HS65). Therefore, the hot-tearing susceptibility increases. In addition to the effect on the rigidity, these large intermetallic particles can effectively block the feeding channels in the mushy zone, decreasing the possibility of crack healing.

Generally, the decreased permeability of the mush in combination with solidifi cation shrinkage leads to the local pressure drop over the semi-solid region, which, in combination with the evolving gas, promotes the formation of voids at available interfaces, mainly on grain boundaries and interfaces with inclusions. The nonuniform thermal stress causes rather signifi cant strains in the semi-solid material that may or may not be sustained by the solid bridges. Even limited access of the liquid to the solid bridge will result in its brittle fracture by the mechanism of liquid-metal embrittlement. This is partly refl ected in the proposal of van Haaften et al. [107] to use the fraction of grain boundaries covered with liquid rather than the fraction of liquid in the constitutive equation for the mechanical behavior of semi-solid alumi-num alloys. The same mechanism may act at subsolidus temperatures when some amount of nonequilibrium liquid is present at grain boundaries or other stress concentrators because of nonequilibrium character of solidifi ca-tion [7] or local remelting [105]. There is also a possibility that the semi-solid material fails macroscopically in a brittle manner (because of fi lm rupture and liquid-metal embrittlement) with ductile rupture of some solid bridges on the microscopic level [101].

Finally, the fraction of bridged grain boundaries becomes so overwhelm-ingly large and the remaining liquid is so scattered in the solid network that the semi-solid material behaves like completely solid material and fails in a ductile manner by ductile pore coalescence and high-temperature creep.




The outline of these mechanisms is given in Table 5.5. Figures 5.23, 5.24 and 5.31 illustrate the correlation between these mechanisms and the develop-ment of the structure during solidifi cation.

A criterion that can predict not the probability but the actual occurrence and extent of hot tearing should be based on the application of multi-phase mechanics and fracture mechanics to the failure of semi-solid materials, which is today limited by the lack of knowledge about the actual nucleation and propagation mechanisms. The mechanisms outlined in Table 5.5 are based on the common sense and interpretation of very few experimental observations. What is needed is a thorough and systematic study of frac-tures occurring in solidifying materials with the aim of singling out the nature and the critical dimensions of defects or structure features that can cause the nucleation of hot cracks. It is also necessary, in our opinion, to acknowledge that different mechanisms of crack propagation are possible at different fractions of solid. Therefore, different models should be applied to the development of hot tears in ingots, billets, and castings depending on the alloy composition, structure, and the level of stresses that are pres-ent. For example, coarse-grained material with a large solidifi cation range and high coherency temperature is likely to fail due to liquid fi lm rupture. In the case of alloys with a considerable amount of eutectics, e.g., foundry

TABLE 5.5

Possible Mechanisms Acting in the Hot Tearing Phenomenon [94]

Temperature Range/Fraction of Solid Nucleation of Crack*

Propagation of Crack Fracture Mode

Between coherency and rigidity temperatures; 50–80% solid

Grain boundary covered with liquid, shrinkage or gas pore

a. Liquid fi lm rupture

b. Filled gap

a. Brittle, intergranular

b. Healed crack

Below rigidity temperature; 80 to 99% solid

Pore, surface of particle or inclusion, liquid fi lm or pool, vacancy clusters

a. Liquid fi lm rupture; liquid metal embrittlement of solid bridges

b. Plastic deformation of bridges

a. Brittle, interganular

b. Ductile failure of bridges possible

Close to the solidus; 98–100% solid

Pore, surface of particle or inclusion, segregates at grain boundary, liquid at stress concentration point, vacancy clusters

a. Liquid metal embrittlement

b. Plastic deformation of bridges, creep

a. Brittle, intergranular, transgranular propagation is possible

b. Macroscopically brittle or ductile, intergranular; transgranular propagation is possible

* The crack initiator should be located in the place of stress concentration.



Hot Tearing 245

alloys of the Al–Si system, the healing of cracks is most probable. In con-trast, a fi ne-grained alloy that develops coherency late in solidifi cation and does not contain much eutectics, e.g., a commercial wrought alloy, will undergo complex failure involving liquid-metal embrittlement and plastic deformation of solid bridges with a resultant mixed brittle/ductile fracture. Figure 5.32 shows a fl ow chart for the development of a new hot tearing criterion.

In summary, the development of a new hot tearing criterion faces two main challenges. First, we lack knowledge of the actual causes of crack nucleation, that is to say, we do not know exactly what defects or structure defects can act as crack initiators under particular temperature–stress conditions. Sec-ond, there is a possibility that different mechanisms of crack propagation and fi nal failure depend on the fraction of solid at which the fracture occurs and on the alloy structure. The application of multi-phase mechanics and, eventually, fracture mechanics to the phenomenon of hot cracking looks quite promising.

5.4. Effects of Process Parameters on Hot Tearingduring DC Casting

During DC casting, alloy composition and casting parameters are critical for the formation of structure and solidifi cation defects, as we have already shown in Chapters 3 and 4.

Macro- and mesoscopic parmeters:solidification shrinkage; thermal contraction;

liquid feeding; stress−strain conditions

Alloy composition:nonequilibriumsolidification

Distribution of poresand other defects:size, volume fraction

Local (microscopic) parameters:solidification range;

fraction solid at coherency, rigidity and eutectic temperature;stress, strain, strain rate;

critical size of a defect under given stess−strain conditions

Solid fr. < CoherencyNo cracks/healing

Coherency < Sold fr. < RigidityBrittle fracture with Griffith-typecriterion if feeding is insufficient

Sold fr. > RigidityBrittle and/or ductile fracturewith Kc or J- intergral type

criterion

FIGURE 5.32Flow chart for the development of a new hot tearing model and criterion [94].




The compositional dependence of hot tearing susceptibility was discussed in Section 5.3.1. However, the results that we considered previously were obtained from special hot-tearing tests, and not from real-scale DC casting. Grain refi nement is another aspect of compositional effects in hot cracking, particularly important for DC casting. Practice shows that, in general, struc-ture refi nement and homogeneity decrease the vulnerability of an alloy to hot tearing. We will look more closely at this aspect.

We also know that casting parameters play an important role in the occur-rence of casting defects [99, 108, 109]. The most important casting parameter that affects hot tearing is the casting speed [99, 110]. Water fl ow rate has much less impact [110], and the literature data on the infl uence of melt temperature are controversial [16, 110, 111].

Casting speed and other process parameters, i.e., casting temperature and water fl ow rate, are also known to affect the structure formation during solid-ifi cation. This is because of their infl uence on cooling conditions, melt fl ow, and geometry of liquid and semi-liquid parts of the billet (see Chapter 3). It is logical to suggest that the effects of casting parameters on structure forma-tion and hot tearing are correlated.

And, of course, the thermo-mechanical situation in the billet (ingot) is of paramount importance because the distribution and magnitude of stresses and strains create the external conditions for the formation of hot cracks.

5.4.1 Thermo-Mechanical Behavior of a DC-Cast Billet (Ingot)

Temperature and cooling-rate gradients and thermal contraction of the solid phase are the main reasons behind the uneven stress distribution across the billet or ingot. As a result, the regions of tension and compression are formed in different sections of a casting. The sections that are subjected to tensile stresses are most vulnerable to cracking. Hot tearing is likely to occur if ten-sile stresses spread to the semi-solid region of the billet (ingot).

We did not differentiate previously in this book between round-shaped extrusion billets and fl at-shaped rolling ingots. In the case of stress distribu-tion it is, however, important to distinguish these two basic shapes of DC-cast products. The thermo-mechanical behavior of billets is much simpler than that of ingots. In the latter case, the width-to-thickness ratio plays a role in stress distribution. The shape distortions are also more diverse in the case of ingots.

Figure 5.33 demonstrates schemes of stress distribution for a round billet (a) and a fl at ingot (b) [112]. For the billet, the pattern is simple—a region of tensile stresses is located in the center of the billet, while the periphery expe-riences compression. Accordingly, hot cracks usually appear in the central section of the billet.

Stress distribution in the ingot is more complicated with the zones of tension concentrated closer to the short-side surface (along a′–c′ direction in Figure 5.33b) and corners. There is still a possibility of tensile stresses



Hot Tearing 247

in the central section of the ingot but the magnitude of these stresses is usually con-siderably less than those at the short-side periphery (area c–c′–a–a′ in Figure 5.33b). As a result of this stress distribution, hot cracks appear closer to the short side of the ingot. The situation is further complicated by the deformation of the wider (rolling) face of the ingot (along l direction in Figure 5.33b). As the compression stress is higher at the surface than in the interior, and is greater in the middle of the rolling face than closer to the edges (where it in fact changes to the tensile stress), the whole wider face of the ingot bends inward, exhibiting so-called pull-in distortion (Figure 5.34). Con-sequently, the part of the solid shell closer to the mush experiences tension and is prone to cracking. Hot tear can appear if this tension region expands to the mush, as shown in Figure 5.34. In practice, modern molds are designed in a convex shape so as to compensate for the pull-in of the rolling face and, therefore, reduce scalping of the ingot before rolling.

Com

pres

sion

Ten

sion

c ′

a′

b′b

l

b

ca

(a) (b)

FIGURE 5.33Distribution of stresses in vertical cross-section of a round billet (a) and a fl at ingot (b) in a steady-state regime of DC casting. (After Livanov [112].)

Liquid

Mush

Pull-in

Solid

Butt swell

Butt curl

Starting block

FIGURE 5.34Shape distortions typical of DC-cast ingots. A view from the short side of the ingot.




Quite obviously, the increase in the casting speed that results in the deep-ening of the sump and thinning of the shell will make the pull-in more pro-nounced with the consequence of more hot tearing in the subsurface layer.

In addition to “pull-in,” two other shape distortions are typical of DC cast-ing, namely butt curl and butt swell (see Figure 5.34). These defects occur in the initial stage of casting close to the bottom end of the casting, which is nick-named “butt.” Both ingots and billets are prone to butt curl and swell.

Rapid cooling of the bottom end of the casting immediately after the exit from the mold—both from the starting block and from the direct water jet—produces excessive thermal stresses that lift up the corners (edges) of the ingot (billet), forming the butt curl. This defect can lead to dangerous conse-quences as the casting loses the fi rm stand on and the thermal contact with the starting block. As a result, the casting can deviate from the verticality, the bottom part may remelt with subsequent bleed-out of the melt, and the water may enter the formed gap and vaporize with ingot “bumping” on the starting block. Cracks may form due to the stress concentration.

The butt swell is a result of lesser apparent linear thermal contraction of the bottom part of the ingot (billet). This part is formed in the mold closed by the starting block when the sump is shallow. As soon as the casting exits the mold and the direct cooling is applied, the sump deepens and the thermal contrac-tion of the shell becomes more pronounced because the liquid interior does not offer much resistance [28]. Therefore, the bottom appears to be swollen whereas, in fact, the rest of the casting is more contracted. The butt swell leads to the removal of the ingot (billet) butt prior to the downstream processing.

It is clear that the distribution of stresses and strains in the billet (ingot) is of paramount importance for the occurrence of cracks. Nonuniform cooling across the thickness of the billet (ingot) plays the main role in the develop-ment of thermo-mechanical situation upon DC casting. The surface is cooled much faster than the core and, in addition, there is a difference in cooling rates in the subsurface layer that is formed sequentially as the casting passes through the regions of primary cooling, air-gap and secondary cooling (see Figures 3.14a,b and 3.15). In addition, there is a frequently observed accel-eration of cooling in the center of the billet (ingot), a phenomenon that we discussed in detail in Section 3.2 (Figure 3.14c,d). Figure 5.35 shows the experimentally measured distribution of cooling rates in the vertical cen-terplane of a 2024-alloy billet cast at two casting speeds. The measurements were performed by thermocouples traveling downward with the billet as we described in Section 3.2. The cooling rates that are shown in the fi gure are the instant cooling rates (tangents to the cooling curve) taken at different times of solidifi cation. Therefore, these data do not refl ect the total solidifi cation time but rather the instantaneous cooling situation in the specifi c location of the billet. Two conclusions can be drawn from the cooling-rate distribution shown in Figure 5.35. First, there are two distinct regions of high cooling rate, at the surface in the point of water impingement and in the center of the billet. Second, the cooling rates and the gradient of cooling rates in the radial direction of the billet increase as the casting speed increases.



Hot Tearing 249

As a result of uneven cooling and uneven solidifi cation progress in the radial direction of the billet (ingot), a peculiar thermo-mechanical situation is created in DC castings, as shown in Figure 5.33. Let us look at the rather simple situation in a round billet. The solid shell has already cooled suffi -ciently and undergone most thermal contraction, when the inner core of the billet enters the solidifi cation domain and, in particular, passes the isotherm of rigidity. This inner core wants to contract but the solid shell is robust enough to offer a considerable resistance to the shape change. As a result, the contraction of the inner core is constrained and tensile stresses start to build up there, whereas the shell remains under compression.

The build-up of stresses starts from the beginning of casting, passes a transient stage, and then stabilizes in the steady-state regime of casting. The start-up of casting is the most critical stage in the process because the development of stresses is a function of the sump evolution (see Figures 3.3 and 3.4) and the casting recipe (how the casting speed changes in the tran-sient stage of casting).

Three stresses and strain components can be distinguished in the round billet, i.e., axial, radial, and circumferential. The combination of these three components when they are in tension may result in the failure of the semi-solid material with crack propagation in the plane normal to the strongest

450

400

350

300

250

200

150

100

50

Dis

tanc

e fr

om th

e m

elt l

evel

in th

e m

old,

mm

30 mm/min 60 mm/min

Mold bottom

S

L

S

L0.7

1.2

3.5

1.72.25 1.61.4

2.251.8

1.61.4

1.2

0.8

2.5

2.2

1.6

3.2

3.9

2.5

3.23.8

2.2

1.6

FIGURE 5.35Experimentally obtained distribution of cooling rates (isolines marked in K/s) in a 470-mm billet of a 2024 alloy cast at 30 (left) and 60 (right) mm/min [109]. L and S denote liquidus and solidus isotherms, respectively. Mold without hot top has been used.




tensile stress. Suyitno et al. [97, 113] performed a thorough analysis of stress and strain distribution during steady-state and transient (start-up) regimes of DC casting. Some of the results are shown in Figure 5.36. It can be imme-diately seen from Figure 5.36a that the maximum tensile stresses at tempera-tures above the solidus are concentrated in the center of the billet with radial (CR) and circumferential (CC) components prevailing. At the periphery of the billet (10 mm from the surface) only the circumferential component (PC) is in tension. This stress distribution may help explain why the hot crack in the round billet spreads along the axis (normal to radius) and in radial ( normal to circumference) directions.

200150100500−150

−100

−50

0

50

100

150

200

Solidus center

Solidus periphery

Semi-solid

Semi-solid

Str

ess,

MP

a

Time, s

150 200 250 300 350 400 4501005000

5

10

Circ

umfe

rent

ial s

tres

s, M

Pa

15

20

25


PC

PA

PR

CR; CC

CA

12

4

3

(a) (b)

0.010

0.008

0.006

0.004

0.002

0.0000 50 100 150 200 250


300 350 400 450

3

14

2

Circ

umfe

rent

ial v

isco

pla

stic

str

ain

(c)

FIGURE 5.36Calculated development of stresses (a,b) and strains (c) during DC casting of a 200-mm billet of an Al–4.5% Cu alloy: (a) steady-state regime at a casting speed of 120 mm/min, axial (second index = A), radial (R) and circumferential (C) stresses in the center (fi rst index = C) and at the periphery, 10 mm from the surface (P). Solidus line indicates the position of nonequilibrium solidus in the billet, semi-solid region is on the left of this line; (b) and (c) start-up stage of casting, circumferential stress and strain, respectively, numbers correspond to different start-up regimes as shown in Figure 5.30c [97, 113]. (Reproduced with kind permission of Springer Science and Business Media.)



Hot Tearing 251

In a transient regime of casting, in particular during the critical start-up stage, the evolution of stresses and strains depends on the casting regime. There is an obvious correlation between the development of tensile stresses and strains at the centerline of the billet (Figure 5.36b,c), the hot tearing sus-ceptibility (Figure 5.30d), and the depth of the sump and the thickness of the mush (Figure 3.4b,c). The most rigid casting recipe (3 in Figure 5.30c and Figure 5.36b,c) shows the highest tensile stress and strain in the center of the billet, which also reach their maxima at the maximum sump depth (Figure 3.4b). The most gentle start-up mode (2 in Figure 5.30c and Figure 5.36b,c) produces more moderate stresses and strains, which results in less hot tear-ing susceptibility (Figure 5.30d). A realistic start-up regime (4 in Figure 5.30c) suffi ciently reduces the maximum tensile stress and strain (Figure 5.36b,c) and, correspondingly, the hot tearing possibility (Figure 5.30d).

5.4.2 Effects of Composition and Casting Speed on Hot Tearingduring DC Casting

It is interesting to know whether the compositional dependence of hot tearing (see Figures 5.21 and 5.22) is still valid in DC casting, and not overwhelmed by the specifi c thermo-mechanical situation that is caused by cooling condi-tions. In order to check this, several binary Al–Cu alloys with compositions given in Table 5.6 were tested upon casting 200-mm billets in a pilot DC caster [99]. An experiment scheme with ramping up and down the casting speed was chosen, as illustrated in Figure 5.37a.

The billets were checked for the occurrence of hot cracks in horizontal sec-tions refl ecting different casting speeds and in the vertical centerplane of the billet. The large sections were cut and polished, and the hot crack suscepti-bility (HCS) was quantifi ed as the area affected by cracks in the horizontal cross-section (Acrack) divided by the area of the billet cross-section (Atotal), as shown in Figure 5.37b.

Hot cracks were observed only in alloys 1–3 from Table 5.6. Cracks appeared in the central part of the billet and had a typical spider-type shape in the billet cross-section, as shown in Figure 5.38. In most cases cracks had the appearance of spreading from the center in radial directions.

TABLE 5.6

Chemical Composition of Tested Alloys as Determined by Spectrum Analysis

Alloy No. Cu, wt% Fe, wt% Si, wt%

Other Impurities, Total wt%

1 1.03 0.16 0.04 0.042 1.98 0.18 0.06 0.033 2.93 0.19 0.10 0.044 4.49 0.19 0.06 0.03




60040020000

50

100

Cas

ting

para

met

er

150

200

Billet length, mm

AtotalAcrack

(a)

(b)

Water flow rate, l/min


FIGURE 5.37Process chart of DC casting experiment with ramping the casting speed (a) and a scheme for hot tearing quantifi cation (b) [99]. (Reproduced with kind permission of Springer Science and Business Media.)

FIGURE 5.38Experimentally observed hot crack in the centerplane of a 200-mm billet from an Al–2% Cu alloy cast according to the schedule shown in Figure 5.37a. Billet bottom is on the left. Horizontal slice in the center corresponds to the maximum casting speed.



Hot Tearing 253

The dependence of hot cracking susceptibility on the casting speed and copper concentration in the examined billets is illustrated in Figure 5.39. Hot cracking depends strongly on the casting speed. The casting speed required for the initiation of crack is higher than the casting speed at which the crack stops or heals.

The concentration dependence of hot tearing shows the existence of the compositional range of maximum hot cracking susceptibility, between 0.5 and 1.5% Cu. It should be noted that almost no hot tearing at any given casting speed (the range was extended up to 220 mm/min) was observed in alloys that contained more than 4% Cu (alloys containing up to 5.6% Cu were studied). The larger hot tearing sensitivity at lower copper concentra-tions can be explained by a thicker mushy zone in these alloys (region with hindered feeding or low permeability), less residual liquid available for feed-ing (represented by the amount of nonequilibrium eutectics in Figure 3.27e), more time spent in the vulnerable temperature range [6], and larger defor-mations induced by thermal contraction [24].

We have already discussed that there is a correlation between the dimen-sions of the sump and mush and the development of stresses in the billet (Section 5.4.1). Figure 5.40 shows the effect of copper concentration on the vertical distance between the liquidus and solidus (transition region) in the billet cast at two speeds in the examined range. These data are obtained by computer simulation where nonequilibrium solidifi cation has been assumed, with the equilibrium liquidus and the nonequilibrium solidus, the latter was taken as a temperature of the binary eutectic, 548°C. The transition region becomes wider with the increasing casting speed and decreasing copper

0.05

0.04

0.03

0.02

0.01

0.00

0.50.

0

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

1416

18 −20 −18 −16 −14 −12 −10

12

10

HC

S

Cu, %

Casting speed up, cm/min Casting speed down, cm/min

FIGURE 5.39Effect of composition and casting speed on hot tearing susceptibility of DC-cast Al–Cu alloys [99]. The casting schedule is shown in Figure 5.37. (Reproduced with kind permission of Springer Science and Business Media.)




concentration, which agrees well with the hot tearing tendency. Another observation is that the transition region tends to narrow in the central part of the billet. This feature becomes more pronounced at higher casting speed and copper concentration.

Casting experiments with ramping the casting speed up and down exhibit one peculiar feature. The maximum of hot tearing corresponds not to the maximum casting speed but to a certain speed at the deceleration stage of casting (Figures 5.37a and 5.39). Such behavior has been also reported by Commet et al. [114] and explained in terms of the thermal inertia in the development of the sump. We have considered this phenomenon in detail in Chapter 3 (see Figure 3.5). This observation proves that the most important parameter for the development of hot cracking is the sump depth rather than the casting speed proper.

10

20

30

40

4080120160200

0 1.02.0

3.04.0

Cu, %

5.0

50

60


10

20

30

40

4080120160200

0 1.02.0

3.04.0

Cu, %

5.0

50

60

Billet cross-section, mm(b)

(a)

Dis

tanc

e be

twee

nliq

uidu

s an

d so

lidus

, mm

Dis

tanc

e be

twee

nliq

uidu

s an

d so

lidus

, mm

FIGURE 5.40Effect of copper on the width of the transition region in a 200-mm billet cast at (a) 100 mm/min and (b) 200 mm/min [99]. (Reproduced with kind permission of Springer Science and Business Media.)



Hot Tearing 255

Thermomechanical simulation of the billet shows that tensile stresses and strains are concentrated in its central part, which is in line with our previous discussion in Section 5.4.1. What is more important is that these tensile stresses and strains start to appear already in the mushy zone, and this “ penetration” of tensile stress and strain into the mushy zone strongly increases with increasing casting speed, as demonstrated in Figure 5.41 for strains (the pattern for stresses looks similar).

The stress–strain situation is a necessary but not suffi cient condition for the appearance of hot cracks. This becomes clear when we compare alloys with different copper concentration (Figure 5.39). The feeding of the solidi-fying material with the melt should be inadequate for compensation of the

(a) (b)

FIGURE 5.41Distribution of strains (positive values mean tensile strains) in the vertical cross-section of a 200-mm billet cast at (a) 100 mm/min and (b) 200 mm/min [99]. TL and TS are the temperatures of liquidus and solidus, respectively. Surface is on the left and the centerline (CL) is on the right of each image. The position of the liquidus isotherm differs from those shown elsewhere in this book (e.g., Figures 3.6, 3.16) because in the simulations shown in this fi gure fl uid fl ow has not been taken into account. (Reproduced with kind permission of Springer Science and Business Media.)




solidifi cation shrinkage and thermal contraction [15, 80] (see also Sections 5.3.1 and 5.3.2). Hence, the amount of liquid available at the crucial stage of solidifi cation, when the semi-solid material is most vulnerable and the hot cracking susceptibility is high, is extremely important. Figure 3.27 clearly demonstrates that the amount of eutectics (last liquid to solidify) is decreas-ing toward the center of the billet, with this tendency more pronounced at higher casting speeds and lower copper concentrations. This observation fi ts well into the mechanism of hot tearing, proving that the amount of available liquid at the end of solidifi cation is lower in the most critical part of the billet and in the most crack-sensitive compositional range. The amount of eutectic structure constituent, therefore, can be an important structure indicator of the vulnerability of the alloy to hot cracking at the particular location in the billet.

One of the common practices to improve the structure and properties of as-cast material is grain refi nement (Section 2.4). Apart from making the grain size smaller and its distribution more homogeneous across the billet, grain refi nement results in a lower thermal contraction in the solidifi cation range (Figures 5.7, 5.9, and 5.10) through the delay in the rigidity development; improved tensile strength (Figure 5.13a) and ductility (Figure 5.17a) of a semi-solid material; and lower permeability of the mushy zone at high volume fractions of solid (Equation 4.6). The complex interaction of these phenomena generally results in a decreased hot tearing susceptibility (Figure 5.22). Recently the positive effect of grain refi nement on the development of hot tears in commercial 1050, 3104, and 5182 alloys was demonstrated by Lin et al. [104].

First of all, let us look at the effect of grain refi nement on the development of hot tears during DC casting. We studied the structure of a 200-mm billet from a commercial 7075 alloy [115, 116]. In the fi rst experiment, part of the bil-let was cast without grain refi nement, then grain-refi ning Al–Ti–B rod was fed to the melt in the launder. The transition from coarse to fi ne structure is obvious on the macrostructure, as shown in Figures 5.42a, 3.21b, and 3.22. The crack readily appears from start-up of casting at a speed of 80 mm/min and propagates along grain boundaries (Figure 5.42b). The crack, however, vanishes when the grain refi ning is started and the grains become smaller, as vividly demonstrated in Figure 5.42a,c. The crack again re-appears when the casting speed is increased to 120 mm/min. In the second experiment, the grain refi ner was added in the furnace. In this case, no cracks were found throughout the billet irrespective of the casting speed. The grain size, as shown in Figure 3.21b, decreases dramatically with the grain refi ner added (from 1080 to 165 µm), but depends only slightly on the casting speed (165 and 95 µm at 80 and 120 mm/min, respectively) and does not depend on the way the refi nement was performed. Figure 3.21d demonstrates that the dendrite arm spacings in the center of the billet are close for grain-refi ned and non-grain-refi ned billets, 22–23 µm. We may conclude that grain refi nement can effi ciently hinder the development of hot crack in high-strength aluminum alloys. The fact that the crack re-appeared at a higher casting speed in the



Hot Tearing 257

1000

µm

(a)

(b) (c)

FIGURE 5.42Crack propagation and healing during DC casting of a 7075 alloy: (a) macrostructure showing the transition region from nongrain-refi ned to grain-refi ned structure; (b) propagation of hot crack along grain boundaries in nongrain-refi ned part of the billet; and (c) microstructure of the zone where hot crack stopped [117].




fi rst experiment and does not appear at all in the second experiment may be due to different localization of stresses and strains in the billet that has been already weakened by a crack.

There are, however, some experimental data showing that structures with very fi ne grains exhibit somewhat enhanced hot tearing [73]. Several phe-nomena may play a role here [117].

Grain refi nement can affect permeability in a nonlinear manner. The structure modifi cation may include the transition from columnar dendritic to equiaxed dendritic and then to cellular, nondendritic grains. As a result, the structure parameter that determines the permeability changes from den-drite arm spacing to grain size (Equation 4.6). The coherency temperature and, therefore, the region where stress development and feeding take place becomes narrower upon grain refi ning or, in other words, corresponds to higher volume fractions of solid. There is also a change in the liquid distri-bution between the grains with associated different capillary pressures and stress localization.

The decrease of permeability associated with the grain refi nement, espe-cially for grain sizes below 300 µm, can be fully compensated for by the delay of thermal strain development and reduction of liquid fi lm thickness [117]. As a result, the hot tearing susceptibility decreases with grain refi ne-ment as long as the grain remains dendritic [104]. This analysis agrees well with our results, as demonstrated in Figure 5.42 and with casting practice [73, 118].

If the grain refi nement is accompanied by the transition from dendritic to nondendritic grain morphology, the analysis based on interplay between permeability and stress development shows the hot tearing susceptibility may increase again, especially for cellular grain size below 50 µm [119]. At the same time, we see that for grain sizes above 100 µm the hot tearing sus-ceptibility of fi ne grains is almost always less than that of coarser grains, irrespective of their dendritic or globular morphology [119].

There are only a few examples of commercial DC-cast billets or ingots with nondendritic grain structure. One of the technical means to achieve the nondendritic structure in commercial-size billets and ingots from alu-minum alloys is ultrasonic (cavitation) melt treatment [120]. There are no direct reports on the change of hot cracking susceptibility upon transition to nondendritic structure. However, nondendritic structure with grain sizes between 20 and 80 µm has been obtained in large ingot and billets from high-strength 2XXX and 7XXX series alloys cast with cavitation melt treat-ment [120]. No cracks, either hot or cold, have been found in these billets and ingots, whereas billets and ingots with dendritic grain structure cast under the same conditions but without ultrasonic treatment always had cracks. These practical data prove that analytical models cannot encompass the entire complexity of the nature but, at the same time, they can be very use-ful in the analysis of contributions of individual phenomena that frequently counteract one another in reality.



Hot Tearing 259

5.4.3 Effect of Melt Temperature on Hot Tearing duringDC Casting

In contrast to casting speed, the melt temperature has not received much attention with regard to its infl uence on hot tearing in DC-cast billets. Only few experimental results are available on the subject, which can be explained by technological diffi culties accompanying high pouring temperatures dur-ing DC casting. Grün and Schneider [121] examined billets of grain-refi ned commercial aluminum obtained by level pour DC casting at different pour-ing temperatures, 700 to 740°C. They concluded that the increase in melt temperature resulted in the development of feathery columnar grains and higher temperature gradients closer to the mold. Tarapore [122] and Reese [123] reported the increased depth of the sump, higher temperature gradients in the liquid bath, and a thinner surface liquation layer corresponding to a higher melt temperature upon DC casting. The effects of melt temperature on the structure, hot tearing, and quality of experimental and shape cast-ings have been studied and reported on several occasions, e.g., [3, 16, 72, 124]. Under conditions of moderate superheating (<250 K), the observations agree well with each other, i.e., the following phenomena occur with increasing melt temperature: coarsening of grain structure, development of columnar grains, and higher hot cracking susceptibility. However, direct applicability of these results to DC casting is unclear, and more direct experiments are required.

Such experiments were performed during DC casting of an Al–2.8% Cu alloy [111]. This alloy was chosen because it provides an opportunity for hot cracks to occur (Figure 5.39) but, at the same time, it is not at the peak of hot-tearing susceptibility, which makes casting safer. A casting schedule similar to that shown in Figure 5.37a was used. The melt temperature in the furnace (T1) was 700, 720, 740, and 760°C corresponding to 47, 67, 87, and 107°C of superheat, respectively. The temperature drop over the melt delivery sys-tem was measured by a thermocouple placed at the entrance to the hot top (T2 in Figure 5.43a). Additional temperature data were collected from a ther-mocouple inside the mold assembly, in the center at the bottom edge of the hot top, as shown by T3 in Figure 5.43a. The homogeneity of temperature dis-tribution in the hot top and in the mold depends on the casting regime (Fig-ure 5.43b). In the steady-state mode, the temperature drop over the hot top (difference between T2 and T3 in Figure 5.43) decreases and become negli-gible. In contrast, ramping up of the casting speed increases the temperature difference because of the faster temperature rise at the inlet (T2) as compared to the temperature change inside the mold (T3).

These rather dramatic temperature changes do not cause adequate changes in the geometry of the sump [125]. Table 5.7 summarizes the results of tem-perature measurements and calculated sump dimensions. The only differ-ence is narrowing (!) of the transition zone in the center of the billet upon increasing the melt temperature. This is a consequence of a faster downward




moving of the liquidus isotherm as compared to the solidus and coherency isotherms.

The very slight changes in the geometry of the sump suggest that there should not be so much difference in hot tearing susceptibility of the tested alloy. The experimental results, however, show less hot cracking during cast-ing at a higher melt temperature (see Table 5.8).

Macrocrack is a crack visible with the naked eye in the cross-section of the billet. It has dimensions in the range of centimeters and usually spreads in radial directions in the horizontal cross-section of the billet, as shown in Fig-ure 5.38. Figure 5.44 demonstrates at a higher magnifi cation that macrocracks propagate along grain boundaries. Microcracks are cracks observed at grain boundaries in an optical microscope. They usually separate several grains (Figure 5.44b,c). Frequently one can observe a rather thick line of eutectic

Inlet

T2T3

Hot top

Mold

Billet

Casting direction

Time

Casting speed

Par

amet

er

T1

T2

T2

T3T3

(a) (b)

FIGURE 5.43Scheme of temperature measurements (a) and a process chart for DC casting of a 200-mm billet from an Al–2.8% Cu alloy (b): T1 = the temperature in the furnace; T2 = temperature at the inlet; and T3 = temperature at the bottom of hot top inside the mold.

TABLE 5.7

Effect of Melt Temperature and Casting Speed on Temperature Distribution and Sump Dimensions in a 200-mm Billet from an Al–2.8% Cu Alloy [111, 126]

Regime

Vcast

mm/min/T1, °C

Melt Temperature, °C T2/T3 in Figure 5.43

Width of Transition Zone, mm

Center/Periphery

Width of Mushy

Zone, mm Center/

Periphery

Sump Depth,

mm

Steady 200/700 675/675 145/13 24.5/7 166Transient* 695/675 100/13 11/7 123Steady 200/760 725/725 138/13 23/7.5 169Transient* 750/725 92/13 11/7.5 125

* Ramping rate in the transition mode 113.2 mm/min2.



Hot Tearing 261

along grain boundaries of several grains. We interpret this as a healed crack that has been fi lled with the liquid during the last stages of solidifi cation (Figure 5.44c,d). In addition to healed cracks, a series of small pores along several grain boundaries is observed (Figure 5.44d).

TABLE 5.8

Experimentally Observed Hot Tearing and Related Structure Features in 200-mm Billets from an Al–2.8% Cu Alloy [111]

Melt Temperature in the Furnace, °C

Ramping Casting Speed, mm/min

100 150 200

700 No Macrocrack Macrocrack720 No Microcracks and

healed cracksMicrocracks and healed cracks

740 No Pores along grain boundaries and healed cracks

Numerous micro- and healed cracks

760 No No Pores along grain boundaries and healed cracks

100 µm1000 µm

500 µm 200 µm(d)(c)

(a) (b)

FIGURE 5.44Typical structures related to hot tearing observed in the central part of billets cast at a speed of 200 mm/min (upon ramping) and different melt temperatures in the furnace: (a) 700°C, inter-crystalline macrocracks; (b) 720°C, intercrystalline microcrack and healed cracks; (c) 740°C, intercrystalline microcrack, series of pores, and healed cracks; and (d) 760°C, series of pores, healed crack.




The experimental results and computer simulations show that upon increasing the melt temperature the mushy zone retains its dimensions in the center of the billet and the transition region overall becomes slightly thinner (Table 5.7), meaning that under the same casting conditions the alloy spends the same or less time in the vulnerable range. At the same time, the liquid bath (distance to the liquidus) and the sump as a whole become slightly deeper with increasing melt superheat, resulting in a larger metallo-static pressure onto the mushy zone and, therefore, better feeding of the melt to the potential cracks. This is revealed in the structure as “healed” cracks, relatively long paths spread along several grain boundaries and fi lled with eutectics, as shown in Figure 5.44c,d. We have already noted in the previous section that the amount of nonequilibrium eutectics representing the last liq-uid available for solidifi cation is a characteristic structure feature refl ecting the vulnerability of the alloy to hot tearing: the greater the amount of eutec-tics, the lesser the hot tearing [99]. Figure 3.27c,d shows that the amount of eutectics, especially in the center of the billet, which is most vulnerable to hot tearing, increases with the melt temperature, which corresponds well to the decreased hot tearing. We can suggest that, upon increasing the melt super-heat, a coarser dendritic structure (Figure 3.23) may present wider channels for the liquid phase, and a stronger melt fl ow in the mushy zone (Fig ure 3.9) may further facilitate the liquid feeding of the solid phase in the center of the billet, thereby producing more eutectics. In addition to the feeding phe-nomena, one of the main causes of hot tearing is the tensile stress/strain that arises in the center of the billet from inhomogeneous thermal contraction of the coherent solid skeleton in the mushy zone. It has been shown that the thermal contraction is preceded by the expansion caused by evolution of gas dissolved in the melt [15, 24, 27]. This expansion can considerably lower the overall stress/strain in the mush and decrease the vulnerability of the mate-rial to hot tearing. One can argue that even a small increase in hydrogen solubility at a higher melt temperature results in more gas evolving during solidifi cation (the process actually occurs in the slurry zone where the expan-sion is observed and not in the mush where it causes the porosity) and the resultant pre-shrinkage expansion diminishes the hot tearing susceptibility.

5.4.4 Structural Features Associated with Hot Tearingin DC Casting

There are certain structure features that can be associated with hot tearing. We have already mentioned the amount of eutectic and degree of porosity. It is possible that different mechanisms of fracture are acting at different stages of solidifi cation, as we discussed in Section 5.3.3. There are also differ-ent levels of semi-solid failure, from chains of pores through healed micro-cracks to fully developed macrocracks (Figure 5.44).

A more thorough analysis of fracture surfaces and microstructure features around the cracked region is required and has been performed on cracked billets from alloys given in Table 5.6 [103].



Hot Tearing 263

Recall that hot tears are observed under given casting conditions (Fig-ure 5.37a) only in the alloys containing 1−3% Cu (Figure 5.39). The hot tear surfaces of the Al−(1–3)% Cu alloys as they appear in the center of the bil-let at a casting speed of 200 mm/min are shown in Figures 5.45–5.47. The fracture surface is smoother at a higher copper concentration, with regions of eutectics covering at least part of the surface. These eutectic regions indi-cate the existence of liquid fi lm at the fracture surface of alloys containing appreciable amount of copper. The fracture in the alloys containing 2–3% Cu is obviously intergranular. At a copper concentration of 1%, the fracture surface is dominated by bridged grain boundaries. In this case, the fracture surface shows features of brittle and, possibly, transgranular failure.

A micrograph in Figure 5.48 shows the place in the Al–3% Cu billet where the macro-crack stops. One can see a “path” ahead of the crack tip that extends over the length of several grains. This path is fi lled with eutectic and, closer

100 µm

50 µm

10 µm

Fractured bridges

FIGURE 5.45Fracture surface of a hot tear in an Al–1% Cu alloy (no. 1 in Table 5.6), SEM [103]. (Reproduced with kind permission of Elsevier.)




to the crack tip, contains micropores (insert b in Figure 5.48). These pores are retained until the end of solidifi cation and are either fi lled with eutectic (insert c) or remain empty (insert d).

The hot tear surfaces observed in the billets of Al−Cu alloys containing 2 and 3% Cu are in accordance with previous observations for model and commercial alloys [3, 19, 46, 101, 126] in terms of visible dendrites on the frac-ture surface and liquid fi lm covering the surface of these dendrites. The solid bridging, which is clearly seen on fractures at a copper concentration of 2% (Figure 5.46), has been also reported in several papers, but not for the fracture surface of a hot tear [19, 102, 127]. Apparently, the hot tear propagates either through the fully liquid fi lm or through the liquid fi lm and solid bridges, as has been suggested on several occasions [9, 19, 104] (see also Section 5.3). The fi rst mechanism will result in the smooth hot tear surface and the second one will result in the hot tear surface with fractured solid bridges.

Eutectic

Bridges

10 µm

50 µm

100 µm




Hot Tearing 265

The fraction of a bridged grain boundary at a given solid fraction during solidifi cation depends on the alloying content, and tends to be less in more alloyed materials [127]. This is evident from the eutectic fraction in the as-cast sample, bearing in mind that the nonequilibrium eutectic liquid is the last available liquid that solidifi es. Figure 3.27e shows that the amount of eutectic in billets increases with increasing concentration of copper in alloys. The greater the amount of eutectic available, the greater the probability of shrinkage compensation by liquid feeding and the possibility of crack healing. In Figures 5.44c,d and 5.48 we can see a solute-rich (eutectic) path along several grain boundaries as a continuation of the hot crack, which could be evidence of fl uid fl ow in the dendritic network and crack healing. The eutectic-liquid feeding will prevent formation of a cavity that results from solidifi cation shrinkage, deformation due to thermal contraction,

Eutectic

Eutectic

10 µm

50 µm

100 µm





and gas release. If the eutectics amount is small and insuffi cient to cover grain boundaries and to form a continuous liquid fi lm, then solid grains coalesce through bridging, and the intergranular crack should propagate through these bridges. At the same time, a semi-solid material acquires strength through coalescence and bridging of grains. This has two conse-quences. On the one hand, the stress can now be transferred through the semi-solid mush and the forces of thermal contraction of the external shell of a billet can be translated into tensile stresses in the center of the billet. On the other hand, the build-up of strength can be faster than the build-up of stresses, and at a certain (high) solid fraction the mush would be strong

(a)

(b)

(c)

(d)

2 µm

2 µm20 µm

FIGURE 5.48Region around the hot-crack tip in the Al–3% Cu billet (a) and micropores along the grain boundary ahead of the crack tip (inserts c–d) [103]. Arrows point at the eutectic-fi lled path (healed crack). (Reproduced with kind permission of Elsevier.)



Hot Tearing 267

enough to withstand the existing stresses. However, the last phenomenon is only possible in the absence of stress raisers and pre-cracks such as pores and liquid fi lms and packets. The existence of stress concentrators causes the appearance of local stresses that might be considerably higher than the global stresses. The presence of pre-cracks saves crack nucleation energy, freeing it for crack propagation, which becomes quite evident from the analysis of a microstructure shown in Figure 5.48. In the alloy with 3% Cu the amount of eutectics was enough to heal the crack, but we can easily imagine that the propagation of a crack through a boundary that consists of pores and is partially wet with liquid would be very easy. These observa-tions and their interpretation allow us to make the following conclusions. First, liquid feeding plays an important role in reducing hot tear develop-ment at the last stage of solidifi cation. Second, the bridged grain boundary will not necessarily reduce the hot tear propagation.

Hot tearing in the most susceptible Al−1% Cu alloy is quite peculiar. The fracture surface in Figure 5.45 exhibits brittle fracture of solid bridges. At this copper concentration, the amount of nonequilibrium eutectic liquid is as low as 1 vol.% (Figure 3.27e). About 90% of grain boundaries are bridged at the last stage of solidifi cation, hence the permeability of the system is very limited [102]. Therefore, the last remaining liquid cannot fl ow in a long path to counteract the shrinkage and deformation. The crack cannot propagate along liquid fi lm that virtually does not exist at this stage of solidifi cation. Instead, the hot tear may develop through the bridged grain boundaries. The hot tear initiator might be formed in the last liquid that is isolated in certain sites, e.g., triple-junctions, due to the interrupted liquid network. Stresses are transmitted through the coalesced dendritic network. It is noteworthy that the amount of thermal contraction accumulated in the solidifi cation range of an Al–1% Cu alloy and therefore the thermal stress–strain experienced by this alloy is higher than for alloys with a higher concentration of copper (Figure 5.6a). At a certain moment the stress concentrates at the liquid–solid interface and reaches the value suffi cient for crack propagation. In the case of liquid metal embrittlement, the energy required for the propagation of a crack/pore fi lled with liquid through the solid grain boundary is the lowest as compared to the energy of other means of crack propagation [60]. There-fore, the crack can easily spread through solid bridges, and the fracture will be brittle, as shown in Figure 5.45. In principle, the fracture caused by liquid metal embrittlement can be transgranular [60].

Porosity is one of the main features of the structure that is believed to be related to hot tearing. In some hot tearing models and criteria, the appearance of a pore is considered to be the beginning of hot cracking (see Sec tions 5.3.1 and 5.3.2). Porosity is caused by solidifi cation shrinkage and hydrogen evolution during the last stages of solidifi cation when shrinkage cannot be compensated for by melt feeding and gas cannot escape to the melt surface, due to low permeability of the mushy zone. Shrinkage and/or gas precipitation are the driving forces for the initiation of pores, and the same forces facilitate pore growth to a macroscopic size. Porosity usually




concentrates in the center of the billet and inversely correlates with the hot tear fraction [128, 129].

Figure 5.49 demonstrates the distribution of porosity in the cross-section of billets with different copper concentration and cast at different speeds. The amount of porosity tends to increase with copper concentration and reaches a maximum at approximately 3% Cu. The porosity becomes signifi cantly more pronounced with increasing casting speed from 100 mm/min to 160 mm/min,

4020

8060

120140

100160180

0 1.02.0

3.04.0

Cu, %


(a)

(b)

(c)

Por

osity

, %

0.00

0.02

0.04

0.060.08

0.10

Por

osity

, %

0.00

0.02

0.040.06

0.08

0.10

Por

osity

, %

0.00

0.020.040.06

0.080.10

FIGURE 5.49Effect of casting speed and copper concentration (noted in the fi gure) on the distribution of porosity in the cross-sections of 200-mm Al–Cu billets cast at (a) 200 mm/min; (b) 160 mm/min, and (c) 100 mm/min [103]. (Reproduced with kind permission of Elsevier.)



Hot Tearing 269

and then remains virtually unaffected by further increases in casting speed. At a high casting speed and around the center of the billet, the porosity has irregular shape and is distributed along solute-rich grain boundaries (Fig-ure 5.44d, 5.48). At a low casting speed, the pores are more rounded.

As we showed, the maximum hot tearing in Al–Cu alloys produced by DC casting corresponds to the compositional range 0.5–1.5% Cu, irrespective of the casting speed (Figure 5.39). Results of porosity distribution shown in Figure 5.49 give only very small values for this compositional range, while the maximum amount of porosity is observed at approximately 3% Cu when the hot tearing susceptibility of Al–Cu alloys is small. The inverse relation of porosity and hot tearing susceptibility is attributed to the closely related mechanisms of both defects. The pore can either slowly grow to a larger size or quickly develop into a hot tear (Figure 5.48). The stress concentration near a pore can be relieved by the hot tear formation. As a result, we observe much less porosity in the regions where hot tears appeared. In other words, the pores that should have been there are consumed by the crack during its nucleation and propagation. Upon increasing the concentration of copper in an alloy, fewer cracks are formed because of a smaller thermal contraction in the solidifi cation range, and more existing cracks are healed because of a larger amount of available liquid and a lesser fraction of bridged grain boundaries. Therefore, more pores remain in the structure and that appears as the maximum in Figure 5.49b,c. At a copper concentration greater than ~3.5%, both the porosity and hot tearing decrease with increasing copper concentration. This decrease is evidently due to better feeding conditions at higher copper concentrations, which enables more complete compensation for solidifi cation shrinkage.

The appearance of hot tearing, as we showed in this chapter, is a result of complex interplay between thermo-mechanical situation on the scale of the billet (casting speed, shape of the sump, cooling conditions), accumulation of thermal strain in the solidifi cation range (alloy composition, onset of thermal contraction), localization of stresses and strains at certain structure defects (porosity, liquid fi lms), and possibilities to feed the forming cavities and gaps by the liquid (eutectic amount and permeability).

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Dendritic Coherency, Des Plaines, IL: AFS, 1996. 2. C.J. Quaak. Ph.D. Thesis. Delft, the Netherlands: Delft University of Technol-

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13, pp. 41–58. 13. B. Rogberg. Scand. J. Met., 1983, vol. 12, pp. 51–66. 14. G.K. Sigworth. AFS Trans., 1996, vol. 104, pp. 1053–1062. 15. D.G. Eskin, Suyitno, L. Katgerman. Progr. Mater. Sci., 2004, vol. 49, no. 5,

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