Phase transformations in steels: Volume 2: Diffusionless transformations, high strength steels,...

Phase transformations in steels Volume 1: Fundamentals and diffusion-controlled transformations (ISBN 978-1-84569-970-3) Edited by two leading experts in the field, and with contributions from some of the most distinguished figures in steel research, this two-volume work summarises the vast amount of recent research on phase transformations in steels. The book covers both fundamental aspects (thermodynamics, diffusion, etc.) and more particular features (bainite, martensite, etc.). Volume 1 reviews fundamentals, diffusion-controlled, bainite and diffusional-displacive transformations.
Microstructure evolution in metal forming processes: Modelling and applications (ISBN 978-0-85709-074-4) Metal forming processes involve varying degrees of deformation to the metal substrate. This deformation results in changes to the microstructure of the metal. These microstructural changes need to be monitored and controlled. This book looks at the evolution of microstructure during metal forming processes and its modelling and control to produce steels and other metals with the right properties.
Nanostructured metals and alloys: Processing, microstructure, mechanical properties and applications (ISBN 978-1-84569-670-2) Nanostructured metals and alloys have enhanced tensile strength, fatigue strength and ductility and are suitable for use in applications where strength or strength-to-weight ratios are important. Part I of this important book reviews processing techniques for bulk nanostructured metals and alloys. Parts II and III discuss microstructure and mechanical properties, whilst Part IV outlines applications of this new class of material.
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techniques
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Part I Diffusionless transformations 1
1 Crystallography of martensite transformations in steels 3
P. M. Kelly, The University of Queensland, Australia
1.1 Introduction 3 1.2 Martensite transformations in steels 4 1.3 Phenomenological theory of martensite crystallography
(PTMC) 10 1.4 The post phenomenological theory of martensite
crystallography (PTMC) period 18 1.5 Strain energy – the Eshelby/Christian model and the
infinitesimal deformation (ID) approach 23 1.6 Interfacial dislocation models 25 1.7 Future trends 28 1.8 Conclusions 29 1.9 References 30
2 Morphology and substructure of martensite in steels 34 T. Maki, Kyoto University, Japan
2.1 Morphology and crystallographic features of martensite in ferrous alloys 34
2.2 Morphology and substructure of lath martensite 38 2.3 Morphology and substructure of lenticular martensite 46 2.4 Morphology and substructure of thin plate martensite 50 2.5 Conclusions 54 2.6 References 56
Contents
v
© Woodhead Publishing Limited, 2012
3 Kinetics of martensite transformations in steels 59 G. B. Olson and Z. D. Feinberg, Northwestern University, USA
3.1 Introduction 59 3.2 Mechanism and kinetics of martensitic transformation 60 3.3 Mechanically induced transformations 63 3.4 Transformation plasticity constitutive relations and
applications 66 3.5 Conclusions 79 3.6 References 80
4 Shape memory in ferrous alloys 83 D. Dunne, University of Wollongong, Australia
4.1 Introduction 83 4.2 Fe-Pt alloys 89 4.3 Fe-Ni and Fe-Ni-C alloys 93 4.4 Fe-Ni-Co-based alloys 96 4.5 Austenitic stainless steels with low stacking fault energy
(SFE) 99 4.6 Fe-Mn-based alloys 100 4.7 Summary 115 4.8 Acknowledgements 118 4.9 References 118
5 Tempering of martensite in carbon steels 126 G. Krauss, Colorado School of Mines, USA
5.1 Introduction 126 5.2 Martensitic microstructures prior to tempering heat
treatments 127 5.3 Classification of aging and tempering stages: general
considerations 130 5.4 Changes in martensitic fine structure due to aging 131 5.5 The stages of tempering 132 5.6 Conclusions 145 5.7 References 145
Part II Phase transformations in high strength steels 151
6 Phase transformations in microalloyed high strength low alloy (HSLA) steels 153
R. C. Cochrane, University of Leeds, UK
6.1 Introduction to microalloyed high strength low alloy (HSLA) steels 153
viiContents
6.2 Brief historical review of the development of microalloyed steels 155
6.3 Solubility of microalloying elements in austenite and ferrite 157 6.4 Precipitation 161 6.5 Effects of microalloying on transformation kinetics 177 6.6 Phase transformations during high strength low alloy
(HSLA) steels processing 185 6.7 Controlled processed ferrite/bainite and acicular ferrite
steels 199 6.8 Conclusions and future trends 205 6.9 Acknowledgements 207 6.10 References 207
7 Phase transformations in transformation induced plasticity (TRIP)-assisted multiphase steels 213
P. J. Jacques, Université Catholique de Louvain (UCL), Belgium
7.1 Introduction 213 7.2 Historical perspectives on the emergence of transformation
induced plasticity (TRIP)-assisted multiphase steels 215 7.3 Influence of parameters of the thermomechanical process
on the formation of multiphase microstructures containing retained austenite 223
7.4 Conclusion and future trends 242 7.5 References 243
8 Phase transformations in quenched and partitioned steels 247
J. G. Speer, Colorado School of Mines, USA
8.1 Introduction to the quenching and partitioning concept 247 8.2 Microstructure development fundamentals and alloy designs 252 8.3 Mechanical behavior, potential applications, and
implementation status 260 8.4 Conclusions 267 8.5 References 268
9 Phase transformations in advanced bainitic steels 271 F. G. Caballero and C. Garcia-Mateo, National Centre for
Metallurgical Research (CENIM-CSIC), Spain
9.1 Introduction 271 9.2 Design of third generation of advanced high strength steels 273 9.3 Carbide-free bainitic steels: a material ready for the
nanocentury 283
viii Contents
9.4 Conclusions and future trends 290 9.5 Acknowledgement 291 9.6 References 291
10 Phase transformations in high manganese twinning-induced plasticity (TWIP) steels 295
B. C. De Cooman, Pohang University of Science and Technology, South Korea
10.1 Introduction 295 10.2 Fe-Mn-X alloys 297 10.3 Strain-induced twinning 307 10.4 Twinning-induced plasticity (TWIP) industrialization 327 10.5 Conclusions 327 10.6 Acknowledgements 328 10.7 References 328
11 Phase transformations in maraging steels 332 W. Sha, Queen’s University Belfast, UK, H. Leitner, University of
Leoben, Austria, Z. Guo, Sente Software Ltd, UK and W. Xu, ArcelorMittal Global R&D Gent, Belgium
11.1 State of the art of ultra high strength steels 332 11.2 Types of maraging steels 334 11.3 Microstructure and precipitates in maraging steels 339 11.4 Reverted austenite and mechanical properties 342 11.5 Evolution of precipitates and the overall process 346 11.6 Precipitation kinetic theory in Fe-12Ni-6Mn maraging type
alloy 349 11.7 Research trends 356 11.8 References 359
Part III Modelling phase transformations 363
12 First principles in modelling phase transformations in steels 365
M. H. F. Sluiter, Delft University of Technology, The Netherlands
12.1 Introduction 365 12.2 Ab initio description of phase stability of pure iron 370 12.3 Ab initio phase stability of iron carbides 374 12.4 Substitutional alloying elements 377 12.5 Ab initio description of diffusivity in bcc Fe 381 12.6 Future trends 384 12.7 References 385
ixContents
13 Phase field modelling of phase transformations in steels 405
M. Militzer, The University of British Columbia, Canada
13.1 Introduction 405 13.2 Phase field methodology 406 13.3 Austenite formation 414 13.4 Austenite decomposition 418 13.5 Future trends 428 13.6 References 429
14 Molecular dynamics modeling of martensitic transformations in steels 433
H. M. Urbassek and L. Sandoval, Universität Kaiserslautern, Germany
14.1 Introduction 433 14.2 Interatomic interaction potentials 434 14.3 Martensitic transformations in iron: case studies 443 14.4 Transformations in ferrous nanosystems 449 14.5 Conclusions and future trends 459 14.6 Acknowledgement 460 14.7 References 460
15 Neural networks modeling of phase transformations in steels 464
C. Capdevila, National Centre for Metallurgical Research (CENIM-CSIC), Spain
15.1 Introduction 464 15.2 Essence of the method 465 15.3 On the quest of critical temperatures 472 15.4 Determining microstructural parameters 488 15.5 Development of continuous cooling transformation (CCT)
diagrams 496 15.6 Conclusions and future trends 498 15.7 References 500
Part IV Advanced analytical techniques for studying phase transformations in steels 505
16 Application of modern transmission electron microscopy (TEM) techniques to the study of phase transformations in steels 507
D. Boyd and Z. Yao, Queen’s University, Canada
x Contents
preparation 508 16.3 Conventional transmission electron microscopy (CTEM)
of steels 510 16.4 Modern transmission electron microscopy (TEM) of steels 513 16.5 In-situ transmission electron microscopy (TEM) 524 16.6 Future trends: emerging transmission electron microscopy
(TEM) techniques 525 16.7 Sources of further information and advice 528 16.8 Conclusions 529 16.9 References 529
17 Atom probe tomography for studying phase transformations in steels 532
M. K. Miller, Oak Ridge National Laboratory, USA
17.1 Introduction 532 17.2 Outline of the technique 533 17.3 Specimen requirements 535 17.4 Recent developments 536 17.5 Interpretation of data 537 17.6 Characterizing and understanding phase transformations
in various steels 538 17.7 Future trends 553 17.8 Conclusion 554 17.9 Acknowledgments 554 17.10 References 554
18 Electron backscatter diffraction (EBSD) techniques for studying phase transformations in steels 557
S. Zaefferer, N.-N. Elhami and P. Konijnenberg, Max Planck Institute for Iron Research, Germany
18.1 Introduction 557 18.2 Fundamentals of electron backscatter diffraction
(3D-EBSD) technique 558 18.3 The current standard of 2D electron backscatter diffraction
(EBSD) applications 561 18.4 3D electron backscatter diffraction (3D-EBSD) 569 18.5 Conclusions and future development of the technique 579 18.6 References 583
xiContents
19 Application of synchrotron and neutron scattering techniques for tracking phase transformations in steels 588
S. S. Babu, The Ohio State University, USA
19.1 Introduction 588 19.2 X-ray and neutron scattering techniques 590 19.3 Measurements of phase transformation in steels 605 19.4 Conclusions and future trends 624 19.5 Acknowledgements 625 19.6 References 625
Index 634
E-mail: [email protected]
Professor David Edmonds Institute for Materials Research School of Process, Environmental
and Materials Engineering University of Leeds Leeds LS2 9JT UK
Division of Materials School of Mechanical and Mining
Engineering The University of Queensland Brisbane Queensland 4072 Australia
Chapter 2
Dr Tadashi Maki Nippon Steel Corporation 20-1, Shintomi, Futtsu Chiba 293-8511 Japan
(* = main contact)
Chapter 3
G. B. Olson* and Z. D. Feinberg Department of Materials Science
and Engineering Northwestern University 2220 Campus Drive Evanston, IL 60208 USA
Chapter 4
Emeritus Professor Druce Dunne Faculty of Engineering University of Wollongong Northfields Avenue Wollongong NSW 2522 Australia
Chapter 5
Products Research Center The George S. Ansell Department
of Metallurgical and Materials Engineering
Colorado School of Mines Golden, CO 80401 USA
Chapter 6
R. C. Cochrane University of Leeds Formerly British Steel Professor of
Ferrous Metallurgy UK
E-mail: r.cochrane.cochrane@btinternet. com
(UCL) Institute of Mechanics Materials and Civil Engineering
(iMMC) Division of Engineering of
Materials and Processes (IMAP) Place Sainte Barbe, 2 B-1348 Louvain-la-Neuve Belgium
Chapter 8
Products Research Center The George S. Ansell Department
of Metallurgical and Materials Engineering
Colorado School of Mines Golden, CO 80401 USA
National Centre for Metallurgical Research (CENIM-CSIC)
Av. Gregorio del Amo, 8 E-28040 Madrid Spain
Chapter 10
B. C. De Cooman Materials Design Laboratory Graduate Institute of Ferrous
Technology Pohang University of Science and
Technology Pohang South Korea
Wei Sha* School of Planning, Architecture
and Civil Engineering Queen’s University Belfast Belfast BT7 1NN UK
Early Stages of Precipitation University of Leoben Franz-Josef-Straße 18 A-8700 Leoben Austria
Zhanli Guo Sente Software Ltd Surrey Technology Centre 40 Occam Road Guildford GU2 7YG UK
Wei Xu OCAS ArcelorMittal Global R&D Gent BE-9060 Zelzate Belgium
Chapter 12
Marcel H. F. Sluiter Department of Materials Science
and Engineering, 3ME Delft University of Technology Mekelweg 2 2628 CD Delft The Netherlands
Chapter 13
Process Engineering The University of British Columbia 309-6350 Stores Road Vancouver BC Canada V6T 1Z4
Fachbereich Physik und Forschungszentrum OPTIMAS
Universität Kaiserslautern Erwin-Schrödinger-Straße D-67663 Kaiserslautern Germany
Chapter 15
C. Capdevila Materalia Group Department of Physical Metallurgy National Centre for Metallurgical
Research (CENIM-CSIC) Avda. Gregorio del Amo, 8 E-28040 Madrid Spain
Chapter 16
Materials Engineering Queen’s University Kingston, ON Canada K7L 3N6
Chapter 17
Division Oak Ridge National Laboratory Oak Ridge, TN 37831-6136 USA
Chapter 18
Dr Stefan Zaefferer*, Nahid-Nora Elhami, Peter Konijnenberg
Department of Microstructure Physics and Alloy Design Max Planck Institute for Iron
Research Max-Planck-Str. 1 D-40237 Duesseldorf Germany
E-mail: [email protected]; [email protected];
Sudarsanam Suresh Babu Department of Materials Science
and Engineering The Ohio State University 1248 Arthur E. Adams Drive #130, Columbus, OH 43221 USA
A new and comprehensive book on phase transformations in steels is both timely and welcome. It is gratifying near the beginning of a new, technology- dominated, century to see a group of experts and well accomplished researchers, some of whom have devoted major parts of their professional activities to this area, as well as a group of younger researchers and steel users, all willing to assemble together a new two-volume publication on steels. Strikingly, unlike many other groups of important metallic materials, it is the onset of transformations in steels resulting from the various thermal and mechanical treatments that make steels so special. This is possible mainly because of the unique properties of iron (Fe) which exhibits three different simple crystal structures; bcc, fcc and bcc again, as temperature rises. Even more unique is the fact that contrary to the usually observed order of the sequence of phase changes observed with temperature, the gamma phase at higher temperatures, is the ‘more open’ phase than the bcc alpha phase, and hence more able to absorb substantial amounts of alloying element additions. As a result, on quenching or cooling, and other heat treatments, all kinds of phase transformations can take place, and their understanding, manipulation, and utilization constitutes the essence of the importance that steels have exhibited in the past in the development of civilizations and related technologies. The various chapters bring nicely up to date the vast assembled knowledge of steel transformations in the literature: from the more basic aspects (thermodynamics, diffusion, kinetics, etc.), through the more particular transformation features (nucleation and growth, bainite, martensite, massive, shape memory, etc.), to some aspects of the more recent and advanced analytical possibilities (synchrotron, atom probe, etc.). Perhaps it is fitting also to mention that the bewildering role of magnetism in iron is the basis of much of this behavior. It is well documented that the ferromagnetic transition in the bcc-Fe phase makes the bcc phases more stable at lower temperatures than the fcc-gamma phase, but still too few people realize that it is the anti-ferromagnetic transition in the gamma phase at temperatures near 0 K that makes the crystalline closed-packed (therefore
Foreword
xvii
‘wrong’) gamma phase return to stability on heating. Without these unusual features of iron, phase transformations in steels would not take place and the enormous versatility and benefits of steels in the progress of society would be lost. It may also be time to admit that the ferromagnetic alpha phase has actually a bc-tetragonal symmetry due to the magnetic moments, if the more modern standards of phase definition are adopted, and so the bcc (and paramagnetic) beta phase which has been banished from the iron phase diagrams since the 1920s should be rightfully restored to its original position. Undoubtedly, research on transformations in steels will continue in the future, as more sophisticated heat treatments are devised and more advanced techniques are brought into use to study the results, particularly at the micro and nano scales. The present book is likely to serve here as a good basis for future advances.
Ted Massalski Professor of Materials Science, Engineering and Physics
Carnegie Mellon University
Introduction
Steel has been available as a high tonnage engineering material for nearly two centuries. During this time it has had a very creditable track record and one which is crucial to engineering progress, especially in providing the infrastructure in underdeveloped and developing parts of the world, which still dwarf in size and population the more developed nations. This is why the volume of steel production continues to increase, leading to the continual need to consider more economic ways of manufacturing using steel in order to minimise energy consumption and preserve natural resources. Despite commendable efforts by scientists and engineers to understand fully the processing-microstructure-property relationships in steels, these continue to present new challenges to researchers because of the complexity of the phase transformation reactions and the wide spectrum of microstructures and properties achievable. Thus, an important theme and objective of this book is to follow the development of our understanding of phase transformations in iron alloys and steels through to the development of modern commercial steels, and in particular to highlight the clear connection between phase transformation studies, no matter how isolated and remote they may seem at the outset, to the emergence of new steels with enhanced engineering properties. Unlike many other metals, the combination of several characteristics, such as magnetism, allotropic phase changes and the different solubility and diffusion behaviour of interstitial and substitutional elements, makes iron- based alloys unique and is responsible for a diversity of phase transformations. The first chapter of this book provides a historical perspective on the first pioneering attempts to gain insight into the complexity of these reactions. All aspects of phase transformations (thermodynamics, diffusion, kinetics and crystal structure) must be properly understood in order to develop a complete picture of the transformation reactions in steels. Thus it was deemed necessary to devote the first section of the book to the fundamental principles of thermodynamics, diffusion and kinetics, and in addition, owing to its growing importance in helping to understand transformations, the phase boundary interface separating parent and product, now much more amenable to observation and analysis using the increased power of modern metallographic instrumentation, as well as modelling.
xix
xx Introduction
Starting from the earliest studies on phase transformations in steels, a large number of theories and definitions have emerged leading to continual debates amongst researchers. Only with the development of more advanced experimental capabilities have some of these issues been satisfactorily resolved while others still provoke conflicting opinions. This book aims to represent the current status of knowledge on steel phase transformations whilst also highlighting the challenges facing future researchers in this field. As mentioned in the Foreword, and demonstrating how the Fe-C system continues to generate important issues, magnetism plays an important role in the phase transformations of iron and steels due to the ferromagnetic and anti-ferromagnetic transitions that take place. Thus it is suggested that paramagnetic beta phase should be restored to the Fe-C phase diagram. The most important transformations in steels, and the area where almost all research has been concentrated, are those which result in the final microstructure and properties. These involve decomposition of the high temperature g-phase, austenite, which takes place on cooling and, dependent upon steel alloying and cooling conditions and also whether mechanical working occurs, could follow different paths resulting in a large diversity of lower temperature phase types and their mixtures. These phase transformations could be classified based upon microstructure, thermodynamics or mechanisms and in the present book the phase transformations are classified according to their mechanism. In this scheme the phase transformations in steels are customarily divided into two major groups, which are named according to whether long-range diffusion of atoms occurs or not, namely diffusional or non-diffusional (diffusionless). Each type of phase transformation is then characterised by a set of specific features, including but not limited to composition, crystal structure, shape change and carbon mobility. It is generally accepted that the formation mechanisms of proeutectoid grain boundary allotriomorphs (of a-ferrite and cementite) and pearlite are diffusional. These reactions take place within the higher temperature region of the low temperature phase field with slow kinetics and generally do not require significant undercooling below the g Æ a transition temperature. In contrast, the formation of martensite with a structure change but composition inherited from parent austenite occurs by a diffusionless transformation at rapid cooling and/or large undercoolings. In-depth presentations of the current state of phase transformation theory for the former type of reactions are given in Volume 1, Part II, whereas the latter is addressed in Volume 2, Part I. These constitute the more traditional microstructures which have long been studied; Henry Clifton Sorby, for example, first identified pearlite around the middle of the 19th century. Moreover, they have long provided the properties of the high-tonnage carbon and alloy steels used in construction and many engineering applications. Nevertheless, as described in these sections, significant progress has been made in understanding their
xxiIntroduction
formation, both for ferrite/pearlite and for basic martensite, in the latter case the phenomenological theory of martensite crystallography and, more recently, the proposals deriving from interface mechanics embodied in the so-called topological model, which attempt to describe the mechanistic aspects of the transformation. This demonstrates the rich variety of transformations in iron- based alloys, especially when one also adds the shape memory effect, which is of immense interest and commercialisation in non-ferrous systems. Although significant advances have been made in developing a basic understanding of the nucleation and growth processes, and in validation of various theories, questions still remain due to the limitations of even the most powerful experimental techniques and the complexities of multiphase microstructures forming under a variety of conditions, generally at elevated temperatures. Examples include: elucidating the exact path for carbon diffusion; determining the embryo structure, location and evolution; measuring the effect of so-called ‘solute drag’ on interface migration; determining the diffusivities and binding energies of elements in multi-component systems; accurately measuring interfacial and strain energies; providing explanations on the differences between the predicted rates of diffusion of substitutional elements at low temperatures and the observed solute clustering. Proving again the complexity, even previously well-accepted ideal cases of partitioning of alloying elements under local equilibrium (LE) or paraequilibrium (PE) conditions for diffusional transformations are now challenged by assumption of negligible partitioning of substitutional elements under local equilibrium (NP-LE). However, the issues most difficult to resolve, not unexpectedly, have been related to the intermediate products formed between the classical diffusional (e.g. ferrite/pearlite) and diffusionless (e.g. martensite) ones. A variety of morphologies of these products including Widmanstätten ferrite, upper bainite, lower bainite and carbide-free bainite, as well as granular bainite and the so-called ‘acicular ferrite microstructures’, are considered to exhibit a mixture of characteristics familiar to both classes of transformation, which has fuelled continuous debate regarding the exact formation mechanisms. Perhaps the main discord concerned with the fundamentals of the reaction mechanism has been related to the nature of the bainite transformation (Volume 1, Part III), which essentially reduces to the behaviour and location of carbon during the formation of the bainitic ferrite crystals. As mentioned above, better resolution of such questions might evolve from real-time measurement of carbon concentrations in parent austenite and product ferrite during transformation at elevated temperatures. Nevertheless, there have been significant positive advances in these phase transformation studies. In this quest for greater understanding of the bainite reaction mechanism, experimental steels have been developed which contain untransformed austenite, useful for studying features of the transformation
xxii Introduction
mechanism, but which have subsequently been shown can impart valuable properties to a new generation of formable high strength steels for automotive use that has eventually led to commercialisation, e.g. transformation induced plasticity (TRIP) steels. Chapters on these new steels can be found in Volume 2, Part II, alongside comparative chapters on the new twinning induced plasticity (TWIP) steels and high alloyed maraging steels. Almost all modern high-volume metal production processes are continuous, involving continuous cooling, often associated with mechanical forming, such that complex dynamic changes are more often the norm and sometimes even difficult to simulate in a laboratory environment. Thus, near-equilibrium microstructures are not always the ones which could lead to commercial success. Consequently, given the different industrial processes required in the production of steel in all its various forms, which are continually being updated or modified, a section dealing with parameters involved in transformation other than temperature was considered necessary. External factors, such as deformation, heating rate or application of electromagnetic field could either accelerate or retard the phase transformations depending upon the chosen set of conditions (Volume 1, Part IV). Although a significant body of evidence has been accumulated over time on the effects of these parameters, the underlying mechanisms are not yet fully understood. The phenomenon of restoration of prior austenite morphology and orientation at slow or fast heating rates and absence of it at intermediate heating rates continues to puzzle physical metallurgists. The explanations put forward for this structural inheritance also lack direct and comprehensive experimental evidence. Many of the significant advances to our understanding of phase transformations in the evolution of steel microstructure during the last 50 years would not have been possible without the parallel development of higher resolution microscopes and related techniques. In the last two decades significant advances have been made in many characterisation techniques (Volume 2, Part IV) and microstructure observations have moved from only ex-situ to also in-situ ones. It is now possible using in-situ transmission electron microscopy, neutron and synchrotron scattering or electron backscattering diffraction coupled with energy dispersive X-ray spectroscopy, to observe the progress of phase transformations not only on heating or cooling, but under external load too. Recent leaps in the development of atom probes and aberration corrected transmission electron microscopes enable the collection of compositional and crystallographic information with atomic resolutions (<0.1 nm). The ability to gather microanalytical data at high resolutions has become increasingly important with the realisation that relatively low bulk concentrations of alloying elements can have disproportionately large effects on transformation behaviour. The exact structure of grain and interphase boundaries and solute segregation to them can now be revealed more clearly.
xxiiiIntroduction
The improved resolution limit is especially valuable with the increased trend towards production of steels with ultrafine and nano-sized grains and precipitates. Perhaps it should be mentioned that more and more use of 3D techniques in addition to more customarily utilised 2D provides invaluable information on the morphology and distribution of various phases and their crystallography, which helps to fine-tune existing theories and indicates the route for other experiments. But whilst researchers should remain vigilant to artefacts related to each technique and continue to analyse data diligently, these newly developed techniques will allow gathering of the essential information for advancement or validation of existing theories and models, as well as provide the necessary input data for rapidly developing modelling methodologies. However, we must remain mindful that these instruments and their applications, as will be evident from this section in the book, have become extremely specialised and expensive, and are not widely available, and consequently much of the metallographic work on commercial steel microstructures is still conducted at much lower resolutions by more conventional microscopy. This emphasises the need for consistent descriptions and classifications of microstructure and transformation behaviours across the length scales. As far as has been possible, we have tried to maintain a similar nomenclature throughout the book. The major new inclusion in this book derives from probably the most significant and totally new topic or field of activity in phase transformations to emerge during the latter part of the main period covered, namely phase transformations modelling. A full section (Volume 2, Part III) has been devoted to this fairly embryonic but rapidly growing field, including all of the well-known approaches: first principles, phase field, molecular dynamics, neural networks. The models provide qualitative and semi-quantitative insight into phase transformations. Some good examples of the preliminary applications to ferrous transformations will be found, some of which have already produced useful advances whilst others are meeting the extensive challenges arising from the complexity of the subject. The hope exists that eventually steels may be designed from first principles taking into account the complexities of phase change associated with those of processing on a large scale, so often difficult to reproduce accurately in the laboratory, or alternatively to study during commercial production. However, it is clear that despite the progress made, the lack of reliable experimental data for input into the models hinders their development. For first principles models reliable experimental data are needed for validation of the potentials. As mentioned previously, quantitative interfacial and strain energy data, data on diffusivities and nucleation, are urgently required to further advance modelling and the theories of ferrous phase transformations.
xxiv Introduction
Finally, the success of applying the knowledge of phase transformations to design of advanced high strength steels should be acknowledged (Volume 2 Part II). This part begins with a chapter on high strength low alloy (HSLA) or microalloyed steels which have probably been the category of steels that have seen the most resource-intensive development during the latter part of the period covered by this book, and still do, driven mainly by the ever more stringent engineering requirements for steels needed in the recovery and transmission of oil and gas. In the quest for greater strength and toughness combined with weldability, extensive data and understanding have been accumulated on the influence of alloying and controlled deformation processing and cooling on the phase transformation and precipitation reactions. The pathway from the development of quenched and tempered steels and HSLA steels to dual phase, transformation-induced plasticity, nanostructured bainitic (‘Nanobain’), twinning-induced plasticity and quenched and partitioned steels is marked by gradual increase in complexity of processing schedules and the microstructures formed. In the latter steels, the direct application of phase transformation sequences in the design of processing schedules led to either significant strength advantage or desirable combinations of high strength/high ductility in formable steels. These manipulations of steel microstructures also enable the achievement of cost savings due to leaner steel compositions and consequently the reduced use of natural resources, coupled with socio-economic benefits. This project would not have been possible without support from Woodhead Publishing staff and the enthusiasm and co-operation of authors and co-authors in joining us in this task – which apart from confirming our inception of the idea, has made it a more worthwhile and also an enjoyable activity over the last two years. Our authors must also be congratulated on their efforts to produce comprehensive overviews of the topics, including fair and balanced treatments of various theories and models where appropriate. There can be no doubt that it has been an immense task and we can attest to the considerable work which has gone into the production of the manuscript for this book. It will always be a snapshot of where we have reached in this discipline by the year of publication, but it will also we hope, and because of the quality of the chapters provided, stand as a useful source for reference, advanced teaching and learning for a long time to come. In particular, it is hoped that this book will inspire a young generation of scientists and engineers to further advance the knowledge on phase transformations in steels, which remains a fascinating and significant field to explore.
Elena Pereloma University of Wollongong
David Edmonds University of Leeds
P. M. Kelly, The University of Queensland, Australia
Abstract: This chapter describes the unique features of martensitic transformations in steels. It covers the characteristics that serve to distinguish and identify the different types of ferrous martensite and then moves on to tackle the most impressive, but often complex and mathematically inscrutable, theory of phase transformations ever produced – the phenomenological theory of martensite crystallography (the PTMC). The approach concentrates on what the mathematics attempts to achieve and not on the mathematics itself. A general comparison between theory and experiment is included as well as attempts to identify features that have proved difficult to explain and hence led to subsequent improvements in the theory. Finally, the chapter identifies the need for further work, either to provide critical experimental evidence to test the theories or to suggest fruitful areas for future research.
Key words: martensite, crystallography, habit plane, orientation relationship, shape strain.
1.1 Introduction

of the crystallography of martensite is often never fully appreciated. In this chapter the emphasis is on describing what the mathematics attempts to achieve and not on the mathematics itself. Wherever possible, the approach will be descriptive and will avoid becoming submerged in what is often regarded as incomprehensible mathematics. Important concepts that are essential foundation stones for the PTMC will be explained. The various alternative theoretical treatments and modifications to the PTMC will be discussed and compared with the original theory. However, because of its unsurpassed success as a predictive theory, the PTMC will receive the lion’s share of attention and, in many cases, shown to be at least equivalent to the later models/theories. The strength of any predictive theory rests on its ability to account for any experimental observations. Hence, the comparison between theory and experiment will be covered, but not in minute detail. There is an extensive amount of quite sophisticated experimental data on the crystallography of ferrous martensites in steels that has been collected over more than half a century, and it is impossible to cover all of this individual detail in a single chapter. Instead the emphasis will be on summaries that have appeared in textbooks or reviews and the reader is encouraged to go back to these sources for information on individual sets of observations. Wherever appropriate this comparison between theory and experiment will attempt to identify particular features that have proved difficult to explain via the PTMC. These examples have often led to developments/improvements in the theoretical treatment. Hence this theoretical/experimental comparison will serve not only to test the theories themselves, but also to provide a historical perspective on the development of our understanding of martensite crystallography in the last five decades. It is hoped it will also identify the need for further work, either to provide critical experimental evidence to test the theories or to suggest fruitful areas for future research. Finally, the success of this chapter on the crystallography of martensite will depend on its ability to demonstrate the power of the PTMC and to encourage others to face the mathematical maelstrom of matrix algebra in the hope of appreciating its contribution to the understanding of a unique form of phase transformation in solids.
1.2 Martensite transformations in steels
1.2.1 The characteristics of martensite transformations

this form of transformation are that it leads to a change in crystal structure that occurs in an athermal, diffusionless fashion involving the simultaneous, co-operative movement of atoms over distances less than an atomic diameter and is accompanied by a macroscopic change of shape of the transformed volume (Bilby and Christian, 1955; Christian, 1965, 1975, 1990; Petty, 1970; Nishiyama, 1978; Cohen et al., 1979). While the co-operative atom movements may involve some small ‘shuffles’ (Christian, 1990), there is no need to ‘reconstruct’ the crystal structure of the matrix, as there is in a conventional diffusional transformation (Christian, 1975). From the point of view of the crystallography of the transformation, the displacive character is particularly important. The shape change that results from this displacive component is relatively large and dominated by shear, as opposed to the relatively small changes in volume that accompany the transformation. In a surface polished prior to the transformation, the shape change associated with the formation of a martensite plate leads to surface tilts and the change in direction of surface scratches, as illustrated in Fig. 1.1. The shape change, its magnitude and direction, therefore constitute the most important and defining features associated with a martensitic transformation.
Surface polished before transformation
Polished and etched cross-section
LIS Slip or twinning

The other important crystallographic characteristics of martensite in steels are its morphology, the orientation relationship between the matrix and product martensite phases, the internal substructure of the martensite itself and the nature of the interface. These crystallographic features need to be referred to particular phases, such as the face centred cubic (fcc) parent phase austenite denoted by the subscript F, the body centred cubic (bcc) or tetragonal (bct) martensite phase denoted by the subscript B and the relatively rare hexagonal close-packed (hcp) epsilon (e) martensite denoted by the subscript H. Martensite in steels is often plate-like with a well-defined habit plane – the plane defined by the plate itself. Laths are another relatively common morphology. Martensite laths are ruler-shaped particles that have a habit plane, as well as a specific crystallographic long direction. On rare occasions, rod-like or multi-faceted lath shaped particles may form. The habit plane of a plate or the major facet plane of a lath is often used as a means of distinguishing between the various types of martensite formed in different steels, or in the same steel under differing conditions. The major types of ferrous martensite consist of the {259}F martensite plates formed in Fe-Ni alloys with more than 29% Ni, Fe-Ni-C, Fe-24.5at%Pt, and Fe-Al-C, the {225}F martensite plates formed in high carbon and/or high alloyed carbon steels, the {557}F lath martensite typical of low carbon steels and the {1 12}F bcc laths and {111}F hexagonal close-packed epsilon martensite formed in low stacking fault energy stainless steels (Nishiyama, 1978; McDougall and Wayman, 1992). It must be remembered that these so-called habit planes are generally ‘irrational’, i.e. they cannot strictly be represented by simple, single-digit Miller indices. However, rather than use a more complex system to represent the habit plane, they are usually, in the interests of brevity at the expense of precision, expressed in terms of the nearest low-index plane. The actual habit planes do not coincide exactly with these low-index planes – the so-called {225}F habit plane is more like {2 2 4.9}F, the reported {259}F habit is closer to {3 10 15}F and {557}F is more accurately described as a plane close to, but not exactly of the form {hhl}F that is between 9° and 11° from {111}F. An orientation relationship (OR) expresses the relationship between planes and directions in one phase, such as the austenite matrix (F) with corresponding planes and directions in the other phase, i.e. the martensite (B). Typical austenite-martensite ORs are the Kurdjumov–Sachs (K-S) OR (Kurdjumov and Sachs, 1930):
(111)F//(101)B
the Nishiyama–Wasserman (N-W) OR (Nishiyama, 1934; Wassermann, 1935):

[121]F//[101]B
and the intermediate Greninger–Troiano (G-T) OR (Greninger and Troiano, 1949):
(111)F//(101)B
[110]F 2.5° from [111]B
[121]F 2.5° from [101]B

are responsible for the actual transformation from austenite to martensite must satisfy certain requirements. For a martensite transformation to occur, these interface dislocations must be completely mobile and capable of rapid movement as the interface propagates. Because of its diffusionless nature, any interface dislocation movement associated with the transformation must be conservative and not involve any net atom flux or the creation or destruction of lattice sites. In developing a dislocation model of the austenite/martensite interface or in postulating details of the transformation mechanism that may involve the creation of interface dislocations, all of these relatively strict conditions must be met. By comparison, in the case of a diffusion-controlled transformation, this interface dislocation movement criterion associated with no atom flux is not necessary, as non-conservative climb is possible and the interface dislocations merely have to satisfy geometric considerations. The combination of these crystallographic characteristics has a pronounced impact on the development of a satisfactory theoretical model for a martensitic transformation. A successful theory must be capable of predicting a planar interface that corresponds to the habit plane of a martensite lath or plate, must derive the correct features of the OR and shape change, must be consistent with any internal substructure within the martensite plates, and finally, must only result in totally glissile arrangements of dislocations in the interface. How this is done is covered in the following sections.
1.2.2 Early theories of martensite crystallography


Frank also considered the {225}F transformation and developed a model where the close-packed planes (111)F and (101)B in the two phases met along the common close-packed directions [110]F and [111]B lying in the {225}F habit plane interface (Frank, 1953). The spacing of the close-packed planes in the two phases differed slightly, and to achieve perfect matching a small rotation about their common intersection in the habit plane was necessary. In addition, a shear on the (112)B planes produced by an array of screw dislocations in the interface is needed to ensure that matching between successive planes remains ‘in-step’. This is essentially the same as the inhomogeneous second shear proposed by Greninger and Troiano. This two-dimensional model was criticised because it only applied to the {225}F transformation where the matching close-packed directions lie in the habit plane and it did not account for the {259}F habit plane. This was subsequently remedied when a three-dimensional prism matching theory was later developed (Bilby and Frank, 1960). The geometric matching conditions were obviously far more complex, but a second shear on (112)F was still required. This prism matching model predicted an elliptical locus of habit plane positions. The magnitude of the shape deformation varied along this habit plane locus and was a minimum at a position that corresponded to {259}F. For the same set of lattice parameters this was identical with the predictions arrived at somewhat earlier using the PTMC.
1.3 Phenomenological theory of martensite crystallography (PTMC)
1.3.1 Key features of the PTMC


austenite cell shown in Figs 1.2 (b) and (c) has the carbon atoms arranged in these very specific positions. Adding interstitial carbon atoms at random to this bct unit cell would result in it having a c/a ratio greater than unity. In other words, the interstitial carbon atoms in the martensite will make its
Fe atoms C atom positions
[001]F [001]F
[100]F
[001]B
(d) Austenite Martensite

unit cell tetragonal, with the degree of tetragonality linearly proportional to the carbon content. This provides the experimental proof that completely justifies the choice of correspondence. Figure 1.2 illustrates another important point. The variant of the correspondence shown in Fig. 1.2 is such that:
[100]F becomes [110]B,
[010]F becomes [110]B, and,
[001]F becomes [001]B.
There are two other major variants of this correspondence, one with [100]F becoming [001]B and one with [010]F becoming [001]B. This latter major variant is the one selected by Bowles and Mackenzie. With the correspondence shown in Fig. 1.2 and the lattice parameters of the austenite and the martensite, the total strain necessary to convert the matrix austenite to the product martensite can be derived. This total strain is known as the Bain strain B. Note that throughout this chapter ‘bold sans serif’ type will be used to represent matrices (in capitals) and vectors (in lower case). If the fcc austenite lattice parameter is aF and the lattice parameters of the bct martensite are aB and cB, then the Bain strain can be represented by three components h1, h2 and h3 along the [100]F, [010]F and [001]F directions in the austenite lattice, where:
h1 = h2 = ÷2(aB/aF),
h3 = (cB/aF)

(Christian, 1976). This concept meant that the shape strain associated with a martensite transformation had to be an invariant plane strain of the type illustrated in Fig. 1.3 – in other words a shear g in a direction parallel to the habit plane, plus an expansion (or contraction) x normal to the habit plane. The Bain strain B is sufficient to convert the matrix austenite crystal structure to that of the product martensite, but it seldom satisfies the two very stringent conditions required to produce an invariant plane strain. The first of these is that one of the principal strains must be zero and the second, equally important condition, is that the other two principal strains must be of opposite sign, i.e. one strain must be an expansion, while the other is a contraction (Bilby and Christian, 1955; Christian, 1956). If the strain involved in the martensite transformation can be made to satisfy these two conditions, then it will be possible to form a martensite plate where the habit plane of the plate is invariant. The two versions of the PTMC were both aimed at ensuring that the shape strain of the martensite transformation was an invariant plane strain. The final point about the PTMC is that the WLR and BM theories are both phenomenological. This means that all the theories attempt to do is to relate the crystallographic features of the final transformed martensite product to those of the original matrix austenite. This is a purely ‘before and after’ description. Although governed by the very stringent conditions associated with the invariant plane concept, the PTMC does not pretend to offer any information about the actual mechanism of transformation. It is
Austenite Martensite Transforms to:
Habit plane Habit plane
x = DV

not a mechanistic model that describes individual atom movements. All the PTMC does is to specify, via an elegant analysis based on matrix algebra, the very strict geometrical conditions that must be met to get from the initial state to the final state. The mathematical steps taken in this process and the order in which they are carried out do not necessarily bear any particular relevance to the way the transformation actually occurs. This is pure mathematical manipulation, designed to go from ‘before’ to ‘after’. The PTMC predictions of the habit plane, the orientation relationship between austenite and martensite and the magnitude and direction of the shape strain can then be compared with experimental observations.
1.3.2 How the PTMC works

quadratic equation, there will be two solutions for g, both of which lead to an invariant line strain (Wechsler et al., 1953). Normally, the smaller of the two is adopted on the grounds that this minimises the strain components of the LIS L. To convert this invariant line strain BL to an invariant plane strain, the other two principal strains of BL must be opposite in sign. This is the second condition that must be satisfied and means that BL will generate at least one other undistorted line in addition to the original invariant line. This pair of undistorted lines defines an undistorted plane. However, only the original undistorted line is both undistorted and unrotated. The second undistorted line is not necessarily unrotated, but can be made completely invariant, i.e. undistorted and unrotated, via a rigid body rotation R about the original invariant line. This rigid body rotation has no effect on the morphological or crystallographic features of the ‘rigid body’ that is rotated. All it does is to ensure that there is now a pair of invariant lines that define an invariant plane. In other words the combination RBL is an invariant plane strain, which is exactly what is required by the theory to represent the shape strain S. The WLR formulation of the theory can therefore be represented via the matrix algebra ‘short-hand’ notation as:
S = RBL [1.1]
Because the theory is phenomenological, the mathematical steps taken to generate the shape strain S in eq. [1.1] do not necessarily indicate actual physical processes that have occurred during the transformation. However, the resultant shape strain has real, physically measurable characteristics.
Outline of block of austenite that has
transformed to martensite
has transformed to martensite
Surface of austenite crystal
Surface of austenite crystal
{225}F Habit (b) Twinning on
(112)[111]B

The habit plane corresponds to the invariant plane and, on a pre-polished surface, measurements of the surface tilts and change in direction of scratches illustrated in Fig. 1.1 can be used to determine the direction and magnitude of the shape strain S. Similarly, the orientation relationship between the austenite and the martensite depends on the correspondence, on which B is based, and the rotation R. The LIS L has no effect on the orientation relationship, but the shear that gives L its lattice invariant characteristics may be experimentally observable as regular slip or twinning, as shown in Figs 1.1 and 1.4. The BM treatment of the PTMC follows directly from the original observation (Greninger and Troiano, 1949) that the shape strain S is, on its own, not capable of transforming fcc austenite to bcc (or bct) martensite. Hence the BM approach begins with the invariant plane strain S and combines this with an ‘invisible’ second shear H, which also deforms the crystal lattice. The total deformation that results from the BM combination SH must then be equal to the WLR total deformation RB and so the BM version of the PTMC can be represented as:
SH = RB [1.2]
In order to maintain the ‘invisibility’ of the ‘second’ shear H and to ensure that it cannot make up part of the shape change, the shape deformation S must equal SHH–1, where H–1 is the inverse of H. In other words, H–1 must be an equally opposite lattice invariant deformation that exactly balances any shape changes resulting from H. So, Eq. [1.2] can be written as:
SHH–1 = S = RBH–1 [1.3]

or {3 10 15}F habit plane in iron-nickel and iron-nickel carbon alloys with low martensite start (Ms) temperatures. The PTMC was able to explain all the crystallographic features of the {259}F martensite, which was not surprising, since Greninger and Trioiano’s work on this type of martensite was the catalyst that lead to the development of the PTMC. However, there was a measure of marked disappointment when the PTMC appeared to have some difficulties in relation to the {225}F type of ferrous martensite. The need to account for {225}F martensite had always been recognised. It appears in Bowles initial introduction of the concept of an ‘invisible’ second shear (Bowles, 1951) and was the basis for Frank’s original lattice matching model (Frank, 1953). Hence, it was not surprising to see a number of attempts to adapt the PTMC to the case of the {225}F transformation. The first of these had already been incorporated in the BM version of the PTMC. Bowles and Mackenzie purposely permitted a small relaxation to the invariant plane condition by introducing a small dilatation (<2%) that allowed the distances in the habit plane to be slightly different in the two phases. So, the habit plane was nearly invariant, but it was still an unrotated plane in the two phases. This allowed the PTMC to be more versatile, and increasing the dilatation parameter d from unity (an exactly invariant habit plane) to around 1.015 (1.5% strain allowed in the habit plane) the predicted habit plane moved from {259}F to {225}F (see, for example, fig. 2.11 in Petty, 1970, or fig. 5 in Bowles and Mackenzie, 1954b). No satisfactory physical explanation of the significance of this dilatation was put forward and consequently this explanation for {225}F martensite was occasionally regarded with some suspicion by other workers in the field. Wechsler, Otte and Wechsler, Lieberman and Read all adopted a different approach in an attempt to account for the {225}F martensite habit plane. They tried different rational slip or twinning systems in the austenite or the martensite as the LIS (Wechsler, 1959; Otte, 1960; Wechsler et al., 1960). These LIS systems were capable of predicting a variety of habit planes, but only a few came close to {225}F and even these possible solutions were not always really convincing. In some cases the variant of {225}F predicted was not correct and in others the magnitude g of the LIS was relatively large.
1.4 The post phenomenological theory of martensite crystallography (PTMC) period
1.4.1 Experiments and more trials of the theory


martensite forms as bands on the {111}F planes of the austenite and can be produced by a change in the stacking sequence from fcc to hcp via a shear of a/6<112>F on every second {111}F plane, with no need for a LIS or ‘second’ shear. This shear can occur inhomogeneously by distributing the transformation shear over the three <112>F directions lying in the {111}F plane of a single band. This could lead to the fcc austenite to hcp e transformation occurring with essentially no shape change. The bcc a martensite can form within a band of hexagonal e, via a single invariant plane strain, plus a slight ‘shuffle’ of atoms on adjacent (000l)e planes. Alternatively, the fcc austenite to bcc martensite transformation can occur directly with a LIS on (111)/[121]F (Kelly, 1964, 1965). In this case the LIS corresponds to the formation of stacking faults within the parent austenite. Hence, the bcc martensite will always be associated with bands of faulting in the austenite and these faulted bands could be close to the hcp e structure, so that the bcc martensite could appear as if it had formed from the hexagonal e. The predicted habit plane for this bcc martensite is (1 12)F at a maximum dilatation (d = 1.018), and it is possible to form twin-related bcc martensite plates with this same habit plane arranged at right angles to the bands of faulting or hexagonal e. In such situations the shape strains of the twin-related pair would have shear components that are exactly opposite and would effectively cancel each other (Kelly, 1965). For values of the dilatation parameter d closer to unity, a habit plane of the type {225}F is predicted. But this habit plane is (2 25)F and is close to 90° from the close- packed fcc plane (111)F that is parallel to (101)B. This is not the same as the normal {225}F martensite, where the habit plane is less than 30∞ away from the close-packed fcc plane (111)F that is parallel to (101)B. The orphan child in all of this burgeoning experimental work and further applications of the PTMC was the lath martensite formed primarily in low carbon steels. The main reason for the dearth of experimental attention devoted to what was subsequently to become known as the ‘{557}F lath transformation’ was that it invariably formed at high temperatures and it was difficult to find any retained austenite matrix to use as the basis for measurements of the habit plane, orientation relationship or shape strain. In fact even now, nearly half a century later, there has never been a reliable measurement of the shape strain of lath martensite in steels. little theoretical attention was devoted to lath martensite in the decade or two that followed the development of the PTMC, mainly because of the obsession with explaining the plate-like {225}F martensite that was much easier to deal with experimentally.
1.4.2 Alternative theories



the time this comment was made, the various published applications of the double shear theory had not been able to account for all of these observed crystallographic features of {225}F martensite. However, some two decades later an extended series of systematic double shear trials, where the larger of the two LIS shears incorporated a component of the twinning shear observed in {225}F martensite (Kelly, 1992c), led to a number of double shear combinations that simultaneously accounted for, not only the observed habit plane, orientation relationship and shape strain, but was also able to account for the previously observed real variation in shape strain direction of 40° or more (see Muddle et al., 1976, and fig. 9 in McDougall and Wayman, 1992). A similar application of the double shear theory (Kelly, 1992a, 1992b) was able to account for all the currently known crystallographic features of {557} F lath martensite, including the apparently large values of the shape strain, the orientation relationship and the observed array of a/2[11 1]B dislocations in the austenite/martensite interface (Sandvik and Wayman, 1983). All of this is amply reviewed in the section on ‘The {557}F lath transformation’ in McDougall and Wayman (1992). While the criticisms of the generalised double shear versions of the PTMC mentioned above are difficult to justify and, in this modified form, the theory appears to provide the required flexibility to account very well for the majority of the crystallographic features of martensite in steels and other materials, there is still room for doubt. One question often raised in informal discussions was whether or not such a double shear arrangement could still lead to an array of interface dislocations that were sufficiently mobile to permit the extremely rapid propagation of the austenite/martensite interface. Despite these niggling doubts about the mechanistic viability of the double shear versions of the theory, the PTMC has to be regarded as probably the best predictive, as opposed to explanatory, theory of phase transformations in crystalline solids. No other theory of martensitic or diffusional phase transformations would appear to even come close to the PTMC in this regard.
1.5 Strain energy – the Eshelby/Christian model and the infinitesimal deformation (ID) approach


(Shibata-Yanagisawa and Kato, 1990; Navruz and Durlu, 1999; Navruz, 2001). If valid, the infinitesimal strain approximation allows strain and rotation matrices to be added, rather than multiplied, so that in ID terms the PTMC equation [1.1], namely S = RBL, becomes:
T i = Si = Ri + Bi + Li [1.4]
While this certainly simplifies the subsequent mathematical manipulation, unless at least two of the terms on the right-hand side of eq. [1.4] satisfy the infinitesimal strain approximation by having strains that are less than 0.01, T i is not going to be equal to Si and the predictions of the ID theory will no longer be the same as those of the PTMC, as they should be. For example, in the case of {259}F martensite, the strains in Bi are in the range 0.13–0.24 and the magnitude of the LIS in Li is >0.2 (Wayman, 1964). These are clearly not infinitesimal strains by any stretch of the imagination and the predictions made by the matrix addition version of the ID theory in this case, and in any other application to martensite in steels for that matter, will not be consistent with those of the PTMC. If the infinitesimal strain approximation is not used when it is inappropriate and the ID analysis is conducted in a rigorous fashion with matrix multiplication where necessary, then the predictions will be exactly the same as those of the PTMC (Mura et al., 1976; Kato et al., 1977; Hayakawa and Oka, 1984; Ledbetter and Dunn, 1999, 2000; Kelly, 2003). Unfortunately, there is now little simplification in the mathematics of the rigorous ID approach.
1.6 Interfacial dislocation models

(Olson and Cohen, 1986). The emphasis on what was termed the ‘topological’ characteristics of interface dislocations has the potential to provide an atomistic mechanism for the martensite transformation that goes well beyond the purely phenomenological approach in theories like the PTMC. Recently, Pond and co-workers have developed an interfacial dislocation theory termed the ‘Topological Model’ (TM) (Pond and Celotto, 2003; Pond et al., 2003, 2006, 2007). This was based on a habit plane made up of terraces and steps/disconnections, as shown in Fig. 1.5, and the martensitic transformation proceeds by the movement of the interface dislocations associated with these regularly spaced disconnections. The initial version was essentially two-dimensional and avoided the need to incorporate a lattice invariant shear. The mathematics was relatively simple compared with the PTMC and the TM offered considerable promise as a means of exploring the more mechanistic aspects of martensite formation. The determination of the overall interface habit plane orientation was based on the premise that the array of interface dislocations must lead to a situation where there is ‘no long range strain’ in the habit plane. The analysis in appendix B of Pond et al. (2003) and section 3.2 of Pond et al. (2007) led to the following equation for the angle q of the habit plane to the terrace planes lying in the xy plane of Fig. 1.5:
bztan2q + bytanq + heyy = 0 [1.5]
A martensite interface with no long range strain is in effect equivalent to the invariant plane strain concept used in the PTMC and it was to be expected
a
b
h
bcy = heyy/tanq bz = (hb – ha) h/d = tanq


1.7 Future trends

crystallographic features of martensite in steels. For example, although this type of analysis is capable of justifying the change in habit plane position from {259}F to {225}F as the t/R ratio increases from zero to ~0.1, it does not obviously account for the fact that there do not appear to be any martensite habit planes located between these two positions. Why the dramatic change in habit plane, with no evidence for a gradual movement from one to the other? A recent possible explanation for this sudden transition introduces another important factor: the role of the interfacial surface energy in determining the crystallographic characteristics of martensite (Kelly, 2006). Why should the reduction of strain energy completely dominate the features of a displacive martensitic transformation? Is it not possible that the interfacial surface energy also plays a role? If so, how important are the relative influences of strain and surface energy in martensite transformations? Surely a strain energy dominated transformation can make some sacrifices in order to achieve a reduction in surface energy. Is this reduction in interfacial surface energy sufficient to compensate for the increase in strain energy associated with the change from the {259}F habit to the {225}F habit when the t/R ratio is increased to ~0.1? All this string of questions does is to highlight what would appear to be a promising area for future research, namely the role of interfacial surface energy in governing the crystallographic characteristics of martensite in steels. All the required theoretical and experimental tools are available for a concerted attack on this topic. On the theoretical side, interfacial dislocation models like the TM, combined with the elegant O-lattice formulation developed by Zhang and her co-workers (Zhang and Weatherly, 2005), should be able to make predictions that can be verified (or otherwise) by HRTEM examination of martensite interface dislocation structures. This particular aspect of martensitic transformations is crying out for further, more sophisticated analysis, verified by careful experiments.
1.8 Conclusions

1.9 References Acton, A F and Bevis, M (1969) ‘A generalised martensite crystallography theory’,
Mater. Sci. Eng., 5, 19–29. Bain, e C (1924) ‘The nature of martensite’, Trans. AIME, 70, 25–35. Bilby, B A and Christian, J W (1955) The mechanism of phase transformations in metals.
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Eshelby, J D (1959) ‘The elastic field outside an ellipsoidal inclusion’, Proceedings of the Royal Society of London A, 252, 561–569.
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martensite in steels
T. Maki, kyoto University, Japan
Abstract: Martensite in ferrous alloys exhibits various morphologies, chiefly lath, lenticular and thin plate, depending on chemical compositions and Ms temperature. This chapter reviews crystallographic features and substructures for each of these specific forms. Furthermore, the chapter discusses crystallographic features of packet and block in lath martensite, the origin of dislocation structure in lath and lenticular martensites, and the origin of the midrib in lenticular martensite.
Key words: morphology of ferrous martensite, lath martensite, lenticular martensite, thin plate martensite, substructure of ferrous martensite.
2.1 Morphology and crystallographic features of martensite in ferrous alloys

© W
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0 0.5 1.0 1.5 2.0 C content (mass%)
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2.2 Formation range of various types of a¢ martensite (lath, butterfly, lenticular and thin plate) as a function of formation temperature (Ms) and carbon content in Fe-Ni-C alloys (Maki and Tamura, 1984).

remain poorly defined. However, the Ms temperature, the strengths of parent austenite and product martensite, the critical resolved shear stress for slip and twinning in martensite, and the stacking fault energy of austenite are considered to be important factors (Davies and Magee, 1971; Krauss and Marder, 1971; Maki et al., 1972; Carr et al., 1978). Lath and lenticular are the two major morphologies of a¢ martensite (Reed, 1

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