C9 alloys

Dr E.R. Wallach Lent Term 2013-14

Materials Science Pt II C9 Alloys Synopsis and reading list University of Cambridge

[email protected] Page (i) 2013-14

i Part II Materials Science and Metallurgy

C9 Alloys (9 lectures)

This course deals with the design and use of metallic alloys with a focus on the development and control of microstructure, the relationship between microstructure and properties, and applications.

1. Introduction. Sustainability. Basis of lattice types. Hume Rothery rules for solid solutions.

Summaries of mechanical and physical properties.

Production of light alloys (Al, Ti, Mg).

2. Aluminium alloys. Phase diagrams. Alloys and tempers. Alloy characteristics. Review of preciptation hardening, oxidation, corrosion resistance and fatigue.

3. Titanium alloys. Pure Ti. Alloying Ti. Specific alloys: , + , and . Superplasticity.

4. Magnesium alloys. Mg alloys. Heat treatment of Mg alloys.

5. Anisotropy. Microstructural and crystallographic. Single crystal and polycrystalline materials. Effect on properties. Examples.

6.. Steels. Review of plain C, alloy steels and cast irons. Commercial steels: high-strength, low-alloy (HSLA), bainitic, dual-phase, transformation induced plasticity (TRIP). Stainless steels.

7. Copper alloys. Overview copper alloys.

8. Nickel alloys: overview and superalloys.

9. Non-destructive testing

Reading list

1. Light Alloys: from traditional alloys to nanocrystals, Polmear I. J., pub. Elsevier Butterworth-Heinemann, 4th edition (2006) Dept. library: Eb153 2. Steels, microstructure and properties, Bhadeshia H. & Honeycombe R., pub. Butterworth-Heinemann, 3rd edition (2006) Dept. library: De100 3. Structure and properties of engineering materials, Henkel D. & Pense A.W., pub. Tsinghua University Press / McGraw Hill, 5th edition (2008) Dept. library: AB222 4. An introduction to textures in metals, Hatherley M. & Hutchinson W.B., pub. Institution of Metallurgists Monograph 5 (1979) Dept. library: Mc6b 5. Bainite in Steels, Bhadeshia H.K.D.H., Dept. library: De96 2nd ed., Institute of Materials. 2001. Chapter 13 Modern bainitic steels

Also can download from www.msm.cam.ac.uk/phase-trans/newbainite.html 6. Non-destructive testing, Halmshaw R., pub. Edward Arnold, 2nd edition (1991) Dept. library: Ma100 7. Non-destructive testing excellent website:

www.ndt-ed.org/EducationResources/CommunityCollege/communitycollege.htm

Materials Science Pt II C9 Alloys Lecture 1: Metals and alloys University of Cambridge

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1. Metals and alloys

1. Introduction

In the periodic table, 87 elements are classified as metals, 61 of which are commercially available1.

The most commonly used metals and alloys are based on Al, Cu, Fe, Ni, Pb, Sn and Zn.

Advantages of metallic materials include: huge range of alloys and tempers allowing optimisation of properties for diverse applications;

their generally high electric conductivity, thermal conductivity, strength, corrosion resistance;

ease of shaping both by casting and subsequently by deformation processing;

ability to manufacture smart materials e.g. based on their superconducting, optical and magnetic properties plus biocompatibility.

Major metallic alloy systems, all with distinctive properties, include:

steels low cost, high strength (over 90% by weight of all metal usage is steel);

aluminium alloys high specific strength, corrosion resistance, specific conductivity;

titanium alloys higher specific strength and higher temperature application;

copper high electrical & thermal conductivity, easy to form/cast, corrosion resistance;

nickel high temperature strength and creep resistance (superalloys). Applications include:

Metal Industries Applications

Steels Very wide Automotive, ships, buildings, white goods

Aluminium alloys Aerospace, packaging, sports equipment, energy, construction

Aircraft, food containers, power cables, building cladding

Titanium alloys Biomedical, aerospace Body implants & medical, military airframe and engines, spacecraft

Copper alloys Construction, electronics, coins, transport

Plumbing, wiring, circuit boards, electronic components

Nickel superalloys Aerospace Aircraft engines and space craft

Challenges for the future: Sustainability issues are increasingly important because of

greater awareness and hence consumer pressure;

legislation Kyoto agreement (ended in 2012 and future very uncertain - Doha, Qata, 2012);

scarcity as key metals, especially rare earth metals are limited in their abundance.

Sustainability is more narrowly focussed on

abundance of different elements and whether or not economic alternatives exist;

energy to extract embodied energy and to shape;

greenhouse gas emissions when extracting and shaping (main emphasis normally on CO2).

See Figs. 1.1 and 1.2 on next page.

1 www.ceram.com/materials/metals/



Figure 1.1 Reserves versus annual world production of various elements [CES software]

Figure 1.2 CO2 emissions versus embodied energy, both for primary production [CES software]



1.2 Background to metals and alloys

a) Basis of different lattice types for metals As mentioned on page 1, there are 87 known metals in the periodic table. They can be grouped in various ways, e.g. ferrous, non-ferrous and noble, or classified as shown in Figure 1.3 below.

noble metals - generally unreactive, e.g. silver, platinum, gold and palladium;

alkali metals - very reactive with low melting points and soft, e.g. potassium and sodium;

alkaline earth metals less reactive, higher melting points and harder than alkali metals, e.g. calcium, magnesium and barium;

transition metals - hard, shiny, strong, and easy to shape, e.g. iron, chromium, nickel, and copper;

other metals diverse properties, e.g. aluminium, gallium, indium, tin, thallium, lead and bismuth.

Figure 1.3 Periodic table 2.

Question arises of whether the periodic table can explain, in a first-order manner, the different lattice type for metals since it is the electron distribution, and the resulting energy of a given arrangement within the material, that determines the lattice type.

A simple approach, by Hume-Rothery, considered the correlation between electronic configuration and crystal structure.

Crystal structures were shown to be the same for many non-transition metallic elements and alloys having the same average number of valence electrons per atom, e/a.

This did not extend to the transition metals since, as explained by later researchers, their d electron orbitals are relatively more localised than the outer-shell s and p electron orbitals; the latter have a greater influence on the long-range order. It appeared that the ratios e/a are: bcc structures form in alloys with < 1.5 outer-shell s, p electrons per atom, hcp structures form in alloys with 1.7 2.1 outer-shell s, p electrons per atom, fcc structures form in alloys with 2.5 3.0 outer-shell s, p electrons per atom, diamond structures in alloys with 4.0 outer-shell s, p electrons per atom.

This fits for elements in the third row of the periodic table on adding an additional electron, namely from Na, Mg, Al to Si. However, deviations are noted in the fourth row of the periodic table for both Ca (fcc and not hcp) and Ga (orthorhombic and not fcc).

The majority of transition element metals near their melting temperatures have bcc structures. This can be explained by the presence of vacant d orbitals which means that electrons from outer-shell orbitals can be accommodated rather than going into p orbitals. 2 Smell-O-Mints, www.jschilling.net/sw_smellomints.php



More recent modelling is based on many-electron calculations but these tend to be complex and it is often necessary to make approximations. This is problematic given that the energy differences of possible crystal structures for a given element often are small, less than 1% of the bonding energy,

One approach is to consider the energy contributions from

a. the bonding or conduction electrons although, in metals, the potential and kinetic energies of these electrons are substantially, though not totally, structure independent;

b. the Coulomb interaction energy between the positive metal ions and the sea of electrons .

b) Hume Rothery rules for solid solutions The majority of metals used in commercial applications are alloys which are typically are solid solutions or, alternatively, comprise two (or more) phases. For substitutional alloys, the following Hume Rothery rules indicate the extent of solid-solubility.

Rule 1: Atomic size factor or the 15% rule: extensive substitutional solid solubility may occur if the relative difference between the atomic radii (r) of the two elements is less than 15%, i.e.

for solid solubility, rsolute - rsolventrsolvent

15%

Conversely, if the difference > 15%, solubility generally is limited.

Rule 2: Crystal structures of the two elements must be identical for appreciable solid solubility.

Rule 3: Valency. The solute and solvent atoms should typically have the same valency in order to achieve maximum solubility. For different valencies, a metal will dissolve a metal of higher valency to a greater extent than one of lower valency.

Rule 4: Electronegativities need to be similar for maximum solubility, i.e. a solute and solvent should be close in the electrochemical series. When the difference in electronegativities increases, intermetallic compounds tend to form rather than substitutional solid solutions.

Darken-Gurry maps can be used to show the effects on solid-solubility of electronegativity (vertical axis) and atomic radius (horizontal axis). Ellipses are added to show the effects of the above rules.

Two DarkenGurry plots are shown in Fig. 1.4 for aluminium3 and Fig 1.5 for palladium4 as solvents.

Figure 1.4 High solubility expected if the solute atom is within first ellipse (



It has been suggested in the case of the Pd that the discrepancy between predicted and observed extents of solid-solubility are due to the fact that the electrons in the d and f orbitals (especially) in some elements do not behave as if completely delocalised. Such electrons retain some unpaired electron characteristics, e.g. their spin, which accounts for the magnetic properties of these metals. This is consistent with the Hume-Rothery explanation for transition metal structures.

For interstitial alloys, the following Hume Rothery rules indicate the extent of solid-solubility. Interstitial solid solutions are more likely to be formed if

- a solute is smaller than the interstitial sites in the solvent lattice of a solvent;

- a solute has approximately the same electronegativity as the solvent. In practice, there are very few elements that can form ions which are sufficiently small to fit in interstitial sites, and so appreciable solubility is rare for interstitial solid solutions.

Possible metal ions that may form interstitial solid solutions are: Li, Na, B. Plus non-ions H, C, N

Many interstitial solid solutions have a strong tendency to spontaneous ordering and examples of ordered or partially interstitial solid solutions include Al-Li.

c) Intermetallics Intermetallic compounds are metallic phases but, unlike the alloys described above, each generally has a very limited composition range, i.e. intermetallics tend to have a narrow and fixed stoichiometry. Ordering within the crystal lattice is thus common. One consequence is that typically they are quite hard and strong.

d) Defects

All metallic crystal lattices have defects - perfect lattices, with all atoms of the same type in identical positions and no missing atoms, do not exist. Defects are crucial to both mechanical and physical properties of metals and their presence and distribution can be controlled in order to optimise desired properties intentionally used to manipulate the mechanical properties of a material.

There are three major categories of crystal defect:5

point defects, where an atom is missing or irregularly placed in a lattice structure. Point defects include:

lattice vacancies, self-interstitial atoms, substitutional alloying or impurity atoms, interstitial impurity atoms;

line defects, which are groups of atoms in irregular positions, e.g. dislocations are line defects;

planar defects, which are interfaces between homogeneous regions of a material. Planar defects include

grain boundaries, stacking faults external surfaces.

5 www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/crystal_defects.htm



1.3 Mechanical properties of metals and alloys - summary

Strength grain refinement

work hardening

texture strengthening

solid solution hardening

solute pinning

precipitation hardening

ordered structures

two phase strengthening

intermetallic hardening

oxide dispersion strengthening

Toughness grain refinement

dislocation motion

control of particles

stress distribution

composites

Creep large grain size

solid solution hardening

coherent precipitates

pinned grain boundaries

Fatigue small grain size

strengthened surface (ideally in compression use of shot peening)

tough interior



1.4 Physical properties of metals and alloys include

Conductivity electrical (and resistance increases with temperature)

thermal Magnetic soft magnets

hard (permanent) magnets Density high and three major crystal classes with long range atomic ordering Melting temperature huge range from mercury (-39C) to tungsten (3400C)

The physical properties of transition metals strongly depend on the number of d electrons and the strength of the d-orbital interactions, as is shown below in Fig. 1.6 for cohesive energy, bulk modulus and melting temperature. Cohesive energy Bulk modulus

Melting temperature (C)

Figure 1.6 Variation in the number of d electrons, Nd, and cohesive energy, bulk modulus6 and melting temperature.

6 www.synl.ac.cn/org/non/zu1/knowledge/Hume-Rothery-rules.pdf



1.5 Light alloys (Al, Ti, Mg)

Some properties of commercially pure metals

[Polmear (3rd edition), Journal of Metals. 54 (2002) 4248 and Steel World, 2 (1997) 59]

All three alloys have: - excellent strength to weight ratios - corrosion resistance due to stable surface oxides see Ellingham diagram, Figure 1.8.

Hence widespread usage in aerospace and transportation applications.

Figure 1.6 Comparative weights of different alloys for the same stiffness. [Polmear, Light Alloys, 4th edition, p 4, 2006]

Increasingly changing situation for usage of alloys from Al, Ti or Mg due to:

- composite materials development, e.g. C fibre in epoxy (Boeing, British Aerospace aircraft) metal matrix SiC in Al or Ti (e.g. car engines7) ceramic matrix (e.g. Si-SiC nuclear fusion8)

- cost: as materials cost is small part, generally, of final product price

- recycling: all three metals are very energy intensive to produce from ores and so recycling is increasingly promoted, especially for Al alloys.

Figure 1.7 Years of supply (based on known mineral reserves versus recycle rate for various metals.

[Norgate and Rankin, 2002]

7 http://en.wikipedia.org/wiki/Metal_matrix_composite 8 http://composite.about.com/od/aboutcompositesplastics/l/aa030205.htm



1.6 Production of light alloys Al, Ti and Mg [see next page for abundance of elements] 1.6.1 Aluminium production9

Aluminium is produced in a two-stage process:

(i) the ore bauxite - iron and aluminium hydroxides/oxides - is refined to produce alumina Al2O3

Bayer process: Al2O3.xH2O + 2 NaOH 2 NaAlO2 + (x+1) H2O

2 NaAlO2 + 2 H2O 2 NaOH + Al2O3.3H2O

(ii) the alumina (aluminum oxide trihydrate) is reduced electrolytically to give metallic aluminum

Hall-Hroult process: 2Al2O3 + 3 C 4 Al + 3 CO2 Four tons of bauxite produce 2 tons of alumina from which one ton of aluminium is formed. 1.6.2 Titanium production10

(a) Kroll process

(i) reduction of titanium ore rutile TiO2 or ilmenite FeO.TiO2 using coal and chlorine gas at 800C

TiO2 + 2 Cl2 + 2 C TiCl4 + 2 CO2

(ii) fractionally distillation of TiCl4 to separate from other chlorides, formed from other metals in the ore, under an argon or nitrogen atmosphere, and is stored in totally dry tanks;

(iii) reduction of TiCl4 in a batch process using molten Mg (reaction at 1100C) or Na (550C) under argon to yield Ti porous sponge (note that Na approach is used in the UK only).

TiCl4 + 2 Mg Ti + 2 MgCl2

The Ti is solid at the reaction temperature allowing easy separation from the MgCl2.

(iv) melting of sponge, or sponge plus a master alloy to form an ingot which then is primary fabricated into billet, bar, sheet, strip or tube.

The Kroll process is both time-consuming and expensive, in part because of the batch processing required for the TiCl4 reduction. (b) FFC Cambridge process11

A completely different approach, the FFC Cambridge process, is based on the direct electrochemical reduction of TiO2 to Ti in molten CaCl2. First developed here in the Department between 1996 and 1997, the process is being developed for commercial usage and also has potential for other oxides. The process typically takes place between 900 - 1100C, with an anode (typically carbon) and a cathode (the oxide being reduced) in a bath of molten CaCl2. 1.6.3 Magnesium production

(a) electrolytic reduction of MgCl2 at temperatures ~ 700C. The MgCl2 is obtained from sea water. the two common ores dolomite MgCO3-CaCO3 and magnesite MgCO3.

(b) the Pidgeon thermic process in which Si or ferro-silicon is used as a reducing agent to extract

Mg from its two common ores dolomite MgCO3-CaCO3 and magnesite MgCO3. The reaction is highly endothermic. Mg is produced as a vapour which allows its separation.

Si (s) + 2 MgO (s) SiO2 (s) + 2 Mg (g) (~1200 - 1500C under vacuum)

Mg (g) Mg (liq, s) (temperature < 1090C, condensation)

From the Ellingham diagram, the reaction is thermodynamically unfavourable but occurs, utilising Le Chatelier's principle, due to the Mg removal by condensation at temperatures < 1090C.

9 www.rocksandminerals.com/aluminum/process.htm 10 www.chemguide.co.uk/inorganic/extraction/titanium.html or www.madehow.com/Volume-7/Titanium.html 11 Chen G.Z., Fray D.J. & Farthing T.W., Nature, 407, 361-364 (21 September 2000)



Figure 1.8 Ellingham diagram [www.2classnotes.com/digital_notes_print.asp?p=Thermodynamics_of_Metallurgy]

Figure 1.9 Elemental abundance in earth's upper continental crust

[http://en.wikipedia.org/wiki/Abundance_of_the_chemical_elements]

Figure 1.10 Aluminium production: HallHroult process [http://en.wikipedia.org/wiki/Hall-Heroult_process]



Figure 1.11 Titanium production: Kroll process

[www.titaniumexposed.com/titanium-industries.html]

Figure 1.12 Titanium production: FFC process [www.ornl.gov/sci/propulsionmaterials/pdfs/Emerging_Titanium.pdf]

.

Materials Science Pt II C9 Alloys Lecture 2: Aluminium alloys University of Cambridge


2. Aluminium Alloys 2.1 Typical Phase Diagrams

Since aluminium exists solely with fcc crystal structure, there are no allotropic phase changes - unlike Fe, C, Si, S all of which can exist individually in several different crystalline forms. Control of microstructure and hence properties is by alloying, mainly through solid-solution hardening and precipitation. Up to 70 wt% of zinc can dissolve in aluminium (at temperatures ~ 400C), followed by magnesium (17 wt% at 450C), copper (5.7 wt%) and silicon (1.65 wt%). Typical eutectic and peritectic phase diagrams are illustrated in Fig. 2.1; these two forms describe the vast majority of phase diagrams for aluminium alloys.

Figure 2.1 Typical phase diagrams for aluminium alloys, illustrating a eutectic and peritectic.

The solubility of solute in the aluminium matrix phase (either denoted by or by ) depends on the phase with which the is in equilibrium. In the AlCu system, the stable precipitate is CuAl2 but metastable GP1 zones can form preferentially as they are easier to nucleate (they have lower surface energy so the activation energy is less). Thus, the free energy curve for GP1 zones is located above that for CuAl2, as shown in the figure below. The common tangent construction shows that this leads to an increase in the solubility of copper in when it is in equilibrium with GP1 zones at a particular temperature see points P and Q. In addition, note that for a given composition, a greater undercooling is required before GP1 zones can precipitate (see points R and S in the figure below).

Figure 2.2 The solubility of solute in is larger when it is in equilibrium with GP1 zones compared

with when it is in equilibrium with CuAl2, as is also shown on free energy (G) diagram. In the AlCu system, the enthalpy of mixing, HM is positive. Hence, at low temperatures, there will be a tendency for like atoms to cluster, giving rise to a miscibility gap (Fig. 2.3). The enthapy of mixing is given by: HM = Na z (1 x) x where = AA + BB 2 AB x is concentration of B in binary A,B solution z is the coordination number Na is Avogadros number By considering the entropy changes when mixing two types of atoms, the thermodynamics of solid solutions can be described and the free energy of mixing GM is given by:

GM = HM - T SM

= Na z (1 x) x + Na kT {(1-x) ln (1- x) + x ln (x) } (see www.doitpoms.ac.uk/tlplib/solid-solutions/thermodynamics.php)

P Q R S

P Q



Figure 2.3 A eutectic phase diagram with a hidden miscibility gap (left) and free energy of

mixing plotted as a function of temperature and enthalpy HM of mixing.

In the above figure: - HM = 0 corresponds to an ideal solution where the atoms of different species always tend

to mix at random and it is always the case that A/ xA > 0; - when HM < 0 the atoms prefer unlike neighbours and it is always the case that A/ xA > 0; - when HM > 0 the atoms prefer like neighbours so for low temperatures and for certain

composition ranges A/ xA < 0 giving rise to the possibility of uphill diffusion. The miscibility gap at any temperature can be determined by the usual common tangent construction. Noting that the regular solution model has symmetry about x = 0.5, the compositions corresponding to the common tangent construction can in this special case be obtained by setting

0 =xGM

that is Na z (1 2 x) + Na kT ln(xx1

) = 0

and, in the limit of small x (low solid solubility), this gives x = exp

kTz

The solubility therefore changes exponentially with the reciprocal of temperature, and increases as HM tends to zero. This is illustrated for a variety of solutes in aluminium in Fig. 2.4 below.

Figure 2.4 Solubility of a variety of solutes in aluminium. Copper has the largest solubility, i.e. the smallest enthalpy of solution. Solid solution strengthening is useful but it leads only to an increase of about 40 MPa in the strength of commercial alloys. However, the copper solubility decreases exponentially as temperature falls and this is used to facilitate precipitation hardening in aluminium alloys.



2.2 Aluminium alloys and tempers Two families: cast products - use in as-cast condition so cooling rate and use of grain refiners important since

small grain size improves strength and toughness; - many based on Al- 12wt% Si which is the eutectic composition and hence the

lowest melting point, and also on Al- Zn (for die-casting especially); wrought products (rolled, extruded, forged);

- final properties rely on appropriate heat-treatment/working; - alloys are in two major classes of either precipitation hardened or work hardened; - precipitation alloys: strength controlled by precipitate distribution, size and

coherency; - worked alloys: strength from final grain size and defect density.

Alloys are classified by their compositions according to a US system: Main additions Strengthening Major applications

1xxx pure aluminium work harden Foil & electrical conductors

2xxx Al-Cu Ppte: CuAl2 Al-Cu-Mg for aircraft wing sheet

3xxx Al-Mn work-harden General purpose cookware

4xxx Al-Si Si needles Casting alloy, modified with sodium

5xxx Al-Mg work-harden Very common, corrosion resistant, structural & boats

6xxx Al-Si-Mg Ppte: Mg2Si Extruded products e.g. building artefacts, golf clubs

7xxx Al-Zn-Mg Ppte: MgZn2 High strength alloy

8xxx Other incl. Al-Li Ppte: Li3Al Low density & increased modulus alloy e.g. aircraft Possible strengthening mechanisms include: work-hardening solid-solution hardening grain size control two-phase alloys precipitates of optimised spacing and coherency oxide dispersion strengthening. Temper designation Aim: to describe the likely strength as a consequence of fabrication history.

Two families of suffixes after the alloy designation.

-Tx for precipitation hardened alloys where x is a number corresponding to a specific treatment, e.g. T4 solution treated and then naturally aged

T6 solution treated and artificially aged.

-F, O or Hx for wrought alloys e.g. F as fabricated O annealed Hx strain hardened and where the value of x denotes extent of hardening H4 half hard, H8 fully hard. T6 is a very common heat treatment for aircraft alloys (typically 2xxx, i.e. Al-Cu), which after solution treatment might be aged for 68 h at 150170C to obtain the required tensile properties.

More complex heat treatments also used, e.g. better combination of tensile and fatigue properties if alloys aged for a shorter time at 150170, followed by some natural ageing at ambient temperatures.

Natural ageing generally leads to secondary precipitation on a finer scale.



2.3 Pure aluminium for electrical applications: - highest electrical conductivity at ambient temperature than any other element for a given weight; - its weight specific electrical conductivity is about twice that of copper; - used extensively for overhead electrical cables; - high purity aluminium has a very low yield strength of ~7 MPa and so overhead power

distribution cables are reinforced with steel see Fig. 2.5 below; - in some applications, e.g. electrical motors, the use of aluminium windings increases the

volume of the equipment, so copper is used instead despite the disadvantage in weight.

Figure 2.5 Aluminium overhead power line cable, reinforced with steel wire cores 2.4 Alloy family characteristics 1xxx These are minimally alloyed and generally used in the annealed condition with yield strengths

y 10 MPa. Applications: electrical conductors, chemical equipment, foil and architecturally. 2xxx Al-Cu precipitation hardened alloys, and used extensively in civil aircraft due to their high

strength to weight ratios. These alloys generally are not fusion weldable, and aircraft are riveted. Various alloy additions can be made to optimise their properties. Most recently, the addition of Li has been investigated.

Lithium as an alloy element in aluminium alloys is unique in that it, unusually for most alloying additions, significantly improves stiffness: each 1 wt.% of lithium reduces the density of an AL-Li alloy by about 3% and increases the stiffness by ~5%.

The alloy 2090 has a composition of 2.7 wt.% Cu, 2.2 wt.% Li and 0.12 wt.% Zr.

3xxx These are the AlMn or AlMnMg alloys with moderate strength ductility and excellent corrosion resistance. The strength, at about y 110 MPa, comes from dispersoids which form in the early stages of solidification. The Mn concentration is restricted to about 1.25 wt% to avoid excessively large primary Al6Mn particles. Magnesium (0.5 wt%) gives solid solution strengthening and the AlMnMg alloy is used in the H or O conditions. Beverage cans represent the largest single use of either aluminium or magnesium alloys. A typical alloy has the chemical composition Al0.7Mn0.5Mg wt%.

4xxx AlSi is a simple binary eutectic with eutectic composition ~11 wt.% Si. Used only for castings (e.g. aluminium car engine blocks with hyper euctectic composition of ~18 wt.% Si) or for brazing other aluminium alloys (based on eutectic composition).

5xxx The magnesium concentration is usually maintained to less than 34 wt% in order to avoid Mg5Al8. The strength is in the range y 40 160 MPa with rapid work hardening during deformation. Work hardened aluminium alloys tend to soften with age because the microstructure is not stable even at ambient temperature. Therefore, it is better to excessively work harden and then to anneal to the required strength and stability. The alloys, which have excellent corrosion resistance, are used to make the bodies of boats or vehicles. They are readily welded.

6xxx This Al-Mg-Si family of alloys relies on Mg2Si precipitation hardening. These alloys are readily extruded and also anodized. Hence they are used both architecturally as well as for sports equipment.

7xxx High strength alloy based on MgZn2 precipitation hardening. Tendency to stress corrosion for greater than (Mg + Zn) > 6 wt.%.

8xxx Various other alloys including Li based with Li3Al pptes. Low density, increased stiffness leads to aircraft applications. Problem with poor toughness.

Dispersion strengthened alloys: Molten aluminium is broken up into droplets which are immediately oxidised on their surfaces. On compaction, the surface oxide breaks up into highly stable dispersoids in an aluminium matrix. There are alloys with up to 20 wt% of alumina. Other particles such as SiC can be added in large quantities these are often called metal matrix composites.



2.5 Precipitation See Part IA and Part IB lecture notes which cover the following key points.

(a) Age hardening involves the rapid cooling of a solid solution from a high temperature to one at which it becomes supersaturated so that ex-solution of solute (precipitation) begins on ageing. Note that it is not just the solute concentration which is supersaturated but also the vacancy concentration and the vacancies act as heterogeneous nucleation sites.

(b) The need to age in a manner to avoid precipitatefree zones. The latter form either due to either vacancy or solute depletion in the vicinity of grain boundaries.

(c) The role of metastable precipitates in the development of precipitation hardening (more coherent metastable precipitates, with lower surface energies, decreases the nucleation activation energy).

2.6 Oxidation and corrosion resistance Aluminium oxide forms extremely readily, as shown by Al2O3 line location on the Ellingham diagram. The natural alumina film (210 nm thick) protects in neutral environments but not in alkaline or in strong acids (with the exception of concentrated nitric acid which is a strong oxidising agent). Note that the nature of the oxide changes both with temperature (amorphous to crystalline as the temperature is raised) and also with composition (spinels can form in Al-Mg alloys) The naturally formed oxide film can be thickened by immersion in hot acid to some 12 m thickness. Even thicker films (1020 m) can be obtained by anodising aluminium. This involves making the component an anode in dilute H2SO4 solution. The film contains a cellular structure of open pores; these can be sealed by boiling in water which makes the cells expand by hydration. On drying the cells remain closed. The cells can be filled with dye before sealing to produce coloured aluminium. An increase in the current density and voltage during anodising causes microscopic arcing which locally induces the oxide to fuse and solidify rapidly. With sufficient arcing, a tenacious, hard and fully dense alumina coating is formed. This plasma electrolytic oxidation process can be exploited in making components such as rollers, which require wear resistance. Zinc in solid solution lowers the AlZn electrode potential; such alloys are therefore used for cladding and as galvanic anodes for sacrificial protection. The presence of intermetallic compounds in an aluminium alloy reduces corrosion resistance. For example, iron and silicon compounds are regions where the alumina film is weakened. As a result, pure aluminium corrodes at a much lower rate than alloys, and hence pure aluminium (or Al-Zn alloys) is often used to clad aluminium alloys to protect against corrosion. Such cladding can be introduced by roll-bonding together the two alloys of interest.

2.7 Fatigue There are two major difficulties. Coherent precipitates are cut by dislocations; each passage of a dislocation shears the particle, producing steps at the entry and exit sites, thereby reducing the particle crosssection on the slipplane (Fig. 2.6). This makes it easier for a subsequent dislocation to cut the particle. Slip then tends to focus on particular planes, leading to stress concentrations which promote fatigue. It is better therefore to have a mixture of fine, coherent and bigger semicoherent precipitates so that the danger of inhomogeneous slip is reduced. Fatigue is also initiated at pores in thick aluminium components. This can only be controlled by careful processing, and by rolling deformation where this is permitted.

Figure 2.6 The effect of a dislocation passing through a coherent precipitate.

Materials Science Pt II C9 Alloys Lecture 3: Titanium alloys University of Cambridge


Titanium Alloys 3.1 Pure Titanium Melts at 1670C but use restricted to < 400C Density 4.51 g cm3 Pure titanium has excellent resistance to corrosion and is used widely in the chemical industries. Ti forms a passive oxide film which makes it particularly resistant to corrosion in oxidising solutions. The corrosion resistance can be further improved by adding palladium (0.15 wt%), which makes hydrogen evolution easier at cathodic sites so that the anodic and cathodic reactions balance in the passive region. Many chemical plants use steel vessels which are protected by titanium alloys; titanium sheet (0.5 mm thick) is frequently a loose liner or may be roll or explosion bonded to the steel. Titanium condenser tubes are used in power plants and in desalination plants. Titanium appears ideal, given its high melting temperature, for use in components which operate at elevated temperatures, especially where large strength to weight ratios are required.

Figure 3.1 Specific strength (yield stress divided by density) versus temperature However, if titanium alloys rub against other metals at elevated temperatures, the titanium alloy oxidises extremely rapidly and causes severe damage. This limits its application, in the harsh environment of aero engines, to regions where the temperature does not exceed 400C. The world production of titanium (currently electrolytically) is, therefore, relatively small, hundreds of thousands of tonnes, which compares with steel at 750 million tonnes per annum. Some 80% of all the titanium produced is used in the aerospace industries. Car suspension springs could easily be made of titanium with a great reduction in weight but titanium is not available in the large quantities needed at the price required for automobile applications. The target price for titanium needs to be reduced to about 30% of its current value for serious application in massmarket cars. This now is potentially possible by replacing the traditional Kroll process and subsequent refinement by electrolysis of fused salts see Section 1.6.2. The crystal structure of titanium at ambient temperature and pressure is closepacked hexagonal () with a c/a ratio of 1.587. Due to the distortion from the ideal c/a ratio of 1.67, slip is possible on the pyramidal, prismatic and basal planes in the closepacked directions. At about 890C, titanium undergoes an allotropic transformation to a bodycentred cubic phase which remains stable to the melting temperature. 3.2 Alloying of Ti All elements which are within the range 0.851.15 of the atomic radius of titanium alloy substitutionally and have a significant solubility in titanium as per Hume Rothery rules.

Elements with an atomic radius less than 0.59 that of Ti occupy interstitial sites and also have substantial solubility (e.g. H, N, O, C).

The ease with which solutes dissolve in titanium makes it difficult to design precipitationhardened alloys. Boron has a similar but larger radius than C, O, N and H; it is therefore possible to induce titanium boride precipitation. Copper precipitation is also possible in appropriate alloys.



Figure. 3.2. Plot of atomic radius versus Pauling electronegativity for elements. Notice many elements of similar

size to titanium, and B, H, N, O and C all fall in interstitial range of HumeRothery rules. Alloying elements can be categorised according to their effect on the stabilities of the and phases:

Al, O, N, Ga, Zr and Sn are stabilisers; Mo, V, Si, W and Ta are stabilisers.

Cu, Mn, Fe, Ni, Co and H are also stabilisers but form the eutectoid. The eutectoid reaction is frequently sluggish (since substitutional atoms involved) and is suppressed.

Figure 3.3. Phase diagrams for Ti alloys Molybdenum and vanadium have the largest influence on stability and are common alloying elements. Tungsten is rarely added due to its high density. Cu forms TiCu2 which makes the alloys agehardening and heat treatable; such alloys are used as sheet materials. It is typically added in concentrations less than 2.5 wt% in commercial alloys. Interstitials Interstitials inevitably cause changes in the lattice parameters. Body centred cubic Ti has three octahedral interstices per atom whereas hcp Ti has one per atom. The latter are therefore larger, so that the solubilities of O, N, and C are much higher in the phase. Hydrogen is the most important interstitial. Titanium is capable of absorbing up to 60 at% of hydrogen, which can also be removed by annealing in a vacuum. Hydrogen enters the tetrahedral holes which are larger in b.c.c. than c.p.h. Thus the solubility of hydrogen is larger in . The enthalpy of solution of hydrogen in Ti is negative (H < 0).

H2 2H

G = G0 + RT ln 2

2H

Hpa

so that RT

H exp RS exp

2

2H

=

Hpa

The solubility actually decreases with temperature (Figure. 3.4). This contrasts with iron which shows the opposite trend.



Figure 3.4. Solubility of hydrogen in titanium

Because of this characteristic, titanium had been considered as a candidate material for the first wall of magnetically confined fusion reactors. The hydrogen-based plasma is not detrimental since at 500C and 1 Pa pressure, the Ti does not pick up enough hydrogen for embrittlement. An additional feature is that Ti resists swelling due to neutron damage. A large enough concentration of hydrogen induces the precipitation of hydrides. TiH1.52.0 has a cubicF lattice and its precipitation causes embrittlement due to a volume expansion of about 18%. There are regions of hydrostatic tension at crack tips where it forms preferentially, leading to large increases in the crack growth rate, some 50fold during fatigue. The hydride reaction can also be used to store hydrogen reversibly:

2.2 FeTiH1.04 + H2 2.2 FeTiH1.95

The energy to weight ratio for such a cell is about a tenth that of petrol. However, one problem with this method of hydrogen storage is that hydride formation is accompanied by a considerable volume expansion, which in turn can embrittle the alloy. Amorphous alloys of titanium are better in this respect, since they do form hydrides and yet reversibly accommodate large quantities of hydrogen by an expansion of the nearest neighbour distance. The ZrTi Laves phase Ti0.24Zr0.76(Ni0.55Mn0.3V0.065Fe0.085)2.1 has been found to reversibly accommodate nearly 1.5 wt% of hydrogen, with a battery rating of some 440 mA h g1. 3.3 Specific alloys alloys Aluminium is the main alloying element. The combined effect of the stabilisers is expressed as:

aluminium equivalent, wt% = Al + 1/3 Sn + 1/6 Zr + 10 (O + C + 2N) If this exceeds about 9 wt% then there may be detrimental precipitation reactions, generally by the formation of Ti3X which has an ordered h.c.p. structure. The presence of a small amount of the more ductile phase in virtually all alloys is advantageous for heat treatment and the ability to forge. The alloys may therefore contain 0.5 - 2 wt% of Mo, e.g.

Ti 6Al 2Sn 4Zr 2Mo where the Zr and Sn give solid solution strengthening. A near alloy has been developed, with good elevated temperature properties (T < 590 C):

Ti 6Al 4Sn 3.5Zr 0.5Mo 0.35Si 0.7Nb 0.06C The niobium is added for oxidation resistance and the carbon to allow a greater temperature range over which the alloy is a mixture of + , in order to facilitate thermomechanical processing. This particular alloy is used in the manufacture of aeroengine discs and has replaced discs made from much heavier nickel base superalloys. The final microstructure of the alloy consists of equiaxed primary grains, Widmansttten plates separated by the phase. + alloys Most + alloys have highstrength and formability, and contain 46 wt% of stabilisers which allow substantial amounts of to be retained on quenching from the + phase fields, e.g.

Ti 6Al 4V



Al reduces density, stabilises and strengthens while vanadium provides a greater amount of the more ductile phase for hotworking. This alloy, which accounts for about half of all the titanium that is produced, is popular because of its strength (1100 MPa), creep resistance at 300C, fatigue resistance and castability. One difficulty with the phase, which has a bodycentred cubic crystal structure, is that like ferritic iron, it has a ductilebrittle transition temperature. The transition temperature tends to be above room temperature, with cleavage fracture dominating at ambient temperatures. Burnresistant alloys Titanium fires can occasionally occur in aero engines or in titanium based heat exchangers used in the chemical industries. The addition of chromium in concentrations exceeding 10 wt% helps improve the burnresistance of titanium alloys. The alloy Ti35V15Cr wt% has sufficient chromium to resist burning in an aeroengine environment to temperatures up to about 510C. Chromium is not found to be effective in binary TiCr alloys where it does not encourage the formation of a continuous film of protective oxide. Quenching from Quenching the phase leads to the formation of h.c.p. martensite. This is not particularly hard and there are increasing quantities of retained in the microstructure as the solute concentration increases and the MS temperature decreases (Fig. 3.5). The habit plane of the martensite is close to {3 3 4} and the crystallographic relationships between the original and the martensitic are:

(1 1 0) || (0 0 0 1) and [1 1 1] || ([1 1 2 0]

Figure 3.5 Martensitic transformation from Transformation to The phase is metastable and forms from in alloys based on titanium, zirconium and hafnium. It is important because its formation generally leads to deterioration in mechanical properties. There is also an increase in the electrical resistance as forms and, in TiNb alloys, its formation influences superconduction. The to transformation is diffusionless, occurs below the T0 temperature and frequently cannot be suppressed even by quenching at 11,000C s1. It is reversible and diffusionless but is not martensitic in the classical sense since there is no invariantplane strain shape deformation. However, it does involve the coordinated motion of atoms. Titanium aluminides Ti3Al and TiAl The most successful of the aluminides has a lamellar structure made up of alternating layers of an ordered hexagonal (D19) Ti3Al and 2 compound and ordered f.c.t. (L10) TiAl or . The phase forms with its most closely packed plane parallel to the basal plane of the 2:

{1 1 1} || {0 0 0 1}2 < 1 1 0 > || < 1 1 2 0 > 2

The lamellar microstructure is a direct consequence of this orientation relationship. Ductility is about 4- 6% at ambient temperature and the aluminide tends to be more ductile. Their densities are about 4.5 g cm2 and the aluminium makes them resistant to oxidation or burning. The alloys have been extensively studied for aerospace and automotive turbochargers because of their high strength, low density and creep resistance.

. Ms Mf



3.4 Superplasticity Superplasticity is ability of polycrystalline material to deform to very large strains without failure.

- strains greater than 200% common and several commercial materials can show over 1000% while development alloys can exceed 4000%

- need two-phase microstructure which remains stable at processing temperature (T 0.5 Tm)

- grain size must be (and has to remain) very small, few m diameter

- strain rate must be low and is range limited (10-4 to 10-2 s-1)

= k [

m] where m is strain-rate sensitivity, and for superplasticity 0.4 < m < 0.9

- consequence of resistance to necking (which otherwise limits elongation). Many different alloys can be superplastically formed provided the above conditions are fulfilled. The + alloy Ti - 6 Al - 4 V is readily superplastically formed at ~ 950C using stresses ~ 10 MPa

and controlled strain rates as above Exploit in simple forming operations such as blow forming / deep draw.

Can also incorporate diffusion bonding (solid-state joining) as part of a combined manufacturing operation, e.g. to form stiff honeycomb structures. Apply pressure at elevated temperature for time to promote bonding and then use inert gas at high pressure to cause superplastic shape change. 3.4.1 Theory a) T < 0. 4 Tm True stress - true strain described by = k n

Load (P) instability, i.e. dP = 0, occurs when d TdT

=

i.e. when the equivalent uniform strain T* = n

Note if d TdT

> any local neck is stable and overall work-hardening occurs instead.

pressure stop off so no bonding



10-5 10-3 10-1 strain rate

m

b) T > 0.4 Tm Additional time dependence, hence

= k' n [

m] Note that at T < 0.4 Tm m 0.03 and = k n

If minimal strain hardening occurs at higher temperatures, n 0

and

Relationship between m and uniform elongation at higher temperatures

= k [

m] = PA hence

= 1A

1/m

Pk

1/m

also

= 1t

l

l

= 1l

l

t

= - 1A

A

t

Combining these two equations

- dA dt

= A 1 A 1 m P k

1 m

= P k 1 m 1

A (1-m)/m

Hence for m < 1: - area reduced more rapidly as the value of A decreases

- as m tends to 1, the diffuse neck becomes more stable

Measurement of m

Use two different strain rates 1

and 2

Then

m = d log

d log

log

log =

ln 2 /1( )ln

2 /

1

In practice, m varies with temperature, grain size, and strain rate

(which depends on stress )

log

log



3.4.2 Models for superplasticity Require: two-phase microstructure which remains stable at processing temperature (T 0.5 Tm);

stable fine grain size which is (and remains) very small, few m diameter;

equiaxed grain structure with relatively high grain boundary (gb) misorientations;

similar strength of both phases to allow deformation of both with no gb cavitation;

ability for material to undergo dynamic recrystallisation rather than creep during deformation to avoid build up of dislocation density or networks;

mobile gbs to counteract stress build-up at gb triple points and so facilitate gb sliding.

Observe: little grain growth and preservation of original small equiaxed grain structure; shear at grain boundaries leading to mutual displacement of neighbouring grains;

continuous grain boundary migration, sliding and rotation;

low final dislocation density;

detrimental gb cavitation especially if two phases in duplex alloy have different hardness;

texture of material reduced. Models: a. Grain boundary sliding

relative shearing of neighbouring grains plus slip and/or diffusion to maintain grain continuity; rotation and exchange of neighbouring grains (Ashby-Verrall see Fig. 3.6 below).

! Figure 3.6 Superplasticity model of Ashby-Verrall

[Ashby M.F. and Verrall R.A, Acta Met., 21 p29, 1973] b. Diffusional flow and creep as in deformation maps

Figure 3.7 Deformation map for copper with grain size of 100 m



high stress: dislocation core diffusion and glide leading to dislocation climb; low stress: grain boundary diffusion (Coble creep) or bulk diffusion (Nabarro Herring); rate controlled by vacancy creation & annihilation at grain boundaries.

c. Dislocation glide

dislocations glide in a grain and reach the grain boundary and hence dislocation pile up; pile-up stress results in a higher stress in the adjacent grain and hence slip initiates in it; dislocations will also climb resulting in more slip; dynamical recovery and recrystallisation also needed to prevent work-hardening.

3.4.3 Grain refinement methods a. Mechanical working of two-phase alloys

- ideally similar volume fractions and hardness;

- classical recovery and recrystallisation;

- final grain size determined by amount of initial cold work plus recrystallisation temperature and time;

- used for Ti / alloys, Al-CU-Zn eutectics.

b. Mechanical working of other duplex alloys (e.g. eutectics, precipitation hardened)

- typically alloys with < 10% precipitates;

- fine pptes < 0.1 m inhibit dislocation movement so subgrains smaller and recrystallises to form small equiaxed grains with high angle gbs (hence easier superplastic gb sliding);

- coarser pptes result in localised strain which promotes high angle gbs on recrystallisaton;

- used for Al-Cu-Zr Supral alloys, and Al-Mg-Zr.

c. Thermal cycling through phase transformation

- repeated phase transformations result in fine grains due to repeated nucleation at gbs.;

- often need additional small pptes. to ensure stable grain structure when superplastic forming;

- used in HSLA steels and uranium.

d. Phase separation from non-equilibrium phase

- quench to form martensite and then many available sites to nucleate second phase when tempering;

- also spinodal decomposition e.g. Zn 22wt.% Al

Materials Science Pt II C9 Alloys Lecture 4: Magnesium alloys University of Cambridge

[email protected] Page 25 of 61 2013-14

4. Magnesium Alloys 4.1 Introduction Magnesium is the lightest of the structural metals (density of only 1740 kg m-3, although most magnesium alloys have slightly higher densities due to the alloying additions needed. The world production of Mg is relatively small compared to other structural metals such as Al and steel. However, the alloy is being promoted strongly in China which now produces ~ 50% of the worlds Mg using the Pidgeon process (see Section 1.6). About half Mg usage is as an alloying addition to aluminium alloys, e.g. the 5xxx series of alloys such as 5083 with 4.5 wt.% Mg. Other metallurgical uses include:

- pressure die castings, e.g. parts for the car industry to aid fuel economy including transmission casings cast in AZ91D resulting in 25% weight saving over Al alloys steering components using AM50A & AM60B alloys (more ductile) instrument panels, intake manifolds, cylinder head covers, inner boot lid sections GM Savana & Express vans in the USA use up to 26 kg of Mg alloys.

- desulphurisation of steel and also removal of bismuth from lead - inoculation of grey cast iron (flake to spheroidal graphite to improve toughness) - sacrificial anodes to protect steel structures from corrosion, e.g. ships, oil and gas pipelines.

4.2 Magnesium alloys

Common magnesium alloys are shown below1.

Alloy designation Alloying additions (wt.%) Uses Reasons for use

AZ91 9.0 Al, 0.7 Zn, 0.13 Mn General casting Good castability, good mechanical properties at T

Materials Science Pt II C9 Alloys Lecture 4: Magnesium alloys University of Cambridge


4.3 Major alloying additions Al improves castability solid solution strengthens precipitation hardening at low T (

Materials Science Pt II C9 Alloys Lecture 5: Anisotropy University of Cambridge


5. Anisotropy 5.1 Introduction

The response of many materials, natural and man-made, are not uniform when used in service, i.e. the material behaves in an anisotropic manner. This is a consequence of the dependence of properties on a materials atomic structure chemical composition microstructure and phase distribution defects fabrication history, i.e. deformation & heat treatments. Anisotropy often can be beneficial and hence exploited in high technology applications, e.g.

- liquid crystals used in watches and many other electronic displays, - piezo-electric effect used in sensors or to generate ultrasound waves, - preferred microstructure of turbine blades in a jet engine, and - fabrication of high strength polymers (ropes as well as synthetic spiders silk).

Anisotropy can be described in two ways: microstructural and crystallographic.

The former can apply to all materials including natural materials such as wood, while the latter clearly applies only to crystalline materials whether natural (e.g. minerals such as quartz) or man-made (many metallic alloys).

Figure 5.1 Microstructural anisotropy in wood and extruded commerical purity Al [See DoITPoMS TLP The structure and mechanical behaviour of wood www.doitpoms.ac.uk/tlplib/wood/

plus DoITPoMS Sample 604 www.doitpoms.ac.uk/miclib/] 5.2 Microstructural anisotropy in polycrystalline materials

This includes the distribution and sizes of: - grains; - phases; - precipitates; - dislocations.

The extent of and also any variations in microstructural anisotropy generally can be characterised using image analysis to capture an image digitally and then using image processing and an appropriate statistical package. Hence the relative area fractions of different phases can be readily assessed as well as orientation as shown using the approach shown in Fig. 5.2.

Micrograph of metal grains Image processed Measure no. of intercepts Polar plot of mean using grid of parallel lines intercept length

Figure 5.2 Characterising microstructural anisotropy by measuring number of intercepts using a grid of parallel lines which is rotated to various orientations.

[Russ J.C., The Image Processing Handbook, 4th Ed., Taylor & Francis Inc, 2002]



Composites can present extremes of microstructural anisotropy, as is shown in Figure 5.3.

Figure 5.3 Variation of fracture stress with fibre orientation for a composite [http://aluminium.matter.org.uk/ Anisotropy module, page 4]

For composites, the analysis is relatively straightforward using the rule of mixtures, i.e.

L = Vf fb + (1 Vf) mb where L = fracture stress in longitudinal direction fb = fracture stress of the ceramic fibre mb = fracture stress of the metal Vf = volume fraction of the ceramic fibres

Certain types of microstructural anisotropy in metallic alloys can be treated rigorously, e.g. the variation of yield strength Y with the mean grain size d by the Hall-Petch equation:

Y = i + k d1/2

where i is the lattice friction stress (i.e. stress to move dislocations other than near gb pile-ups) k is a constant. However, since microstructural anisotropy in metallic alloys generally is less easy to describe than that in composites, predictions of properties arising from it are more difficult than for composites. 5.3 Crystallographic anisotropy in single crystals 5.3.1 Transport properties such as diffusion, thermal and electrical conductivities

Single crystals have regular long-range arrangements of atoms/ions. However, the properties will not be the same in every direction, unlike a gas, an amorphous solid, or even a polycrystalline solid. Mechanical and physical properties generally show an angular variation with respect to the major crystal axes in a single crystal and also reflect the inherent symmetry of the crystal. This is the basis of the piezoelectric, pyroelectric and ferroelectric effects in perovskites, as was introduced in Part IA. The variation in behaviour is described by Neumanns principle1 (of symmetry), namely:

the symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of the crystal.

The variation of a property such as diffusion or thermal conductivity in a single crystal is described using a second rank tensor. Diffusion in a material is described using Ficks first law in which the flux Ji is given by:

Ji = - Dij dCdx j

where dCdx j

is the concentration gradient and Dij is the diffusion coefficient.

This can be illustrated by a representation surface, the shapes of which2 are - sphere for cubic lattices (in which the lattice parameters a = b = c), - a biaxial ellipsoid for hexagonal or tetragonal lattices (in which the lattice parameters a = b c), - a triaxial ellipsoid for orthorhombic lattices (a b c).

1 As introduced in Course C4 Tensors in Section 1.9. 2 DoITPoMS TLP Tensors www.doitpoms.ac.uk/tlplib/tensors, section The effects of crystal symmetry.

Fracture stress (MPa)

Fibre orientation ()



A representation surface for hexagonal or tetragonal lattices is shown below in Fig. 5.4.1-2

Figure 5.4 Representation surface for self-diffusion in magnesium [modified from DoITPOMS TLP Anisotropy www.doitpoms.ac.uk/tlplib/anisotropy]

If the concentration gradient is in the same direction as one of the principal axes (x, y or z) then the resulting flux will be in the same direction. However, if it is an any other angle to the principal angles, the consequence of the differences in the magnitudes of Dy and Dz, is that the resulting flux is not in the same direction as the concentration gradient. The direction and magnitude of the flux may be calculated using direction cosines but also are shown conveniently using the above representation surface. Using the representation surface, a line is drawn to show the direction of the concentration gradient relative to the two principal axes as then:

- the direction of the resulting flux is given by the normal to the tangent to the ellipse at the point where line for the concentration gradient crosses the ellipse;

- the (magnitude of the diffusion coefficient)1/2 is proportional to the length of the radius in that chosen direction.

Consider diffusion in, say, an hcp Mg single crystal. A unit cell has two lattice parameters a and c, and the ratio c/a ideally is (8/3) or 1.633. This suggests that diffusion within the close-packed basal plane (0001) should be higher than that normal to the basal plane, i.e. in the c direction or [0001]. This has been confirmed experimentally; the measured values were Dx or Dy = 1.85 x 10-12 m2 s-1 and Dz = 1.0 x 10-12 m2 s-1 at a temperature of ~425C.3 Hence the representation surface would be similar to that in Fig. 5.4 above. 5.3.2 Mechanical properties: crystal orientation and texture hardening

Plastic deformation by dislocation movement occurs when the applied force/s F on a body of cross-sectional area A results in a shear stress in a slip system which exceeds the critical resolved shear stress CRSS.4 A slip system is a combination of a close (or closest )packed plane and a close packed direction in that plane. The resolved shear stress on a close packed plane and in a close packed direction is given by the expression

= FA

cos cos

where is the angle between the tensile force direction and the normal to the slip plane and is the angle between the tensile force direction and slip direction in the slip plane. The product cos cos is known as the Schmid factor.

1 As introduced in Pt II Course C4 Tensors in Section 8.1 The representation surface for second rank tensors. 2 DoITPoMS TLP Anisotropy www.doitpoms.ac.uk/tlplib/anisotropy, section Anisotropy ellipsoid. 3 McKie D and McKie C, Crystalline Solids, Thomas Nelson, p 367 1974. 4 Part IA Course D and Pt II Course C6 Crystallography in Section 6 Deformation and texture.

1D z

1D x

dCdx j

or grad C Ji



(a) fcc and bcc single crystals There are 12 independent slip systems in fcc metals of the form and the same number in bcc of the form . If a tensile stress is applied to a single crystal, two approaches can be used to find on which slip system the resolved shear stress will be maximum: OILS rule or Diehls rule.1 The latter uses a stereographic projection as shown in Fig. 5.5 for an fcc or bcc single crystal on which twenty-four slip systems are shown. The approach to finding the slip system with the maximum resolved shear stress is implicit in the figure and has been covered elsewhere.1,,2 Note that the three corners of each stereographic triangle are of the form 100, 110. 111.

Figure 5.5 Stereographic projection for fcc or bcc crystal showing 24 triangles corresponding to the 24 slip

systems. [From Pt. II Course C6 Crystallography, Section 6] The actual location of the tensile axis with respect to the particular (111) plane normal and [110] slip direction affects the Schmid factor, and also can affect the number of slip systems that can operate initially. Accordingly, the magnitude of the applied force F required for plastic deformation, varies with the location of the tensile axis as represented on the stereogram. From the expression for the Schmid factor, the load needed for plastic deformation will be minimum if both angles and are 45. Conversely, a higher load would be needed if the tensile axis was at some other orientation, e.g. if it was near the ,110> or corners of a stereographic triangle. This is texture hardening and applies to all crystal systems, not just in fcc which was used above to introduce the concept. (b) hcp single crystals and work softening

Texture hardening is very evident in hcp single crystals in which there are only three slip systems, namely the three close packed directions in the only close-packed plane, the basal plane (0001). Hence if a force is applied at 90 to the (0001) plane, there can be no resolved shear stress in the plane and so the yield stress would be infinitely high (unless slip took place on a different plane). As the angles between the tensile axis and slip plane normal and slip direction both are decreased from 90, the load needed for plastic deformation would decrease until it reached its minimum value when both angles and were 45. As the angles decreased further below 45, the load would again increase and would become infinite if the applied force was in a direction parallel to the (0001) plane. This can be observed in practice and the decrease in the necessary load is called work softening. An example for a cadmium single crystal is shown in Fig. 5.6. Initially, the Schmid factor is high due to the orientation of the tensile axis with respect to the single crystal. As deformation proceeds, the tensile axis rotates towards the slip direction or, if the axis along which the load is applied is fixed, then the slip system rotates during deformation. In either case, the Schmid factor can decrease and so the load for plastic flow decreases.

1 DoITPoMS TLP Slip in Single Crystals www.doitpoms.ac.uk/tlplib/slip, section Slip geometry. 2 As introduced in Pt II Course C6 Crystallography in Section 6 Deformation and texture.



Figure 5.6 Schematic load-extension curves for tensile deformation of two cylindrical cadmium crystals.1

In Fig. 5.6, the solid line shows the behaviour of a crystal showing geometric softening, where the load decreases once plastic deformation commenced. The dotted line is for a sample in which no geometric softening occurs, i.e. the tensile axis is at a different angle to the operative slip system. The rise in load in both cases as the extension increases is due to normal work hardening. (c) Variation of other mechanical properties, e.g. Youngs modulus Given the different packing densities in different directions in single crystals, it is not surprising that certain properties will reflect this. As an example, the anisotropy of Youngs modulus for an aluminium single crystal has been estimated by calculation to increase by ~ 15% when the tensile direction is rotated from the [100] to the close-packed [110 direction, as is shown below.

Figure 5.7 Effect of single crystal orientation on the Young modulus of Al.2 5.3.3 Magnetic anisotropy in single crystals

Magnetic anisotropy can occur as a consequence of:

- magnetocrystalline anisotropy where atomic lattice structure affects the ease of magnetisation; - shape anisotropy where a magnetising field applied to a non-spherical particle is not the same in

all directions;2 - magnetoelastic anisotropy where an applied stress can alter magnetic response.

Figure 5.8 Magnetocrystalline anisotropy: variation in applied field H required to achieve the same induced field B for two different crystallographic axes, i.e. easy and hard directions.1

1 DoITPoMS TLP Slip in Single Crystals www.doitpoms.ac.uk/tlplib/slip, section Slip in HCP metals 4. 2 http://aluminium.matter.org.uk/ - choose anisotropy section

B

H

.



Magnetocrystalline anisotropy occurs because the ease of aligning electron spins is affected by the crystallographic direction in a unit cell. The terms soft and hard directions are used to differentiate between the magnitudes of the applied magnetic field H required to induce a field M of a given magnitude. This is shown in Fig. 5.8. Two consequences arise. Firstly, magnetocrystalline anisotropy energy can be minimised by forming domains such that the electron spins are aligned in easy crystallographic directions. However, in any domain walls, there must be a change in the direction of the magnetisation and the electron spins will not all be aligned along easy axes. Hence magnetocrystalline energy is minimised in materials with large domains and correspondingly few domain walls. Secondly, the hysteresis loop on reversing an applied field will be larger if magnetisation takes place along hard directions rather than soft. There will be a higher energy associated with the larger hysteresis loop and this means lower efficiencies (and more heat evolution) in applications such as motors or transformers see Fig 5.9.

Figure 5.9. Hysteresis loops for hard and soft magnetic materials [www9.dw-world.de/rtc/infotheque/electronic_components/inductors.html]

Hard and soft directions in iron, nickel and cobalt are as follows:

Fe Ni Co bcc fcc hexagonal

Easy Intermediate

Hard 5.4 Crystallographic anisotropy in polycrystalline metals and alloys

In a polycrystalline material with sufficient equiaxed grains in random orientations, the properties would be expected to be isotropic due to the averaging of properties associated with individual grains or crystallographic directions. However, this is not common in practice due both to microstructural anisotropy (Section 5.2) and also due to crystallographic anisotropy. The latter arises as a consequence of preferred crystallographic orientations of many grains with respect to the overall shape of the body, e.g. in the rolling or extrusion direction of a body. This texture is measured using X-ray diffraction to provide either pole figures or orientation distribution functions.2 Texture in a polycrystalline material can be beneficial in that it can lead to optimisation of properties for different applications, e.g. by increasing yield strength, improving formability, minimising magnetic hysteresis losses. However, it also can be a liability if a material is loaded in service inappropriately in a wrong direction. 1 DoITPoMS TLP Ferromagnetic Materials www.doitpoms.ac.uk/tlplib/slip, section Domains. 2 See Pt II Course C6 Crystallography, Section 6 Deformation and texture.

H

B



5.4 Origins of crystallographic anisotropy in polycrystalline metals and alloys (a) Solidification textures

The preferred orientation of dendritic and columnar grains is . This is exploited for cast magnetic materials which can be solidified in a temperature gradient to ensure a fibre texture, i.e. in grains grown parallel to the casting direction. AlNiCo is a magnetic alloy fabricated in this way1 using resin-bonded sand moulds. Magnetic properties are optimised after casting by heating them above their Curie temperature, and cooling in an applied magnetic field at a controlled temperature rate. This takes advantage of both the fibre texture arising from the casting process and then the easy magnetisation direction. The final microstructure comprises iron and cobalt-rich precipitates in a Ni-Al matrix and the Curie temperature of these magnets is ~ 800C which is one of the highest Curie temperatures for any magnetic material. In practice, AlNiCo magnets are used up to temperatures of ~ 500C. The composition of AlNiCo alloys is 812% Al, 1526% Ni, 524% Co, balance Fe. The alloys also may contain up to 6% Cu and up to 1% Ti. Note that sintering is now an alternative production route for many magnetic alloys including AlNiCo. In a different approach, a samarium-cobalt alloy was solidified in a magnetic field of several Tesla in order to ensure the c-axis of the hexagonal alloy was aligned with the solidification grain structure.2 This orientated material was for bulk anisotropic permanent magnets.

(b) Deformation textures

During the deformation of a single crystal, the tensile axis or direction rotates towards the operative slip direction or, if the direction along which the load is applied is fixed, then the slip system rotates during deformation. This is to optimise the Schmid factor. When a polycrystalline alloy is plastically deformed, the individual grains will try to rotate in a similar fashion and there will be a resulting preferred orientation of grains relative to the tensile direction. Deformation textures are described in terms of

- fibre textures [u v w] developed in uni-axial process such as extrusion or wire drawing - sheet or rolling textures {h k l} in which planes {h k l} lie parallel to the rolling plane and a

direction of the type is parallel to the rolling direction. Different textures arise in different alloys or in the same alloy deformed at different temperatures. Examples: - fcc pure metals or alloys with high stacking fault energies {112} - fcc alloys including those with low stacking fault energies {110} - bcc alloys include {100} Note that a possible way to minimising a rolling texture is to consider cross-rolling, i.e. changing the orientation of a sheet by 90 between rolling passes. This can be successful for some fcc alloys but has the opposite effect in some bcc in which the rolling texture then becomes more pronounced.

(c) Annealing or recrystallisation textures Consider the differences between a deformed and recrystallised alloy. deformed annealed

dislocation density high low grain shape elongated equiaxed yield strength high lower texture strong strong and maybe more intense

1 www.fecrco.com/cast-alnico.html and also www.duramag.com/alnico.html 2 Legrand B.A. et al, Orientation by solidification in a magnetic field. A new process to texture SmCo

compounds used as permanent magnets, Journal of Magnetism and Magnetic Materials, 173, pp 20-28, 1997.



During recovery of a heavily worked alloy, dislocations realign to form subgrains with low angle grain boundaries within the original but now deformed, strongly elongated grains. During subsequent recrystallisation, the subgrains with favoured orientations grow and so the resulting annealed alloy has a more intense and different texture than the original deformed alloy. Examples: - fcc alloys with high stacking fault energies include {100} so-called cube texture - bcc alloys {111} which is particularly advantageous when deep drawing to form cans The variation with yield stress and texture in a recrystallised Al-Mg alloy is shown in Fig. 5.10. Note that the highest value of the yield stress is for the sample cut parallel to the rolling direction. The true strain to failure (elongation) is much greater for the 45 which has a value approximately 25% greater than for the sample cut parallel to the rolling direction.

Figure 5.10. Uniaxial stress-strain curve for recrystallised alloy 5754-O [http://aluminium.matter.org.uk/ - choose anisotropy section]

(d) Transformation or inheritance textures

When a diffusionless, displacive or martensitic phase transformation occurs, there will normally be a crystallographic relationship between the original and new phases. The Bain model proposed for the transformation of fcc austentite to bct martensite would suggest the following relationships:

[0 0 1]fcc || [0 0 1]bcc [1 1 0]fcc || [1 0 0]bcc [1 1 0]fcc || [0 1 0]bcc

Other variants include the Kurdjumov-Sachs relationship in which

{111}fcc || {110}bcc and fcc || bcc However, the experimentally observed orientation relationships are irrational and not as simple as above1,2.

Figure 5.11. Orientation relationships between parent (fcc) and martensite (bcc) phases for (a) Bain, (b) NishiyamaWassermann and (c) KurdjumovSachs paths. Blue atoms indicate a bcc unit cell. The red arrows indicate part of the motion initiating the transformation. The dashed arrows indicate the invariant direction which

is shared by the parent and martensite phases.2

1 See Pt II Course C6 Crystallography, Section 8 Crystallography of martensitic transformations. 2 http://iopscience.iop.org/1367-2630/11/10/103027/fulltext/



5.5 Applications of texture in practice. A few examples where texture is beneficial include:

(a) strengthening of alloy sheet see Section 6;

(b) drawing of sheet, e.g. drink cans in steel and aluminium alloys;

(c) piezoelectric, pyroelectric and ferroelectric devices (as in Pt. IA, course B);

(d) iron-silicon transformer core steel. (b) Drawing of sheet, e.g. beverage cans in steel and aluminium alloys1

Drink cans are extremely thin and are made by extensive deformation by deep-drawing. The texture of the alloy sheet prior to drawing is controlled and is chosen both to

- maximise the deformation while avoiding instability (local necking) in the thickness of the can;

- minimise the formation of so-called 'ears' on the final deep drawn cup - see Fig. 5.12. Aluminium drink cans are made using two alloys:

- can body from highly formable 3104 H19 temper, nominally 1% Mn, 1% Mg, balance Al; - can end from 5182 due to its higher strength, nominally 4.5% Mg, 0.3% Mn, balance Al.

The full process for the can body involves blanking, cupping and finally drawing and ironing the side-walls. The can end is made by blanking, drawing, curl forming, riveting and production of the score line for the easy open end.

After manufacture, the can body and can end are transported to a filling plant where the beverage is put into the can and the two components are attached using a folded seam and a small amount of a sealing compound.

Figure 5.12. (a) Stages in the drawing and ironing of a drink can.

(b) minimal and maximum 'earing' in can bodies as a consequence of anisotropy in the sheet deformation.

(d) Iron silicon transformer steel The ferrous alloy used for sheet from which electrical transformers are made has to be magnetically soft in order to minimise energy losses as the magnetic field reverses. This is achieved by controlling both the composition of the sheet and its crystallographic texture. An ideal alloy is grain orientated silicon sheet (Goss texture) Fe-3wt.% Si iron since the addition of Si modifies the equilibrium diagram so that there are no phase transformations on heating, as well as:

- lowering the anisotropy constant K (a measure of the magnetic anisotropy);

- increasing the electrical resistivity which reduces eddy current losses;

- enabling one of two optimal textures (see Fig. 5.13) cube on face or {100} texture in which a {100} plane lies in the sheet plane, or cube on edge {011} Goss texture in which a {011} plane lies in the sheet plane which

can increase the magnetic flux density by up to 30% relative to a steel without this texture. The silicon modifies the Fe-C phase diagram to that shown in Fig. 5.14. This stabilises the ferrite phase and suppresses the transformation to austenite even at the high processing temperatures.

1 http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=84&pageid=-1941055071

b c a



Figure 5.13. Cube-on-edge texture and the cube texture in grain oriented silicon steel.1

This avoids phase changes during processing which otherwise result in too small grains in the final sheet and poorer soft magnetic properties; the final optimal soft magnetic grain size is ~ 5 mm. A disadvantage of Si additions is that Si raises the ductile-brittle transition to room temperature for alloys with 4 wt.% Si as is shown in Fig. 5.14. To maintain the single ferrite phase field at lower Si contents, e.g. between 2 - 3 % Si, the C content needs to be low. Hence a typical composition (in wt.%) is:

3.2 %Si, 0.03 %C, 0.08%Mn, 0.02%S.

Figure 5.14. Effect of Si on the equilibrium diagram of Fe-C alloys and the effect of Si on the ductile brittle transition temperature.

The magnetically favoured Goss texture is produced by secondary recrystallization during high temperature anneals in controlled atmospheres of hydrogen. Texture formation is aided by fine particles of MnS which inhibit normal grain growth; the number is subsequently reduced to avoid domain wall pinning in usage. A typical manufacturing sequence will be of the form:

- hot roll at 1300C to 2 mm and then remove oxide; - cold roll to 0.2 mm in two steps with intermediate softening anneal at 800 - 1000C; - decarburise at 800C in moist H2 which also allows recrystallisation during which the presence of

MnS particles helps to stop excessive grain growth; - anneal in dry H2 at 1100 - 1200C for several days to form the Goss texture by grain growth.

MnS, having fulfilled its role in the earlier recrystallisation step, also is reduced and this avoids domain wall pinning in service; the resulting Mn goes into solution;

- shaped by cutting or punching followed by a stress relieving anneal at 800C in dry N2. Sheets may be coated with MgO before the anneal in dry H2 as this then produces a surface coating of magnesium silicate which keeps the sheet in tension and so minimises stress magnetostrictive losses.

1 http://softmagneticalloy.com/soft_magnetic_materials.htm

Materials Science Pt II C9 Alloys Lecture 6: Steels University of Cambridge


6. Steels and high-temperature materials 6.1 Iron-base alloys: overview

Iron

Steels Stainless steels Cast irons

---- plain carbon ---- ferritic --- grey -- flake or -- spherodised ---- low alloy & creep resistant ---- austenitic graphite (SG)

---- IF interstitial free ---- martensitic --- white -- whiteheart

---- thermo mechanical ---- duplex (/) -- blackheart

-- HSLA ---- controlled transformn

-- bainitic --- others -- austenitic

-- dual phase -- martensitic

-- TRIP

C9 alloys

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