Phase Transformations in Metals and Alloys SECOND EDITION

D.A. Porter Rautaruukki Oy Research Centre Raahe Finland

K.E. Easterling Formerly School of Engineering University ofExeter Exeter UK

London Glasgow Weinheim New York Tokyo Melbourne Madras

Contents

Preface to the second edition Preface to thefirst edition

1 Thermodynamics and Phase Diagrams 1.1 Equilibrium 1.2 Single Component Systems

1.2.1 Gibbs Free Energy as a Function of Tempcrature 1.2.2 Pressure Effects 1.2.3 The Driving Force for Solidification

1.3 Binary Solutions 1.3.1 The Gibbs Free Energy of Binary Solutions 1.3.2 Ideal Solutions 1.3.3 Chemical Potential 1.3.4 Regulr Solutions 1.3.5 Activity 1.3.6 Real Solutions 1.3.7 Ordered Phases 1.3.8 Intermediate Phases

1.4 Equilibrium in Heterogeneous Systems 1.5 Binary Phase Diagrams

1.5.1 A Simple Phase Diagram 1.5.2 Systems with a Miscibility Gap 1.5.3 Ordered Alloys 1.5.4 Simple Eutectic Systems 1.5.5 Phase Diagrams Containing Intermediate Phases 1.5.6 The Gibbs Phase Rule 1.5.7 The Effect of Temperature on Solid Solubility 1.5.8 Equilibrium Vacancy Concentration

1.6 The Influence of Interfaces on Equilibrium 1.7 Ternary Equilibrium 1.8 Additional Thermodynamic Retationships for Binary Solutio 1.9 The Kinetics of Phase Transformations

References Further Reading Exercises

VI Contents

Diffusion 60 2.1 Atomic Mechanisms of Diffusion 61 2.2 Interstitial Diffusion 63

2.2.1 Interstitial Diffusion as a Random Jump Process 63 2.2.2 Effect of TemperatureThermal Activation 66 2.2.3 Steady-State Diffusion 69 2.2.4 Nonsteady-State Diffusion 69 2.2.5 Solutions to the Diffusion Equation 71

Homogenization 71 The Carburization of Steel 73

2.3 Substitutional Diffusion 75 2.3.1 Self-Diffusion 75 2.3.2 Vacancy Diffusion 79 2.3.3 Diffusion in Substitutional Atloys 82 2.3.4 Diffusion in Dilute Substitutional Alloys 91

2.4 Atomic Mobility 92 2.5 Tracer Diffusion in Binary Alloys 94 2.6 Diffusion in Ternary Alloys 96 2.7 High-Diffusivity Paths 98

2.7.1 Diffusion along Grain Boundaries and Free Surfaces 98 2.7.2 Diffusion along Dislocations 102

2.8 Diffusion in Multiphase Binary Systems 103 References 106 Further Reading 106 Exercises 106

Crystal Interfaces and Microstructure 110 3.1 Interfacial Free Energy 110 3.2 Solid/Vapour Interfaces 112 3.3 Boundaries in Single-Phase Solids 116

3.3.1 Low-Angle and High-Angle Boundaries 116 3.3.2 Special High-Angle Grain Boundaries 122 3.3.3 Equilibrium in Polycrystalline Materials 124 3.3.4 Thcrmally Activated Migration of Grain Boundaries 130 3.3.5 The Kinetics of Grain Growth 139

3.4 Interphase Interfaces in Solids 142 3.4.1 Interface Coherence 143

Fully Cohcrent Interfaces 143 Semicoherent Interfaces 145 Incoherent Interfaces 147 Complex Semicoherent Interfaces 148

3.4.2 Second-Phase Shape: Interfacial Energy Effects 149 Fully Coherent Precipitates 149 Partially Coherent Precipitates 151 Incoherent Precipitates 152 Precipitates on Grain Boundaries 153

Contents VII

3.4.3 Second-Phase Shape: Misfit Strain Effects 154 Fully Coherent Precipitates 154 Incoherent Inclusions 158 Plate-Like Precipitates 160

3.4.4 Coherency Loss 160 3.4.5 Glissile Interfaces 163 3.4.6 Solid/Liquid Interfaces 168

3.5 Interface Migration 171 3.5.1 Diffusion-Controlled and Interface-Controlled Growth 175

References 180 Further Reading 182 Exercises 182

Solidification 185 4.1 Nucleation in Pure Metals 185

4.1.1 Homogeneous Nucleation 186 4.1.2 The Homogeneous Nucleation Rate 190 4.1.3 Heterogeneous Nucleation 192 4.1.4 Nucleation of Melting 197

4.2 Growth of a Pure Solid 197 4.2.1 Continuous Growth 198 4.2.2 Lateral Growth 198

Surface Nucleation 200 Spiral Growth 201 Growth from Twin Intersections 202

4.2.3 Heat Flow and Interface Stability 203 4.3 Alloy Solidification 207

4.3.1 Solidification of Single-Phase Alloys 208 Equilibrium Solidification 208 No Diffusion in Sohd, Perfect Mixing in Liquid 208 No Diffusion in Solid, Diffusional Mixing in Liquid 212 Cellular and Dendritic Solidification 214

4.3.2 Eutectic Solidification 222 Growth of Lamellar Eutectics 223

4.3.3 Off-Eutectic Alloys 229 4.3.4 Peritectic Solidification 231

4.4 Solidification of Ingots and Castings 233 4.4.1 Ingot Structure 233

Chili Zone 234 Columnar Zone 235 Equiaxed Zone 236 Shrinkage Effects 236

4.4.2 Segregation in Ingots and Castings 237 4.4.3 Continuous Casting 238

Heat Flow in Welding and Continuous Casting 239

viii Contents

4.5 Solidification of Fusion Welds 243 Influence of Welding Speed 245 Geometry of Crystal Growth 248

4.6 Solidification during Quenching from the Melt 249 4.7 Case Studies of some Practical Castings and Welds 249

4.7.1 Casting of Carbon and Low-Alloy Stcels 249 4.7.2 Casting of High-Speed Steels 251 4.7.3 Stainless Steel Weld Metal 256

References 259 Further Reading 260 Exercises 260

5 Diffusional Transformations in Solids 263 5.1 Homogeneous Nucleation in Solids 265 5.2 Heterogeneous Nucleation 271

Nucleation on Grain Boundaries 271 Dislocations 274 Excess Vacancies 275

5.2.1 Rate of Heterogeneous Nucleation 276 5.3 Precipitate Growth 279

5.3.1 Growth behind Planar Incoherent Interfaces 279 5.3.2 Diffusion-Controlled Lengthening of Plates or Needles 283 5.3.3 Thickening of Plate-like Precipitates 285

5.4 Overall Transformation KineticsTTT Diagrams 287 5.5 Precipitation in Age-Hardening Atloys 291

5.5.1 Precipitation in Aluminium-Copper Alloys 291 GP Zones 291 Transition Phascs 292

5.5.2 Precipitation in Aluminium-Silvcr Alloys 302 5.5.3 Quenched-in Vacancies 303 5.5.4 Age Hardening 304 5.5.5 Spinodal Decomposition 308 5.5.6 Particle Coarsening 314

Low y 316 Low Xc 316 LowD 317

5.6 The Precipitation of Ferrite from Austenite 317 5.7 Cellular Precipitation 322 5.8 Eutectoid Transformations 326

5.8.1 The Pearlite Reaction in F e - C Alloys 326 Nucleation of Pearlite 327 Pearlite Growth 330 Pearlitc in Off-Eutectoid F e - C Alloys 333

5.8.2 The Bainite Transformation 334

Contents ix

Upper Bainite 334 Lower Bainite 337 Transformation Shears 337

5.8.3 The Effect of Alloying Elements on Hardenability 338 5.8.4 Continuous Cooling Diagrams 344 5.8.5 Fibrous and Tnterphase Precipitation in Alloy Steels 349

5.9 Massive Transformations 349 5.10 Ordering Transformations 358 5.11 CaseStudies 366

5.11.1 Titanium Forging Alloys 366 5.11.2 The Weldability of Low-Carbon and Microalioyed

Roiled Steels 372 References 377 Further Reading 378 Excrcises 379

Diffusionless Transformations 382 6.1 Characteristics of Diffusionless Transformations 383

6-1.1 The Solid Solution of Carbon in Iron 385 6.2 Martcnsite Crystallography 389

6.2.1 The Bain Model of the fec > bet Transformation 391 6.2.2 Comparison of Crystallographic Theory with

Experimental Results 396 6.3 Theories of Martensite Nucleation 397

6.3.1 Formation of Coherent Nuclci of Martensite 398 6.3.2 Role of Dislocations in Martensite Nucleation 401 6.3.3 Dislocation Strain Energy Assisted Transformation 406

6.4 Martensite Growth 409 6.4.1 Growth of Lath Martensite 410 6.4.2 Plate Martensite 412 6.4.3 Stabilization 415 6.4.4 Effect of External Stresses 415 6.4.5 Role of Grain Sizc 416

6.5 Pre-martensite Phcnomcna 416 6.6 Tempering of Ferrous Martcnsites 417

Carbon Segregation 420 e-Carbide 421 Cementite 422 Alloy Carbides 422 Effect of Retained Austenite 426 Recovery, Recrystallization and Grain Growth 426 Temper Embrittlement 427

6.7 Gase Studies 428 6.7.1 Carbon and Low-Alloy Quenched and Tempcred Steels 428 6.7.2 Controllcd Transformation Steels 430

x Contents

6.7.3 The'Shape-Memory'Metal: Nitinol 431 References 437 Further Reading 439 Exercises 439

Solutions to exercises 441 Compiled by John C. Ion

Index 510