ELSEVIER RECRYSTALLIZATION and Related Annealing Phenomena 数烤 03a Second Edition M.Hatherly
RECRYSTALLIZATION AND RELATED ANNEALING PHENOMENA SECOND EDITION by F.J.HUMPHREYS University of Manchester Institute of Science and Technology, UK and M.HATHERLY University of New South Wales,Australia 2004 山吃 ELSEVIER Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo
RECRYSTALLIZATION AND RELATED ANNEALING PHENOMENA SECOND EDITION by F.J. HUMPHREYS University of Manchester Institute of Science and Technology, UK and M. HATHERLY University of New South Wales, Australia 2004 Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo
CONTENTS Colour plates xvii Symbols XXi Abbreviations xxiii Preface to the first edition XXV Preface to the second edition xxvii Acknowledgements XXiX CHAPTER 1 INTRODUCTION 1 1.1 The annealing of a deformed material 1 1.1.1 Outline and terminology 1 1.1.2 The importance of annealing 4 1.2 Historical perspective 4 1.2.1 The early development of the subject 4 1.2.2 Some key literature(1952-2003) 6 1.3 Forces,pressures and units 9 1.3.1 Pressure on a boundary 9 1.3.2 Units and the magnitude of the driving pressure 10 CHAPTER 2 THE DEFORMED STATE 11 2.1 Introduction 11 2.2 The stored energy of cold work 12 2.2.1 Origin of the stored energy 12 2.2.2 Measurements of overall stored energy 14 2.2.3 Relationship between stored energy and microstructure 16 2.3 Crystal plasticity 24 2.3.1 Slip and twinning 24 2.3.2 Deformation of polycrystals 25
CONTENTS Colour plates xvii Symbols xxi Abbreviations xxiii Preface to the first edition xxv Preface to the second edition xxvii Acknowledgements xxix CHAPTER 1 INTRODUCTION 1 1.1 The annealing of a deformed material 1 1.1.1 Outline and terminology 1 1.1.2 The importance of annealing 4 1.2 Historical perspective 4 1.2.1 The early development of the subject 4 1.2.2 Some key literature (1952–2003) 6 1.3 Forces, pressures and units 9 1.3.1 Pressure on a boundary 9 1.3.2 Units and the magnitude of the driving pressure 10 CHAPTER 2 THE DEFORMED STATE 11 2.1 Introduction 11 2.2 The stored energy of cold work 12 2.2.1 Origin of the stored energy 12 2.2.2 Measurements of overall stored energy 14 2.2.3 Relationship between stored energy and microstructure 16 2.3 Crystal plasticity 24 2.3.1 Slip and twinning 24 2.3.2 Deformation of polycrystals 25 v
vi Contents 2.4 Cubic metals which deform by slip 26 2.4.1 The microstructural hierarchy 27 2.4.2 The evolution of the deformation microstructure in cell-forming metals 28 2.4.3 Non-cell-forming metals 35 2.5 Cubic metals which deform by slip and twinning 35 2.5.1 Deformation twinning 35 2.5.2 The effect of stacking fault energy 37 2.6 Close packed hexagonal (CPH)metals 39 2.7 Deformation bands 41 2.7.1 The nature of deformation bands 41 2.7.2 The formation of deformation bands 42 2.7.3 Transition bands 42 2.7.4 The conditions under which deformation bands form 42 2.8 Shear bands 44 2.8.1 Metals of medium or high stacking fault energy 44 2.8.2 Metals of low stacking fault energy 44 2.8.3 The formation of shear bands 47 2.8.4 The conditions for shear banding 47 2.9 The microstructures of deformed two-phase alloys 48 2.9.1 Dislocation distribution in alloys containing deformable particles 50 2.9.2 Dislocation distribution in alloys containing non-deformable particles 52 2.9.3 Dislocation structures at individual particles 57 2.9.4 Deformation zones at particles 60 CHAPTER 3 DEFORMATION TEXTURES 67 3.1 Introduction 67 3.2 Deformation textures in face-centred cubic (FCC)metals 68 3.2.1 Pure metal texture 68 3.2.2 Alloy texture 72 3.3 Deformation textures in body-centred cubic (BCC)metals 74 3.4 Deformation textures in close packed hexagonal(CPH)metals 76 3.5 Fibre textures 78 3.6 Factors which influence texture development 79 3.6.1 Rolling geometry and friction 79 3.6.2 Deformation temperature 80 3.6.3 Grain size 81 3.6.4 Shear banding 2 3.6.5 Second-phase particles 82 3.7 Theories of deformation texture development 8 3.7.1 Macroscopic models
2.4 Cubic metals which deform by slip 26 2.4.1 The microstructural hierarchy 27 2.4.2 The evolution of the deformation microstructure in cell-forming metals 28 2.4.3 Non-cell-forming metals 35 2.5 Cubic metals which deform by slip and twinning 35 2.5.1 Deformation twinning 35 2.5.2 The effect of stacking fault energy 37 2.6 Close packed hexagonal (CPH) metals 39 2.7 Deformation bands 41 2.7.1 The nature of deformation bands 41 2.7.2 The formation of deformation bands 42 2.7.3 Transition bands 42 2.7.4 The conditions under which deformation bands form 42 2.8 Shear bands 44 2.8.1 Metals of medium or high stacking fault energy 44 2.8.2 Metals of low stacking fault energy 44 2.8.3 The formation of shear bands 47 2.8.4 The conditions for shear banding 47 2.9 The microstructures of deformed two-phase alloys 48 2.9.1 Dislocation distribution in alloys containing deformable particles 50 2.9.2 Dislocation distribution in alloys containing non-deformable particles 52 2.9.3 Dislocation structures at individual particles 57 2.9.4 Deformation zones at particles 60 CHAPTER 3 DEFORMATION TEXTURES 67 3.1 Introduction 67 3.2 Deformation textures in face-centred cubic (FCC) metals 68 3.2.1 Pure metal texture 68 3.2.2 Alloy texture 72 3.3 Deformation textures in body-centred cubic (BCC) metals 74 3.4 Deformation textures in close packed hexagonal (CPH) metals 76 3.5 Fibre textures 78 3.6 Factors which influence texture development 79 3.6.1 Rolling geometry and friction 79 3.6.2 Deformation temperature 80 3.6.3 Grain size 81 3.6.4 Shear banding 82 3.6.5 Second-phase particles 82 3.7 Theories of deformation texture development 83 3.7.1 Macroscopic models 83 vi Contents
Contents vii 3.7.2 Recent models 86 3.7.3 The texture transition 86 CHAPTER 4 THE STRUCTURE AND ENERGY OF GRAIN BOUNDARIES 91 4.1 Introduction 91 4.2 The orientation relationship between grains 92 4.3 Low angle grain boundaries 95 4.3.1 Tilt boundaries 95 4.3.2 Other low angle boundaries 97 4.4 High angle grain boundaries 98 4.4.1 The coincidence site lattice 98 4.4.2 The structure of high angle boundaries 100 4.4.3 The energy of high angle boundaries 102 4.5 The topology of boundaries and grains 104 4.5.1 Two-dimensional microstructures 105 4.5.2 Three-dimensional microstructures 106 4.5.3 Grain boundary facets 108 4.5.4 Boundary connectivity 108 4.5.5 Triple junctions 109 4.6 The interaction of second-phase particles with boundaries 109 4.6.1 The drag force exerted by a single particle 109 4.6.2 The drag pressure due to a distribution of particles 112 CHAPTER 5 THE MOBILITY AND MIGRATION OF BOUNDARIES 121 5.1 Introduction 121 5.1.1 The role of grain boundary migration during annealing 121 5.1.2 The micro mechanisms of grain boundary migration 122 5.1.3 The concept of grain boundary mobility 123 5.1.4 Measuring grain boundary mobilities 124 5.2 The mobility of low angle grain boundaries 124 5.2.1 The migration of symmetrical tilt boundaries under stress 124 5.2.2 General low angle boundaries 126 5.3 Measurements of the mobility of high angle boundaries 134 5.3.1 The effect of temperature on grain boundary mobility in high purity metals 135 5.3.2 The effect of orientation on grain boundary migration in high purity metals 137
3.7.2 Recent models 86 3.7.3 The texture transition 86 CHAPTER 4 THE STRUCTURE AND ENERGY OF GRAIN BOUNDARIES 91 4.1 Introduction 91 4.2 The orientation relationship between grains 92 4.3 Low angle grain boundaries 95 4.3.1 Tilt boundaries 95 4.3.2 Other low angle boundaries 97 4.4 High angle grain boundaries 98 4.4.1 The coincidence site lattice 98 4.4.2 The structure of high angle boundaries 100 4.4.3 The energy of high angle boundaries 102 4.5 The topology of boundaries and grains 104 4.5.1 Two-dimensional microstructures 105 4.5.2 Three-dimensional microstructures 106 4.5.3 Grain boundary facets 108 4.5.4 Boundary connectivity 108 4.5.5 Triple junctions 109 4.6 The interaction of second-phase particles with boundaries 109 4.6.1 The drag force exerted by a single particle 109 4.6.2 The drag pressure due to a distribution of particles 112 CHAPTER 5 THE MOBILITY AND MIGRATION OF BOUNDARIES 121 5.1 Introduction 121 5.1.1 The role of grain boundary migration during annealing 121 5.1.2 The micro mechanisms of grain boundary migration 122 5.1.3 The concept of grain boundary mobility 123 5.1.4 Measuring grain boundary mobilities 124 5.2 The mobility of low angle grain boundaries 124 5.2.1 The migration of symmetrical tilt boundaries under stress 124 5.2.2 General low angle boundaries 126 5.3 Measurements of the mobility of high angle boundaries 134 5.3.1 The effect of temperature on grain boundary mobility in high purity metals 135 5.3.2 The effect of orientation on grain boundary migration in high purity metals 137 Contents vii
viii Contents 5.3.3 The influence of solutes on boundary mobility 145 5.3.4 The effect of point defects on boundary mobility 150 5.3.5 The scope of experimental measurements 153 5.4 Theories of the mobility of high angle boundaries 153 5.4.1 Theories of grain boundary migration in pure metals 153 5.4.2 Theories of grain boundary migration in solid solutions 160 5.5 The migration of triple junctions 165 5.5.1 Introduction 166 5.5.2 The importance of triple junction mobility 167 CHAPTER 6 RECOVERY AFTER DEFORMATION 169 6.1 Introduction 169 6.1.1 The occurrence of recovery 169 6.1.2 Properties affected by recovery 171 6.2 Experimental measurements of recovery 173 6.2.1 The extent of recovery 173 6.2.2 Measurements of recovery kinetics 174 6.3 Dislocation migration and annihilation during recovery 178 6.3.1 General considerations 178 6.3.2 The kinetics of dipole annihilation 179 6.3.3 Recovery kinetics of more complex dislocation structures 181 6.4 Rearrangement of dislocations into stable arrays 185 6.4.1 Polygonization 185 6.4.2 Subgrain formation 186 6.5 Subgrain coarsening 188 6.5.1 The driving force for subgrain growth 188 6.5.2 Experimental measurements of subgrain coarsening 189 6.5.3 Subgrain growth by boundary migration 193 6.5.4 Subgrain growth by rotation and coalescence 200 6.5.5 Recovery mechanisms and the nucleation of recrystallization 206 6.6 The effect of second-phase particles on recovery 207 6.6.1 The effect of particles on the rate of subgrain growth 208 6.6.2 The particle-limited subgrain size 210 CHAPTER 7 RECRYSTALLIZATION OF SINGLE-PHASE ALLOYS 215 7.1 Introduction 215 7.1.1 Quantifying recrystallization 217 7.1.2 The laws of recrystallization 220
5.3.3 The influence of solutes on boundary mobility 145 5.3.4 The effect of point defects on boundary mobility 150 5.3.5 The scope of experimental measurements 153 5.4 Theories of the mobility of high angle boundaries 153 5.4.1 Theories of grain boundary migration in pure metals 153 5.4.2 Theories of grain boundary migration in solid solutions 160 5.5 The migration of triple junctions 165 5.5.1 Introduction 166 5.5.2 The importance of triple junction mobility 167 CHAPTER 6 RECOVERY AFTER DEFORMATION 169 6.1 Introduction 169 6.1.1 The occurrence of recovery 169 6.1.2 Properties affected by recovery 171 6.2 Experimental measurements of recovery 173 6.2.1 The extent of recovery 173 6.2.2 Measurements of recovery kinetics 174 6.3 Dislocation migration and annihilation during recovery 178 6.3.1 General considerations 178 6.3.2 The kinetics of dipole annihilation 179 6.3.3 Recovery kinetics of more complex dislocation structures 181 6.4 Rearrangement of dislocations into stable arrays 185 6.4.1 Polygonization 185 6.4.2 Subgrain formation 186 6.5 Subgrain coarsening 188 6.5.1 The driving force for subgrain growth 188 6.5.2 Experimental measurements of subgrain coarsening 189 6.5.3 Subgrain growth by boundary migration 193 6.5.4 Subgrain growth by rotation and coalescence 200 6.5.5 Recovery mechanisms and the nucleation of recrystallization 206 6.6 The effect of second-phase particles on recovery 207 6.6.1 The effect of particles on the rate of subgrain growth 208 6.6.2 The particle-limited subgrain size 210 CHAPTER 7 RECRYSTALLIZATION OF SINGLE-PHASE ALLOYS 215 7.1 Introduction 215 7.1.1 Quantifying recrystallization 217 7.1.2 The laws of recrystallization 220 viii Contents
Contents 7.2 Factors affecting the rate of recrystallization 221 7.2.1 The deformed structure 221 7.2.2 The grain orientations 225 7.2.3 The original grain size 227 7.2.4 Solutes 228 7.2.5 The deformation temperature and strain rate 229 7.2.6 The annealing conditions 229 7.3 The formal kinetics of primary recrystallization 232 7.3.1 The Johnson-Mehl-Avrami-Kolmogorov (JMAK)model 232 7.3.2 Microstructural path methodology 235 7.4 Recrystallization kinetics in real materials 239 7.4.1 Non-random spatial distribution of nuclei 239 7.4.2 The variation of growth rate during recrystallization 241 7.5 The recrystallized microstructure 248 7.5.1 The grain orientations 248 7.5.2 The grain size 248 7.5.3 The grain shape 249 7.6 The nucleation of recrystallization 250 7.6.1 Classical nucleation 250 7.6.2 Strain-induced grain boundary migration(SIBM) 251 7.6.3 The preformed nucleus model 257 7.6.4 Nucleation sites 259 7.7 Annealing Twins 261 7.7.1 Introduction 261 7.7.2 Mechanisms of twin formation 263 7.7.3 Twin formation during recovery 264 7.7.4 Twin formation during recrystallization 264 7.7.5 Twin formation during grain growth 266 CHAPTER 8 RECRYSTALLIZATION OF ORDERED MATERIALS 269 8.1 Introduction 269 8.2 Ordered structures 270 8.2.1 Nature and stability 270 8.2.2 Deformation of ordered materials 271 8.2.3 Microstructures and deformation textures 272 8.3 Recovery and recrystallization of ordered materials 274 8.3.1 L12 structures 275 8.3.2 B2 structures 278 8.3.3 Domain structures 279 8.4 Grain growth 280 8.5 Dynamic recrystallization 282 8.6 Summary 282
7.2 Factors affecting the rate of recrystallization 221 7.2.1 The deformed structure 221 7.2.2 The grain orientations 225 7.2.3 The original grain size 227 7.2.4 Solutes 228 7.2.5 The deformation temperature and strain rate 229 7.2.6 The annealing conditions 229 7.3 The formal kinetics of primary recrystallization 232 7.3.1 The Johnson–Mehl–Avrami–Kolmogorov (JMAK) model 232 7.3.2 Microstructural path methodology 235 7.4 Recrystallization kinetics in real materials 239 7.4.1 Non-random spatial distribution of nuclei 239 7.4.2 The variation of growth rate during recrystallization 241 7.5 The recrystallized microstructure 248 7.5.1 The grain orientations 248 7.5.2 The grain size 248 7.5.3 The grain shape 249 7.6 The nucleation of recrystallization 250 7.6.1 Classical nucleation 250 7.6.2 Strain-induced grain boundary migration (SIBM) 251 7.6.3 The preformed nucleus model 257 7.6.4 Nucleation sites 259 7.7 Annealing Twins 261 7.7.1 Introduction 261 7.7.2 Mechanisms of twin formation 263 7.7.3 Twin formation during recovery 264 7.7.4 Twin formation during recrystallization 264 7.7.5 Twin formation during grain growth 266 CHAPTER 8 RECRYSTALLIZATION OF ORDERED MATERIALS 269 8.1 Introduction 269 8.2 Ordered structures 270 8.2.1 Nature and stability 270 8.2.2 Deformation of ordered materials 271 8.2.3 Microstructures and deformation textures 272 8.3 Recovery and recrystallization of ordered materials 274 8.3.1 L12 structures 275 8.3.2 B2 structures 278 8.3.3 Domain structures 279 8.4 Grain growth 280 8.5 Dynamic recrystallization 282 8.6 Summary 282 Contents ix
Contents CHAPTER 9 RECRYSTALLIZATION OF TWO-PHASE ALLOYS 285 9.1 Introduction 285 9.1.1 The particle parameters 286 9.1.2 The deformed microstructure 286 9.2 The observed effects of particles on recrystallization 287 9.2.1 The effect of particle parameters 287 9.2.2 The effect of strain 289 9.2.3 The effect of particle strength 291 9.2.4 The effect of microstructural homogenisation 292 9.3 Particle stimulated nucleation of recrystallization 293 9.3.1 The mechanisms of PSN 294 9.3.2 The orientations of grains produced by PSN 298 9.3.3 The efficiency of PSN 301 9.3.4 The effect of particle distribution 302 9.3.5 The effect of PSN on the recrystallized microstructure 302 9.4 Particle pinning during recrystallization(Zener drag) 304 9.4.1 Nucleation of recrystallization 304 9.4.2 Growth during recrystallization 306 9.5 Bimodal particle distributions 306 9.6 The control of grain size by particles 307 9.7 Particulate metal-matrix composites 309 9.8 The interaction of precipitation and recrystallization 310 9.8.1 Introduction 310 9.8.2 Regime I-Precipitation before recrystallization 312 9.8.3 Regime II-Simultaneous recrystallization and precipitation 314 9.8.4 Regime III-Recrystallization before precipitation 316 9.9 The recrystallization of duplex alloys 316 9.9.1 Equilibrium microstructures 317 9.9.2 Non-equilibrium microstructures 318 CHAPTER 10 THE GROWTH AND STABILITY OF CELLULAR MICROSTRUCTURES 321 10.1 Introduction 321 10.2 The model 322 10.3 Stability of single-phase microstructure 326 10.3.1 Low angle boundaries-Recovery 326 10.3.2 High and low angle boundaries-Recrystallization 328 10.3.3 High angle boundaries-Grain growth 328 10.3.4 The stability of microstructures after very large strains 329 10.4 Stability of two-phase microstructures 329 10.5 Summary 331
CHAPTER 9 RECRYSTALLIZATION OF TWO-PHASE ALLOYS 285 9.1 Introduction 285 9.1.1 The particle parameters 286 9.1.2 The deformed microstructure 286 9.2 The observed effects of particles on recrystallization 287 9.2.1 The effect of particle parameters 287 9.2.2 The effect of strain 289 9.2.3 The effect of particle strength 291 9.2.4 The effect of microstructural homogenisation 292 9.3 Particle stimulated nucleation of recrystallization 293 9.3.1 The mechanisms of PSN 294 9.3.2 The orientations of grains produced by PSN 298 9.3.3 The efficiency of PSN 301 9.3.4 The effect of particle distribution 302 9.3.5 The effect of PSN on the recrystallized microstructure 302 9.4 Particle pinning during recrystallization (Zener drag) 304 9.4.1 Nucleation of recrystallization 304 9.4.2 Growth during recrystallization 306 9.5 Bimodal particle distributions 306 9.6 The control of grain size by particles 307 9.7 Particulate metal-matrix composites 309 9.8 The interaction of precipitation and recrystallization 310 9.8.1 Introduction 310 9.8.2 Regime I – Precipitation before recrystallization 312 9.8.3 Regime II – Simultaneous recrystallization and precipitation 314 9.8.4 Regime III – Recrystallization before precipitation 316 9.9 The recrystallization of duplex alloys 316 9.9.1 Equilibrium microstructures 317 9.9.2 Non-equilibrium microstructures 318 CHAPTER 10 THE GROWTH AND STABILITY OF CELLULAR MICROSTRUCTURES 321 10.1 Introduction 321 10.2 The model 322 10.3 Stability of single-phase microstructure 326 10.3.1 Low angle boundaries – Recovery 326 10.3.2 High and low angle boundaries – Recrystallization 328 10.3.3 High angle boundaries – Grain growth 328 10.3.4 The stability of microstructures after very large strains 329 10.4 Stability of two-phase microstructures 329 10.5 Summary 331 x Contents
Contents xi CHAPTER 11 GRAIN GROWTH FOLLOWING RECRYSTALLIZATION 333 11.1 Introduction 333 11.1.1 The nature and significance of grain growth 334 11.1.2 Factors affecting grain growth 335 11.1.3 The Burke and Turnbull analysis of grain growth kinetics 335 11.1.4 Comparison with experimentally measured kinetics 337 11.1.5 Topological aspects of grain growth 339 11.2 The development of theories and models of grain growth 341 11.2.1 Introduction 341 11.2.2 Early statistical theories 342 11.2.3 The incorporation of topology 343 11.2.4 Deterministic theories 347 11.2.5 Recent theoretical developments 349 11.2.6 Which theory best accounts for grain growth in an ideal material? 350 11.3 Grain orientation and texture effects during grain growth 351 11.3.1 Kinetics 351 11.3.2 The effect of grain growth on grain boundary character distribution 353 11.4 The effect of second-phase particles on grain growth 356 11.4.1 Kinetics 357 11.4.2 The particle-limited grain size 358 11.4.3 Particle instability during grain growth 363 11.4.4 Grain rotation 365 11.4.5 Dragging of particles by boundaries 367 11.5 Abnormal grain growth 368 11.5.1 The phenomenon 369 11.5.2 The effect of particles 370 11.5.3 The effect of texture 374 11.5.4 Surface effects 376 11.5.5 The effect of prior deformation 378 CHAPTER 12 RECRYSTALLIZATION TEXTURES 379 12.1 Introduction 379 12.2 The nature of recrystallization textures 380 12.2.1 Recrystallization textures in fcc metals 380 12.2.2 Recrystallization textures in bcc metals 387 12.2.3 Recrystallization textures in hexagonal metals 390
CHAPTER 11 GRAIN GROWTH FOLLOWING RECRYSTALLIZATION 333 11.1 Introduction 333 11.1.1 The nature and significance of grain growth 334 11.1.2 Factors affecting grain growth 335 11.1.3 The Burke and Turnbull analysis of grain growth kinetics 335 11.1.4 Comparison with experimentally measured kinetics 337 11.1.5 Topological aspects of grain growth 339 11.2 The development of theories and models of grain growth 341 11.2.1 Introduction 341 11.2.2 Early statistical theories 342 11.2.3 The incorporation of topology 343 11.2.4 Deterministic theories 347 11.2.5 Recent theoretical developments 349 11.2.6 Which theory best accounts for grain growth in an ideal material? 350 11.3 Grain orientation and texture effects during grain growth 351 11.3.1 Kinetics 351 11.3.2 The effect of grain growth on grain boundary character distribution 353 11.4 The effect of second-phase particles on grain growth 356 11.4.1 Kinetics 357 11.4.2 The particle-limited grain size 358 11.4.3 Particle instability during grain growth 363 11.4.4 Grain rotation 365 11.4.5 Dragging of particles by boundaries 367 11.5 Abnormal grain growth 368 11.5.1 The phenomenon 369 11.5.2 The effect of particles 370 11.5.3 The effect of texture 374 11.5.4 Surface effects 376 11.5.5 The effect of prior deformation 378 CHAPTER 12 RECRYSTALLIZATION TEXTURES 379 12.1 Introduction 379 12.2 The nature of recrystallization textures 380 12.2.1 Recrystallization textures in fcc metals 380 12.2.2 Recrystallization textures in bcc metals 387 12.2.3 Recrystallization textures in hexagonal metals 390 Contents xi
xii Contents 12.2.4 Recrystallization textures in two-phase alloys 390 12.3 The theory of recrystallization textures 393 12.3.1 Historical background 393 12.3.2 Oriented growth 394 12.3.3 Oriented nucleation 397 12.3.4 The relative roles of oriented nucleation and oriented growth 400 12.3.5 The role of twinning 401 12.4 The evolution of textures during annealing 403 12.4.1 The cube texture in fcc metals 403 12.4.2 The recrystallization textures of low-carbon steels 407 12.4.3 Recrystallization textures of two-phase alloys 408 12.4.4 Texture development during grain growth 411 CHAPTER 13 HOT DEFORMATION AND DYNAMIC RESTORATION 415 13.1 Introduction 415 13.2 Dynamic recovery 416 13.2.1 Constitutive relationships 417 13.2.2 Mechanisms of microstructural evolution 418 13.2.3 The microstructures formed during dynamic recovery 419 13.2.4 Texture formation during hot deformation 424 13.2.5 Modelling the evolution of microstructure 427 13.3 Discontinuous dynamic recrystallization 427 13.3.1 The characteristics of dynamic recrystallization 428 13.3.2 The nucleation of dynamic recrystallization 429 13.3.3 Microstructural evolution 431 13.3.4 The steady state grain size 433 13.3.5 The flow stress during dynamic recrystallization 434 13.3.6 Dynamic recrystallization in single crystals 435 13.3.7 Dynamic recrystallization in two-phase alloys 436 13.4 Continuous dynamic recrystallization 437 13.4.1 Types of continuous dynamic recrystallization 437 13.4.2 Dynamic recrystallization by progressive lattice rotation 438 13.5 Dynamic recrystallization in minerals 441 13.5.1 Boundary migration in minerals 442 13.5.2 Migration and rotation recrystallization 444 13.6 Annealing after hot deformation 444 13.6.1 Static recovery 445 13.6.2 Static recrystallization 446 13.6.3 Metadynamic recrystallization 447 13.6.4 PSN after hot deformation 448 13.6.5 Grain growth after hot working 450
12.2.4 Recrystallization textures in two-phase alloys 390 12.3 The theory of recrystallization textures 393 12.3.1 Historical background 393 12.3.2 Oriented growth 394 12.3.3 Oriented nucleation 397 12.3.4 The relative roles of oriented nucleation and oriented growth 400 12.3.5 The role of twinning 401 12.4 The evolution of textures during annealing 403 12.4.1 The cube texture in fcc metals 403 12.4.2 The recrystallization textures of low-carbon steels 407 12.4.3 Recrystallization textures of two-phase alloys 408 12.4.4 Texture development during grain growth 411 CHAPTER 13 HOT DEFORMATION AND DYNAMIC RESTORATION 415 13.1 Introduction 415 13.2 Dynamic recovery 416 13.2.1 Constitutive relationships 417 13.2.2 Mechanisms of microstructural evolution 418 13.2.3 The microstructures formed during dynamic recovery 419 13.2.4 Texture formation during hot deformation 424 13.2.5 Modelling the evolution of microstructure 427 13.3 Discontinuous dynamic recrystallization 427 13.3.1 The characteristics of dynamic recrystallization 428 13.3.2 The nucleation of dynamic recrystallization 429 13.3.3 Microstructural evolution 431 13.3.4 The steady state grain size 433 13.3.5 The flow stress during dynamic recrystallization 434 13.3.6 Dynamic recrystallization in single crystals 435 13.3.7 Dynamic recrystallization in two-phase alloys 436 13.4 Continuous dynamic recrystallization 437 13.4.1 Types of continuous dynamic recrystallization 437 13.4.2 Dynamic recrystallization by progressive lattice rotation 438 13.5 Dynamic recrystallization in minerals 441 13.5.1 Boundary migration in minerals 442 13.5.2 Migration and rotation recrystallization 444 13.6 Annealing after hot deformation 444 13.6.1 Static recovery 445 13.6.2 Static recrystallization 446 13.6.3 Metadynamic recrystallization 447 13.6.4 PSN after hot deformation 448 13.6.5 Grain growth after hot working 450 xii Contents