The main purpose of this book is to put forward the fundamental role of grain boundaries in the plasticity of crystalline materials.
To understand this role requires a multi-scale approach to plasticity: starting from the atomic description of a grain boundary and its defects, moving on to the elemental interaction processes between dislocations and grain boundaries, and finally showing how the microscopic phenomena influence the macroscopic behaviors and constitutive laws.
It involves bringing together physical, chemical and mechanical studies. The investigated properties are: deformation at low and high temperature, creep, fatigue and rupture.
Preface xi
Chapter 1 Grain Boundary Structures and Defects Jany Thibault-Penisson Louisette Priester 1
1.1 Equilibrium structure of grain boundaries 1
1.1.1 Geometric description and elements of bicrystallography 2
1.1.2 Grain boundary structure in terms of intrinsic dislocations 6
1.1.3 Grain boundary atomic structure - structural unit model 10
1.1.4 Energetic atomic description 15
1.2 Crystalline defects of grain boundaries 18
1.2.1 Point defects - intergranular segregation 19
1.2.2 Linear defects: extrinsic dislocations 29
1.2.3 Volume defects-grain boundary precipitation 38
1.3 Conclusion 41
1.4 Bibliography 42
Chapter 2 Elementary Grain Boundary Deformation Mechanisms Jean-Philippe Couzinie Louisette Priester 47
2.1 Dislocation in close proximity to a grain boundary 48
2.2 Elastic interaction between dislocations and grain boundaries: image force 49
2.3 Short range (or core) interaction between dislocations and grain boundaries 52
2.3.1 Geometric and energetic criteria for slip transmission 54
2.3.2 Elementary mechanisms of dislocations at grain boundaries 67
2.3.3 Atomic scale simulations of interaction mechanisms between dislocations and grain boundaries 64
2.3.4 Experimental observations of interaction mechanisms 69
2.3.5 Elastic stress fields associated with extrinsic dislocations 77
2.4 Relaxation of stress fields associated with extrinsic dislocations 81
2.4.1 Relaxation processes in a grain boundary 82
2.4.2 Evolution of stress fields with relaxation time 84
2.4.3 Experimental studies of grain boundary relaxation phenomena 86
2.4.4 Conclusion 96
2.5 Relationships between elementary interface mechanisms and mechanical behaviors of materials 98
2.6 Bibliography 102
Chapter 3 Grain Boundaries in Cold Deformation Colette Rey Denis Solas Olivier Fandeur 109
3.1 Introduction 109
3.2 Plastic compatibility and incompatibility of deformation at grain boundaries 111
3.2.1 General points 111
3.2.2 Calculation of incompatibilities in a bicrystal 116
3.3 Internal stresses in polycrystal grains 117
3.3.1 Notions of crystalline plasticity, single crystal behavior for use in polycrystalline models 118
3.3.2 Internal stresses in polycrystals 122
3.3.3 Stress relaxation mechanisms 125
3.4 Modeling local mechanical fields using the finite element method (FEM) 129
3.4.1 Aggregates 130
3.4.2 From single crystal to polycrystal using finite transformations 131
3.4.3 Identification of the constitutive and hardening law parameters 134
3.4.4 Examples of local mechanical fields proposed by the polycrystalline models 135
3.5 Hall-Petch's law, geometrically necessary dislocations 139
3.5.1 Definition 139
3.5.2 Modeling the grain size effect in polycrystals, comparison with experiments 140
3.6 Sub-grain boundaries and grain boundaries in deformation and recrystallization 145
3.6.1 Deformation sub-boundaries and grain boundaries 145
3.6.2 Recrystallization sub-grain boundaries 146
3.7 Conclusion 155
3.8 Bibliography 156
Chapter 4 Creep and High Temperature Plasticity: Grain Boundary Dynamics Sylvie Lartigue-Korinek Claude Paul Carry 165
4.1 Introduction 165
4.2 Grain boundaries and grain growth 168
4.2.1 Kinetics and grain growth law 169
4.2.2 Grain boundary segregation and precipitation - influence on the boundary mobility 171
4.3 Grain boundaries and creep: mechanisms and phenomenological laws 174
4.3.1 Grain boundary mechanisms 175
4.3.2 Creep models and kinetics 183
4.3.3 Constitutive creep laws and deformation mechanism maps 189
4.3.4 Limit of the models, grain boundaries chemistry and creep 193
4.4 Grain boundaries and superplasticity 197
4.4.1 Phenomenology and microstructural mechanisms 197
4.4.2 The different models 202
4.4.3 Grain growth and superplastic deformation 206
4.5 Prospects: creep of nanograined materials 208
4.6 Bibliography 209
Chapter 5 Intergranular Fatigue André Pineau Stephen Antolovich 217
5.1 Introduction 217
5.2 Low temperature intergranular fatigue 221
5.2.1 Several scales to be considered to explain intergranular fatigue 221
5.2.2 Study of a iron and of other BCC metals and metallic alloys 222
5.2.3 Intergranular fatigue of FCC metals and metallic alloys 234
5.3 High temperature fatigue 252
5.3.1 General information 252
5.3.2 Austenitic stainless steels 254
5.3.3 Nickel-based superalloys 260
5.4 Conclusion 271
5.5 Acknowledgements 272
5.6 Bibliography 272
Chapter 6 Intergranular Segregation and Crystalline Material Fracture Anna Fraczkiewicz Krzysztof Wolski 281
6.1 Grain boundaries and fracture 282
6.1.1 Fracture parameters-different types of fracture 282
6.1.2 Intergranular fracture 285
6.2 Intergranular segregation 286
6.2.1 The origin of segregation 286
6.2.2 Thermodynamics of equilibrium segregation - existing models 287
6.2.3 General characteristics of intergranular equilibrium segregatio 294
6.2.4 Non-equilibrium segregation 295
6.2.5 Heterogeneity of the intergranular segregation: effects of the grain boundary structure 295
6.3 Segregation and intergranular fracture 297
6.3.1 Intergranular embrittlement mechanisms 297
6.3.2 From embrittling segregations to strengthening segregations 302
6.4 Intergranular fracture induced by liquid metals 308
6.4.1 Phenomena occurring under contact with a liquid metal 308
6.4.2 Liquid metal embrittlement 309
6.4.3 Intergranular penetration 311
6.4.4 Intergranular diffusion in the case of the Cu-Bi system 312
6.4.5 Intergranular wetting in the case of the Ni-Bi system 313
6.4.6 Intergranular penetration mechanism 317
6.4.7 Case of the Al-Ga system 319
6.4.8 Conclusion 320
6.5 General conclusion 320
6.6 Bibliography 321
Appendices 327
Appendix 1 Bicrystallography and Topological Characterization of Interfacial Defects Sylvie Lartigue-Korinek Louisette Priester 329
Appendix 2 Appendices of Chapter 3 Colette Rey Denis Solas Olivier Fandeur 333
A2.1 Notations 333
A2.2 Infinitesimal deformations 334
A2.2.1 Plastic deformation and rotation 334
A2.3 Finished transformations 335
A2.3.1 Geometry 335
A2.3.2 Kinematics 336
A2.4 Incompatibility in finished transformations 337
A2.5 Calculation of the geometrically necessary dislocation densities 338
List of Authors 341
Index 343
Overview
The main purpose of this book is to put forward the fundamental role of grain boundaries in the plasticity of crystalline materials.
To understand this role requires a multi-scale approach to plasticity: starting from the atomic description of a grain boundary and its defects, moving on to the elemental interaction processes between dislocations and grain boundaries, and finally showing how the microscopic phenomena influence the macroscopic ...