Modeling High Temperature Materials Behavior for Structural Analysis (eBook)

Preface 6
Contents 12
1 Introduction 15
1.1 High-Temperature Inelasticity in Structural Materials 16
1.1.1 Uni-axial Stress State 16
1.1.2 Multi-axial Effects 36
1.2 High-Temperature Inelasticity in Structures 44
1.2.1 Examples for Creep in Structures 44
1.2.2 Examples for Thermo-mechanical Cycling 53
1.3 Microstructural Features and Length Scale Effects 66
1.4 Temporal Scale Effects 73
1.5 Modeling Approaches and Objectives 74
1.5.1 Modeling Approaches 74
1.5.2 Objectives, Modeling Requirements, and Steps for Structural Analysis 80
References 82
2 Continuum Mechanics in One Dimension 92
2.1 Motion, Derivatives, and Deformation 93
2.2 Conservation of Mass 96
2.3 Balance of Momentum 96
2.4 Balance of Energy 98
2.5 Entropy Inequality 100
2.6 Dissipation Inequality, Free Energy, and Stress 101
References 103
3 Elementary Uni-axial Constitutive Models 104
3.1 Heat Transfer 104
3.2 Thermo-elasticity 107
3.3 Non-linear Viscosity, Viscoplasticity, and Rigid Plasticity 109
3.4 Elasto-plasticity 112
3.5 Hardening, Softening, and Ageing 119
3.5.1 Strain Hardening 119
3.5.2 Kinematic Hardening 123
3.5.3 Phase Mixture Models for Hardening and Softening 128
3.5.4 Ageing 133
3.6 Damage 136
3.6.1 Kachanov-Rabotnov Model 137
3.6.2 Continuum Damage Mechanics 144
References 149
4 Three-Dimensional Continuum Mechanics 154
4.1 Motion, Derivatives and Deformation 155
4.1.1 Motion and Derivatives 155
4.1.2 Deformation Gradient and Strain Tensors 157
4.1.3 Velocity Gradient, Deformation Rate, and Spin Tensors 163
4.2 Conservation of Mass 172
4.3 Balance of Momentum 172
4.3.1 Stress Vector 172
4.3.2 Integral Form 173
4.3.3 Stress Tensor and Cauchy Formula 174
4.3.4 Local Forms 177
4.4 Balance of Angular Momentum 178
4.5 Balance of Energy 179
4.6 Entropy and Dissipation Inequalities 181
References 183
5 Constitutive Models 185
5.1 Heat Transfer 186
5.2 Material and Physical Symmetries 188
5.3 Thermo-elasticity 191
5.3.1 Preliminary Remarks 191
5.3.2 Isotropic Materials 194
5.3.3 Anisotropic Materials 196
5.3.4 Linear Elasticity 199
5.4 Non-linear Viscosity, Viscoplasticity, and Rigid Plasticity 202
5.4.1 Preliminary Remarks 202
5.4.2 Isotropic Materials 210
5.4.3 Initially Anisotropic Materials 217
5.4.4 Functions of Stress and Temperature 235
5.5 Elasto-plasticity 239
5.5.1 Multiplicative Decomposition of Deformation Gradient 240
5.5.2 Small Strains 248
5.6 Hardening and Softening Rules 250
5.6.1 Time and Strain Hardening 252
5.6.2 Kinematic Hardening 254
5.6.3 Phase Mixture Models for Hardening and Softening 262
5.7 Damage Processes and Damage Mechanics 266
5.7.1 Scalar-Valued Damage Variables 266
5.7.2 Damage-Induced Anisotropy 278
References 284
6 Examples of Constitutive Equations for Various Materials 295
6.1 Basic Approaches of Identification 295
6.2 Isotropic Materials 297
6.2.1 Type 316 Steel 297
6.2.2 Steel 13CrMo4-5 298
6.2.3 Steel X20CrMoV12-1 299
6.2.4 Aluminium Alloy BS 1472 311
6.3 Initially Anisotropic Materials 314
6.3.1 Forged Al-Cu-Mg-Si Alloy 315
6.3.2 Multi-pass Weld Metal 320
References 330
Appendix A Basic Operations of Tensor Algebra 335
Appendix B Elements of Tensor Analysis 354
Index 375