Preface
Chapter 1 Fundamental theory of fracture mechanics of nonhomogeneous
materials 1
1.1 Internal crack 2
1.1.1 Basic equations for nonhomogeneous materials 2
1.1.2 Crack-tip fields for homogeneous materials 3
1.1.3 Crack-tip fields for nonhomogeneous materials 6
1.1.4 Crack-tip fields for nonhomogeneous orthotropic materials 12
1.2 Interface crack 14
1.2.1 Crack-tip fields of an interface crack 14
1.2.2 Crack-tip fields of an interface crack between two nonhomogeneous media 19
1.3 Three-dimensional curved crack 23
1.3.1 Internal crack 23
1.3.2 Interface crack 25
References 26
Chapter 2 Exponential models for crack problems in nonhomogeneous materials 28
2.1 Crack model for nonhomogeneous materials with an arbitrarily oriented crack 29
2.1.1 Basic equations and boundary conditions 29
2.1.2 Full field solution for a crack in the nonhomogeneous medium 31
2.1.3 Stress intensity factors (SIFs) and strain energy release rate (SERR) 36
2.2 Crack problems in nonhomogeneous coating-substrate or double-layered structures 38
2.2.1 Interface crack in nonhomogeneous coating-substrate structures 38
2.2.2 Cross -interface crack parallel to the gradient of material properties 45
2.2.3 Arbitrarily oriented crack in a double-layered structure 54
2.3 Crack problems in orthotropic nonhomogeneous materials 69
2.3.1 Basic equations and boundary conditions 69
2.3.2 Solutions to stress and displacement fields 71
2.3.3 Crack-tip SIFs 77
2.4 Transient crack problem of a coating-substrate structure 78
2.4.1 Basic equations and boundary conditions 78
2.4.2 Solutions to stress and displacement fields 79
2.4.3 Crack-tip SIFs 84
2.5 Representative examples 85
2.5.1 Example 1: Arbitrarily oriented crack in an infinite nonhomogeneous medium 85
2.5.2 Example 2: Interface crack between the coating and the substrate 88
2.5.3 Example 3: Crossing-interface crack perpendicular to the interface in a double-layered structure 89
2.5.4 Example 4: Inclined crack crossing the interface 94
2.5.5 Example 5: Vertical crack in a nonhomogeneous coating-substrate structure subjected to impact loading 96
Appendix 2A 98
References 99
Chapter 3 General model for nonhomogeneous materials with general elastic properties 101
3.1 Piecewise-exponential model for the mode I crack problem 102
3.1.1 Piecewise-exponential model (PE model) 102
3.1.2 Solutions to stress and displacement fields 105
3.1.3 Crack-tip SIFs 111
3.2 PE model for mixed-mode crack problem 112
3.2.1 Basic equations and boundary conditions 112
3.2.2 Solutions to stress and displacement fields 114
3.2.3 Crack-tip SIFs 119
3.3 PE model for dynamic crack problem 119
3.3.1 Basic equations and boundary conditions 119
3.3.2 Solutions to stress and displacement fields 123
3.3.3 Crack-tip SIFs 126
3.4 Representative examples 127
3.4.1 Example 1: Mode I crack problem for nonhomogeneous materials with general elastic properties 127
3.4.2 Example 2: Mixed-mode crack problem for nonhomogeneous materials with general elastic properties and an arbitrarily oriented crack 134
3.4.3 Example 3: Dynamic Mode I crack problem for nonhomogeneous materials with general elastic properties 139
Appendix 3A 145
References 151
Chapter 4 Fracture mechanics of nonhomogeneous materials based on piecewise-exponential model 153
4.1 Thermomechanical crack models of nonhomogeneous materials 154
4.1.1 Crack model for nonhomogeneous materials under steady thermal loads 154
4.1.2 Crack model for nonhomogeneous materials under thermal shock load 157
4.2 Viscoelastic crack model of nonhomogeneous materials 170
4.2.1 The correspondence principle for viscoelastic FGMs 170
4.2.2 Viscoelastic models for nonhomogeneous materials 173
4.2.3 PE model for the viscoelastic nonhomogeneous materials 174
4.3 Crack model for nonhomogeneous materials with stochastic properties 177
4.3.1 Stochastic micromechanics-based model for effective properties 177
4.3.2 Probabilistic characteristics of effective properties at transition region 182
4.3.3 Crack in nonhomogeneous materials with stochastic mechanical properties 183
4.4 Examples 188
4.4.1 Example 1: Steady thermomechanical crack problem 188
4.4.2 Example 2: Viscoelastic crack problem 195
4.4.3 Example 3: Crack problem in FGMs with stochastic mechanical properties 198
References 202
Chapter 5 Fracture of nonhomogeneous materials with complex interfaces 205
5.1 Interaction integral (I-integral) 207
5.1.1 J-integral 207
5.1.2 I-integral 208
5.1.3 Auxiliary field 208
5.1.4 Extraction of the SIFs 210
5.2 Domain-independent I-integral (DII-integral) 211
5.2.1 Domain form of the I-integral 211
5.2.2 DII-integral 214
5.3 DII-integral for orthotropic materials 220
5.4 Consideration of dynamic process 223
5.5 Calculation of the T-st
