Table of Contents
Foreword vii
Preface ix
List of Tables xvi
List of Figures xvii
Chapter 1 Fundamentals of Fracture Mechanics 1
1.1 Historical Perspective 1
1.2 Stress Intensity Factors (SIF) 4
1.3 Energy Release Rate (ERR) 6
1.4 J-Integral 7
1.5 Dynamic Fracture 9
1.6 Viscoelastic Fracture 13
1.7 Essential Work of Fracture (EWF) 16
1.8 Configuration Force (Material Force) Method 18
1.9 Cohesive Zone and Virtual Internal Bond Models 21
Chapter 2 Elements of Electrodynamics of Continua 26
2.1 Notations 27
2.1.1 Eulerian and Lagrangian descriptions 27
2.1.2 Electromagnetic field 31
2.1.3 Electromagnetic body force and couple 32
2.1.4 Electromagnetic stress tensor and momentum vector 34
2.1.5 Electromagnetic power 35
2.1.6 Poynting theorem 36
2.2 Maxwell Equations 36
2.3 Balance Equations of Mass, Momentum, Moment of Momentum, and Energy 39
2.4 Constitutive Relations 42
2.5 Linearized Theory 44
Chapter 3 Introduction to Thermoviscoelasticity 55
3.1 Thermoelasticity 55
3.2 Viscoelasticity 57
3.3 Coupled Theory of Thermoviscoelasticity 60
3.3.1 Fundamental principles of thermodynamics 60
3.3.2 Formulation based on Helmholtz free energy functional 61
3.3.3 Formulation based on Gibbs free energy functional 64
3.4 Thermoviscoelastic Boundary-Initial Value Problems 67
Chapter 4 Overview on Fracture of Electromagnetic Materials 70
4.1 Introduction 70
4.2 Basic Field Equations 71
4.3 General Solution Procedures 73
4.4 Debates on Crack-Face Boundary Conditions 76
4.5 Fracture Criteria 78
4.5.1 Field intensity factors 78
4.5.2 Path-independent integral 80
4.5.3 Mechanical strain energy release rate 83
4.5.4 Global and local energy release rates 85
4.6 Experimental Observations 87
4.6.1 Indentation test 87
4.6.2 Compact tension test 91
4.6.3 Bending test 93
4.7 Nonlinear Studies 95
4.7.1 Electrostriction/magnetostriction 95
4.7.2 Polarization/magnetization saturation 96
4.7.3 Domain switching 97
4.7.4 Domain wall motion 100
4.8 Status and Prospects 101
Chapter 5 Crack Driving Force in Electro-Thermo-Elastodynamic Fracture 103
5.1 Introduction 103
5.2 Fundamental Principles of Thermodynamics 104
5.3 Energy Flux and Dynamic Contour Integral 106
5.4 Dynamic Energy Release Rate Serving as Crack Driving Force 108
5.5 Configuration Force and Energy-Momentum Tensor 108
5.6 Coupled Electromechanical Jump/Boundary Conditions 110
5.7 Asymptotic Near-Tip Field Solution 111
5.8 Remarks 118
Chapter 6 Dynamic Fracture Mechanics of Magneto-Electro-Thermo-Elastic Solids 120
6.1 Introduction 120
6.2 Thermodynamic Formulation of Fully Coupled Dynamic Framework 121
6.2.1 Field equations and jump conditions 121
6.2.2 Dynamic energy release rate 124
6.2.3 Invariant integral 125
6.3 Stroh-Type Formalism for Steady-State Crack Propagation under Coupled Magneto-Electro-Mechanical Jump/Boundary Conditions 128
6.3.1 Generalized plane crack problem 128
6.3.2 Steady-state solution 129
6.3.3 Path-independent integral for steady crack growth 134
6.4 Magneto-Electro-Elastostatic Crack Problem as a Special Case 136
6.5 Summary 137
Chapter 7 Dynamic Crack Propagation in Magneto-Electro-Elastic Solids 139
7.1 Introduction 139
7.2 Shear Horizontal Surface Waves 140
7.3 Transient Mode-III Crack Growth Problem 146
7.4 Integral Transform, Wiener-Hopf Technique, and Cagniard-de Hoop Method 150
7.5 Fundamental Solutions for Traction Loading Only 159
7.6 Fundamental Solutions for Mixed Loads 164
7.7 Evaluation of Dynamic Energy Release Rate 174
7.8 Influence of Shear Horizontal Surface Wave Speed and Crack Tip Velocity 176
Chapter 8 Fracture of Functionally Graded Materials 179
8.1 Introduction 179
8.2 Formulation of Boundary-Initial Value Problems 180
8.3 Basic Solution Techniques 183
8.4 Fracture Characterizing Parameters 195
8.4.1 Field intensity factors 195
8.4.2 Dynamic energy release rate 201
8.4.3 Path-domain independent integral 202
8.5 Remarks 204
Chapter 9 Magneto-Thermo-Viscoelastic Deformation and Fracture 206
9.1 Introduction 206
9.2 Local Balance Equations for Magnetic, Thermal, and Mechanical Field Quantities 207
9.3 Free Energy and Entropy Production Inequality for Memory-Dependent Magnetosensitive Materials 209
9.4 Coupled Magneto-Thermo-Viscoelastic Constitutive Relations 210
9.5 Generalized J-Integral in Nonlinear Magneto-Thermo-Viscoelastic Fracture 215
9.6 Generalized Plane Crack Problem and Revisit of Mode-III Fracture of a Magnetostrictive Solid in a Bias Magnetic Field 218
Chapter 10 Electro-Thermo-Viscoelastic Deformation and Fracture 221
10.1 Introduction 221
10.2 Local Balance Equations for Electric, Thermal, and Mechanical Field Quantities 222
10.3 Free Energy and Entropy Production Inequality for Memory-Dependent Electrosensitive Materials 224
10.4 Coupled Electro-Thermo-Viscoelastic Constitutive Relations 225
10.5 Generalized J-Integral in Nonlinear Electro-Thermo-Viscoelastic Fracture 231
10.6 Analogy between Nonlinear Magneto- and Electro-Thermo-Viscoelastic Constitutive and Fracture Theories 234
10.7 Reduction to Dorfmann-Ogden Nonlinear Magneto- and Electro-elasticity 236
Chapter 11 Nonlinear Field Theory of Fracture Mechanics for Paramagnetic and Ferromagnetic Materials 237
11.1 Introduction 237
11.2 Global Energy Balance Equation and Non-Negative Global Dissipation Requirement 238
11.3 Hamiltonian Density and Thermodynamically Admissible Conditions 241
11.3.1 Generalized functional thermodynamics 241
11.3.2 Generalized state-variable thermodynamics 243
11.4 Thermodynamically Consistent Time-Dependent Fracture Criterion 246
11.5 Generalized Energy Release Rate versus Bulk Dissipation Rate 246
11.6 Local Generalized J -Integral versus Global Generalized J -Integral 248
11.7 Essential Work of Fracture versus Nonessential Work of Fracture 250
Chapter 12 Nonlinear Field Theory of Fracture Mechanics for Piezoelectric and Ferroelectric Materials 252
12.1 Introduction 252
12.2 Nonlinear Field Equations 253
12.2.1 Balance equations 253
12.2.2 Constitutive laws 255
12.3 Thermodynamically Consistent Time-Dependent Fracture Criterion 256
12.4 Correlation with Conventional Fracture Mechanics Approaches 258
Chapter 13 Applications to Fracture Characterization 264
13.1 Introduction 264
13.2 Energy Release Rate Method and its Generalization 264
13.3 J-R Curve Method and its Generalization 268
13.4 Essential Work of Fracture Method and its Extension 271
13.5 Closure 273
Bibliography 276
Index 299
