Fracture Mechanics of Piezoelectric Solids with Interface Cracks (eBook)

Preface 6
Contents 8
1 Introduction 10
References 18
2 Linear Theory of Electroelasticity 23
2.1 On the Physics of Piezoelectricity 23
2.2 Fundamental Electroelastic Relations 25
2.3 Piezoelectric Ceramics 31
2.4 Two-Dimensional Problems of Piezoelectricity 35
2.5 Boundary Conditions 37
References 45
3 Basic Concepts of Fracture Mechanics 46
3.1 The Main Fracture Criteria of Materials 46
3.2 The Crack Between Two Different Isotropic Materials 54
3.3 Fracture Criteria of Piezoelectric Materials 60
References 64
4 An Electrically Permeable Crack Between Two Different Piezoelectric Materials 65
4.1 General Solutions to the in-Plane Problems of Transversely Isotropic Piezoelectric Materials 66
4.2 Interface Crack with Two Contact Zones 70
4.3 Interface Crack with One Contact Zone 81
4.4 “Fully Open” Interface Crack 93
References 101
5 Electrically Impermeable Interface Cracks in Piezoelectric Materials 102
5.1 Contact Zone Model of an Interface Crack 103
5.2 Oscillating Interface Crack Model 116
5.3 Formulation and Solution of the Problem for a Non-oscillating Case 121
References 125
6 An Electrically Limited Permeable Crack Between Two Piezoelectric Materials 126
6.1 Oscillating Model 127
6.2 Contact Zone Model 136
6.3 Effect of Electric Permeability on the Nearby Crack Tip Distribution of the Electromechanical Fields in a Homogeneous Piezoceramic Material 145
6.4 Effect of Electric Permeability of an Interface Cracks on the Characteristics of the Electromechanical Field in the Vicinity of it Tip 148
References 156
7 An Electrically Conducting Interface Crack Between Two Piezoelectric Materials 157
7.1 Special Presentation of the Solution of Basic Equations 158
7.2 Solution of the Problem in the Framework of the Contact Zone Model 161
7.3 Comparison to the Case of Crack Faces Without Electrodes 170
7.4 Numerical Results 172
References 178
8 A Crack with Electromechanical Pre-fracture Zones 179
8.1 Electric Saturation Zones of an Electrically Impermeable Crack in a Homogeneous Piezoceramic Material 180
8.2 Modeling of Electromechanical Pre-fracture Zones for an Electrically Impermeable Crack 187
8.3 An Electrically Limited Permeable Crack with Electromechanical Pre-fracture Zones 198
8.4 Analysis of Electromechanical Pre-fracture Zones for Interface Cracks 206
References 214
9 Analytically-Numerical Approach for the Analysis of an Interface Crack in a Finite-Sized Piezoelectric Bimaterial Compound 215
9.1 Finite Element Formulation for the Piezoelectric Problem 216
9.2 “Fully Open” Crack-Tip Model for an Interface Crack 221
9.3 Closed Crack-Tip Model for an Interface Crack 228
9.4 Interface Cracks in a Bimaterial Disk Specimen Under Concentrated Load 236
References 239