Fracture Mechanics of Piezoelectric and Ferroelectric Solids 压电与铁电体的断裂力学PDF|Epub|txt|kindle电子书版本网盘下载

Fracture Mechanics of Piezoelectric and Ferroelectric Solids 压电与铁电体的断裂力学PDF格式电子书版下载

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Chapter 1 Introduction1

1.1 Background of the research on fracture mechanics of piezoelectric/ferroelectric materials1

1.2 Development course and trend3

1.3 Framework of the book and content arrangements4

References6

Chapter 2 Physical and Material Properties of Dielectrics9

2.1 Basic concepts of piezoelectric/ferroelectric materials9

2.2 Crystal structure of dielectrics12

2.3 Properties of electric polarization and piezoelectricity16

2.3.1 Microscopic mechanism of polarization17

2.3.2 Physical description of electric polarization17

2.3.3 Dielectric constant tensor of crystal and its symmetry20

2.4 Domain switch of ferroelectrics21

2.4.1 Electric domain and domain structure21

2.4.2 Switching of electric domain and principles for domain switch26

References31

Chapter 3 Fracture of Piezoelectric/Ferroelectric Materials—Experiments and Results33

3.1 Experimental approaches and techniques under an electromechanical coupling field35

3.1.1 High-voltage power supply35

3.1.2 High voltage insulation35

3.1.3 Moire interferometry40

3.1.4 Digital speckle correlation method42

3.1.5 Method of polarized microscope43

3.1.6 Experimental facilities44

3.2 Anisotropy of fracture toughness45

3.3 Electric field effect on fracture toughness46

3.4 Fracture behavior of ferroelectric nano-composites52

3.5 Measurement of strain field near electrode in double-layer structure ofpiezoelectric ceramics55

3.6 Observation of crack types near electrode tip58

3.7 Experimental results and analysis related to ferroelectric single crystal out-of-plane polarized60

3.7.1 Restorable domain switch at crack tip driyen by low electric field61

3.7.2 Cyclic domain switch driven by cyclic electric field64

3.7.3 Electric crack propagation and evolution of crack tip electric domain65

3.8 Experimental results and analysis concerning in-plane polarized ferroelectric single crytal67

3.8.1 Response of specimen under a positive electric field67

3.8.2 Crack tip domain switch under low negative electric field68

3.8.3 Domain switching zone near crack tip under negative field69

3.8.4 Evolution ofelectric domain near crack tip under alternating electric field72

References75

Chapter 4 Basic Equations of Piezoeleetrie Materials77

4.1 Basic equations77

4.1.1 Piezoelectric equations77

4.1.2 Gradient equations and balance equations83

4.2 Constraint relations between various electroelastic constants84

4.3 Electroelastic constants of piezoelectric materials85

4.3.1 Coordinate transformation between vector and tensor of the second order85

4.3.2 Coordinate transformation of electroelastic constants86

4.3.3 Electroelastic constant matrixes of piezoelectric crystals vested in 20 kinds ofpoint groups88

4.4 Governing differential equations and boundary conditions of electromechanical coupling problems92

4.4.1 Governing difierential equations of electromechanical coupling problems92

4.4.2 Boundary conditions of electromechanical coupling95

References95

Chapter 5 General Solutions to Electromeehanical Coupling Problems of Piezoelectric Materials97

5.1 Extended Stroh formalism for piezoelectricity97

5.1.1 Extended Stroh formalism98

5.1.2 Mathematical properties and important relations of Stroh formalism102

5.2 Lekhniskii formalism for piezoelectricity107

5.3 General solutions to two-dimensional problems of transversely isotropic piezoelectric materials112

5.3.1 The general solutions to the anti-plane problems of transversely isotropic piezoelectric materials112

5.3.2 The general solutions to the in-plane problems of transversely isotropic piezoelectric materials—Stroh method113

5.3.3 The general solutions to the in-plane problems of transversely isotropic piezoelectric materials—Lekhniskii method116

5.4 General solutions to three-dimensional problems of transversely isotropic piezoelectric materials119

References123

Chapter 6 Fracture Mechanics of Homogeneous Piezoelectric Materials125

6.1 Anti-plane fracture problem127

6.2 In-plane fracture problem130

6.3 Three dimensional fracture problem135

6.3.1 Description of problem136

6.3.2 Derivation of electroelastic fields138

6.4 Electromechanical coupling problem for a dielectric elliptic hole142

6.4.1 Anti-plane problem of transversely isotropic piezoelctric material containing dielectric ellipic holes142

6.4.2 Generalized plane problems of piezoelectric materials containing a dielectric elliptic hole149

6.5 Influence on crack tip field imposed by electric boundary conditions along the crack surface158

References158

Chapter 7 Interface Fracture Mechanics of Piezoelectric Materials161

7.1 Interfacial cracks in piezoelectric materials under uniform electromechanical loads163

7.1.1 Tip field of interfacial crack163

7.1.2 Full field solutions for an impermeable interfacial crack167

7.2 Effect of material properties on interfacial crack tip field170

7.3 Green's functions for piezoelectric materials with an interfacial crack172

7.3.1 Brief review of Green's functions for piezoelectric materials172

7.3.2 Green's functions for anti-plane interfacial cracks174

References179

Chapter 8 Dynamic Fracture Mechanics of Piezoelectric Materials183

8.1 Scattering of elastic waves in a cracked piezoelectrics185

8.1.1 Basic concepts concerning propagation of elastic wave in a piezoelectrics185

8.1.2 Dominant research work on elastic wave scattering caused by cracks in piezoelectrics188

8.1.3 Scattering of Love wave caused by interficial cracks in layered elastic half-space ofpiezoelectrics190

8.2 Moving cracks in piezoelectric medium197

8.2.1 Anti-plane problems of moving interficial cracks198

8.2.2 The plane problem of moving cracks203

8.3 Transient response of a cracked piezoelectrics to electromechanical impact load210

8.3.1 Anti-plane problems of cracked piezoelectrics under impact electromechanical loads211

8.3.2 Transient response of crack mode-Ⅲ in strip-shaped piezoelectric medium216

8.3.3 In-plane problems of cracked piezoelectrics under the action of impact electromechanical loads217

8.4 Dynamic crack propagation in piezoelectric materials222

8.4.1 Dynamic propagation of conducting crack mode-Ⅲ223

8.4.2 Dynamic propagation of dielectric crack mode-Ⅲ229

References233

Chapter 9 Nonlinear Fraeture Mechanics of Ferroelectric Materials235

9.1 Nonlinear fracture mechanical model236

9.1.1 Electrostriction model236

9.1.2 Dugdale model(striP saturation mode)244

9.2 Domain switching toughening model248

9.2.1 Decoupled isotropy model249

9.2.2 Anisotropy model for electromechanical coupling252

9.3 Nonlinear crack opening displacement model262

9.3.1 Definition of crack opening displacement263

9.3.2 Crack opening displacement δ0 caused by piezoelectric effect265

9.3.3 Effect △δof domain switching on crack opening displacement266

9.4 Interaction between crack tip domain switching of BaTi03 single crystal and crack growth under electromechanical load272

9.4.1 Experiment principle and technology273

9.4.2 Experimental phenomena273

9.4.3 Analysis ofdomain switching zone276

9.4.4 Ferroelastic domain switching toughening285

References289

Chapter 10 Fracture Criteria293

10.1 Stress intensity factor criterion294

10.2 Energy release rate critefrion294

10.2.1 Total energy release rate criterion294

10.2.2 Mechanical strain energy release rate criterion297

10.3 Energy density factor criterion305

10.4 Further discussion on stress intensity factor criterion305

10.5 COD criterion308

References310

Chapter 11 Electro-elastic Concentrations Induced by Electrodes in Piezoelectric Materials313

111 Electroelastic field near surface electrodes314

11.1.1 Electroelastic field near stripe-shaped surface electrodes314

11.1.2 Electroelastic field near circular surface electrodes322

11.2 Electroelastic field near interface electrode328

11.2.1 General solution to the interface electrode of anisotropic piezoelectric bi-materials329

11.2.2 Electroelastic field near the interface electrode in transversely isotropic piezoelectric bi-materials332

11.3 Electroelastic field in piezoelectric ceramic-electrode layered structures334

11.3.1 Laminated structure model,experimental set-up and finite element calculation model334

11.3.2 Numerical calculation and experimentally measured results337

References340

Chapter 12 Electric-Induced Fatigue Fracture343

12.1 Experimental observation and results344

12.1.1 Electrically induced fatigue experiment by Cao and Evans(1994)344

12.1.2 Electrically induced fatigue experiment of samples containing penetrating cracks346

12.2 Phenomenological model356

12.2.1 Model Ⅰ356

12.2.2 Model Ⅱ360

12.3 Domain switching model361

12.3.1 Electrically induced fatigue investigated by means of crack tip intensity factor361

12.3.2 Investigation of electrically induced fatigue by means of crack opening displacement(COD)369

References375

Chapter 13 Numerical Method for Analyzing Fracture ofPiezoelectric and Ferroelectric Materials377

13.1 Generalized variation principle380

13.1.1 Generalized variation principle of linear elastic mechanics380

13.1.2 Variation principle of electromechanical coupling problem382

13.2 Finite element method for piezoelectric material fracture384

13.2.1 Basic format of finite element for piezoelectric fracture384

13.2.2 Calculation example:the electromechanical field around the circular hole in an infmite piezoelectric matrix387

13.2.3 Calculation example:model ofpiezoelectric material with two-sided notches389

13.3 Meshless method for piezoelectric material fracture391

13.3.1 Basic format of electromechanical coupling meshless method391

13.3.2 Some problems about electromechanical coupling meshless method393

13.3.3 Numerical example397

13.4 Nonlinear finite element analysis of ferroelectric material fracture397

13.4.1 Solution of field quantity with given electric domain distribution398

13.4.2 New electric domain distribution and finite element iterative process determined by field quantity404

13.4.3 Calculation example:Ferroelectric crystal containing insulating circular hole plus vertical electric field406

13.4.4 Calculation example:Ferroelectric crystal containing insulating crack plus electric field(E=0.72Ec)perpendicular to crack surface411

References415

Appendix The Material Constants ofPiezoelectric Ceramics417