Chapter 1 Introduction

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

1.2 Development course and trend

1.3 Framework of the book and content arrangements

References

Chapter 2 Physical and Material Properties of Dielectrics

2.1 Basic concepts of piezoelectric/ferroelectric materials

2.2 Crystal structure of dielectrics

2.3 Properties of electric polarization and piezoelectricity

2.3.1 Microscopic mechanism of polarization

2.3.2 Physical description of electric polarization

2.3.3 Dielectric constant tensor of crystal and its symmetry

2.4 Domain switch of ferroelectrics

2.4.1 Electric domain and domain structure

2.4.2 Switching of electric domain and principles for domain switch

References

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

3.1 Experimental approaches and techniques under an electromechanical coupling field

3.1.1 High-voltage power supply

3.1.2 High voltage insulation

3.1.3 Moire interferometry

3.1.4 Digital speckle correlation method

3.1.5 Method of polarized microscope

3.1.6 Experimental facilities

3.2 Anisotropy of fracture toughness

3.3 Electric field effect on fracture toughness

3.4 Fracture behavior of ferroelectric nano-composites

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

3.6 Observation of crack types near electrode tip

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

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

3.7.2 Cyclic domain switch driven by cyclic electric field

3.7.3 Electric crack propagation and evolution of crack tip electric domain

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

3.8.1 Response of specimen under a positive electric field

3.8.2 Crack tip domain switch under low negative electric field

3.8.3 Domain switching zone near crack tip under negative field

3.8.4 Evolution ofelectric domain near crack tip under alternating electric field

References

Chapter 4 Basic Equations of Piezoeleetrie Materials

4.1 Basic equations

4.1.1 Piezoelectric equations

4.1.2 Gradient equations and balance equations

4.2 Constraint relations between various electroelastic constants

4.3 Electroelastic constants of piezoelectric materials

4.3.1 Coordinate transformation between vector and tensor of the second order

4.3.2 Coordinate transformation of electroelastic constants

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

4.4 Governing differential equations and boundary conditions of electromechanical coupling problems

4.4.1 Governing difierential equations of electromechanical coupling problems

4.4.2 Boundary conditions of electromechanical coupling

References

Chapter 5 General Solutions to Electromeehanical Coupling Problems of Piezoelectric Materials

5.1 Extended Stroh formalism for piezoelectricity

5.1.1 Extended Stroh formalism

5.1.2 Mathematical properties and important relations of Stroh formalism

5.2 Lekhniskii formalism for piezoelectricity

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

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

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

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

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

References

Chapter 6 Fracture Mechanics of Homogeneous Piezoelectric Materials

6.1 Anti-plane fracture problem

6.2 In-plane fracture problem

6.3 Three dimensional fracture problem

6.3.1 Description of problem

6.3.2 Derivation of electroelastic fields

6.4 Electromechanical coupling problem for a dielectric elliptic hole

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

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

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

References

Chapter 7 Interface Fracture Mechanics of Piezoelectric Materials

7.1 Interfacial cracks in piezoelectric materials under uniform electromechanical loads

7.1.1 Tip field of interfacial crack

7.1.2 Full field solutions for an impermeable interfacial crack

7.2 Effect of material properties on interfacial crack tip field

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

7.3.1 Brief review of Green's functions for piezoelectric materials

7.3.2 Green's functions for anti-plane interfacial cracks

References

Chapter 8 Dynamic Fracture Mechanics of Piezoelectric Materials

8.1 Scattering of elastic waves in a cracked piezoelectrics

8.1.1 Basic concepts concerning propagation of elastic wave in a piezoelectrics

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

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

8.2 Moving cracks in piezoelectric medium

8.2.1 Anti-plane problems of moving interficial cracks

8.2.2 The plane problem of moving cracks

8.3 Transient response of a cracked piezoelectrics to electromechanical impact load

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

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

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

8.4 Dynamic crack propagation in piezoelectric materials

8.4.1 Dynamic propagation of conducting crack mode-Ⅲ

8.4.2 Dynamic propagation of dielectric crack mode-Ⅲ

References

Chapter 9 Nonlinear Fraeture Mechanics of Ferroelectric Materials

9.1 Nonlinear fracture mechanical model

9.1.1 Electrostriction model

9.1.2 Dugdale model(striP saturation mode)

9.2 Domain switching toughening model

9.2.1 Decoupled isotropy model

9.2.2 Anisotropy model for electromechanical coupling

9.3 Nonlinear crack opening displacement model

9.3.1 Definition of crack opening displacement

9.3.2 Crack opening displacement δ0 caused by piezoelectric effect

9.3.3 Effect △δof domain switching on crack opening displacement

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

9.4.1 Experiment principle and technology

9.4.2 Experimental phenomena

9.4.3 Analysis ofdomain switching zone

9.4.4 Ferroelastic domain switching toughening

References

Chapter 10 Fracture Criteria

10.1 Stress intensity factor criterion

10.2 Energy release rate critefrion

10.2.1 Total energy release rate criterion

10.2.2 Mechanical strain energy release rate criterion

10.3 Energy density factor criterion

10.4 Further discussion on stress intensity factor criterion

10.5 COD criterion

References

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

111 Electroelastic field near surface electrodes

11.1.1 Electroelastic field near stripe-shaped surface electrodes

11.1.2 Electroelastic field near circular surface electrodes

11.2 Electroelastic field near interface electrode

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

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

11.3 Electroelastic field in piezoelectric ceramic-electrode layered structures

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

11.3.2 Numerical calculation and experimentally measured results

References

Chapter 12 Electric-Induced Fatigue Fracture

12.1 Experimental observation and results

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

12.1.2 Electrically induced fatigue experiment of samples containing penetrating cracks

12.2 Phenomenological model

12.2.1 Model Ⅰ

12.2.2 Model Ⅱ

12.3 Domain switching model

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

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

References

Chapter 13 Numerical Method for Analyzing Fracture ofPiezoelectric and Ferroelectric Materials

13.1 Generalized variation principle

13.1.1 Generalized variation principle of linear elastic mechanics

13.1.2 Variation principle of electromechanical coupling problem

13.2 Finite element method for piezoelectric material fracture

13.2.1 Basic format of finite element for piezoelectric fracture

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

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

13.3 Meshless method for piezoelectric material fracture

13.3.1 Basic format of electromechanical coupling meshless method

13.3.2 Some problems about electromechanical coupling meshless method

13.3.3 Numerical example

13.4 Nonlinear finite element analysis of ferroelectric material fracture

13.4.1 Solution of field quantity with given electric domain distribution

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

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

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

References

Appendix The Material Constants ofPiezoelectric Ceramics