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Foreword
Preface
Contents
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 of piezoelectric 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 driven 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 of electric domain near crack tip under alternating electric field
References
Chapter 4 Basic Equations of Piezoelectric Materials
4.1 Basic equations
4.1.1 Piezoelectric equations
4.1.2 Gradient equations and balance equations Gradient 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 of point groups
4.4 Governing differential equations and boundary conditions of electromechanical coupling problems
4.4.1 Governing differential equations of electromechanical coupling problems
4.4.2 Boundary conditions of electromechanical coupling
References
Chapter 5 General Solutions to Electromechanical 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 of piezoelectrics
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-Ⅲin 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 Fracture 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 δ_0 caused by piezoelectric effect
9.3.3 Effect △δ of domain switching on crack opening displacement
9.4 Interaction between crack tip domain switching of BaTiO_3 single crystal and crack growth under electromechanical load
9.4.1 Experiment principle and technology
9.4.2 Experimental phenomena
9.4.3 Analysis of domain 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 criterion
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
11.1 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 ModelⅠ
12.2.2 ModelⅡ
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 of Piezoelectric 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 infinite piezoelectric matrix
13.2.3 Calculation example:model of piezoelectric 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=0.72E_c) perpendicular to crack surface
References
Appendix The Material Constants of Piezoelectric Ceramics
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