Fracture Mechanics of Piezoelectric and Ferroelectric Solids

Frontmatter

Chapter 1. Introduction

Abstract

This chapter summarizes briefly the research background, development history and future trend of fracture mechanics of piezoelectric/ferroelectric materials. In Section 1.3, the structure and arrangement of the present book are introduced.

Daining Fang, Jinxi Liu

Chapter 2. Physical and Material Properties of Dielectrics

Abstract

In this chapter, we introduce some basic concepts of piezoelectric/ ferroelectric media, mainly including the crystal structure of dielectrics, microscopic mechanism and physical explanation of electric polarization, dielectric constant tensor of crystal and its symmetry. Some fundaments on the domain switching of ferroelectrics are described.

Daining Fang, Jinxi Liu

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

Abstract

This chapter addresses the experimental works on the fracture of piezoelectric/ferroelectric materials. Firstly, the experimental methods for the fracture of piezoelectric/ferroelectric materials under electromechanical coupling fields are introduced and the pioneer works on the anisotropy of fracture toughness in piezoelectric ceramics are briefly reviewed. Then, our experimental results on the fracture of ferroelectric materials are presented, including the effects of electric field on the fracture toughness, the toughening effect in ferroelectric nano-composites, the measurement of strain fields near an electrode in piezoelectric laminated structures, and domain switching near a crack tip in ferroelectric single crystals.

Daining Fang, Jinxi Liu

Chapter 4. Basic Equations of Piezoelectric Materials

Abstract

In this chapter, we introduce the basic equations of piezoelectric materials. These equations include four types of the piezoelectric equations that describe the electromechanical coupling, gradient equations and equilibrium equation. The relations between the electro-elastic material constants appearing in different piezoelectric equations are provided. A set of governing differential equations for mechanical displacements and electrical potential are derived in a fixed rectangular coordinate system.

Daining Fang, Jinxi Liu

Chapter 5. General Solutions to Electromechanical Coupling Problems of Piezoelectric Materials

Abstract

Based on the complex variable theory, the Stroh-type and Lekhniskii-type formalisms for two dimensional deformation problems of general anisotropic piezoelectric solids are presented. The general solutions to the anti-plane, in-plane and three dimensional problems are also derived for transversely isotropic piezoelectric materials widely used in engineering. This chapter plays an important role in Chapters 6–8 and 11.

Daining Fang, Jinxi Liu

Chapter 6. Fracture Mechanics of Homogeneous Piezoelectric Materials

Abstract

This chapter is concerned with three basic cracks (antiplane, in-plane and penny-shaped) in infinite piezoelectric media. The closed-form expressions of electro-elastic fields are derived and their singularities at crack tips are analyzed in detail. The antiplane and two dimensional deformation problems for an infinite piezoelectric solid with a dielectric elliptical hole are solved to investigate the effect of the electrical boundary conditions along the crack surfaces on the fracture behaviors.

Daining Fang, Jinxi Liu

Chapter 7. Interface Fracture Mechanics of Piezoelectric Materials

Abstract

In this chapter, we consider the interfacial crack problem in piezoelectric bi-materials. Based on the Stroh formalism in Chapter 4, the behavior of the crack tip fields is examined and the full field solution is given. Different from the cracks in homogeneous piezoelectric materials, the electro-elastic fields at interfacial crack tips exhibit the oscillatory singularity which strongly depends on the properties of bi-materials. The Green’s functions for anti-plane interfacial cracks are illustrated in Section 7.3.

Daining Fang, Jinxi Liu

Chapter 8. Dynamic Fracture Mechanics of Piezoelectric Materials

Abstract

This chapter focuses on the dynamic fracture of piezoelectric materials. The problems considered include: the scattering of Love wave caused by interfacial cracks in piezoelectric layered structures (Section 1); the electroelastic fields produced by moving cracks (Section 2); the transient response of cracked piezoelectric under impact electromechanical loads (Section 3); the dynamic crack propagation of a Mode III crack in piezoelectric materials (Section 4). Some numerical results are provided to show the influence of the inertial effect on the dynamic fracture.

Daining Fang, Jinxi Liu

Chapter 9. Nonlinear Fracture Mechanics of Ferroelectric Materials

Abstract

This chapter presents recent theoretical works on the nonlinear fracture of piezoelectric/ferroelectric materials. Firstly, the nonlinear fracture mechanics models for ferroelectric materials are briefly reviewed including the nonlinear electrostriction fracture model, the Duldale fracture model and the domain-switch toughening model. Then, our theoretical works on the anisotropic switching toughening model and the nonlinear COD model are presented. Finally, our experimental works on the in-situ observation of crack propagation and domain switch are provided, and comparison with theoretical predictions is given.

Daining Fang, Jinxi Liu

Chapter 10. Fracture Criteria

Abstract

In this chapter, we evaluate the application of several criterions for the fracture of piezoelectric materials. The stress intensity factors obtained from the linear piezoelectric theory and total energy release rate can not be used to establish the fracture criterion. The stress intensity factors calculated based on the strip electric saturation model and energy density factor can be used to explain the electrically-induced fracture phenomenon in a smaller range of applied electric field. The facture loads predicted by the mechanical energy release rate, local energy release rate and COD criterion are in good agreement with the experiment results.

Daining Fang, Jinxi Liu

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

Abstract

This chapter specializes in the electro-elastic fields induced by the surface or internal electrode in piezoelectric materials or structures. In Section 1, the distributions of the electro-elastic fields near strip-shaped and circular surface electrodes in a piezoelectric half-space are given. In Section 2, the analytical solution to the interfacial electrodes in anisotropic piezoelectric bi-materials is obtained using the Stroh method and the characteristics of coupled fields are revealed. In Section 3, the deformation and stress distributions of piezoelectric ceramic-electrode stacked structure are simulated by the finite element method and measured experimentally.

Daining Fang, Jinxi Liu

Chapter 12. Electric-Induced Fatigue Fracture

Abstract

This chapter presents both the experimental and theoretical works on the electric field induced fatigue cracking (EIFC) in ferroelectric materials. Firstly, the experimental observations and results of EIFC are briefly reviewed and our experimental works on EIFC are presented. Then the phenomenological model for EIFC based on the experiments is proposed. Finally, a domain switching model for EIFC is proposed and comparison with the experiments is also presented.

Daining Fang, Jinxi Liu

Chapter 13. Numerical Method for Analyzing Fracture of Piezoelectric and Ferroelectric Materials

Abstract

This chapter presents recent numerical methods simulating the fracture behavior of piezoelectric/ferroelectric materials. Firstly, the generalized variational principle for the coupled electromechanical problems is derived. Then, the linear finite element model for piezoelectric materials is given together with the analysis of piezoelectric fracture. Later, the meshless method for fracture of piezoelectric materials is proposed and calibrated. Finally, nonlinear finite element analysis on the fracture of ferroelectric materials is presented.

Daining Fang, Jinxi Liu

Backmatter