Fracture Mechanics of Piezoelectric Materials

1R18. Fracture Mechanics of Piezoelectric Materials. - Qing-Hua Qin (Dept of Mech and Mechatronic Eng, Univ of Sydney, Sydney, Australia). WIT Press, Southamptom, UK. 2001. 282 pp. ISBN 1-85312-856-2. $149.00.Reviewed by C Zhang (Dept of Civil Eng, Hochschule Zittau/Goerlitz, Univ of Applied Sciences, Theodor-Koerner-Allee 16, Zittau, D-02763, Germany).Piezoelectric materials have wide engineering applications in smart structures and devices such as transducers, sensors, and actuators. Since piezoelectric materials are usually very brittle, their fracture behavior is very important to the mechanical integrity and reliability of these materials in engineering applications. Though many diverse research works have been carried out in recent years, a comprehensive and unified treatment on fracture mechanics of piezoelectric materials is still lacking. This book is perhaps the first extensive and detailed monograph on the subject, and it contains many recent research results, including the author’s. The book contains seven chapters entitled: Linear theory of piezoelectricity; Basic solution approaches for crack problems of piezoelectric materials; Cracks in piezoelectric materials; Cracks in thermoelectroelastic solids; Fracture criteria for piezoelectric materials; Analyzing crack problems by the boundary element method; and Experiments. Each chapter contains an introduction and a reference list to the subject under investigation. Thus, each chapter is self-contained and can be considered more or less independently of other chapters. In Chapter 1, the basic governing equations and the commonly-used terminology of linear piezoelectricity are briefly summarized for later use. Three different electric boundary conditions are reviewed and discussed, namely, the permeable, the partially permeable (by air or vacuum), and the impermeable boundary conditions. Then, the fundamental relations for two-dimensional problems are given. Two solution methods are explained subsequently: the Stroh formalism and the Lekhnitskii formalism. Chapter 2 deals with some basic solution methods for crack analysis in piezoelectric materials. The corresponding boundary value problems are formulated and the asymptotic crack-tip solutions for the mechanical and electric fields are given. As crack-tip characterizing parameters, the stress and the electric displacement (SED) intensity factors, the extended path-independent J-integral, and the energy release rate are presented. Five solution methods are briefly discussed. In particular, they are: the Green’s function method, the Fourier transform technique, the potential function method, the finite element method (FEM), and the boundary element method (BEM). Several crack problems in piezoelectric materials are treated in Chapter 3. They include the semi-infinite crack, the finite Griffith crack, the elliptical hole, the interface crack, crack dislocation interactions, macro and micro crack interactions, crack kinking, crack deflection in bimaterials, and the elliptical crack. The piezoelectric solids investigated are either infinite, semi-infinite (half-plane), or a strip of infinite length but finite width. Most of these problems are dealing with two-dimensional in-plane or anti-plane cracks. Special attention is given to derive the asymptotic crack-tip field and to obtain relations between the SED intensity factors, the energy release rate, and the applied mechanical and electric loading. Different solution techniques, such as the extended Lekhnitskii formalism, the conformal mapping technique, the Green’s function method, the Fourier transform method, and the singular integral equation method, have been applied for this purpose. Several numerical results are also presented, and they are obtained mainly by using the singular integral equation method. In addition, criteria for crack kinking and propagation are also discussed. Crack problems in thermoelectroelastic materials are analyzed in Chapter 4. In contrast to piezoelectric crack problems investigated in Chapter 3, thermal effects are taken into account in addition to mechanical and electric coupling. After an introduction and a summary of the basic theories of thermopiezoelectricity, the Fourier transform method, the Green’s function method, and the conforming mapping technique are used to obtain the temperature and the electroelastic fields. Various crack problems are analyzed in this chapter, and they include crack-tip singularity, cracks in infinite, semi-infinite and bimaterial solids, multiple crack problems, macro and micro crack interactions, the penny-shaped crack, the interaction between a hole and a crack, and the interaction between an inclusion and cracks. For some crack problems mentioned above, numerical results obtained by a singular integral equation method are presented and compared with the finite element (FE) results. In Chapter 5, fracture criteria for piezoelectric materials are presented. In particular, the fracture criteria using the stress intensity factors, the total energy release rate, the mechanical strain release rate, and the local energy release rate are explained. Advantages and drawbacks of these fracture criteria are discussed. As remarked by the author, further research works are required to verify which of these fracture criteria is suitable to describe the fracture behavior of piezoelectric materials properly. A boundary element method for crack analysis of thermoelectroelastic materials is presented in Chapter 6. Singular boundary integral equations are applied to determine the temperature discontinuity, the crack opening displacements (displacement discontinuity), and the potential discontinuity. To solve the singular boundary integral equations numerically, a numerical solution procedure is presented. A technique based on the least-square method is adopted to obtain the SED intensity factors numerically. Numerical examples are given to show the efficiency and the accuracy of the BEM developed by the author. Finally, experimental techniques are briefly described in Chapter 7. Three experimental techniques to determine the fracture toughness of piezoelectric materials are explained: the indentation fracture test, the double torsion test, and the mode I and the mixed mode fracture test. Some experimental results from literature are reported and they are compared with those obtained by the FEM. The book deals primarily with linear and static crack problems in transversely isotropic piezoelectric materials such as piezoelectric ceramics. Crack-tip nonlinearities such as dielectric break-down, polarization switching, local de-poling and domain reversal, and dynamic crack problems are not investigated. A few typographical errors in the book are found by the reviewer. Some shorted notations are not explained in the proper place, and some of the figures could be better presented and organized. The book is otherwise well written and contains figures of high quality. It is a specialized monograph on fracture mechanics of piezoelectric materials. Fracture Mechanics of Piezoelectric Materials is strongly recommended for purchase by scientific libraries. It is also highly recommendable to graduate students, professional researchers, and engineers from applied mechanics, material sciences, applied mathematics, and physics, who are working on and interested in this research subject.