AN EXACT SOLUTION OF CRACK PROBLEMS IN PIEZOELECTRIC MATERIALS

摘要/Abstract

摘要： An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper,the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown for these solutions that: (i) the stress intensity factor is thesame as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i. e., it is always positive, anti independent of the electric lode. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.

关键词: piezoelectric material, plane problem, crack, energy release rate, exact solution

Abstract: An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper,the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown for these solutions that: (i) the stress intensity factor is thesame as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i. e., it is always positive, anti independent of the electric lode. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.

Key words: piezoelectric material, plane problem, crack, energy release rate, exact solution

高存法;樊蔚勋. AN EXACT SOLUTION OF CRACK PROBLEMS IN PIEZOELECTRIC MATERIALS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(1): 51-58.

Gao Cunfa;Fan Weixun. AN EXACT SOLUTION OF CRACK PROBLEMS IN PIEZOELECTRIC MATERIALS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(1): 51-58.

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