Interaction of a piezoelectric screw dislocation with an insulating crack

摘要

The electrical and mechanical fields induced by a piezoelectric screw dislocation near an electrically insulating elliptical cavity in a piezoelectric material are derived through the image dislocation approach by considering the electric field inside the cavity. When the cavity is reduced to a crack, three outcomes are possible. The three outcomes correspond to three different electrical boundary conditions along the crack faces, depending on the alpha/beta ratio, where alpha is the ratio of the minor semiaxis to the major semiaxis of the ellipse and beta is the ratio of the dielectric constant of the cavity to the effective dielectric constant of the piezoelectric material. The crack is electrically impermeable when alpha/beta --> infinity; the crack becomes electrically permeable as alpha/beta --> 0. Since the minimum of the dielectric constant has a finite non-zero value and a real crack also has a non-zero width, the alpha/beta ratio will generally have a finite non-zero value, resulting in a semi-impermeable crack. Furthermore, the difference in the electric boundary conditions leads to great differences in the image force acting on the dislocation, in the intensity factors and in the J integral for crack propagation induced by the dislocation. [References: 22]