Interaction of a piezoelectric screw dislocation with an insulating crack

Abstract

Abstract 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 α/β; ratio, where α; is the ratio of the minor semiaxis to the major semiaxis of the ellipse and β; 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 α/β; → ∞ the crack becomes electrically permeable as α/β; → 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 α/β; 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.