Interaction of a piezoelectric screw dislocation with an insulating crack

Author： Zhang Tong-Yi Wang Tian-Hong Zhao Ming-Hao

ISSN： 0141-8610

Source： Philosophical Magazine. A. Physics of Condensed Matter. Defects and Mechanical Properties, Vol.82, Iss.15, 2002-10, pp. : 2805-2824

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