The electrical and mechanical fields induced by a piezoelectric screw dislocation near to an electrically insulating elliptical cavity in a piezoelectric material were derived using the image dislocation approach by considering the electric field inside the cavity. When the cavity was reduced to a crack, three outcomes were possible. The three outcomes correspond to three different electrical boundary conditions along the crack faces, depending upon the α/β ratio, where α was the ratio of the minor semi-axis to the major semi-axis of the ellipse and β was the ratio of the dielectric constant of the cavity to the effective dielectric constant of the piezoelectric material. The crack was electrically impermeable when α/β → ∞; the crack became electrically permeable as α/β → 0. Since the minimum of the dielectric constant had a finite non-zero value and a real crack also had a non-zero width, the α/β ratio will generally had a finite non-zero value, resulting in

a semi-impermeable crack. Furthermore, the difference in the electric boundary conditions led 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.

Interaction of a Piezoelectric Screw Dislocation with an Insulating Crack. T.Y.Zhang, T.H.Wang, M.H.Zhao: Philosophical Magazine A, 2002, 82[15], 2805-24