A piezoelectric material with a periodic distribution of slant mode-III cracks

By using the dislocation layer modelling, electroelastic analysis of a periodic distribution of slant cracks in a piezoelectric material is made under anti-plane shear and in-plane electric loading. The cracks are assumed to be either electrically permeable or impermeable. With the aid of the fundamental solution for a screw dislocation, the problem is reduced to solving a singular integral equation. In particular, closed-form solutions of electroelastic field are derived for both coplanar and parallel periodic cracks, respectively. By using a collocation technique and the quadrature formula for slant cracks, the resulting singular integral equation is solved approximately by a system of algebraic equations, and the field intensity factors as well as mechanical strain energy release rate are obtained. Numerical results show the effects of electric loading and geometric parameters on the normalized mechanical strain energy release rate.