Mode III analysis of a piezoelectric rectangular plane weakened by multiple cracks and cavities

Abstract

This study presents an analytical model for a piezoelectric rectangular plane weakened by multiple cracks and cavities, under in-plane electric displacement and anti-plane shear stress. The defects are considered either electrically permeable or impermeable. First, the piezoelectric rectangular plane is weakened by a Volterra-type screw dislocation. The electric and stress displacement fields of the domain under consideration are determined using finite Fourier transform. Then, the problem is reduced into a set of Cauchy integral equations in the piezoelectric rectangular plane using the distributed dislocation approach. The solution to these integral equations determines electric displacement and stress intensity factors and hoop stress around cavities in the piezoelectric rectangular plane. Also, the boundary of the plastic zone is found using the stress field in the vicinity of crack tips and the Von Mises yield criterion. Finally, multiple numerical results are provided to illustrate the capability of the dislocation method in handling different cases of crack and cavity configurations and arrangements.