Asymmetric impermeable wedge crack in a piezoelectric material under anti-plane deformation

A problem of an inclined wedge crack in transverse isotropic piezoelectric material under electromechanical loading is analyzed. A single anti-plane mechanical and in-plane electrical loads are applied at a point either on wedge surface or on crack surface. By using Mellin transform, the problem based on the generalized displacement and stress vector is formulated. The derived equation is solved employing the Wiener-Hopf technique, from which the intensity factors and the energy release rates are obtained in closed forms. With material properties of PZT-5H, the intensity factors and energy release rate for wedge and crack surface loadings are calculated numerically and investigated. The closed form solutions can be used as a Green’s function for arbitrarily coupled anti-plane mechanical and inplane electrical loading cases.