Fracture mechanics for a mode III crack in a piezoelectric material

The mechanical and electric fields in a piezoelectric material around an elliptical cylinder cavity and the electric field within the cavity are formulated by complex potentials. The electric field inside the cavity is uniform and varies with the shape of the ellipse. When the cavity is reduced to a slit crack, the electric field strength inside the cavity is inversely proportional to the permittivity of the cavity. When the ratio of the short semi-axis of the ellipse over the long semi-axis is much smaller than the ratio of the permittivity of the cavity over that of the material, it can be used as the electric boundary condition that the electric field strength along the crack faces equals the remote one. In this case, the energy release rate for crack propagation depends only on the applied stress and can be represented in terms of the stress intensity factor as in a pure elastic body without coupling with the electric field. Electric loading may promote or retard crack propagation depending on whether it increases or decreases the applied stress.