Electro-mechanical yielding for a limited permeable crack in an interlayer between piezoelectric materials

A plane problem for a limited permeable crack in a thin interlayer between two piezoelectric semi-infinite spaces with the same physico-mechanical properties is considered. It is assumed that the mechanical and electrical yielding occurs at the crack continuations in the interlayer. We model these crack continuations as zones with constant cohesive normal stress and electrical displacements. It is also assumed that, outside the crack with its continuations, the semi-infinite spaces are bonded. In this way, a problem for a crack in a homogeneous piezoelectric material with unknown pre-fracture zone lengths and electrical displacements in the crack region is formulated. This problem is solved analytically. The unknown pre-fracture zone lengths are found from the conditions of stress and electrical displacement finiteness at the tips of these zones. The electrical displacement in the crack region is found from the condition of the limited permeability of the crack. The crack opening and the electrical potential jump at the initial crack tip as well as the energy release rate are found in analytical form. The dependence of these values on the applied electro-mechanical loading at infinity is investigated.