A DIELECTRIC BREAKDOWN MODEL FOR AN INTERFACE CRACK IN A PIEZOELECTRIC BIMATERIAL

摘要

A mode III electrically conductive crack between two piezoelectric semi-infinite spaces under the action of anti-plane mechanical loading and in-plane electrical field parallel to the crack faces is considered. All electromechanical quantities are presented as piecewise analytic vector functions. The problem is solved analytically, revealing an oscillating singularity at the crack tips in the stress and electric fields. To eliminate the electric field singularity the dielectric breakdown (DB) model is applied. According to this model, the electric field along some zone of the crack continuation is initially assumed to be equal to the electric breakdown strength and the length of this zone remains still unknown. A nonhomogeneous combined Dirichlet--Riemann boundary value problem for the crack with DB zone is formulated. An exact analytical solution of this problem is presented and the DB zone length is found from the electric field finiteness at the end point of this zone. The simple transcendental equation with respect to DB zone length is solved numerically and all required electromechanical quantities are found in closed analytical form. The DB model for a crack in a homogeneous material is also considered and compared with known results. looseness=-1.