Bond zone model for a conductive crack at the interface of piezoelectric materials under anti-plane mechanical and in-plane electric loadings

An electrically conductive crack between two semi-infinite piezoelectric spaces under the action of anti-plane mechanical loading and in-plane electrical field parallel to the crack faces is considered. An exact analytical solution of this problem is found and the oscillating singularity is revealed at the crack tips. A new model, which is free from oscillation, is also developed for a conductive interface crack. This model is based on the introduction of a mechanically bonded zone at the conducting crack tip characterizing by zero crack faces displacement jump. The most reasonable length of this zone is found from the condition of a smooth crack closing. The validity confirmation of the bond zone model is given by means of description of conductive crack formation process. Some recommendations concerning the use of suggested model for the study of finite and infinite sized bodies with electrically conducting interface cracks are formulated.