Interaction between an electrically permeable crack and the imperfect interface in a functionally graded piezoelectric sensor

For a cracked piezoelectric sensor with an imperfect interface, the interaction between the crack and the imperfect interface is a problem of practical significance. Such a problem is investigated by the method of singular integral equation in the present work. The interface is assumed to be mechanically compliant and weakly conducting. Parametric studies on stress intensity factors (SIFs) indicate that when the crack is near to the interface SIFs increase as the interface change from perfection to imperfection, and the mechanical imperfection generally has more remarkable influence on SIFs than the dielectric imperfection does. For a crack in the piezoelectric layer and near to the interface, the SIF gets less sensitive to the variation of the substrate thickness if the interface becomes imperfect. The interfacial imperfection has less influence on the fracture behavior of a stiffer piezoelectric layer.