On a piezoelectric material containing a permeable elliptical crack

This study presents the failure criteria for a permeable crack embedded in an in®nite piezoelectric solid, which is separately subjected to a set of uniform electromechanical loads. Based on the equivalent inclusion method, a permeable crack is treated as an elliptical inclusion where its elastic moduli and piezoelectric constants are considered to be zero, while the dielectric constants remain ®nite. In addition, the interaction between the crack and the applied electromechanical loading is examined by introducing the change of total potential energy function. With this energy function, the energy release rates and the critical loads for fracture are acquired separately in a closed form for a simple tension, in-plane and out-plane shears, and normal electric ¯ux density applied. The closed forms for energy release rate and critical electromechanical loading reveal that they are a function of the aspect ratio of the elliptical crack, the type of the electromechanical loading, and the piezoelectric properties. Moreover, analysis results indicate that the distinct electric ®elds can retard the dilation of the elliptical crack, particularly for an in-plane electric ®eld incited in perpendicular to the crack face