Fracture criteria for piezoelectric materials containing multiple cracks

Abstract

This study presents a failure criteria for multiple permeable cracks embedded in an infinite piezoelectric solid, which is separately subjected to a set of uniform-electromechanical loads. Based on the equivalent inclusion method, permeable cracks are initially treated as elliptical inclusions with fictitious eigenstrains and eigenelectric fields, in which their elastic moduli and piezoelectric coefficients are taken as zero while dielectric constants remain finite. Consequently the interaction energy between the cracks and the applied electromechanical loading can be simply expressed in terms of the applied electromechanical loads and the equivalent eigenfields. With this energy function, the energy release rates and the critical loads for fracture are separately acquired in a closed form for a simple tension, in-plane and out-of-plane shears, as well as normal electric flux density applied. The closed forms for energy release rate and critical electromechanical loading reveal that these forms are a function of the aspect ratio of the permeable elliptical cracks, type of the electromechanical loading, volume fraction of the cracks, and piezoelectric properties. Analysis results indicate that the different mechanical loading propagates the expansion of the elliptical cracks. Meanwhile, the distinct electric fields can retard the dilation of the elliptical cracks, particularly for an in-plane electric field incited perpendicularly with cracked faces.