Fracture mechanics of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelect rics or on the interfaces between two dissimilar piezoelectric materials ba sed on the continuity of normal electric displacement and electric potentia l across the crack faces. The explicit analytic solutions are obtained for a single crack in an infinite piezoelectric or on the interface of piezoele ctric bimaterials. For homogeneous materials it is found that the normal el ectric displacement D-2, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the cr ack slit, the perturbed electric fields induced by the crack are also const ant and not affected by the applied electric displacement fields. For bimat erials, generally speaking, an interface crack exhibits oscillatory behavio r and the normal electric displacement D-2 is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D-2 is also constant along the crack faces and the electric field E-2 has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homog eneous materials and bimaterials having certain symmetry. Both the crack fr ont parallel to the poling axis and perpendicular to the poling axis are di scussed. It is revealed that the energy release rates are always positive f or stable materials and the applied electric displacements have no contribu tion to the energy release rates.