3D FRACTURE MECHANICS FOR A MODE I CRACK IN PIEZOELECTRIC MEDIA

This paper deals with mode I fracture problems for a planar crack in an infinite piezoelectric solid subjected to electric and tension loading. The finite-part integral concept is used to prove rigidly hypersingular integral equations for the crack by using three-dimensional linear piezoelectricity theory. Investigations on the singularities and the singular stress and electric displacement fields in the vicinity of the crack are made by the dominant-part analysis of the two-dimensional hypersingular integrals. Thereafter the stress and electric displacement intensity factor K-fields and the energy release rate G are exactly obtained by the definitions similar to those of elasticity. Then, a numerical method for the solution of the hypersingular integral equations is developed, in which the displacement and electric potential differences across the crack surfaces are approximated with a product of basic density functions and polynomials. Numerical solutions of several typical planar cracks are obtained with high accuracy.