Dielectric Breakdown Model for an Electrically Semi-Permeable Penny-Shaped Crack in Three-Dimensional Piezoelectric Media

The dielectric breakdown (DB) model for a penny-shaped crack under a semi-permeable boundary condition in a three-dimensional piezoelectric medium is studied. An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity, and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack. The effect of electric boundary conditions on crack faces is discussed on the basis of DB model. By comparing the DB model with the polarization saturation (PS) model for different piezoelectric materials, some interesting phenomena related to the electric yielding zone and local J-integral are observed.