Boundary integrate equation method for semi-permeable vertical planar cracks in 3D piezoelectric media

In this paper, the boundary integral equation method is developed to study a vertical planar crack under the electrically semi-permeable boundary condition. The crack face is parallel to the poling direction and normal to the plane of isotropy in three-dimensional (3D) transversely isotropic piezoelectric media. The result shows that the singularity order is still the ordinary r−1/2 at the crack tip. The mode I stress intensity factor is related only to the displacement discontinuity or the mechanical loading in the normal direction of the crack plane, whilst the other field intensity factors are coupled together by other extended displacement discontinuities. When the crack is extended infinitely in the y-direction, the problem is reduced to a two-dimensional (2D) one, and the corresponding coupling behavior is simplified.