Solution method of interface cracks in three-dimensional transversely isotropic piezoelectric bimaterials

An analysis method is proposed for planar interface cracks of arbitrary shape in three-dimensional transversely isotropic piezoelectric bimaterials based on the analogy between the hyper-singular boundary integral–differential equations for interface cracks in purely elastic media and those in piezoelectric media with the electrically impermeable crack condition. The poling direction is along the z-axis of the Cartesian coordinate system and perpendicular to the interface. The singular indexes and the singular behaviors of the near crack-tip fields are studied. The results show that the extended stress σzz−c2Dz has the classical singularity r−1/2, while the extended stress σzz+c4Dz possesses the well-known oscillating singularity r−1/2±iε or the non-oscillating singularity r−1/2±κ, where σzz and Dz are, respectively, the stress and electric displacement components, and c2 and c4 are two material constants. The three-dimensional transversely isotropic piezoelectric bimaterials are categorized into two groups, i.e., ε-group with non-zero value of ε and κ-group with non-zero value of κ. Two new extended stress intensity factors KI1 and KI2 corresponding, respectively, to the extended stresses σzz−c2Dz and σzz+c4Dz are defined for interface cracks in three-dimensional transversely isotropic piezoelectric bimaterials. The material related constants including ε or κ for 15 bimaterials are calculated. The extended intensity factor of a penny-shaped interface crack is presented as an application of the proposed method.