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

Abstract

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 σ zz − c 2 D z has the classical singularity r −1/2, while the extended stress σ zz + c 4 D z possesses the well-known oscillating singularity r −1/2±i ε or the non-oscillating singularity r −1/2± κ , where σ zz and D z are, respectively, the stress and electric displacement components, and c 2 and c 4 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 K I1 and K I2 corresponding, respectively, to the extended stresses σ zz − c 2 D z and σ zz + c 4 D z 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.