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 sigma(zz)-c(2)D(z) has the classical singularity r(-1/2) while the extended stress sigma(zz)+c(4)D(z) possesses the well-known oscillating singularity r(-1/2 +/- ie) or the non-oscillating singularity r(-1/2 +/-kappa), where sigma(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., epsilon-group with non-zero value of epsilon and kappa-group with non-zero value of kappa. Two new extended stress intensity factors K-11 and K-12 corresponding, respectively, to the extended stresses sigma(zz)-c(2)D(z) sigma(zz)+c(4)D(z) are defined for interface cracks in three-dimensional transversely isotropic piezoelectric bimaterials. The material related constants including, E or K for 15 bimaterials are calculated. The extended intensity factor of a penny-shaped interface crack is presented as an application of the proposed method. (C) 2007 Elsevier Ltd. All rights reserved.