Phase field fracture modeling of transversely isotropic piezoelectric material with anisotropic fracture toughness

Abstract

Fracture analysis of piezoelectric devices and structures is of great importance in science and engineering. In the present work, a new phase field fracture model in the context of transversely isotropic electro-elasticity is developed by means of the variational method. A structural tensor is introduced in the crack surface density function to quantify the anisotropy in fracture toughness. To characterize the asymmetric fracture behavior of piezoelectric solid, the contribution of the mechanical energy is employed to drive the crack propagation. An efficient and robust staggered scheme is adopted to deal with the corresponding fracture problems, which is implemented in the commercial finite element software Abaqus. Numerical simulations are carried out to investigate the effect of the anisotropic fracture toughness, poling direction and external electrical field on the fracture behavior of the piezoelectric materials. The anisotropic fracture toughness would significantly affect the crack path and fracture load. With the help of the nonlinear regression method, a phenomenological model is proposed to predict the fracture load. The present researches may benefit the safety assessment of piezoelectric materials in practical applications.