A finite element method combined with three-dimensional anisotropic piezoelectric continuum damage mechanics is presented to simulate quasi-static crack propagation behavior in piezoelectric ceramics in this paper. In this method, the three-dimensional anisotropic piezoelectric damage constitutive model is utilized for characterizing the effects of mechanical and electrical damages on the fields near the crack tip, the combined-damage from the dominant mechanical and electrical damage components is regarded as the fracture criterion, and the gradient of combined-damage is assumed to control crack growth direction. A set of numerical simulations of the midspan crack propagation in a three-point bending PZT-4 beam are performed in various loading conditions. After the numerical results are validated by comparison with the corresponding experimental ones, the effects of mechanical and electrical loads on the cracking be havior are respectively evaluated. It is found from the obtained results that mechanical and electrical loads influence on the damage fields in the vicinity of the crack-tip, as well as the crack growth rate, in a significant way. With the increment in mechanical loading, the crack growth rate obviously increases. This means that positive and negative electric fields enhance and inhibit crack propagation, respectively.

Due to external loads, damage extension forces will drive mechanical and electrical damages to evolve in piezoelectric materials from the viewpoint of continuum damage mechanics, so it is important for understanding piezoelectric fracture mechanism and estimating the utilizing life and safety of a piezoelectric device to study the damage extension forces. Based on the static piezoelectric damage constitutive model established in our previously published papers, general expressions of the damage extension forces are given. The finite element method and the iterative procedure are utilized to calculate the extension forces at crack-tips in the samples for the experiments of Park and Sun's, and then the linear and nonlinear fracture criteria are presented. It is revealed from the list of the normalized mean square deviations that the nonlinear criterion is better.