Effect of electrostatic tractions on the fracture behavior of a piezoelectric material under mechanical and/or electric loading

The pre-cracked parallel-plate capacitor model is further developed to study analytically the effect of electrostatic tractions induced by Maxwell stress and piezoelectricity on the fracture behavior of a piezoelectric material under mechanical and/or electric loading. The results indicate that the Maxwell stress and piezoelectricity induced tractions are independent and dependent on the direction of an applied electric field, respectively. Hysteresis loops in the curves of crack opening (or closing) versus applied mechanical strain and in the curves of crack opening (or closing) versus applied electric field occur under positive fields much easier than negative fields due to the piezoelectricity. Because of the potential presence of hysteresis loops, the fracture criterion must be composed of two parts: the energy release rate must exceed a critical value and the mechanical load must be higher than the critical value for crack opening.