Electrical Nonlinearity in Fracture of Piezoelectric Ceramics

The structural reliability of piezoelectric ceramics in smart sensors and actuators is hindered by the lack of an appropriate fracture mechanics model. Recent experimental observations of their cracking behavior under combined electrical and mechanical loads contradict predictions made by the linear theory. Evidently, a fracture criterion suitable for piezoelectrics must account for material nonlinearity. Because these materials are typically mechanically brittle, we expect electrical ductility to be the dominant effect. By adopting a multiscale viewpoint, we identify a region of electrical nonlinearity near the crack tip in which the mechanical response of the material remains linear. The equilibrium equations for a fully anisotropic solid have closed-form solutions if the material’s behavior is assumed to be entirely linear outside of the plane of the crack. This approximation is equivalent to Dugdale’s model of the plastic zone in cracked metal sheets. The energy release rate derived using this load for specimens with cracks perpendicular to the poling direction. A remarkable feature of our model is that the energy release rate is strictly independent of the form of the nonlinear electrical constitutive relation. In fact, the material may even experience domain switching in the Dugdale zone without affecting the fracture criterion determined by our formulation.