Multiscale energy release rates in fracture of piezoelectric ceramics

The reliable use of piezoelectric ceramics as actuators in smart structures hinges on a fundamental understanding of the fracture process in these materials. However, despite the success of fracture mechanics theories in explaining the cracking behavior of a wide range of engineering materials, the extension of these accepted criteria to piezoelectrics fails to predict even qualitatively their response to combined electrical and mechanical loads. A new fracture criterion is presented here, in which a multiscale point of view is adopted in order to account for a zone of combined mechanical brittleness and electrical ductility near the crack tip. As a starting point for the investigations, we assume that the region of electrical nonlinearity is confined to a line segment ahead of the crack, analogous to the Dugdale zone of plasticity in metals. This mathematical simplification represents the physical situation in which a distribution of excess electric dipoles is aligned on a finite segment in an otherwise linear piezoelectric solid. By applying this model to both insulated and conducting cracks subjected to far-field loading, we obtain local-scale energy release rates whose dependence on applied tractions and electric fields agrees with the trends observed experimentally. One important feature of the analytical expressions for crack driving force is that they are independent of the strength and size of the nonlinear zone.