Fracture analysis of piezoelectric materials with defects using energy density theory

The objective of this paper is to extend a failure criterion, which is based on the energy density factor, for an elliptical cavity or a line crack embedded in an infinite piezoelectric solids, subjected to a combined in-plane electrical and mechanical loading. In the present analysis, the exact electric boundary conditions are applied at the rim of the cavity/ crack. This is to avoid the common assumption of impermeable or permeable crack, which does not reflect the practical situation. The direction of crack initiation or subsequent post-failure, and the critical loads for fracture, can be predicted using the total energy density factor, S. This factor is a function of the aspect ratio of the elliptical cavity, the electromechanical loading, core region outside the crack tip, permittivity of vacuum and material constants. The results obtained agree with the experimental observation, i.e. a positive electric field enhances crack growth while a negative electric field impedes crack growth. Moreover, the results indicate that the critical fracture loads are under-estimated by the assumption of impermeable crack and over-estimated when the crack is assumed to be permeable for E₂^app > 0, where E₂^app is the applied electric field. However, the fracture loads are over-estimated by the assumption of impermeable crack and under-estimated when the crack is assumed to be permeable for E₂^app < 0. The energy density criterion has the advantage of possessing the capability to implement the exact electric boundary conditions. This is due to the fact that the criterion can link the behavior of a crack to that of an elliptical cavity by consistent application of this criterion to a thin layer near the cavity/crack boundary.