Fracture analysis of piezoelectric materials with defects using energy density theory

The objective of this paper is to extend a failure criterion, which is base d on the energy density factor, for an elliptical cavity or a line crack em bedded in an infinite piezoelectric solids, subjected to a combined in-plan e electrical and mechanical loading. In the present analysis, the exact ele ctric 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 pr edicted using the total energy density factor, S. This factor is a function of the aspect ratio of the elliptical cavity, the electromechanical loadin g, core region outside the crack tip, permittivity of vacuum and material c onstants. 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 critic al fracture loads are under-estimated by the assumption of impermeable crac k and over-estimated when the crack is assumed to be permeable for E-2(app) > 0, where E-2(app) is the applied electric field. However, the fracture l oads are over-estimated by the assumption of impermeable crack and under-es timated when the crack is assumed to be permeable for E-2(app) < 0. The ene rgy density criterion has the advantage of possessing the capability to imp lement 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 ca vity by consistent application of this criterion to a thin layer near the c avity/crack boundary. (C) 2001 Elsevier Science Ltd. All rights reserved.