Piezoelectric Boundary Element Crack Closure Calculation of 3D Strain Energy Release Rates

Abstract

Piezoceramic materials are very brittle and susceptible to fracture, especially under the severe loading conditions which may occur in service as sensors and actuators in smart structures. The presence of these cracks alters the mechanical and electrical fields inside the body, which can cause failure from a catastrophic fracture event or the cumulative effects of cyclic fatigue. A three-dimensional boundary element program is developed to evaluate the effect of flaws on piezoelectric materials. The program is based on the linear governing equations of piezoelectricity and relies on a numerically evaluated Green's function for solution. Mode I fracture is examined, combining the linear boundary element solution with the modified crack closure integral to determine strain, rather than total, energy release rates since this is the appropriate predictor for crack growth in piezoelectric materials. Solutions for a two-dimensional slit crack and three-dimensional penny-shaped and elliptical cracks are presented. These solutions are developed using the insulated crack face electrical boundary condition. The boundary element method combined with modified crack closure is shown to accurately calculate strain energy release rates for linear piezoelectric fracture.