Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic

Abstract

Structural reliability concerns of various electromechanical devices call for a better understanding of the mechanisms of fracture in piezoelectric ceramics subjected to combined mechanical and electrical loading. For these materials, due to unexplained discrepancies between theory and experiments, even the basic criterion of fracture remains a point of controversy. A viewpoint adopted in this paper is to model piezoelectric ceramics as a class of mechanically brittle and electrically ductile solids. As a first step toward understanding the effects of electric yielding, a strip saturation model is developed for a finite crack perpendicular or parallel to the poling axis of an infinite poled piezoelectric ceramics medium with electrical polarization reaching a saturation limit along a line segment in front of the crack. This model may be considered as a generalization of the classical Dugdale model for plastic yielding near cracks in thin metal sheets. The essential features of the strip saturation model are analyzed via a simplified electroelasticity formulation. Two energy release rates emerge from this analysis. An “apparent” or global energy release rate appears when evaluating J-integral along a contour surrounding both the electrical yielding strip and the crack tip. Under small scale yielding conditions, this energy release rate is equal to that of a linear piezoelectric crack without electrical yielding. A “local” energy release rate is obtained by evaluating J along an infinitesimal contour near the crack tip. The local energy release rate gives predictions which seem to be in broad agreement with experimental observations. It is also interesting that the local energy release rate is independent of the strength and size of electrical yielding.