The energy release rate and the J - integral of an electrically insulated crack in a piezoelectric material

In this work, we examine the energy release rate and the J-integral of an electrically insulated crack in a piezoelectric solid under remotely uniform electrical/mechanical loads. We model the crack as a slender elliptical flaw to take into account the electric field inside the crack and obtain the exact and explicit solution. The analytic results show that the energy release rate, in general, does not equal to the J-integral and that the J-integral is path-dependent due to the electric traction on the crack faces. However, the energy release rate is equal to the sum of the J-integral along an infinitesimal circle around the crack tip and the average driving force produced by the electric field on the entire crack surface. Under combined mechanical and electrical loading, the energy release rate may be positive or negative, depending on the level of the mechanical load and the strength of the electric field as well. The effect of electric field on the fracture behavior is mechanical load-dependent, which has been observed in experiments.