Cracks with surface charge in poled ferroelectrics

A solution is developed for a prismatic elliptical cavity inserted into an infinite, poled, ferroelectric body subjected to uniform mechanical and electrical loading at infinity consistent with planar fields. The surface of the cavity is also permitted to attract free charge in such a way that the electric field in the cavity remains uniform. The solution is used to develop the mechanical and electrical intensity factors at the tip of the crack obtained by allowing the minor axis of the ellipse to become very small. The energy release rate upon propagation of the crack is also derived. It is found that both the polarization of the ferroelectric and the free charge on the surface of the crack can have a very substantial effect on the magnitudes of both the intensity factors and the energy release rate. The reality of remanent polarization in common ferroelectrics means that it cannot be neglected in the fracture mechanics of such materials. Furthermore, it is likely that remanent polarization leads to free charge being attracted to crack surfaces, so consideration of the latter would also seem to be of importance in the fracture mechanics of ferroelectrics.