Electrical fracture toughness for a conducting crack in ferroelectric ceramics

Conducting cracks in ferroelectric ceramics under purely electrical loading are analyzed to investigate the effects of electric fields on fracture behavior. The asymptotic problem of conducting cracks in a mono-domain ferroelectric material as well as in a poly-domain ferroelectric material is considered and the relation between the crack tip stress intensity factor and the applied intensity factor of electric field under small scale conditions is investigated. In order to evaluate the crack tip stress intensity factors due to the domain switching, the shape of the domain switching zone attending the crack tip must be determined. The evaluation of the shape is carried out based on the nonlinear domain switching model. It is shown that the switching zone boundary and the crack tip stress intensity factors due to the switching depend strongly on the angle of the polarization vector and the ratio of the coercive electric field to the yield electric field. The electrical fracture toughness of unpoled poly-domain ferroelectrics is examined. Employing a Reuss type approximation, the crack tip stress intensity factors for an unpoled poly-domain material are obtained. The ratio of the critical electrical energy release rate to the critical mechanical energy release rate is obtained. (C) 2003 Elsevier Ltd. All rights reserved.