Analysis of strip electric saturation model of crack problem in piezoelectric material

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491±510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement ®eld is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric ®eld and increases linearly with the increase of the negative applied electric ®eld. For a crack parallel to the poling axis, the failure stress is not e€ected by the parallel applied electric ®eld. In order to analyse the existed experimental results, the stress ®elds ahead of the tip of an elliptic notch in an in®nite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under di€erent remote electric displacement ®elds. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement ®eld depending on the ®eld direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475±1480