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For recent decades, due to the intrinsic electromechanical coupling, piezoelectric ceramics have been used widely in the modern aeronautical and astronautic engineering, the medical apparatus and the instruments, etc. However, their brittleness might result in damage and failure. Therefore, it is very important theoretically and practically for fracture analysis, reliability design and lifetime prediction of piezoelectric ceramics to investigate the fracture mechanism. On the basis of linear piezoelectric fracture mechanics, some solutions were obtained by Pak (1990, 1992), Sosa and Pak (1990), Sosa (1991, 1992), Suo et al (1992), Suo (1993) and others, but they contradict the piezoelectric fracture experiments (Park and Sun, 1995; Heyer et al, 1998). The linear piezoelectric fracture mechanics predicted that the stress intensity factors were independent of the applied electric field, but the experimental results (Park and Sun, 1995; Heyer et al, 1998) showed that an existing electric field might impede or accelerate crack propagation, which was related to the applied electric field direction. Regarding piezoelectric ceramics as a class of mechanically brittle and electrically ductile solids, Gao et al (1997) put forward a strip saturation model analogous with the classical Dugdale model for plastic yielding, in which electrical displacement is assumed to yield when electric field is up to its linear limit. Yang and Zhu (1998) thought that piezoelectric nonlinearity comes from domain switching, so they proposed a small-scale domain-switching model to explain the toughening mechanism. Fulton and Gao (2001) proposed an electrical nonlinearity model based on piezoelectric microstructure. They simulated polarization switching and saturation in ferroelectrics by using a collection of discrete electric dipoles superimposed on a medium satisfying the linear piezoelectric constitutive law, and then derived a local crack driving force which generates a qualitative match to experimental observations. Based on the field limiting space charge model, Zhang et al (2003) proposed a charge-free zone model, and estimated the electric field at the tip of an electrically conductive crack according to the electric field intensity factor. Assuming that the electric field in a strip ahead of the crack tip is equal to the dielectric breakdown strength, Zhang et al (2005) developed a strip dielectric breakdown model similar to the strip saturation model. 5

Analysis of Mechanical and Electrical Damages in Piezoelectric Ceramics