Closed form solutions for all three modes of fracture for an infinite piezoelectric medium containing a center crack subjected to a combined mechanical and electrical loading were obtained. The explicit mechanical and electrical fields near the crack tip were derived, from which the strain energy release rate and the total potential energy release rate were obtained by using the crack closure integral. The suitability in using the stress intensity factor, the total energy release rate, or the mechanical strain energy release rate as the fracture criterion was discussed.

The Vickers indentation technique was used to determine the apparent fracture toughness of PZT-4 piezoceramic under the influence of electric fields. The toughness was measured in terms of the mechanical strain energy release rate. Using the analytical mechanical strain energy release rate for an infinite piezoelectric medium with a center crack and far field in-plane mechanical and electrical loadings, the mechanical strain energy release rate was obtained for Vickers indentation. The effect of the electric field was included. The proposed formula was evaluated with the experimental results. It was found that the fracture toughness depended on the indentation force. Vickers indentation tests were also performed on depoled PZT-4 specimens; these test results indicated that the fracture toughness of depoled PZT-4 was also dependent on the indentation force. To eliminate the indentation force dependence, a modified stress intensity formula based on Vickers indentation was proposed.

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