Fracture criteria for piezoelectric materials were investigated. Mode I and mixed mode fracture tests were performed on PZT-4 piezoelectric ceramics to verify the validity of the mechanical strain energy release rate as a fracture criterion. Experimental results indicated that crack extension could be aided or impeded by an electric field, depending on the field direction. Further, the direction of crack extension was studied. A crack closure method, together with finite element analysis, was introduced to calculate the mechanical strain energy release rate. The maximum mechanical strain energy release rate was used to predict fracture loads under combined mechanical and electrical loads. It was found that the mechanical strain energy release rate criterion is superior to other fracture criteria and predicts fracture loads fairly accurately.

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A noncontact, fast, accurate, low-cost, broad-range, full-field, easy-to-implement three-dimensional (3D) shape measurement technique is presented. The technique is based on a generalized fringe projection profilometry setup that allows each system component to be arbitrarily positioned. It employs random phase-shifting, multifrequency projection fringes, ultrafast direct phase unwrapping, and inverse self-calibration schemes to perform 3D shape determination with enhanced accuracy in a fast manner. The relative measurement accuracy can reach 1/10,000 or higher, and the acquisition speed is faster than two 3D views per second. The validity and practicability of the proposed technique have been verified by experiments. Because of its superior capability, the proposed 3D shape measurement technique is suitable for numerous applications in a variety of fields.

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