Stochastic analysis on crack path of polycrystalline ceramics based on the difference between the released energies in crack propagation

The crack path of polycrystalline ceramics has been theoretically analysed with a stochastic model based on the difference between the released energies in intergranular and transgranular crack propagation. Assuming that the path with the lowest released energy should be realized as the actual crack path, the expected values of the fraction of transgranular fracture on fracture surface and the fracture toughness of polycrystalline ceramics were formulated as functions of grain size and the critical energy release rates of grain and grain boundary. By comparison between the theory and the experimental results it was shown that the stochastic model proposed here expressed the change of the crack path and the fracture toughness of polycrystalline Al2O3, relative to grain size.