Fracture model and estimation of probability distribution of fracture toughness for polycrystalline ceramics

In this paper, a fracture model for polycrystalline ceramics is proposed. In the model, it is assumed that fracture toughness along a crack front has a distribution and that the fracture toughness for the macro-material is the mean value of those. It follows from the model that the probability distribution of fracture toughness for polycrystalline ceramics with a crack of the same configuration can be approximated by a normal distribution and that the coefficient of variation of fracture toughness for polycrystalline ceramics with a crack of the similar figure is inversely proportional to the root of the crack front length. In order to examine the theoretical results, indentation fracture tests of alumina ceramics are carried out. The experimental results agree with the theoretical results.