Statistical analysis of fracture in graphite

Abstract

A statistical model is proposed to study the fracture of graphite. This model, based on a more general one proposed by She et al., uses a local fracture criterion for a microcrack, a distribution function for microcracks and the weakest link principle to predict failure probability as a function of applied loading and distribution of microcracks. The model considers the effect of the three-dimensional stress state and therefore gives a general representation of both the effects of complex loading and microcrack distribution. The inputs to the model can be determined by either studying the microstructural features of the graphite or by choosing inputs to make the model prediction fit a set of experimental results. The latter method is used to apply the model to failure results of Rose and Tucker. One set of results is used to calibrate the model which is then applied to predict the failure behavior of a second set of experimental results. Finally, the effect of the various input variables on failure probability is studied first by considering a graphical representative of failure probability as a function of input variables and second by writing the equations in terms of nondimensional variables.