Statistical comparison of two fracture criteria

Abstract

Two fracture criteria are compared within the stochastic model of brittle fracture of a component with the random ensemble of crack-like defects. The component comprises a random array of internal defects, represented by equivalent cracks. Under assumption of stochastic independence of defects and Poisson distribution of defects population the probability of fracture is determined. This probability is dependent on local fracture criterion applied to an arbitrary crack. The maximum normal stress and energy release rate criteria were applied to check as to whether they may yield significantly different prediction of above probability. Computer calculations show that with the increase of defects density the difference in predictions of above two criteria became unsignificant and for both limiting fracture-stress curves converges to maximum stress theory. For low densities energy release rate criterion yields more conservative predictions in almost all range of λ. The limiting fracture-stress curves deviate in this case from both the maximum stress and von Mises theories.