Internal residual stresses in elastically homogeneous solids: II. Stress fluctuations near a crack tip and effective energy release rate

We consider a linearly elastic composite medium which consists of an homogeneous matrix containing a crack and a homogeneous and statistically uniform random set of ellipsoidal inclusions; the elastic properties of the matrix and the inclusions are the same, but the stress-free strains ¯uctuate. We obtain the estimation of both the statistical average and the conditional average of stress intensity factors. The relations for the second statistical moments of stresses in the vicinity of the crack tip, averaged over the ensemble realization, are proposed as well. A method for construction of the e€ective strength surface of matrix composites, according to the properties of their components is developed. The expression for e€ective energy release rate is also derived. The fracture probabilities of separate components are calculated