It was pointed out that fluctuating microstructural stresses arose because of elastic anisotropy and anisotropic thermal expansion of the constituent crystals. Due to the random nature of the crystal arrangement, the internal stresses had to be treated as random field quantities. A statistical method was presented here which gave the probability distribution of the internal stresses directly. It was noted that grain boundary damage occurred if a certain invariant of the random local stress tensor attained a critical value. This value depended upon the local grain facet size; which was also a random quantity. Monte Carlo simulations were used to evaluate the resultant convolution integral. It was found that the statistical method yielded results that were similar to those of deterministic theories, but the numerical calculations were much faster.

W.S.Kreher: Computational Materials Science, 1996, 7[1-2], 147-53