Statistical Properties of Residual Stresses and Intergranular Fracture in Ceramic Materials

The problem addressed in this paper concerns the statistical characterization of the state of residual stress generated in polycrystalline ceramics during cooling from the fabrication temperature. Detailed finite element simulations are carried out for an ensemble of large numbers of randomly oriented, planar hexagonal grains with elastic and thermal expansion anisotropy, and brittle grain interfaces. The calculations show that the distribution of normal and shear tractions induced by thermal contraction mismatch among grains is gaussian and that these tractions are statistically independent random variables. Although the gaussian nature of the distributions remains unaffected by the introduction of elastic anisotropy, the results indicate that elastic anisotropy has a significant effect on the residual stresses for finite departures from isotropy. When the hexagonal grains are randomly distorted, the magnitude and distribution of residual stresses are found to be insignificantly altered. Spontaneous microfracture due to the generation of internal stresses is also simulated in the analysis by allowing for the nucleation and growth of intergranular microcracks when the fracture energy along the grain facets exceeds a certain critical value. When such microcracking is incorporated into the computation, the levels of residual stress are markedly reduced as a consequence of stress dissipation. The dependence of intergranular microcracking on grain size and temperature variation is examined and the predicted trends on material degradation or the complete suppression of microfracture are discussed in the light of available experimental results.