MICROSTRUCTURAL THERMAL-STRESSES IN CERAMIC MATERIALS

The problem addressed concerns the analytical characterization of the state of residual stress in a polycrystalline ceramic material following cooling from the fabrication temperature. It is shown that, under mild assumptions on the behavior and microstructure of the material, the covariance matrix of the microstructural residual stresses can be obtained in closed form from the equations of elasticity. The analysis does not take thermally induced microcracking into consideration and the solid is idealized as remaining essentially intact during the cooling process. However, the results so obtained are subsequently used to derive first-order estimates of microcrack densities.