On modeling of microstresses and microcracking generated by cooling of polycrystalline porous ceramics

Motivated by experimental observations on the temperature dependence of the effective Young's modulus and thermal expansion of porous polycrystalline ceramics, we model microstresses generated by cooling, and resulting microcracking. These microstresses are due to the mismatch in the thermal expansion and elastic properties between anisotropic randomly oriented grains. In the example of cordierite, the thermal expansion anisotropy is very strong, and one of the three principal values of the thermal expansion tensor is even negative. This necessitates tensor treatment of the problem. Model results shed light on the strength of interfaces, by relating the onset of microcracking observed at certain temperature (identified by the onset of stiffness reduction) to maximal tensile stresses at this temperature. The model also provides a possible explanation of the fact that, at a certain temperature drop, microcracking stops (as indirectly implied by thermal expansion data).