Probabilistic thermal conductivity analysis of dense stabilized zirconia ceramics

In the present paper, a reliability analysis of the effective thermal conductivity of almost fully dense stabilized zirconia ceramics is described. The methodology is used to estimate (i) the probability for the material conductivity value to exceed a critical threshold and (ii) the sensitivity of the effective thermal conductivity to the variability of microstructural heterogeneities. A stochastic model enclosing the probability distributions of microscopic random variables coupled to a heat transfer model was thus established. This approach has been applied to a specific random microstructure exhibiting a highly segregated bimodal distribution of grain sizes and a small pore volume fraction. Due to the complexity of the ceramic microstructure, three representative volume elements were made to depict the ceramic material at different scales. Three-dimensional Voronoï mosaics are used to generate artificial microstructures with a very large number of grains. A computational homogenization method is employed to derive the effective thermal properties of the heterogeneous material for one iteration of random variables. Once the number of iterations achieves a representative sampling of the basic variables, the numerical reliability and sensitivity analysis are carried out. The confidence that can be given to the sensitivity and reliability estimates has been successfully quantified through experimental measurements of thermal diffusivity by the laser flash technique on a series of zirconia samples.