Shear and bulk moduli of isotropic porous and cellular alumina ceramics predicted from thermal conductivity via cross-property relations

Based on alumina as a paradigmatic example, shear and bulk moduli have been numerically calculated on computer-generated digital random microstructures representing isotropic porous materials with convex or concave pores and for cellular materials with closed or open cells. On the other hand, the relative elastic moduli cross-property relations (CPRs) have been predicted from the numerically calculated relative thermal conductivities. It has been shown that the Pabst-Gregorovg cross-property relation (PG-CPR) with constant CPR exponent 4/3 or its generalized version with the correct Poisson-ratio-dependent CPR exponents (for alumina 1.316 and 1.426, respectively, for the shear and bulk modulus) provides the best prediction currently available, although its accuracy is significantly worse for the bulk modulus (maximum differences between predicted and calculated values ranging from -0.05 to + 0.09 relative property units/RPU) than for the shear modulus, where the accuracy is excellent for all microstructures (maximum difference smaller than +/- 0.02 RPU).