Cross-Property Relations between Elastic and Thermal Properties of Porous Ceramics

The cross-property relations between the elastic moduli and the thermal conductivity of porous ceramics are reviewed from the viewpoint of micromechanics (composite theory). Consequences of the rigorous Milton-Torquato and Gibiansky-Torquato relations (in the form of bounds, i.e. inequalities derived between bulk or shear moduli on the one hand and thermal conductivity on the other) are compared to various approximate relations (equalities) recently proposed between the tensile modulus (Young’s modulus) and thermal conductivity, among them the two new cross-property relations proposed by the authors. The relations are critically discussed and applied to the case of porous alumina, zirconia and alumina-zirconia composite ceramics.