Elasticity of porous ceramics—A critical study of modulus−porosity relations

Based on the concept of intrinsic elastic moduli an overview of modulus–porosity relations is given, which includes exponential and power-law expressions as well as the Hasselman relation and a relation recently proposed by Pabst and Gregorová. The formal structure of these relations is compared and the physical meaning of the parameters discussed. It is recalled that certain popular relations violate the Hashin–Shtrikman upper bounds and are, therefore, useless (Spriggs relation, Ishai–Cohen relation). Coble–Kingery relations are recalled in their correct form and an improved version of the Gibson–Ashby relation for the shear modulus is proposed. Selected relations are applied to describe the porosity dependence of the relative tensile moduli of alumina, zirconia, silicon nitride and silicon carbide prepared with corn-starch as a pore-forming agent. Porous ceramics with this type of (matrix-inclusion-based) microstructure are shown to follow approximately a modified exponential relation and can be fitted by a master curve with critical porosity 68.4%.