Effective elastic properties of alumina-zirconia composite ceramics -: Part 2.: Micromechanical modeling

In this second paper of a series on the Effective elastic properties of alumina-zirconia composite ceramics, principles of micromechnical modeling are reviewed and the most important relations are recalled. Rigorous bounds (Voigt-Reuss bounds) are given for the (scalar) effective elastic moduli (tensile modulus E, shear modulus G and bulk modulus K) of polycrystalline ceramics as calculated from monocrystal data (i.e. components of the elasticity tensor). Voigt-Reuss bounds and Hashin-Shtrikman bounds of the elastic moduli are given for two-phase composites. For porous materials, which can be considered as a degenerate case of two-phase composites where one phase is the void phase (with zero elastic moduli), micromechanical approximations (so-called dilute approximations, Dewey-Mackenzie formulae) are given. Apart from a heuristic extension of the dilute approximations in the form of so-called Coble-Kingery relations, semi-empirical extensions of the micromechanical approximations are given for the tensile modulus (Spriggs relation, modified exponential and Mooney-type relations, generalized / Archie-type power law relation, Phani-Niyogi / Krieger-type power law relation, Hasselman relation), including the new relation E/E-0 = (1 - phi) (1 - phi/phi(c)) recently proposed by the authors, where E is the effective tensile modulus, phi the porosity, E the tensile modulus of the dense (i.e. pore-free) ceramic material and phi(c) the critical porosity.