Ceramics-Silikáty 48, (1) 14 - 23 (2004)

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 HashinShtrikman 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/E₀ = (1 - Φ) · (1 - Φ/Φ_C), recently proposed by the authors, where E is the effective tensile modulus, Φ the porosity, E₀ the tensile modulus of the dense (i.e. pore-free) ceramic material and Φ_C the critical porosity.