Mechanical properties of multiphase materials and rocks: a phenomenological approach using generalized means

Difficulties associated with specifying details of microstructure and distributions of internal stress and strain within multiphase rocks prompt the development of semi-empirical models to connect the effective properties of composites to the properties of their components. We apply here generalized means to describe the elastic moduli (E, K and G) and flow strength of an isotropic multiphase composite material in terms of its component properties, volume fractions and microstructures. The microstructures are expressed by a scaling parameter J, which is mainly controlled by the shape and distribution (continuity and connectivity) of the phases. The case J = 1 yields the arithmetic mean or Voigt average and the case J = -1 yields the harmonic mean or Reuss average. The geometrical mean occurs as J approaches zero. The means with J = -0.5 or J = 0.5 provides good agreement with the experimental data of Young's modulus for the two-phase composites in which strong or weak inclusions are shaped like spheres isolated in a continuous host medium. For most composite materials in which the inclusions are of somewhat arbitrary geometry, the means with J = -0.25 and J = 0.25 do well at predicting the measured values of Young's modulus for those with weak-phase continuous (the volume fraction of strong phase f(s) less than or equal to 0.5) and strong-phase continuous (f(s) less than or equal to 0.7) structures, respectively. In the intermediate range (0.5 less than or equal to f(s) less than or equal to 0.7), J is expected to vary progressively from -0.5 to 0.5 or from -0.25 to 0.25 due to the transition in microstructure. Thus the generalized means offer a promising, phenomenological approach for the prediction of elastic and rheological properties of multiphase materials and rocks, especially for those consisting of more than two unlike phases. As an example, the approach is applied to interpret the sharpness of the 410-km seismic discontinuity as a corollary of the transition from an olivine- to a wadsleyite-dominant structure. (C) 2004 Elsevier Ltd. All rights reserved.