Generalized means as an approach for predicting Young’s moduli of multiphase materials

Difficulties associated with specifying details of microstructure and distributions of internal stress and strain within multiphase materials prompt the development of semi-empirical models to connect the effective properties of composites to the properties of the components. We propose here the generalized means as an approach for predicting the Young’s modulus (E) 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 phase geometry, continuity, and connectivity. 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 0. The means with J=−0.25 and J=0.25 provide a quite good agreement with the experimental data of Young’s modulus for a wide variety of two-phase composites with weak-phase continuous (Vs≤0.5) and strong-phase continuous (Vs≥0.7) structures, respectively. In the intermediate range (0.5≤Vs≤0.7), J is expected to vary progressively from −0.25 to 0.25 due to the transition in microstructure. For porous materials (e.g., glass foams) with non-interconnecting spherical pores, J=∼0.5. Thus the generalized means offers a promising approach for the prediction of elastic properties of multiphase materials if the microstructural exponent J has been determined.