An estimate of average elastic moduli of composites and polycrystals

We propose a new averaging approach by modifying the Mori-Tanaka prediction of a two-phase composite in which two types of inhomogeneities are embedded in a matrix material the volume of which vanishes as a limit. As for two-phase materials, it is well known that the two predictions made by the Mori-Tanaka method, when the material properties of the matrix and the spherical inhomogeneity are exchanged, coincide with the Hashin-Shtrikman upper and lower bounds. The present model, on the other hand, yields a pair of averages which lie somewhere between Hashin-Shtrikman's bounds, and both of them asymptotically approach one of the bounds in particular when the volume fraction of one of the phases is very small. This characteristic is similar to that of the estimates made by Hill's self-consistent method. Predictions made by the present method are compared with experimental data in order to show the eligibility of our method. Also, it is considered to be applicable even to polycrystalline materials, because the present approach apparently does not have a matrix portion.