On the application of Mori-Tanaka's theory involving transversely isotropic spheroidal inclusions

Abstract

Based on the new structure recently established by Weng for the Mori-Tanaka theory, the effective elastic moduli of three types of composite containing transversely isotropic spheroidal inclusions are explicitly derived. For a multiphase composites with aligned, identically shaped inclusions, the derived moduli are believed to be generally reliable, where the three extreme cases involving circular fibers, spheres, and thin discs all lie on or within the respective Hashin-Shtrikman-Walpole bounds. For a multiphase aligned composite whose inclusion phases differ in shape, the M-T moduli tensor can lose its diagonal symmetry, which, for a hybrid composite containing fibers and another aligned spheroids, is found to be severest when the spheroids take the shape of thin discs, and tends to decrease as their aspect ratio increases. When the transversely isotropic spheroidal inclusions are randomly oriented in an isotropic matrix, the M-T moduli with spherical inclusions are shown to always lie on or within the isotropic Hashin-Shtrikman-Walpole bounds. Such a desired property however is not always assured with other inclusion shapes, where the needle and disc-like inclusions may cause the M-T moduli and Walpole's self-consistent estimates to lie outside the H-S-W bounds.