The theoretical principle for the determination of the overall elastoplastic behavior for three types of two-phase composites reinforced with rigid spheroidal inclusions is established. In the first type the inclusions are aligned unidirectionally (1-D) whereas in the second type they are randomly oriented on a plane (2-D), both leading to transversely isotropic composites. The third type of composite involves a 3-D random orientation leading to a globally isotropic material. The theory is based on the energy approach recently proposed by Qiu and Weng (1992) and, while intended only for a modest concentration of inclusions, it can cover a wide range of inclusion shapes, from discs to spheres and all the way to needles (or fibers). It is shown, among others, that the axial response of the 1-D composite is the strongest when reinforced with fibers whereas discs provide the strongest reinforcement under the transverse loading. The outcome is reversed for the 2-D composite. As a consequence of a uniform boundary displacement, the 3-D isotropic composite reinforced with the extreme shapes of rigid needles (aspect ratio → ∞) or discs (aspect ratio → 0) turns out to be also ideally rigid with the entire external stress being carried by the rigid inclusions. For other inclusion shapes, the elastoplastic behavior with prolate inclusions are almost always stiffer as compared to those with oblate shapes with a reciprocal aspect ratio. The asymptotic moduli of the two-phase composites containing the two extreme inclusion shapes are given in terms of the disc and needle density parameters, and the overall elastoplastic behavior for the three different microgeometries are also given as a function of these parameters.
Meso-Scale Transmission Electron Microscope Tomography Applied for Wax Distribution in Toner Particles
