Abstract
In this study, micromechanical modeling will be performed for composite materials containing fillers oriented randomly in the matrix. The purpose of this study is to derive more general and explicit solutions for the effective thermal and electromagnetic properties of such composite materials without restricting the properties and shapes of the fillers. For this purpose, it is assumed that the physical properties of the filler are the same anisotropic properties as orthorhombic materials, and the shape of the fillers is ellipsoidal. This model is analyzed by micromechanics combining the Eshelby's equivalent inclusion method with the self-consistent method or the Mori-Tanaka's theory. Solutions of the effective thermal and electromagnetic properties both for composite materials containing many kinds of fillers with different shapes and physical properties and for polycrystalline materials can be also derived. Using the obtained solutions, the effect of the shape, the anisotropy, and the volume fraction of the filler on the effective thermal conductivity is examined for the carbon filler / polyethylene and the two types of quartz particles (and voids) / polyethylene. As a result, for the carbon filler / polyethylene, it is found that the effective thermal conductivity of the material when the shape of the filler is flat is about 20% higher than that when the shape of the filler is fibrous. Furthermore, when the shape of the carbon filler is flat, the result when the carbon filler is assumed to be isotropic is significantly different from that when the filler is assumed to be anisotropic. From the above, when the filler is oriented randomly in the material, it is found that simultaneously considering not only the shape of the filler but also its anisotropic properties is important to accurately evaluate the effective physical properties of the composite material. For two types of quartz particles (and voids) / polyethylene materials, the experimental result agrees better with the result of the Mori-Tanaka's theory than that of the self-consistent method, even if the volume fraction of the filler is more than 50%. From the above results, it is found that the analytical solutions of this study can generally explain the experimental results and can be applied to actual materials.