Micromechanical analysis for effective elastic moduli and thermal expansion coefficient of composite materials containing ellipsoidal fillers oriented randomly

In this study, we examine to derive the solutions of effective elastic moduli and thermal expansion coefficient for composite materials containing ellipsoidal fillers oriented randomly in the material using homogenization theories, which are the self-consistent method and the Mori–Tanaka method. This analysis is carried out by micromechanics combining Eshelby’s equivalent inclusion method for each theory. The solutions for effective elastic moduli and thermal expansion coefficient obtained on each theory are expressed by common coefficients composed of both the physical properties of the constituents of the composite material and geometrical factors depending upon the shape of the fillers. Moreover, these solutions enable us to calculate effective elastic moduli and thermal expansion coefficient for composite materials that contain randomly oriented fillers of various shapes and physical properties. By taking the limit of eliminating the existence of the matrix for these solutions, we can derive effective physical properties of polycrystalline materials. Using the obtained solutions, we investigate the effects of the shape of the fillers on the effective elastic moduli and thermal expansion coefficient. As a result, we confirm that these effective properties fall within the lower and upper bounds, and find that a characteristic result appears when the shape of the fillers is flake or oblate. Through comparisons between the analytical and experimental results, we confirm the practical usability of the solutions obtained in this analysis. Furthermore, we determine originally the shape factor for the filler and can show that this factor has the potential to provide guidelines for the optimal design of filler shape to improve the effective elastic properties of materials.