Analytical solutions for macroscopic elastic moduli and thermal expansion coefficient of composite materials containing coated fillers oriented randomly based on the double inclusion method

Abstract

In this study, micromechanical analysis will be performed to derive explicit solutions of the macroscopic elastic moduli and thermal expansion coefficient for composite materials, where spheroidal-coated fillers are oriented randomly in the material. This analysis is carried out by combining the double inclusion method with the self-consistent method or the Mori-Tanaka theorem. Furthermore, using these solutions, explicit solutions of the macroscopic elastic moduli and thermal expansion coefficient are also derived for composite materials containing various types of coated fillers with different physical properties and shapes. To verify the validity of the obtained solutions, the results of the analytical solutions are compared with the experimental ones for a composite material in which carbon nanotube (CNT) fillers with Al4C3 interfacial layer are randomly oriented in an Al matrix. The analytical results show good quantitative agreement with the experimental ones. Additionally, the analytical results are compared with the approximate numerical results using the finite element method for the macroscopic thermal expansion coefficient, and find good agreement within a certain range of the volume fraction and the interfacial layer thickness of the CNT fillers. Furthermore, the changes in the macroscopic Young's modulus and the thermal expansion coefficient are investigated by continuously changing the aspect ratio of the CNT filler. The results show that to exhibit high elastic modulus and low thermal expansion in CNT/Al composites, the CNT fillers should have a shape closer to being spherical or flattened rather than fibrous. Moreover, design guidelines are proposed for the shape of the CNT fillers and interfacial layer thickness for a given volume fraction of the CNT fillers. In conclusion, the validity of the proposed analytical solutions is verified and demonstrated their usefulness for practical materials.