Micro-mechanical model for the effective thermal conductivity of the multi-oriented inclusions reinforced composites with imperfect interfaces

Abstract

For the accurate prediction of the Effective Thermal Conductivities (ETCs) of the Multi-Oriented Inclusions Reinforced Composites (MOIRCs) with imperfect interfaces, i.e., Weakly Conducting (WC) or Highly Conducting (HC) interfaces, this work develops a two-step mean-field homogenization method, in which the MOIRCs is virtually decomposed into a set of pseudo-grains, each of which is equivalent as a two-phase composite with imperfect interfaces and firstly homogenized by using the Mori-Tanaka (M-T) or Double-Inclusion (D-I) model, followed by the homogenization of all the pseudo-grains based on the assumption of the uniform intensity or heat flux and on the inclusion orientation distribution. The M-T and D-I models are derived by extending the solution of the Eshelby's single inclusion problem to the heat transfer behaviors of the two-phase composites with imperfect interfaces. Through the comparison with the Finite Element (FE) homogenization method, the developed two-step mean-field homogenization method and the corresponding models are validated to accurately and efficiently predict the ETCs of the MOIRCs with imperfect interfaces. The simulation results show that the presence of WC interface decreases the ETCs of the MOIRCs, while the existence of HC interface has an opposite effect on the ETCs of the MOIRCs. In addition, the ETCs of the MOIRCs with imperfect interfaces show an asymptotic behavior with the variation of interfacial thermal conductance.