Effects of general imperfect interface/interphase on the in-plane conductivity of thermal composites

Abstract

The effects of general imperfect interphase/interface models on effective and local thermal conductive responses of fiber reinforced-composites are investigated. A physical interphase model is firstly introduced and then extended to the weakly conducting (WC) and highly conducting (HC) interfaces by satisfying the discontinuity conditions of temperature and normal heat flux, respectively. To simulate different geometric arrangements of fibers, hexagonal and square repeating unit cells (RUCs) are used in this paper. Regarding simulation technique, the locally-exact homogenization theory (LEHT) is extended by considering the aforementioned interphase/interface models to re-produce the localized temperature and heat flux distributions in the unit cells and then to predict the macroscopic thermal conductivities. The present method does not require mesh discretization and pre-processing, but directly obtains the accurate analytical expression of internal domains after solving the thermal differential equations. The unknown coefficients are obtained through applying imperfect interphase/interface conditions and weak-form periodic boundary conditions. Finally, the effective Fourier's formula is established to obtain the overall thermal conductivities of composites. The LEHT is advantageous in fast convergence, numerical stability and computational efficiency, thus providing a good numerical tool in studying the influence of interface parameters on composites. The generated numerical results are in good agreement with the analytical or numerical simulations in the literature. On this basis, the effects of interfacial geometric and physical parameters on the macroscopic coefficients and local thermal responses of the composites are tested. Finally, the thickness of a physical interphase is varied to test its applicability in generating equivalent effect with WC interface and HC interface. Generally, the imperfect interfacial effects play important roles in the thermal conductive response of composite materials. In the meantime, the proposed method is of great significance for the study of thermal conductions of composite microstructures.