Computation of the Effective Conductivity of Unidirectional Fibrous Composites With an Interfacial Thermal Resistance

Abstract

W e present numerical calculations of the effective thermal conductivity of unidirectional brous composite materials with an interfacial thermal resist ance bet ween the cont inuous and dispersed components. W e rst develop a continuous variat ional formulation of the heat conduction problem and then apply the method of homogenization to derive the appropriat e cell problem. Next , we solve the latter using the nite element met hod and present and validate effective conductivity results for ordered composit es. Finally, to highlight the wide applicability of our approach, we also present a posteriori contact conduct ance results for a disordered composite whose microstructure is based on a real optical micrograph. INTROD UCTIONThe determination of the macroscopic behavior of composite materials is of fundamental and practical importance, particularly now, as new composites are being developed continually for the automotive and aerospace industries, electronic packaging, thermal insulation, and many other applications [1^4]. Typical microstructures of composites consist of unidirectional long ¢bers (mono¢laments), short chopped ¢bers (whiskers), or particles or voids dispersed in a solid matrix. One of the most important macroscopic thermal properties of composite materials is the effective thermal conductivity, which depends on the conductivities, relative amounts, geometries, and spatial distributions of the constituent phases. A recent comprehensive review of heat conduction in composites is presented by Furma·ski [3].Most manufacturing processes of composite materials do not ensure a perfect thermal contact between the constituent phases [1, 2, 5^8]. Therefore, in practice, the effective conductivity also depends on the interfacial thermal resistance, or contact resistance, between the continuous phase (the matrix) and the dispersed phase.

Scattering of Thermal Waves and Non-steady Effective Thermal Conductivity of Unidirectional Fibrous Composites with Functionally Graded Interface

“…In Fig. 10, the results obtained from the present model, the effective medium theory [4], and Hasselman and Johnson [12] are plotted. Close agreement is seen to exist between the models at low volume fractions; however, the present model predicts a lower value of the effective thermal conductivity than does the effective medium theory.…”

“…The Maxwell solution [3] is the starting point to find the effective thermal conductivity of two-phase material systems, but it is only valid for very low concentrations of the dispersed phase. Subsequently, many structural models, e.g., parallel, Maxwell-Eucken [4], and effective medium theory models [5], were proposed. Recently, Samantray et al [6] applied the unit-cell approach to study the effective thermal conductivity of two-phase materials.…”

Scattering of thermal waves and non-steady effective thermal conductivity of composites with coated particles

“…The Maxwell solution [3] was the starting point of finding the effective conductivity of two-phase material systems, but it was valid only for very low concentration of the dispersed phase. Subsequently, many structural models, e.g., Parallel, Maxwell-Eucken [4], and Effective Medium Theory models [5], were proposed. Recently, Samantray et al [6] applied the unit-cell approach to study the effective thermal conductivity of two-phase materials.…”

Improved variational bounds for conductive periodic composites with 3D microstructures and nonuniform thermal resistance

“…Several different discretization schemes have been employed to investigate conduction in composite materials being the finite elements approach one of the more frequently used. The finite element methodology implemented in [33], originally developed to calculate the effective conductivity of unidirectional fibrous composites with interfacial thermal resistance, has been extended in several important directions mainly for three-dimensional media: fibrous composites with 3D parallelepipedonal-cell microstructures [6], monodisperse solid spherical particles distributed in a continuous phase [23], ordered composite materials reinforced with longitudinally aligned circular-cylindrical anisotropic short fibers [24,25] and the limiting cases of ordered arrays of perfectly aligned prolate ellipsoids of revolution and circular cylinders [26]. In [28], the finite element method using representative volume elements is compared with homogenization techniques (the equivalent inclusion methods, the mean field approach and the differential effective medium) to investigate the effect of interfacial conductance on global conductivity for composites with short fibers and spherical inclusions.…”