Effect of interfacial characteristics on effective conductivities of composites containing randomly distributed aligned long fibers

The effect of interfacial characteristics on the effective thermal conductivity, k(eff), of composites containing randomly distributed aligned long fibers is studied. An expression for the reduced effective thermal conductivity, k(eff)/k(1), is derived with pair interactions rigorously taken into account. Two types of interfaces are treated: one with finite thickness and one with no thickness but possessive of certain thermal barriers. The expressions of k(eff)/k(1) for these two types of interfaces are found to be identical but with different definitions for involved multipole polarizabilities, theta(n). The effect of interfacial characteristics, quantified as the relative interfacial thickness, delta/a, reduced interfacial thermal conductivity, sigma(3), and Blot number, Bi, on k(eff)/k(1) is thoroughly investigated. It is further found that interfacial characteristics may be well represented by the dipole polarizability, theta(1), although higher orders of multipole polarizabilities appear in the expression of k(eff)/k(1). Comparison of the present results with those obtained from three less rigorous models, the equivalent inclusion model, modified effective medium theory, and modified Hashin and Shtrikman's bounds, is also presented. The present results stay well within the bounds for the combined area fraction of interface and inclusion, f, up to 0.5. Finally, the effect of microstructure on k(eff)/k(1) is examined by a comparison of present results with those for square and hexagonal arrays. The randomness in configuration tends to intensify the thermal interactions between the effective inclusion and the matrix such that, under the same condition, k(eff)/k(1) values of the random array deviate farther from unity than those of the regular arrays. Copyright (C) 1996 Elsevier Science Ltd