EFFECTIVE CONDUCTIVITY OF COMPOSITES WITH SPHERICAL INCLUSIONS - EFFECT OF COATING AND DETACHMENT

An expression for the reduced effective thermal conductivity, k(eff)/k (1), of a random array of coated or debonded spherical inclusions with pair interactions rigorously taken into account is derived. Pair inte ractions are evaluated through solution of a boundary value problem in volving two coated or debonded spheres with twin spherical expansions. The resulting k(eff)/k(1) is of O(f(2)) accuracy, where f is the comb ined volume fraction of the inclusion and interface. The effect of int erfacial characteristics manifested as the reduced thermal conductivit y, sigma(3), and relative thickness, delta/a, of the interfacial layer is thoroughly investigated. It is found that k(eff)/k(1) can be appro ximately viewed as a function of f and the dimensionless dipole polari zability, theta(1), over a large parameter domain, despite the existen ce of higher order polarizabilities in the expression of k(eff)/k(1). The value of theta(1) alone determines whether the effective inclusion is enhancing (theta(1) > 0), neutral (theta(1) = 0), or impairing (th eta(1) < 0) to the matrix. Furthermore, the evaluation of k(eff)/k(1) for the present model system can be approximately replaced with that f or composites containing inclusions of no interface but possessive of a reduced thermal conductivity of (1 + 2 theta(1))/(1 - theta(1)). A c ontour plot of k(eff)/k(1) on the theta(1) - f domain that is useful i n estimating k(eff)/k(1) for interfacial properties characterized by a n arbitrary combination of sigma(3) and delta/a, is constructed. (C) 1 996 American Institute of Physics.