Influence of void shape, void volume and matrix anisotropy on effective thermal conductivity of a three-phase composite

By using high conductivity carbon fibers in a graphitizable carbon matrix, very high values for the thermal conductivity of a composite can be obtained in the direction parallel to the fibers. The carbon matrix of this material exhibits anisotropy and is oriented in the direction of the fibers. Thermal conductivity of the matrix material is of the same order as that of the carbon fibers. The processing of such materials invariably introduces voids up to 25% giving rise to a three phase system of fibers, matrix and voids. The void volume, shape and distribution will have a significant impact on the overall or effective thermal conductivity of the composite. Current empirical or simplified models do not show clearly this effect and experimental measurements are non-existent. Hence, we have adopted a numerical approach consisting of a unit cell to explore the influence of void volume and shape on the effective conductivity of a unidirectional sample. The effective conductivity of a composite consisting of spherical, oval and crack-type voids up to 25% in the direction transverse and parallel to the fiber is calculated and compared with electric circuit analogies and a generalized dispersion formulation for effective thermal conductivity, The results clearly show that the effect of porosity on thermal conductivity cannot be described solely by void volume. The shape and the distribution of the voids affect the effective thermal conductivity which is not captured by any existing models. The finite element models developed should prove useful for the estimation of effective thermal conductivity and hence provide a tool for evaluating analytical continuum models.