Effect of fibre orientation on the thermal conductivity of a uniaxial carbon fibre-reinforced aluminoborosilicate glass-matrix composite for various specimen geometries

Abstract

The development of fibre-reinforced brittle-matrix composites has led to major improvements in such properties as fracture toughness, brittleness and strength [1-6]. Generally, the thermal conductivity of the fibres exceeds that of the matrix, so increases in thermal diffusivity and/or conductivity of the composite are observed as well [7-11]. The thermal conductivity of fibreor whisker-reinforced composites has received a great deal of theoretical interest [11-18]. In general, the thermal conductivity of such composites has been shown to be a function of the thermal conductivity values and the volume fractions of the fibres and matrix, the fibre orientation and the degree of thermal contact at the fibre-matrix interface. The effective thermal conductivity of a uniaxial composite in any direction relative to the fibres can be calculated from the values of the thermal conductivity parallel and perpendicular to the fibre direction [18]. The above theories generally have assumed that the composite is infinite in extent and have not taken into account the possible effect of finite size of the composite specimen. As pointed out by Nye [19] and Carslaw and Jaeger [20], the net direction of heat flow within single crystals with anisotropic thermal conductivity does not necessarily coincide with the direction of the imposed temperature gradient. This should also be relevant for fibre-reinforced composites, which in general are expected to exhibit anisotropic thermal conductivity. Depending on the fibre angle, the presence of insulated boundaries parallel to the imposed temperature gradient can interfere with the net heat flow within the composite. In this respect the recent analysis of Hasselman et al. [21] showed that depending on the orientation of the fibres, the effective thermal conductivity of a uniaxially reinforced composite strip of finite width can be much less than the value for an infinitely large plate. For a composite strip with insulated sides with a temperature gradient imposed along the length of the strip, the effective thermal conductivity along the length of the strip was derived to be [21]