Anisotropy of heat conduction in fibre-reinforced composites
Fibre-reinforced composites usually exhibit anisotropy of thermal as well as mechanical properties. For example, in a unidirectional carbon fibre-reinforced plastic of 60% volume fraction, the longitudinal thermal conductivity may be greater than that in the transverse direction by a factor of 50, and greater than that of the unreinforced polymer by more than two orders of magnitude. In order to evaluate the engineering applications of thermal anisotropy, this thesis concentrates on the development and validation of a generalised finite element model of heat conduction in an anisotropic medium. This uses a variational formulation of the anisotropic time-dependent heat conduction equation, and is implemented for two and threedimensional quadratic finite elements. The model may be used for the solution of problems having any combination of steady or time-dependent boundary conditions (fixed temperature, convection, radiation, heat flux and internal heat generation), as well as nonlinear properties. Anisotropy is specified by the components of the two or threedimensional thermal conductivity tensor; efficient representation of nonhomogeneous materials is achieved by the specification of properties at element integration points. Theoretical validation of the model is carried out by means of a number of mathematical solutions to orthotropic and anisotropic problems. Experimental validation is performed by comparison of calculations with measured steady-state surface temperatures on a cylindrical specimen of unidirectional carbon fibre-reinforced epoxy resin. The thermal property data for this exercise are obtained from measurements of principal thermal conductivities on absolute and comparative steady-state apparatus. The use of the finite element model in two industrial applications is briefly described. These concern thermal cycling during composite fabrication with reinforced thermoplastic tape, and an analysis of heat transfer in a composite propeller blade.