The use of homogenization methods for estimating anisotropic viscosities of composite melts

Abstract

A model for the prediction of the various viscosity components of an anisotropic two-phase fluid is developed so as to simulate the behaviour of a unidirectional composite with discontinuous fibres during the flow process. The approach considered here is based upon the use of a transversely isotropic viscosity tensor proposed in a previous paper to describe the purely viscous behaviour of a composite melt. The fibre is replaced by a reinforcement inclusion assumed to be purely viscous and isotropic. The viscous law is transposed in a Laplace-Carson space in which the behaviour becomes linearly elastic and is investigated by means of classical homogenization methods. The solutions are then compared with the results of other studies and predictive values obtained from variational bounding methods given previously, which have been applied to a viscous composite cylinder assembly (CCA) which is statistically transversely isotropic. Finally, axial elongational and in-plane shearing viscosities are also compared with published experimental data.