Homogenisation of the Local Thermal Conductivity in Injection-Moulded Short Fibre Reinforced Composites

Abstract

This paper deals with predicting the effective thermal conductivity (ETC) of injection-moulded short fibre reinforced polymers (SFRPs) using two different homogenisation schemes: a scheme based on the dielectric theory for pseudo-oriented inclusions and a two-step homogenisation model based on the mean-field homogenisation approach. In both cases, the fibre orientation tensor (FOT) obtained from Autodesk Moldflow® simulation was used. The Moldflow FOT predictions were validated via structure tensor analysis of micro-computed X-ray tomography (micro-CT) scans of the part. In the dielectric-wise approach, the orientation of fibres was originally defined by a scalar parameter, which is related to the diagonal components of the FOT. In the two-step homogenisation approach, an interpolative model based on the Mori–Tanaka theory is used in the first step for calculating the ETC for the ideal case of unidirectional fibre alignment, followed by a second step in which orientation averaging based on the FOT inside each element is applied. The ETC was calculated using both schemes for the specific case of uniform fibre orientation distribution and at three different locations with non-identical FOTs of an injection-moulded SFRP part. The results are compared with each other and evaluated against the direct numerical simulation for the uniform fibre orientation and experimental measurements for the injection-moulded SFRP. This shows that while the two-step homogenisation can predict the ETC in the full range of orientations between the perfectly aligned and uniformly distributed fibres, the dielectric-wise approach is only capable of modelling the ETC when distributions are close to the two extreme ends of the orientation spectrum.