Insights into complex rheological behaviour of carbon fibre/PEEK from a novel numerical methodology incorporating fibre friction and melt viscosity

A recent rheological study of carbon-fibre-reinforced PEEK (CF/PEEK) demonstrated highly complex behaviour, involving phenomenological differences at low and high strain rates. To explain the behaviour, it was hypothesised that CF/PEEK responds as a yield-stress fluid at low strain rates, with boundary-lubricated, fibre-fibre friction determining the viscosity, and as a viscous fluid at high strain rates, with polymer melt viscosity dominating the response. In this paper, a novel finite-element methodology, incorporating fibre friction and melt viscosity in the same model, is employed to study this hypothesis. Two-fibre models investigate how fibre friction and melt viscosity combine to produce an overall composite viscosity. Representative-volume-element (RVE) models examine multi-fibre/melt response, and demonstrate that inclusion of fibre friction produces the observed yield-stress behaviour at low strain rates, and viscous behaviour at high strain rates. Another phenomenon which affects rheological measurements of such composites is shear banding in the sample, which occurs in the yield-stress regime. This effect is demonstrated in the models, and analysis of load transfer between fibres and melt explains how it arises, and how it leads to diminished values of measured viscosity. The results pave the way for improved process models for high-throughput manufacturing processes such as Automated Tape Placement.