Numerical simulation of fibre reorientation in the consolidation of a continuous fibre composite material

When a rectangular sample of aligned, continuous fibre-reinforced composite is subjected to normal pressure, it has been observed that resin is squeezed out parallel to the fibres and the fibres flow transversely. The fibres deform so that the sample becomes barrel-shaped. A three-dimensional code has been developed to simulate this flow. The material is modelled as a transversely isotropic continuum in which the fibre direction is specified at each point by a vector a. The system of coupled equations is solved using a finite difference technique. The transverse and longitudinal viscosities are assumed to be functions of the fibre volume fraction which increases as the resin is forced to percolate parallel to the fibres. The stress equations of motion are discretized using central differences for a fixed orientation and the discretized equations are solved using a pseudo-time technique. The converged solution is then used to determine the change in fibre direction at each point of the continuum. The process is repeated in real time using the new fibre orientation. In the momentum equations, the viscous terms are treated explicitly and the pressure gradient implicitly. A projection method is used to ensure that the mass is conserved at each time step. The results are in broad agreement with the experimental observations and demonstrate the success of the continuum model to predict flow behaviour.