A statistical approach to permeability of clustered fibre reinforcements

The focus is set on mesoscale modelling of permeability of real fabrics used in composite manufacturing. Of particular interest is the effect of expected perturbations from perfect geometries, such as fibre bundle crimp, on the permeability. To start with, variational methods are used to calculate the permeability of individual gaps between fibre bundles. Based on this study a network of unit cells is formed enabling studies of two- and three-dimensional flow through the structure. From such an analysis the overall permeability of an arbitrary distribution of unit cell permeabilities can be calculated. Here random and controlled distributions are simulated. The former is an approximate representation of a continuous strand mat and the latter may describe Non-Crimp Fabrics. The result is that for random distributions, the permeability decreases with the maximum variation in unit cell while for a controlled permeability distribution the overall permeability can as well increase as decrease depending on the type of perturbation. In both cases the type of flow: one-, two- or three-dimensional strongly influence on the quantitative result. Hence, for the type of fabrics studied, it is necessary to model the full 3D-flow through to get a correct permeability value.