Stochastic analysis of fibre volume fraction and permeability in fibre bundles with random filament arrangement

For fibre bundles with non-uniformly distributed filaments, probabilities for the occurrence of defined local filament arrangements, determining geometrical constants for permeability calculation, were described as functions of the local fibre volume fraction. Because of changing inter-filament gap geometries, the local transverse permeability decreases discontinuously with increasing local fibre volume fraction, while the local axial permeability decreases continuously. Axial bundle permeabilities, derived from log-normally distributed local permeabilities, tend to be higher than predictions for uniform filament arrangements, while transverse bundle permeabilities tend to be lower. This implies that assuming uniformity of filament arrangements is inappropriate for realistic modelling of bundle properties. For fibre bundles with rectangular cross-section, the transverse permeability decreases in width-direction and increases in thickness-direction with increasing aspect ratio of the bundle cross-section, while the axial permeability is not affected. This is of high practical relevance, in particular for spread-tow reinforcements with high aspect ratios.