Probability density function of in-plane permeability of fibrous media: Constant Kozeny coefficient

TL;DR

This paper investigates the statistical distribution of in-plane permeability in fibrous media, demonstrating that permeability follows a gamma distribution and is significantly more variable than fibre volume fraction.

Contribution

It introduces an analytical method to derive the permeability PDF using the Kozeny-Carmen equation and validates it against experimental data, revealing key distribution characteristics.

Findings

Permeability follows a gamma distribution.

Fibre volume fraction follows a normal distribution.

Permeability variability exceeds fibre volume fraction variability by an order of magnitude.

Abstract

This study addresses the issue of whether or not a normal distribution appropriately represents permeability variations. To do so, (i) the distribution of local fibre volume fraction for each tow is experimentaly determined by estimation of each pair of local areal density and thickness, (ii) the Kozeny-Carmen equation together with the change of variable technique are used to compute the PDF of permeability, (iii) using the local values of fibre volume fraction, the distribution of local average permeability is computed and subsequently the goodness of fit of the computed PDF is compared with the distribution of the permeability at microscale level. Finally variability of local permeability at the microscale level is determined. The first set of results reveals that (1) the relationship between the local areal density and local thickness in a woven carbon-epoxy composite is modelled by a bivariate normal distribution, (2) while fibre volume fraction follows a normal distribution, permeability follows a gamma distribution, (3) this work also shows that there is significant agreement between the analytical approach and the simulation results. The second set of results shows that the coefficient of variation of permeability is one order of magnitude larger than that of fibre volume fraction. Future work will consider other variables, such as type of fabrics, the degree of fibre preform compaction to determine whether or not the bivariate normal model is applicable for a broad range of fabrics.