Through-thickness permeability study of orthogonal and angle-interlock woven fabrics

Abstract

Three-dimensional (3D) woven textiles, including orthogonal and angle-interlock woven fabrics, exhibit high inter-laminar strength in addition to good in-plane mechanical properties and are particularly suitable for lightweight structural applications. Resin transfer moulding (RTM) is a cost-effective manufacturing process for composites with 3D-woven reinforcement. With increasing preform thickness, the influence of through-thickness permeability on RTM processing of composites becomes increasingly significant. This study proposes an analytical model for prediction of the through-thickness permeability, based on Poiseuille’s law for hydraulic ducts approximating realistic flow channel geometries in woven fabrics. The model is applied to four 3D-woven fabrics and three 2D-woven fabrics. The geometrical parameters of the fabrics were characterized by employing optical microscopy. For validation, the through-thickness permeability was determined experimentally. The equivalent permeability of inter-yarn gaps was found to account for approximately 90 % of the through-thickness permeability for the analysed fabrics. The analytical predictions agree well with the experimental data of the seven fabrics.

Appendix

The frictional pressure loss in flow along a duct with arbitrary cross section, e.g. the duct formed by interwoven yarns, is usually expressed in terms of a friction factor $\xi$ (also called a resistance coefficient) which is defined as [27]

$$ \xi = \frac{\Delta P}{L} \cdot \frac{{2D_{h} }}{{\rho V^{2} }}, $$

(a1)

where $\Delta P$ and L are the pressure loss and the length of flow channel, D _h is the hydraulic diameter as defined below, ρ is the density of the fluid and V is the mean velocity over the duct cross section. The hydraulic diameter is defined as four times the duct cross-sectional area A′ divided by the wetted perimeter O

$$ D_{\text{h}} = 4A'/O $$

(a2)

For a circular tube, D _h is equivalent to its geometrical diameter. The friction factor can be derived analytically for many cross sections (circular, triangular, quadratic, etc.) in laminar flows [18, 28] and can be expressed as

$$ \xi = c' \cdot \frac{\mu }{{\rho VD_{\text{h}} }}, $$

(a3)

where c’ is a dimensionless shape factor and μ is the fluid viscosity. Then Eqs. a1 and a3 give

$$ \frac{\Delta P}{L} = c' \cdot \frac{\mu V}{{2D_{\text{h}}^{2} }} $$

(a4)

Comparing Eq. 1 with Eq. a4 gives

$$ {\text{K}} = \frac{{2D_{\text{h}}^{2} }}{c'} $$

(a5)

The Hagen–Poiseuille equation describes a laminar fluid flow along a circular tube (diameter D _h), which has a relationship of pressure gradient and flow velocity

$$ \frac{\Delta P}{L} = \frac{32\mu V}{{D_{\text{h}}^{2} }} $$

(a6)

Comparison of Eqs. a6 and 1 gives the equivalent permeability of a circular tube

$$ {\text{K}}_{t} = \frac{{D_{\text{h}}^{2} }}{32} $$

(a7)

This implies that the value of c’ is 64.

When converting ducts with arbitrary rectangular cross section to virtual ducts with circular cross section, friction constants reported in the literature [29] for rectangular ducts with different width/length ratios, α, were divided by c’ to obtain c as listed in Table 3. These values can be fitted with a polynomial (coefficient of correlation R ² = 1):

$$ c = 1.5 - 2.0364\alpha + 2.964\alpha^{2} - 2.724\alpha^{3} + 1.677\alpha^{4} - 0.491\alpha^{5} $$

(a8)

According to Eq. a8, the value of c can be obtained for calculation of K _g for arbitrary gap length and width ratios, as demonstrated for the seven fabrics in Table 3.