Permeability characterization of a biaxial stitched fabric: Insights from 2D flow experiments under unsteady and steady flow regimes

This study investigated in-plane permeability of a biaxial stitched E-glass fabric preform using 2D (radial) flow experiments under constant-injection pressure at fiber volume fractions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 41–54%. Unsteady permeability was determined through a repeated set of experiments on separate specimens and by tracking elliptical flow front propagation with time along x , y axes and θ = 45°. The fabric exhibited an anisotropic behavior with unsteady permeability along the production line ( x -direction) being significantly higher than permeability along the transverse line ( y -direction). The ratios of principal permeability components, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow> <mml:mi>u</mml:mi> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow> <mml:mi>u</mml:mi> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mfrac> </mml:mrow> </mml:math> were <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>5.67</mml:mn> <mml:mo>±</mml:mo> <mml:mn>2.14</mml:mn> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>3.72</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.90</mml:mn> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>3.97</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.87</mml:mn> </mml:mrow> </mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.41</mml:mn> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.46</mml:mn> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.54</mml:mn> </mml:mrow> </mml:math> , respectively. For steady permeability characterization, analytical relationship (driven from Darcy’s Law) between the permeability and process parameters (inlet hole diameter, resin viscosity, inlet and exit pressures) is usable only if the exit flow rate is measured at an elliptical mold edge, which is not practical as these characterization experiments are usually conducted with a non-elliptical mold (circular or square). In this study, steady permeability was calculated by using experimental steady flow rate, an assumption that the anisotropy ratio calculated in the unsteady regime remains constant at steady state, and a straightforward numerical iterative solution. The ratio of steady to unsteady permeabilities, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow> <mml:mi>u</mml:mi> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mfrac> </mml:mrow> </mml:math> was determined as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.97</mml:mn> <mml:mo>±</mml:mo> </mml:mrow> </mml:math> 0.33, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.76</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.54</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.26</mml:mn> </mml:mrow> </mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.41</mml:mn> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.46</mml:mn> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.54</mml:mn> </mml:mrow> </mml:math> , respectively. This study presents a valuable methodology and key insights into the permeability of a biaxial fabric, extendable to other fabric types and contribute to advanc