Stochastic Geometric Properties Of Woven Textiles

This paper addresses geometric variability of woven textiles used in composites manufacturing. Variability in tow directions and unit cell size is quantified by applying an image analysis procedure to two representative materials; a pre-impregnated carbon/epoxy satin weave textile and a commingled glass/polypropylene fabric, and the spatial autocorrelation of stochastic variables is characterized. It is found that variability in tow orientations is significant in both the pre-impregnated material and the fabric, whereas variability in the unit cell size is significant only in the commingled fabric. Variability in the weft directions is more significant than in the warp direction. Highly anisotropic spatial autocorrelation of tow orientations is observed in both materials with the major direction of autocorrelation normal to the corresponding set of tows. The correlation structures identified are decomposed using Cholesky factorization and Monte Carlo simulation of a stochastic textile is performed. This enables stochastic simulations of forming to be carried out based on a simplified finite element model of woven material draping. The results of these simulations show that variability in the woven material geometry induces significant variations in the formed geometry.