3-D geometric modeling of a draped woven fabric

One of the components required for design and optimisation of fabric reinforced products is a realistic and accurate 3-D geometry model for a repeating element of the reinforcement. Such a model, which reflects the deformations that result from weaving the fibre bundles and forming (draping) the woven fabric over a product mould, is proposed in the present paper. A fibre bundle architecture, which exhibits undulation and variable cross-section dimensions, is introduced to this effect. Every bundle is described by its in-plane centreline path, its double curved horizontal midplane and the thickness distribution of the cross-sections. These parameters are, in turn, defined by invariant shape functions and variable fibre bundle dimensions. The selected geometry description enables straightforward determination of individual fibre paths. In order to verify the model experimentally, cross-sections are cut out from undeformed laminates with plain-weave reinforcements, and laminates of which the plain-weaves have been subjected to stretching or shear deformations during draping. The laminate crosssections are made along and perpendicular to the mean directions of the impregnated fibre bundles (yarns). All yarns exhibit out-of-plane undulation, and curvature and twist of the midplane. Correlation between experiment and the proposed modeling scheme is good. Draping results in significant fibre reorientations and variations between the individual fibre paths, which are not reflected by existing modeling schemes. These geometry deviations may significantly affect the stress distribution, and should be taken into account in order to predict material properties accurately.