Modeling Woven Fabric Tensile Strength Using Statistical Bundle Theory

Abstract

Previous statistical models, developed to predict the strength of loose fiber bundles and composite materials, have been applied to the problem of predicting the tensile strength of woven fabrics when the underlying strength distributions of the warp and weft threads are known. The woven fabric was first assumed to act as a single loose bundle of threads with no thread interactions (equal load sharing), and Daniels' model was applied. In the second stage, a more complex chain-of-bundles model, which provides a method to take interactions into account, was then used. With this model, the effect of interactions due to interyarn friction and thread crimp can be seen in the number of sub-bundles forming the chain. The length of each of these sub-bundles, called the "overload length," is a measure of the influence of the crossing threads. Finally, a third refinement that accounts for interactions through localized, non-equal load sharing among yams was used. Experiments were performed using four different fabrics—three cotton fabrics of plain, twill, and satin construction, and one 100% polyester fabric of plain construc tion—to determine the applicability of the models. Warp and weft yams were extracted from the fabrics and tested in tension. The strength data for these yams were fitted to a two-parameter Weibull distribution using the method of maximum likelihood. The simple loose bundle model consistently underestimated the fabric strength, although the predicted values were generally better for the fabrics with longer float lengths, indicating that interyarn friction from the interlacings plays a positive role in fabric tensile strength. With the chain-of-bundles model, the ratio of the thread crimps is a predictor of the overall frictional effect. Localized load sharing results in a conservative approach, with the actual fabric properties falling between this and the simpler chain- of-bundles model incorporating equal load sharing.