On Modelling the Statistical Strength of Yarns and Cables Under Localized Load-Sharing Among Fibers

Abstract

This paper describes a statistical model for the strength of long, slender, fibrous structures such as yarns and cables. Emphasis is on the effect of strong mechanical interactions among fibers that arise from the presence of friction or a binding matrix. Basic features are that the structure is viewed as a long chain of statistically and structurally independent bundles whose lengths depend on the local mechanics of fibers at breaks. Within each bundle, localized load-sharing occurs among non-failed fiber elements depending on the local mechanics and fiber spatial geometry. The strengths of the fiber elements vary statistically and are modelled by a Weibull distribution. The analysis is for bundles with few fibers, though previous results under more idealized conditions suggest that the key features of the results will prevail also for much larger bundles. Key conclusions are that, for all practical purposes, a Weibull distribution describes the statistical strength of yarns and cables. The variability in fiber strength has a strong negative effect on the median strength of the yarn or cable and very little effect on its variability in strength. As the load-sharing becomes more diffuse, the median strength of the yarn or cable rises moderately. The size effect for the strength of the cable is very mild when compared to that for the fiber.