Statistical Theory for the Strength of Twisted Fiber Bundles with Applications to Yarns and Cables

Abstract

This paper describes a statistical model for the strength of twisted bundles of stiff fibers. The model evolves from the classic model for bundle strength and is most applicable for short bundles with low friction between filaments; however, the model is believed to yield insight into the strength behavior of longer yarns and cables. The individual filaments follow helical paths and are assumed to vary randomly in strength and slack. In twisted yarns the filament slack is introduced to model the resulting effects of incomplete filament migration during twisting, though certain parameters are difficult to estimate experimentally. As bundle size increases, bundle strength is asymptotically normally dis tributed, and the asymptotic mean and variance are given. In a first application we consider the strength of twisted yarns under typical assumptions for stiff aramid fibers. Random variation in fiber strength and imperfect fiber migration yield dramatic reductions in yarn-strength efficiency as the yarn helix angle increases; at the same time the variability in yarn strength increases substantially, though it diminishes as the number of filaments is increased. In a second application a Monte Carlo simulation approach is used to study the strength of a torque-balanced cable with three helical layers of a few aramid-strength memhers. Typical amounts of variability in member strength result in large decreases in strength efficiency. However, weakest-link results are shown to understate the cable strength.