Prediction of statistical strengths of twisted fibre structures

Abstract

A new approach, based on Daniels' statistical model for a parallel fibre bundle and the recent results on yarn mechanics by the present author, is introduced to predict the strengths of twisted yarns including the effects of interfibre friction and the fibre fragmentation mechanism during yarn extension. By calculating the lateral pressure in a twisted yarn, the critical fibre length of the fibre fragmentation process has been determined, and was found to decrease together with the increasing yarn strain. This, according to the Weakest link theorem, will lead to a substantial increase of fibre strength. Incorporating this conclusion into Daniels' result yielded a more realistic prediction of the strength and its boundary for a twisted fibre structure. The key differences between a filament yarn and a short-fibre yarn and their effects on strengths are also discussed. The major results from the study are illustrated schematically.