Estimation of yarn strength based on critical slipping length and fiber length distribution

Yarn strength is composed of the total contributions made by all breaking and slipping fibers which are determined by critical slipping length lc. Though the definition of lc has been the focus of many research projects, it still remains unsolved. In this study, idealized assumptions were made on yarn structure, and lc was then estimated. At the same time, the actual contributions that breaking fibers and slipping fibers make to yarn strength were recalculated based on an idealized yarn structure, which was analyzed with the conditional probability method according to fiber length distribution. Then, yarn strength was computed by simulating random fiber arrangement in the yarn. It could be seen from calculated results that the critical slipping length declines as yarn twist multiplier increases. Meanwhile, as the twist multiplier increases, the calculated yarn strength rises to the highest point and then declines, which is in agreement with traditional spinning theory. Thus, the calculation of yarn strength based on critical slipping length could reflect the yarn breaking mechanism with a change in the yarn twist multiplier, and could be applied for further prediction of yarn strength.