A joint influence of the distributions of fiber length and fineness on the strength efficiency of the fibers in yarn

The length and fineness of fibers are critical to the strength of yarns. Much research has been conducted on the issue in the past decades. Zeidman and Sawhney introduced a new parameter called strength efficiency (SE) of fibers in a yarn using an elaborate probabilistic method. Their final formula, a non-dimensional measure, describes the influence of the fiber length distribution on the strength of yarn. The result, however, is based on the assumption that the fibers are identical in all respects including their cross-sectional area. The influence of fiber fineness can not be seen in their formula. In fact the joint influence of fiber length and fineness is rarely studied. We derive a new strength efficiency of the joint influence of fiber length and fineness on the basis of Zeidman’s result. The conclusion is helpful to the understanding of the comprehensive influence of fiber length and fineness on the strength of yarn. Furthermore, we give a plausible method to estimate the critical length defined by Zeidman. The result can be applied to the research of the properties between fibers and yarns.