Mechanics of Elastic Performance of Textile Materials

Abstract

This paper is concerned with the quantitative analysis of some of the factors which determine the strength of cordage strands and plied yarns. When integrated with the analyses covered in Part IX of this series [1], a complete picture is given of the effects of the factors considered on translation of the strength of cordage fibers into singles yarns, strands, or plied yarns and, by direct projection, into cordage ropes. The problem is solved by a combined mechanical-statistical analysis similar in type to that given previously [1], assuming simplified idealized geometrical forms and a normal distribution of yarn properties. It is shown that such assumptions produce results which agree, within the limits of engineering accuracy, with experiment. Checks were available for: 9-rope strands of varying twist structure, all made of Manila abaca fiber; a small Sansevieria 3-ply rope; and small size bundles of Manila abaca fiber used as laboratory models to illustrate the effect of the number of singles in a strand or plied yarn. The factors which are analyzed mathematically for their mechanical effects include: singles yarn twist; strand or plied yarn twist; number of singles which are stranded; elastic properties of the singles yarns; and uniformity of the mechanical properties of the singles yarns. Significant losses occur in the translation of the strength of the yarns into the strands and ropes, efficiencies of the order of 75% being theoretically calculated and experimentally verified. How ever, the major cause of the low over-all 40% translation of fiber strength into strands and ropes resides in the low fiber-to-yarn translation of only 55%. The losses from yarns to strands are indicated to result from both low uniformity of yarn elongation to break and inclination of yarns to the strand and rope axes, these effects being equal in magnitude for most of the structures studied. The coefficients of variation of yarn rupture elongation of about 10% for the yarns examined in this work appear, on the basis of the inherent variability of 20%-30% for their con stituent fibers, to be the result of nonuniformities created by processing. Such levels of nonuni formity do not lend themselves, at present, to significant reduction by alterations of manufacturing techniques. Thus, it appears that improvements in yarn-to-strand or -plied yarn translational efficiencies can be practically accomplished only by strand and rope twist reductions or by the use of more extensible fibers and yarns. Results of the simplified geometric analyses are checked by comparison with the results of a more precise geometrical analysis of plied structures as developed by Chow [4]. Differences between the results of the two approaches are shown to be negligible for practical ranges of twisted struc tures, justifying the assumptions leading to the simplified analyses. The results, which are presented graphically over a range of the variables in excess of those presently used in cordage structures, are immediately applicable to the engineering calculations of strength of cordage structures, tire cord, and sewing threads. The limits of applicability are defined by the validity of the assumed simplified geometry.