MEASUREMENTS OF THE FLEXURAL RIGIDITY OF FIBER ADN YARN

Abstract

The two elastica methods (long column and loop) to measure the flexural rigidity of the fiber and yarn are devised.In the long column method, a sample of length l is standed perpendicularly and a load larger than its critical one of the buckling is applied to the top (free) end. In measuring the vertical deflection xα ie the interval between a horizontal line and loaded end is measured experimentaly, the flexural rigidity is obtained by the folloing equation:Where; F(α, k) denominator of perfect elliptical integration of the 1st kind, k=sinα/2 where α is tangent of loaded end of the distorted sample, this α is obtained by the graph (Fig. 3) indicating the relations between xα/l-k-F(α, k). When the sample's own weight is negligible small, this formula is available to the cantilever method loaded at its free end. In this case, it is convenient to obtain α using a graph of yα/l-k (Fig. 2), where yα is the vertical deflection from its initial coordinate and Pcos α sin α is used replaing P. These long column method is applicable only for large deniers of above 20 denier and yields incorrect results at lower deniers.The loop method is a development from the above method, applicable to more fine filaments. This principle is reported by D. Sinclare in 1950 (ref. cited No.10). As shown in Fig. 4 & 5, looped sample is extended verticaley between torsion balance and cathetometer. If the height a from the vertical line between two clamped ends where distance is large enough to neglect the end moment, and loop apex, and tension T are measured experimentally, EI is obtained from the equation:It is more convenient to make fiber into a bundle to measure finer samples.In order to measure EI of the fiber bundle, stable ply twist yarn is used, when twisted yarn composed of m filaments is folded, expected stable ply is obtained (Fig. 7). In this case, there are relations denoted in eqs. 1-3 between apparent flexural rigidity of twisted sample Bn and EI of a filament, especialy when the twisted angle with fiber axis (π/2-θ) is very small, i.e. θ=90, The results of EI of a filament from this method is larger than that from the other single yarn method, its value increases as θ is increased.