Development of a Constitutive Theory for Short Fiber Yarns Part II: Mechanics of Staple Yarn With Slippage Effect

Abstract

A general constitutive theory governing the mechanical behavior of staple yarns and including the effect of fiber slippage during yarn extension is presented in this paper. A differential equation describing the stress transfer mechanism as well as the slippage influence in a staple yarn is applied by which both the distributions of fiber tension and lateral pressure along a fiber length are derived. A so-called fiber slippage ratio λ is defined in terms of fiber and yarn properties to specify the length along both ends of a fiber that is slipping during yarn extension. Factors such as fiber dimensions and properties, the effect of the discontinuity of fiber length within the structure, and fiber orientations in the yarn are all included in the theory. The slippage effect is incorporated into the results obtained in Part I of this study, so that the tensile and shear moduli as well as Poisson's ratios of the yarn with slippage effect are theoretically determined. Comparisons of these properties in both cases with and without the slippage mechanism are provided in this paper.