Development of a Constitutive Theory for Short Fiber Yarns: Mechanics of Staple Yarn Without Slippage Effect

This article reports an attempt to develop a general constitutive theory governing the mechanical behavior of twisted short fiber structures, starting with a high twist case, so that the effect of fiber slippage during yarn extension can be ignored. A differential equation describing the stress transfer mechanism in a staple yarn is proposed by which both the distributions of fiber tension and lateral pressure along a fiber length during yarn extension are derived. Factors such as fiber dimensions and properties and the effect of the discontinuity of fiber length within the structure are all included in the theory. With certain assumptions, the relationship between the mean fiber-volume fraction and the twist level of the yarn is also established. A quantity called the cohesion factor is defined based on yarn twist and fiber properties as well as on the form of fiber arrangement in the yarn to reflect the effectiveness of fiber gripping by the yarn. By considering the yarn structure as transversely isotropic with a variable fiber-volume fraction depending on the level of twist, the tensile and shear moduli as well as the Poisson's ratios of the structures are theoretically determined. All these predicted results have been verified according to the constitutive restraints of the continuum mechanics, and the final results are also illustrated schematically.