A Comprehensive Stress and Breakage Analysis of Staple Fiber Yarns: Part I: Stress Analysis of a Staple Yarn Based on a Yarn Geometry of Conical Helix Fiber Paths

This paper, which is a preliminary to a general investigation of the stress-strain and breakage behavior of staple yarns, deals with the stress analysis of a staple yarn under axial strain, based on an ideal yarn geometry that allows for fiber migration, assuming conical helix fiber paths. The position and dimensions of a yarn element based on this conical helix model are defined first, in relation to yarn dimensions, and the radial equilibrium conditions are obtained. The axial stress at any point on the yam cross section under a given strain is then expressed by using the characteristic stress-strain curve of the fiber for both small and large strains. Thus the stress distribution over the cross section can also be determined.