Theory of Extension of Elastic Continuous Filament Yarns

This paper is concerned with the theoretical investigation of small extension of linearly elastic continuous filament yarns. The yarn is treated as a solid composed of thin fibers with helical configuration and infinitesimal cross sections. The theory of elastic curved rods is employed in our analysis. In comparison with previous works on the same topic, the theory presented in this paper is more rigorous and complete, and some assumptions used in previous studies are omitted here. In this paper, stress analysis is made for yarns with different angles of twist. The possibility of partial separation of fibers in the binormal directions is considered. The effect of superposition of a twisting moment on the extended yarn is also discussed.