A Constitutive Model for Blended Yarn Extension with Fragmented Low-Elongation Fibers

Abstract

A simple micromechanical model is developed for the interactions in a parallel square-stacked mixed array of elastic fibers representing the microstructure of a blended yarn undergoing axial extension. The mixed array consists of a small fraction of relatively high modulus, low elongation-to-break (LE) fibers dispersed among high elongation-to-break ((HE) fibers. The LE fibers are assumed to break into fragments, and the LE fiber fragments are assumed to slip relative to neighboring fibers in regions near the fragment tips. The fiber array experiences lateral compression arising from the remote tension on the twisted yarn, and frictional forces acting at slipping fiber-to-fiber contact surfaces are assumed to obey Amontons' law. Solutions of a dimensionless boundary value problem for deformations in a unit cell of the fiber array are presented. Dimensionless parameters involving the constituent LE and HE fiber properties are identified and their influence on blended yarn tensile behavior is illustrated.