Analysis of the Relaxation Modulus of Spun Yarns

In this paper, the relaxation modulus of a single spun yarn is modeled in terms of the relaxation modulus of the constituent fibers of the yarn. A generalized Maxwell model is employed to describe the viscoelastic characteristic function of individual fibers subject to a given step function of tensile strain. The thermal history is considered by a temperature-related reduced time by assuming a thermo-rheologically simple material. The physical ageing process of textile fibers is considered by introducing an ageing related reduced time for glassy semi-crystalline polymer fibers. The effect of humidity is ignored. The model is extended to consider relaxation moduli of fibers undergoing different initial strain levels. With this general relaxation model of fiber, the response of the yarn to a step function of the yarn tensile strain is calculated using a force analysis method and a discrete fiber modeling approach. Experimental validation shows that the prediction agrees reasonably well with the experimental data.