The Longitudinal Rheological Behavior of Non-uniform Fibers

This paper is concerned with a mathematical analysis of the longitudinal rheological behavior of dimensionally and structurally variable fibers. At first, the general relation ships for the stress-strain behavior of such fibers are derived by ignoring time effects. The uniform and non-uniform fibers are compared for the case when stress and strain follow a power law relationship, and the stress-strain behavior of non-uniform wool fibers is calculated to illustrate the effect with actual fibers. Structural and dimensional non- uniformities are shown to have considerable significance. When both variabilities are present, the two non-uniformities may act additively or subtractively, depending on the relationships between them. In considering time effects, the behavior of several rheological models is examined. The uniform and non-uniform specimens are compared for creep (constant load), stress relaxation (constant extension) and stress-strain behavior at constant rates of loading and straining. To illustrate the applications possible with actual fibers, the creep behavior of wet wool fibers is briefly treated.