A New Concept of the Mechanical Behavior of Fibers

Abstract

The first portion, Part I, of this paper presents a review of the various theories of mechanical behavior of fibers. It is shown that the linear three-element model gives a fairly good qualitative description of relaxation, creep, and stress-strain phenomena. With this linear model extended to give a dis tribution of relaxation times, the time scales of the relaxation and creep functions are expanded to ranges which approach those observed experimentally. However, the more compli cated linear model is cumbersome, particularly when used to explain stress-strain data, and it does not yield the proper values of the elastic and viscous constants when the rate of strain is changed by a large factor. The three-element model with Hookean springs and Eyring dashpot is discussed, and it is shown that it accomplishes the extension of the time scale for relaxation and creep, and also yields relationships involving changes in the rate of elongation of stress-strain experiments which agree quite well with data on acetate rayon. The use fulness of graphical methods of analysis of stress-strain curves is pointed out. For other fibers, the agreement with experi ment is not so good. Efforts to generalize the Eyring model by considering the "energy barriers" to be asymmetric, em ployment of non-Hookean springs, and increasing the number of elements in the model have given better agreement of theory with experiment but leave much to be desired in the explana tion of the behavior of wool fibers.