2—stress–strain–time Relationships of Non–uniform Textile Materials

A general relationship has been derived between the extension of, and the load applied to, a specimen of non-uniform cross-sectional area. The behaviour of uniform and non-uniform specimens has been compared analytically for a power law relationship between stress and strain, and is shown to differ significantly when the non-uniform specimen was a truncated cone or when the area varied according to the Gaussian frequency distribution. The extensions under load of typical, non-uniform keratin fibres have been determined by numerical integration to illustrate a general method which may be used for any cross-sectional area distribution and for any stress-strain relationship. The creep behaviour of non-uniforni specimens has been similarly treated, with a brief note on the stress-relaxation of non-uniform specimens and on the effect of non-uniformity on such properties as breaking stress, breaking strain and work to extend. As an example of the profound effects which may be caused by nonuniformity, a typical keratin fibre, having a coefficient of variation of crosssection of 16%, subjected to a particular load, extends 60% more than a uniform fibre having the same average cross-sectional area. Similar mathematical procedures can be employed not only to study other rheological phenomena of any dimensionaliy non-uniform niaterial, but also to advance knowledge of the structural irregularities of textile fibres and the mechanical behaviour of textile assembles.