A Mechanical Model of Helical Elements in Textured Yarns

Abstract

The helical model of the spontaneously collapsed filaments in twist-textured yarns is defined as reflecting the limiting case of a free-filament segment with infinite length (or number of coils) between two reversal points. The fundamental relationships linking fiber properties and parameters of the texturing process with geometrical and mechanical characteristics of the helices are derived directly from the differential equations of the three-dimensional elastica. Bicomponent and similar fibers are interpreted as a special case of twist-textured filaments with original (permanently set) helical angle equal to π/2; for this case an explicit functional relationship between contraction and stretching force is obtained.

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