28—A MIGRATING-FILAMENT THEORY OF YARN PROPERTIES

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Abstract
The theory is based on the assumption that the paths of all the filaments in a continuous-filament yarn are identical, except for a displacement along, and rotation about, the yarn axis. The path of the single filament is characterized by a regular periodic migration between the axis and the periphery; the form of this path is derived on the basis of the assumption of a uniform packing density. The equations by which the path is defined involve two dimensionless parameters, one related to the twist and the other to the period of migration. Formulae are derived for the retraction on twisting, and for the stress-strain curve, for yarns in which migration occurs. These are shown to reduce to the corresponding formulae derived from the coaxial-helix theory in the limiting case when the rate of migration is small. Numerical examples are worked out to show the effect of the rate of migration on the retraction and the stress. From these results it is concluded that for rates of migration in the range likely to be encountered in actual yarns, the difference between the migrating-filament and coaxial-helix theories is in the most extreme case barely significant. This conclusion provides a justification for the general application of the simpler coaxial-helix theory in dealing with the mechanical properties of yarns.

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