On Neck Formation in the Cold Drawing of Viscoelastic Fibers

Abstract

An asymptotic expression has been obtained for the axial tension in a slender rod of a non-linear viscoelastic material undergoing inhomogeneous stretch. This expression, which is valid to within an error of fourth order in diameter, gives the tension per unit cross-sectional area as a functional of the history of the local stretch and its first two spatial derivatives. The theory that results from treating the expression as exact is consistent with thermodynamical principles, and it yields a functional-differential equation for the stretch field that is amenable to numerical analysis. Computed solutions for creep under static loads show that for an appropriate class of materials with slowly fading memory there is a range of applied loads for which an initially homogeneous deformation evolves into a well defined neck whose edges, after a period of relatively quiescent incubation, advance rapidly along the fiber and in so doing transform moderately stretched material into highly stretched, i.e., drawn, material. The calculated fiber profiles and the predicted dynamics of neck formation and growth are in good accord with familiar observations.