Rheology of Neck Formation in the Cold Drawing of Polymeric Fibers

An asymptotic formula has been obtained for the axial tension in nonlinear viscoelastic fibers undergoing inhomogeneous stretch. The formula, which is valid to within an error of the fourth order in diameter, expresses the tension per unit cross-sectional area in terms of the history of the local axial stretch and its first two derivatives with respect to distance along the fiber axis. The theory obtained by treating the formula as exact is consistent with thermodynamical principles, and permits computation of the stretch field resulting from a specified tensile loading history. Numerical results for creep under static load 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 are in accord with familiar observations of neck formation in polymeric materials susceptible to cold drawing.