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On the rheology of cold drawing. I. Elastic materials

In this, the first paper in a series on neck formation and steady-state drawing of polymeric fibers and films under uniaxial tension, the emphasis is laid on those aspects of the mechanics of cold drawing that are not sensitive to viscoelastic effects and, therefore, can be treated by use of constitutive assumptions appropriate to elastic materials. It is here shown that a unidimensional theory which has been employed to model the mechanics of slender bars in tension6 can be derived as an approximation for three-dimensional bars and, in a sense which can be made precise, is valid to within an error of the order of the fourth power of the thickness. A particular constitutive equation for incompressible, three-dimensional, elastic materials is explored in detail and is found to yield, for such slender bars as thin fibers and wide (but thin) strips of film, equations of equilibrium whose solutions are in good qualitative accordance with the necks and drawing configurations observed in practice.