Interaction of nonhomogeneous shear, nonlinear viscoelasticity, and yield of a solid polymer

Abstract

A constitutive equation for small strain viscoelastic response is considered in which stress relaxation. occurs faster as strain increases. The constitutive equation is of single integral type and has a psuedo- or material time function which is calculated from a strain dependent shift function. First, it is shown that such a constitutive equation can account for yield as observed in polymers for a number of different stress and strain histories. Next, the constitutive equation is used in the analysis of the problem in which a hollow cylinder is fixed at its inner surface and a moment history is applied to its outer surface. This causes the cylindrical surfaces to rotate about the central axis, thereby inducing a radial shear strain distribution. It is shown that there is a time when the material near the inner support begins to yield and a layer of large shear strain gradient begins to grow rapidly. It is also shown that the stress or strain history at a material element will generally not be one of the standard histories used to study yield.