Application of a large deformation viscoelastic model to the unstable necking of polyethylene

Abstract

A large deformation, rate dependent model is applied to high temperature stretching of polyethylene. The theory is physically motivated, consisting of a model of a network of chain molecules to represent regions dominated by amorphous polymer, with embedded rigid spheres to introduce strain concentration similar to that caused by hard crystalline regions. Dependence on time and rate is introduced via shear stress driven diminution of the sphere radii. Experimentally, the rate dependence of the stress is such that, under tensile deformation, there is no necking associated with the initial yield point. Necking occurs at higher strains; this is associated with a weakening of rate dependence with increasing strain, which is a natural feature of the theory. It provides a realistic model of large tensile deformations, which in general involve the evolution of necking instabilities. It is implemented in a finite element scheme by using the package ABAQUS.