A Constitutive Equation for the Elasto-Viscoplastic Deformation of Glassy Polymers

Constitutive equations for finite elastic-plastic deformation of polymers and metals are usually formulated by assuming an isotropic relation between the Jaumann rate of the Cauchy-stress tensor and the strain-rate tensor. However, the Jaumann-stress rate is known to display spurious non-physical behaviour in the elastic region. Replacing the Jaumann-stress rate by a Truesdell-stress rate results in an adequate description in the elastic region, but gives rise to a volume decrease during plastic flow in tensile deformation. In this paper a "compressible-Leonov model" is introduced, in which the elastic volume response is rigorously separated from the elasto-viscoplastic isochoric deformation. This has the advantage that the model can be extended in a straightforward way to include a spectrum of relaxation times. It is shown that in the limit of small elastic strains, the compressible Leonov model reduces to the Jaumann-stress rate model, but diverges from the Truesdell-stress rate model. Finally, a comparison is made of the above mentioned models in a homogeneous uniaxial tensile test and a homogeneous plane-stress shear test, using polycarbonate (PC) as a model system. All models considered in this paper are "single mode" models (i.e. one relaxation time), and, therefore, cannot describe the full (non)linear viscoelastic region, nor the strain-hardening or strain-softening response.