Finite viscoplasticity of non-affine networks: Stress overshoot under shear

A constitutive model is derived for the viscoplastic behavior of polymers at finite strains. A polymer is treated as an equivalent network of chains bridged by permanent junctions. The elastic response of the network is attributed to elongation of strands, whereas its plastic behavior is associated with sliding of junctions with respect to their reference positions. A new kinetic equation is proposed that expresses the rate of sliding of junctions in terms of the Cauchy stress tensor. Constitutive equations for an equivalent non-affine network are developed by using the laws of thermodynamics, where internal dissipation of energy reflects two processes at the micro-level: sliding of chains along entanglements and friction of strands between junctions. A similarity is revealed between these relations and the "pom-pom" model. The governing equations are applied to study stress overshoot at simple shear of an incompressible medium. Adjustable parameters in the stress-strain relations are found by fitting experimental data on polycarbonate melt reinforced with short glass fibers and polystyrene solution. Fair agreement is demonstrated between the observations and the results of numerical simulation.