A constitutive model for the viscoplastic behavior of rubbery polymers at finite strains

A constitutive model is derived for the viscoplastic behavior of rubbery 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 the elongation of strands, whereas its plastic behavior is associated with the sliding of nodes with respect to their initial positions. Unlike conventional stress-strain relations in finite viscoplasticity, the rate-of-strain tensor for the sliding of junctions is expressed in terms of the rate-of-strain tensor for macro-deformation. Constitutive equations are developed by using the laws of thermodynamics. These relations are simplified for simple shear of an incompressible medium with finite strains. The governing equations are determined by 3 material constants. To verify the model, a series of shear tests is performed on polycarbonate melts reinforced with short glass fibers. Adjustable parameters in the stress-strain relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. It is shown that the material constants change with the filler content in a physically plausible way.