Modeling the viscoelastoplastic behavior of amorphous glassy polymers

Constitutive equations are derived for the viscoelastic and viscoplastic responses of amorphous glassy polymers at isothermal loading with small strains. A polymer is modeled as an ensemble of cooperatively relaxing regions (CRR) that are rearranged at random times as they are thermally agitated. At relatively low stresses, CRRs are bridged by links that ensure that the macro-strain in a specimen coincides with micro-strains in relaxing regions. When the average stress exceeds a threshold strength for the links, some of them break, and relaxing domains begin to slide with respect to one another. Rearrangement of CRRs reflects the viscoelastic behavior, whereas sliding of micro-domains is associated with the viscoplastic response of glassy polymers. Kinetic equations are proposed for the evolution of viscoplastic strains and the strength of an ensemble of links. These equations are verified by comparison with experimental data in tensile relaxation tests and in tensile and compressive tests with constant strain rates. Fair agreement is demonstrated between results of numerical simulation and observations for a polyurethane resin and poly(methyl methacrylate).