Modeling the viscoelastoplastic response of amorphous glassy polymers

Abstract

Constitutive equations are derived for the viscoelastoplastic response of amorphous glassy polymers at isothermal loading with small strains. A polymer is treated as an ensemble of cooperatively relaxing regions (CRR) which rearrange at random times as they are thermally agitated. Rearrangement of CRRs reflects the viscoelastic response of the bulk medium. At low stresses, CRRs are connected with each other, which implies that the macro-strain in a specimen coincides with micro-strains in individual relaxing regions. When the average stress exceeds some threshold level, links between CRRs break and relaxing domains begin to slide one with respect to another. Sliding of micro-domains is associated with the viscoplastic behavior of polymers. Kinetic equations are proposed for viscoplastic strains and for the evolution of the threshold stress. These equations are validated by comparison with experimental data in tensile relaxation tests and in tests with constant strain rates. Fair agreement is demonstrated between results of numerical simulation and observations for a polyurethane resin and poly(methyl methacrylate).