A Simple Model for the Deformation-Induced Relaxation of Glassy Polymers

            Strain hardening has long been an observed feature of polymer glasses in extension; explanations to date have often been phenomenological.   Recent experiments by Ediger and coworkers (Lee et al. Science 323, 231, 2009) have found strain hardening to be accompanied by a striking and unexplained dip in the segmental relaxation time, i.e., a non-monotonicity in the segmental relaxation time under constant load. Here we explain such behavior and develop a simple constitutive equation for polymer glasses by combining a minimal model flow-induced liquefaction of a glass with a description of the stress carried by strained polymers. Under constant load, liquefaction of segmental motion permits strong flow that creates polymer-borne stress. This slows the deformation enough for the segmental modes to re-vitrify, causing strain hardening. In this way, the observed non-monotonicity in the segmental relaxation modes is produced, both on loading and on unloading. We compare predictions of this theory with measurements of segmental relaxation time during loading by the Ediger group, and show semi-quantitative agreement of our theory with these data.  We also address the elastic recoil and change in segmental relaxation time that occur during unloading of stress.