(173d) 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.