A hybrid Brownian dynamics/constitutive model for yielding, aging, and rejuvenation in deforming polymeric glasses†
We present a hybrid model for polymeric glasses under deformation that combines a minimal model of segmental dynamics with a beads-and-springs model of a polymer, solved by Brownian dynamics (BD) simulations, whose relaxation is coupled to the segmental dynamics through the drag coefficient of the beads. This coarse-grained model allows simulations that are much faster than molecular dynamics and successfully capture the entire range of mechanical response including yielding, plastic flow, strain-hardening, and incomplete strain recovery. The beads-and-springs model improves upon the dumbbell model for glassy polymers proposed by Fielding et al. (Phys. Rev. Lett., 2012, 108, 048301) by capturing the small elastic recoil seen experimentally without the use of ad hoc adjustments of parameters required in the model of Fielding et al. With appropriate choice of parameters, predictions of creep, recovery, and segmental relaxation are found to be in good agreement with poly(methylmethacrylate) (PMMA) data of Lee et al. (Science, 2009, 323, 231–234). Our model shows dramatic differences in behavior of the segmental relaxation time between extensional creep and steady extension, and between extension and shear. The non-monotonic response of the segmental relaxation time to extensional creep and the small elastic recovery after removal of stress are shown to arise from sub-chains that are trapped between folds, and that become highly oriented and stretched at strains of order unity, connecting the behavior of glassy polymers under creep to that of dilute polymer solutions under fast extensional flows. We are also able to predict the effects of polymer pre-orientation in the parallel or orthogonal direction on the subsequent response to extensional deformation.
- This article is part of the themed collection: Polymers