Multi-step deformation experiment and development of a model for the mechanical behavior of polymeric glasses

Abstract

Traditional models for stress-strain behavior of glassy polymers are based on the assumption that the critical features of the stress-strain response can be explained by changes in the molecular mobility. The four-step deformation experiments consisting of (i) an initial constant strain rate loading, (ii) unloading to specified stress, (iii) creep under that stress and (iv) second constant strain rate loading, challenges that assumption. Specifically, existing models fail to predict the experimentally observed large second stress overshoot in case of a slight unloading. Until now there has remained a possibility that the mobility was actually lower in case of a partial rather than complete unloading, which would preserve the main assumption, if not particular details, of these specific constitutive models. By performing direct optical experiments using the photobleaching technique simultaneously with the mechanical four-step experiments it is shown that a lower molecular mobility upon partial unloading does not take place. As traditional models cannot account for these experimental results, a new model has been developed where the changes of molecular structure manifest not in the relaxation time, but in the shear modulus, which is function of an internal variable that is the fraction of the efficiently packed material. This fraction obeys a population balance equation, where the steady-state fraction is controlled by the applied stress. In the absence of deformation, the efficiently packed fraction increases, which explains the increase in the modulus in the course of physical aging below Tg. The model qualitatively describes the four-step experiment as well as single step loading experiments.