Theory of Bauschinger effect in glassy polymers

We propose a theory for strain hardening and Bauschinger effect. Reorganizations for monomer relaxation take place on a scale N of order 1000 monomers. At this scale, free energy barriers decrease under the effect of the stress, which leads to yielding and the onset of plastic flow. Conversely, monomer orientation increases the barriers by a quantity μ N Tr(q²) where q is the local, nematic-like order parameter whose distribution is computed in 3D during the course of deformation and µ is an energy scale of typical order 0.2-0.3 kT. As the chains have been significantly oriented at the monomer scale due to deformation, this term overcompensates the decrease of free energy barriers due to the increasing stress and is responsible for strain hardening. These two contributions to the free energy barriers have very different kinetics. The contribution related to the stress relaxes immediately as a function of the applied stress whereas the orientational contribution relaxes by rotational diffusion, which is very slow deep in the glassy state. We show that the slow relaxation of monomer orientation explains the various memory effects observed in the strain hardening regime and generically named Bauschinger effect