Theory of Bauschinger and Some Other Memory Effects in Glassy Polymers

We proposed recently that the strain hardening of glassy polymers is attributed to the increase of free energy barriers for α-relaxation as a consequence of local orientation of Kuhn segments during the course of deformation. As the chains have been significantly oriented at the Kuhn segments scale, the contribution of Kuhn segments orientation to free energy barriers may become large and may then overcompensate the decrease of free energy barriers due to the increasing stress, the latter being responsible for yield and the onset of plastic flow. We show that the slow relaxation of Kuhn segments orientation explains the various memory effects observed in the strain hardening regime and generically named Bauschinger effect. It explains the fact that the stress-strain curve of a second deformation after some waiting time at some point in the strain hardening regime rejoins the reference curve, and that a yield stress is present for this second deformation. Indeed, the degrees of freedom which control the free energy barriers associated with yield relax on the time scale of the experiment, whereas Kuhn segments orientations, that is the degrees of freedom which control the free energy barriers associated with plastic flow in the strain hardening regime, relax slowly. We calculate the evolution of the relaxation time distributions, as well as that of the dominant relaxation time and of the Kuhn segments orientations, during successive deformations (traction-traction, traction-compression, compression-traction, compression-compression). These predictions could be tested experimentally.