Strain hardening of glassy polymers : theory and simulation

Glassy polymers submitted to an applied stress undergo yield at deformations of a few percent and stresses of some 10 MPa, followed by a slow drop in stress under plastic deformation corresponding to the strain-softening regime. Some polymers of high molecular weight display an increase of stress in the large amplitude regime of deformation. The typical slope of stress versus strain in this regime, GR, is of order 10⁷ – 10⁸ Pa well below Tg. We propose a theory which unifies these effects and what has been observed regarding dynamical heteroegenties. The model is solved in 3D with a spatial resolution on the nanoscale. Simulation results are in agreement with experimental data, such as the elastic modulus (G’∼1 GPa Pa and its temperature dependence), the yield stress and the yield behavior (strain softening), and the strain hardening regime (GR∼10 MPa) without introducing new adjustable paramters as compared to the scale of dynamical heterogeneties. In particular we show that the strain hardening mechanism suppresses the development of shear bands on the sacle of a few tens of nanometers, making the materials tougher. Our model allows in principle to describe various thermo-mechanical histories regrading polymer samples.