Dr. Didier R. Long, Co-founder, Co-head of Laboratory of Polymers and Advanced Materials, UMR 5268 – CNRS/Solvay, 69192 Saint-Fons, France

Title: Strain hardening of glassy polymers : theory and simulation

Abstract: Over the past twenty years empirical evidence has shown that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of ξ ≃ 3 – 5 nm. A model for the dynamics of non-polar amorphous polymers, based on percolation of slow domains, has been developed and solved by 3D numerical simulations [1]. This so-called PFVD model succeeds in explaining many features observed in glassy polymers: the heterogeneous nature of the dynamics, the violation of the Stokes law observed for small probes, ageing and rejuvenation asymmetry, the shift of glass transition temperature in thin films. Experiments show that, under applied deformation, polymers undergo yield at deformations of a few percent and stresses of some 10 MPa, followed by a quick drop in stress and plastic flow, namely the strain-softening. Yield behavior is often described through the phenomenological Eyring model, according to which stress reduces free energy barriers.

In our model, we propose that the elastic energy stored at the scale of dynamical heterogeneities effectively reduces the free energy barriers between configurations and accelerates local dynamics [2]. After plastic flow, some polymers of high molecular weight display an increase of stress with increasing strain in the large amplitude regime of deformation. The typical slope, namely hardening modulus GR, is of order 10 7 – 10 8 Pa well below Tg. Classical theories involving the entropic response of the rubbery network cannot explain such a high value. GR is also found to increase upon cooling, as well as with strain rate and cross-linking density. The model of Chen et Schweizer [3], based on the suppression of density fluctuations caused by a deformation-induced local anisotropy, reproduces many features related to strain-hardening but lacks of a detailed spatial description. Analogously, we assume that local deformation induces a reduction of mobility, at the scale of dynamical heterogeneities, by orienting monomers in the drawing direction. We assume that consequent strengthening of monomer-monomer interactions results in a local increase of the glass transition temperature. Simulations show hardening moduli GR of order 10 – 100 MPa a few 10 K below Tg. This modulus decreases with temperature. The strain hardening regime is observed from strain amplitudes of about 20%. The effects of cross-linking and strain rate are studied and agree with experimental data. An enhanced ageing process is observed at large strains and is key for strain hardening mechanism.