Physics of strain hardening in glassy polymers – PoSH

Some glassy polymers with high molecular weights exhibit a strain hardening (SH) regime at large deformation in plastic flow during which the stress increases. This regime, which is the focus of this project, is very important because without SH polymer glasses are fragile. Understanding deformation mechanisms of glassy polymers on the microscopic scale, from the linear regime up to the strain hardening regime is an important and current scientific challenge. Long’s group has developed a microscopic theory for plasticity, according to which relaxation takes place by reorganizations at a scale of about 5 nm. The stored elastic energy at this scale corresponds to a reduction of free energy barriers which enables plastic flow. This group has developed a companion numerical tool for calculating plastic flow in 3D, with a 5 nm spatial resolution that allows calculate the distribution of relaxation times and its evolution under applied strain, during ageing and rejuvenation for any thermo-mechanical history. It is based upon a dynamical equation regarding the evolution of a tensorial nematic order parameter S on the monomer scale. The orientation enhances the monomer-monomer interactions and leads to an increase of the free energy barriers. Preliminary results of this model reflect the basic features of strain hardening such as the SH regime itself, the Bauschinger effects and the evolution of the distribution of relaxation time as measured by the Ediger group. The reorientation dynamics at the monomer scale and its relaxation appear to be key to describe the physics of strain hardening. In this project, a joint experimental and theoretical approach will be developed to study the local orientation and its relaxation behavior under various thermo-mechanical loading histories by X-ray scattering, NMR and Differential Scanning Calorimetry (DSC).

Current results for the order of magnitude of S calculated by the model are in rough agreement with values obtained by NMR a long time ago. Spiess and coworkers showed that S can reach values of about 0.2 at 100% of deformation, close to values obtained during preliminary NMR tests by Saalwächter et al. (one of the applicants), who developed a new and efficient approach of data analysis to be used in this project. The NMR part, focusing on segmental ordering measured in quenched samples without significant dynamics, will thus provide molecular information on the local segmental ordering of different chemical moieties and allow us to calibrate the X-ray studies that provide relatives values for the orientation. The tensile machine developed by P-A Albouy allows simultaneous X-ray patterns acquisition and mechanical solicitations. The NMR and X-ray studies will thus allow to monitor how S relaxes during ageing, heating, stretching, compression and other types of mechanical solicitations along successive different axes. Similar studies will be performed by DSC in order to study how mechanical energy is stored in the glassy disordered materials. In summary, we will be able confront in detail the prediction of our numerical model with mechanical experiments, calorimetric experiments (stored elastic energy, which gives access to the decrease of free energy barriers) and X-ray as well as NMR experiments. These experiments will allow to test and to develop further the theory. The outcome of this project will be a detailed microscopic description of the physics of strain hardening and a generic, quantitative theory of relaxation mechanisms in glassy polymers in the large strain regime, which will be also of applied interest.