12. Nanostructural Response to Plastic Deformation in Glassy Polymers

A closed form stress-strain relation is proposed for modeling the postyield behavior of amorphous polymers based on the shear transformation zones (STZs) dynamics and free volume evolution. Use is made of the classical free volume theory by Cohn and Turnbull (J Chem Phys 31:1164, 1959), and also STZ-mediated plasticity model for amorphous metals by Spaepen (Acta Metall 25:407, 1977) and Argon (Acta Metall 27:47, 1979) for developing a new homogenous plasticity framework for glassy polymers. The variations of free volume content and STZs activation energy during large deformation are parametrized considering the previous experimental measurements using positron annihilation lifetime spectroscopy (PALS) and thermal analysis with differential scanning calorimetry (DSC), respectively. The proposed model captures the softening-hardening behavior of glassy polymers at large strains with a single formula. This study shows that the postyield softening of the glassy polymers is a result of the reduction of the STZs nucleation energy as a consequence of increased free volume content during the plastic straining up to a steady-state point. Beyond the steady-state strain where the STZ nucleation energy reaches a plateau, the increased number density of STZs, which is required for finite strain, brings about the secondary hardening continuing up to the fracture point. This model also accurately predicts the effect of strain rate, temperature, and thermal history of the sample on its postyield behavior which is in consonance with experimental observations. Implication of the model for interpreting the localization and indentation size effect of polymers is also discussed.