From macroscopic yield criteria to atomic stresses in polymer glasses

The relationship between macroscopic shear yield criteria and local stress distributions in deformed polymer glasses is investigated via molecular dynamics simulations on different scales of coarse-graining. Macroscopic shear stresses at the yield point obey a pressure-modified von Mises {(pmvM)} criterion for many different loading conditions and strain rates. Average local stresses in small volume elements obey the same yield criterion for volumes containing approx. 100 atoms or more. Qualitatively different behavior is observed on smaller scales: the average octahedral atomic shear stress has a simple linear relationship to hydrostatic pressure regardless of macroscopic stress state and failure mode. Local plastic events are identified through a threshold in the mean-squared nonaffine displacement and compared to the local stress state. We find that the {pmvM} criterion only predicts local yield events when stress and displacements are averaged over at least 100 atoms. By contrast, macroscopic shear yield criteria appear to lose their ability to predict plastic activity on the atomic scale.