On couple-stress elasto-plastic constitutive frameworks for glassy polymers

Various experimental studies have revealed length scale dependent deformation of different materials at micron and sub-micron length scales. In metals, such length scale dependent deformations are considered to be associated with geometrically necessary dislocations arising from an increase in strain gradients related to non-uniform plastic deformation. Recent experiments, however, have shown that the nature of length scale dependent deformation in polymers is quite different from metals as in polymers size effects have been observed in pure elastic as well as in elasto-plastic deformation. It is shown in this study that similar to metals, size effects in polymers can be associated with an increase in higher order displacement gradients with decreasing length scale. However, the experimental results discussed here reveals that, in contrast to metals, these higher order displacement gradients are mainly of elastic nature even when glassy polymers deform elasto-plastically. Taking the effects of these elastic higher order displacement gradients into account, a couple-stress theory is developed to predict size effect in glassy polymers with elasto-plastic deformation.