Evolution of strain localization in glassy polymers: A numerical study

An explicit numerical implementation is described, for a constitutive model of glassy polymers, previously proposed and validated. Then it is exploited within a Finite Element continuum model, to simulate spontaneous strain localization (necking) occurring during extension of a prismatic bar of a typical glassy polymer. Material parameters for atactic polystyrene are employed. The material model is physically based and highly non-linearly viscoelastic. Three of its principal features are critical in simulations of strain localization: rate-dependence of plastic flow stress; strain-induced structural rejuvenation, represented by increase of Tool’s fictive temperature and leading to pronounced post-yield strain softening; and molecular alignment during extension, giving rise to strain-hardening. In all simulations there is a peak in nominal stress, satisfying the condition for localization to occur. Nevertheless, the simulations show that the process of strain localization varies considerably, depending on details of the extension sequence and on assumed values for certain material parameters. A characteristic feature observed is that strain localization in such a material occurs in two stages. There is an initial spurt associated with strain-softening, followed by a slower growth of localization that eventually subsides, ultimately giving way to uniform extension of the neck. But the details of evolution of the strain distribution vary greatly. The rapidity and severity of localization are increased by decreased temperature, increased strain-rate or greater structural rejuvenation. A simple one-dimensional stability analysis is successful in explaining the results.