Predicting the brittle-to-ductile transition in amorphous polymers

Brittle-ductile transition (BDT) is an important characteristic of amorphous (and semicrystalline) polymers. For a given strain rate, at temperatures above BDT, the polymers exhibit strain softening followed by yield and strain hardening, while at temperatures below BDT, the same materials exhibit brittle failure at relatively low strains. Surprisingly, today there is no simple model describing BDT as a function of polymer chemistry, sample history, deformation type, and strain rate. Experimental data suggest that BDT is often, though not always, associated with the β-transition. We formulate a simple scalar model to describe the visco-elasto-plastic shear stress-strain curves as functions of temperature and strain rate. We also show that within this model, there is always an upper bound on the strain rate where the material can have a uniform viscoplastic flow; this upper bound is assumed to represent the BDT for a given temperature. We stipulate that this upper bound is inversely proportional to the Johari-Goldstein β-relaxation time. Using our "general" Sanchez-Lacombe "two-state, two-(time)scale" (SL-TS2) model, we estimate the BDT for three polymers (polystyrene, poly(methylmethacrylate), and poly(vinylchloride)) and find a good agreement with experimental data.