A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures

The mechanical response of solid amorphous polymers is strongly dependent on the temperature and strain rate. More specifically, the yield stress increases dramatically for the low temperatures as well as for the high strain rates. To describe this behavior, we propose a new formulation of the cooperative model of Fotheringham and Cherry where the final mathematical form of the model is derived according to the strain rate/temperature superposition principle of the yield stress. According to our development, the yield behavior can be correlated to the secondary relaxation and we propose an extension of the model to temperatures above the glass transition temperature. For a wide range of temperatures and strain rates (including the impact strain rates), the predicted compressive yield stresses obtained for the polycarbonate (PC) and the polymethylmethacrylate (PMMA) are in excellent agreement with the experimental data found in the literature.