A unified model for stiffness modulus of amorphous polymers across transition temperatures and strain rates

In many applications, polymer materials undergo a large variety of mechanical loading conditions, wherein the influences of temperature and strain rate are of prime importance. Mahieux and Reifsnider [Mahieux CA, Reifsnider KL. Polymer 2001;42:3281. [19]] have proposed a statistical model to describe the stiffness variation of polymers over a wide range of temperatures. However, this model does not consider any frequency/strain rate dependence of the stiffness modulus. Starting from this consideration, we propose here to transform this latter model into a robust physically based model for the prediction of the stiffness modulus for a wide range of temperatures and frequencies/strain rates. This new formulation has been successfully validated for two amorphous polymers, polymethylmethacrylate (PMMA) and polycarbonate (PC), using dynamic mechanical analysis and uniaxial compression testing. Good agreement has been found between theory and experiment for the non-linear behavior of the initial Young's modulus, at the very high strain rates.