Constitutive modeling of the finite strain behavior of amorphous polymers in and above the glass transition

Abstract

A constitutive model is developed to capture the rate-dependent stress–strain behavior of an amorphous polymer (poly(ethylene terephthalate)-glycol (PETG)) at temperatures in and above the glass transition ( θ g). As a polymer goes through its glass transition, it exhibits a dramatic decrease in elastic modulus and yield stress, and continues to show strong dependence on strain rate and temperature. The mechanical recognition of the glass transition phenomenon itself depends on the applied deformation rate. The model is able to capture this strong dependence on temperature, strain rate, and strain state for uniaxial and plane strain compression experiments to very large strains. In particular, it captures the dramatic drop in modulus from below to above θ g and the corresponding drop in yield or flow stress. The model also captures the dependence on rate, temperature, and state of deformation of strain hardening, including the dramatic stiffening that occurs at very large strains. The model predictions are additionally compared to stress–strain data for poly(ethylene terephthalate) (PET) to identify the areas where strain-induced crystallization plays a role in its compressive mechanical behavior. No significant modifications are needed for the model to capture the behavior of PET in uniaxial compression, in spite of the fact that PET undergoes strain-induced crystallization upon deformation near θ g and PETG does not. This suggests that the primary mechanism for dramatic strain hardening in biaxial deformation of PET is not strain-induced crystallization, but rather molecular orientation and alignment.