A finite strain thermodynamically-based constitutive modeling and analysis of viscoelastic-viscoplastic deformation behavior of glassy polymers

In elastic and plastic deformation of glassy polymers and with the increase of deformation, the material would exhibit elastic, viscoelastic, and viscoelastic-viscoplastic (VE-VP) responses in sequence. These deformation behaviors should be constitutively modeled in such a way to accurately and efficiently simulate many important physical behaviors and phenomena involved in polymer deformation and processing. The elastic and viscoelastic deformation behavior in the pre-yield region can be well represented by the existing constitutive models. However, the VE-VP response in the post-yield region, such as stress relaxation and strain recovery behaviors, cannot be well modeled yet. In this research, a series of uniaxial compression tests of the stress relaxation and the loading-unloading-recovery behaviors of glassy polymer were firstly carried out. The experimental phenomena show strain-rate-dependent characteristics that cannot be explained by the thermally-activated viscosity/viscoplasticity theory. Therefore, it is proposed that a glassy polymer can be treated as a glassy network linked by the secondary bonds and entanglements; while the glassy network is locally yielded and elastically distorted in the pre-yield region, giving rise to a glassy network resistance (GNR) which accounts for the strain-rate-dependent characteristics. A finite strain thermodynamically-based constitutive model was then proposed to incorporate the effects of the GNR. Finally, the newly proposed model was calibrated and its predictive capability was elaborated with the comparison of experiments as well as two widely reported models. The predicted results demonstrate that the GNR is critical in controlling the post-yield stress relaxation and strain recovery. In addition, the nonlinear evolution of the GNR plays a key role in controlling the nonlinear pre-peak hardening and the nonlinear unloading curve. This research thus not only provides a new constitutive theory for modeling of the VE-VP deformation behavior of glassy polymers, but also advances the understanding of the mechanical responses of glassy polymers in deformation process.