A fully coupled thermo-viscoelastic-viscoplastic-damage framework to study the cyclic variability of the Taylor-Quinney coefficient for semi-crystalline polymers

In the present work, a rigorous and consistent thermo-viscoelastic-viscoplastic ductile damage model is proposed to address the variability of the Taylor-Quinney coefficient (the storage to anelastic energy rate ratio) during the anelastic deformation of thermoplastic polymers. More specifically, the constitutive model developed is mainly dedicated to the description of recoverable viscoelastic effects occurring on different time scales, irreversible strains observed above the stress threshold and energy responses arising from the anelastic deformation process (storage of energy, dissipation of energy, thermomechanical coupling, etc.). One of the aims of this paper is to evaluate the partitioning between stored and heat energy without assuming any Taylor-Quinney values. The proposed approach is incorporated into the framework of Thermodynamics of Irreversible Processes and Generalized Standard Materials formalism to offer the thermodynamic consistency of all the constitutive equations. The numerical algorithm for the proposed model is implemented in the well-known finite element code Abaqus via the user material subroutine UMAT using an implicit formulation of the constitutive equations coupled with a radial return mapping algorithm. The model is then calibrated and validated across monotonic tensile and cyclic tensile-tensile tests by comparing predicted and experimentally observed energy responses. This comparison shows a good level of accordance between experimental findings and model predictions in terms of stress-strain responses for both monotonic and cyclic thermomechanical loading conditions. The model can also numerically capture the cyclic kinetics of the storage and dissipation energies. The capabilities of the fully-coupled model have been demonstrated through simulating the thermo-mechanical response of a complex 3D structure. The numerical analysis establishes the model's capability to accurately render the spatio-temporal patterns of the Taylor-Quinney coefficient and the self-heating induced part of the ductile damage.