A compact constitutive model to describe the viscoelastic-plastic behavior of glassy polymers

Polymer materials are generally susceptible to cyclic long-term loadings. Despite the continuous increase and popularization of polymer components, their cyclic deformation behavior is still, by far, under-explored. To this end, the development of effective polymer failure assessment tools for improving their cyclic loading properties is highly desirable. Most of the existing models are, however, based on elastic or hyperelastic initial responses that limit their ability to accurately predict the cyclic stress-strain hysteresis loops, and more so at stress levels below the peak yield stress.

In a recent research paper published in the International Journal of Plasticity, Professor Thierry Barriere and Dr. Xavier Gabrion from the FEMTO-ST Institute in collaboration with Dr. Sami Holopainen from Tampere University proposed a compact constitutive model to describe the viscoelastic-plastic behavior of glassy polymers for improved prediction of loops below the peak yield stress. The proposed model was inspired by the renowned Haward and Thackray model and its three-dimension extension capabilities, which was supplemented by a few thermodynamic internal variables for predicting the viscous deformation behavior under cyclic loading. It was worth noting that the mechanically motivated cyclic deformation was modeled at constant temperatures with stress levels maintained below the peak yield stress.

Comprehensive uniaxial tension experiments were conducted to validate and demonstrate the practical applicability of the model. The compact formulation along with the calibration scheme enabled accurate prediction of the shapes of the hysteresis loops. Besides, it gave a remarkable representation of the ratcheting behaviors of the polymers including the cyclic hardening.  For the glassy polymers, in particular, the improved damage prediction under cyclic long-term loadings was attributed to the presence of both the viscoelastic and plastic elements.

Unlike the conventional state-of-the-art model capable of predicting cyclic stress-strain hysteresis loops, the proposed model exhibited several advantages. For instance, it requires fewer materials parameters and internal state variables which simplifying its implementation. A linear spring separate to the viscoelastic-plastic elements can be used to describe the elastic portion of the deformation. Furthermore, this model allows the definition of the purely plastic and viscoelastic deformation based on the specified stress that controls the corresponding micromechanisms. On the other hand, the evidence of the creep-recovery tests also showed the capability of the models.

Overall, the proposed models exhibited improved prediction accuracy due to the compact formulation. Being much simpler and easy to implement, it can be used as build-in features in different finite-element packages. Despite the remarkable results, the study insights highlight the need to evaluate the model under cyclic shear or torsional as well as multidimensional loadings, taking into consideration the effects of temperature changes. Altogether, the research findings will advance the design of high-performance polymer materials by paving way for experiments involving multi-axial cyclic plasticity-that is currently under-researched.