An Internal Variable Approach to Model Relaxation Processes Near the Glass Transition Regime of Amorphous Thermoplastics
Frederik Hille 1*, Johannes Keursten 1, Sabine Enders2, Thomas Böhlke 1
1 Karlsruhe Institute of Technology (KIT) - Institute of Engineering Mechanics; 2 Karlsruhe Institute of Technology (KIT) - Institute of Technical Thermodynamics and Refrigeration
Keywords: glass transition, enthalpy relaxation, thermodynamical consistency
When predicting the material behavior of thermoplastic materials for a wide range of temperatures, it is important to incorporate the influence of their distinct glass transition regime. In this context, there are two phenomena to highlight. First, there is a significant difference in their material properties, such as the stiffness, above and below the glass transition temperature. Secondly, there is a noticeable process and rate dependency in the material behavior in the glass transition regime, i.e., viscoelasticity in the mechanical case [1]. However, such relaxation phenomena can also be observed for caloric quantities, such as the heat capacity, which depend on the temperature rate in the vicinity of the glass transition temperature. In the case of heating processes even a non-monotonic change with respect to the temperature can be observed. In this contribution, we give an introduction to an internal variable approach to model caloric relaxation processes, similar to the works of Lion et al. [2] and Keursten et al. [3]. Based on the standard linear solid model, analogies to classical viscoelasticity can be drawn. This allows us to derive clear restrictions on the introduced material parameters to ensure thermodynamic consistency. Additionally, the influence of energetic and dissipative effects can be separated. The predictive capabilities of the model will be investigated using exemplary experimental data. By measuring the heat capacity in a DSC experiment, the presented model gives access to the evolution of the internal variable. Special focus will be put on the determination of the relaxation time, in particular with respect to different rate dependencies.
References
- U. W. Gedde, M. S. Hedenqvist, M. Johansson, L. Berglund, and J. Wohlert, Fundamental Polymer Science, Springer Nature Switzerland, 2025.
- A. A. M. C. A. J. M. Lion, Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid, Continuum Mechanics and Thermodynamics, 29, 2017.
- J. Keursten, S. Enders, and T. Böhlke, Constitutive theory and simulation of entropy and enthalpy relaxation in the glass transition regime, Advanced Structured Materials, 238, 2025.