Multiscale Modeling of Strain-Induced Crystallization in Polymers
Final Report Abstract
The present project deals with the thermodynamically consistent modeling of the strain-induced crystallization (SIC). This phenomenon is concerned with the change of polymer chains configuration and takes place at the nanoscale. However, the process significantly influences macroscopic mechanical and thermal properties of polymers and plays an important role when planning manufacturing processes as well as applications of the final product. The concepts developed within the project make it possible to obtain information about the SIC phenomenon from a specific point of view. By fitting homogenized quantities to experimental data, such as the stress, the crystallinity degree and the temperature, they give insight into the microstructure developed in the process, which is not otherwise accessible when using current experimental methods. Thus, the size and shape of the crystalline regions, the mutual interaction and the influence of heat on the crystallization can be investigated. In particular, the models developed in the project use the thermodynamic framework for material modeling based on the Coleman-Noll procedure and the minimum principle of the dissipation potential in order to derive evolution equations for the internal variables. This procedure requires suitable assumptions for the Helmholtz free energy and the dissipation potential. The dissipation potential in this case assumes two internal variables: the regularity of the polymer chain network and the flexibility of polymer chains as a result of heat generation by crystallization. The Helmholtz energy includes the Arruda-Boyce model, a crystalline energy term, a purely thermal energy part and a mixed energy contribution dependent on temperature and thermal flexibility. In a final step, each of the two internal variables are coupled with the crystalline deformation gradient and the thermal deformation gradient by assuming conditions that yield the following special features. Firstly, the evolution of the regularity depends on the evolution direction defined in terms of deviatoric crystallization Mandel stresses. Secondly, the chosen setup yields evolution equations which are able to simulate, depending on the sign of the driving force rate, the formation and the degradation of crystalline regions accompanied by the temperature change during a cyclic tensile test. The boundary value problem corresponding to the described process includes the balance of linear momentum and balance of energy, and serves as a basis for the implementation within an FEM code. The numerical results support expectations that the higher network regularity leads to a faster development of the crystalline regions, as well as that the neighboring nuclei yield the merging of crystalline regions. In addition, results on the temperature distribution show that heat is generated in the crystalline region, whereas the adjacent amorphous area cools down. Simulations also indicate that the temperature especially increases at places with clusters of crystalline regions, while the amorphous matrix outside these areas hardly experiences any temperature changes at all. The statistical aspects of the phenomenon are captured through the suitable simulation of the initial configuration, whereas the volume averaging procedure is used to provide diagrams depicting the effective polymer behavior. The proposed continuum mechanical models show some important advantages: On one hand, they investigate process mechanisms as well as their transferability to alternative polymer materials and their potential role in the material design. On the other hand, embedded in the finite element method, they offer time efficient solutions especially compared to the ab initio techniques typically used for the simulations at the nanolevel. Due to the compatibility with multiscale strategies, the models are even capable of simulating practical applications, thereby demonstrating the influence of crystallization.
Publications
- (2017). Continuum mechanical modeling of strain-induced crystallization in polymers. Proceedings of the 7th GACM Colloquium on Computational Mechanics, 579-582
Aygün, S., Klinge, S. and Govindjee, S.
- (2017). Mechanical modeling of the strain-induced crystallization in polymers. PAMM, 17(1), 389-390
Aygün, S. and Klinge, S.
(See online at https://doi.org/10.1002/pamm.201710164) - (2018). Study of the microstructure evolution caused by the strain-induced crystallization in polymers. PAMM, 18(1), e201800224
Aygün, S. and Klinge, S.
(See online at https://doi.org/10.1002/pamm.201800224) - (2019). Coupled thermomechanical model for strain-induced crystallization in polymers. PAMM, 19(1), e201900342
Aygün, S. and Klinge, S.
(See online at https://doi.org/10.1002/pamm.201900342) - (2019). Modeling the thermomechanical behavior of strain-induced crystallization in unfilled polymers. Proceedings of the 8th GACM Colloquium on Computational Mechanics, 151-154
Aygün, S. and Klinge, S.
- (2020). Continuum mechanical modeling of strain-induced crystallization in polymers. International Journal of Solids and Structures, 196-197, 129-139
Aygün, S. and Klinge, S.
(See online at https://doi.org/10.1016/j.ijsolstr.2020.04.017)
