Modeling and FE simulation of coupled water diffusion and viscoelasticity in relaxation tests of polyamide 6

Polyamides can absorb or desorb water from or to their surrounding environment. The impact of this process is significant as water molecules lead locally to a swelling and a coupling of diffusion and deformation behavior. To model these phenomena, a strongly coupled chemo-mechanical (or diffuso-mechanical) model is required, considering both local water concentration and the viscoelastic material behavior of polyamide. In the present work, we derive and apply such a model to polyamide 6. A diffusion equation describing changes in water concentration is coupled to the balance of linear momentum in polyamide 6. The interaction between deformation and concentration is derived from thermodynamic considerations by introducing a free energy consisting of a mechanical and a chemical part. The mechanical part describes a linear viscoelastic model and includes chemical strains due to the presence of water molecules. The chemical part builds upon the theory of Flory and Huggins, that takes into account changes in enthalpy and entropy of mixing due to the interaction of polymer and water molecules. The coupling of deformation to water concentration arises due to a dependency of the water flux on the hydrostatic stress inside the polyamide. We successfully apply the derived model in Finite-Element simulations to predict the drying of polyamide 6 specimens without any coupling to mechanical loads. In addition, we reproduce experimentally obtained data from relaxation measurements, where the drying of polyamide specimens leads to an increase in relaxation modulus.