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
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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.