A Time and Hydration Dependent Viscoplastic Model for Polyelectrolyte Membranes in Fuel Cells

Document Type


Subject Area(s)

Mechanical Engineering, Chemical Engineering


Ionomers are co-polymers with ionic groups. One of the interesting applications of ionomer membranes is as electrolytes in proton exchange membrane (PEM) fuel cells. The most commonly used membranes in PEM fuel cells are perfluorosulfonic acid (PFSA) membranes, e.g., Nafion® from DuPontTM. Besides its dependency on temperature and hydration due to phase inversion and cluster formation, Nafion® as a polymer, exhibits strong time and rate effects. In this work, the stress–strain behavior of Nafion® at different strain rates has been obtained in an environmental chamber for various temperatures and hydrations. After a certain strain was reached in each test, stress relaxation was performed for an hour to observe the relaxation behavior of Nafion®. We attempted to use a nonlinear, time-dependent constitutive model to predict the hygro-thermomechanical behavior of Nafion®. Because a substantial component of the response is unrecoverable, a viscoplastic model was employed. The proposed two-layer viscoplasticity model consisted of an elastoplastic network that was in parallel with an elastic-viscous network (Maxwell model) which separates the rate-dependent and rate-independent behavior of the material. After obtaining the necessary parameters for different hydrations, this model showed reasonably accurate success in predicting the stress–strain behavior at different strain rates, and matched the relaxation test results. Finite element simulations based on the proposed two-layer viscoplasticity model were in good agreement with test results and can be used to study the stress–strain state of the ionomer membranes in fuel cell configurations.