Modeling and Simulation of the Mechanical Properties of Reinforced Fuel Cell Membranes
Authors: Mazrouei Sebdani Mohsen , Kjeang Erik , Baroody Heather 
Published: July 2022

Polymer electrolyte fuel cells (PEFCs) have gained popularity over internal combustion engines due to their zero CO2 emission, low working temperature, and high efficiency. However, transportation markets generally require high durability and reliability, which remains a significant challenge for PEFC developers. For instance, the thin, ion-conducting membranes used in PEFCs must be able to withstand both chemical and mechanical stresses during dynamic operation. Reinforced membranes even still there are durability challenges that remain even though it is more robust. These membranes have limited mechanical strength, and micro-cracks may allow hydrogen permeation and cause ultimate fuel cell failure. Dynamic stresses caused by temperature and humidity cycles are causing micro-cracks to form and propagate. Because the membrane is constrained by the other parts of the membrane-electrode assembly (MEA), any change in temperature and humidity can create swelling strain and thermal strain in the membrane, resulting in residual stress [1]. The first step in understanding this damaging phenomenon is to simulate the membrane's visco-elastic and visco-plastic behavior while taking temperature, humidity, and strain rate into account. The objective of the present work is to develop such a constitutive mechanical model for mechanically reinforced membranes, which are commonly used in modern PEFCs.
Khorasany et al. [2] developed a fatigue lifetime model based on the elastic-plastic constitutive method and Smith-Watson-Topper (SWT) fatigue equilibrium for conventional, non-reinforced fuel cell membranes. In the present work, for strains below the yield point, the linear elasticity by Hooke's law has been considered and the visco-elastic and visco-plastic behaviors of the membrane have been neglected, but for every temperature and humidity, the related Young’s modulus and Poisson’s ratio have been obtained from prior experiments, and for plastic yield response, the Von Mises yield criterion has been selected. Khattra et al. [3] used the G’Sell-Jonas theory for the constitutive model of a non-reinforced membrane, which can only be employed for tensile stresses, while in this study, a generalized G’Sell-Jonas approach; equation 1, has been developed for the reinforced membrane that can also be used for compressive stresses that are common during in-situ fuel cell conditions. This phenomenological theory accounts for the effects of temperature, humidity, and strain rate on membrane mechanical properties and, when combined with thermal and swelling strains, provides a comprehensive model of membrane behavior for both ex-situ and in-situ conditions. For the reinforced membrane, tensile stress-strain tests in two principal in-plane directions have been done that showed its isotropic behavior and, therefore, provide input data for the parameters of the proposed generalized G’Sell-Jonas model.

σ(ε,T,H)generalized G'Sell-Jonas=step(ε)K(T,H)(1-e-w(H)abs(ε))eh(H)ε^2

(1)

step(ε)=+1 ε≥0, -1 ε<0

In the above equations, K, w, and h are empirical parameters dependent on temperature (T) and humidity (H), and ε is strain. Elastic modeling based on Von-Mises has been studied for constitutive models with stresses below 1 MPa, while isotropic work hardening based on the generalized G'Sell-Jonas theory has been considered for higher stresses in order to follow plastic behavior. In elastic mode, the membrane's Young’s modulus is calculated using a function of humidity and temperature derived from tensile tests. Tensile tests under four environmental conditions and two strain rates in two principal in-plane directions, as well as fatigue tests for extracting S-N curves for this membrane, have been obtained using dynamic mechanical analysis (DMA).
Based on Figure 1, the mechanical strength of this isotropic reinforced membrane decreases with increasing temperature and humidity, but the effect of temperature is greater. Because of the viscoelastic nature of the membrane, by increasing the strain rate, the membrane stiffness has been increased too. In the fatigue tests done in DMA, the force track is 150% (= ×100%), R-value = , and frequency is 10 Hz.
FEM modeling based on G’Sell-Jonas’s theory shows a strong agreement with the experiments that has been illustrated in Figure 1. The fatigue lifetime distribution based on generalized G’Sell-Jonas’s theory and SWT parameters extracted from Khorasany’s paper [2] have been simulated that reveals when the maximum stress in fatigue cycles is more than 17-18 MPa, a huge drop in fatigue lifetime is observed.

Acknowledgments

Funding for this research has been provided by AVL Fuel Cell Canada and Mitacs.

References

Alavijeh, A.S., et al., Effect of hygral swelling and shrinkage on mechanical durability of fuel cell membranes. Journal of Power Sources, 2019. 427: p. 207-214.

Khorasany, R.M., et al., Mechanical degradation of fuel cell membranes under fatigue fracture tests. Journal of Power Sources, 2015. 274: p. 1208-1216.

Khattra, N.S., et al., Residual fatigue life modeling of fuel cell membranes. Journal of Power Sources, 2020. 477: p. 228714.

Figure 1