Proton exchange membrane fuel cells (PEMFC) have gained popularity over internal combustion engines due to their low work temperature, and high efficiency. On the other hand, PEMFCs have struggled to achieve a large market share due to their poor durability and reliability. These fuel cells' membranes aren't particularly strong, and microcracks allow hydrogen to pass through[1]. As a result, the cracks' propagation will degrade overall performance. Dynamic stresses caused by temperature and humidity cycles are causing micro-cracks to form and spread, which were formed during the membrane fabrication and assembly procedures. Because the membrane is constrained by both of its walls (between two bipolar plates) in the membrane-electrode assembly (MEA), any change in temperature and humidity can create swelling strain and thermal strain in the membrane, resulting in tensile stress in-plane and in-thickness[2]. It's worth noting that 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.

Khorasany et al [3]developed a fatigue lifetime prediction model based on the elastic-plastic constitutive method and Smith-Watson-Topper (SWT) fatigue equilibrium. In this study, 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 has 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. Narinder and et al [4] , used G’Sell-Jonas theory for a unreinforced membrane only can use for tensile stresses while in this study, a generized G’sell-Jonas approach; equation 1, has been developed for reinforced membrane that can also use for compressive stress that is common in-situ condition of the membrane. This phenomenal 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 this reinforced membrane, tensile test in two directions in-plane has been done that shows its isotopic behavior and therfore this generized G’Sell-Jonas can be fitted on it.

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 = +1 for ε≥0, -1 for ε<0

In the above equations, K, w, and h are fitting parameters. Elastic modeling based on Von-Mises has been studied for consecutive models with stresses smaller than 1 MPa, while isotropic work hardening based on the G'Sell-Jonas theory has been considered for bigger stresses in order to follow plastic behavior. In elastic mode, the membrane's young modulus is calculated using a function of humidity and temperature derived from tensile tests. Tensile tests in four critical corners of PEM fuel cell operation in two directions, as well as fatigue tests for extracting S-N graphs of this membrane for ex-situ circumstances, have been obtained using Dynamic Mechanical Analysis (DMA).

Based on Figure 1, the mechanical strength of this isotropic reinforced membrane decreases by increasing temperature and humidity but this effect of temperature is more. In the fatigue tests done in DMA, the force track is 150% (= ×100%)), frequency is 10 Hz. the max stress and min stress applied by DMA on the membrane are defined as the following equations:

	(2)
=	(3)
= (when )	(4)
	(5)

In Figure 2, the fatigue lifetime ditstribusion based on generised G’Sell-Jonas’s theory and SWT parameters extracted form Khorasani paper has been demonstrated.

Acknowledgements

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

References

1. Mølmen, L., Materials Reliability in PEM Fuel Cells. 2021, Jönköping University, School of Engineering.
2. 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.
3. Khorasany, R.M., et al., Mechanical degradation of fuel cell membranes under fatigue fracture tests. Journal of Power Sources, 2015. 274: p. 1208-1216.
4. Khattra, N.S., et al., Residual fatigue life modeling of fuel cell membranes. Journal of Power Sources, 2020. 477: p. 228714.