(Invited) Numerical Modeling of the Growth of Fatigue Cracks in PFSA Membranes
Authors: Santare Michael H , Karlsson Anette M , Ding Guoliang , Kusoglu Ahmet 
Published: February 2020

The initiation and propagation of cracks in polymer electrolyte membranes is not well understood but it is generally considered to be caused by a combination of chemical, mechanical and hygrothermal stressors resulting in combined effects which can accelerate degradation. One such effect is the chemical decomposition of ionomer causing local defects, which can act as crack-initiation sites and can grow under mechanical stresses, leading to enhanced crossover and higher rates of chemical decomposition. It has recently been shown that defect-growth is a good metric to monitor the membrane’s lifetime and fatigue behavior since there exists a correlation between the gas crossover and defect size in membranes. Thus, investigation of crack-growth mechanisms due to mechanical stresses during RH cycling is of great interest for understanding the factors controlling chemical/mechanical durability and developing strategies for improved membrane stability.
The mechanical stresses in the membrane are associated with swelling and shrinkage as a result of environmental changes inside the cell during operation. Hydration and heating lead to hygrothermal swelling strains in the membrane. However, the membranes are generally constrained in the fuel cell system by gas diffusion layers (GDL), bipolar plates and gaskets, preventing the membrane from expanding. Consequently, significant compressive stresses can develop. If these stresses exceed the elastic limit, residual tensile stresses may develop during dehydration shrinkage in the membrane. In these cases, the membrane is subjected to cyclical compressive and tensile stresses during the cyclical hydration-dehydration and heating-cooling occurring during fuel cell operation. Such loading is typically referred as fatigue loading and can cause crack propagation. Thus, with the combination of the cyclic fatigue loading and the environmental factors, microcracks can easily initiate and grow into through-thickness cracks, increasing the gas crossover through the membrane and causing the eventual catastrophic failure of the PEM fuel cells.
Characterizing this fatigue crack growth under RH cycling is essential for understanding and improving the mechanical durability of PEM fuel cells. Currently, there is very little work on modelling in-situ crack growth in polymer electrolyte membrane and thus far, no attempt has been made to model the in-situ crack-propagation in a membrane using time-dependent viscoelastic-plastic membrane mechanical properties, which is important for an accurate representation of damage accumulation with time. However, considerable research has been devoted to modeling fatigue crack growth in other materials. In 1967, Rice first suggested the use of plastically dissipated energy as a criterion to study fatigue crack propagation in ductile materials. Following the work of Rice, there have been a number of analytical, experimental and numerical investigations into the application of plastically dissipated energy in predicting fatigue crack propagation. In the numerical investigations, the accumulation of plastically dissipated energy under cyclical loading is calculated in a defined region ahead of the crack tip and compared to a critical value, presumed to be a material parameter. Once the accumulation reaches the critical value, the crack propagates via a node release algorithm.
In the present work, we develop a numerical simulation to study in-situ crack growth in the through-thickness direction under humidity cycling in a PEM fuel cell model. The temperature-humidity-time-dependent viscoelastic-plastic membrane properties used in the simulation are taken from separate mechanical characterization experiments conducted in our lab. We show that the plastically dissipated energy criterion can qualitatively capture a range of well-established phenomena seen experimentally and in operating fuel cells. Namely; (1) crack propagation in unreinforced perfluorosulfonic acid (PFSA) membrane, (2) crack propagation in expanded polytetrafluoroethylene (ePTFE) reinforced PFSA membrane, (3) the differences between the two, 4) the differences between crack propagation under the channel and land regions in a typical flow channel architecture, (5) the effect of fuel cell clamping pressure on membrane cracking.