A Numerical Investigation of The Fracture Energy of Materials for Fuel Cell End Plates

Nowadays, with increasing energy requirements, the use of clean energy resources has become important. Fuel cells are an important key for clean energy technology due to wide range of utilization areas such as automotive, portable power applications, electricity generation, space, aviation and naval technologies. Additionally, they have many significant properties such as not producing harmful gases, therefore they do not cause environmental and chemical pollution. Besides, they have not any moving parts, also they do not produce noise. By comparison to fossil fuel, fuel cells have high efficiency that reaches up to 60% in appropriate conditions. Proton Exchange Membrane Fuel Cell (PEMFC) has many advantages than other fuel cell types due to simple structure, higher efficiency and low operating temperature. PEMFC may consist of one or more stacks to generate more electricity. End plate of PEMFC holds together all parts of it. Therefore, the material selection for end plate is important to provide safe conditions. To use PEMFC safely, investigation of material fracture energy is required to decide that the material is in safe conditions or not. There are three fracture energy modes which are mode I, mode II and mode III. There are many methods to investigate failure of material at different modes. Unlike other methods, Arcan specimen gives facility to evaluate of mode I, mode II and mixed modes. The main purpose of this paper was to compare the results of fracture energy (stain energy release rate) of different materials for end plates in fuel cells. Another goal was to select a suitable material was selected as PEMFC end plate.


INTRODUCTION
Fossil fuels are used for energy procurement widely, so environmental pollution rises due to harmful gases release. The usage of clean energy sources has started to increase in order to prevent environmental pollution. For this reason, fuel cells have seen as a significant option among clean energy sources with its positive sides. Besides, research and development on fuel cells have become important issue. There are advantages of fuel cell's properties such as, being environmentally and friendly, not producing harmful gases, high efficiency, noiseless, no moving parts and therefore low maintenance required. At First, fuel cells were used in space and marine technology, usage of them has started to become more widespread with the great advances in fuel cells [1,2].
Fuel cells are devices that convert chemical energy to electrical energy directly. They generally produce electricity and water by the reaction of Hydrogen and Oxygen. As a result of chemical reaction, they do not create harmful waste for the environment. Only water and heat are produced after chemical reaction, it is the most important feature of fuel cells in energy production [2][3][4][5].
Generally, fuel cells are classified as Alkaline Fuel Cell (AFC), Direct Methanol Fuel Cell (DMFC), Proton Exchange Membrane Fuel Cell (PEMFC), Phosphoric Acid Fuel Cell (PAFC), Molten Carbonate Fuel Cell (MCFC) and Solid Oxide Fuel Cell (SOFC). Each of them has advantages with their specific features according to usage areas. PEMFC is used more widely today than other fuel cells. With its high voltage, current and power density, low pressure operation, corrosion-resistant electrolyte usage, tolerance to pressure change, simple structure, low temperature operation, portable usage, it is more accurate choice than the other fuel cells with its advantages [2,6,7].
Metal, non-metal and composite materials are used as material of end plates in fuel cells. Composite materials are also preferred in fuel cells due to their light weight, corrosion resistance and high mechanical properties [8]. There are studies with composite on bipolar flow plates and end plate plates. However, there are many studies on bipolar flow plates, few studies on end plates [9][10][11][12].
Fracture energy is an important case to decide safe conditions of material. When different loads are applied to specimen, it is significant to determine what kind of breakage may occur. There are three fracture modes which are mode I (opening), mode II (sliding shear) and mode III (tearing) [13]. These modes are evaluated by using methods for mode I Double Cantilever Beam (DCB), for mode II End Notched Flexure (ENF), for mode III Crack Rail Shear (CRS) and Asymmetric Double Cantilever Beam (ADCB), Asymmetric Tapered Double Cantilever Beam (ATDCB), Crack Lap Shear (CLS) and Single Leg Bending (SLB) methods are used to calculate fracture energy of material. To compute fracture energy of mixed mode which is combining load form of mode I and mode II, different methods are required. The use of different test cases can lead to difficult test conditions and results. To carry out mixed mode conditions to test material, Arcan specimen is efficient due to facility observation of different mixed modes [14][15][16].
In this study, numerical analysis of fracture energy for different materials was compared for selected end plate of PEM-FC. Strain energy release rates were calculated numerically by using Arcan specimen for mode I, mode II and mixed modes. To decide appropriate material for PEMFC end plate, the fracture energy results were compared for wide range of material system.

DESCRIPTION OF SET-UP
Fuel cells are devices that convert chemical energy to electrical energy directly. PEMFC is common type fuel cell and it contains membrane, gas diffusion layer (GDL), catalyst layer (CL), bipolar flow plate (BFP) or bipolar plate and end plate. Membrane, GDL and CL are joined together to form a membrane electrode assembly (MEA). Parts of PEMFC are shown in Figure 1. A single fuel cell consists of a MEA and two BFP producing about 1.2 V [17]. This assembly of cell is called a fuel cell stacks. For more voltage, more cells are stacked [18]. Stacks are clamped between two end plates to hold them together [10,19]. In PEMFC fuel cells, an end plate is used to hold the stacks together. Generally end plates have to be possessed of low density, electrochemical stability, high mechanical strength and stiffness and electrical insulation. So, metal, non-metals and composites materials can be used as fuel cell end plate [19][20][21]. End plate materials are used with different thickness and design by changing their material properties. Yu et. al. [10] determined size of composite plate as given in Figure 2. Besides they set down thickness of composite material as 10 mm for stainless steel and 15 mm for composite material. Fuel cell stacks are combined with end plates, so it has to have high flexural stiffness to keep together all parts in ideal conditions. If there is too much contact pressure, this condition can compress gas diffusion layer (GDL) and can change GDL porosity. Besides, gas and water flow will not transfer from PEMFC flow channels sufficiently. However, if there is little contact pressure, this can cause high contact resistance between back of GDL and bipolar flow plates (BFP) that can reduce performance of fuel cell. Hence, PEMFC end plate should high flexural stiffness. If it has low flexural stiffness, it may yield a non-uniform contact pressure in the whole plate as given in Figure 3 [10]. Composite materials are combined with two or more components therefore they may have different mechanical properties at each direction. When different loads are applied to specimen by varying angles, it is important to determine what kind of failure may occur. Also, fracture energy is important in order to decide safe conditions of material [13,22].

THEORITICAL BACKGROUND
The fracture energy of material is investigated by using linear elastic fracture mechanics which is used to calculate the strain energy release rate at the crack tip [23]. It is a useful tool for composite material cracks when the specimen is orthotropic material [15]. The Generalized Hooke's law is given in the following equation [24,25]. (1) Expressions of letters are strain (ε), normal stress (σ), shear stress (τ), shearing strain (γ) and constants (a ij ). Elastic constants are given as the following relationships. xy yx xz zx Where E x , E y , E z are elastic modulus in direction of x, y, z. G xy , G xy , G yz are shear modulus in each plane and υ xy , υ yx , υ yz are Poisson's ratio.
In case of a thin plate, principal axes are in xy plane and assuming conditions are given as: If the Eq. (3) assumptions are written in Eq. (1), then equation is turned into Eq. (4).
The another assumptions are given in Eq.
Where the terms of constants b ij are defined in terms of the following nonzero entries a ij of the compliance matrix: The strain energy release rates are calculated by Eq. (10). Where G I and G II are mode I and mode II strain energy release rates, E I and E II effective moduli, K I and K II are mode I and mode II stress intensity factors, respectively.

FINITE ELEMENT MODELING OF MIXED MODE FRACTURE
Finite element analysis was carried out by using J-integral method for numerical calculation. Arcan specimen is applied constant 1000 N load by using Abaqus. Arcan Specimen modelling in Abaqus is shown in Figure 4. The model was created using eight nodes and collapsed elements of the model (CPE8RH). The mesh was focused around the crack tip, and linear elastic finite element analysis was performed under the plane strain conditions. Composite materials show distinct characteristics in each direction, but metal and ceramic materials have the same properties due to homogeneous sturucture. Therefore, all materials have different properties so they give different starin energy release rate results under mode I, mode II and mixed loading conditions. Arcan Specimen numerical deformation results are given in Figure 6. It can be seen that the material undergoes different deformation in each mode.

RESULTS AND DISCUSSION
In this study, the values of strain energy release rates for mode I, mode II, and mixed mode were obtained by using 2D Arcan specimen model by changing loading angles. Constant value of the load 1000 N is applied to different materials in order to compare the results and investigate the loading angle variations of fracture energy parameters. The end plate should be assembled with ideal clamping pressure. That can be affected performance of PEMFC parts. Particularly, MEA performance depends on change of clamping pressure. Therefore, PEMFC efficiency is affected from changing the clamping pressure. The end plate provides de-sired working conditions so decision of convenient material is significant. Besides, the end plate should have low density, electrochemical stability, high rigidity, insulating property and corrosion resistance [20,21].
Generally metals, non-metals and composite materials can be used as fuel cell end plate [19,20]. In this study, steel, titanium, aluminum, boron-epoxy, UD graphite-epoxy, CP graphite-epoxy, kevlar-KM2, glass-polyester, CFRP (Carbon Fiber Reinforced Polymer), aluminum6061, AlSiC (Aluminum Silicon Carbide), T300 (T300/976 UD tape), ceramic and GFRP (Glass Fiber Reinforced Polymer) are selected as end plate of PEMFC material system. The elastic properties of all materials used in numerical analysis are listed in the Table 1 [26][27][28][29][30][31][32][33][34][35]. In this paper, strain eneregy release rate of the 14 different materials were investigated by numerical analysis of Arcan specimen. Additionally, their fractu-  Values of mode I strain energy release rates versus loading angle for various materials are shown in Table 2 and Figure  7. As it can be seen, for all materials used in this investigation the mode I fracture energy decreases as the mode II loading contribution increases. The mode I fracture energy has the maximum value for the Kevlar-KM2 and the minimum value for the steel among the studied materials under all loading angle conditions.   Table 3 and Figure 8 show the mode II fracture energy of the materials system under study. It reveals that the mode II fracture energy has its highest value at 90 degrees loading angle and increases as the mode II loading contribution increases for all investigated materials. For all materials under study in this investigation, Glass-Polyester has the highest G II fracture energy value; on the other hand the G II value of steel has the lowest among the materials.  The total strain energy release rates obtained by G T = G I +G II in different loading angles are shown for the all materials in Table 4 and Figure 9. Total strain energy release under mixed-mode loading conditions changes with the loading angle. In pure mode I loading angle, they have the highest G T value for all materials. As loading angle increases towards mode II conditions its value decreases. As compared for all the materials, Kevlar-KM2 has the highest G T value in pure mode I, pure mode II and all mixed mode conditions. On the other hand, G T of steel has the lowest value among all material in mode I, mode II and mixed mode loadings.  [36][37][38], were found to ensure the maximum value of G IC /G I among studied composite materials. In this study, a numerical attempt was made to explain some of the important issues related to the fracture energy of the selected material used in the end plates of the fuel cell. Due to the importance of the issue, there is still significant activity in this area. Therefore, some future research in this area may be required to perform parallel design exercises using numerical and experimental fracture approaches on commonly used materials as end plate material.

CONCLUSION
In this paper, PEMFC end plates materials and their strain energy release rates were investigated by numerical analysis of Arcan specimen under different loading conditions. Firstly, stress intensity factors are obtained for each material by finite element analyzing Arcan specimen using Abaqus package program finite element and fracture energy of materials in mode I, mode II and mixed mode conditions were calculated. According to the results, for loading angles close to mode I condition, mode I fracture was dominant. For loading angles close to mode II condition, mode II strain energy release rates became dominant. Besides, it was concluded that the total strain energy release rate under mixed mode loading conditions decreases with the increasing loading angle. Among the studied metals, steel, titanium and aluminum were found to have superior fracture energy values. Various applications of composite materials in primary and secondary structures have made them as a suitable alternative to metal materials. Composite materials with strength and stiffness combined with lightness have proven their application through many applications in various fields. Due to their importance in engineering applications, in this investigation, CP graphite-epoxy, kevlar-KM2 and GFRP were confirmed to warrant the appropriate fracture resistance among studied composite materials. Kevlar-KM2 has lower density and higher fracture toughness values than CP graphite-epoxy and GFRP. Therefore, kevlar-KM2 was found as an appropriate composite material for PEMFC end plate by considering fracture energy and density of the material parameters.