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Numerical investigation of formed residual stresses and the thickness of stainless steel bipolar plate in PEMFC
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 5 5 e6 8 6 3
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Numerical investigation of formed residual stresses and the thickness of stainless steel bipolar plate in PEMFC Shugen Xu a,*, Kewei Li b, Yang Wei a, Wenchun Jiang a a b
College of Chemical Engineering, China University of Petroleum (Huadong), Qingdao 266580, China School of Chemical Machinery, Dalian University of Technology, Dalian 116024, China
article info
abstract
Article history:
Stainless steel bipolar plates are regarded as a good substitute for traditional graphite bi-
Received 9 November 2015
polar plates in proton exchange membrane fuel cells. Stamping is a first selection for the
Received in revised form
manufacture of stainless steel bipolar plates. In addition to paying more attention to the
23 February 2016
stamping channel shape, a good prediction, and an efficient evaluation of the formed re-
Accepted 1 March 2016
sidual stress and thinning of bipolar plates are necessary. In this paper, the formed stress
Available online 31 March 2016
and deformation of SS304 stainless steel BPP with a thickness of 0.1 mm was investigated by a 2D plane strain FE model. Numerical results showed that formed BPP has a large re-
Keywords:
sidual stress, especially in the bending zone. Residual stresses distribution along the inner
Residual stress
surface, outer surface, and direction of thickness was non-uniform. Geometrical di-
Bipolar plate
mensions have a great effect on residual stress and formed thickness. With an increase of
Stainless steel
the upper die width and die depth, the peak residual stress increased, and the formed
Stamping
thickness became less uniform. With an increase of the curve radius, the residual stress
PEMFC
decreased, and the formed thickness became more uniform. Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Proton exchange membrane fuel cells (PEMFC) have a great many advantages among the various fuel cells, such as quick starting, low temperature operation, high energy density, and near-zero pollution, and they are therefore a possible alternative to combustion engines [1e3]. A PEMFC stack contains bipolar plates (BPP), membrane electrode assemblies (MEA), gasket and endplate, and other parts. Among all the parts of the PEMFC stack, BPPs are the high volume and high cost ones. For a single cell, BPPs are used for both the anode and cathode.
A PEMFC stack structure has hundreds of single cells assembled together. BPPs take up at least 60% of the stack weight and make up at least 30% of the costs [4e6]. A good material for BPPs should have the properties of good electrical conductivity, high mechanical strength, light weight, high corrosion resistance, and low cost. Traditionally, graphite and graphite composite plates have been used to product BPPs due to their high corrosion resistance and low interfacial contact resistance. However, this material is very expensive to process. Mass production cannot be used due to its brittleness, and a certain thickness is required due to its high gas permeability. Therefore, in order to reduce the cost
* Corresponding author. Tel.: þ86 532 86983482; fax: þ86 532 86983480. E-mail address: [email protected] (S. Xu). http://dx.doi.org/10.1016/j.ijhydene.2016.03.005 0360-3199/Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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and enhance performance, various materials have been considered as alternatives to graphite, including composite materials, titanium, aluminum, and stainless steel [7]. Stainless steel has higher electrical conductivity, mechanical strength, surface conductivity, thermal conductivity, corrosion resistance, with low density and material costs. Thus, it has received much attention in recent years as an alternative material for BPPs [8e10]. Considering precision, production rate, and cost effectiveness, stamping is the first selection for stainless steel BPPs manufacturing [11]. Although the stamping process is much faster than the traditional mechanical machining method, its shortcoming is that precision manufacturing is difficult. Forming defects such as springback, high residual stress, thinning, and wrinkles occur [8]. The properties of formed metallic sheets are strongly affected by the formed residual stresses. Residual stresses can significantly affect the strength and fracture characteristics of components [12,13]. Their effects may either be beneficial or detrimental depending on the magnitude, sign, and distribution of the stresses [14]. Therefore, in addition to paying more attention to stamping shape and thinning of thickness, a good prediction and an efficient evaluation of the formed residual stress are necessary. In general, the formed residual stress field depends on several main factors including material properties, structural dimensions, and external constraint conditions. The approaches to formed residual stress include experimental methods, numerical methods, and theoretical methods. Experimental methods, such as X-ray diffraction [13], neutron diffraction [15], and ultrasonic methods [16] are used to measure the residual stress in engineering. With the development of computer technology, FEM has proven to be an effective tool in analyzing the bipolar plate stamping process [17]. It can be employed to simulate the forming process, formed residual stress field, and wall thinning. The application of FEM has become more and more popular in order to predict residual stresses and formed thickness of components for assessment purposes [18]. Hu et al. [1] used a 3D FE model to predict imperfections and thickness variations during the stamping process. Liu et al. [17] used the commercial software ABAQUS to investigate control parameters of the rubber pad formation of a 0.1 mm-thick SS304 sheet. Peng et al. [18] established a plane strain FEA model with different channel geometries to analyze the effect of significant parameters such as grain size, lubricant condition, and hardness of soft punch on formed BPP properties. Chen et al. [19] established an elasticeplastic deformation FEA model using the traditional material model and the scale-factor modified material model to simulate the metallic BPPs channel. For stamped BBPs with a thickness of 0.1 mm, it is difficult to measure the residual stress distribution along the thickness. In addition, it is not clear whether or not the geometrical dimensions have an effect on the residual stress and formed thickness of BPP. In this paper, a FE model was developed to estimate the residual stress and formed thickness in a stamped BPP. The residual stress and formed thickness distribution were investigated, with the aim of providing a reference for optimizing die stamping technology for stainless steel BPP.
FE analysis of stamping process Geometrical model and meshing A commercial finite element software ABAQUS10.0 was applied to the FE simulations in this study. Fig. 1 shows the main dimensions of the upper and lower die for stamping BPP. This model is the same as that in reference [8]. Here we used their experimental results to compare with our numerical simulation results, with the aim of verifying our finite element model and discussed the effect of geometry and friction factor on formed residual stress. For convenience of calculation, a part of the die and BPP was selected for the FE analysis. Although real forming is a 3D procedure, it is often considered sufficient to represent a BPP structure with a plane strain FE model. 2D plane strain simulations are much faster and easier to perform. Therefore, the methodology described here is based on a 2D plane strain. The upper and lower die are defined as a rigid body, and the sheet is defined as an elastoplastic body with SS304 mechanical properties. The finite element mesh is shown in Fig. 2. In total, 445 nodes and 352 elements were meshed for the sheet. The element type for residual stress analysis was CPE4R, a 4-node bilinear plane strain quadrilateral element with reduced integration and hourglass control.
Material properties Stressestrain relations of SS304 sheet with different thickness were tested by Peng [18]. A sheet with thin thickness has relative low resistant flow stress. SS304 sheets that were used in the numerical simulation in this paper were 0.1 mm, which is widely used as bipolar plate material in the PEMFC environment. Thus, the constitution model of a sheet with a thickness of 0.1 mm was used for structural analysis of the stamping process, residual stress, and deformation. The Young's modulus and Poisson's ratios of SS304 were 193 GPa and 0.3, respectively. The relation of stressestrain can be expressed as follows:
Fig. 1 e Cross-section of upper and lower die.
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During structural analysis, in order to prevent rigid body motion, boundary conditions should be applied. Because of the cyclic symmetry of the FE model, B1 and B2 are constrained in X-direction, as shown in Fig. 3. The load type in the verification FE model is concentric force. However, it is difficult to know the proper force magnitude for a certain channel depth. In other FE models, a displacement load of the upper die is applied instead of force load. In order to investigate the stress distribution, three paths P1 through P3 were defined, as shown in Fig. 3. P1 is along the inner surface, while P2 is along the outer surface, and P3 passes the node with peak Von Mises stress, and through the whole thickness of BPP, as shown in Fig. 4.
Verification of the FE model
Fig. 2 e FE mesh of plate.
sk ¼ 1421ð1 þ εÞ0:561
(1)
where sk is flow stress, and ε is the strain.
In order to verify the present FEM model, a FE model with the same geometrical, material and load type as those used in Jin's paper was generated [8]. The curve of the die was 0.2 mm, and the load type was a straight load 100 kN. The thickness of BPP at typical zone was compared. As shown in Fig. 4, the profile of cross-section and thickness of BPP under different straight loads was measured by Jin and calculated by the FE model. In fact, Ref. [8] provided the channel depth of BPP is 0.508 mm, which can be regarded as a scale bar. Thus, the thickness can be calculated by AutoCAD software, as shown in Fig. 4(a). The thickness of BPP at the same zone of our FE model can be calculated by the ABAQUS software, as shown in Fig. 4(b). It can be seen that the predicted results from the FE analysis are in relatively good agreement with the experimental measurements. Therefore, the FE program developed here can be used for residual stress analysis on BPP forming in this paper.
Structural analysis The residual stress was calculated by using the static structural analysis in ABAQUS. The contact pair was defined between the upper die and sheet, and the sheet and lower die. Friction behavior was considered in the model, and the penalty function method was used. The material properties relevant to the formed residual stress are the elastic modulus, yield strength, and Poisson's ratio. Because of few phase transformations in the austenitic stainless steel SS304 during the forming process, the strains generated by phase changes were not considered. Thus, the total strain rate can be decomposed into two components as follows: ε ¼ εe þ εp e
Results and discussion Forming stress distribution contour In this model, die dimensions are shown in Fig. 1, and the friction factors was 0.1. Fig. 5 shows the Von Mises stress contour during the forming process. When the displacement of the upper die was 0.2 mm, the peak Von Mises stress was 556.0 MPa. The peak stress increased as the upper die moved towards the lower die. The maximum stress reached 942.4 MPa when the displacement of upper die was 0.6 mm.
(2) p
where ε and ε are the elastic strain and plastic strain, respectively. The elastic strain is calculated with Hooke's law, Young's modulus, and the Poisson's ratio. The plastic strain depends on the yield criterion and isotropic hardening model. In this simulation, Von Mises yield surface and isotropic hardening model were used. In the isotropic hardening model, the yield surface expands with the accumulated plastic strain, but the center of the yield surface remains in the same place in the stress space.
Fig. 3 e Boundary conditions and reference paths.
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Fig. 4 e A comparison of the profile of cross-section and thickness by our FEM and Jin's experiment. (a) Experimental result and (b) FE result.
After the upper die left the sheet, springback occurred and Von Mises stress decreased to 228.5 MPa, which was the residual stress in the formed BPP. Fig. 6 shows the Von Mises stress evolution in point A during the forming process. The location of point A is shown in Fig. 5(d). It can be seen that the Von Mises stress changes with the displacement of upper die, and this can be divided into two steps. The first step is loading, and the stress increased according to the stressestain relation of SS304. The second strep is unloading, which is according to the unloading law of steel. The Von Mises equivalent plastic stain increased with the gradual movement of upper die, as shown in Fig. 7. The thickness of the sheet at point A was gradually thinned during the stamping process, as shown in Fig. 8. The initial thickness was 0.1 mm, and the final thickness was 0.073 mm. Thus, the thinning percentage was 27%.
Residual stress distribution and formed thickness Fig. 9 shows the stress contours of Von Mises stress, horizontal stress (S11), vertical stress (S22), and longitudinal stress (S33). The peak stresses of Von Mises stress, S11, S22, and S33 were 228.5 MPa, 110.2 MPa, 51.5 MPa, and 257.5 MPa, respectively. The peak stresses were located on the bending area, as shown in Fig. 9. Fig. 10 shows the residual stress distribution along P1, the inner surface of BPP. Along P1, Von Mises stress and S33 had the same changing trends. They gradually increased along CD,
then decreased along DE, and increased again along EF. Compared with the other stresses, S22 was relatively small. The residual stress S11 along DE demonstrated a bending type distribution. The peak tensile stress was 109.9 MPa at point D, and the compressive stress was 103.3 MPa at point E. Fig. 11 shows the residual stress distribution along P2, the outer surface of BPP. For a cyclic geometrical feature, the outer surface of the current channel is the inner surface of the neighboring channel. Thus, the residual stress distribution along P2 was similar to that along P1 but in a reverse direction. Fig. 12 shows the residual stress distribution along P3, through the thickness of formed BPP. The Von Mises stress and S33 showed a trend of gradual decrease. The residual stresses S11 and S22 along P3 showed a significant bending type distribution. The stress in the middle point of P3 was zero. Residual stresses S11 and S22 in the outer surface were tensile and became compressive in the inner surface. Fig. 13 shows the thickness of formed BPP along P1. The maximum thickness of the formed BPP was 0.88 mm, and the minimum thickness of formed BPP was 0.73 mm. The minimum thickness was located at point E, the bending zone of BPP. According to the above analysis, the sheet had a large forming stress during the stamping process. If the peak Von Mises stress is larger than the true stress of the ultimate tensile strength, the sheet will be cracked or necked. If the compressive stress is too large, the sheet has a risk of wrinkling. In this model, the maximum and minimum thinning percentages were 27% and 12%, respectively. This indicates that non-uniform deformation occurred during the stamping process. Non-uniform thinning depends on material selection, die shape design, and friction conditions. How to prevent or decrease the non-uniform thinning should be carefully investigated.
Effect of die geometrical dimensions on residual stress and thickness In order to study the effect of die geometrical dimensions on formed residual stress and thickness, FE models with different upper die widths, die depths, and curve radii were built.
Effect of upper die width on residual stress and thickness In order to obtain the effect of the width of the upper die on residual stress and formed thickness of BPP, with the rest of the forming parameters kept constant, five models with widths of 0.6 mm, 0.7 mm, 0.8 mm, 0.9 mm, and 1.0 mm were established. The cross-section profiles of formed BPP are listed in Fig. 14. Fig. 15 shows the effect of upper die depth on the residual Von Mises stress along P3. It shows that the five models had almost the same stress distribution, but all the peak residual stresses increased with increased upper die width. Fig. 16 shows the effect of upper die width on formed BPP thickness along P1. It was also observed that the minimum thickness decreased with increased upper die width.
Effect of die depth on residual stress and thickness In order to obtain the effect of die depth on residual stress and formed thickness of BPP, with the rest of the forming
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Fig. 5 e Von Mises stress during the forming process (a) u ¼ 0.2 mm, (b) u ¼ 0.4 mm, (c) u ¼ 0.6 mm, and (d) unloaded.
Fig. 6 e Von Mises stress evolution at point A during the forming process.
Fig. 7 e Von Mises equivalent plastic strain evolution at point A during the forming process.
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Fig. 8 e BPP thickness evolution at point A during the forming process.
parameters kept constant, four models with widths of 0.4 mm, 0.5 mm, 0.6 mm, and 0.7 mm were established. The crosssection profiles of formed BPP are shown in Fig. 17. Fig. 18 shows the effect of die depth on the residual stresses in BPP along P3. It shows that the four models had the same stress distribution. The residual stress increased with increased die depth. When the die depth was 0.4 mm, the peak
Fig. 10 e Formed residual stress distribution along P1.
stress was 179.3 MPa, which means that too shallow a die depth can cause a little stress. When the die depth increased to 0.7 mm, the peak stress was 242 MPa. Fig. 19 shows the effect of die depth on BPP thickness along P1. It was observed that the die depth did not affect the thickness distribution. It was shown that maximum formed thickness decreased with increased die depth. When the die
Fig. 9 e Formed residual stress contour of BPP (a) Von Mises stress, (b) S11, (c) S22, and (d) S33.
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Fig. 11 e Formed residual stress distribution along P2.
Fig. 14 e Cross-section profiles of BPP with different upper die widths.
Fig. 12 e Formed residual stress distribution along P3.
Fig. 15 e Effect of upper die width on residual Von Mises stress along P3.
Fig. 13 e Formed BPP thickness along P1.
Fig. 16 e Effect of upper die width on BPP thickness along P1.
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Fig. 17 e Cross-section profiles of BPP with different die depths.
Fig. 18 e Effect of die depth on residual stress along P3.
Fig. 20 e Cross-section profiles of BPP with different curve radii.
Fig. 21 e Effect of the curve radius on residual stress along P3.
depth increased to 0.7 mm, the thickness greatly decreased, as shown in Fig. 19.
Effect of the curve radius on residual stress and thickness In order to obtain the effect of the curve radius on residual stress and formed thickness of BPP, with the rest of the forming parameters kept constant, four models with curve radii of 0.15 mm, 0.2 mm, 0.25 mm, and 0.3 mm were built. The cross-section profiles of formed BPP are shown in Fig. 20.
Fig. 19 e Effect of die depth on BPP thickness along P1.
Fig. 21 shows the effect of the curve radius on the residual stresses in BPP along P3. It shows that the four models had the same stress distribution. The formed residual stress decreased with increased curve radius. When the curve radius was 0.15 mm, the peak Von Mises stress was 235.8 MPa, which
Fig. 22 e Effect of the curve radius on BPP thickness along P1.
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means that too small a curve radius can cause too large a Von Mises stress. When the curve radius increased to 0.3 mm, the peak Von Mises stress was 198.7 MPa. Fig. 22 shows the effect of the curve radius on BPP thickness along P1. It was observed that the curve radius did not affect the thickness distribution. It was shown that maximum formed thickness increased with increased curve radius. When the curve radius was 0.15 mm, the minimum thickness along P1 was 0.068 mm. When the curve radius increased to 0.3 mm, the minimum thickness along P1 was 0.08 mm. This indicates that a larger curve radius can decrease the residual stress and make the formed BPP thickness more uniform.
Conclusions The forming stress and deformation of SS304 stainless steel BPP with a thickness of 0.1 mm was numerically determined by a 2D plane strain FE model. The effect of geometrical dimensions on residual stresses and formed thickness was discussed. Based on the obtained results, the following conclusions may be drawn: (1) During the stamping process of the stainless steel BPP, large forming stresses are generated in the bending zone, and then the stresses decrease when the upper die separates from the BBP. The stress evolution is according to the unloading law. With increased displacement of upper die increasing, the Von Mises equivalent plastic strain is increased, and the thickness of BPP is non-uniformly decreased. (2) The formed BPP has a large residual stress, especially in the bending zone. Residual stresses distribution along the inner surface, outer surface, and thickness direction are non-uniform. The horizontal and vertical stresses along the thickness direction show a significant bending type distribution. (3) The geometrical dimensions have a great effect on residual stress and formed thickness. With an increase of upper die width and die depth, the peak residual stress is increased, and formed thickness becomes less uniform. With an increase of the curve radius, the residual stress is decreased, and the formed thickness becomes more uniform. When the radius is increased to 0.3 mm, the minimum thickness is 0.8 mm.
Acknowledgment The authors wish to express their gratitude for the financial support by National Natural Science Foundation of China (51404284, 11372359), Fundamental Research Funds for the Central Universities (15CX05011A, 15Cx08006A), Applied Fundamental Research Funds of Qingdao City (15-9-1-95-jch), the Natural Science Foundation for Distinguished Young Scholars of Shandong Province (JQ201417), and Taishan Scholar Funding of Shandong Province (ts201511018). Thanks to Dr. Edward C. Mignot, Shandong University, for linguistic advice.
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references
[1] Hu Q, Zhang D, Fu H, Huang K. Investigation of stamping process of metallic bipolar plates in PEM fuel cell-numerical simulation and experiments. Int J Hydrogen Energy 2014;39(25):13770e6. [2] Tu Z, Zhang H, Luo Z, Liu J, Wan Z, Pan M. Evaluation of 5 kW proton exchange membrane fuel cell stack operated at 95 C under ambient pressure. J Power Sources 2013;222:277e81. [3] Costamagna P, Srinivasan S. Quantum jumps in the PEMFC science and technology from the 1960s to the year 2000-Part II. Engineering, technology development and application aspects. J Power Sources 2001;102:253e69. [4] Li X, Sabir I. Review of bipolar plates in PEM fuel cells: flowfield designs. Int J Hydrogen Energy 2005;30:359e71. [5] Lim J, Kim M, Kim K, Lee D. Innovative gasketless carbon composite bipolar plates for PEM fuel cells. Int J Hydrogen Energy 2012;37:19018e26. [6] Lee YB, Lee CH, Kim KM, Lim DS. Preparation and properties on the graphite/polypropylene composite bipolar plates with a 304 stainless steel by compression molding for PEM fuel cell. Int J Hydrogen Energy 2011;36:7621e7. [7] Jin CK, Jeong MG, Kang CG. Fabrication of titanium bipolar plates by rubber forming and performance of single cell using TiN-coated titanium bipolar plates. Int J Hydrogen Energy 2014;39:21480e8. [8] Jin CK, Koo JY, Kang CG. Fabrication of stainless steel bipolar plates for fuel cells using dynamic loads for the stamping process and performance evaluation of a single cell. Int J Hydrogen Energy 2014;39:21461e9. € Koc¸ M. Effect of manufacturing [9] Mahabunphachai S, Cora ON, processes on formability and surface topography of proton exchange membrane fuel cell metallic bipolar plates. J Power Sources 2010;195:5269e77. [10] Tawfik H, Hung Y, Mahajan D. Metal bipolar plates for PEM fuel cell-A review. J Power Sources 2007;163:755e67. [11] Mehta V, Cooper JS. Review and analysis of PEM fuel cell design and manufacturing. J Power Sources 2003;114:32e53. [12] Tong L, Hou G, Chen Y, Zhou F, Shen K, Yang A. Experimental investigation on longitudinal residual stresses for coldformed thick-walled square hollow sections. J Constr Steel Res 2012;73:105e16. [13] Martins JA, Cardoso LP, Fraymann JA, Button ST. Analyses of residual stresses on stamped valves by X-ray diffraction and finite elements method. J Mater. Process Tech 2006;179:30e5. [14] Nakamoto K, Katahira K, Ohmori H, Yamazaki K, Aoyama T. A study on the quality of micro-machined surfaces on tungsten carbide generated by PCD micro end-milling. CIRP Ann e Manuf Technol 2012;61:567e70. [15] Woo W, Vyacheslav E, Hubbard CR, Lee H, Park KS. Residual stress determination in a dissimilar weld overlay pipe by neutron diffraction. Mater. Sci Eng, A 2011;528:8021e7. [16] Ya M, Marquette P, Belahcene F, Lu J. Residual stresses in laser welded aluminium plate by use of ultrasonic and optical methods. Mater. Sci Eng, A 2004;382:257e64. [17] Liu Y, Hua L. Fabrication of metallic bipolar plate for proton exchange membrane fuel cells by rubber pad forming. J Power Sources 2010;195:3529e35. [18] Peng L, Liu D, Hu P, Lai X, Ni J. Fabrication of metallic bipolar plates for proton exchange membrane fuel cell by flexible forming process-numerical simulations and experiments. J Fuel Cell Sci Tech 2010;7:03100901e9. [19] Chen TC, Ye JM. Analysis of stainless steel bipolar plates micro-stamping processes. Przeg Elektrotech 2012;88:121e6.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Numerical investigation of formed residual stresses and the thickness of stainless steel bipolar plate in PEMFC Shugen Xu a,*, Kewei Li b, Yang Wei a, Wenchun Jiang a a b
College of Chemical Engineering, China University of Petroleum (Huadong), Qingdao 266580, China School of Chemical Machinery, Dalian University of Technology, Dalian 116024, China
article info
abstract
Article history:
Stainless steel bipolar plates are regarded as a good substitute for traditional graphite bi-
Received 9 November 2015
polar plates in proton exchange membrane fuel cells. Stamping is a first selection for the
Received in revised form
manufacture of stainless steel bipolar plates. In addition to paying more attention to the
23 February 2016
stamping channel shape, a good prediction, and an efficient evaluation of the formed re-
Accepted 1 March 2016
sidual stress and thinning of bipolar plates are necessary. In this paper, the formed stress
Available online 31 March 2016
and deformation of SS304 stainless steel BPP with a thickness of 0.1 mm was investigated by a 2D plane strain FE model. Numerical results showed that formed BPP has a large re-
Keywords:
sidual stress, especially in the bending zone. Residual stresses distribution along the inner
Residual stress
surface, outer surface, and direction of thickness was non-uniform. Geometrical di-
Bipolar plate
mensions have a great effect on residual stress and formed thickness. With an increase of
Stainless steel
the upper die width and die depth, the peak residual stress increased, and the formed
Stamping
thickness became less uniform. With an increase of the curve radius, the residual stress
PEMFC
decreased, and the formed thickness became more uniform. Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Proton exchange membrane fuel cells (PEMFC) have a great many advantages among the various fuel cells, such as quick starting, low temperature operation, high energy density, and near-zero pollution, and they are therefore a possible alternative to combustion engines [1e3]. A PEMFC stack contains bipolar plates (BPP), membrane electrode assemblies (MEA), gasket and endplate, and other parts. Among all the parts of the PEMFC stack, BPPs are the high volume and high cost ones. For a single cell, BPPs are used for both the anode and cathode.
A PEMFC stack structure has hundreds of single cells assembled together. BPPs take up at least 60% of the stack weight and make up at least 30% of the costs [4e6]. A good material for BPPs should have the properties of good electrical conductivity, high mechanical strength, light weight, high corrosion resistance, and low cost. Traditionally, graphite and graphite composite plates have been used to product BPPs due to their high corrosion resistance and low interfacial contact resistance. However, this material is very expensive to process. Mass production cannot be used due to its brittleness, and a certain thickness is required due to its high gas permeability. Therefore, in order to reduce the cost
* Corresponding author. Tel.: þ86 532 86983482; fax: þ86 532 86983480. E-mail address: [email protected] (S. Xu). http://dx.doi.org/10.1016/j.ijhydene.2016.03.005 0360-3199/Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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and enhance performance, various materials have been considered as alternatives to graphite, including composite materials, titanium, aluminum, and stainless steel [7]. Stainless steel has higher electrical conductivity, mechanical strength, surface conductivity, thermal conductivity, corrosion resistance, with low density and material costs. Thus, it has received much attention in recent years as an alternative material for BPPs [8e10]. Considering precision, production rate, and cost effectiveness, stamping is the first selection for stainless steel BPPs manufacturing [11]. Although the stamping process is much faster than the traditional mechanical machining method, its shortcoming is that precision manufacturing is difficult. Forming defects such as springback, high residual stress, thinning, and wrinkles occur [8]. The properties of formed metallic sheets are strongly affected by the formed residual stresses. Residual stresses can significantly affect the strength and fracture characteristics of components [12,13]. Their effects may either be beneficial or detrimental depending on the magnitude, sign, and distribution of the stresses [14]. Therefore, in addition to paying more attention to stamping shape and thinning of thickness, a good prediction and an efficient evaluation of the formed residual stress are necessary. In general, the formed residual stress field depends on several main factors including material properties, structural dimensions, and external constraint conditions. The approaches to formed residual stress include experimental methods, numerical methods, and theoretical methods. Experimental methods, such as X-ray diffraction [13], neutron diffraction [15], and ultrasonic methods [16] are used to measure the residual stress in engineering. With the development of computer technology, FEM has proven to be an effective tool in analyzing the bipolar plate stamping process [17]. It can be employed to simulate the forming process, formed residual stress field, and wall thinning. The application of FEM has become more and more popular in order to predict residual stresses and formed thickness of components for assessment purposes [18]. Hu et al. [1] used a 3D FE model to predict imperfections and thickness variations during the stamping process. Liu et al. [17] used the commercial software ABAQUS to investigate control parameters of the rubber pad formation of a 0.1 mm-thick SS304 sheet. Peng et al. [18] established a plane strain FEA model with different channel geometries to analyze the effect of significant parameters such as grain size, lubricant condition, and hardness of soft punch on formed BPP properties. Chen et al. [19] established an elasticeplastic deformation FEA model using the traditional material model and the scale-factor modified material model to simulate the metallic BPPs channel. For stamped BBPs with a thickness of 0.1 mm, it is difficult to measure the residual stress distribution along the thickness. In addition, it is not clear whether or not the geometrical dimensions have an effect on the residual stress and formed thickness of BPP. In this paper, a FE model was developed to estimate the residual stress and formed thickness in a stamped BPP. The residual stress and formed thickness distribution were investigated, with the aim of providing a reference for optimizing die stamping technology for stainless steel BPP.
FE analysis of stamping process Geometrical model and meshing A commercial finite element software ABAQUS10.0 was applied to the FE simulations in this study. Fig. 1 shows the main dimensions of the upper and lower die for stamping BPP. This model is the same as that in reference [8]. Here we used their experimental results to compare with our numerical simulation results, with the aim of verifying our finite element model and discussed the effect of geometry and friction factor on formed residual stress. For convenience of calculation, a part of the die and BPP was selected for the FE analysis. Although real forming is a 3D procedure, it is often considered sufficient to represent a BPP structure with a plane strain FE model. 2D plane strain simulations are much faster and easier to perform. Therefore, the methodology described here is based on a 2D plane strain. The upper and lower die are defined as a rigid body, and the sheet is defined as an elastoplastic body with SS304 mechanical properties. The finite element mesh is shown in Fig. 2. In total, 445 nodes and 352 elements were meshed for the sheet. The element type for residual stress analysis was CPE4R, a 4-node bilinear plane strain quadrilateral element with reduced integration and hourglass control.
Material properties Stressestrain relations of SS304 sheet with different thickness were tested by Peng [18]. A sheet with thin thickness has relative low resistant flow stress. SS304 sheets that were used in the numerical simulation in this paper were 0.1 mm, which is widely used as bipolar plate material in the PEMFC environment. Thus, the constitution model of a sheet with a thickness of 0.1 mm was used for structural analysis of the stamping process, residual stress, and deformation. The Young's modulus and Poisson's ratios of SS304 were 193 GPa and 0.3, respectively. The relation of stressestrain can be expressed as follows:
Fig. 1 e Cross-section of upper and lower die.
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During structural analysis, in order to prevent rigid body motion, boundary conditions should be applied. Because of the cyclic symmetry of the FE model, B1 and B2 are constrained in X-direction, as shown in Fig. 3. The load type in the verification FE model is concentric force. However, it is difficult to know the proper force magnitude for a certain channel depth. In other FE models, a displacement load of the upper die is applied instead of force load. In order to investigate the stress distribution, three paths P1 through P3 were defined, as shown in Fig. 3. P1 is along the inner surface, while P2 is along the outer surface, and P3 passes the node with peak Von Mises stress, and through the whole thickness of BPP, as shown in Fig. 4.
Verification of the FE model
Fig. 2 e FE mesh of plate.
sk ¼ 1421ð1 þ εÞ0:561
(1)
where sk is flow stress, and ε is the strain.
In order to verify the present FEM model, a FE model with the same geometrical, material and load type as those used in Jin's paper was generated [8]. The curve of the die was 0.2 mm, and the load type was a straight load 100 kN. The thickness of BPP at typical zone was compared. As shown in Fig. 4, the profile of cross-section and thickness of BPP under different straight loads was measured by Jin and calculated by the FE model. In fact, Ref. [8] provided the channel depth of BPP is 0.508 mm, which can be regarded as a scale bar. Thus, the thickness can be calculated by AutoCAD software, as shown in Fig. 4(a). The thickness of BPP at the same zone of our FE model can be calculated by the ABAQUS software, as shown in Fig. 4(b). It can be seen that the predicted results from the FE analysis are in relatively good agreement with the experimental measurements. Therefore, the FE program developed here can be used for residual stress analysis on BPP forming in this paper.
Structural analysis The residual stress was calculated by using the static structural analysis in ABAQUS. The contact pair was defined between the upper die and sheet, and the sheet and lower die. Friction behavior was considered in the model, and the penalty function method was used. The material properties relevant to the formed residual stress are the elastic modulus, yield strength, and Poisson's ratio. Because of few phase transformations in the austenitic stainless steel SS304 during the forming process, the strains generated by phase changes were not considered. Thus, the total strain rate can be decomposed into two components as follows: ε ¼ εe þ εp e
Results and discussion Forming stress distribution contour In this model, die dimensions are shown in Fig. 1, and the friction factors was 0.1. Fig. 5 shows the Von Mises stress contour during the forming process. When the displacement of the upper die was 0.2 mm, the peak Von Mises stress was 556.0 MPa. The peak stress increased as the upper die moved towards the lower die. The maximum stress reached 942.4 MPa when the displacement of upper die was 0.6 mm.
(2) p
where ε and ε are the elastic strain and plastic strain, respectively. The elastic strain is calculated with Hooke's law, Young's modulus, and the Poisson's ratio. The plastic strain depends on the yield criterion and isotropic hardening model. In this simulation, Von Mises yield surface and isotropic hardening model were used. In the isotropic hardening model, the yield surface expands with the accumulated plastic strain, but the center of the yield surface remains in the same place in the stress space.
Fig. 3 e Boundary conditions and reference paths.
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Fig. 4 e A comparison of the profile of cross-section and thickness by our FEM and Jin's experiment. (a) Experimental result and (b) FE result.
After the upper die left the sheet, springback occurred and Von Mises stress decreased to 228.5 MPa, which was the residual stress in the formed BPP. Fig. 6 shows the Von Mises stress evolution in point A during the forming process. The location of point A is shown in Fig. 5(d). It can be seen that the Von Mises stress changes with the displacement of upper die, and this can be divided into two steps. The first step is loading, and the stress increased according to the stressestain relation of SS304. The second strep is unloading, which is according to the unloading law of steel. The Von Mises equivalent plastic stain increased with the gradual movement of upper die, as shown in Fig. 7. The thickness of the sheet at point A was gradually thinned during the stamping process, as shown in Fig. 8. The initial thickness was 0.1 mm, and the final thickness was 0.073 mm. Thus, the thinning percentage was 27%.
Residual stress distribution and formed thickness Fig. 9 shows the stress contours of Von Mises stress, horizontal stress (S11), vertical stress (S22), and longitudinal stress (S33). The peak stresses of Von Mises stress, S11, S22, and S33 were 228.5 MPa, 110.2 MPa, 51.5 MPa, and 257.5 MPa, respectively. The peak stresses were located on the bending area, as shown in Fig. 9. Fig. 10 shows the residual stress distribution along P1, the inner surface of BPP. Along P1, Von Mises stress and S33 had the same changing trends. They gradually increased along CD,
then decreased along DE, and increased again along EF. Compared with the other stresses, S22 was relatively small. The residual stress S11 along DE demonstrated a bending type distribution. The peak tensile stress was 109.9 MPa at point D, and the compressive stress was 103.3 MPa at point E. Fig. 11 shows the residual stress distribution along P2, the outer surface of BPP. For a cyclic geometrical feature, the outer surface of the current channel is the inner surface of the neighboring channel. Thus, the residual stress distribution along P2 was similar to that along P1 but in a reverse direction. Fig. 12 shows the residual stress distribution along P3, through the thickness of formed BPP. The Von Mises stress and S33 showed a trend of gradual decrease. The residual stresses S11 and S22 along P3 showed a significant bending type distribution. The stress in the middle point of P3 was zero. Residual stresses S11 and S22 in the outer surface were tensile and became compressive in the inner surface. Fig. 13 shows the thickness of formed BPP along P1. The maximum thickness of the formed BPP was 0.88 mm, and the minimum thickness of formed BPP was 0.73 mm. The minimum thickness was located at point E, the bending zone of BPP. According to the above analysis, the sheet had a large forming stress during the stamping process. If the peak Von Mises stress is larger than the true stress of the ultimate tensile strength, the sheet will be cracked or necked. If the compressive stress is too large, the sheet has a risk of wrinkling. In this model, the maximum and minimum thinning percentages were 27% and 12%, respectively. This indicates that non-uniform deformation occurred during the stamping process. Non-uniform thinning depends on material selection, die shape design, and friction conditions. How to prevent or decrease the non-uniform thinning should be carefully investigated.
Effect of die geometrical dimensions on residual stress and thickness In order to study the effect of die geometrical dimensions on formed residual stress and thickness, FE models with different upper die widths, die depths, and curve radii were built.
Effect of upper die width on residual stress and thickness In order to obtain the effect of the width of the upper die on residual stress and formed thickness of BPP, with the rest of the forming parameters kept constant, five models with widths of 0.6 mm, 0.7 mm, 0.8 mm, 0.9 mm, and 1.0 mm were established. The cross-section profiles of formed BPP are listed in Fig. 14. Fig. 15 shows the effect of upper die depth on the residual Von Mises stress along P3. It shows that the five models had almost the same stress distribution, but all the peak residual stresses increased with increased upper die width. Fig. 16 shows the effect of upper die width on formed BPP thickness along P1. It was also observed that the minimum thickness decreased with increased upper die width.
Effect of die depth on residual stress and thickness In order to obtain the effect of die depth on residual stress and formed thickness of BPP, with the rest of the forming
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Fig. 5 e Von Mises stress during the forming process (a) u ¼ 0.2 mm, (b) u ¼ 0.4 mm, (c) u ¼ 0.6 mm, and (d) unloaded.
Fig. 6 e Von Mises stress evolution at point A during the forming process.
Fig. 7 e Von Mises equivalent plastic strain evolution at point A during the forming process.
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Fig. 8 e BPP thickness evolution at point A during the forming process.
parameters kept constant, four models with widths of 0.4 mm, 0.5 mm, 0.6 mm, and 0.7 mm were established. The crosssection profiles of formed BPP are shown in Fig. 17. Fig. 18 shows the effect of die depth on the residual stresses in BPP along P3. It shows that the four models had the same stress distribution. The residual stress increased with increased die depth. When the die depth was 0.4 mm, the peak
Fig. 10 e Formed residual stress distribution along P1.
stress was 179.3 MPa, which means that too shallow a die depth can cause a little stress. When the die depth increased to 0.7 mm, the peak stress was 242 MPa. Fig. 19 shows the effect of die depth on BPP thickness along P1. It was observed that the die depth did not affect the thickness distribution. It was shown that maximum formed thickness decreased with increased die depth. When the die
Fig. 9 e Formed residual stress contour of BPP (a) Von Mises stress, (b) S11, (c) S22, and (d) S33.
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Fig. 11 e Formed residual stress distribution along P2.
Fig. 14 e Cross-section profiles of BPP with different upper die widths.
Fig. 12 e Formed residual stress distribution along P3.
Fig. 15 e Effect of upper die width on residual Von Mises stress along P3.
Fig. 13 e Formed BPP thickness along P1.
Fig. 16 e Effect of upper die width on BPP thickness along P1.
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Fig. 17 e Cross-section profiles of BPP with different die depths.
Fig. 18 e Effect of die depth on residual stress along P3.
Fig. 20 e Cross-section profiles of BPP with different curve radii.
Fig. 21 e Effect of the curve radius on residual stress along P3.
depth increased to 0.7 mm, the thickness greatly decreased, as shown in Fig. 19.
Effect of the curve radius on residual stress and thickness In order to obtain the effect of the curve radius on residual stress and formed thickness of BPP, with the rest of the forming parameters kept constant, four models with curve radii of 0.15 mm, 0.2 mm, 0.25 mm, and 0.3 mm were built. The cross-section profiles of formed BPP are shown in Fig. 20.
Fig. 19 e Effect of die depth on BPP thickness along P1.
Fig. 21 shows the effect of the curve radius on the residual stresses in BPP along P3. It shows that the four models had the same stress distribution. The formed residual stress decreased with increased curve radius. When the curve radius was 0.15 mm, the peak Von Mises stress was 235.8 MPa, which
Fig. 22 e Effect of the curve radius on BPP thickness along P1.
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means that too small a curve radius can cause too large a Von Mises stress. When the curve radius increased to 0.3 mm, the peak Von Mises stress was 198.7 MPa. Fig. 22 shows the effect of the curve radius on BPP thickness along P1. It was observed that the curve radius did not affect the thickness distribution. It was shown that maximum formed thickness increased with increased curve radius. When the curve radius was 0.15 mm, the minimum thickness along P1 was 0.068 mm. When the curve radius increased to 0.3 mm, the minimum thickness along P1 was 0.08 mm. This indicates that a larger curve radius can decrease the residual stress and make the formed BPP thickness more uniform.
Conclusions The forming stress and deformation of SS304 stainless steel BPP with a thickness of 0.1 mm was numerically determined by a 2D plane strain FE model. The effect of geometrical dimensions on residual stresses and formed thickness was discussed. Based on the obtained results, the following conclusions may be drawn: (1) During the stamping process of the stainless steel BPP, large forming stresses are generated in the bending zone, and then the stresses decrease when the upper die separates from the BBP. The stress evolution is according to the unloading law. With increased displacement of upper die increasing, the Von Mises equivalent plastic strain is increased, and the thickness of BPP is non-uniformly decreased. (2) The formed BPP has a large residual stress, especially in the bending zone. Residual stresses distribution along the inner surface, outer surface, and thickness direction are non-uniform. The horizontal and vertical stresses along the thickness direction show a significant bending type distribution. (3) The geometrical dimensions have a great effect on residual stress and formed thickness. With an increase of upper die width and die depth, the peak residual stress is increased, and formed thickness becomes less uniform. With an increase of the curve radius, the residual stress is decreased, and the formed thickness becomes more uniform. When the radius is increased to 0.3 mm, the minimum thickness is 0.8 mm.
Acknowledgment The authors wish to express their gratitude for the financial support by National Natural Science Foundation of China (51404284, 11372359), Fundamental Research Funds for the Central Universities (15CX05011A, 15Cx08006A), Applied Fundamental Research Funds of Qingdao City (15-9-1-95-jch), the Natural Science Foundation for Distinguished Young Scholars of Shandong Province (JQ201417), and Taishan Scholar Funding of Shandong Province (ts201511018). Thanks to Dr. Edward C. Mignot, Shandong University, for linguistic advice.
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