materials
Article Analysis of Deep Drawing Process for Stainless Steel Micro-Channel Array
Tsung-Chia Chen, Jiang-Cheng Lin and Rong-Mao Lee * Department of Mechanical Engineering, National Chin-Yi University of Technology, Taichung City 411, Taiwan; [email protected] (T.-C.C.); [email protected] (J.-C.L.) * Correspondence: [email protected]; Tel.: +886-4-2392-4505 (ext. 7168)
Academic Editors: Te-Hua Fang, Chien-Hung Liu, Ming-Tsang Lee and Tao-Hsing Chen Received: 30 December 2016; Accepted: 15 April 2017; Published: 18 April 2017
Abstract: The stainless steel bipolar plate has received much attention due to the cost of graphite bipolar plates. Since the micro-channel of bipolar plates plays the role of fuel flow field, electric connector and fuel sealing, an investigation of the deep drawing process for stainless steel micro-channel arrays is reported in this work. The updated Lagrangian formulation, degenerated shell finite element analysis, and the r-minimum rule have been employed to study the relationship between punch load and stroke, distributions of stress and strain, thickness variations and depth variations of individual micro-channel sections. A micro-channel array is practically formed, with a width and depth of a single micro-channel of 0.75 mm and 0.5 mm, respectively. Fractures were usually observed in the fillet corner of the micro-channel bottom. According to the experimental results, more attention should be devoted to the fillet dimension design of punch and die. A larger die fillet can lead to better formability and a reduction of the punch load. In addition, the micro-channel thickness and the fillet radius have to be taken into consideration at the same time. Finally, the punch load estimated by the unmodified metal forming equation is higher than that of experiments.
Keywords: micro-forming; deep drawing; micro-channel
1. Introduction Fuel cells are composed of several single-cells, which are serially connected with bipolar plates to generate sufficient current and voltage. Bipolar plates play the role of fuel input channel as well as of an electric bridge for reducing contact resistance or impedance when being connected with conducting wires [1–3]. Bipolar plates therefore become the key to miniaturizing the full cell, where bipolar plates represent more than 80% by weight and 40% by cost of the fuel cell [4,5]. In addition, both of the power generation efficiency and the manufacturing cost are determined by this component as well. In this case, the efficiency of heat radiating and electric conduction, which are highly related to the design of flow field, materials, and manufacturing methods of bipolar plates, should be taken into account [6,7]. Graphite and metallic materials are currently the most popular materials for bipolar plates. A composite bipolar plate made of the graphite/phenol formaldehyde resin was introduced for fuel cell applications [8]. The interaction between electrical conductivity, the shape factor and the orientation factor has been investigated. However, for reducing processing difficulty and manufacturing cost, metallic materials have received much more attention than graphite now [9,10]. The performance and long-term stability of bipolar plates made from Ti metal and stainless steels have been revealed by Park et al. [11]. The performance of Ti is lower than that of stainless steel due to the decrease in ohmic loss regions. On the other hand, stainless steels perform better as bipolar plates with regard to cell performance, cell resistance and durability. In order to produce channels for delivering fuel on metal sheets as well as reducing costs, numerous metal forming processes have been proposed such as stamping, drawing, and hydraulic pressure [10,12–14]. A metal bipolar plate manufactured
Materials 2017, 10, 423; doi:10.3390/ma10040423 www.mdpi.com/journal/materials Materials 2017, 10, 423 2 of 14 by stamping is regarded as an alternative to the graphite bipolar plate [15]. However, the errors of micro-channel dimensions by stamping are definitely encountered, and lead to performance loss. An investigation into bipolar plate structural parameters has been carried out by Imanmehr and Pourmahmod [16]. According to the analysis results, the parameters of micro-channels have a great impact on outlet voltage at high current densities. For increasing the contact area of gas, the flow channel number should be increased as much as possible [14]. However, these micro-channels can hardly be machined by conventional methods due to their dimensions. The effect of micro-channel width on fuel cell performance has been studied [17]. The best overall performance is from the narrowest channel width, and a computational fluid dynamics model was developed to study performance variation against channel width. Similar researches regarding the effects of channel dimensions were also reported [3,13,18]. As mentioned above, the stainless steel becomes one of the most popular materials for bipolar plates due to the cost, the power generation performance, and the corrosion resistance. Though the performance of anti-corrosion for stainless steel is fine, the high strain hardening exponent of this material leads to difficulty in manufacturing. Since the micro-channel plays an important role in chemical reaction performance, such as the gas reaction area and the transport channel of solution and electron, a study regarding the deep drawing of micro-channel arrays for stainless steel sheets has been accomplished in this work. The differences between macro and micro effects are studied as well. The purpose of this work is to discuss the parameters of deep drawing process for metallic micro-channels.
2. Basic Theory
2.1. Stiffness Equation The Lagrangian formulation can be employed to explain the properties of plastic flow. According to the Lagrangian formulation the rate equation for virtual work is as follows [19]:
Z ◦ • • Z Z • (σij − 2σikεkj)δεijdV + σjk LikδLijdV = f δvidS (1) E E V V S f where vi is the velocity, the rate of nominal traction is ti, and V and Sf are referred to the material volume and the surface respectively. Since both the virtual work rate equation and the constitutive relation are linear, they can be replaced with increments defined with respect to any monotonously increasing measures, such as the increase in the displacement of the tool. The complete global stiffness matrix can be stated as follows: [K]{∆u} = {∆F} (2) in which: Z Z [K] = [B]T([Cep] − [Q])[B]dV + [E]T[Z][E]dV (3) ∑ E ∑ E
2.2. Selective Reduced Integration Formulation The plastic medium volume is incompressible. Therefore, over-strong constraint for thin plates will be engaged when the full integration technique is applied for finite elements. This situation is due to the setting of no shear strain γxz and γyz during the deformation [20]. For solving such problems, in which the volumetrically in stiff contribution is involved, the selective reduced integration has been verified as an effective method [21]. The generalized formulation of selective reduced integration Materials 2017, 10, 423 3 of 14 proposed by Hughes [22] has been employed in this work. In addition, the four-node quadrilateral degenerated shell element [23] is utilized in the intensive analysis.
2.3. Scale Factors for Micro-Forming Process of Sheet Metal Generally, the size effect can be neglected for the thickness of sheet metal within 1.0 mm. However, the metallic sheet thickness in micro-forming process is of micron range and the traditional material model is therefore no longer suitable for analyses under this condition. A modified model without considering size effect has been employed in this work. A traditional material model can be defined as follows: n σ = K(ε0 + ε p) (4) The thickness of the metallic sheet in the following analysis is 50 µm. As a result, the size effect should be taken into account for the amendment of stress-strain relations. Consequently, Equation (4) is further amended as follows:
bt n(cedt−1) σ(t, ε) = aKe (ε0 + ε p) (5) where a, b, c, d are the correction coefficients. t is the metallic sheet thickness. These correction coefficients can be given according to Ref. [24] and Equation (5) therefore becomes
0.3152t n(1.0106e−0.01029t−1) σ(t, ε) = 0.73667Ke (ε0 + ε p) (6) Both the traditional material model, Equation (4), and the modified material model, Equation (6), are enclosed in the following finite element analyses. Experiments are conducted for the performance verification of these two models.
3. Numerical Analysis for Micro-Channel Array Forming Process Four-node quadrilateral degenerated shell elements are utilized in this work for deriving the stiffness matrix, and Finite Element Analysis (FEA) [25] is employed for the pre-processing and post-processing. Since the die and stainless steel plates are supposed to be symmetric, the simulation is performed against a 1/4 figure to effectively reduce the analysis time for arithmetic processing. The die and the metallic plate are then meshed with quadrilateral elements. These meshed data are transformed to the 3D elastic-plastic FEA program for the following simulation analysis. Since the die is too small to be manufactured by conventional methods, electric discharge machining is utilized for the die fabrication. The micro-channel array forming process is illustrated in Figure1. The dimensions of tools for the micro-channel array forming process are listed in Table1, where the die gap is set to be 1.1 times the plate thickness, in accordance with traditional empirical rules. Since the thickness of the stainless steel sheet used in this study is 0.05 mm, the die gap is designed to be 0.055 mm. The mechanical properties of the stainless steel sheet is illustrated in Table2. The die and the metallic plate are meshed into quadrilateral elements (see Figure2). These meshed data are then loaded into the 3D elastic-plastic FEA program for the following numerical analysis. Figure3 is the cross-section schematic diagram of the processed plate. L1 and L2 sections are the main objects for the following investigation, including the thickness distribution and the contour. In the micro-channel array deep drawing process, the die will directly contact the blank surface. That means the node for die contact and separation should be defined. Nodes are therefore divided into two categries: contact node and free node. The boundary conditions of the material meshing quadrilateral elements are demostrated in Figure4. Materials 2017, 10, 423 4 of 14 Materials 2017, 10, 423 4 of 14
Materials 2017, 10, 423 4 of 14 Materials 2017, 10, 423 4 of 14
FigureFigure 1. Micro-channel1. Micro-channel array array formingforming process process for for stainless stainless steel steel plates. plates.
Table 1. Dimensions of tools. Figure 1. Micro-channelTable array 1. Dimensions forming process of tools. for stainless steel plates. Figure 1. Micro-channelItems array forming process Dimensions for stainless (mm) steel plates. Width of channelItemsTable 1. ( WDimensions) Dimensions of tools. 0.75 (mm) Height of channelTable 1. Dimensions(h) of tools. 0.5 WidthItems of channel (W) Dimensions 0.75 (mm) Radius of die (Rd) 0.25 WidthHeight ofItems ofchannel channel (W ()h ) Dimensions 0.50.75 (mm) RadiusRadius of punch of die (Rp)) 0.250.2 WidthHeight of of channel channel ( W(dh) 0.750.5 Radius of punch (Rp) 0.2 HeightRadius of ofchannel die (R d()h ) 0.250.5 Table 2. Mechanical properties of stainless steel SUS304. RadiusRadius of of punch die (R (dR) p) 0.250.2 Material (SUS304)TableRadius 2. EMechanical (GPa) of punch properties ν(Rp) σy of(MPa) stainlessK0.2 steel(MPa) SUS304. n ε0 Tradition Table 2. Mechanical207 0.3 properties of341 stainless steel1819 SUS304. 0.576 0.077 MaterialScale (SUS304) Factor TableE 2.(GPa) Mechanical 198 ν 0.3properties σy of 306(MPa) stainless steelK 1361 (MPa)SUS304. 0.582n 0.077ε0 Material (SUS304) E (GPa) ν σy (MPa) K (MPa) n ε0 Remarks: E: Modulus of elasticity; ν: Poisson’s ratio; σy: Yield stress. MaterialTraditionTradition (SUS304) E 207 (GPa)207 0.30.3ν σy (MPa) 341 K (MPa)1819 1819 0.576 0.576n 0.077ε 0.0770 Scale Factor 198 0.3 306 1361 0.582 0.077 ScaleTradition Factor 207 198 0.3 0.3 341 306 1819 1361 0.576 0.582 0.077 0.077 Scale FactorRemarks: E: Modulus 198 of elasticity; 0.3 ν: Poisson’s 306 ratio; 1361σ : Yield stress. 0.582 0.077 Remarks: E: Modulus of elasticity; ν: Poisson’s ratio; σyy: Yield stress. y Remarks: E: Modulus of elasticity; ν: Poisson’sPunch ratio; σ : Yield stress.
Punch Punch Holder
Holder
BlankHolder
Blank Blank Die
Figure 2. Finite element model.Die Die
Figure 2. Finite element model. Figure 2. Finite element model. Figure 2. Finite element model.
L1 L2
Figure 3. Measurement schematic diagram. L1 L2 L1 L2
Figure 3. Measurement schematic diagram.
FigureFigure 3. 3.Measurement Measurement schematic schematic diagram. diagram.
Materials 2017, 10, 423 5 of 14 Materials 2017, 10, 423 5 of 14
Materials 2017, 10, 423 5 of 14
Figure 4. Boundary conditions of blank. Figure 4. Boundary conditions of blank. 4. Experimental Results and DiscussionFigure 4. Boundary conditions of blank. 4. Experimental Results and Discussion The micro-channel array deep drawing process for stainless steel plate is shown in Figure 5. In The4. Experimental micro-channel Results array and deepDiscussion drawing process for stainless steel plate is shown in Figure5. total, there are five steps in this geometric deformation process. The plate is gradually deformed In total, thereThe micro-channel are five steps array in this deep geometric drawing deformationprocess for stainless process. steel The plate plate is shown is gradually in Figure deformed 5. In during micro-channel forming until the unloading state. Throughout the entire micro-channel duringtotal, micro-channel there are five forming steps in until this geometric the unloading deformation state. Throughout process. The the plate entire is gradually micro-channel deformed forming forming process, the contact, separation, and friction conditions can be accurately estimated by the process,during the contact,micro-channel separation, forming and until friction the conditionsunloading state. can be Throughout accurately estimatedthe entire bymicro-channel the r-minimum r-minimumforming ( rprocess,min) rule. the The contact, rmin rule separation, is mainly and for fricti the ondefinition conditions of canboundary be accu conditionsrately estimated for degenerated by the (rmin) rule. The rmin rule is mainly for the definition of boundary conditions for degenerated four-node four-noder-minimum shell (elementsrmin) rule. Theduring rmin ruledeformation is mainly foranalyses the definition. Figure of 6 boundary is the prototype conditions of for tools degenerated employed in shell elements during deformation analyses. Figure6 is the prototype of tools employed in the the micro-channelfour-node shell arrayelements drawing during experiment, deformation includinanalyses.g Figure punch, 6 isdie the bottom, prototype and of blanktools employed holder. The in test micro-channel array drawing experiment, including punch, die bottom, and blank holder. The test rig andthe themicro-channel electro press array (JANOME drawing experiment,JP-5004, JANOME including Sewingpunch, die Machines bottom, and Co., blank Ltd., holder. Tokyo, The Japan) test for rig and the electro press (JANOME JP-5004, JANOME Sewing Machines Co., Ltd., Tokyo, Japan) for micro-channelrig and the arrayelectro formingpress (JANOME process JP-5004, are shown JANOME in Figures Sewing 7 andMachines 8 respectively. Co., Ltd., Tokyo, Japan) for micro-channelmicro-channel array array forming forming process process are are shown shown inin FiguresFigures 7 and 8 respectively.
Stroke=0mmStroke=0mm
Stroke=0.125mm Stroke=0.125mm
Stroke=0.25mm Stroke=0.25mm
Stroke=0.5mm
Stroke=0.5mm
After unloading
After unloading FigureFigure 5. The 5. The geometric geometric deformation deformation of thin metal metal sheet sheet against against various various strokes. strokes.
Figure 5. The geometric deformation of thin metal sheet against various strokes.
Materials 2017, 10, 423 6 of 14 Materials 2017, 10, 423 6 of 14 Materials 2017, 10, 423 6 of 14 Materials 2017, 10, 423 6 of 14
Figure 6. The prototype of tools for the micro-channel array forming process. Figure 6. The prototype of tools for the micro-channel array forming process. Figure 6. The prototype of tools for the micro-channel array forming process. Figure 6. The prototype of tools for the micro-channel array forming process.
Figure 7. The test rig for the micro-channel array forming process. Figure 7. The test rig for the micro-channel array forming process. Figure 7. The test rig for the micro-channel array forming process. Figure 7. The test rig for the micro-channel array forming process.
Figure 8. The electro press for the micro-channel array forming process (JANOME JP-5004). Figure 8. The electro press for the micro-channel array forming process (JANOME JP-5004). Figure 8. The electro press for the micro-channel array forming process (JANOME JP-5004). Figure 8. The electro press for the micro-channel array forming process (JANOME JP-5004).
Materials 2017, 10, 423 7 of 14 Materials 2017, 10, 423 7 of 14 Materials 2017, 10, 423 7 of 14 4.1. Comparisons between Experimental Results and Simulation Results 4.1. Comparisons between Experimental Results and Simulation Results Two models, i.e., macro and micro, are employed in the simulation of the micro-channel array Two models, i.e., macro and micro, are employed in the simulation of the micro-channel array deep drawing process for stainless steel plate. Since Since the the thickness thickness of of the the stainless steel steel plate for deep drawing process for stainless steel plate. Since the thickness of the stainless steel plate for experiments is is merely 50 μµm, the contour measurements of the finishedfinished workpieces is accomplished experiments is merely 50 μm, the contour measurements of the finished workpieces is accomplished by using a laserlaser displacementdisplacement system,system, as as shown shown in in Figure Figure9 (Keyence9 (Keyence LC-2430, LC-2430, Osaka, Osaka, Japan). Japan). Some Some of by using a laser displacement system, as shown in Figure 9 (Keyence LC-2430, Osaka, Japan). Some ofthe the processed processed workpieces workpieces are are shown shown in Figurein Figure 10 .10. of the processed workpieces are shown in Figure 10.
Figure 9. Laser displacement system (Keyence LC-2430) for contour measurements of stamped Figure 9.9. LaserLaser displacement displacement system system (Keyence (Keyence LC-2430) LC-2430) for contour for contour measurements measurements of stamped of stamped stainless stainless steel plates. stainlesssteel plates. steel plates.
Figure 10. Processed workpiece of micro-channel array forming process. Figure 10. ProcessedProcessed workpiece of micro-channel array forming process. Figure 11 is a comparison between theoretical estimations and experimental results for the L1 Figure 11 is a comparison between theoretical estimations and experimental results for the L1 sectionFigure contour. 11 is The a comparison channel depth between is about theoretical 0.5 mm. estimations However, and the experimental effect of material results springback for the L section contour. The channel depth is about 0.5 mm. However, the effect of material springback1 resultssection in contour. an upward The channel curl of depththe peripheral is about 0.5part mm. of the However, stainless the steel effect plate. of material Namely, springback the channel results will results in an upward curl of the peripheral part of the stainless steel plate. Namely, the channel will deviatein an upward from the curl center of the of peripheral stainless partsteel of plate the stainlessand move steel downwa plate. Namely,rd. As a theresult, channel the deformation will deviate deviate from the center of stainless steel plate and move downward. As a result, the deformation trendfrom thecould center be ofpredicted stainless more steel plateprecisely and moveby the downward. material model As a result, of modified the deformation scale factor trend than could by trend could be predicted more precisely by the material model of modified scale factor than by traditionalbe predicted material more precisely models. byA thecomparison material modelbetween of theoretical modified scale estimations factor than and by experimental traditional material results traditional material models. A comparison between theoretical estimations and experimental results for the L2 section contour is shown in Figure 12. Similarly, the difference in channel depth between for the L2 section contour is shown in Figure 12. Similarly, the difference in channel depth between these three results (experimental results, traditional material model and modified scale-factor these three results (experimental results, traditional material model and modified scale-factor
Materials 2017, 10, 423 8 of 14
Materialsmodels.Materials 2017 2017 A,comparison ,10 10, ,423 423 between theoretical estimations and experimental results for the L2 section88 of of 14 14 contour is shown in Figure 12. Similarly, the difference in channel depth between these three results (experimentalmaterialmaterial model) model) results, is is mainly mainly traditional due due to to materialthe the peripheral peripheral model curvature andcurvature modified of of the the scale-factor stainless stainless steel materialsteel plate. plate. model) The The maximum maximum is mainly depthduedepth to theerrorerror peripheral betweenbetween curvature thesethese twotwo of thematerialmaterial stainless modelsmodels steel plate.isis aboutabout The 0.035 maximum0.035 mm.mm. depth TheThe performanceperformance error between ofof these thethe modified scale factor material model is still better than that of traditional material model for L2 twomodified material scale models factor is aboutmaterial 0.035 model mm. is The still performance better than of that the modifiedof traditional scale material factor material model modelfor L2 sectionissection still better contour contour than estimation. estimation. that of traditional material model for L2 section contour estimation.
L1 L1
Figure 11. The contour comparison of L1 section. FigureFigure 11.11.The Thecontour contourcomparison comparisonof ofL L11 section.section.
L2 L2
Figure 12. The contour comparison of L2 section. FigureFigure 12.12.The Thecontour contourcomparison comparisonof ofL L22 section.section.
The thickness of the L1 section is shown in Figure 13. The range of thickness variation is The thickness of the L1 section is shown in Figure 13. The range of thickness variation is 0.0264~0.033The thickness mm. Based of the on L 1Figuresection 13, is the shown experimental in Figure result 13. The is between range of the thickness results variationof the two is 0.0264~0.0330.0264~0.033 mm.mm. Based Based on on Figure Figure 13, the13, experimentalthe experimental result result is between is between the results the of results the two of theoretical the two theoreticaltheoretical models.models. InIn addition,addition, amongamong allall thethe processedprocessed channelschannels inin oneone plate,plate, thethe firstfirst channelchannel isis themodels. thinnest. In addition, The thickness among allvariations the processed for these channels three in results one plate, (experimental the first channel results, is the traditional thinnest. Thethe thicknessthinnest. variationsThe thickness for these variations three results for these (experimental three results results, (experimental traditional material results, models traditional and materialmaterial modelsmodels andand modifiedmodified scalscale-factore-factor materialmaterial model)model) areare simisimilar,lar, andand nono significantsignificant errorerror isis observed. The thickness of the L2 section is shown in Figure 14. The L2 section is thicker than the L1 observed. The thickness of the L2 section is shown in Figure 14. The L2 section is thicker than the L1 section.section. The The thickness thickness difference difference is is about about 0.003 0.003 mm. mm.
Materials 2017, 10, 423 9 of 14 modified scale-factor material model) are similar, and no significant error is observed. The thickness of the L2 section is shown in Figure 14. The L2 section is thicker than the L1 section. The thickness Materialsdifference 2017 is, 10 about, 423 0.003 mm. 9 of 14
0.07 Materials 2017, 10, 423 9 of 14 Scale factor Tradition 0.07 Experiment
0.06 Scale factor Tradition Experiment 0.06
0.05
0.05 Thickness(mm) 1
L 0.04 Thickness(mm) 1
L 0.04
0.03
0.03
0.02 0.02 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 0 2 4 6 8 10 12X-AXIS 14 16(mm) 18 20 22 24 26 28 30 X-AXIS(mm)
Figure 13. TheThe thickness thickness variation variation of the L 1 section.section. Figure 13. The thickness variation of the L1 section.1
0.07 0.07 ScaleScale factor factor TraditionTradition ExperimentExperiment
0.06 0.06
0.05 0.05 Thickness(mm) 2
L 0.04 Thickness(mm) 2
L 0.04
0.03
0.03
0.02
0 2 4 6 8 1012141618202224262830 0.02 X-AXIS(mm)
0Figure 2 4 14. 6The 8thickness 1012141618202224262830 variation of the L2 section. Figure 14. The thickness variationX-AXIS(mm) of the L2 section.
The relationship ofFigure punch 14. load The and thickness stroke variationis revealed of thein Figure L2 section. 15. The curve variations for Thethese relationship three results of (experimental punch load and results, stroke tradit is revealedional material in Figure model 15. Theand curvemodified variations scale-factor for these threeThematerial results relationship (experimentalmodel) are of similar;punch results, namely,load traditional and the stroke punch material is load re modelvealed increased and in Figure modifiedwith increasing 15. scale-factor The stroke.curve material variationsHowever, model) for theseare similar; significantthree namely,results errors the(experimental are punch observed load once results, increased the stroke tradit with exional increasingceeds material a threshold. stroke. model The However, largeand errormodified significant is due scale-factor to errors the are materialobservedincrease model) once in thecontact are stroke similar; area exceeds between namely, a die threshold. theand punch blank. The Acload largecording increased error to Figure is with due 15, toincreasing the the simulation increase stroke. inresults contact However, for area the modified scale-factor material model is much better than those of traditional material model. significantbetween die errors and blank.are observed According once to the Figure stroke 15 ,ex theceeds simulation a threshold. results The for large the modified error is scale-factordue to the increasematerial in model contact is much area betterbetween than die those and ofblank. traditional According material to Figure model. 15, the simulation results for the modified scale-factor material model is much better than those of traditional material model.
Materials 2017, 10, 423 10 of 14 Materials 2017, 10, 423 10 of 14
4000
Materials 2017, 10, 423 Tradition 10 of 14 Scale factor 4000 experiment
Tradition 3000 Scale factor experiment
3000
2000 Punch Load(N) Punch
2000
Punch Load(N) Punch 1000
1000
0
0 0.10.20.30.40.5 Displacement(mm) 0 Figure 15. The relationship of punch load and stroke. Figure0 15. The relationship0.10.20.30.40.5 of punch load and stroke. Displacement(mm) 4.2. Effect of Tool Radius on the Micro-Channel Array Forming Process of Stainless Steel Plates 4.2. Effect of Tool Radius on theFigure Micro-Channel 15. The relationship Array Forming of punch Processload and ofstroke. Stainless Steel Plates The dimensional effect of punch fillet radius on the thickness of stainless steel plate is demonstrated Thein4.2. Figure Effect dimensional 16.of Tool The Radius parameters effect on the of ofMicro-Channe punchthe micro-channel filletl Array radius Formingarray on forming Process the thickness process of Stainless areof asSteel follows: stainless Plates steel plate is demonstrated in Figure 16. The parameters of the micro-channel array forming process are as follows: * The Punch dimensional fillet radius: effect 0.05 of mm, punch 0.1 fillet mm, radius 0.15 mm,on the 0.2 thickness mm, and of 0.25 stainless mm steel plate is demonstrated *in FigureStroke: 16. 0.5 The mm parameters of the micro-channel array forming process are as follows: * Punch fillet radius: 0.05 mm, 0.1 mm, 0.15 mm, 0.2 mm, and 0.25 mm * Coefficient of friction: 0.2 * *Stroke: Punch 0.5 fillet mm radius: 0.05 mm, 0.1 mm, 0.15 mm, 0.2 mm, and 0.25 mm * Stroke: Blank thickness: 0.5 mm 0.5 mm * Coefficient of friction: 0.2 * Coefficient of friction:0.03 0.2 * Blank thickness: 0.5 mm * Blank thickness: 0.5 mm t=0.05mm;=0.2; stroke=0.5mm Last Stroke 0.03 0.028 Spring Back
t=0.05mm;=0.2; stroke=0.5mm Last Stroke 0.0260.028 Spring Back
0.0240.026 Min. Thickness(mm)
0.0220.024 Min. Thickness(mm)
0.0220.02
0.0180.02
0 0.05 0.1 0.15 0.2 0.25 0.3 The Radius of Punch (mm) 0.018 Figure 16. The relationship between sheet thickness and punch fillet radius. 0 0.05 0.1 0.15 0.2 0.25 0.3 The Radius of Punch (mm) The thickness increases linearly when the fillet radius is increased. The minimal thickness is Figure 16. The relationship between sheet thickness and punch fillet radius. 0.0201 mm againstFigure 16.a punchThe relationship fillet radius between of 0.05 sheet mm. thickness The thickest and punchsheet filletthickness radius. is 0.0278 mm againstThe a thicknesspunch fillet increases radius linearlyof 0.25 mm. when Apparently, the fillet radius an acute is increased. angle of channelThe minimal would thickness be formed is Themore0.0201 thickness easily mm againstby a increases small a punch punch linearly fillet fillet radius radius when of than the 0.05 filletby mm. a radiuslarge The one, thickest is increased.and maysheet lead thickness The to minimalmaterial is 0.0278 fracture. thickness mm is 0.0201Theagainst mm punch against a punch load a againstfillet punch radius stroke fillet of radiusunder 0.25 mm.various of 0.05 Apparently, punch mm. Thefillet an thickest radiuses acute angle sheet is reported of thickness channel in Figure would is 0.0278 17. be It mmformedshould against be noticed that a small punch fillet radius leads to a large punch load; e.g., the maximal load (about a punchmore fillet easily radius by a ofsmall 0.25 punch mm. Apparently,fillet radius than an acuteby a large angle one, of channel and may would lead to be material formed fracture. more easily by a small The punch punch load fillet against radius stroke than under by a various large one, punch and fillet may radiuses lead to is materialreported in fracture. Figure 17. The It punchshould load be noticed that a small punch fillet radius leads to a large punch load; e.g., the maximal load (about against stroke under various punch fillet radiuses is reported in Figure 17. It should be noticed that a small punch fillet radius leads to a large punch load; e.g., the maximal load (about 5000 N) is induced Materials 2017, 10, 423 11 of 14 Materials 2017, 10, 423 11 of 14 by aMaterials5000 tool N) radius 2017 is , induced10 of, 423 0.05 by mm. a tool As radius a result, of 0.05 the mm. punch As loada result, can the be reducedpunch load by can increasing be reduced11 the of by14 punch filletincreasing radius. the punch fillet radius. 5000 N) is induced by a tool radius of 0.05 mm. As a result, the punch load can be reduced by increasing the punch fillet4000 radius. t=0.05mm;=0.2; 4000 stroke=0.5mm Rp=0.05mm
t=0.05mm;R=0.2;p=0.1mm
stroke=0.5mmRp=0.15mm 3000 Rp=0.05mm Rp=0.2mm Rp=0.1mm Rp=0.25mm Rp=0.15mm 3000 Rp=0.2mm
Rp=0.25mm
2000 Punch Load(N) Punch 2000 Punch Load(N) Punch
1000
1000
0
0 0.1 0.2 0.3 0.4 0.5 Displacement(mm) 0
Figure 17. Punch0 load 0.1 against stroke 0.2 under various 0.3 punch 0.4 fillet radiuses. 0.5 Figure 17. Punch load against strokeDisplacement(mm) under various punch fillet radiuses.
Figure 18 showsFigure the 17. relationshipPunch load against between stroke the unde meanr various channel punch height fillet radiuses.of the L 1 section and the Figurepunch fillet 18 shows radius. theA large relationship punch fillet between radius leads the meanto a hi channelgh channel height height of of thethe L1 section,section e.g., and the punchthe fillet maximumFigure radius. 18 showsmean A largechannelthe relationship punch height fillet isbetween achieved radius the leadsby mean a punch to channel a high fillet height channel radius of ofthe height 0.25 L1 sectionmm. of the Since and L1 thethesection, e.g.,punch theflowability maximum fillet ofradius. material mean A large is channel regulated punch height fillet by the radius is fillet achieved leads radius, to by thea hi a deepgh punch channel drawing fillet height radiusprocess of the of can 0.25L 1be section, mm.performed Sincee.g., the flowabilitythemore maximum smoothly of material mean when is channel regulateda large heightfillet by radius theis achieved fillet is applied. radius, by a The thepunch deepmean fillet drawingchannel radius heightof process 0.25 of mm. canthe LSince be2 section performed the flowabilityagainst fillet of radius material is shownis regulated in Figure by the 19. fillet The radius,variation the trend deep ofdrawing the L2 sectionprocess height can be is performed similar to more smoothly when a large fillet radius is applied. The mean channel height of the L2 section against morethat of smoothly the L1 section when height, a large but fillet the radius measured is applied. height ofThe the mean L2 section channel is a heightlittle bit of higher the L 2than section the fillet radius is shown in Figure 19. The variation trend of the L2 section height is similar to that of the againstheight offillet the radiusL1 section is shown (about in 0.02 Figure mm). 19. This The is variationdue to the trend reducing of the of L the2 section peripheral height contact is similar area toof L section height, but the measured height of the L section is a little bit higher than the height of the 1 thatthe channelof the L by1 section buckling. height, but the measured height2 of the L2 section is a little bit higher than the L1 sectionheight (aboutof the L 0.021 section mm). (about This 0.02 is due mm). to This the is reducing due to the of reducing the peripheral of the peripheral contact areacontact of thearea channel of by buckling.the channel by buckling.
L1
L1
Figure 18. The relationship between the tool radius and the channel height of the L1 section.
Figure 18. The relationship between the tool radius and the channel height of the L1 section. Figure 18. The relationship between the tool radius and the channel height of the L1 section.
Materials 2017, 10, 423 12 of 14 Materials 2017, 10, 423 12 of 14
Materials 2017, 10, 423 12 of 14
L2
L2
2 Figure 19. The relationship between the tool radiusradius and the channel height of the L2 section. Figure 19. The relationship between the tool radius and the channel height of the L2 section. The practically processed workpieces are shown in Figure 20. In total, five kinds of strokes have The practically processed workpieces are shown in Figure 20. In total, five kinds of strokes been appliedThe inpractically the experiments, processed includingworkpieces 0.4 are mm, shown 0.45 in mm,Figure 0.5 20. mm, In total, 0.55 fivemm kinds and 0.6of strokesmm. Significant have have been applied in the experiments, including 0.4 mm, 0.45 mm, 0.5 mm, 0.55 mm and 0.6 mm. fracturesbeen haveapplied been in the observed experiments, in the including plates at0.4 strokes mm, 0.45 of mm, 0.55 0.5 mm mm, and 0.55 0.6 mm mm. and As0.6 amm. result, Significant the stroke Significant fractures have been observed in the plates at strokes of 0.55 mm and 0.6 mm. As a result, limitationfractures for havemicro-channel been observed array in deepthe plates drawing at strokes processes of 0.55 inmm this and work 0.6 mm. is about As a result,0.5 mm. the stroke the strokelimitation limitation for micro-channel for micro-channel array deep array drawing deep processes drawing in processes this workin is thisabout work 0.5 mm. is about 0.5 mm.
Figure 20. Processed stainless steel plate (a) stroke of 0.5 mm; (b) stroke of 0.55 mm; (c) stroke of 0.6 mm. FigureFigure 20. 20. ProcessedProcessed stainless stainless steel steel plate plate (a) stroke (a) stroke of 0.5 of mm; 0.5 mm;(b) stroke (b) stroke of 0.55 of mm; 0.55 ( mm;c) stroke (c) strokeof 0.6 mm. of 0.6 mm. 5. Conclusions 5. Conclusions 5. Conclusions3D elastic-plastic finite element analysis has been employed in this work to analyze the 3Dmicro-channel elastic-plastic array finite deep drawingelement process analysis for stainlesshas been steel employed plate. The in r-minimum this work rule to is analyzeapplied the micro-channel3Dto simplify elastic-plastic arraythe calculation deep finite drawing during element the process non-linear analysis for stainlesspr hasocess. been The steel employedmain plate. results The inare r this-minimumsummarized work to ruleas analyzefollows: is applied the micro-channel array deep drawing process for stainless steel plate. The r-minimum rule is applied to to simplify(1) The the maximum calculation channel during depth the non-linearfor a 50 μm pr stainlessocess. Thesteel main sheet resultsis about are 0.5 summarized mm. This is verified as follows: simplify the calculation during the non-linear process. The main results are summarized as follows: (1) The maximumby both of the channel simulation depth results for aand 50 theμm experimental stainless steel results. sheet is about 0.5 mm. This is verified
(1) byThe(2) both maximumOn ofthe the basis simulation channel of the finished depth results for workpieces, and a 50 theµm experimental stainlessthe material steel fracture results. sheet isis aboutmainly 0.5 located mm. Thisin the is contact verified by area between the punch and the bottom die fillet. As a result, more attention should be (2) Onboth the of basis the simulation of the finished results workpieces, and the experimental the material results. fracture is mainly located in the contact devoted to fillet radius design. (2) On the basis of the finished workpieces, the material fracture is mainly located in the contact area area(3) Thebetween deep drawingthe punch process and canthe bebottom performed die fillet.more smoothlyAs a result, when more a large attention fillet radius should is be devotedbetweenapplied. to the fillet In punch other radius words, and design. the a small bottom tool die fillet fillet. radius As may a result, lead to more an increase attention of fracture. should be devoted to (3) Thefillet(4) Thedeep radius simulation drawing design. performance process can of bethe performedmodified scale-factor more smoothly material modelwhen isa betterlarge thanfillet that radius of is (3) applied.The deepthe traditional In drawing other words, material process a model.small can be tool performed fillet radius more may smoothly lead to when an increase a large of fillet fracture. radius is applied. (4) TheIn other simulation words, performance a small tool fillet of th radiuse modified may leadscale-factor to an increase material of fracture.model is better than that of (4) theTheAcknowledgments: traditional simulation material performance This research model. was of the sponsored modified by the scale-factor Ministry of materialScience and model Technology is better in Taiwan than thatunder of the Grants MOST 105-2221-E-167-007. traditional material model. Acknowledgments: This research was sponsored by the Ministry of Science and Technology in Taiwan under Grants MOST 105-2221-E-167-007.
Materials 2017, 10, 423 13 of 14
Acknowledgments: This research was sponsored by the Ministry of Science and Technology in Taiwan under Grants MOST 105-2221-E-167-007. Author Contributions: T.-C. Chen and J.-C. Lin conceived and designed the experiments; J.-C. Lin performed the experiments; T.-C. Chen, J.-C. Lin and R.-M. Lee analyzed the data; T.-C. Chen and R.-M. Lee contributed reagents/materials/analysis tools; R.-M. Lee wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
References
1. Yu, H.N.; Lim, J.W.; Suh, J.D.; Lee, D.G. A graphite-coated carbon fiber epoxy composite bipolar plate for polymer electrolyte membrane fuel cell. J. Power Sources 2011, 196, 9868–9875. [CrossRef] 2. Kumar, A.; Ricketts, M.; Hirano, S. Ex situ evaluation of nanometer range gold coating on stainless steel substrate for automotive polymer electrolyte membrane fuel cell bipolar plate. J. Power Sources 2010, 195, 1401–1407. [CrossRef] 3. Peng, L.; Lai, X.; Liu, D.; Hu, P.; Ni, J. Flow channel shape optimum design for hydroformed metal bipolar plate in PEM fuel cell. J. Power Sources 2008, 178, 223–230. [CrossRef] 4. Petrach, E.; Abu-Isa, I.; Wang, X. Investigation of elastomer graphite composite material for proton exchange membrane fuel cell bipolar plate. J. Fuel Cell Sci. Technol. 2009, 6, 0310051–0310056. [CrossRef] 5. Gautam, R.K.; Banerjee, S.; Kar, K.K. Bipolar plate materials for proton exchange membrane fuel cell application. Recent Pat. Mater. Sci. 2015, 8, 15–45. [CrossRef] 6. Koc, M.; Mahabunphachai, S. Feasibility investigations on a novel micro-manufacturing process for fabrication of fuel cell bipolar plates: Internal pressure-assisted embossing of micro-channels with in-die mechanical bonding. J. Power Sources 2007, 172, 725–733. [CrossRef] 7. Iranzo, A.; Munoz, M.; Lopez, E.; Pino, J.; Rosa, F. Experimental fuel cell performance analysis under different operating conditions and bipolar designs. Int. J. Hydrogen Energy 2010, 35, 11434–11447. [CrossRef] 8. Kakati, B.K.; Yamsani, V.K.; Dhathathreyan, K.S.; Sathiyamoorthy, D.; Verma, A. The electrical conductivity of a composite bipolar plate for fuel cell applications. Carbon 2009, 47, 2413–2418. [CrossRef] 9. Mahabunphachai, S.; Koc, M. Fabrication of micro-channel arrays on thin metallic sheet using internal fluid pressure: Investigations on size effects and development of design guidelines. J. Power Sources 2008, 175, 363–371. [CrossRef] 10. Hu, P.; Peng, L.; Zhang, W.; Lai, X. Optimization design of slotted-interdifitated channel for stamped thin metal bipolar plate in proton exchange membrane fuel cell. J. Power Sources 2009, 187, 407–414. [CrossRef] 11. Park, Y.-C.; Lee, S.-H.; Kim, S.-K.; Lim, S.; Jung, D.-H.; Lee, D.-Y.; Choi, S.-Y.; Ji, H.; Peck, D.-H. Performance and long-term stability of Ti metal and stainless steels as a metal bipolar plate for a direct methanol fuel cell. Int. J. Hydrogen Energy 2010, 35, 4320–4328. [CrossRef] 12. Peng, L.F.; Hu, P.; Lai, X.M.; Mei, D.Q.; Ni, J. Investigation of micro/meso sheet soft punch stamping process-simulation and experiments, materials and design. Mater. Des. 2009, 30, 783–790. [CrossRef] 13. Zhang, B.; Zhang, Y.F.; He, H.; Li, J.M.; Yuan, Z.Y.; Na, C.R.; Liu, X.W. Development and performance analysis of a metallic micro-direct methanol fuel cell for high-performance applications. J. Power Sources 2010, 195, 7338–7348. [CrossRef] 14. Chen, Y.L.; Zhan, H.B.; Lee, S.J.L.; Zhu, S.M. Micro-ECM of maze flow channel on bipolar plates of fuel cell. Key Eng. Mater. 2011, 458, 125–130. [CrossRef] 15. Qiu, D.; Yi, P.; Peng, L.; Lai, X. Channel dimensional error effect of stamped bipolar plates on the characteristics of gas diffusion layer contact pressure for proton exchange membrane fuel cell stacks. J. Fuel Cell Sci. Technol. 2015, 12, 041002. [CrossRef] 16. Imanmehr, S.; Pourmahmod, N. A parameteric study of bipolar plate structural parameters on the performance of proton exchange membrane fuel cell. J. Fuel Cell Sci. Technol. 2012, 9, 051003. [CrossRef] 17. Kianimanesh, A.; Yu, B.; Yang, Q.; Freiheit, T.; Xue, D.; Park, S.S. Investigation of bipolar plate geometry on direct ethanol fuel cell performance. Int. J. Hydrogen Energy 2012, 37, 18403–18411. [CrossRef] 18. Park, W.T.; Jin, C.K.; Kang, C.G. Improving channel depth of stainless steel bipolar plate in fuel cell using process parameters of stamping. Energy Convers. Manag. 2016, 124, 51–60. [CrossRef] 19. McMeeking, R.M.; Rice, J.R. Finite-element formulations for problems of large elastic-plastic deformation. Int. J. Solids Struct. 1975, 11, 601–616. [CrossRef] Materials 2017, 10, 423 14 of 14
20. Hinton, E.; Owen, D.R. Finite Element Software for Plates and Shell; Pineridge: Swansea, UK, 1984. 21. Hughes, T.J.R. The Finite Element Method; Prentice-Hall: Englewood Cliffs, NJ, USA, 1987. 22. Hughes, T.J.R. Generalization of selective integration procedures to anisotropic and nonlinear media. Int. J. Numer. Methods Eng. 1980, 15, 1413–1418. [CrossRef] 23. Adam, F.M.; Mohamed, E.; Hassaballa, A.E. Degenerated four nodes shell element with drilling degree of freedom. J. Eng. 2013, 3, 10–20. 24. Peng, L.F.; Liu, F.; Ni, J.; Lai, X.M. Size effects in thin sheet metal forming and its elastic-plastic constitutive model. Mater. Des. 2007, 28, 1731–1736. [CrossRef] 25. Huang, Z.G.; Li, J.W. Heating and thermostatic analysis of an oven-controlled quartz crystal oscillator. Smart Sci. 2016, 4, 45–51. [CrossRef]
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).