National Sun Yat-sen University Institutional Repository:Item 987654321/38883

(1)

行政院國家科學委員會專題研究計畫期中進度報告

子計畫三：微型質子交換膜燃料電池元件薄膜電極體與流道

板界面封裝暨結構可靠度之研究(2/3)

計畫類別：整合型計畫計畫編號： NSC94-2218-E-110-006- 執行期間： 94 年 08 月 01 日至 95 年 07 月 31 日執行單位：國立中山大學機械與機電工程學系(所) 計畫主持人：錢志回計畫參與人員：林智偉、石益三、許哲彰、黃衍龍報告類型：精簡報告報告附件：出席國際會議研究心得報告及發表論文處理方式：本計畫可公開查詢

中華民國 95 年 5 月 10 日

(2)

行政院國家科學委員會補助專題研究計畫

□ 成果報告

■ 期中進度報告

（計畫名稱）

中文名稱：微型質子交換膜燃料電池元件薄膜電極體與流道板界面封裝暨結構

可靠度之研究

英文名稱：The Interface Reliability Analysis of MEA and Flow Field Plate during

Bonding and Package Process

計畫類別：□ 個別型計畫 ■ 整合型計畫

計畫編號：NSC － 94 － 2218 － E － 110 － 006

執行期間： 93 年 08 月 01 日至 96 年 07 月 31 日

整合型總計畫主持人：

謝曉星教授

計畫主持人：

錢志回教授

計畫參與人員：林智偉、石益三、許哲彰、黃衍龍

成果報告類型(依經費核定清單規定繳交)：■精簡報告 □完整報告

本成果報告包括以下應繳交之附件：

□赴國外出差或研習心得報告一份

□赴大陸地區出差或研習心得報告一份

□出席國際學術會議心得報告及發表之論文各一份

□國際合作研究計畫國外研究報告書一份

處理方式：除產學合作研究計畫、提升產業技術及人才培育研究計畫、列

管計畫及下列情形者外，得立即公開查詢

□ 涉及專利或其他智慧財產權，□一年□二年後可公開查詢

執行單位：

國立中山大學機械與機電工程學系

中華民國

95 年 05 月 05 日

(3)

Abstract

This is the second year’s mid-term report of subproject-3 of a three-year main project. The main aim of this subproject is to analysis the interface reliability of MEA and flow field plate during package process, by using the experimental and numerical method, as well as evaluates bonding strength of the interface. In the first year, in order to study the reliability of flow field plate, the study is concentrated on predicting the stress distribution between the sputtered Ag layer and the SU8 substrate of a micro-channel in polymer electrolyte membrane fuel cell (PEMFC) through simulation of stress state and flow field in the channel. In this second year, the study is concentrated on predicting the fracture behavior between the sputtered Ag layer and the SU8 substrate of the micro-channel. A crack at bimaterial interface was used for studying the effect of the flow-induced stress intensity factor (SIF) on the crack-tip. Then, the results are used to predict the fracture behavior between the sputtered Ag layer and the SU8 substrate of the micro-channel. In the first half of this year, the efforts were concentrated on setting up the crack model and the analysis process. In the second half of this year, the efforts will be concentrated on studying the effects of the variation of micro-channel construction and the crack length and the gas inlet velocity and pressure on the flow induced stress states and SIF in a bimaterial interface. Keywords: Fuel cells; Stress Intensity Factor; Micro-channels; Interface Reliability

摘要

此為三年期整合計畫的子計畫三之第二年期中報告。本子計畫的主要目的為分析薄膜電極體（MEA）與流道板界面於實際運作時界面封裝及結構可靠度評估,並建立實驗與數值模擬等分析模式。在第一年為了研究流道的可靠度，將研究重點置於藉由商用套裝軟體

ANSYS® 8.0 來分析在 PEMFC 微流道中濺鍍層 Ag 和基材 SU8 間的應力分佈情況。在本第

二年之研究重點為分析在PEMFC 微流道中濺鍍層 Ag 和基材 SU8 間的破裂行為。在初期階段，先分析由流體導致之應力對位於雙材料之層間裂縫之應力集中因子的響影；再將此結果運用來分析微流道中濺鍍層Ag 和基材 SU8 的間破裂行為情況。本年度前半年，計畫成果著重於裂縫模型以及解析過程之建立；後半年將著重在微流道結構變化、裂縫長度和入口氣體速度及壓力對於應力分佈及應力集中因子的影響。關鍵詞: 燃料電池; 應力集中因子; 微流道; 界面可靠度 1. Introduction

Fuel cell is an electrochemical device that converts chemical energy (oxidation potential) into electrical energy directly. It operates like a battery and has similar characteristics with a battery. It produces electricity from supplying to the cell with the oxidant (typically air) and hydrogen. A fuel cell is not limited by its internal energy storage capacity as a battery. The

electrochemical reactions are [1] ：

Anode ： H2Î2H++2e- Cathode： 2 1 O2+2H++ e-Î H2O Net reaction：H2+ 2 1 O2Î H2O

Figure 1 [2] illustrates the basic construction of a fuel cell ： a positively

(4)

2

charged anode, a negatively charged cathode, and an electrolyte. Hydrogen and oxidant are fed to the anode and cathode, respectively. When hydrogen and oxidant pass through the electrolyte, the electrochemical reaction occurs and the cell continues to produce electrical energy and heat. In order to guiding the electrons, one thin Ag film was sputtered on the SU8. Figure 2 shows the structure of the bipolar plates.

Figure 1. The construction of a Polymer Electrolyte Membrane Fuel Cell (PEMFC)

Figure 2. The construction of Flow field plate

2. Literature Review

Kumar and Reddy [1] optimized the dimension value for channel width, land width and channel depth to 1.5, 0.5 and 1.5 mm, respectively. Studies on the effect of channel shapes showed that triangular and hemispherical shaped cross-section resulted in increase in hydrogen consumption by around 9%. Consequently, their conclusion would lead to improve fuel cell efficiency. Guo and Li [3] focused on the size effect

induced by the variation of dominant factors and phenomena in the flow and heat transfer as the device scale decreases. For example, surface friction induced flow compressibility makes the fluid velocity profiles flatter and leads to higher friction factors and Nusselt numbers; surface roughness is likely responsible for the early transition from laminar to turbulent flow and the increased friction factor and Nusselt number and, other effects, could lead to different flow and heat transfer behaviors from that at conventional scales. Tang, Yang, and Ku [4,5,6] simulated a three-dimensional (3-D) thin-wall model with flow-structure interactions was introduced and solved using ADINA to investigate the wall deformation and flow properties of blood flow in carotid arteries with symmetric and asymmetric stenoses. The Navier-Stokes equations were used as the governing equations for the fluid. The tube wall was assumed to be hyperelastic, homogeneous, isotropic and incompressible. The nonlinear large strain Ogden material model was used for the wall with the elastic properties determined experimentally for a silicone tube with a 78% stenosis by diameter. Figiel, Kamiiski, and Lauke [7] presented computational analysis of a compression shear fracture test, proposed for interface fracture toughness determination and crack propagation analysis in curved layered composite. Numerical analysis using contact finite elements is paid to the near crack-tip displacements and stresses. The comparison between finite element method and analytically determined stress is made. Bjerken and Persson [8] presented a method

(5)

for obtaining the complex stress intensity factor for an interface crack in a bimaterial using a minimum number of computations. A crack closure integral method for homogenous materials developed by Rybicki and Kanninen had been modified to include mismatch in material properties. The main advantages of this method are that it is straightforward and easy to use and that the number of calculations needed to obtain the stress intensity factors can be held to a minimum. Ikeda and Miyazaki [9] presented an application of fracture mechanics to the interface crack between dissimilar materials. In their study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack.

There is no discussion about the flow field effect on the micro-channel wall with an interface edge-crack. The main aim of this year is to study about this area.

3. Research Objective

The efficiency of the fuel cell depends on both the kinetics of the electrochemical process and performance of the components. In the second year, the study is concentrated on predicting the flow-induced fracture behavior of a crack at bimaterial interface, i.e., between the sputtered Ag layer and the SU8 substrate of the micro-channel in PEMFC. This would help one to have a better understanding of the reliability of the micro-channel and the life of the designed fuel cell.

4. Numerical Model

4.1 Model Used

A single crooked micro-channel with rectangular cross-section isolated from a bipolar plate were adopted as the model. The cross-sectional area of the micro-channel is 200×10-6m(height) by 200×10-6m (width), and the length of the channel is 2×10-2m. The width between two legs of the crooked channel is 100µm and both the inner and outer crooked radius are 20µm. Figure 3 shows the meshed model of the straight channel. The ANSYS®8.0 element type FLUID142 was chosen to analyze the flow-field in the micro-channel. Fig.4 shows the crooked channel. In order to avoid the stress concentration at the crooked corner, the round corner was necessary to be requested. The mesh size of the round corner had to be smaller then the size of the other channel parts. The gas was chosen as the hydrogen. The flow-field was chosen as a single-path design.

Figure 5 shows the meshed composite layers with a small edge-crack portion (length = 200×10-6m) on the micro-channel wall. The wall layers were composed of sputtered Ag layer and SU8 substrate. The thickness of Ag and SU8 are 400×10-9 m and 200×10-6 m, respectively. Material constants chosen are EAg = 76GPa,

νAg = 27.8GPa, ESU8 = 5.63GPa, and νSU8 =

2.133GPa. SOLID PLANE 82 element of ANSYS®8.0 was chosen in this model. This model was used for simulating the distribution of stresses in the interface with a small edge-crack on the tube wall. Table 1 shows the material properties of Ag、SU8 and Hydrogen. [10] [11] [12].

(6)

4

Figure 3. The meshed rectangular cross-sectional channel model

Figure 4. The crooked channel

Figure 5. The meshed composite layers with a small edge-crack

Table 1. Material properties

Modulus of Elasticity Poisson’s Ratio Shear Modulus Ag 76GPa 0.37 27.8GPa

SU8 5.63Gpa 0.32 2.133GPa Density (kg/m3₎ Dynamic Viscosity(N-s/m2₎ Hydrogen 0.65063 8.849e-6 4.2 Boundary Conditions

The mass-flow-inlet of the hydrogen reactant gas was kept constant as 8 c.c./s. The operating temperature and pressure were set as 298K and 2 atm, respectively. According to the mass-flow equation, the inlet velocity can be found from：

Q = A×V (1)

where Q is the mass-flow-inlet of the reactant gas, and A is the cross-sectional area. The inlet velocity was calculated as 200 m/s and it was normal to the cross-section of the channel. For the flow-field boundary conditions, the velocity at each channel wall was set as zero and the inlet velocity was 200m/s. The outlet pressure of the channel is set as zero. For the composite layer model, all degrees of freedom of the substrate (SU8) were set as zero in every direction and edge-crack surfaces were free surfaces. The applied loadings which acted on the top Ag surface were flow induced wall shear stresses and pressures.

The following assumptions were made： (1) Steady state and laminar flow.

Property Material

(7)

(2) The effect of gravity is neglected.

(3) Isothermal conditions exist in the model. (4) The flow-field on the tube wall is

assumed no-slip.

(5) The materials are all assumed isotropic and homogeneous.

4.3 Characterization of a Crack at Bimaterial Interfaces

There is a fundamental difference between the analysis and interpretation of the stress intensity factors for interface cracks in bimaterials as compared to cracks in homogenous materials. Bimaterails exhibit a coupling of tensile and shear effects. The stress field is characterized by a complex stress intensity factor, K, together with the biomaterial constant, ε, relating the elastic properties of the two materials. Consider two isotropic elastic solids jointed along the x1

axis as shown in Figure 6 [8]. Let Ej and νj

denote the Young’s modulus and the Poisson’s ratio of the jth material, respectively. The corresponding shear modulus, µj, is obtained as ) 1 ( 2 _j j j E ν µ + = (2)

The complex stress field in the vicinity of the crack tip, assuming traction free crack surface, is [4]

[ ]

_∑

₊

[ ]

_∑

= i I i II r Kr r Kr αβ ε αβ ε αβ θε π ε θ π σ ( , ) 2 Im ) , ( 2 Re (3)

Figure 6. Geometry and coordinates definitions for an interface crack

where the indices α and β take on the values 1 and 2. The angular functions∑I

αβ(θ,ε)and

∑II

αβ(θ,ε) equal unity along the interface

ahead of the crack tip (θ =0). The polar coordinates r and θ are defined in Figure 6. The equation (3) also can be transformed as [5] ε π σ σ _ri r K i 2 12 22 + = (4)

where K=KI + iKII denotes the complex stress

intensity factors. The stress fields depend on the biomaterial constant ε written in terms of the second elastic Dundur’s mismatch parameter βD [5] as ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + − = D D β β π ε 1 1 ln 2 1 (5) ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 2 2 1 1 2 2 1 + + + − − − = κ µ κ µ κ µ κ µ β_D (6) ⎩ ⎨ ⎧ + − − = ) 1 ( ) 3 ( 4 3 j j j ν ν ν κ (7)

Therefore, one can calculate the SIF (stress intensity factor) from local stress fields by using Equation (4).

For Plane Strain For Plane Stress

(8)

6

4.4 Analysis Process

5. Results and Discussions

After analyzing the crooked channel, one found that the most serious wall shear stress and velocity occurred at the inner corner. The results were shown in Figure 7 and Figure 8. So, the inner corner portion of the micro-channel wall (Figure 9) was selected for the crack simulation after the wall shear stresses were obtained.

Figure 7. Wall shear stress (Pa) distributions with the present design

Figure 8. Velocity (m/s) distributions with the present design

Figure 9. The chosen portion of channel for the edge-crack interface simulation

Simulations were performed for different sets of crack length, inlet velocities, and inlet pressures. The range of crack length was varied from 40×10-8 m to 60×10-8 m, resulting in total three different dimensions (40×10-8m, 50×10-8m, and 60×10-8m). The other chosen values of inlet pressures and inlet velocities were shown in the Table.2. The stress intensity factor corresponding to different parameter combinations will be discussed.

Computational Fracture Mechanics

Element Type Chosen

Crack Modeling

Crack-Tip Mesh Type Determined

Compute Shear Stresses and Normal Stresses near

the Crack-Tip

Stress Intensity Factor Calculation

(9)

Inlet Velocity (m/s) 150 175 200 Inlet Pressure (kPa) 202.6 253.3 303.9 Crack Length (×10-8_{m) 40 50 60}

Table 2. Parameter Variation

Figures 10 and 11 show the local max equivalent stresses with respect to different inlet velocities and inlet pressures, respectively. It can be seen that the stress increases as the velocity or the pressure increases. For calculating the stress intensity factors, the quarter-point element length (Figure 5) [10,11] was selected as the value of r in equation (4) in order to calculate the KI and KII. The results are shown in the

figures 12, 13 and 14. In those figures, the values of K are calculated as . It can be seen that KII is greater than KI since

the major loadings are shear loadings. Also, it can be concluded that the variations of hydrogen inlet velocities only affect the values of KI & KII slightly, but the variations

of hydrogen inlet pressures affect the values of KI & KII seriously. The value of KI

increases with the increases of the crack length as one might expect. However, the value of KII decreases slightly as the crack

length increases. Fig. 15 shows the variations of the near tip stresses with respect to the different crack lengths. It can be seen that due to the great differences between the material constants (EAg = 76GPa, νAg =

27.8GPa, ESU8 = 5.63GPa, νSU8 = 2.133GPa),

the shear stresses decreases as the crack length increases, and so causes the decreases of KII. 3.5 3.55 3.6 3.65 3.7 3.75 140 160 180 200 Inlet Velocity (m/s) Ma xi m u m L oc al S tr es (G P a)

Figure 10. Local max equivalent stresses .vs. inlet velocities 0 1 2 3 4 200 220 240 260 280 300

Inlet Pressure (kPa)

M ax im um L ocal S tr es (G P a)

Figure 11. Local max equivalent stresses .vs. inlet pressures 50000 100000 150000 200000 250000 Inlet Velocity (m/s) SI F (P a( m ) 1/ 2) K Figure 12. SIF values .vs. inlet velocities 2 2 II I K K + 150 175 200 KI KII

(10)

8 50000 100000 150000 200000 250000

Inlet Pressure (kPa)

SI F( Pa (m ) 1/ 2 ) K Figure 13. SIF values .vs. inlet pressures

50000 100000 150000 200000 250000 Crack Length (×10-8m) SI F (P a( m ) 1/ 2) K Figure 14. SIF values .vs. crack lengths

0.1 0.15 0.2 0.25 0.3 Crack Length (×10-8m) St re ss (G Pa )

Figure 15. Near tip normal and shear stresses .vs. crack lengths

6. Conclusion and Self Commentary

Numerical results of the stress intensity factors KI and KII at a cracked

Ag-SU8 interface on a single crooked channel wall in a micro-PEMFC are presented. Simulations were performed by using the commercial package software Ansys® 8.0. The results show that the inlet pressure and crack length affect the stress intensity factors more than the inlet velocity

does. Also, the results show that as the crack length increases, the value of KI will increase,

but the value of KII decreases slightly. The

results are accepted to present at the 4th ASME International Conference on Fuel Cell Sciences, Engineering and Technology, June 19-21, 2006, Irvine, California, U.S.A.

In the second half of this year, the efforts will be concentrated on studying the effects of the variation of micro-channel construction and the crack length and the gas inlet velocity and pressure on the flow induced stress states and SIF in a bimaterial interface by using the Taguchi technique.

7. References

[1] A. Kumar and R. G. Reddy, “Effect of channel dimensions and shape in the flow-field distributor on the performance of polymer electrolyte membrane fuel cells”, Journal of Power Sources, 113, (2003), pp.11–18.

[2] S. Haasl, “Assembly of micro-systems for optical and fluidic applications”, Ph. D. Dissertation, The Royal Institute of Technology, Stockholm, Sweden, 2005. [3] Z. Y. Guo and Z. X. Li, “Size effect on

microscale single-phase flow and heat transfer”, International Journal of Heat and Mass Transfer, 46, (2003), pp. 149–159. [4] D. Tang, C. Yang, D. N. Ku, “A 3-D

thin-wall model with fluid-structure interactions for blood flow in carotid arteries with symmetric and asymmetric stenosis”, Computers and Structures, 72, (1999), pp. 357-377.

[5] D. Tang, C. Yang, S. Kobayashi, D. N. Ku, “Steady flow and wall compression in steno tic arteries: A three-dimensional thick-wall

202.6 253.3 303.9 KI KII

40 50 60 KI KII

Inlet velocity = 200 (m/s) Crack length = 50×10-8_(m)

Inlet pressure = 303.9 (kPa) Inlet velocity = 200 (m/s)

40 50 60 σ22 σ12

(11)

model with fluid-wall interactions”, Journal of Biomechanical Engineering, 123, (2001), pp. 548-557

[6] D. Tang, C. Yang, Y. Huang, D. N. Ku, “Wall stress and strain analysis using a three-dimensional thick-wall model with fluid–structure interactions for blood flow in carotid arteries with stenoses”, Computers & Structures , 72, (1999), pp.341-356

[7] L. Figiel, M. Kaminski, B. Lauke, “Analysis of a compression shear fracture test for curved interfaces in layered composites”, Engineering Fracture Mechanics, 71, (2004), pp.967-980

[8] C. Bjerken, C. Persson, “A numerical method for calculating stress intensity factors for interface cracks in bimaterials”, Engineering Fracture Mechanics, 68, (2001), pp.235-246

[9] T. Ikeda, N. Miyazaki, “Mixed mode fracture criterion of interface crack between dissimilar materials”, Engineering Fracture Mechanics, 59, (1998), pp.725-735

[10] http://www.matweb.com [11] http://www.gersteltec.ch

[12] http://hyperphysics.phy-astr.gsu.edu/hba se/kinetic/menfre.html

[13] K. Aslantas, S. Tasgetiren, “Modelling of spall formation in a plate made of austempered ductile iron having a subsurface-edge crack”, Computational Materials Science, Volume 29, Issue 1, January, 2004, Pages 29-36

[14] Z. Ren, S. Glodez, G. Fajdiga, M. Ulbin, “Surface initiated crack growth simulation in moving lubricated contact”, Theoretical and Applied Fracture Mechanics, v 38, n 2,