固態氧化物燃料電池（SOFC）由陶瓷材料的陽極、電解質、陰極所組成（通常稱為PEN），因為在高溫下運作，使得SOFC相較於其它燃料電池擁有最高的效率。然而，SOFC在高溫下運作會因為熱膨脹係數不匹配以及溫度梯度而產生明顯的熱應力，因此，對於一個可靠的SOFC設計及運作而言，完整的SOFC熱應力分析是必要的，而本研究的目的就是利用有限元素模擬軟體來分析平板式SOFC在暫態及穩態運作時的熱應力分佈。
首先，利用電化學及熱傳分析產生含三層單元電池之SOFC電池堆在各個啟動及穩態階段的溫度分佈圖，然後將這些獲得的溫度場輸入此三維三層電池堆的有限元素模型中，每個單元電池基本上都包含了PEN、金屬連接板、鎳網以及封裝玻璃陶瓷。在以往的研究中，封裝玻璃陶瓷的結構功能並未被考慮，因此，為了提供更接近實際情況的熱應力分析結果，本研究所建立之三層電池堆有限元素分析模型將包含玻璃陶瓷，特別是將探討玻璃陶瓷黏滯行為對電池堆熱應力分佈的影響。除此之外，亦將探討電池堆支撐條件、溫度梯度以及週期運作的影響。模擬結果顯示，在給定的三種不同電池堆支撐條件情況下，熱應力分佈的差異並不大。在三層電池堆中，各個單元電池的熱應力分佈並沒有明顯的差異，這可以歸因於垂直於面板方向的溫度梯度並不明顯。藉由考慮玻璃陶瓷在高溫時的黏滯特性，模擬結果顯示PEN及玻璃陶瓷在工作環境溫度下皆有應力鬆弛的現象。模擬週期運轉對熱應力影響的運算結果顯示，PEN及封裝玻璃陶瓷的熱應力將隨著運轉週期數的增加而有明顯的增加。

Solid oxide fuel cells (SOFCs) utilize ceramics as the anode, electrolyte, and cathode (often called a positive electrode-electrolyte-negative electrode, PEN) and operate at high temperatures such that they have the highest efficiencies of all fuel cells. The high-temperature operation, however, gives rise to significant thermal stresses caused from the mismatch of coefficient of thermal expansion (CTE) and temperature gradients in the SOFC system. Therefore, a comprehensive thermal stress analysis of SOFC stack is necessary for the success in design and operation of a SOFC system. The aim of this study is, by using finite element simulation, to characterize the thermal stress distribution in a planar SOFC stack during transients and steady operation.
An integrated electrochemical and thermal analysis was first conducted to generate the temperature profiles in a 3-cell SOFC stack during various start-up and steady stages. The obtained temperature fields within the cell stack were subsequently applied to a thermal stress analysis using a 3-D finite element model of a 3-cell stack. Each unit cell consists basically of a PEN assembly, interconnect, nickel mesh, and gas-tight glass-ceramic seals. Incorporation of the glass-ceramic sealant, which was never considered in other previous studies, into the 3-cell FEA model would produce more realistic results in thermal stress analysis. In particular, the effect of viscous behavior of glass-ceramic sealant on thermal stress distribution within the cell stack was investigated. In addition, the effects of stack support condition, temperature gradient, cyclic operation were also characterized. Modeling results indicated that a change in the support condition at the bottom frame of the 3-cell stack would not cause significant changes in the thermal stress distribution. Thermal stress distribution did not differ significantly in each unit cell within the 3-cell stack due to a negligible out-of-plane thermal stress gradient. By considering the viscous characteristics of glass-ceramic sealant at temperatures above the glass-transition temperature (Tg), relaxation of thermal stresses in PEN and glass-ceramic sealant was predicted. Effect of operating cycles on the variation of thermal stress was also simulated and the results indicated that a significant increase in thermal stress in PEN and glass-ceramic sealant would be expected with increasing cycle number.

REFERENCES
1. K. Kendall, N. Q. Minh, and S. C. Singhal, “Cell and Stack Designs,” Chapter 8 in High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications, edited by S. C. Singhal and K. Kendall, Elsevier, Kidlington, UK, 2003.
2. H. Yakabe, Y. Baba, T. Sakurai, and Y. Yoshitaka, “Evaluation of the Residual Stress for Anode-Supported SOFCs,” Journal of Power Sources, Vol. 135, 2004, pp. 9-16.
3. T. L. Wen, D. Wang, M. Chen, H. Tu, Z. Lu, Z. Zhang, H. Nie, and W. Huang, “Material Research for Planar SOFC Stack, ” Solid State Ionics, Vol. 148, 2002, pp. 513-519.
4. W. Z. Zhu and S. C. Deevi, “A Review on the Status of Anode Materials for Solid Oxide Fuel Cells,” Materials Science and Engineering, Vol. A362, 2003, pp. 228-239.
5. H. Yokokawa, N. Sakai, T. Horita, and K. Yamaji, “Recent Developments in Solid Oxide Fuel Cell Materials,” Fuel Cells, Vol. 1, 2001, pp. 117-131.
6. R. M. Ormerod, “Solid Oxide Fuel Cells,” Chemical Society Reviews, Vol. 32, 2003, pp.17-28.
7. H. C. Yu and K. Z. Fung, “Electrode Properties of La1-xSrxCuO2.5-? as New Cathode Materials for Intermediate-Temperature SOFCs,” Journal of Power Sources, Vol. 133, 2004, pp. 162-168.
8. H. U. Anderson and F. Tietz, “Interconnects,” Chapter 7 in High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications, edited by S. C. Singhal and K. Kendall, Elsevier, Kidlington, UK, 2003.
9. K. Hilpert, D. Das, M. Miller, D. H. Peck, and R. Weiβ, “Chromium Vapor Species over Solid Oxide Fuel Cell Interconnect Materials and Their Potential for Degradation Processes,” Journal of the Electrochemical Society, Vol. 143, 1996, pp. 3642-3647.
10. J. W. Fergus, “Sealants for Solid Oxide Fuel Cells,” Journal of Power Sources, Vol. 147, 2005, pp. 46-57.
11. S. B. Sohn and S. Y. Choi, “Suitable Glass-Ceramic Sealant for Planar Solid-Oxide Fuel Cells,” Journal of the American Ceramic Society, Vol. 87 , 2004, pp. 254-260.
12. K. L. Ley, M. Krumpelt, R. Kumar, J. H. Meiser, and I. Bloom, “Glass-Ceramic Sealants for Solid Oxide Fuel Cells: Part I. Physical Properties,” Journal of Materials Research, Vol. 11, 1996, pp. 1489-1493.
13. S. P. Simner and J. W. Stevenson, “Compressive Mica Seals for SOFC Applications,” Journal of Power Sources, Vol. 102, 2001, pp. 310-316.
14. K. P. Recknagle, R. E. Williford, L. A. Chick, D. R. Rector, and M. A. Khaleel, “Three-Dimensional Thermo-Fluid Electrochemical Modeling of Planar SOFC Stacks,” Journal of Power Sources, Vol. 113, 2003, pp. 109-114.
15. C. S. Montross, H. Yokokawa, and M. Dokiya, “Thermal Stresses in Planar Solid Oxide Fuel Cells due to Thermal Expansion Differences,” British Ceramic Transactions, Vol. 101, 2002, pp. 85-93.
16. A. Selimovic, M. Kemm, T. Torisson, and M. Assadi, “Steady State and Transient Theraml Stress Analysis in Planar Solid Oxide Fuel Cells,” Journal of Power Sources, Vol. 145, 2005, pp. 463-469.
17. H. Yakabe, Y Baba, T. Sakurai, M. Satoh, I. Hirosawa, and Y. Yoda, “Evaluation of Residual Stresses in a SOFC Stack,” Journal of Power Sources, Vol. 131, 2004, pp. 278-284.
18. W. Fischer, J. Malzbender, G. Blass, and R. W. Steinbrech, “Residual Stresses in Planar Solid Oxide Fuel Cells,” Journal of Power Sources, Vol. 150, 2005, pp. 73-77.
19. “Structural Elements,” Chapter 15 in ABAQUS Analysis User’s Manual V6.5, ABAQUS, Inc., Rising Sun Mills, USA, 2004.
20. K. S. Weil, J. E. Deibler, J. S. Hardy, D. S. Kim, G.-G. Xia, L. A. Chick, and C. A. Coyle, “Rupture Testing as a Tool for Developing Planar Solid Fuel Cell Seals,” Journal of Material Engineering and Performance, Vol. 13, 2004, pp. 316-326.
21. D. W. Richerson, Modern Ceramic Engineering: Properties, Processing, and Use in Design, 2nd Ed., Marcel Dekker, Inc., New York, USA, 1992, Chapter 5.
22. A. Selcuk and A. Atkinson, “Strength and Toughness of Tape-Cast Yttria-Stabilized Zirconia,” Journal of the American Ceramic Society, Vol. 83, 2000, pp. 2029-2035.
23. B. N. Nguyen, B. J. Koeppel, S. Ahzi, M. A. Khallel, and P. Singh, “Crack Growth in Solid Oxide Fuel Cell Materials: From Discrete to Continuum Damage Modeling,” Journal of the American Ceramic Society, Vol. 89, 2006, pp. 1358-2368.
24. N. P. Bansal and E. A. Gamble, “Crystallization Kinetics of a Solid Oxide Fuel Cell Seal Glass by Differential Thermal Analysis,” Journal of Power Sources, Vol. 147, 2005, pp. 107-155.
25. Metals Handbook, 10th Ed., Vol. 2, ASM International, Materials Park, OH, 1990, pp. 437-441.
26. W. Koster, “The Temperature Dependence of the Elasticity Modulus of Pure Metals,” Zeitschrift fur Metallkunde, Vol. 39, 1948, pp. 1-9. (in German)
27. Y. P. Chyou, T. D. Chung, J. S. Chen, and R. F. Shie, “Integrated Thermal Engineering Analyses with Heat Transfer at Periphery of Planar Solid Oxide Fuel Cell,” Journal of Power Sources, Vol. 139, 2005, pp. 126-140.
28. L. K. Chiang, Institute of Nuclear Energy Research, Long-Tang, Taiwan, unpublished work, 2006.
29. J. Malzbender, R. W. Steinbrech, and L. Singhesier, “Failure Probability of Solid Oxide Fuel Cells,” pp. 293-298 in Proceedings of the 29th International Conference on Advanced Ceramics and Composites, January 23-28, Cocoa Beach, Florida, 2005.
30. N. P. Bansal, J. B. Hurst, and S. R. Choi, “Boron Nitride Nanotubes-Reinforced Glass Comosites,” Journal of the American Ceramic Society, Vol. 89, 2006, pp. 388-390.