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Solid oxide fuel cell (SOFC) is considered to be a highly efficient device to convert chemical fuels directly into electrical power. Because of multilayer composite arrangement of cells, mismatch of the thermal expansion coefficients, chemical/thermal gradient, or phase change of the materials will result in residual stresses, which are reflected in the pronounced bending of unconstrained cells and cause a reliable problem. Considerable efforts have been devoted to the analysis of residual stresses in an elastic multilayer system, and one of the efforts that are to improve not only electrochemical performance for high energy conversion efficiency but also long term stability, is to process a continuously gradient anode functional layer (CG-AFL) between dense electrolyte and porous anode. Hence to understand the stress distribution and deformation of the multilayer with a CG-AFL is needed for the cell design. As the chemical reduction takes place at the interface between NiO-YSZ and the previously reduced porous Ni-YSZ, a reduced layer, together with the unreduced layer and the electrolyte will cause the residual stresses to be re-distributed. In this paper, taking the CG-AFL into account, the curvature and residual stresses of half-cell during reduction are analyzed. The results show that the curvature of half-cell with a CG-AFL increases as the reduction process. And the curvature would also increase as the thickness of the CG-AFL increases, and decrease with the increase of the index of power function that expresses young's modulus and thermal expansion coefficient of gradient layer. The residual stresses among the layers are correspondingly influenced by the thickness of the gradient layer, the index of power function and reduction extent. When taking power function as a linear function, the gradient layer obviously reduces the residual stress in the electrolyte. However, the increase of the index in power function will cause the increase of electrolyte residual stress. These mentioned analyses reveal that the CG-AFL cannot offer a solution that simultaneously improves the residual stress and curvature in a half-cell in terms of thickness and profile exponent of CG-AFL, i.e., the mitigation of residual stress will give rise to the increase of curvature, and vice versa. On the other hand, for part-reduced half-cell, the maximum tensile stress is found at anode/gradient layer interface in anode layer, which may facilitate structural failure since tensile residual stress is so high that it reaches the fracture strength of anode material. Consequently, it is important to ensure that the anode is fully reduced in practice. In conclusion, the existing gradient layer is helpful for enhancing the cell reliability via suitable design.
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Keywords:
- solid oxide fuel cell /
- graded functional layer /
- curvature /
- residual stress
[1] Radovic M, Lara-Curzio E 2004 Acta Mater. 52 5747
[2] Atkinson A, Sun B 2007 Mater. Sci. Tech. -Lond. 23 1135
[3] Malzbender J 2010 J. Eur. Ceram. Soc. 30 3407
[4] Mller A C, Herbstritt D, Ivers-Tiffe E 2002 Solid State Ionics 152 537
[5] Kong J, Sun K, Zhou D, Zhang N, Mu J, Qiao J 2007 J. Power Sources 166 337
[6] Yang Y Z, Zhang H O, Wang G L, Xia W S 2007 J. Therm. Spray Techn. 16 768
[7] Wang Z, Zhang N, Qiao J, Sun K, Xu P 2009 Electrochem. Commun. 11 1120
[8] Mccoppin J, Barney I, Mukhopadhyay S, Miller R, Reitz T, Young D 2012 J. Power Sources 215 160
[9] Sun C Q, Fu Y Q, Yan B B, Hsieh J H, Lau S P, Sun X W, Tay B K 2002 J. Appl. Phys. 91 2051
[10] Zhang X, Hao F, Chen H, Fang D 2015 Mech. Mater. 91 351
[11] Zhong Z, Wu L Z, Chen W Q 2010 Adv. Mech. 40 528 (in Chinese) [仲政, 吴林志, 陈伟球 2010 力学进展 40 528]
[12] Su B, Yan H G, Chen J H, Chen G, Du J Q 2013 Chin. J. Nonferrous. Met. 23 201 (in Chinese) [苏斌, 严红革, 陈吉华, 陈刚, 杜嘉庆 2013 中国有色金属学报 23 201]
[13] Zhang K, Lu Y J, Wang F H 2015 Acta Phys. Sin. 64 064703 (in Chinese) [张凯, 陆勇俊, 王峰会 2015 物理学报 64 064703]
[14] Duan B X, Li C L, Ma J C, Yuan S, Yang Y T 2015 Acta Phys. Sin. 64 067304 (in Chinese) [段宝兴, 李春来, 马剑冲, 袁嵩, 杨银堂 2015 物理学报 64 067304]
[15] Hsueh C H, Lee S 2003 Compos. Part B: Eng. 34 747
[16] Hsueh C 2003 J. Cryst. Growth 258 302
[17] Malzbender J, Wakui T, Steinbrech R W 2006 Fuel Cells 6 123
[18] Zhang T, Zhu Q, Huang W L, Xie Z, Xin X 2008 J. Power Sources 182 540
[19] Xiang Z, Haibo S, Fenghui W, Kang L, Jianye H 2014 Fuel Cells 14 1057
[20] Zhang N, Xing J 2006 J. Appl. Phys. 100 103519
[21] Zhang N 2007 Thin Solid Films 515 8402
[22] Zhang N, Chen J 2010 Compos. Part B: Eng. 41 375
[23] Williamson R L, Rabin B H, Drake J T 1993 J. Appl. Phys. 74 1310
[24] Sun B, Rudkin R A, Atkinson A 2009 Fuel Cells 9 805
[25] Wang X, Wang F H, Jian Z Y, Gu Z P, Zhang K 2014 Rare Metal Mat. Eng. 43 346 (in Chinese) [王霞, 王峰会, 坚增运, 顾致平, 张凯 2014 稀有金属材料与工程 43 346]
[26] Atkinson A, Seluk A 1999 Acta Mater. 47 867
[27] Sarantaridis D, Atkinson A 2007 Fuel Cells 7 246
[28] Malzbender J, Fischer W, Steinbrech R W 2008 J. Power Sources 182 594
[29] Seluk A, Atkinson A 2000 J. Am. Ceram. Soc. 83 2029
[30] Sarantaridis D, Chater R J, Atkinson A 2008 J. Electrochem. Soc. 155 B467
[31] Tietz F 1999 Ionics 5 129
[32] Minh N Q 1993 J. Am. Ceram. Soc. 76 563
[33] Ettler M, Timmermann H, Malzbender J, Weber A, Menzler N H 2010 J. Power Sources 195 5452
[34] Faes A, Hessler-Wyser A, Zryd A 2012 Membranes 2 585
[35] Fouquet D, Muller A C, Weber A, Ivers-Tiffee E 2003 Ionics 9 103
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[1] Radovic M, Lara-Curzio E 2004 Acta Mater. 52 5747
[2] Atkinson A, Sun B 2007 Mater. Sci. Tech. -Lond. 23 1135
[3] Malzbender J 2010 J. Eur. Ceram. Soc. 30 3407
[4] Mller A C, Herbstritt D, Ivers-Tiffe E 2002 Solid State Ionics 152 537
[5] Kong J, Sun K, Zhou D, Zhang N, Mu J, Qiao J 2007 J. Power Sources 166 337
[6] Yang Y Z, Zhang H O, Wang G L, Xia W S 2007 J. Therm. Spray Techn. 16 768
[7] Wang Z, Zhang N, Qiao J, Sun K, Xu P 2009 Electrochem. Commun. 11 1120
[8] Mccoppin J, Barney I, Mukhopadhyay S, Miller R, Reitz T, Young D 2012 J. Power Sources 215 160
[9] Sun C Q, Fu Y Q, Yan B B, Hsieh J H, Lau S P, Sun X W, Tay B K 2002 J. Appl. Phys. 91 2051
[10] Zhang X, Hao F, Chen H, Fang D 2015 Mech. Mater. 91 351
[11] Zhong Z, Wu L Z, Chen W Q 2010 Adv. Mech. 40 528 (in Chinese) [仲政, 吴林志, 陈伟球 2010 力学进展 40 528]
[12] Su B, Yan H G, Chen J H, Chen G, Du J Q 2013 Chin. J. Nonferrous. Met. 23 201 (in Chinese) [苏斌, 严红革, 陈吉华, 陈刚, 杜嘉庆 2013 中国有色金属学报 23 201]
[13] Zhang K, Lu Y J, Wang F H 2015 Acta Phys. Sin. 64 064703 (in Chinese) [张凯, 陆勇俊, 王峰会 2015 物理学报 64 064703]
[14] Duan B X, Li C L, Ma J C, Yuan S, Yang Y T 2015 Acta Phys. Sin. 64 067304 (in Chinese) [段宝兴, 李春来, 马剑冲, 袁嵩, 杨银堂 2015 物理学报 64 067304]
[15] Hsueh C H, Lee S 2003 Compos. Part B: Eng. 34 747
[16] Hsueh C 2003 J. Cryst. Growth 258 302
[17] Malzbender J, Wakui T, Steinbrech R W 2006 Fuel Cells 6 123
[18] Zhang T, Zhu Q, Huang W L, Xie Z, Xin X 2008 J. Power Sources 182 540
[19] Xiang Z, Haibo S, Fenghui W, Kang L, Jianye H 2014 Fuel Cells 14 1057
[20] Zhang N, Xing J 2006 J. Appl. Phys. 100 103519
[21] Zhang N 2007 Thin Solid Films 515 8402
[22] Zhang N, Chen J 2010 Compos. Part B: Eng. 41 375
[23] Williamson R L, Rabin B H, Drake J T 1993 J. Appl. Phys. 74 1310
[24] Sun B, Rudkin R A, Atkinson A 2009 Fuel Cells 9 805
[25] Wang X, Wang F H, Jian Z Y, Gu Z P, Zhang K 2014 Rare Metal Mat. Eng. 43 346 (in Chinese) [王霞, 王峰会, 坚增运, 顾致平, 张凯 2014 稀有金属材料与工程 43 346]
[26] Atkinson A, Seluk A 1999 Acta Mater. 47 867
[27] Sarantaridis D, Atkinson A 2007 Fuel Cells 7 246
[28] Malzbender J, Fischer W, Steinbrech R W 2008 J. Power Sources 182 594
[29] Seluk A, Atkinson A 2000 J. Am. Ceram. Soc. 83 2029
[30] Sarantaridis D, Chater R J, Atkinson A 2008 J. Electrochem. Soc. 155 B467
[31] Tietz F 1999 Ionics 5 129
[32] Minh N Q 1993 J. Am. Ceram. Soc. 76 563
[33] Ettler M, Timmermann H, Malzbender J, Weber A, Menzler N H 2010 J. Power Sources 195 5452
[34] Faes A, Hessler-Wyser A, Zryd A 2012 Membranes 2 585
[35] Fouquet D, Muller A C, Weber A, Ivers-Tiffee E 2003 Ionics 9 103
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