Thermal Stress Analysis of Solid Oxide Fuel Cell with Anode Functional Layer

doi:10.15541/jim20160341

Abstract

Abstract:

In order to reduce the thermal stress of solid oxide fuel cell in the process of preparation and working, and improve the electrochemical performance of the cell, the functionally graded layer is introduced into the cell. Due to the property of the functionally gradient material changes continuously or stepwise in a certain direction, the layer can reduce the difference of material parameters and relieve the thermal mismatch stress between layers effectively. On the basis of the previous research and the idea of hierarchical method, the anode functional layer is introduced into the solid oxide fuel cell, and the material parameters of the sub-layers are controlled through the anode functional layer number and the nonlinear gradient component exponent n. Thermal stress of the solid oxide fuel cell is studied at 800℃ within the operating temperature. The results show that the maximum tensile stress of the anode layer and the maximum compressive stress of the electrolyte layer decreases by introducing the anode functional layer. With the same anode functional layer number, the maximum tensile stress increases with the exponent n, and the maximum compressive stress of the electrolyte layer decreases with the exponent n increase. The thermal stress may lead to cracks and destroy the solid oxide fuel cell structure. This research provides theoretical basis for design and optimization of the solid oxide fuel cell.

Key words: solid oxide fuel cell, hierarchical method, anode functional layer, thermal stress

CLC Number:

TM911

XIE Jia-Miao, WANG Feng-Hui. Thermal Stress Analysis of Solid Oxide Fuel Cell with Anode Functional Layer[J]. Journal of Inorganic Materials, 2017, 32(4): 400-406.

Figures/Tables 11

Fig. 1 Geometry models of SOFC(a) Without AFL; (b) With AFL

Fig. 2 Different layer cases of AFL

Table 1 Material properties of electrodes and electrolyte[19-21]

	T	NiO-YSZ	YSZ	LSM	NiO
E/GPa	20℃	127.3	215	110	110
E/GPa	800℃	105.5	185	118	90
$\mu $	20℃	0.33	0.308	0.36	0.34
$\mu $	800℃	0.33	0.313	0.36	0.34
CTE /×10^-6	20℃	11.77	7.6	9.8	13.0
	800℃	12.42	10.5	11.8	13.0
	1400℃	12.50	10.5	11.8	13.1

Fig. 3 Model of graded elements[22]

Fig. 4 Relationship between volume fraction and normalized position of NiO in AFL

Table 2 Volume fraction of NiO in AFL sublayers

Layer	AFL	NiO volume fraction
Layer	AFL	n=2	n=1	n=0.5
1	AFL1	20%	40%	56%
2	AFL1	5%	20%	40%
2	AFL2	45%	60%	69%
3	AFL1	2.5%	13%	32%
	AFL2	20%	40%	56%
	AFL3	55%	66%	73%
4	AFL1	1.3%	10%	27%
	AFL2	11.3%	30%	49%
	AFL3	31.0%	50%	63%
	AFL4	61.0%	70%	75%
5	AFL1	1%	8%	25%
	AFL2	7%	24%	43%
	AFL3	20%	40%	56%
	AFL4	39%	56%	66%
	AFL5	65%	72%	76%

Fig. 5 Minimum principal stress of YSZ under 20℃

Table 3 Comparison results of the maximum compressive stresses of YSZ

	Presented model	Experimental	Numerical analysis
Max. compressive stresses of YSZ /MPa	633.3	670^[29]	608.46^[30]
Error	—	5.8%	3.9%

Fig. 6 (a) Maximum tensile stresses of anode with the layers of AFL and the exponent n; (b) contour of anode without AFL; (c) contour of two layers of AFL (n=0.5)

Fig. 7 (a) Maximum compressive stresses of YSZ with the layers of AFL and the exponent n, (b) contour of YSZ without the AFL and (c) contour of YSZ with two layers of the AFL (n=0.5)

Fig. 8 Maximum principal stress difference of interface element between YSZ and anode (x=1, z=1)

References 30

[1]	LAURENCIN J, DELETTE G, LEFEBVRE-JORD F, et al.A numerical tool to estimate SOFC mechanical degradation: case of the planar cell configuration. J. Eur. Ceram. Soc., 2008, 28(9): 1857-1869.
[2]	DUAN Z S, YANG M, YAN A Y, et al.Ba0.5Sr0.5Co0.8Fe0.2O3-δ as a cathode for IT-SOFCs with a GDC interlayer. J. Power Sources, 2006, 160(1): 57-64.
[3]	CHEN X, LIN Z Z, YIN C, et al.Theoretical prediction of the growth and surface structure of platinum nanoparticles. Acta Phys. Sin., 2012, 61(7): 076801.
[4]	SELÇUK A, MERERE G, ATKINSON A. The influence of electrodes on the strength of planar zirconia solid oxide fuel cells. J. Mater. Sci., 2001, 36(5): 1173-1182.
[5]	LIANG L J, LI K, YAN D, et al.Mechanical property and deformation behavior of SOFCs. J. Inorg. Mater., 2015, 30(6): 633-638.
[6]	CHEN X, YANG J, PU J, et al.Finite element analysis of thermal stresses in planar SOFCs. J. Inorg. Mater., 2007, 22(2): 339-343.
[7]	彭晓领. 组元磁化法制备ZrO2/Ni梯度功能材料研究. 浙江: 浙江大学博士学位论文, 2008.
[8]	ERDOGAN F, WU B H.Crack Problems in FGM layers under thermal stresses. J. Therm. Stresses, 1996, 19(3): 237-265.
[9]	LEE Y D, ERDOGAN F.Residual/thermal stresses in FGM and laminated thermal barrier coatings. Int. J. Fracture, 1995, 69(2): 145-165.
[10]	ZHA S W, ZHANG Y L, LIU M L.Functionally graded cathodes fabricated by Sol-Gel/slurry coating for honeycomb SOFCs. Solid State Ionics, 2005, 176(1/2): 25-31.
[11]	JIANG T Z, WANG Z H, REN B Y, et al.Compositionally continuously graded cathode layers of (Ba0.5Sr0.5)(Fe0.91Al0.09)O3-δ-Gd0.1Ce0.9O2 by wet powder spraying technique for solid oxide fuel cells. J. Power Sources, 2014, 247: 858-864.
[12]	MCCOPPIN J, BARNEY I, MUKHOPADHYAY S, et al.Compo-sitional control of continuously graded anode functional layer. J. Power Sources, 2012, 215: 160-163.
[13]	WANG Y S, GROSS D. Analysis of a crack in a functionally gradient interface layer under static and dynamic loading. Key Eng. Mater., 2000, 183-187: 331-336.
[14]	WANG Y S, HUANG G Y, GROSS D.On the mechanical modeling of functionally graded interracial zone with a griffith crack: anti-plane deformation. J. Appl. Mech.-T. ASME, 2003, 70(5): 676-680.
[15]	HUANG G Y, WANG Y S, YU S W.A new multi-layered model for in-plane fracture analysis of functionally graded materials (FGMS). Chin. J. Theor. Appl. Mech., 2005, 37(1): 1-8.
[16]	MÜLLER A C, HERBSTRITT D, IVERS-TIFFÉE E. Development of a multilayer anode for solid oxide fuel cells. Solid State Ionics, 2002, 152-153: 537-542.
[17]	KONG J R, SUN K N, ZHOU D, et al.Ni-YSZ gradient anodes for anode-supported SOFCs. J. Power Sources, 2007, 166(2): 337-342.
[18]	ANANDAKUMAR G, Li N, VERMA A, et al.Thermal stress and probability of failure analyses of functionally graded solid oxide fuel cells. J. Power Sources, 2010, 195(19): 6659-6670.
[19]	NAKAJO A, WUILLENIN Z, HERLE J V, et al.Simulation of thermal stresses in anode-supported solid oxide fuel cell stacks. Part I: Probability of failure of the cells. J. Power Sources, 2009, 193(1): 203-215.
[20]	CLAGUE R, MARQUIS A J, BRANDON N P.Finite element and analytical stress analysis of a solid oxide fuel cell. J. Power Sources, 2012, 210(15): 224-232.
[21]	JIANG W C, LUO Y, ZHANG W Y, et al. Effect of temperature fluctuation on creep and failure probability for planar solid oxide fuel cell. J. Fuel Cell Sci. Tech.-T. ASME, 2015, 12(5): 051004- 1-10.
[22]	KIN J H, PAULINO G H.Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. J. Appl. Mech., 2002, 69(4): 502-514.
[23]	HIRANO T, WAKASHIMA K.Mathematical modeling and design. MRS Bull., 1995, 20(1): 40-42.
[24]	GIANNAKOPOULOS A E, SURESH S, FINOT M, et al.Elastoplastic analysis of thermal cycling: layered materials with compositional gradients. Acta Metal. Mater., 1995, 43(4): 1335-1354.
[25]	WILLIAMSON R L, RABIN B H, DRAKE J T.Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces. Part I. Model description and geometrical effects. J. Appl. Phys., 1993, 74(2): 1310.
[26]	AMADA S.Hierarchical functionally gradient structures of bamboo, barley, and corn. MRS Bull., 1995, 20(1): 35-36.
[27]	TEIXEIRA V. Numerical analysis of the influence of coating porosity and substrate elastic properties on the residual stresses in high temperature graded coatings. Surf. Coat. Tech., 2001, 146-147(2): 79-84.
[28]	HSIEH C L, TUAN W H.Elastic and thermal expansion behavior of two-phase composites. Mat. Sci. Eng. A-Struct., 2006, 425(1/2): 349-360.
[29]	YAKABE H, BABA Y, SAKURAI T, et al.Evaluation of the residual stress for anode-supported SOFCs. J. Power Sources, 2004, 135(1/2): 9-16.
[30]	FAN P F, LI G J, ZENG Y K, et al.Numerical study on thermal stresses of a planar solid oxide fuel cell. Int. J. Therm. Sci., 2014, 77: 1-10.