Mechanical Characterization of Solid Oxide Fuel Cells and Sealants

 

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Literature review 
39 
3-26
). When loaded at elevated temperature, the inclined cell walls were deformed via creep 
bending. Their equation for the creep of open-cell foams can be expressed as [161]:
𝜀̇ =
0.6
(𝑛 + 2)
(
1.7(2𝑛 + 1)
𝑛
)
𝑛
𝑃
−(3𝑛+1) 2
⁄
𝐴 𝜎
𝑛
𝑒𝑥𝑝 (−
𝑄
𝑅𝑇
)
 
(3-14) 
where 
P
is the porosity and 
n
the stress exponent.
Figure 3-26 : An open-cell foam in the Gibson and Ashby model [161].
Mueller et al. [162] assumed a linear relationship of the elastic moduli between the foam and 
dense material based on microcellular model. With this linear relationship of the elastic moduli, 
the creep rate of a foam was linked to the porosity [44]. The creep rate according to this model 
can be expressed as a function of porosity [162] as:
𝜀̇ = 𝐹
−(1+𝑛) 2 
⁄
∙ (1 − 𝑃)
(1−𝑛) 2
⁄
∙ 𝐴𝜎
𝑛
𝑒𝑥𝑝 (−
𝑄
𝑅𝑇
)
 
(3-15) 
𝐹 = 𝐸 𝐸
0
⁄
= 𝑓(𝑃)
(3-17) 
where 
F
is the function of porosity, which is related to the elastic modulus of porous (
E
) and 
dense (
E
0
) material.

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Literature review 
40 
Focusing onto porous SOFC anode material, Kwok et al. [163] derived two analytical models for 
the creep rate of porous bodies by extending the Hashin-Shtrikman bound and Ramakrishnan-
Arunchalam model. Hashin-Shtrikman [109] analyzed the bounds between two different phases 
in a porous materials, while the Ramakrishnan-Arunchalam model [112] assumed the hollow 
spheres as the structure of porous materials. The joined Hashin-Shtrikman / Ramakrishnan-
Arunchalam creep respectively model can be expressed as follows:
𝜀̇ = (
12
12 + 11 𝑃
)
−(𝑛+1) 2
⁄
(1 − 𝑃)
−𝑛
𝐴𝜎
𝑛
𝑒𝑥𝑝 (−
𝑄
𝑅𝑇
)
 
(3-17) 
𝜀̇ = (
2
2 + 𝑃
)
−(𝑛+1) 2
⁄
(1 − 𝑃)
−(3𝑛+1) 2
⁄
𝐴𝜎
𝑛
𝑒𝑥𝑝 (−
𝑄
𝑅𝑇
)
 
(3-18) 
 
3.4.5.
Mechanical properties of anode-relevant materials 
3.4.5.1.
Elastic properties
The elastic moduli of cell layers are also considered as important parameters for analysis and 
simulations of stress states. Literature data for elastic moduli of typical cell layer materials are 
summarized in 
Table
 3-4
. 

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Literature review 
41 
Table 3-4: Elastic moduli of typical SOFC materials. 
Layers 
Material 
Porosity 
(%) 
Test method 
Elastic modulus (GPa) 
Ref. 
RT 600°C 800°C 
Electrolyte 
8YSZ 
8YSZ 
3YSZ 
~ 0% 
~2% 
~0% 
Impulse 
excitation 
190 157 
205 
190 113 
[164] 
[165] 
[166] 
YSZ 
~0% 
Nano-
indentation 
224 
[167] 
Anode 
support 
NiO-3YSZ 
~11% 
~30% 
Impulse 
excitation 
155 
80 
[168] 
~16% 
Slender 
cantilever beam 
136 
[139] 
Ni-8YSZ 
~45% 
~40% 
Impulse 
excitation 
45 24 
55 
[103] 
[169] 
~24% 
Nano-
indentation 
110 
[170] 
NiO-8YSZ 
~27% 
Impulse 
excitation 
74 68 
[103] 
- 
Nano-
indentation 
219 
[170] 
Cathode 
LSM 
~30% 
~3% 
Impulse 
excitation 
41
108 98 
[165]
LSCF 
~25% 
Nano-
indentation 
91 
[171] 
Buffer layer 
GCO 
~3% 
Impulse 
excitation 
201 
[105] 
Impulse excitation has been used in most of the studies to investigate elastic modulus, since the 
value obtained from indentation test might be significantly influenced by the indentation region, 
due to porous structure and substrate effects [167, 172].
Previous studies reported the elastic modulus as a function of temperature for typical cell 
materials [103, 164]. Bause [103] reported the temperature dependency of 8YSZ and Jülich 
anode materials in reduced and oxidized state (