Mechanical Characterization of Solid Oxide Fuel Cells and Sealants

 
(3-17)
 
(3-18) and (3-15), respectively. To analyze the porosity effect 
numerically, the creep rates obtained experimentally are compared with the analytical models in 
Figure
 5-20
. The analytical models were used to model the creep rates at 800 ºC under 10 MPa, 
in fact, the tendency of the models was similar for the other data sets. Among the analytical 
models, the Hashin-Shtrikman yielded the good approximation in range of 50-70% equivalent 
porosity, while the Ramakrishnan model provides the closet prediction when the equivalent 
porosity is above 70% in agreement with [44]. 
Figure 5-20: Comparison of the creep rates obtained from analytical models and ring-on-ring 
bending tests at 800°C. 
5.1.3.4.3.
Comparison of 4-point and ring-on-ring bending creep
for material C 
Once the stress exponent is determined (see section 5.1.3.3), the creep rate of 4-point bending 
test can also be determined by equation (3-12). A comparison of creep rates of 4-point and ring-
on-ring creep along with reference data is shown in 
Figure
 5-21
.  

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Results and discussion 
101 
The literature results [140] are slightly higher than the values obtained in this work, the reason 
might be assigned to material difference and/or experimental uncertainty. Creep rates of material 
C obtained from ring-on-ring tests are around 3 times lower than the values obtained from 4-
point bending tests. This effect might be assigned to 1) stress distribution changes in 4-point 
bending and ring-on-ring bending tests and also 2) the limitation of analytical equation used for 
ring-on-ring creep. As mentioned above, the equations used for ring-on-ring creep calculation 
assumes a stress exponent of 1, which is not the case for the material in the current study. Since 
this could be the origin of the differences between 4-point bending and ring-on-ring creep, the 
accuracy of ring-on-ring creep determination is discussed in the following subsection. 
Figure 5-21: Comparison of creep rates obtained via 4-point and ring-on-ring tests along with 
reference data [140].
5.1.3.5.
FEM simulation 
A FEM analysis was carried out to analyze the origin of different creep behavior in ring-on-ring 
and 4-point bending tests, creep parameters derived from 4-point bending test in this work were 
used as input for the simulation (
Table
4-9
in section 4.3.3). In the FEM simulation the creep 
rates were derived in two ways, i) from the equivalent creep strain by ANSYS and ii) from the 

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Results and discussion 
102 
deflection using the simulated displacement with the analytical formulas (Equation (3-12) and 
(4-5)). The creep rates obtained by these two methods are termed “FEM Result” and “FEM 
Equation”, respectively, in the following. The creep strain at the bottom surface of the specimen, 
which is rather constant within the area enclosed by the loading ring, was taken as the FEM 
numerical result. An example of the simulated creep strain under 30 MPa at 800ºC by 4-point 
bending test is shown in 
Figure
 5-22
. 
Figure 5-22: The equivalent creep strain simulated by ANSYS for a 4-point bending test under 
30 MPa at 800 ºC. 
The comparison of simulations and experimental data is shown in 
Figure
 5-23
. Both simulation 
results for 4-point bending creep (FEM Result and FEM Equation) show an agreement with 
experimental results at rather low stresses (10 and 15 MPa). The experimental value is slightly 
lower (the difference is smaller than 9%) than the simulation values which might be caused by 
friction during the real testing. The friction is not taken into account in case of simulation, while 
it seems that friction has an effect on creep rate. However, the FEM Result and FEM Equation 
also agree with each other (the difference is smaller than 4%), indicating the rather accurate 
analysis for creep in 4-point bending tests. 
The FEM Equation and experimental data of ring-on-ring bending creep, both based on 
formulation, show general agreement. Similarly the friction effect might play an important role 
for this difference, which could have a stronger effect on ring-on-ring test due to the larger 
contacted area. While the FEM Results yielded around 50% and 72% higher creep rate compared 
to values of FEM Equation and experimental result, respectively, indicating the limitation of an 

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Results and discussion 
103 
analytical formulation to analyze data from ring-on-ring tests (Equation (4-5)). The formula 
analysis neglected changes of geometry, stress distribution due to the creep deformation and 
assume the unit stress exponent. It seems that the neglected changes of stress distribution and 
geometry play an important role in an accurate determination of ring-on-ring test creep rates.
To assess the inaccuracy caused by stress exponent in ring-on-ring equation