Mechanical Characterization of Solid Oxide Fuel Cells and Sealants

4-6
 ). A 
half-spherical connection gear was used to avoid the misalignment during the force transfer.
Figure 4-6: 
 
Ring on ring test set-up and schematic illustration of a ring-on-ring bending test. 
The measurement procedure followed the DIN 51105 standard. Assuming that the creep 
mechanism is dominated by diffusion (n ~1), the creep rate could be estimated by following 
equations:
𝜎 =
3𝐹
2𝜋𝑡
2
[(1 + 𝜈) ln (
𝑟
2
𝑟
1
) +
1 − 𝜈
2
(
𝑟
2
2
− 𝑟
1
2
𝑟
3
2
)]
(4-4) 
𝜀̇ =
𝑡 (1 − 𝜈)
(1 − 𝜈
2
)𝑟
1
2
[(1 + 𝜈) 𝑙𝑛 (
𝑟
2
𝑟
1
) +
1 − 𝜈
2 (
𝑟
2
2
− 𝑟
1
2
𝑟
3
2
)]
[(
𝑟
2
𝑟
1
)
2
− 1 − 𝑙𝑛 (
𝑟
2
𝑟
1
) +
1
2 (
1 − 𝜈
1 + 𝜈) (
(𝑟
2
2
− 𝑟
1
2
)𝑟
2
2
𝑟
3
2
𝑟
1
2
)]
𝑑̇
 
(4-5) 
 
where 
F
is the applied force, 
t
the thickness of the sample, 
ν
the Poisson’s ratio, 
𝑑̇
is the 
displacement rate measured from the bottom of the specimen, and 
𝑟
1
, 
𝑟
2
and 
𝑟
3
are the loading 
ring, supporting ring and specimen radius, respectively.

---

Experimental 
66 
The ring-on-ring tests were carried out for anode materials (Ni-8YSZ). The purpose of the tests 
was to investigate the bending creep behavior of the anode, which were further compared with 4-
point bending creep and compressive creep tests. The tests along with the specimens are 
described in 
Table
 4-7
.  
Table 4-7: Ring-on-ring creep tests.
Ni-8YSZ 
Condition 
Temp. (°C) 
Stress (MPa) 
5 
10 
20 
30 
A 
4% H
2
/Ar 
800 
- 
1 
1 
1 
900 
- 
1 
1 
1 
B 
800 
- 
1 
1 
- 
900 
- 
1 
1 
1 
C 
800 
- 
1 
- 
- 
900 
- 
1 
1 
1 
D 
800 
1 
1 
1 
- 
900 
- 
1 
1 
1 
(2) Four-point bending test
In a four-point bending test, a bar-shaped specimen is placed on two supporting rods and the load 
is applied by the two loading rods, as illustrated in 
Figure
 4-7
.  
Figure 4-7: Four-point bending set-up and schematic illustration of a four-point bending test. 
F/2 
F/2 
L
i
L 
m 

---

Experimental 
67 
The bar-shaped specimens of reduced state anode material (Ni-8YSZ) were tested to determine 
the creep behavior. The equations used for analysis are discussed and shown in previous section 
conditions are given inTable 4-8: The anode specimens and testing conditions of four-point bending creep tests. 
Ni-8YSZ 
Condition 
Temp. (°C) 
Stress (MPa) 
10 
20 
C 
4% H
2
/Ar 
800 
1 
1 
900 
1 
1 
4.3.3.
Finite element simulation
The creep behavior of the anode materials was simulated to compare the behavior with analytical 
and experimental results. The comparison of the analytical formulations and experiments was 
based on creep rates obtained from ring-on-ring and four-point bending tests. 
All numerical simulations were performed using the software ANSYS 14.5. 2D analysis of the 
creep test was used in order to reduce computation time. An example of the meshed model for 
ring-on-ring simulations is given very similar but in other symmetrical arrangement. In the case of ring-on-ring testing the 
boundary condition was that the axis of symmetry was constrained against movement in x-
direction and a selected node against y-direction. In the case of 4-point bending, the boundary 
condition was similar. Loads were directly applied on selected nodes. The simulation was based 
on the Norton creep relationship. The material data used for the simulation are summarized in 
loaded /constrained by a point load/constraint. Simulation models of four-point and ring-on-ring 
bending tests consisted of around 14000 finite elements each.

---

Experimental 
68 
Figure 4-8: Meshed 2D model with 0.03 mm finite element size in the case of axisymmetric 
anode arrangement.
Table 4-9: