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Electrolyte
Anode
Results and discussion
89
5.1.3.
Creep behavior
5.1.3.1.
Compressive creep
The most straightforward way to assess creep behavior of ceramics is a compressive test.
However, this requires special specimens that were produced as sintered bars in a rather dense
state (20% porosity), i.e. it was not possible to add the pore formers typical for porous SOFC
cells to the warm pressed materials and hence the porosity was only a result of the reduction
associated shrinkage of the NiO particles.
The analysis of the steady-state creep rates was based on a linear fit of the data, reaching the
regime of an inelastic flow characterized by a nearly constant slope in the experimental curve. To
avoid the primary creep regime, the testing time was typically adjusted to between 20 and 25 h.
Examples of typical deformation – time curves are shown in
Figure
5-14
(a)
.
The results for this type “A” bar-shape specimens are presented in a Norton’s plot in
Figure
5-14
(b)
. The stress exponent was determined from the slope of the ln
(𝜀̇)
versus ln (
σ
) representation
at a constant temperature
T
. An average stress exponent of 1.2 ± 0.3 was derived (see also
Table
5
-
5
), indicating a diffusional dominated creep mechanism. Laurencin et al. [140] reported similar
values of stress exponent, i.e. 1.1 for 750 °C and 1.7 for 800 °C, also indicating a diffusion creep
mechanism for Ni-8YSZ anode materials.
Results and discussion
90
a)
b)
Figure 5-14: a) Typical deformation – time curves; b) compressive creep rates as a function of
applied stresses.
Results and discussion
91
The activation energy
Q
was calculated from a ln (
𝜀̇
) versus 1000/
T
plot at a constant stress
(
Figure
5-15
). The derived activation energies for a temperature range of 800°C to 900ºC were
220 kJ/mol, 265 kJ/mol and 279 kJ/mol for stresses of 30, 63 and 100 MPa, respectively,
yielding an average value of 255 ± 31 kJ/mol. The derived creep parameters are summarized in
Table
5-5
.
Figure 5-15: Creep rates as a function of temperatures
Table 5-5: Creep parameters of the Norton's law determined via compression test.
Temperature (°C)
Pre-factor
A
(s
-1
MPa
-n
)
Stress exponent,
n
Q
(KJ/mol)
800
850
900
50
2.8
7.5
0.8
1.4
1.3
-
-
800 - 900°C
-
-
255 ± 31
5.1.3.2.
Ring-on-ring creep test
In order to assess if the creep is the same under compression and tension, ring-on-ring bending
tests were carried out. In addition porosity and composition was varied to assess both effects for
plate-shaped specimens of material A, B, C and D.
Results and discussion
92
Material A yielded creep rates of 3.4
·
10
-10
s
-1
and 1.6
·
10
-9
s
-1
at 800°C and 900°C, respectively
for an applied stress of 30 MPa , which are very similar to the values obtained from the
compressive tests (3.3
·
10
-10
and 2.8
·
10
-9
s
-1
). This indicates a similar creep behavior of rather
dense Ni-8YSZ anode material (~ 20 % porosity) under tension and compression for such a low,
nevertheless application relevant, applied stress. Note that a higher applied stress might cause
faster creep under tension due to well-known micro-crack formation for ceramics under tensile
loads at elevated temperature (creep rupture effects) [200]. It has been suggested that materials
with higher porosity, tensile creep rates should be higher than compressive creep rates due to
densification [182, 201].
The activation energy of material A was also obtained from a creep rate-temperature plot as
shown in
Figure
5-16
. The derived activation energies for a temperature range of 800 °C to 900
ºC were 221 kJ/mol, 135 kJ/mol and 161 kJ/mol for applied stresses of 10, 20 and 30 MPa,
respectively, yielding an average value of 172 ± 44 kJ/mol.
Figure 5-16: Creep rates as a function of temperatures of material A by ring-on-ring bending
test.
Results and discussion
93
The activation energies of materials B, C and D were also determined (
Figure
5-17
), which are
156 kJ/mol, 177 kJ/mol and 81 kJ/mol for the temperatures 800 °C and 900 °C (stresses either 10
or 20 MPa), respectively.
Figure 5-17: Creep rates as a function of temperatures of material B, C and D, ring-on-ring
bending tests.
5.1.3.3.
Four-point bending creep test
The equations used for ring-on-ring test assume a purely diffusional mechanism (n = 1), which
might not to be the case according to the parameters derived from compression tests, i.e.
although the standard deviation has to be considered, it appeared that n might be slightly above
unity. Hence, due to the limitation of equation
(4-5)
of ring-on-ring creep, i.e. n = 1,
complementary tests on material C were carried out using four-point bending and compared to
ring-on-ring bending test results. Note, the four-point bending that were analyzed using a more
complex set of equations that is not based on the assumption that n = 1.
Since the equation of 4-point bending creep includes stress exponent and deformation rate as
input data, the stress exponent needs to be determined first. By deriving the equations of 4-point
Results and discussion
94
bending and creep, the deformation rate in the center of specimen has a straightforward
relationship with half applied load as:
ln
𝜕𝑦
𝜕𝑡
= 𝑛 ∙ ln
𝐹
2
+ ln 𝐻
(5-1)
where
n
is stress exponent,
F
is applied load and
H
is a function of specimen geometry. The
detailed derivation of equation can be found in the
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