Full text of DOI:10.1111/j.1151-2916.2001.tb01063.x

J. Am. Ceram. Soc., 84 [11] 2625–32 (2001)
journal
Compression Creep Characteristics of
8-mol%-Yttria-Stabilized Cubic-Zirconia
B. Sudhir and Atul H. Chokshi
Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India
Constant stress compression creep tests were conducted on
8-mol%-yttria-stabilized cubic-zirconia (8YCZ) over stress
(␴), temperature, and grain-size ranges from ϳ20 to 300 MPa,
1673 to 1773 K, and 4 to 8 ␮m, respectively. Creep data were
analyzed in terms of the relationship ␧˙ ؔ ␴n, where ␧˙ is the
strain rate and n the stress exponent. Although the experimen-
tal data yielded a stress exponent of n Ϸ 2, analysis of the
results with compensation of significant concurrent grain
growth revealed that the true stress exponent was n Ϸ 1. The
results were consistent with deformation by the Coble creep
mechanism. Experiments at stresses greater than ϳ100 MPa
revealed a transition from grain-size-dependent Coble diffu-
sion creep to grain-size-independent intragranular dislocation
creep.
and it is not clear whether the data correspond to steady-state
deformation. Significant concurrent cavitation has been re-
ported in some studies.9,14 Studies on static grain growth have
revealed that cubic-zirconia is prone to extensive grain
growth,16–18 which also has been noted in some investigations
on creep deformation.8,9,14 The detailed study by Dimos and
Kohlstedt8 on a 25-mol%-yttria-stabilized cubic-zirconia indi-
cates that deformation is controlled by the Nabarro–Her-
ring19,20 diffusion creep mechanism with a stress exponent of
n Ϸ 1 and p Ϸ 2. However, subsequent studies by Wakai and
co-worker10,11 have revealed that creep in an 8-mol%-yttria-
stabilized cubic-zirconia (8YCZ) is associated with a stress
exponent of n Ϸ 2. Another complication with studies on
zirconia is the possibility of the formation of amorphous
grain-boundary films in materials with significant impurity
content.11
It is well-known that concurrent grain growth can significantly
affect the determination of the grain-size exponent,21 stress expo-
nent,22 and activation energy.23 However, none of the earlier
studies on cubic-zirconia have analyzed their data in the context of
concurrent grain growth.
There have been several studies on creep in single crystals of
cubic-zirconia,24–26 and the data indicate that creep is associated
with stress exponents of Ͼ3. Examination of data reported in
polycrystalline and single-crystal cubic-zirconia indicate that,
whereas tests on polycrystalline materials have generally involved
stresses of less than ϳ100 MPa, single crystals have been tested
largely at stresses Ͼ100 MPa. Although there have been several
studies of metallic alloys showing transitions in deformation
mechanisms with stress, there have been very few such reports in
ceramics.
I. Introduction
UBIC-ZIRCONIA is a good oxygen-ion conductor that is utilized
C
in many high-temperature functional applications, such as
oxygen sensors, solid oxide fuel cells, and combustion controllers
in furnaces. Creep, the time-dependent plastic deformation of a
material under load, is an important design criterion for applica-
tions at elevated temperatures (T Ͼ 0.4Tm, where Tm is the
absolute melting temperature). The rate equation for creep can be
expressed as1
p
n
ADGb b
␴
˙
ε ϭ
(1)
ͩ ͪ ͩ ͪ
kT
d
G
˙
where ε is the steady-state strain rate, A a material-dependent
dimensionless constant, D the diffusion coefficient of the rate-
controlling species, G the shear modulus, b the magnitude of the
Burgers vector, k the Boltzmann constant, T the absolute temper-
ature, d the grain size, p the inverse grain-size exponent, ␴ the
imposed stress, and n the stress exponent.
The present study on an 8YCZ was undertaken with the
following specific objectives: to examine the shapes of the creep
curves; to evaluate the rate-controlling creep parameters n, p, and
Q; to analyze data with regard to microstructural changes occur-
ring during creep deformation; and to examine the possibility of a
transition in deformation mechanism at higher stresses.
Although there have been several studies on creep in poly-
crystalline cubic-zirconia,2–14 a careful examination reveals
several discrepancies in the reported data. Some of the studies
have involved experiments on specimens with significant po-
rosity.3,6,7 Because densification occurs concomitantly with
creep in such tests,15 it is not clear whether the experimental
measurements of longitudinal strain provide meaningful infor-
mation on plastic deformation. Primary creep, with a decreasing
creep rate, has been noted in some studies3,4,8 but not in others.
The studies by St-Jacques and Angers4,5 involve tests typically
II. Experimental Materials and Procedures
The 8YCZ material chosen for this study was obtained in the
form of dense sheets (Ͼ99%, Nikkato Corp., Osaka, Japan);
parallelepiped specimens with nominal dimensions of 3 mm ϫ 3
mm ϫ5 mm were cut for compression testing. Constant stress
compression creep tests were conducted on a computer-interfaced
lever-type machine, using procedures described elsewhere.27 The
creep experiments were conducted in the stress and temperature
ranges of 20–300 MPa and 1673–1773 K, respectively. The stress
was controlled to within 0.5 MPa, using a closed-loop computer
control, and the temperature was maintained within 1 K of the
setpoint. The strain rate versus strain plots were calculated from
strain versus time plots, using a seven-point slope formula, as
described by Evans and Wilshire.28
at strain rates of Ͻ10Ϫ7 Ϫ1; calculations based on the testing
s
times quoted indicate that very small strains are accumulated,
R. F. Cooper—contributing editor
Microstructural measurements were performed on specimens
that were polished to 1 ␮m surface finish and chemically etched
using boiling ortho-phosphoric acid. Inspection of such a polished
and etched section of the as-received material yielded a mean
Manuscript No. 188877. Received December 13, 1999; approved July 10, 2001.
Supported in part by the Aeronautical Research and Development Board (India).
AHC also supported by a Swarnajayanti Presidential Young Investigator award from
the Government of India.
2625

2626
Journal of the American Ceramic Society—Sudhir and Chokshi
Vol. 84, No. 11
Table I. Grain Sizes Obtained under Static
Grain-Growth Conditions
additional experiments were terminated in the steady-state regions
to characterize the microstructure in the steady-state region.
The density of specimens tested at low stresses was determined
using the Archimedes principle with water as the immersion
medium. Sections parallel to the compression stress axis were
polished to 1 ␮m finish and examined initially for cavitation.
Subsequently, the specimens were thermally etched for 2 h at 1723
K for measuring grain sizes; the thermal etching was not expected
to change the final grain size appreciably, because the testing time
of most of the specimens was Ͼ4 h. Mean linear intercept grain
sizes were measured in a direction parallel (L1) and perpendicular
Grain size (␮m)
Time
(h)
1673 K
1723 K
1773 K
1823 K
1873 K
0
2
4.0 Ϯ 0.1 4.0 Ϯ 0.1 4.0 Ϯ 0.1 4.0 Ϯ 0.1 4.0 Ϯ 0.1
4.5 Ϯ 0.1 5.2 Ϯ 0.2 5.0 Ϯ 0.2 6.3 Ϯ 0.4 7.6 Ϯ 0.4
12 4.9 Ϯ 0.1 5.9 Ϯ 0.2 6.7 Ϯ 0.2 7.0 Ϯ 0.7 8.8 Ϯ 0.5
15
8.2 Ϯ 0.3
30 5.7 Ϯ 0.2 6.5 Ϯ 0.2 7.3 Ϯ 0.2 9.2 Ϯ 0.2 12.5 Ϯ 0.6
៮
(L2) to the stress axis, and the grain size was defined as L ϭ
(L1L22)1/3
.
linear intercept grain size of 4.0 ␮m. Measurements of grain
intercepts along two orthogonal directions indicated that the grains
were equiaxed in the as-received condition. To study static grain
growth and the effect of grain size on creep, specimens were
annealed over a range of time–temperature combinations to obtain
grain sizes from 4.5 to 12.5 ␮m (Table I). Because specimens with
grain size of Ն8 ␮m did not exhibit a steady state, creep
experiments were not conducted on specimens having initial grain
sizes Ͼ8 ␮m. To facilitate observation of grain-boundary sliding
on the surface of crept specimens, some specimens were polished
on one of the longitudinal faces to 1 ␮m surface finish before
testing. Initially, experiments were conducted to strains of Ͼ5% to
detect the tertiary stage of creep deformation; subsequently,
III. Experimental Results
(1) Shapes of Creep Curves
The experimental conditions utilized in the present study led to
strain rates in the range of ϳ10Ϫ8–10Ϫ3 sϪ1. Table II summarizes
the steady-state/minimum strain rates and final grain sizes ob-
tained in the present study. Table II also lists the ratios of the
experimentally observed initial strain rates and the estimated initial
strain rates, which are discussed in Section IV(1). Figure 1
illustrates the variation in strain rate with strain for specimens
៮
tested at 1673 K with an initial grain size of LO ϭ 5 ␮m. All the
curves exhibited a primary creep region, with decreased creep rate,
Table II. Steady-State/Minimum Creep Rates, Test Times, Final Grain Sizes, Total Strains, and Ratio of Observed to
Calculated Initial Strain Rates for the Experimental Conditions used in the Present Study
˙
εO(obs)
˙
Ϫ1
៮
៮
˙
T (K)
LO (␮m)
␴ (MPa)
ε (s
)
t (s)
Lf (␮m)
ε (%)
εO(calcd)
1673
5.0 Ϯ 0.2
40.0†
60.0†
63.0
80.0†
83.0
104
1.8 Ϯ 10Ϫ7
2.5 Ϯ 10Ϫ7
3.5 Ϯ 10Ϫ7
4.0 Ϯ 10Ϫ7
7.0 Ϯ 10Ϫ7
1.0 Ϯ 10Ϫ6
1.5 Ϯ 10Ϫ6
2.4 Ϯ 10Ϫ6
4.0 Ϯ 10Ϫ6
4.7 Ϯ 10Ϫ6
3.8 Ϯ 10Ϫ5
2.0 Ϯ 10Ϫ4
6.0 Ϯ 10Ϫ8
1.3 Ϯ 10Ϫ7
2.1 Ϯ 10Ϫ6
5.2 Ϯ 10Ϫ4
224 080
36 500
221 650
23 070
95 570
59 300
26 370
14 630
11 715
1 380
725
6.3 Ϯ 0.4
5.4 Ϯ 0.4
6.3 Ϯ 0.4
5.6 Ϯ 0.4
6.0 Ϯ 0.3
4.1
1.5
9.5
1.1
9.3
8.0
5.9
5.0
11
1.8
9.2
11
5.2
4.9
1.4
6.0
0.7
6.1
2.1
125
140
156
180
205
250
65
8.2 Ϯ 0.3
40.0
150
701 500
10 505
560
10 Ϯ 0.9
180
202
90
1723
4.5 Ϯ 0.1
5.0 Ϯ 0.2
60.0†
20.0†
40.0†
60.0
60.0†
80.0†
83.0
150
9.1 Ϯ 10Ϫ7
8.0 Ϯ 10Ϫ8
3.3 Ϯ 10Ϫ7
8.7 Ϯ 10Ϫ7
7.0 Ϯ 10Ϫ7
1.3 Ϯ 10Ϫ6
1.5 Ϯ 10Ϫ6
8.3 Ϯ 10Ϫ6
1.0 Ϯ 10Ϫ5
3.3 Ϯ 10Ϫ4
2.9 Ϯ 10Ϫ7
8.6 Ϯ 10Ϫ7
1.7 Ϯ 10Ϫ7
4.5 Ϯ 10Ϫ6
21 500
345 780
121 230
59 800
32 910
17 600
46 125
3 135
5.3 Ϯ 0.4
8.3 Ϯ 0.7
7.2 Ϯ 0.4
7.2 Ϯ 0.4
5.7 Ϯ 0.3
5.8 Ϯ 0.3
6.0 Ϯ 0.3
2.8
4.3
4.7
4.8
2.9
2.9
16
7.6
4.5
4.8
1.6
4.0
1.2
7.0
2.1
0.8
1.0
0.8
1.1
180
590
202
115
6.5 Ϯ 0.2
8.2 Ϯ 0.3
60.0†
80.0
60.0
180
37 040
36 000
41 200
460
7.5 Ϯ 0.5
7.6 Ϯ 0.6
8.7 Ϯ 0.5
5.0
1773
5.0 Ϯ 0.2
30.0†
31.0
3.5 Ϯ 10Ϫ7
4.5 Ϯ 10Ϫ7
8.1 Ϯ 10Ϫ7
7.7 Ϯ 10Ϫ7
1.3 Ϯ 10Ϫ6
1.7 Ϯ 10Ϫ6
1.7 Ϯ 10Ϫ6
6.7 Ϯ 10Ϫ6
1.5 Ϯ 10Ϫ3
48 600
189 900
25 240
82 400
17 900
15 300
28 810
17 000
100
6.9 Ϯ 0.5
8.1 Ϯ 0.6
5.9 Ϯ 0.5
6.6 Ϯ 0.4
6.0 Ϯ 0.4
5.8 Ϯ 0.4
2.8
14
2.7
2.4
40.0†
42.0
2.6
7.9
2.6
2.9
5.0
19
50.0†
60.0†
61.0
83.0
197
1.0
0.9
12
†Experiments stopped in steady state.

November 2001
Compression Creep Characteristics of 8-mol%-Yttria-Stabilized Cubic-Zirconia
2627
Fig. 1. Variation in strain rate with strain for specimens tested at 1673 K
with an initial grain size of 5 ␮m.
Fig. 3. Plot of strain rate versus stress for specimens with an initial grain
size of 5 ␮m and tested at temperatures of 1673, 1723, and 1773 K.
and a steady-state region in which the strain rate was essentially
constant; at high stresses, there was also clear evidence for a
tertiary region. Inspection of the data revealed that the extent of
steady-state region decreased with increased stress, temperature,
and grain size. Under all experimental conditions, stresses Ͼ100
MPa did not yield a well-defined steady state; the data corre-
sponded to a direct transition from primary to tertiary creep with a
minimum creep rate between these two regions.
Table II shows the occurrence of extensive grain growth during
creep deformation. The final grain sizes were greater than initial
ones by values ranging from ϳ6% for a specimen with an initial
grain size of 8 ␮m tested at 1723 K and 60 MPa to ϳ66% for a
specimen with an initial grain size of 5 ␮m tested at 1723 K and
20 MPa. The measurements also indicated that, irrespective of the
testing conditions, the grains maintained an essentially equiaxed
shape after creep deformation.
Cavitation was also observed in the deformed specimens.
However, there was no significant or systematic difference in level
of cavitation with stress, grain size, or temperature. The total levels
of cavitation recorded in the present investigation were Ͻ2%, as
determined from density measurements using the Archimedes
principle.
Detailed high-resolution electron microscopy studies revealed
the absence of glassy grain-boundary films in the as-received
condition as well as in creep-tested specimens.29
(2) Microstructural Observations
Figure 2 is a scanning electron microscopy (SEM) micrograph
of the surface of a specimen with an initial grain size of 5 ␮m,
tested at 1673 K and a stress of 60 MPa to a strain of ϳ10%. There
is clear evidence for grain-boundary sliding under such conditions;
also, the difference in observed exposed facet heights along two
opposite grain boundaries of an initially flat polished grain
indicates the occurrence of grain rotation.
(3) Rate-Controlling Creep Parameters
Figure 3 illustrates the variation in steady-state strain rate with
stress for specimens with an initial grain size of 5 ␮m tested at
temperatures of 1673, 1723, and 1773 K. The slopes of the curves
show that the data at all three temperatures correspond to a stress
exponent of ϳ2 at stresses of Ͻ100 MPa. At higher stresses, the
data correspond to minimum creep rates and yield stress exponents
of Ͼ5 at the three temperatures.
The grain-size dependence of creep is illustrated in Fig. 4 in the
form of a logarithmic plot of strain rate versus stress for two
different initial grain sizes at a temperature of 1673 K. Inspection
of the data reveals clearly that deformation is dependent signifi-
cantly on grain size at low stresses and that, at stresses Ͼ100 MPa,
the deformation rates are essentially independent of grain size.
The grain-size dependence of creep, given by the parameter p in
Eq. (1), was evaluated by plotting the strain rate versus the final
៮
grain size (Lf) at a temperature of 1723 K and a stress of 60 MPa,
as shown in Fig. 5. The error bars in Fig. 5 give the 95%
៮
confidence interval in Lf determined from the grain intercept
measurements using standard statistical analysis.30 The data indi-
cate a value for p Ϸ 3 at low stresses; at high stresses, the data
shown in Fig. 4 suggest p ϭ 0.
The activation energy for creep deformation has been deter-
mined from a plot of final grain size and stress-compensated strain
Fig. 2. SEM micrograph of the surface of a specimen having an initial
grain size of 5 ␮m and tested at 1673 K and 60 MPa to a strain of
ϳ10%, showing the occurrence of grain-boundary sliding. Specimen
was tilted by 60° out of plane to clearly visualize the offsets in grain
boundaries.

2628
Journal of the American Ceramic Society—Sudhir and Chokshi
Vol. 84, No. 11
Fig. 6. Arrhenius plot for determining the activation energy for creep
deformation, yielding Q Ϸ 430 Ϯ 130 kJ⅐molϪ1
Fig. 4. Variation in strain rate with stress for specimens with two
different initial grain sizes at a temperature of 1673 K. Note the significant
effect of grain size at low stresses and the lack of grain-size dependence at
higher stresses (Ͼ100 MPa).
.
7 is a comparative plot of static and dynamic grain sizes as a
function of time at a temperature of 1773 K. Static grain growth
studies on 8YCZ by Lee and Chen,16 as well as the grain growth
data from the present study (Table I), are in agreement with the
parabolic growth law.31 This equation has been plotted in Fig. 7
rate versus inverse temperature (Fig. 6); the slope indicates the
activation energy for creep as 430 Ϯ 130 kJ⅐molϪ1 at low stresses.
The error of 130 kJ⅐molϪ1 corresponds to the 95% confidence
interval for activation energy, as determined using statistical
analysis.30
for an initial grain size, LO, of 5 ␮m with Kg ϭ 2.7 ϫ 10Ϫ4
៮
␮m2⅐sϪ1, the grain growth constant determined in the present
study at the temperature of 1773 K. Figure 7 shows that the static
and dynamic grain-size evolutions are comparable, within exper-
imental error, indicating that the imposed stress has no significant
effect on grain-growth kinetics.
IV. Discussion
(1) Influence of Grain Growth on Creep Curves
There are three possible reasons for the observation of an
apparent primary creep region: intrinsic transients in diffusion
creep,32–35 concurrent grain growth,21 and specimen misalign-
ment.36 Although the inherent transients during diffusion creep
Before analyzing the influence of grain growth on creep, it is
necessary to consider the effect of stress on grain growth. Figure
Fig. 5. Logarithmic plot of strain rate versus final grain size at a
temperature of 1723 K and a stress of 60 MPa, yielding an inverse grain
size exponent of p Ϸ 3.
Fig. 7. Comparative plot of static and dynamic grain sizes at a temper-
ature of 1773 K.

November 2001
Compression Creep Characteristics of 8-mol%-Yttria-Stabilized Cubic-Zirconia
2629
Fig. 9. Strain rate, compensated for temperature and grain size, plotted as
Fig. 8. Plot showing the effect of concurrent grain growth on the stress
exponent. Slope of strain rate (left axis) versus stress gives as apparent n Ϸ
2, whereas the slope of strain rate, compensated for grain growth, (right
axis) versus stress gives a true n Ϸ 1.
a function of stress, illustrating that all the experimental data are consistent
with n Ϸ 1, p Ϸ 3, and Q Ϸ 430 kJ⅐molϪ1
.
completely by concurrent grain growth and minor problems with
specimen preparation and alignment.
can be significant for certain combinations of grain size and
temperature,34 estimation of the transient time based on the
equation of Raj34 gives a value of Ͻ2 min for a grain size of 5
␮m at a temperature of 1673 K, using the grain-boundary
diffusion data of Oishi et al.37 Furthermore, the transient strains
(2) Influence of Concurrent Grain Growth on
Creep Parameters
Concurrent grain growth influences creep rate and, hence, the
stress exponent, inverse grain-size exponent, and activation
energy. Figure 8 displays an analysis of the influence of
concurrent grain growth on the stress exponent, using data with
an initial grain size of 5 ␮m tested at 1723 K for all specimens
in which the grain sizes at steady-state creep have been
determined. Based on Eq. (1), changes in grain sizes can be
that are achieved for a steady-state strain rate of 1 ϫ 10Ϫ6 sϪ1
,
the typical value obtained in the present study, should not be
Ͼ0.01%, as determined from the universal creep curve of Gribb
and Cooper.35 The magnitude of these calculated transient times
and strains are significantly lower than the transient time
durations of hours and transient strains of Ͼ1% observed during
some of the experiments in the present study.
p
៮
compensated by plotting data as ε˙L vs ␴. The open datum
Tagai and Zisner21 have reported that concurrent grain growth
can cause a decrease in the creep rate during constant stress testing
and that it is possible to evaluate the influence of grain growth on
creep rate from Eq. (1):
points corresponding to the left axis represent data already
shown in Fig. 3; the filled datum points corresponding to the
right axis represent the same data compensated for grain
growth. Figure 8 shows that, although raw data based on the
initial grain size of 5 ␮m yield a stress exponent of n Ϸ 2, the
true value of the stress exponent is n Ϸ 1. A similar analysis for
the data at 1773 K yielded a true stress exponent of n Ϸ 1;
analysis could not be conducted for the data at 1673 K, because
the paucity of specimens limited grain-growth information at
steady state. The present analysis demonstrates clearly the need
to consider microstructural changes in evaluating the rate-
controlling creep parameters.
p
df
˙
˙
S
ε ϭ ε
(2)
ͩ ͪ
0
d0
˙
˙
where ε0 and εS are the initial and steady-state creep rates, and d0
and df the corresponding grain sizes. Using the experimentally
˙
˙
measured values of εS, d0, df, and p, it is possible to calculate ε0
from Eq. (2), and a ratio of the experimentally observed values at
˙
a low strain of 0.25% (ε0(obs)), and the initial strain rates
˙
calculated from Eq. (2) (ε0(calcd)) are tabulated in Table II. Table
(3) Identification of Rate-Controlling Mechanisms
II shows that there is good agreement between the calculated
˙
values of ε0 and the experimentally measured values at a low strain
At stresses greater than ϳ100 MPa, deformation occurs by a
process independent of grain size; this regime is identified with
intragranular dislocation creep.38 All the steady-state experimental
data obtained in the present investigation at stresses Ͻ100 MPa
(Table II) are shown in Fig. 9 in the form of grain size and
temperature-compensated strain rates versus stress. The creep param-
eters, n ϭ 1, p ϭ 3, and Q ϭ 430 kJ⅐molϪ1, which were determined
from selected data, are a reasonable representation of all the experi-
mental data. These values agree with n Ϸ 1, p ϭ 2.5, and Q ϭ 370
kJ⅐molϪ1 reported recently by Lakki et al.13 for 8YCZ.
of 0.25% in most cases. However, in some experiments, the
observed initial strain rates are significantly higher than the
calculated ones; this could be due to the misalignment in the
loading axis, as explained below.
The lack of specimens with proper planarity or misalignment of
the push rods can result in a pseudoprimary region until the push
rods come into full contact with the specimen surface.36 In the
present experiment, the specimen surfaces were parallel to within
0.02 mm, and the loading axis was aligned to within 1°. Calcula-
tions in the worst-case scenario indicate that these factors can
result in a pseudoprimary region up to strains of Յ0.5% for a
compression specimen with 5 mm height. Consequently, it is
concluded that the observed primary creep can be rationalized
In the absence of an amorphous grain-boundary phase, there are
three different creep mechanisms that can result in Newtonian
viscous deformation:38 Harper–Dorn39 creep, Nabarro–Her-
ring19,20 creep, and Coble40 creep. Harper–Dorn creep involves

2630
Journal of the American Ceramic Society—Sudhir and Chokshi
Vol. 84, No. 11
creep by intragranular dislocation motion, so that p ϭ 0. Nabarro–
Herring and Coble creeps are diffusional deformation processes
involving vacancy flow through the lattice (p ϭ 2) and along grain
boundaries (p ϭ 3), respectively. The creep parameters of the
present experimental data are consistent with the occurrence of
Coble diffusional creep process, with n Ϸ 1 and p Ϸ 3.
There are three additional points to report.
(1) Diffusional creep processes are generally associated with
steady-state deformation from the onset of creep, beyond small
strains necessary for the development of steady-state stress profiles
along grain boundaries. In the present study, the slight errors in
preparing specimens and aligning them, as well as concurrent grain
growth, lead to the observation of an apparent primary creep
region.
(2) Diffusional creep processes are associated with grain-
boundary sliding,32,33 to maintain continuity, and they lead to an
elongation of grains in a direction perpendicular to the compres-
sion stress axis. There is microstructural evidence for grain-
boundary sliding during creep deformation. The experimental
measurements revealing the retention of an equiaxed grain size
after creep is not unreasonable considering the relatively small
strain and errors associated with grain-size measurements. Also,
grain rotation as well as grain growth, which lead to grain
switching,41 can mask the development of grain elongation during
diffusion creep.
(3) The reasons for the discrepancy in rate-controlling pro-
cesses are not clear between the present study (Coble creep) and
the earlier report by Dimos and Kohlstedt8 (Nabarro–Herring
creep). There are two possible explanations for this difference: the
lack of consideration of grain growth in the analysis by Dimos and
Kohlstedt, or a change in the creep mechanism from Coble to
Nabarro–Herring at higher yttria contents. Although the present
study involving 8 mol% yttria leads to significant grain growth and
concurrent cavitation, Dimos and Kohlstedt report grain growth
but no cavitation after creep deformation. The possible influence
of yttrium content on diffusion, grain growth, and cavitation merits
further investigation.
Fig. 10. Comparative plot of the data from the present study with some
of those reported in the literature with the predictions of theoretical Coble
៮
and Nabarro–Herring models, at a temperature of 1723 K and L ϭ 5 ␮m.
1723 K. Inspection of Fig. 10 suggests that the experimentally
observed transition in polycrystalline cubic-zirconia from n ϭ 1 to
n Ͼ 5 indicates a change from diffusion to dislocation creep, which
is consistent with single-crystal data. However, the lack of well-
defined steady-state deformation precludes a complete character-
ization of deformation at high stresses. Therefore, further analysis
for determining the creep mechanism and the rate-controlling
species is limited to the low-stress region and is detailed below.
At sufficiently low stresses, where dislocation mobility is
limited, creep can occur by the stress-directed diffusion of vacan-
cies along grain boundaries (Coble creep) or through the lattice
(Nabarro–Herring). In ionic compounds, the requirement for mass
transport of both the species can result in four potential diffusion
creep mechanisms: Nabarro–Herring and Coble, controlled by
diffusion of either the anion or the cation.43,44 However, it is
recognized that, in cubic-zirconia, O2– diffusion occurs rapidly
through the lattice and grain boundaries and that Y3ϩ diffuses
slightly faster than Zr4ϩ through the lattice and grain boundaries,37
so that creep is controlled by the diffusion of the slower-moving
Zr4ϩ ion along either the grain boundaries or the lattice. Accord-
ingly, it is sufficient to consider only these two independent
processes for identifying the rate-controlling mechanism.
(4) Comparison with Reported Data and
Theoretical Predictions
Figure 10 is a comparative plot of the data from the present
study with those reported by Dimos and Kohlstedt,8 Lakki et al.,13
and Martinez-Fernandes et al.,24 as well as the theoretical predic-
tions of Nabarro–Herring19,20 and Coble,40 calculated at a temper-
ature of 1723 K and mean intercept grain size of 5 ␮m. For the
present study, all steady-state data at a temperature of 1723 K and
៮
stresses Ͻ100 MPa have been normalized to L ϭ 5 ␮m, using a
value of p ϭ 3; however, the minimum creep rate data at stresses
Ն100 MPa have not been modified, because they are independent
of grain size. The data of Dimos and Kohlstedt8 at a temperature
៮
of 1723 K have been recalculated to L ϭ 5 ␮m using their reported
value of p ϭ 2.2. In the case of data reported by Lakki et al.,13 the
strain rates at a temperature of 1563 K and a grain size of 6.8
␮m, the experimental conditions closest to those used in the
present study, have been extrapolated to the temperature of
˙
The Coble diffusion creep rate εCO is given by the following
៮
1723 K and L ϭ 5 ␮m, using their reported values of p ϭ 2.5
expression:
and Q ϭ 370 kJ⅐molϪ1. For the low temperatures of Յ1563 K
and coarser grain size of 6.8 ␮m used in their study, concurrent
grain growth is expected to be negligible.
3
33␦Dgb
b
˙
ε
co ϭ
␴
(3)
ͩ ͪ
kT
d
Figure 10 shows that the data of Lakki et al.13 are in good
agreement with those from the present study, whereas the data of
Dimos and Kohlstedt8 are almost 1 order of magnitude lower. The
lower creep rates reported by Dimos and Kohlstedt may be due to
the lower diffusion rates in 25YCZ, which is in accordance with
the diffusion data of Chien and Heuer,42 where it has been
observed that the lattice diffusion coefficient decreases at higher
yttria content.
where ␦ is the grain-boundary width and Dgb the grain-boundary
diffusion coefficient.
Oishi et al.37 have reported the following expression for
grain-boundary diffusion of Zr4ϩ ions in 16YCZ based on inter-
diffusion experiments:
␦Dgb ϭ 1.5 ϫ 10Ϫ12 exp(Ϫ309000/8.3T) m3⅐sϪ1
(4)
Martinez-Fernandez et al.24 have extensively analyzed the creep
behavior of 9.4YCZ single crystals and have found the dominant
mechanism to be intragranular dislocation motion, with n Ϸ 5,
which is shown in Fig. 10 with their creep data at a temperature of
˙
Nabarro–Herring creep rate εNH is given as
2
28DLb
b
˙
ε
NH ϭ
␴
(5)
ͩ ͪ
kT
d

November 2001
Compression Creep Characteristics of 8-mol%-Yttria-Stabilized Cubic-Zirconia
2631
where DL is the lattice diffusion coefficient.
Chien and Heuer42 have reported the lattice diffusion coeffi-
cient for Zr4ϩ ions in 9.4YCZ from dislocation loop annealing
studies as
V. Summary and Conclusions
There is significant grain growth and cavitation during com-
pression creep deformation of 8YCZ. A short primary creep region
is attributed to concurrent grain growth and slight misalignment
during testing. At stresses Ͼ100 MPa, deformation occurs by a
process independent of the grain size; the data are consistent with
intragranular dislocation creep reported in single-crystal cubic-
zirconia. The experimental results and analysis demonstrate the
need to account for concurrent grain growth in evaluating the creep
parameters; in the present study, concurrent grain growth leads to
an apparent stress exponent of ϳ2, whereas the true value is ϳ1.
The experimental results are consistent with deformation by a
Coble diffusional creep process.
DL ϭ 1.4 ϫ 10Ϫ3 exp(Ϫ511000/8.3T) m2⅐sϪ1
(6)
Lakki et al.13 have conducted tracer diffusion studies on 8YCZ
and determined the lattice diffusion coefficient for Zr4ϩ ions as
DL ϭ 2.2 ϫ 10Ϫ5 exp(Ϫ460000/8.3T) m2⅐sϪ1
(7)
Oishi et al.37 also have reported the lattice diffusion coefficient
for Zr4ϩ ions in 16YCZ from their interdiffusion studies as
DL ϭ 3.1 ϫ 10Ϫ6 exp(Ϫ391000/8.3T) m2⅐sϪ1
(8)
The theoretical predictions† of Coble and Nabarro–Herring
creep based on Eqs. (3)–(8) were calculated at a temperature of
1723 K using a spatial grain size d ϭ 1.74L ϭ 8.7 ␮m and shown
Appendix
៮
In general, creep rate can be expressed by Eq. (1) in terms of the
stress, grain size, and temperature. From this standard creep
equation, the errors in the theoretical Coble creep rate (n ϭ 1 and
p ϭ 3) can be determined as follows:
in Fig. 10.
Figure 10 shows that the experimental creep rates from the
present study, and those from Lakki et al.13,‡ are comparable to the
predicted Coble creep rates.
Furthermore, the Nabarro–Herring strain rates calculated using
the Oishi et al.37 diffusion coefficient are in good agreement with
the creep data of Dimos and Kohlstedt.8 However, the activation
energy of 390 kJ⅐molϪ1 reported by Oishi et al. is significantly
lower than the value of 564 kJ⅐molϪ1 observed by Dimos and
Kohlstedt. Moreover, as shown in the error analysis in the
Appendix, there are significant errors in plotting the theoretical
creep rates, mostly because of errors in determining the activation
energy for diffusion. The error bars shown in Fig. 10 for the
theoretical creep rates have been calculated from the reported
errors in the activation energies in the respective studies.
Because lattice and grain boundaries are independent paths for
vacancy diffusion, creep is controlled by the correspondingly
faster creep process, and combining Eqs. (3) and (5) predicts the
following condition for the domination of Nabarro–Herring creep:
˙
dε ץ␴ 3ץd ץ͑␦D0,gb
͒
ץQ
ϭ
ϩ
ϩ
ϩ
˙
ε
␴
d
␦D0,gb
RT
ϩ higher-order terms
(A–1)
Because the errors are generally small, higher-order terms are
usually neglected in conventional error analysis. Assuming a
nominal error of 10% in all the values—so that ץ␴/␴ ϭ 0.1,
3ץd/d ϭ 0.3, ץ(␦D0,gb)/(␦D0,gb) ϭ 0.1, and ץQ/Q ϭ 0.1—
calculations indicate that, for the present material, where reported
ץQ ϭ 30 kJ⅐molϪ1 and T Ϸ 1723 K, ץQ/RT ϭ 2.1, which is a high
value. Because of these large errors, it is necessary to consider the
higher-order terms in the Taylor expansion given in Eq. (A–1).
The errors in the strain rate are dominated by the errors in the
activation energy. Therefore, it is possible to estimate the error in
strain rate by the following simple procedure:
␦Dgb
d Ͼ
(9)
DL
˙
ε͑Q͒ ϰ exp(ϪQ/RT)
(A–2)
Substitution of Eqs. (4), (6), (7), and (8) into Eq. (9) and
calculation at a temperature of 1773 K, the highest test temperature
in the present study, indicate that Nabarro–Herring creep is
important only at grain sizes Ͼ100 ␮m for all values of the
reported lattice diffusion coefficients. However, for the data
reported by Dimos and Kohlsteadt,8 the uncertainty in diffusion
coefficients at high yttria contents and the lack of consideration of
grain growth preclude a final conclusion regarding the rate-
controlling process.
˙
ε͑Q Ϯ dQ͒
ϭ exp͑ϮdQ/RT͒
(A–3)
˙
ε͑Q͒
For the present material, where dQ ϭ 22 kJ⅐molϪ1 (Oishi et
al.37) and at T ϭ 1723 K, Eq. (A–3) reveals an error in the strain
rate as a factor of 5. Similar estimation of errors has been done for
Nabarro–Herring, and these are shown as error bars for the
respective theoretical predictions in Fig. 10. The present calcula-
tions indicate that the strain rates can be calculated only to 1 order
of magnitude accuracy because of errors in the values of the
activation energy.
Therefore, it is concluded that Coble creep is the dominant
mechanism in the present material at low stresses based on the
following observations.
(1) Theoretical considerations indicate Coble creep to be rate
controlling under the experimental conditions utilized in the
present study.
(2) There is reasonably good agreement between the predicted
creep rates and the experimental data.
(3) The deformation parameters and the microstructural as-
pects are in excellent agreement with the predictions of the Coble
model.
However, to date, there is only one study on grain-boundary
diffusion in cubic-zirconia. Because of the significant errors
caused in theoretical predictions caused by errors in diffusion
coefficients, there is an urgent need to determine the grain-
boundary diffusion coefficients for cubic-zirconia.
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