Heinrich J.G., Aldinger F. (Eds.) Ceramic Materials and Components for Engines
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lower Y-content, transforms more easily. The
thermally induced transformation of
tetragonal to monoclinic phase in 2YM-TZP
between 100 and
400°C
has been confirmed
by high temperature
XRD
[13]. This
phenomenon is
known
as
low-temperature
degradation, and is seen to affect the internal
friction. As such, IET can be a tool in the
assessment of the transformability of the
tetragonal ZrOz-phase, which
is
one of the
factors determining the fracture toughness of
the transformation toughened zirconia
materials. Of the tested materials 2YM-TZP
has the larger room temperature indentation
fracture toughness (10.2
am'")
in
comparison with the 3Y-TZP
(2.5
MPam’”).
However, issues of thermal instability, as
indicated by the IET-results, can inverse the
ranking of suitability for applications under
specific circumstances.
CONCLUSIONS
AND
PROSPECTS
In
this paper, tests performed with
advanced impulse excitation devices have
shown that the elastic and damping properties
of ceramic materials and components can be
accurately determined
as
a hction of
temperature. It has been demonstrated that
the advantageous noise emission properties of
silicon nitride combustion engine valves can
be explained by their stiffhess and damping
characteristics. Further, IET was used to infer
the presence or absence, and the amount of
pockets of amorphous intergranular phase in
Si3N4 from the internal friction T,-peak, while
the creep resistance relates to the internal
friction background. Finally, the martensitic
transformation in Y-TZP, which determines
the material’s fiacture toughness, has been
monitored by JET
as
well. Future efforts will
be concentrated on obtaining quantitative
relations between the IET-accessible
properties on the one hand, and creep and
fracture resistance on the other hand.
ACKNOWLEDGEMENTS
RGD are fellows of the Fund for Scientific
Research
-
Vlaanderen. BB is supported by a
fellowship of the K.U.Leuven Research
Council.
REFERENCES
(1) F. Forster, Z. Metallkunde, Vol. 29 (1937)
(2) G. Roebben, B. Bollen,
A.
Brebels,
J.
Van
Humbeeck,
0.
Van der Biest, Rev. Sci.
109-1 15.
Inst. 68 (1997) 4511-4515.
(3) A.
S.
Nowick, B.
S.
Berry, Anelastic
relaxation in crystalline solids, Academic
Press, New York (1 972).
(4)
J.
W. Lemmens, Dynamic Elastic Modulus
Measurements in Materials, ASTM STP
1045, ed. by
A.
Wolfenden, American
Society for Testing and Materials,
Philadelphia (1 990) 90-99.
(5)
H. Lindner, B. Capers,
H.
Feuer,
J.
Hennicke, P. Claeys,
W.
Kaesler,
K.
Spider,
K.-L.
Weisskopf,
Werkstoffivoche ‘96, Symposium 2, ed.
U.
Koch, DGM, Frankfbrt (1996) 1-6.
(6)
R.-G.
Duan, G. Roebben,
J.
Vleugels,
0.
Van der Biest, to be published.
(7) B. Basu,
L.
Donzel,
J.
Van Humbeeck,
J.
Vleugels, R. Schaller,
0.
Van der Biest,
Scripta Mat. 40 (1999) 759-765.
(8) M. Weller, H. Schubert, P. Kontouros,
Science and Technology of Zirconia V, ed.
by
S.
P.
S.
Badwal, M.
J.
Bannister, and R.
H. J. Hannink, Technomic Publ. Co.,
Lancaster and Base1 (1 993) 546-554.
(9) R. Hamminger,
J.
Heinrich, Mater. Res.
SOC. Symp. Proc., 287 (1993) 513-520.
(10)
S.
Yang, R. F. Gibson, G. M. Crosbie, R.
L.
Allor, Ceramic Industry, October 1995,
117-121.
(1 1)
L.
Donzel, A. Lakki, R. Schaller, Phil.
(1 2) R. Schaller, to appear in
J.
Alloys and
(13) B. Basu,
J.
Vleugels,
0.
Van der Biest, to
Mag. A 76 (1997) 933-944.
Compounds.
be published.
The authors wish to thank Carine
Dewitte (NGK Ceramics Europe) for
supplying the Si3N4 engine valves. GR and
222
VAMAS
Round Robin Testing
of
High Temperature Flexural Strength
Akira Okada and Mineo Mizuno
Japan Fine Ceramics Center, Nagoya, Japan
ABSTRACT
Thirteen laboratories in six countries participated in
the VAMAS round robin to measure the flexural strength
of silicon nitride at high temperatures. At each laboratory,
the four-point flexural strength of silicon nitride was
measured in air at 1200°C. The results are summarized as
follows. (i) A comparison between semi- and fully
articulating fixtures indicates that fully articulating
fixture has the greater strength; (ii) The strength of 30
mm x
10
mm spans is greater than that of 40
mm
x
20
mm spans; (iii) The flexural strength in nitrogen at
1200°C
is
found to be considerably lower than that in air.
The mechanisms responsible for such behavior are
discussed.
INTRODUCTION
Flexural strength is one of the most important
properties of advanced ceramics and the temperature
dependence is the principal indicator of mechanical
performance at elevated temperatures. Since domestic
standards for high temperature flexural strength have
been established in several countries [l, 21, the
international standardization of flexural strength at high
temperatures is now being discussed [3]. Within the
Versailles Project on Advanced Materials and Standards
(VAMAS), the present round robin was proposed in
order to promote the international standardization
process. Thirteen laboratories from six countries took
part (see Table
I).
The main objectives of the round
robin were to clarify the effects of using an articulated
configuration and the size of the spans in four-point
flexure.
EXPERIMENTAL PROCEDURES
Advanced silicon nitride (SN28
I,
Kyocera
Corp.,
Kyoto, Japan) was used for this round robin. Specimens
were machined to dimensions of
3
x 4 x 45
mm3
from
nine plates (lot numbers
1
to
9)
of 50 x
70
x 12
mm3
at
JFCC. Most participants received twelve specimens
while some participants received more. In some cases,
specimens were supplied from the additional set of six
plates (lot numbers 11 to 16)
of
51 x
51
x
11
mm3 for
additional tests.
Each test specimen was placed on a four-point flexural
fixture having a semi- or fully articulated configuration.
Specimens were then heated to a temperature of 1200°C
in a furnace and soaked at this temperature for some time
to ensure a uniform temperature distribution throughout
the specimen. Most of the fracture tests were conducted
using a crosshead speed of 0.5 mdmin. The flexural
strength was calculated according to the equation:
3P@,
-
L,
)
0,
=
2bh2
where
P
is
the maximum load at fracture,
L,
is the outer
span,
L2
is
the inner span, and
b
and
h
are the width and
height of the specimen, respectively.
Weibull statistical analysis was conducted in
accordance with the maximum-likelihood method [4-61
and the
90%
confidence intervals were calculated [5, 61.
Table
1.
Participating laboratories
R
Westemeide: Ftaunhofer
Wtut
fiir
Werkstohha&
Germany
A.
Okada
and
M. Mizuno: Japan Fine
Ceramics
Center, Japan
T.
Yonezawa: JMC
New
Materials Inc,
Japan
S.
-J.
Cho:
Korean
Research
Institute of
Standards
and Science,
Korea
I.
Miyachi:
Kyocera
Corporation,
Japan
S.
R
Choi:
NASA
Glenn
Research
Center,
USA
S.
Sakaguchi:
National
Industrial
Research Institute ofNagoya,
Japan
T
Tanah:
National
Institute
for Research
in
Inoqganic
Materials,
Japan
R
Morrell: National Physical
Laboratory,
UK
H.
Sakai:
NGK
Insulators
Lid,
Japan
K
UmM
NGK
Spark
Plug
Co.
Ltd,
Japan
K
Bredm
Oak
Ridge
National
Laboratory,
USA
V.
M. Sglavo: Univmita
d’egli
Studi di
Trento,
Italy
223
The two-parameter Weibull distribution function is given
by
calculated using all the data shown in gray. The large
variation in Weibull modulus between each laboratory
where
F
is the failure probability under the applied
stress
cr,
m
is the Weibull modulus and
00
is the Weibull
characteristic strength. In the present study, the estimator
of the fracture probability
F,
at the stress
cr
was chosen in
accordance with
JIS
R
1625
[4]
to be:
i
-
0.3
n
+
0.4
6.
=-
(3)
The flexural tests in air using semi-articulating fixtures
of
30 mm x
10
mm spans were performed in Labs A,
C,
D,
E
and F (The thirteen participating laboratories were
labelled randomly as Labs A to
M).
The tests conducted
in Lab
B
were performed in nitrogen atmosphere and
similar tests were also carried out in Lab A. Tests using
semi-articulating fixtures with
40
mm
x
20 mm spans
were performed in Labs A,
G,
H,
I,
K
and
M,
and Labs
H,
J,
K
and L performed tests using fully articulating
fixtures with spans of
40
mm
x 20
mm.
The flexural strengths of as-machined specimens and
as-heat-treated specimens were measured in Lab A at
room temperature. Heat-treatment was conducted at
1200°C
for 10 minutes in order to provide a similar
thermal history to the high temperature flexural tests.
RESULTS AND DISCUSSION
All the data are summarized in three categories:
semi-articulating with spans of 30
mm
x 10 mm,
semi-articulating with spans of
40
mm
x
20
mm
and
!idly articulating with spans of
40
mm
x
20
mm.
According to this classification, the strength of
specimens measured using semi-articulating fixtures with
30
mm x 10
mm
spans is 661+75 MPa averaged over 70
specimens; the strength using semi-articulating fixtures
can be seen and some of the
90%
confidence intervals lie
far outside those obtained from all the data for the same
category of test. The Weibull moduli determined from all
the data for semi-articulating fixtures with 30 mm
x
10
mm spans, semi-articulating fixtures with
40
mm
x
20
mm spans and fully articulating fixtures with
40
mm
x
20 mm spans are 11.7,
9.4
and
9.9,
respectively. The
90%
confidence intervals for these categories are from
10.0 to 13.7, 8.2 to 11.0, and 8.1 to 12.2, respectively.
As a result, the values of
m
and their
90%
confidence
01
9oo
L
I
'
' '
'
I
'
'
'
'
I
'
' '
I
'
+
'
'
I
'J
:I1
,,**
I,,,,
,,(,,
l,,8,1j
0
Pamciponts
(Labs
A
to
M)
D~F
with
40
mm
x
20
mm spans is 622+89 MPa averaged
over 83 specimens; and the strength using fully
Fig.
1.
The results of statistical analyses: a) average
articulating fixtures with spans of
40
mm
x
20
mm
is
and standard deviation of flexural strength, b) Weibull
65 1+101 MPa averaged over
40
specimens (Fig. la). moduli
m
with
90%
confidence intervals, and c)
Weibull characteristic strengths,
cro,
with
90%
confidence
intervals.
Figure
lb
shows the Weibull modulus
m
and 90%
confidence interval for each laboratory with the value
224
intervals in the three categories are similar to each other,
indicating that the Weibull modulus is close to
10.
Figure
1
c shows the Weibull characteristic strengths
no
with 90% confidence intervals. The Weibull
characteristic strengths,
no,
and their 90% confidence
intervals are significantly different between three
categories. The Weibull characteristic strength from
semi-articulating fixtures with 30 mm x
10
mm spans is
691 MPa and the 90% confidence interval
is
from 678 to
703 MPa. This is 5.3% higher than that for 40
mm
x 20
mm spans since the characteristic strength is 656 MPa
and the
90%
interval
is
from 643 to 670 MF’a in this case.
The 90% confidence interval, however, reveals that the
difference is significant because the lower bound for
spans of 30 mm x 10
mm
is
higher than the upper bound
for 40 mm x
20
mm spans. In the case of fully
articulating fixtures with 40
mm
x 20 mm spans, the
characteristic strength is 689 MPa and the confidence
interval extends from 670 to 708 MPa. Although this
is
only 5.0% greater than that for semi-articulating fixtures
with the same spans, the lack of cross-over between the
90% confidence intervals indicates that the difference is
significant.
The strength variation between the different
combinations of spans seems to be connected to the
statistical aspect of brittle failure. The differences in the
mean and Weibull characteristic strengths in
semi-articulating fixtures between 30
mm
x 10
mm
spans
and
40
mm
x 20
mm
spans are 6.3% and 5.3%,
respectively. Assuming that the Weibull modulus
is
10,
the difference in the effective volumes is calculated to be
85%, which is equivalent to a 6.3% difference in Weibull
characteristic strengths. In addition, an analysis of the
effective surface area leads to exactly the same answer of
6.3% difference in strengths. Although the observed
variation is slightly smaller than that predicted, the
results seem to be consistent since the details of each test
in the round robin differ slightly from each other.
The difference in the alignment accuracies may also
affect the strength variation between articulating fixtures.
Marschall and Rudnick reported error analyses from
four-point flexure tests [7] and a fixture design for
minimizing such effects has been proposed
[8].
Further
analysis indicated that friction is the major cause of the
error and it is reduced by using a semi-articulating
fixture [9-111. In light of these analyses, a fully
articulating fixture appears to be the most accurate and
should be superior to the semi-articulating fixture
because of its ability to reduce errors due to twist. The
maximum stress
om,,
due to beam twisting
is
given by
[8,
9,
111
(4)
where
a
=
(L
I
-
L2)12,
k2
is a numerical factor that is a
function of
blh,
and
x
is given by
where
E
is
Young’s modulus,
v
is
Poisson’s ratio and
LT
is the total length of the beam. Since
blh
=
1.33, the
numerical values of
kl
and
kz
are 0.179 and 0.224,
respectively.
Qs
is the angle of twist along the specimen
length and
QF
is
the angle of twist between a pair of load
and contact points. From the parallelism tolerance on the
opposite longitudinal faces of 0.015 mm, the maximum
value in the twist angles
is
approximately estimated to be
Qs
=
0.015 md4.0 mm and
QF
=
0.015 md12.0 mm,
assuming that the minimum length of the rollers is three
times the width of the specimens.
It
is
noteworthy that failure occurs after bottoming of
the specimen when
0
<
x
<
1, and that failure prior to the
bottoming occurs when
x
=
1.
Since, in the present
round robin, the maximum possible error in the present
configuration of test specimens is calculated to be 0.9%
because of
x
=
0.32 at the stress of 650 MPa. The
strength error
is
expected to be much smaller because
such high stresses are generated in a limited volume and
the strength depends on the size of the stressed volume.
The difference in strength between semi- and fully
articulating fixtures therefore seems too large according
to twist error analysis.
Some specimens obtained from lots 2,
5
and 6 exhibit
considerably lower strength. Figure 2 shows strengths
plotted against lot number. In all three categories,
specimens with low strength are found for lots 2, 5 and 6.
225
-
700
n
5
600
5
t8
ul
500
J
0
-
rn
-
-
-
I.1.I.I.I
,I.I,I.l
L
-
In
400
a
2
300
-
u
U
2
00
100
0
0
1
Fig.
2.
Strength plotted against lot number. Open circles:
semi-articulating fixtures with 30
mm
x
10
mm
spans;
closed circles: semi-articulating fixtures with
40
mm
x
20
mm
spans; closed square: fully articulating fixtures
with
40
mm
x
20
mm
spans.
The possibility of severe processing flaws pre-existing in
these specimens seems to be greater than for the other lot
numbers.
Figure 3 shows the results of eliminating data
originating from lots
2,
5,
and
6.
Mean strength with
standard deviation is shown in Fig. 3a. In comparison
with Fig. la, it is clear that the scatter in the data is
considerably reduced and the mean strength slightly
increased as a result of the data selection. Weibull moduli
obtained from the selected specimens are shown in Fig.
3b. The value of the Weibull modulus increases when
only selected data, are used. Weibull characteristic
strengths are plotted in Fig. 3c. The strength increases
slightly as a result of data selection although there are no
significant effects on the
90%
confidence intervals. It is
clear that such behavior results
from
competition
between two factors. One is the reduction in the scatter
of the data leading to a narrowing of the confidence
interval and the other is the decrease in the number of
data points leading to an expansion of the interval.
Eliminating data from lots
2,
5
and
6
leads to an
improved fitting to a Weibull statistical function. Figure
4
shows the Weibull plots obtained for the three
categories: semi-articulated configuration with
30
mm
x
10
mm
spans, semi-articulated configuration with
40
mm
1
PactMpants
(labs
A
to
M)
Pamclpants
(labs
A
to
N)
$4
zm
Pamcipants
(labs
A
to
M)
Fig.
3.
The results of eliminating the data in lots
2,
5,
and
6:
a) average and standard deviation of flexural strength,
b) Weibull modulus
m
with
90%
confidence interval, and
c) Weibull characteristic strength
cso
with
90%
confidence interval.
x
20
mm
spans and fully articulated configuration with
40
mm
x
20
mm
spans. In all cases, the values of the low
strength data are inconsistent with the linear relationship
of
two-parameter Weibull statistics, suggesting the
bimodality in strength distribution. However, selective
removal of some of data changes the distribution,
especially in the low strength region, leading to good
agreement with a two-parameter Weibull statistical
function. This indicates that the statistical distribution of
strengths is different between two groups: specimens of
lots
2,
5
and
6
have a wide distribution of strengths while
the distribution of the other specimens is relatively
226
t
99
90
bQ
70:
f
50
30-
1
20
f
lo-
9
5-
L
sO=691
MPa
-
-
selected data:
..
I-
500
600 700
800
900
IMX)
flexural Strensth
[MPoJ
SO
=
707
MPa
a
n
=
29
I
I
I I
I
Ill
serni-ortiiulating
a11 the data
SO
=
656
MPa
SO
=
672
MPa
300
400
500
600
700
8M)
900
1000
flexural strength
(MPol
spars:
40
mm.
20
mm
fully
articulating
all
the data
rn
=
9.9
SO
=
689
MPa
n
=
40
selected data:
no lot
NO.
2.
5
and
6
a
a
300
400
500
600 700
600
900
1000
flexural
strength
(MPol
Fig.
4.
Weibull plots of flexural strength. Comparison is
made between using all the data and using selected data
after eliminating lots 2,
5,
and
6.
a) Spans of
30
mm
x
10
mm,
semi-articulated configuration, b) spans of
40
mm x 20 mm, semi-articulated configuration, c) spans of
40
mm
x 20
mm,
fully articulated configuration.
narrow.
In
the present round robin, the high temperature
flexural strength was also measured in nitrogen
atmosphere at 1200°C and it was considerably lower than
that
in
air (see Fig.
5).
During high temperature
flexural testing, the specimens suffer both thermal and
atmospheric attack. The thermal history is essentially the
same for specimens in air and nitrogen atmospheres but
Lab.
B
tested in nitrogen
rn
=
13.5
SO
=
640
MPa
n=
10
300
400
500
600 700 800 900
1000
flexural
strength
(MPa)
Fig.
5.
Flexural strength of silicon nitride measured in
nitrogen atmosphere at 12OO0C (Lab
B).
The plots are
compared with tests conducted in air under the same
conditions: spans of
30
mm x
10
mm and
semi-articulating fixture.
99
90
b?
70
2
50
330
g
20
f
10
P5
I
as
machined
SO
=
656
MPa
as-heat-treated
SO
=
774
MPa
600
700
800 900
1000
500
flexural
strength
(MPa)
Fig.
6.
Weibull plots of flexural strengths at room
temperature for as-machined specimens and for
heat-treated specimens. Heat-treatment was carried out at
1200°C in air for 10 minutes.
oxidation effects are particular to the measurements in air.
Additional measurements of flexural strength were thus
performed at room temperature for as-machined
specimens and for heat-treated specimens. This indicates
that a significant increase in the flexural strength of 17%
occurs during exposure in air atmosphere at 1200°C (see
Fig.
6).
It
is
therefore suggested that the higher strengths
in air result from oxidation during flexure testing. The
most plausible explanation is that the oxidative crack
healing takes place, since in silicon nitride significant
healing accompanying strength recovery has been
reported [12,
131.
227
CONCLUSIONS
Round robin tests to measure the flexural strength of
silicon nitride were performed at 1200°C. The tests were
carried out under four-point flexure with either spans of
30 mm x 10 mm or 40 mm x 20 mm, and using either
semi- or fully articulating fixtures.
The strength data obtained at each laboratory exhibit
considerable scatter due to the limited number of test
specimens. However, Weibull statistical analysis
considering the confidence intervals revealed that the
strength in the spans of 30 mm x
10
mm is greater than
that of 40 mm x 20 mm and the fully articulating fixture
leads to greater strength than semi-articulating fixtures.
This is consistent with the prediction from effective
volume/surface area analysis but inconsistent with twist
error analysis because the close tolerance between
parallel sides of the test specimens does not allow such a
large difference in strength between the fully articulating
and semi-articulating fixtures.
The strength measured in nitrogen at
12OO0C was
considerably lower than that in air. This seems to be a
result of oxidative crack healing occurring at 1200°C in
air, since the strength of specimens heat-treated in air at
1200°C for 10 minutes was 17% greater than that of
as-machined specimens.
ACKNOWLEDGMENTS
The authors are grateful to all the participants involved
in this round robin. Helpful comments by George Quinn,
Sung
R.
Choi, Stephen DuQ, Kristin Breder and Roger
Morrell are appreciated and special thanks are due to G.
Q.
and
S.
R. C. for their assistance in calculating errors
of beam twisting. Support by the Science and
Technology Agency in Japan is acknowledged.
REFERENCES
1.
JIS
R 1604 (1987), “Testing Method for Flexural
Strength of Fine Ceramics at Elevated Temperature,”
Japanese Industrial Standard Committee, Japanese
Standards Association, Tokyo.
2.
ASTM Designation: C 12 1 1-92, “Standard Test
Method for Flexural Strength of Advanced Ceramics at
Elevated Temperatures,” American Society for Testing
and Materials, 1992.
3. ISO/CD 17565 (1999), “Fine Ceramics (Advanced
Ceramics, Advanced Technical Ceramics) -Test
Method for Flexural Strength of Monolithic Ceramics
at Elevated Temperatures,”
IS0
Technical Committee
206 (ISOiTC206iWG8).
4. JIS R 1625 (1996), “Weibull Statistics of Strength
Data for Fine Ceramics,” Japanese Industrial Standard
Committee, Japanese Standards Association, Tokyo.
5.
D.
R.
Thoman, L. J. Bain and C. E. Antle, “Influence
on the Parameters of the Weibull Distribution,”
Technometrics,
11
[3], (1969) 445-460.
6. ASTM Designation: C 1239-95, “Standard Practice for
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Weibull Distribution Parameters for Advanced
Ceramics,” American Society for Testing and Materials,
1995.
7. C. W. Marschall and A. Rudnick, “Conventional
Strength Testing of Ceramics”, pp. 69-92
in
“Fracture
Mechanics of Ceramics, vol.
1
,”
edited by R. C. Bradt,
D. P. H. Hasselman and F. F. Lange, Plenum Press,
New York, 1974.
8. R. G. Hoagland, C. W. Marschall and
W. H.
Duckworth, “Reduction of Errors in Ceramic
Bend
Tests,” J. Am. Ceram. SOC., 59 [5/6], (1976) 189-192.
9. F.
I.
Baratta, “Requirements for Flexure Testing of
Brittle Materials,” pp. 194-222
in
“Methods for
Assessing the Structural Reliability of Brittle Materials,
ASTM STP
844,”
edited by
S.
W., Freiman and C. M.
Hudson, American Society for Testing and Materials,
Philadelphia, 1984.
10. L. R. Swank, J. C. Cacery and R.
L.
Allor,
“Experimental Errors in Modulus of Rupture Test
Fixtures,” Ceram. Eng. Sci. Proc.,
11
[9/10], (1990)
1329-1345.
1 1. G. D. Quinn, “Twisting and Friction Errors in Flexure
Testing,” Ceram. Eng. Sci. Proc., 13 [7/8], (1992)
3
19-330.
12. T. Ogasawara, T. Hori and A. Okada, “Threshold
Stress Intensity for Oxidative Crack Healing in
Sintered Silicon Nitride,” J. Mater. Sci. Lett., 13 [6],
(1 994) 404-406.
13.
S.
R. Choi, V. Tikare and R. Pawlik, “Crack Healing
in Silicon Nitride Due to Oxidation,” Ceram. Eng. Sci.
Proc., 12 [9/10], (1991) 2190-2202.
22
8
EFFECT OF HIGH VOLTAGE SCREENING METHOD ON TITANIA
CERAMICS
WITH
DIFFERENT SURFACE FINISHING
A. Kishimoto and
T.
Tanaka
Institute
of
Industrial Science, University
of
Tokyo,
7-22-1 Roppongi, Minato-ku,
Tokyo 106-8558, Japan
ABSTRACT
Effects of high voltage screening were examined on
perpendicular and parallel surface ground titania
rectangular bars.
A
screening field at or below which
30
%
of titania samples break electrically was applied to
each group samples. After high voltage screening, the
surviving samples were subjected to mechanical strength
measurement and resultant strength distribution was
compared to the original distribution. After screening,
the Weibull plots
of
perpendicular ground sample bent to
become a convex curve while plots in the high strength
region remained almost the same, indicating that low
strength samples were selectively eliminated by the high
voltage screening. On the other hand, screening effect
on parallel surface ground sample was very small.
INTRODUCTION
We previously reported the effects of high voltage
screening of dielectric ceramics, by which mechanically
weak ceramic parts can be selectively removed by an
electric method (dielectric breakdown)
[
1-41. The
mechanism is thought based on the analogous roles of
specific microstructures in mechanical fracture and in
dielectric breakdown [5-81. For example, pores often
behave as fracture origins in mechanical fracture, as they
are usually stress concentrators. They also become the
starting points of dielectric breakdown, because the
electric field is inversely proportional to the ratio of
electric permittivity (relative permittivity: the
E,
of an air
gap is approximately unity, which is usually smaller than
the ceramic's bulk) [8,9].
We previously examined the effect of high voltage
screening of titania ceramics with a rough surface finish,
and reported that a mechanically weak ceramic part has a
relatively low dielectric strength [4]. We concluded
that a surface crack beneath a ground groove
is
the
decisive breakdown flaw, as with a mechanical fracture.
These results suggest that such a flaw plays the role of an
electric field concentrator, similar to the role of a crack
in the concentration of mechanical stress.
It is important to now examine high voltage
screening of unidirectionally surface ground ceramics
with crack-like surface flaws that are parallel to the
direction of grinding, since in the previously reported
study the surface grinding was in random directions [4].
In mechanical fracture, it is well known that thin surface
flaws perpendicular to the tension direction become
serious
stress
concentrators [lo]. However, with a
parallel electrode configuration in the electric breakdown
experiment, surface flaws should play an identical role,
irrespective of their planer orientation
[
1
11.
We
examined crack-like surface flaws, which may be a
common weak spot in both mechanical and dielectric
failure, and the influence
of
surface flaws on mechanical
strength distribution after high voltage screening
of
unidirectionally surface ground titania ceramics.
EXPERIMENTAL PROCEDURE
Sample Preparation
Titanium dioxide ceramics were employed because
they can be easily broken electrically at room
temperature. Titanium dioxide powder (Kojundo
Chemical Co. Ltd., Japan, rutile phase, purity 99.99%)
was used as the starting material. Powder compacts
were first formed by uniaxial pressing
(30
MPa for 60
s)
and subsequently fabricated by hydrostatic pressing
(200
MPa for 90
s).
The compact bodies were sintered at
1450°C for 4 h in air. The sintered bodies were cooled
at
150
"C
/h,
to prevent reduction from occurring. The
resultant bodies had relative densities around 98.5%.
After removing the surface layer, they were cut into
rectangular 13
X
4
X
0.3 mm bars with a precision
cutting machine (Maruto Co. Ltd., Japan, MC-603).
The cut ends of the samples were comparable to or
smoother than a surface finished with 800-grit abrasive
paper. To examine the effect
of
the direction of surface
grinding, the
13
x
4
mm planes were ground using #400
abrasive paper. In one group, the grinding was
perpendicular to the long axis and in the second group
grinding was parallel to the long axis. The groups were
called the perpendicular and parallel groups, respectively.
In each group,
30
bars were used
to
measure strength
distribution and approximately 45 bars were used for
screening. The ground surfaces were observed by SEM
Strength measurements and high
voltage screening
Silver electrodes with a diameter of
2.5
mm were
attached to both sides of each test piece. The electrodes
were made with diffused edges to prevent concentration
229
2
...,..
.
,
.
. .
,
. .
,
i
*perpendicular
E=204(MPa)
m=8.8
-
.
-4
2
1
d
L;
-2
-3
-
I=
-
-4
-0-
perpendicular
m=8.1
3
-5t.’.
I
*
“I.. .I”’’
2.8
3
3.2 3.4
hE
4.8 5 5.2 5.4 5.6
In0
Fig.
1
Weibull
plots
of
mechanical strength on Ti02 ceramics ground
with different direction.
Fig. 2 Weibull
plots
of
dielectric strength on Ti02 ceramics ground
with
different direction.
of the electrical field at the edges of the electrode.
The mechanical strength of 30 samples was
measured using a three point bending test, with a span
length of 10 mm and a crosshead speed of
0.5
mm
/
min.
In order to compare the mechanical strength with the
results
of
electrical screening, the maximum bending
stress was applied to the centerline of the electrode.
Fractured samples were subjected to dielectric
breakdown measurement to determine the screening field.
The breakdown test applied
D.C.
voltage, increasing at a
rate of 50V/s. Test pieces were placed
in
silicon oil to
prevent surface flashover. The electric field at which
the current abruptly increased was regarded as the
dielectric strength
(Eb).
The measured mechanical and dielectric strength
distributions of the perpendicular and parallel groups
were compared, and the screening field (Es) at or below
which 30% of each group of samples broke electrically
was determined from the dielectric strength distribution.
The other 45 bars for screening were subjected to the
breakdown (screening) test, in which the strength of the
electric field was increased to that of the screening field
(E,).
Bars that broke during the screening test were
discarded. The mechanical strength of the surviving
samples was measured; during this test, maximum stress
was applied at the centerline of the electrode.
Mechanical strength with or without screening was
compared using Weibull statistics.
Evaluation of strength distribution
The distributions
of
mechanical strength and
dielectric strength were estimated using a two-parameter
Weibull distribution, as follows:
where
s
is the mechanical or dielectric strength, and
so,
m,
and V are the scale parameter, shape parameter
(=
Weibull modulus), and effective volume for each
strength, respectively.
The cumulative probability, F,
was calculated using the mean rank method. For the
mechanical stress screening, the probability of failure
after screening, F(a) is expressed as,
where Ftotal is the probability of failure without screening
and F, is the probability of failure when the screening
stress has been applied [13].
With this equation, the
F
=
1
-
exp[-(s/so)m
Vl
(
1)
F(a)
=
(Ftotal- Fs)4
1
-
Fs)
(2).
strength distribution after screening is a convex curve
approaching the screening stress,
q..
RESULTS
AND DISCUSSION
Mechanical and dielectric strengths
of
parallel and perpendicularly ground
samples
Figure
1
shows the Weibull plots
of
the mechanical
strength for the perpendicular and parallel surface ground
samples.
Both plots show good linearity (correlation
coefficient r
>
0.95),
indicating that the scatter of each
data set can be expressed by a single-mode Weibull
distribution function. The sample with the surface
ground perpendicularly has a relatively small Weibull
modulus (8.8) and average strength, indicating that
grinding introduces surface flaws, which play a role
in
the origin of mechanical fractures.
Figure 2 shows the Weibull plots
of
dielectric
strength for the
two
types of sample. There is no
significant difference between the samples ground
perpendicularly and those ground parallel.
The Weibull
moduli for the perpendicularly and parallel ground
samples were 8.3 and 8.1, and the mean dielectric
strengths were 242 and 240 kV/cm, respectively.
For perpendicularly ground samples, the distributions
of mechanical and dielectric strengths are very similar.
One of the authors has already reported the similarity
of
the two strength distributions, indicating the analogous
nature of the distribution of weak spots in the two types
of failure [4-81.
3-2 High voltage screening of perpendicularly ground
samples
High voltage screening
of
the perpendicularly and
parallel ground samples was conducted. From the
dielectric strength distribution shown
in
Fig.2, the
screening field
(Es)
was determined to be 222 kV/cm, for
which the cumulative dielectric failure probability was
30% in both the perpendicular and parallel cases.
230
2
1
-
co
4
y
-1
-
c
-2
-3
-4
-5
4
u
C
-
48
5
52 5.4
56
4.8 5 5.2 5.4 5.6
ha
ha
Fig
3
High
voltage screening on perpendicular surface ground
Ti02
ceramics
Fig
4
High voltage screening on parallel surface ground
Ti02
ceramics
Figure
3
illustrates the Weibull plots of the electrically weak sample would also be mechanically
mechanical strength of perpendicularly ground samples
with or without high voltage screening. High voltage
screening selectively rejects parts with
a
low
mechanical
weak, leading to the positive correlation.
strength. After high voltage screening, the Weibull plot
bends to form a convex curve, although the plots in the
high strength region are almost the same. This result
shows that the electric method removed mechanically
degraded samples. In other words, samples with
a
severe mechanical flaw tend to have weak dielectric
strength.
Incidentally, the convex curve drawn with a solid
line in Fig.
3,
denoted
0~30,
is the theoretical mechanical
strength at which
30%
of the samples fail during stress
screening. With high voltage screening, some samples
have strengths lower than
0~30.
This occurs because the
correlation between mechanical and dielectric strengths
is not perfect.
Matsuo et al. reported that median cracks in
a
scratch
groove are introduced parallel to the direction of
grinding [lo].
A
coarse abrasive particle would have
increased compressive weight, increasing the depth and
number of such flaws. For this reason, in
perpendicularly ground samples the distribution is
thought to spread to lower region and the average
strength to decrease.
Some authors have reported that when an electric
field is concentrated on a concave surface, a critical
electric field induces an electric avalanche and dielectric
breakdown occurs [6,12], although there are few papers
comparing breakdown strength and surface morphology.
In
our results, high voltage screening selectively
eliminated mechanically weak samples, indicating that as
with mechanical fracture surface cracks beneath the
grooves caused by grinding are the decisive breakdown
flaws. Analogous to the stress concentration in a
mechanical fracture, electric field concentration occurs at
the end of a crack due to the permittivity difference,
leading to the analogy between the mechanical and
dielectric strengths.
In
perpendicularly ground samples, crack-like flaws
are formed perpendicular to the direction of tension.
As
a result, cracks that concentrate the electric field also
concentrate mechanical stress.
In
other words, an
High voltage screening
of
parallel
ground samples
Figure
4
illustrates the Weibull plots of the
mechanical strength of samples with the surface ground
parallel to the tension direction, with and without high
voltage screening. Unlike the perpendicularly ground
samples, no significant difference is observed with or
without screening. The theoretical mechanical strength
at which
30%
of the samples should fail after stress
screening is also very different from the experimental
result. These results indicate that for parallel ground
samples the correlation between mechanical and
dielectric strength
is
very weak, unlike for
perpendicularly ground samples. These results indicate
that some of the microstructures introduced by grinding
play different roles in the
two
types of failure.
Role of cracks introduced by surface grinding
The reason that high voltage screening appears
effective only for perpendicularly ground samples can be
explained in the following way. First, the geometric
shape and dimensions of the surface cracks introduced,
which can be derived from Fig.
2,
are almost the same in
parallel and perpendicularly ground samples. As shown
in Fig.
1,
the effects of such a crack
on
the three point
bending strength differ with different crack directions.
When cracks form that are perpendicular to the tension,
they can become serious flaws, depending
on
their
dimensions. However, cracks that form parallel to the
direction of tension are less serious flaws, even if large.
As
a
result, in the former case, if the fracture stress or the
breakdown field is applied to the same area, both failures
start at the same point, resulting in the correlation of the
two failure strengths.
In
the parallel case, the starting
points are not expected to agree, and therefore screening
has
no
apparent effect.
The connection between electric field distribution
and stress distribution in our experiment explains why
the correlation between mechanical and dielectric
strength is not perfect in the perpendicularly ground
23
I