Heinrich J.G., Aldinger F. (Eds.) Ceramic Materials and Components for Engines
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for structural ceramics,
so
that a more empirical
approach to lifetime prediction has to be adopted. One
approach uses the Monkman-Grant equation3, which
correlates secondary creep rate,
&,
with the time-to-
failure. The time-to-failure is expressed as a power law
function of the creep rate.
For
silicon nitride, the time-
to-failure can also depend
on
the test temperat~re'~:
109
where
Qm
is the temperature dependence of the
Monkman-Grant plot and
tl
and
k
are constants.
Equation
7
fits creep rupture data for silicon nitride
exceptionally well, as can be seen from the data for
SN88
in Fig.
3.16
To obtain failure time as a function of applied
stress and temperature it is necessary to characterize the
creep rate as a function of these parameters. This has
been done recently by Luecke and Wiederh~rn'~, who
suggested that tensile creep in silicon nitride is a
t=f,%
exdQJRT)
b1.14
Qm=137
kJ/mol
10'0
""""
'
""""
'
"'""1
'
"'I'
I
10
100
loo0
loo00
Failure
Time,
h
Fig.
3:
Creep rupture data obtained
on
SN88.
The
curves are fits of the data to equation
7.
cavitation-controlled process. They demonstrated a
strong connection between creep strain and cavity
volume fraction. Based
on
this finding, they derived a
relation between applied stress,
0,
and the secondary
creep rate,
i
:
..
E
=
E,
.
u
.
exp(a.
a).
exp(
-Q,/RT),
(8)
where,
Q,
is the temperature dependence of the creep
rate. An excellent fit of equation
8
to an extensive set
of data was obtained for
SN88,
Fig 418. Similar fits
have been obtained
on
other sets of silicon nitride16*
17.
By substituting the creep rate in equation
8
into
equation
7,
an equation
is
obtained that relates the
creep-rupture lifetime to stress and temperature:
A comparison of the predictions of equation
9
with
actual measurements, Fig.
5,
shows that the predicted
and measured values of the lifetimes lie within a factor
10-10
10
100
5M)
Applied
Stress,
MPa
Fig. 4: Creep data for
SN88
fitted to equation
8.
of two over the entire range of measurements. The
deviation of the data from the expected lifetime is
systematic, positive at both ends of the plot and
negative in the middle, which suggests that equation
9
does not capture the entire functionality of the lifetime.
9
.P
a
B
c
loo
'
'
""""
'
""""
'
'"*""
'
""""
'
'a'LyJ
1
10
100
1000
10000
100000
0
bserv
ed
,
h
Fig.
5:
Lifetime prediction of equation
9,
predicted
versus observed times,
SN88.
Equations
2
and
9
both give relations between
lifetime, temperature and stress: equation
2
for crack
growth as the life-limiting mechanism, equation
9
for
creep rupture as the life limiting mechanism. These
equations can be used to create a fracture mechanism
map, which identifies regions of safe de~ign''~
20,
For
each equation, the allowable tensile stresses, the solid
curves in Fig.
6,
are plotted as a function of temperature
for a fixed time to failure. Separate curves are plotted
for
100
h,
1,000
h, and
10,OOO
h. Each failure
mechanism is marked
on
the diagram. Within the
envelope for each time curve, allowable temperatures
and stresses for safe design are indicated.
STRAIN LIMITED LIFETIME
At elevated temperatures, lifetime can also be
limited by the maximum allowable strain in a
component.
For
normal design criteria, the strain limit
can be as low as
0.5%
strain, which means that even a
fairly brittle material, such as silicon nitride, can be
strain-limited. The problem of defining the strain to
failure for silicon nitride was discussed recently by
Wiederhorn
et
a1.22,
who developed a general equation
to describe the creep of silicon nitride in the primary
112
-
Creep
Rupture
--_-_
0.5%
Strain
700
600
0'
'
"
" "
'
600
900
1200
1500
Temperature,
"C
D=OS
-
Fig.
6:
Fracture mechanism map for
SN88.
100
and secondary stages of creep. Because the critical
strain of
0.5%
was reached towards the beginning of the
secondary creep stage, tertiary creep was ignored in this
treatment. The final equation had three temperature and
stress dependent parameters, the values of which were
obtained by a fit to all of the creep data. The form of
the equation was:
-
-
E
=
E
.
t
+
E
Mp
[I
-
exp(t/r
)],
(10)
where
E
is the secondary creep rate given by
equation
8;
eMp,
is the maximum primary creep strain;
z
is a relaxation time, which can be expressed as a power
function of the minimum creep rate (in a manner similar
to that of the Monkman-Grant plot). Each of these
constants can be obtained from the creep data22.
A
comparison between
the
calculated and measured times
to reach
0.5%
strain is shown in Fig.
7.
In
all cases, the
predicted lifetime lies within
50%
of the measured
lifetime. From the deviation,
it
is possible to determine
the standard deviation of the individual data points,
SD,
which can then be used to give the probability for short
term failures.
2-
300.0
b
.&
3
100.0
A
rr
0
Logarithm
of
Measured Timeto
0.5%
Stram,h
Fig.
7:
Lifetime prediction for
0.5%
strain to failure,
predicted versus measured time.
Once the creep strain is expressed as a function of
stress, temperature, and time, equations relating stress
and temperature can be obtained for
0.5%
strain and a
fixed time. Fig.
6
shows the result of this calculation
for
100
h,
1,000
h
and 10,OOO
h
as dashed lines. For the
0.5%
strain limited failure, the allowable stresses and
temperatures are significantly less than those obtained
for the stress rupture limited failures. For an applied
stress of 100 ma, the allowable temperature has to be
decreased by
60°C
which is substantial for high
temperature operation.
PROBABILISTIC LIFETIME PREDICTIONS
The curves relating temperature to applied stress
shown in
the
fracture mechanism map in Fig.
6
were
calculated for either the mean (creep rupture and strain)
or
median (crack growth) failure times, which are
measures of the central tendency for failure. To
establish a safe engineering stress
or
temperature,
it
is
not the central failure time, but the failure time at a low
probability that is important. One part
in
ten thousand
failures is normally considered to be minimum
acceptable number for commercial ~ervice'~. The
allowable stress and temperature for this minimum
number is easily determined from the equations
presented in this paper.
For
a constant strain to failure, the difference
between the predicted and measured lifetime is used to
determine the standard deviation for the scatter in the
lifetime of components. The standard deviation,
SD,
of
the difference between N measured and calculated
lifetimes, At,, is given by:
r
71/2
500
2
400
61
v)
w
300
200
.5%
"
600
900
1200
1500
Tempemhue,
C
Fig
8:
Fracture mechanism map for
SN88,
10,000 h
lifetime. The figure contains failure probabilities
of
both
0.5
and 0.0001.
For subcritical crack growth as a failure
mechanism, equation
6
can be used directly to
determine the allowable stress for a given lifetime.
Substituting 0.0001 into this equation, and, expanding
t,
in terms of stress and temperature, yields an equation
between failure time, applied stress and temperature.
The relation between stress and temperature can now be
113
obtained by fixing the failure time to a specific value,
say 10,OOO
h.
The relation exhibits a strong dependence
on the Weibull modulus.
Curves of constant time to failure, 10,OOO h, were
determined for both the crack growth failure regime and
the creep regime, assuming 0.5% strain to failure for the
creep regime and actual rupture time for the crack
growth regime, Fig
8.
In the creep regime, the
allowable stress and temperature for the 10,OOO h
lifetime are degraded by a modest amount. For 100
MPa applied stress, the decrease in temperature needed
to assure a failure probability of less than 0.0001 is
about 25 "C. For SN88 the maximum temperature
allowed for a strain of less than 0.5% and at a
probability of less than O.OOO1 is less that 1300 "C.
The effect of the Weibull modulus,
m,
on the
allowable stress is very strong, as can be seen
from
Fig.
8,
where 10,000
h
curves for a failure probability
of
0.0001 have been drawn for Weibull modulus of 10
and 20. These values cover the range usually reported
for silicon nitride. At a temperature of about 900 "C, a
Weibull modulus of 20 reduces the allowable stress
from the median value of about 450 MPa to about 350
MPa. For a Weibull Modulus of 10, the allowable stress
is reduced to less than 200 MPa. These results
demonstrate how important
m
is to component
performance, since an allowable stress of less than
200 MPa lies very close to the design stresses in some
ceramic components. The higher value of
m
yields a
much greater flexibility for safe design.
REFERENCES
(1) M. Van Roode, Design and Testing of Ceramic
Components for Industrial Gas Turbines, in the
International Symposium, Ceramic Materials and
Components for Engines,
June 19-23,2OOO, Goslar,
Germany..
(2) N.J. Tighe and S.M. Wiederhorn, "Effects of
Oxidation on
the
Reliability
of
Silicon Nitride,"
pp. 403-23 in
Fracture Mechanics of Ceramics
5,
Surface Flaws, Statistics, and Microcracking,
R.C.
Bradt, A.G. Evans, D.P.H. Hasselman, and F.F.
Lange, eds., Plenum Press, New York (1983).
(3) F.C. Monkman and N.J. Grant, An Empirical
Relationship between Rupture Life and Minimum
Creep Rate in Creep-Rupture Tests,
Proc. ASTM
56
(4) M.K. Ferber and M.G. Jenkins, Evaluation of the
Elevated-Temperature Mechanical Reliability of a
HIP-ed Silicon Nitride,
J.
Am.
Ceram. SOC.,
75[9]
(5) S.M. Wiederhorn, "Subcritical Crack Growth in
Ceramics," pp. 613-646, in Fracture Mechanics of
Ceramics, Vol. 2, eds., R.C. Bradt, D.P.H.
Hasselman and F. F. Lange, (Plenum Pub. Co.,
New York), 1974.
(6) D. Munz and T. Fett,
Ceramics, Mechanical Proper-
ties, Failure Behaviour, Materials Selection,
Springer (1999).
(7) J.B. Wachtman,
Mechanical Properties of
Ceramics,
John Wiley and Sons, New York (1996).
(1956) 593-620.
(1992) 2453-62.
(8)
S.M. Wiederhorn and E.R. Fuller, Jr., Structural
Reliability of Ceramic Materials,
Muter. Sci.
Eng.
G.D. Quinn, "Review of Static Fatigue in Silicon
Nitride and Silicon Carbide,"
Ceram.
Eng.
Sci.
Proc.
3[
1-21 (1982).
(10
)
W.
Weibull, A Statistical Distribution Function
of
Wide Applicability,
J.
Appl. Mech.
8
(1951)
(11) A. Paluzny and P.F. Nicholls, Predicting Time-
Dependent Reliability of Ceramic Rotors, pp. 95-
112 in
Ceramics for
High
Performance
Applications
-
21,
J.J. Burke, E.N. Lenoe and R.N.
Katz, eds. Brook Hill Publishing Co. Chestnut Hill,
MA (1978).
(12) J.D. Helfinstine, Adding Static and Dynamic
Fatigue Effects Directly to the Weibull
Distribution,
J.
Am. Ceram.
SOC.
63[1-21 (1980)
113. Correction 63[11-121 (1980) 716.
(13) S.M. Wiederhorn and R.F. Krause, Jr., Static
Fatigue of Silicon Nitride at Intermediate
Temperature, to be published.
(14) S.M. Wiederhorn, R.F. Krause, Jr., W.E. Luecke,
J.D. French and B.J. Hockey, Ceramics for Gas
Turbines Program: Final Report to the General
Electric Company, December 1996.
(15) W.E. Luecke,
S.M.
Wiederhorn, B.J. Hockey, R.F.
Krause, Jr. and G.G. Long, "Cavitation Contributes
Substantially to Tensile Creep in Silicon Nitride,"
J.
Am
Ceram. SOC.,
78
[8] (1995) 2085-96.
(16) R.F. Krause, Jr., W.E. Luecke
Jr.,
J.D. French, B.J.
Hockey and S.M. Wiederhorn, Tensile Creep and
Rupture of Silicon Nitride,
J.
Am. Ceram.
SOC.,
(17) W.E. Luecke and S.M. Wiederhorn, A New Model
for Tensile Creep of Silicon Nitride,
J.
Am. Ceram.
71
(1985) 169-186.
(9)
293-297.
82[5]
(1999) 1233-41.
SOC.
82[
101 (1999) 2769-78.
(18) K.J. Yoon, S.M. Wiederhorn and W.E. Luecke,
A
Comparison of Tensile and Compressive Creep
Behavior in Silicon Nitride,"
J.
Am. Ceram.
SOC.
83
(19) M. Matsui, Y. Ishida, T. Soma and I. Oda, Ceramic
Turbocharger Rotor Design Considering Long
Term Durability, pp. 1043-50 in Ceramic Materials
and Components for Engines, W. Bunk and
H.
Hausner eds., Verlag Deutsche Keramische
Gesellschaft, D-5340 Bad Honnef, Germany
(1986).
(20) G.D. Quinn, "Fracture Mechanism Maps for Sili-
con Nitride," pp. 931-9 in Ceramic Materials and
Components for Engines, W. Bunk and H. Hausner
eds., Verlag Deutsche Keramische Gesellschaft, D-
5340 Bad Honnef, Germany (1986).
(21) G.D. Quinn, Fracture Mechanism Maps for Ad-
vanced Structural Ceramics,
Part
1, Methodology
and Hot Pressed Silicon Nitride Results,
J.
Muter.
Sci.,
25
(1990) 4361-4376.
(22) S.M. Wiederhorn, W.E. Luecke and R.F. Krause,
Jr., A Strain-Based Methodology for High
Temperature Lifetime Prediction,
Ceram.
Eng.
Sci.
Proc.
19[4] (1998) 65-78.
[8]
2017-22 (2000).
114
STANDARDISING MEASUREMENT AND TEST METHODS FOR
ADVANCED TECHNICAL CERAMICS
Organisation
CEN TC 1 84
ASTM C28
JIS
IS0
TC206
R.
Morrell
National Physical Laboratory, Teddington, Middlesex,
UK,
TWll
OLW
Published In development
70
15
30 8
40
?
2 20
ABSTRACT
The increasing diversity of engineering applications
for advanced technical ceramics of all types means that
there is increasing expectation placed on suppliers for
assurance of quality and performance against
specification. In addition, specifications are becoming
more stringent as the applications become more
critical, and this means that standardisation becomes
essential for effective trade. The industry has supported
standardisation of basic testing procedures which are
purpose-designed for advanced ceramics, at first
notably in the
UK,
Japan, USA, France and Germany,
and since 1989, internationally in CEN and
ISO.
The
emphasis has been on providing high-quality methods
appropriate to the wide range of product types that are
available, or which may appear commercially in the
future. In addition, application-based standards
incorporating specifications for materials and device
performance are also appearing, notably in the
electrical and biomedical fields. This paper briefly
reviews the status of the standardisation programmes,
and the effect they are having on the ability better to
specify requirements, to control quality, and to provide
reliable data.
In this paper some specific examples of how the
development process has occurred, and some of the
outstanding problem issues relevant to ceramics for
engines are discussed, including:
0
strength and toughness testing;
0
microstructural assessment;
0
‘damage resistance’;
0
surface roughness.
The value of international cooperation is
emphasised, such as through the Versailles Agreement
on Advanced Materials and Standards (VAMAS)
[l],
the European Structural Integrity Society
(ESIS),
and
the International Energy Agency (IEA) programme, in
identifjing and solving some
of
the problems, and in
providing a platform for validation of test procedures
and provision
of
statements
of
confidence in results
from the test methods.
THE FUNCTION OF STANDARDS
Standardised ways of approaching testing and data
acquisition are key to the effective use of and trade in
any material. Once the research phase has matured, the
target is the effective exploitation of the materials as
real products. Standardised procedures are helpful for:
material development
-
consistent measures of what
is achieved
data acquisition
-
baseline property information for
design purposes
data exchange
-
making data sheets believable by
others, also laboratory testing accreditation
material selection
-
for property/performance
comparison
quality assurance
-
does the product meet a
specification?
PROGRESS
Particularly for thermomechanical applications, the
properties of critical interest are wide-ranging and
different from those typically used for traditional
electrotechnical ceramics, with a strong emphasis on
understanding mechanical properties. Thus a whole
new suite of test procedures has been required, and
huge steps have been taken over the last decade to lay
the basis for a testing methodology that is appropriate
to the wide diversity of material types to be addressed,
including monolithic ceramics, composites, and
coatings. As the first stage, the effort has concentrated
on testing materials, rather than components, although
some component standards are being produced in
specific areas, such as orthopaedics.
Independent national work commenced in a number
of countries during the 1980s, including Japan,
UK,
USA, Germany and France. Unified European action
took place from 1989, and an
IS0
committee was
established in 1994 to promote global activity. Table
1
provides an indication of the scale of the work achieved
to date as well as future targets. Full details of
published documents are available fiom standards
bodies and are not covered in this paper
Table
1
-
Advanced technical ceramic material test
method standards production (mid
2000)
(approximate data, excludes electroceramics)
115
FORMULATING
STANDARDS
The standardisation process is not a trivial one when
done properly. It takes considerable time and effort, as
well as background knowledge and consensus-building
abilities among the committee members, to produce a
document which provides a usable test method. The
document is often a balancing act between technical
exactness and practicality. Make the method too
complicated or too expensive, or too specific to a
particular type of material, and it will have limited
take-up by industry and the testing community.
Modem standards making requires more than a
simple test procedure. It needs clear definition
of:
the
applicability
of the method to a particular range
of materials or material types. Not all test
procedures work effectively on all materials,
so
it is
often difficult to be certain of this point.
the test-piece
preparation procedure,
especially
when the results can
be
dependent on the procedure
employed;
the
test method
itself, particularly any variations in
procedure that are required for particular materials
features
or
responses; what to do if there is a
problem; clear acceptance criteria for the result;
any known
‘interferences’
which can lead to
misleading
or
erroneous results;
the required levels of
precision
of measurement of
each parameter, which are practically and
economically realisable;
the anticipated
accuracy
of any individual result as
a deviation ffom the ‘true’ result;
the anticipated within-lab
repeatability
and
between-lab
reproducibility
on the same material;
this can often be in the form of a summary of an
interlaboratory study of the method.
Such information is particularly helphl when
assessing whether differences in apparent properties are
truly significant or not.
In addition, there is an increasing expectation that
test reports incorporate an error assessment to guide the
user in providing an overall confidence statement on
the results.
TECHNICAL BACKGROUND TO
SOME SPECIFIC EXAMPLES
FLEXURAL
STRENGTH
TESTS
Prior to 1990 there were numerous test-piece cross-
sections and spans, as well as a variety of test-jig
functionalities in three- and four-point bending. The
situation has been reviewed in [2]. The current
procedures in ASTM C116 1 and CEN EN 843- 1 for
monolithic ceramics were developed over more than
fifteen years of national and international collaboration
with improving rationalisation of different national
views. The details of the Japanese equivalent,
JIS
R1601 are different (30 mm rather than 40 mm span,
polished rather than machined surfaces). Further
rationalisation is now taking place with the publication
of
IS0
14704, in which the ASTW CEN approach
is
preferred.
Despite the fact that flexural strength is strictly not
a deterministic property, owing to an inability to
control the shapes and sizes of ffacture initiating
features, it is often used as the key mechanical
yardstick for a material. Consequently, in creating
formal standardised test procedures, a large number of
factors needed to be taken into account, including:
the relevance of using material fabricated solely for
testing relative to material fabricated for the end-
use; this appears to
be
particularly the case for
materials such as silicon nitride;
the method of machining the surfaces and edges of
the test-pieces;
the test geometry, including test-piece dimensions
and test spans;
the rate of applying a force;
the test environment employed;
the method
of
applying the force to the test-piece.
An
optimisation exercise by the US
Army
during
the early 1980s [3] was conducted to minimise the
errors introduced by the method of loading the test-
piece and
its
geometry, starting on the premise that the
simple ‘thin-beam’ flexure equation should be retained
for calculation of strength. A narrow window on the
span-to-depth and span-to-width ratios of the test-piece
was found in which errors could
be
maintained
individually at less than 1%, with a total overall error
of less than
2%,
typical of the level needed for
confidence in a test result. The accuracies of definition
of loading geometry were also obtained, typically 0.1
mm being required. Risks of factors such as twist,
either in the test-piece itself or in the manufacture of
the test-jig could be reduced by articulation of the
loading rollers. Free-rolling rollers, not constrained
rods or knife-edges are also required to reduce or
eliminate fiiction effects.
These and further considerations were built into the
prototype method described in MIL-STD-1942, which
subsequently
became
ASTM C
I
16
1.
Collaborations
through the International Energy Agency programmes
involving interlaboratory comparisons encouraged the
same format to
be
employed in Europe, resulting finally
in EN843-1. The Japanese standard
JIS
R1601 defined
in 1981 does not take all these factors into account, but
it is to be hoped that the formalising of the
IS0
standard will bring all countries into line.
The importance of this work cannot be over-
emphasised. By adhering to the geometrical and
hctional criteria within the standards, it should
be
possible to see the true effects of changing material
formulation, fabrication route, or machining condition,
rather than being misled by extraneous effects within a
poorly controlled test.
116
FRACTURE
TOUGHNESS
Although fiacture toughness is not a parameter that
can be used for engineering design in brittle materials,
it is an essential measure of material behaviour for a
variety of applications since it controls thermal shock
resistance, abrasion and erosion resistance, and in some
measure local impact resistance. Compared with
metallic materials, the principal problems in testing
are:
focusing on methods for small test-pieces, and
hence small cost in materials terms;
difficulties in creating a clean, stress-fiee pre-crack
for the applicability of well-defined fracture
mechanical calculations;
small crack opening displacements,
so
that crack
face tractions can exist in long cracks, giving R-
curve behaviour;
the simplest methods have the greatest errors due to
poor calibrations.
Table
2
-
Comparative attributes
of
bar test-piece methods for fracture toughness
Method (see key)
Criterion
Confidence in calibration
’
SCF SEW2
IF
IS
Good
Good
Poor Poor
~
Good
Yes
I
Yes-
I
PossiblyTYes
Relative ranking of materials Yes
Determining long-crack toughness Yes No
I
No
I
No
I
No
No Possiblv
I
No3
I
NOTNO
Determining R-curve effects Yes
Determining short-crack toughness No
No
No
Yes
I
yes
I
No
I
Yes
Producing a fast-fiacture toughness
toughness value
Yes
No
I
No
I
No
I
No
(Producing low scatter of results
I
Possibly Possibly
Yes
Use for fine-grained materials Yes
Use for coarse-grained materials Yes
Yes
Yes Yes Yes
Unlikely Yes Unlikely
Unlikely
Yes
lUse for materials of
K,c
<
6
MPa m”2
I
Yes Yes
Yes
I
Yes
I
Yes
I
Yes
Yes
Use for materials
of
KIc
>
6
MPa m1’2
Sensitivity to crack growth before
fast fiacture
Yes
Yes
Method uses
a moving
crack fiont
method
Probably
Yes Possibly for N/A N/A
fine-grained
materials
Yes6
Yes
No
Possibly6
High
Medium
Low
Medium
Sensitivity to notchlpre-crack
geometry
Possibly
Yes
Suitability for use at elevated
Medium
ICost of facilities required for test
I
Medium
Medium High
I
Medium
I
Low
I
Medium
ASTM
CEN
ASTM
Imaftin~~~I
JIS
I
-
ISO=CEN
Standards ASTM,
JIS
ISO=CEN
Key: SEPB
=
single edge pre-cracked beam, CNB
=
chevron notched beam, SCF
=
surface
crack in flexure, SEVNB
=
single edge vee-notch beam, IF
=
indentation kacture,
IS
=
indentation strength, NIA
=
not appropriate.
Footnotes to table:
I
On a kacture mechanics basis. Quality
of
experimental
results
influenced by the nature
of
the material.
Attributes given are appropriate
for notch root radii
of
typically
5
pm
or
less,
i.e. sharpened by honing.
Unless used initially to grow a crack fiom the notch.
If the notch is considered to have a
short
flaw at its tip, R-curve effects are avoided.
5
There is an increasing likelihood
of
poor
pre-crack generation with increasing toughness; the upper limit may be at
K,<
=
5
MPa m”*, but there are
reports
of
successful and valid results obtained
kom
tougher materials.
The tests can usually be performed up to a temperature at which the material begins to soften
or
crack-heal, or where oxidation commences in the
environment used.
6
117
In addition, not all materials can
be
tested by a
given method; each method has a limited range of
applicability, especially regarding the generation of a
suitable length of pre-crack. Consequently a range of
methods is needed, and these have needed to be
developed to a reliable state before standardisation.
Table 2 lists a variety of bar test-piece methods and
summarises some of the advantages and disadvantages
(being incorporated into [2]). Those which have
been
selected
so
far as formally standardised methods are
also indicated.
So
far, plate and short rod methods have
been ruled out.
It is clear
kom
Table 2 that this field is complex and
needs carefkl thought. A key concern is that different
methods will not give equivalent results, primarily
because they employ different lengths of pre-crack at
the point the measurement is made. However, in fine-
grained materials which show no R-curve effects or
significant subcritical crack growth, equivalence has
been demonstrated. Several round robins have
been
conducted on the methods under the auspices
of
VAMAS Technical Working Area 3 and ESIS Task
Group 6 in order to determine practical capabilities as
well as reproducibilities of testing in order to validate
procedures before standardisation.
Set
of
test-pieces
Razor
blade
with
diamnondpaste
(b)
Figure
1
(a) SEVNB method schematic, and (b) a
3 pm tip radius notch produced in a silicon nitride.
Tests based on simple sawn notches have not
been
included because of substantial evidence that a notch is
not equivalent to a sharp crack for many materials,
particularly the harder, tougher varieties. However,
producing pre-cracks is a skilled task; the SEPB
method requires use of a special compression anvil, and
is not always successfkl, and the SCF method requires
fiactographic skills.
To
overcome this problem, recent
research has
been
aimed at refining a method in which
a sawn notch is honed with diamond paste to have a tip
with an extremely small radius, typically 2
-
10
pm,
which is a much better approximation to a sharp crack
than a sawn notch. Figure 1 shows a schematic of the
technique and a typical notch produced by it. This
SEW method has recently
been
evaluated through an
ESIS/VAMAS round robin
[5]
with excellent
reproducibility, and it has
been
agreed to move the
method towards a formal standard.
MICROSTRUCTURAL
PARAMETERS
Quantifj4ng microstructure is becoming a key
element of specifications, and since microstructure is
critically important in advanced technical ceramics in
defining performance of the product, efforts have been
made in CEN to write standardised procedures tailored
for ceramics but based on the general principles laid
down in ASTM El 12 for metals.
So
far, a standard has
been
published on grain size determination by the
manual line intercept method (ENV 623-3), and one on
phase volume fi-action by a manual grid method has
been approved for publication (prENV 623-5). In both
cases the procedures have been tested out in
CENNAMAS round robins in order to determine
reproducibility [6,7]. For grain size, an update has
recently been agreed which additionally incorporates
grain size distribution measurement. Other parameters
that might be considered for the future are grain shape
and phase dispersion.
The increasingly widespread use of automatic or
semi-automatic image analysis (AIA) to speed up the
analysis of micrographs has posed something of a
dilemma for standardisation because there are no basic
standards for systems
or
software. Digitisation of
images permits a range of analysis techniques different
fi-om those typical of manual methods, for example
those based on area or nearest neighbour distance
measurement. In order to take advantage of the power
of
AIA
considerable additional care needs
to
be
taken
in the preparation of suitable images
so
that the
software can correctly interpret them, e.g. that revealed
grain boundaries are continuous and narrow, but well
defined, and that each phase has uniform brightness
with grey level discrimination fiom other phases. In the
CENNAMAS round robin
[7],
images in which these
conditions were not upheld resulted in much larger
scatter for the AIA assessment of volume fiaction than
for the manual method. The human eye still remains
much better at compensating for poor micrograph
preparation than a computer, despite considerable
advances in pattern recognition programming. Manual
118
intervention to delineate for example, poorly defined
grain boundaries or phase areas, is possible, but slow.
Because of the proprietary nature
of
most
AIA
software,
it may be necessary to ensure conformance with
recognised analysis methods by use of digital reference
micrographs.
PROBLEM AREAS
As
the experimental evaluation of materials widens
with increasing attempts to substitute ceramics for
metallic materials in extreme environments, issues of
how to characterise for such uses arise. In many cases
testing to simulate the application can be
straightforward, but it is usually inappropriate to
attempt to standardise such procedures, because specific
test conditions tend to have little general value. For
example in the field of
corrosionlerosionloxidation,
guidelines on the basic steps in conducting tests and the
potential pitfalls to
be
guarded against are all that is
currently practical. Two fiu-ther areas which continue to
pose problems for standardising are ‘damage resitance’
and roughness determination, which are discussed in
further detail below.
‘DAMAGE RESISTANCE’
Advanced technical ceramics, particularly in the
engineering field, are widely employed for their
hardness and dimensional stability. To perform as
engineering materials they must withstand severe
conditions such as thermal shock, impulsive loading,
localised loading, edge damage, erosion, abrasion
or
sliding wear. It has proved difficult to standardise
assessment methods for many of these performance
attributes, primarily because the results are particularly
sensitive to the details of the test method.
In
thermal
shock,
results are dependent
on
parameters such as emissivity, heat transfer
coefficient and geometry, which are difficult to
model exactly in a test. In fact it is often opined that
a component trial
is by far the safest way of
assessing possibilities.
In
impulsive loading
the impacting energy is
dissipated in a manner dependent on geometry and
support.
In
localised loading,
some progress is being made
using Hertzian indentation as a model
[8].
Resistance to
edge chipping
is becoming
recognised
as
being limited
by
material toughness
(GI=)
[9]
and although quasistatic chipping is a
simple test to perform, the mathematical basis for it
remains uncertain.
In
abrasive and erosive wear,
test results are
system dependent, and rank different materials in
different ways (e.g. Figure
3).
However, recent work
at CRIBC in Belgium
[lo]
has shown that
experimentally based material rankings can vary
with mode of material removal. The development of
correlation equations for different modes of contact
may offer a tool for material selection which is
independent of the actual test apparatus, as long as
the mechanism of removal is appropriately
modelled by the test.
In
sliding wear,
critical evaluation of test methods
reveals that machines are often not relevant to the
application and tests are performed under
conditions which do not give the same mechanism
as would
be
seen in use. Most ceramics suffer fiom
breakaway wear conditions above a critical
speedload combination,
so attention needs to be
focused on determining these conditions in order to
provide information on usability and a useful
materials comparison.
Overall, for these categories
of
test, it is unlikely
that universally accepted standardised methods will be
developed in the shodmedium term.
A
i
a
1
Hardness,
HVO.l
Figure
3
ASTM
G65
test results on various ceramics
using a standard sand abrasive and different wheel
surfaces, indicating different rankings
SURFACE ROUGHNESS
IS0
standards lay a basis for the measurement
of
roughness using traditional stylus machines, but these
are designed primarily for metallic materials. Ceramics
have very short range roughness, and this has posed
problems of reproducibility for many years. EN
623-4
restricts the flexibility offered by the
IS0
standards in
an attempt to improve reproducibility, but a recent EC
sponsored round robin indicated that there is still
considerable variability between different machines. It
is
believed that the origins lie in:
stylus high-fiequency dynamics
-
affects the ability
of the stylus to follow the surface at the typical
traverse
speed
of
0.5
mm/s;
inappropriate digitisation length
-
if too short this
acts as an inadvertent short wavelength filter,
possibly removing short-range information.
Further investigation of this problem is underway at
NPL
at this time.
119
CONCLUDING REMARKS
Good progress has
been
made in developing
0
Crown Copyright 2000, reproduced by permission
of
appropriate standards for ceramics for engineering, but
this has only been achieved by the research effort
dedicated to solving problems of consistency, accuracy
and reproducibility. Much remains to
be
done, but the
work
so
far has already had a considerable positive
impact in the quality of testing and data to the benefit
of the manufacturing and user communities.
Controller, Her Majesty’s Stationery Office
ACKNOWLEDGEMENTS
The author’s involvement in this work is supported
by the UK Department of Trade and Industry through
its materials metrology programme.
REFERENCES
G.
Qui,
VAMAS after twelve, her. Ceram.
Soc.
Bull., 1999, 78(7), 7tG83.
G.D.
Quinn,
R
Morrell, Design
data
for engineering
ceramics: a review of
the
flexure test, J. Amer.
Ceram.
SOC.
199 1,74(9), 2037-66.
F.I.
Baratta, G.D. Quinn, W.T. Matthews, Errors
associated with flexure testing of brittle materials,
Technical report TR 87-35, July 1987,
US
Army
Materials Technology Laboratory, Watertown,
USA.
prEN
XXXX-I:
Advanced technical ceramics
-
monolithic ceramics
-
test methods for
determination of apparent fiacture toughness
-
Part
1:
guide
to
test method selection (to
be
published).
J.
Kubler, Fracture toughness testing using the
SEVNB method; round robin,
VAMAS
Report
No. 37, EMPA, Switzerland,
1999.
L.J.M.G. Dortmans,
R
Morrell, G.
De
With, Round
robin
on
grain size measurement for advanced
technical ceramics, J.
Eur.
Ceram.
Soc.,
1993,12(3),
M. Hendrix, E.G. Bennett,
R
Morrell, L.J.M.G.
Dortmans, G. De With, CENNAMAS phase
volume fraction round robin, Brit. Ceram. Trans.,
1998,76(6), 293-6
S.G.
Roberts,
Hertzian
testing of ceramics, Brit.
Ceram.
Proc.
2000,
Wl),
31-8.
R
Morrell, N.J. McCormick, Edge chipping
as
an
indicator of toughness, PaoRim 2 Conference,
Cairns, Australia, July 1996, Int. Ceram.
Monographs, edited by P. Walls, C. Sorrell, A Ruys,
Australasian Ceramic Society.
205-13.
(10) D.Beugnies, P
Descamps,
J
Tirlq,
et
a/.,
Performance
standards:
a new concept for advanced
ceamics
wear
performance,
Sixth
Euroceramics, Brit.
Cam.
ROC.
1999,60(1), 21 1-2.
120
INVESTIGATIONS ON THE STABLE CRACK GROWTH
OF
INDENTATION CRACKS
T.
Lube
Institut fur Struktur- und Funktionskeramik, Montanuniversitat Leoben,
Peter-Tunner-StraQe
5,
A-8700 Leoben, Austria
ABSTRACT
The stable growth of indentation cracks under an
externally applied load offers an practicable possibility
to study the fracture properties of ceramics. Under sim-
plifying assumptions
-
constant geometry factor
Y
and
residual stress parameter
x
-
a simple relation can be
derived for the dependence of the strength
oIs
of an
indented specimen
on
the indentation load
P:
oIs
oc
P".
The exponent
n
equals
1/3
for materials with constant
toughness and is less than
1/3
for materials exhibiting
R-curve behavior.
For
a more realistic approach, the dependence of
Y
and
x
on
the crack length c has to be considered. In
most cases the value of
Y
for half-elliptical surface
cracks
in
bending specimens decreases with crack ex-
tension. A method to calculate the expected decrease is
proposed and the results are compared with experimen-
tal
data. With the help of model calculations it is shown
how these changes in
Y
influence
o1s
as
denoted
in
common graphic representations.
It becomes apparent that it is indispensable to ac-
count for the decrease in
Y
when
oIs
versus
P
data are
evaluated: the decrease in
Y
may lead to exponents
n
<
1/3
even for materials with constant toughness.
INTRODUCTION
Indentation methods are widely used to determine
the fracture properties of ceramics. The inherently stable
growth of indentation cracks subjected to an external
load and the presumably easy evaluation makes them
especially suitable for the determination of R-curves.
A
variety of techniques has been established for this pur-
pose
[l-61.
The differences
in
these techniques are
mainly founded
in
the way the unknown geometry fac-
tor and residual stress parameter are determined.
A
review of these techniques shows that in some cases
empirical corrections have to be introduced to obtain
reasonable results. The question arises if the correlations
that determine the behavior of indentations crack in
such a test are maybe much more complex and inter-
connected than assumed.
THEORETICAL BACKGROUND
Surface cracks produced by sharp indenters like
Vickers pyramids are usually described
as
half penny
cracks. Due to the irreversible plastic deformation and
damage beneath the indenter point, these cracks are
wedged open by a residual stress field after removal
of
the indenter. From the assumption that the residual
stress intensity factor
K,,
for
a crack
co
produced by a
load
P
is equal to the fracture toughness
K,,
it
is possi-
ble to determine
K,
[7].
The residual stress can be writ-
ten
as:
The parameter
x
is a measure of the strength of the
residual stresses and is usually obtained by calibration
with a material with know fracture toughness.
If a specimen containing such an indentation crack is
additionally loaded by an external stress
o,,
(e.g. a
bending stress) a stress intensity factor
Kappl
is caused.
The total stress intensity
K,,
is given as
(2)
K,,,=K,+K~~I=X~+o,YJF
P
'
where the geometry factor
Y
depends
on
details of the
crack shape and the loading geometry. As
K,,,
decreases
initially more strongly than
Kappl
increases with in-
creasing c, an indentation crack can grow stably for a
certain distance before failure. Applying the conditions
for equilibrium,
Ktot
=
Kc
3
(3)
and for stable crack extension,
(4)
to eq. (2) allows the calculation of the stress
ols,
the
"indentation strength", and critical crack length
c,,
at
failure:
Plotting the experimentally easily accessible quantity
oIs
versus the independent variable
P
(as a measure for
the severity of the flaw)
in
logarithmic coordinates ac-
cording to eq. (5a) yields a straight line. Satisfaction of
the P1'3-dependence is usually taken as validation of the
assumption that the tested material has a single-valued
toughness
[8].
R-curve behaviour
The inherent stable growth of indentation cracks
un-
der an externally applied load offers an interesting pos-
sibility to use them for the measurement of R-curves.
121