Heinrich J.G., Aldinger F. (Eds.) Ceramic Materials and Components for Engines
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(21) A. A. Weresczak, T. P. Kirkland,
H.
T. Lin, and
S.
K. Lee, "Intermediate Temperature Inert Strength
and Dynamic Fatigue
of
Candidate Silicon Nitrides
for
Diesel Exhaust Valves," to be published in
Proc.
Ceram.
Eng.
Sci.
(2000).
(22)
H. T. Lin, M.
K.
Ferber, and P. F.Becher,
"Mechanical Reliability
of
Yb-containing Silicon
Nitride at Intermediate Temperatures," presented at
Am. Ceram. SOC. Annual Meeting, St. Louis, April
30-May 3,2000.
(23) F. F. Lange, "High Temperature Deformation and
Fracture Phenomena
of
Polyphase Si3N4
Materials," Proc. 2nd NATO Advanced Study
Institute of Nitrogen Ceramics (1981) 467-490.
102
FRICTION AND WEAR OF ADVANCED CERAMICS
K.-H.
Zum Gahr
UniversitBt Karlsruhe, Institute of Materials Science I1
and
Forschungszentrum Karlsruhe, Institute for Materials Research
I
P.O.
Box
3640,76021
Karlsruhe, Germany
ABSTRACT
Tribological performance of structural ceramics is
of great interest because of the unique combination of
properties promising high potential for components in
unlubricated or marginal lubricated sliding contact. As
a function of operating conditions a mild to severe
wear transition can occur.
Alumina ceramics offer high hardness, stiffness,
chemical inertness and thermal stability combined with
the economical advantages of relatively low costs and
good availability in a lot of different qualities. Hence,
the experimental results presented are focussed on this
class of advanced ceramics. But many conclusions can
be also transferred to other ceramics. The mechanisms
for the wear transition are generally discussed. Results
are presented from laboratory tests about the mfluence
of microstructural parameters such as grain size, sec-
ond phases etc. of monolithic and multiphase alumina
ceramics on friction and wear in unlubricated sliding
contact against A1203 counterbodies. It is shown that
microstructural design can be very effective in reduc-
ing friction and wear in a given tribosystem
INTRODUCTION
Advanced structural ceramics such as A1203, Sic,
Zr02,
Si3N4 or Sialon are increasingly used for compo-
nents with high tribological, mechanical, chemical and
or thermal requirements. Their favourable properties
are high stiffness and hardness, compressive strength,
temperature stability, corrosion and wear resistance in
nmy cases, as well as low density. However, mono-
lihc ceramics can suffer severe damages under high
loads, owing to their inherent brittleness and lack
of
de-
fect tolerance. As a consequence during the last decade
those
ceramics were primarily developed for achieving
hgh strength and fracture toughness. Most applications
of engineering ceramics are, however, tribological, e.g.
draw-cones, guides, cutting tool inserts, seal rings,
cylinder liners, cam roller followers, bearing parts,
medical prostheses, sand blast nozzles etc. The micro-
structural demands for ceramics used as mechanical
load-bearing components of high strength and fracture
toughness and for those used as tribological compo-
nents resulting in low friction and wear can be substan-
tially different. Using bend tests the long crack resis-
tance is measured and effects such as crack shielding or
microcracking, crack branching and crack deflection may
be favourable. In contrast, tribological interactions are
concentrated on substantially smaller contact areas like
the size of surface asperities or smaller
than
the grain
size of the ceramic material. Only during the last years
the microstructural design of ceramics has gained in-
creasing considerations for tribological parts
[
1-41.
Tribological behaviour of monolithic ceramics such
as alumina is characterized by a transition from mild to
severe wear, whereby mild wear is used to indicate a
relatively low friction coefficient and the value of wear
coefficient k (wear volume divided by normal load and
sliding distance) smaller than
mm3/(N.m) while the
term severe wear is used for k
>
1
O4
mm3/(N.m).
In the following, wear transition, wear mechsms
and microstructural features influencing the tribological
behaviour in sliding contact of self-mated ceramics are
discussed. The experimental data presented were meas-
ured in laboratory tribometers using ball-on-block or
ring-on-block geometries during unlubricated oscillating
sliding contact. Alumina ceramics were chosen as test
materials because of their unique combination of hard-
ness, corrosion resistance, thermal and hydrothermal
stability as well as their economical advantages and
broad acceptance in many applications.
Properties
of
Contacting Bodies
Chemistrymopcgraphy
of
Surfaces
Porosity Hardness, Strength
Grain
size
Young’s
Modulus
Second Phases Fracture Toughness
Materials:
Performance
Contact Geometry
Contact
Mode
Vibrations
Fig.
1
:
Tribological performance depending on properties
of
the
contacting
solid
bodies, loading parameters
of
the hibosystem
and environmental conditions.
103
WEAR
MECHANISMS
AND
WEAR
TRANSITION
material by fatigue processes and pull-outs of single
grains. Densification of grain fragments in the contact
area lead to so-called third-body layers between the
Tribological behaviour depends strongly on the
type of tribosystem, environmental and interfacial
conditions as well as microstructural features and re-
sulting properties of the materials mated in sliding
contact (Fig. 1). Hence, friction and wear are not inher-
ent material properties but a hction
of
parameters of
the complex system considered. It follows, that selec-
tion of a suitable ceramic and also the design of the
microstructure have to consider the specific applica-
tion.
Fig.
2
shows schematically several types of solid-
solid and solid-liquid-solid interactions on ceramic
surfaces during sliding contact. Transgranular (a) or
intergranular
(b)
microcracking due
to
mechanical
interactions of surface asperities is promoted by pores
or preexisting flaws in the surface
or
subsurface region.
Plastic deformation (c) limited on a
thin
surface zone,
mutual transfer (d) of material or wear debris and mi-
cro-abrasion (e) can occur depending on the ceramics
involved and the operating conditions, e.g. load, tem-
perature, humidity etc. Third-body layers
(f)
of aggre-
gated wear debris or tribochemical reaction films (g)
can be formed on the surfaces, e.g. aluminium hydrox-
ide
films
on alumina or
amorphous
silicon oxide films
on Sic or Si3N4, respectively. Increasing humidity or
adsorbed water molecules can result in hydrated sur-
face films (lubricious oxides) and hence low values of
friction coefficient. Smooth surfaces may be formed by
continuous removal of these
thin
reaction films (h) that
favours locally elastohydrodynamic lubrication (i) in
the presence of liquid media.
Fig.
2:
Schematic
representation
of
interactions
between
ce-
ramic solid surfaces during unidirectional sliding contact.
Mild to severe wear transition occurs during unlu-
bricated sliding of monolithic ceramics, e.g. alumina,
depending on operating conditions such as contact
load, speed and time of sliding, contact temperature
and
environment. Mechanisms of mild wear are mainly
characterized by formation and detaching of tribo-
chemical reaction films, plastic micro-deformation and
micro-abrasion. With increasing friction power (Fig.
3)
the wear intensity or the amount of wear at a given
sliding distance increases owing to initiation and
propagation of cracks resulting in localized spalling of
mated ceramics. Severe wear is connected with
high
friction coefficient and wear as a result of
trans-
andor
intergranular cracking under the
high
tensile stresses at
the rear end of the tribological contact. Wear damage
occurs at the surface or below the surface owing to mi-
cro-fracture with grain pull-outs and detachment of sur-
face layers by delamination fracture. The tribological
contact between the mated solids strongly influences
formation and time depending removal of thick third-
body layers consisting of densified wear debris.
=
,v
mm’Mm
.
. .
. . .
. . .
...
. .
.
.. . . . .
I
g
f
5
8
I
<
Friction
Pavr
Density
PY)I
--*
-
Fig.
3:
Amount
of
wear (or wear intensity) and mechanisms
of
interaction
as
a function
of
developed friction power per
unit
area.
According to modelling
[3]
the load dependent wear
transition is caused by the mechanical tensile stresses at
the rear end of the contact area and the speed dependent
wear transition by thermal stresses owing
to
frictional
heating. The severity of tribological contact can be de-
scribed by loading parameters and is influenced by
mi-
crostructure and resulting properties of the mated materi-
als. More general, the severity of tribological contact
should increase with friction power per area, i.e. the prod-
uct of contact pressure p, sliding speed v and friction coef-
ficient
p
(Fig.
3).
Without considering thermal effects, e.g.
at low sliding speeds in unlubricated sliding contact, wear
transition occurs when the mechanically applied contact
pressure exceeds the critical value which increases with
fracture toughness (short crack resistance, particularly),
and hardness but decreases with increasing fixtion coef-
ficient,
Young’s
modulus and initial defect sizes of the
mated ceramics, e.g. grain sue, pores and microcracks
[4].
For estimation
of
the relevant value of fracture tough-
ness, i.e. the material resistance to propagation
of
trans-
granular cracks or cracks at weak grain boundaries or at
interfaces of second phases, the small scale of contact,
the complex stress situation and the short crack length
of
equal to or less than grain size has to be considered.
Remembering that tribological behaviour depends on
parameters of the tribosystem used, the type of counter-
body material can be
an
important factor. Balls of AlzO3,
steel 100Cr6 or cemented carbides WC6Co were mated
with alumina
(A123)
blocks
in
unlubricated oscillating
sliding contact in laboratory air at the normal load of
80
N
[5].
Fig.
4
shows that mating
Alz03
balls with the alu-
104
mina
block resulted in a
sharp
increase in wear inten-
sity if a critical applied contact pressure was surpassed.
This
wear transition, however, was shifted to an about
four times greater value of contact pressure if using the
WC6Co ball and wear intensity increased gradually
with further increasing contact pressure. A far different
behaviour was measured if mating the 100Cr6 balls
with the monolithic alumina Al23.
No
sharp
wear tran-
sition occurred and wear intensity was relatively high
even at low values of contact pressure. Increase in wear
intensity was only moderate with increasing contact
pressure. In the order of A1203, WC6Co and 100Cr6,
hardness decreased and fracture toughness of the balls
increased. Due to their low fracture toughness, the
A1203 balls suffered a lot
of
microcracking and pull-
outs of single grains during high contact pressure and
the amount of linear wear occurred to about equal parts
on the balls and the blocks after a sliding distance of
144 m. The lowest fnction coefficient was measured on
pairs with the WC6Co balls. Worn surfaces of these
pairs displayed evidence of
thm
tribochemical reaction
layers which were rolled up during oscillating sliding
contact. These layers (maybe W03, C0W04 or more
complex [6]) offered lubricating properties and reduced
amount of wear substantially compared with the alu-
mina
block mated with A1203 balls. Two third of the
total linear wear was measured on the A1203 blocks and
only one third on the WC6Co balls. Sliding pairs with
steel 100Cr6 balls exhibited extensive wear (about
90
%)
on the balls. The steel worn by a combination of
micro-abrasion and tribo-oxidation. Material transfer
from the steel balls to the ceramic block led to sliding
contact between steelheel and/or iron oxideliron
ox-
ide, respectively, and resulted in high friction coeffi-
cient and high amount of linear wear after 144 m of
sliding. However, the sensitivity to micro-fracture
controlled wear processes at high contact pressure, i.e.
above about 1000 MPa (Fig. 4) was substantially lower
for the 100Cr6/A1203-pairs than that for the other pairs
owing to the lowest Young's modulus and hardness (or
yield strength) as well as highest fracture toughness of
the steel balls.
E
100000
-
-
-.-@
Y
.
%
d
ioooo
el
-.---
v
I
I000
I
,
f
I
I
I
10
100
I000
Instantaneous Contact Pressure
p.
MPa
Fig.
4: Instantaneous wear intensity dWl/ds (slope of the linear
wear curve
W,
versus sliding length
s)
of the alumina ceramic
A123
during unlubricated oscillating sliding contact against
A1203,
10006 and WC6Co-balls, respectively, versus calcu-
lated
instantaneous contact pressure.
MICROSTRUCTURAL DESIGN
Important microstructural parameters of engineering
ceramics are porosity, size, shape and size distribution of
grains, grain boundary phases, dispersed particles of
different morphology or fibers of a second phase, and
last but not least surface or subsurface flaws such as
isolated large scale pores, cracks or inclusions of a for-
eign substance. The effect of porosity was measured
on
self-mated
3
mol.% Y2O3-Zr02 (TZP) ceramics [7] dur-
ing sliding contact in laboratory air and at presence of
distilled water. Friction coefficient was independent but
wear intensity decreased clearly with increasing porosity
up to about 6 vol.%. At greater porosity both friction and
wear increased substantially. Studies
[8,9]
on self-mated
dense alumina and zirconia ceramics showed that amount
of wear in unlubricated sliding contact was strongly
reduced by decreasing average size of globular grains
while friction coefficient was not influenced.
Figure
5
shows the effect of average size of globular
grains
on
the critical contact pressure for onset of wear
transition [S]. Wear intensity (slope of the curve of
amount of linear wear versus length of the wear path) of
the self-mated alumina increased drastically above a
critical contact pressure. The critical value for this wear
transition was shifted to greater contact pressure with
decreasing average grain size
fiom
12.2
pm
to
0.85
pm.
Values of wear intensity in the region of severe wear, i.e.
at the high wear level, were substantially lower with the
fine-grained material.
!j
10000
5
-
5000
lJj
2000
-
1000
500
U
ZI
.3=
E
200
2
100
-
2
50
-
-
E
10
2
3
5
10
20
Instantaneous Contact Pressure
p.
MPa
Fig.
5:
Instantaneous wear intensity dWl/ds during unlubricated
oscillating sliding contact of self-mated alumina ceramics
with
average grain sizes
of
0.85
pm
and
12.2
pm,
respectively, ver-
sus
calculated instantaneous contact pressure.
Elongated grains with high aspect ratios offer effects
such as crack bridging and crack deflection while small
equiaxed grains reveal greater energy absorption ability.
Multimodal grain structures can result in self-reinforcing
effects
as
in Si3N4 ceramics. Heterogeneity of the ce-
ramic microstructure promotes crack initiation but
may
reduce crack propagation processes depending on the
loading conditions. The property of a grain boundary
phase is one key factor for the onset of wear transition.
Grain boundary phases influence grain boundary strength
and toughness as well as residual stresses or stress and
strain accommodation, respectively, at the grain inter-
105
faces under the applied tribological load. A ductile
grain boundary phase resulting
in
high grain boundary
strength and low elastic mismatch to the grains retards
crack initiation and hence the transition to severe wear.
Crack bridging and crack deflection are more important
for propagation of long cracks and hence improve the
bulk fracture toughness of the material.
the microstructure in a surface zone of a thickness of a
few hundred micrometers only. For this reason, surface
modification was carried out on commercial A1203 ce-
ramic by using a C02 laser beam. Figure
6
shows the
commercial dense A1203 ceramic AD3 and
two
surface-
modified ceramics Al24Hf and Al24TiN, respectively.
The commercial alumina ceramic A124 was surface-
modified
(200
pm thick) by laser treatment [10,11] re-
sulting in a multiphase structure of
soft
and hard phases.
The ceramic Al24Hf (1750 HV5w) contained about
25vol.-%
of
a
soft
fine lamellar eutectic A1203-Hf02
phase along the boundaries of the A1203 grains. The
ceramic Al24TiN
(1900
HV5w)
consisted of about
12
v01.-% of TiN particles
(size
of
1
to
5
pm),
16
v01.-%
of a Ti-0-A1 grain boundary phase and balance alumina.
Hardness of the microstructural modified ceramics was
clearly lower than that of the commercial reference ce-
ramic A123 (2030 HVSW).
Fig.
6:
Scanning electron micrographs
(SEM)
of
commercial
monolithic alumina ceramic A123 and the laser
surface-
modified alumina ceramics A124Hf and A124TiN, respectively.
From the foregoing it follows that a designed mul-
tiphase microstructure containing small grain size and a
proper grain boundary phase should improve tribologi-
cal performance. All tribologically induced interactions
between two solids mated in unlubricated sliding con-
tact are concentrated on a relatively
thin
surface zone.
Hence, it may be sufficient and economical to modify
Fig.
7:
Wear path on the ceramics A123 and A124Hf, respec-
tively,
caused
by
a
Rockwell
diamond
sliding
unidirectionally
under
the
normal
load of
60
N
and
the
sliding
speed
of
10
dmin.
Figure
7
shows an example how the load-bearing ca-
pacity of alumina materials under unlubricated sliding
action of a Rockwell diamond can be substantially
im-
proved by microstructural design. Creating the
soft
la-
mellar eutectic phase of 25 vol.%
in
the ceramic A124Hf
(Fig.
6)
reduced the hardness to 1750 HV, compared
with 2030
HVSW
of the commercial monolithic A1203
ceramic A123 used as reference. At the given normal
load of
60
N
and the sliding speed of 10
dmin
the
ceramic A123 failed by intergranular cracking while the
106
laser surface-modified ceramic A124Hf showed a
smooth groove (Fig.
7)
owing to plastic deformation
but no failure by microcracking.
The beneficial effect of embedding hard (TiN) and
soft
(HfOz, Ti-0-A1) phases
in
alumina on the onset of
wear transition during unlubricated sliding wear is
shown in Fig.
8.
It becomes obvious, that for both
A124Hf and Al24TiN the transition fiom mild to severe
wear or reverse occurs at substantially greater values of
the contact pressure than for the ceramic A123. Differ-
ent benefits of the second phases for the tribological
performance of the surface-modified alumina ceramic
in unlubricated sliding contact against A1203 balls can
be distinguished, e.g. grain refinement and partially
alignment of columnar grains about normal to the
loaded surface owing to laser treatment, reduction of
Young's modulus by embedding
soft
phases in the
thin
modified surface zone, improvement of grain boundary
strength and toughness as well as formation of lubri-
cious oxides (Ti02J by embedding TiN particles.
5
100000
1
,
I
.
5
fn-
10000
U
-
g-
1000
.-
In
C
Q)
C
-
;
100
2
Id
I
-
In
c
101
,
'
,
""I
I
100
1000
-
20
Instantaneous Contact
Pressure
p,
MPa
Fig.
8:
Instantaneous wear intensity dWl/ds of the ceramics
A123, A124Hf and A124TiN during oscillating sliding contact
against unlubricated
A1203
balls
(0
10
mm)
at the normal load
of
80
N
versus calculated instantaneous contact pressure p.
Figure
9
shows the influence of rel. humidity of the
surrounding air at room temperature
on
friction coeffi-
cient and amount of linear wear of the commercial
monolithic alumina A123 and the microstructurally
designed ceramic A124TiN in oscillating sliding con-
tact against A1203 balls
[lo].
Both friction coefficient
and linear wear of the pair with A123 decreased con-
tinuously with increasing humidity down to the value
at presence of distilled water in the contact area. In
contrast, for the ceramic A124TiN these tribological
characteristics were independent of humidity at and
above about 30
%
r.h. to a very good approximation
and the values were also substantially lower
in
humid
air than those of the pairs with the ceramic A123. The
favourable performance of the sliding pair
A1203/A124TiN was attributed to the fine-grained
mi-
crostructure and the grain boundary phase avoiding
micro-fiacture controlled wear processes. Instead tribo-
chemical films on the alumina matrix as well as on the
TiN particles and Ti-Al-0 grain boundary phase were
formed at sufficient humidity and resulted in low fric-
tion and wear.
Fig.
9:
Stationary values of friction coefficient
p
and
amount of
linear wear
W,*
of (a,b) A123 and (c,d) A124TiN after 144 m
of
oscillating sliding contact against
A1203
balls at the normal
load
of
40
N
and the sliding speed. of 0.02
m/s
as
a hnction of
relative humidity or distilled water, respectively.
Mechanisms of mild wear were explained by plastic
deformation, micro-abrasion and formation as well as
detaching of tribochemical films of low shear resistance
(lubricious oxides or hydroxides). Studies
[lo]
on the
A1203 ceramics A123 and A124TiN as a function of tem-
perature up to
500
'C,
showed substantially lower values
of friction coefficient and amount of linear wear of
A124 TiN at ambient temperature and above of 400 "C
than those values of the monolithic A123 (Fig.
10).
In
unlubricated sliding contact against A1203 balls, friction
and wear increased with increasing temperature from
28
"C
to 110 "C for both ceramics. The beneficial effect
of tribochemical films such as aluminium hydroxide on
alumina and/or TiOz.x on TiN particles with A124TiN
occurred
in
humid air (above about
30
%
r.h., Fig.
9)
only. Increasing test temperature reduced formation of
AlOOH surface films on A1203 and led to enhanced
friction owing to desorption of water molecules. At
400 "C and above Ti02.x films could be formed on the
TiN particles and/or the Ti-0-A1 grain boundary phase
and reduced friction coefficient.
1.4 140
5
j(a1~23
Pm
I
g
120
$b)Al'Z3
I
ES3
8.8
I
28
110
250
400
450
500
28
110
250
400
450
500
Tem~etaiure T.
'C
Temperature
T.
g:
28
110
250
400
450
500
28
110
250
400
450
500
Temperature
1.
OC
Temperat~re T.
g:
Fig.10: Stationary values of friction coefficient
p
and
amount
of
linear
wear
WI*
of (a,b) A123 and (c,d) A124TiN after 144
rn
of unlubricated oscillating
sliding
contact against
Alz03
balls
at
the
normal load
of
40
N
and
the sliding speed of 0.02
m/s
as
a
function
of
test
temperature.
107
CONCLUSIONS
Transition from mild to severe wear can be very
detrimental for the reliability of tribological perform-
ance of ceramic materials in unlubricated sliding con-
tact.
This
transition
is
caused by change of interacting
mechanisms from plastic micro-deformation, micro-
abrasion and tribofilm formation
to micro-fracture with
grain pull-outs,
grain
comminution, formation of third-
body layers and delamination fracture of surface layers.
The examples of experimental results on alumina ce-
ramics showed that
this
transition in wear behaviour
can be delayed or even avoided by microstructural
design depending on the operating conditions of the
ceramic components considered.
ACKNOWLEDGEMENTS
These studies were supported by the Ministerium
flir
Wissenschaft und Forschung des Landes Baden-
Wiirttemberg in the scope of the
KKS
programme and
are now supported by the Deutsche Forschungsgemein-
schaft (DFG) in context with the Sonderforschungs-
bereich SFB 483 ‘‘High performance sliding and fric-
tion systems based on advanced ceramics”.
REFERENCES
S.
Jahanmir,
X.
Dong, Mechanism
of
mild to
severe wear transition in a-alumina. J. Tribol.,
114(1992)403-411.
S.M. HSU, Y.S. Nagarajau, Haiyan Liu and
Chuan He, Microstructural design
of
ceramics
for wear. Proc. Intern. Tribology Conf. Yoko-
hama 1995,427-432.
N. Chen, K. Adach and K. Kato, Transition
mechanisms of wear modes in sliding of ceram-
ics. Proc. Intern. Tribology Conf., Yokohama
1995,409-414.
K.-H. Zum Gahr, Modelling and microstructural
modification of alumina ceramic for improved
tribological properties, Wear
200
(1996) 215-
224.
K.-H. Zum Gahr and
J.
Schneider, Multiphase
A1203 ceramic with
high
resistance to unlubri-
cated sliding wear. Proc. Intern. Tribology
Cod, Yokohama 1995,397-402.
H. Engqvist et al., Tribofilm formation on ce-
mented carbides in
dry
sliding conformal con-
tact. Wear 239 (2000) 219-228.
W. Bundschuh and K.-H. Zum Gahr, Influence
of porosity on friction and sliding wear of
tetragonal zirconia polycrystal. Wear 15 1
(1991) 175-191.
K.-H. Zum Gahr, W. Bundschuh and B. Zimmer-
lin, Effect of grain size on fiiction and sliding
wear of oxide ceramics. Wear 162-164 (1993)
269-279.
A. Krell, D. Klaftke, Effects of grain size and
humidity on fretting wear in fine-grained alumina,
A120JTiC, and zirconia.
J.
Am.
Cem SOC. 79
[5] (1996) 1139-1 146.
I.T. Lenke and K.-H. Zum
Gahr,
Mit TiN-
Partikeln lasermodifizierte A1203-Keramik
im
re-
versierenden Gleitkontakt unter Variation der
Luftfeuchte und der Temperatur. Mat.-wiss. u.
Werkstoffiech. 29 (1998) 57-65.
K.-H. Zum Gahr,
J.
Schneider: Surface modifica-
tion of ceramics for improved tribological proper-
ties. Ceramics International 26 (2000) 363-370.
Lifetime Prediction for Silicon Nitride
Sheldon
M.
Wiederhorn
National Institute
of
Standards and Technology
100
Bureau Drive.
Gaithersburg,
MD
20899-8500
ABSTRACT
This paper reviews lifetime prediction methodologies
for high-temperature structural ceramics. The
methodologies consider failure from subcritical crack
growth at low temperatures,
~800
"C to
1000
"C, and
creep, or creep-rupture at high temperatures. The paper
discusses three methods of characterizing crack growth
in
silicon nitride: dynamic fatigue, static fatigue and a
statistical analysis of lifetime. These techniques yield
comparable results, suggesting that dynamic fatigue is
the preferred procedure for characterizing crack growth.
In
the second part, the paper discusses a strain-based
methodology for lifetime prediction. The effect of creep
on
acceptable engineering temperatures and stresses is
considered for an allowable strain of
0.5%
and a failure
probability of
0.0001.
For a given stress and failure
time, a reduction in operating temperature of as much as
40
"C
is needed when strain rather than creep rupture is
considered as the failure criterion.
An
additional
25
"C
reduction is needed to limit the failure probability to
0.0001.
INTRODUCTION
Silicon nitride was developed originally as a
material for gas turbines and is supposed to be
competitive with air-cooled superalloys that can operate
in turbines with inlet temperatures in excess of
1300
"C.
To be economical, silicon nitride has to be used in an
uncooled state and must be resistant to creep,
creep-rupture and corrosion at high temperatures.
In
addition, because stresses can be very high during heat-
up and "trip" conditions, it also has to be resistant to
failure at low temperatures, where brittle rupture and
subcritical crack growth are problems.
Many of these goals have been achieved. Today,
several commercial grades of silicon nitride have the
requisite fracture toughness and resistance to subcritical
crack growth needed for structural reliability at low
temperatures, and, therefore, are also suitable for high
temperature operation. To be sure, there are still serious
problems that must be overcome before silicon nitride
can be used in turbines. Coatings must be developed to
protect silicon nitride from water attack by
high-pressure steam at elevated temperatures, and
improved toughness under severe impact conditions is
necessary to resist impact by metal pieces ingested or
generated by turbines during operation'. These
problems are currently being investigated in a number
of industrial and government laboratories.
To ensure long term reliability, techniques to
predict lifetime also had to be developed. Over the
years, two general methods of lifetime prediction were
developed; one is based
on
toughness, strength and
crack growth susceptibility, the other
on
parameters
related to creep and creep rupture behavior. Other
modes of failure in ceramics (pit formation due to
oxidation*, evaporation of Sic and Si3N4 due to water
attack', surface damage due to hard particle impact',
etc.)
are
not considered here. No general method of
handling these causes of failure has yet been developed.
The first set of methods, is fracture mechanics
based. Subcritical crack growth from microstructural
defects normally present in the body
is
assumed to limit
lifetime. Under the influence of external stresses, cracks
grow from the defects until they reached a critical size,
at which point crack growth accelerates and failure
occurs. Using the framework of fracture mechanics,
relationships were developed to describe lifetime as a
function temperature and applied stress. Although the
theory of fracture mechanics is used,
no
prior
knowledge of the underlying causes of subcritical crack
growth is required for the method. Simple power-law
equations of applied stress and failure stress are used
for lifetime prediction.
The second method of lifetime prediction applies to
failure
at
elevated temperature and is based
on
the creep
and creep rupture behavior. Lifetime is predicted from
the
creep behavior, either by assuming a fixed strain to
failure (the part becomes too large for its function), or
from an empirical relationship between creep rupture
lifetime and creep rate,
e.g.,
the
Monkman-Grant
relationship3. The form of the creep equation is based
on
a theoretical treatment of creep behavior. Therefore,
the better the prediction of creep rate, the more accurate
the lifetime prediction.
Finally, both techniques just mentioned give a
median or average prediction of lifetime.
In
real design
situations, knowledge of
the
scatter in lifetime
prediction is needed in addition to the mean or median
prediction. This requirement necessitates the use of
statistics in the lifetime prediction scheme
so
that
lifetime can
be
predicted at low failure probability. The
techniques that are used for high and low temperature
predictions differ because the modes of failure differ
substantially.
In
this paper, we discuss the techniques that are
used to predict component lifetime and the scatter
in
lifetime. Two modes of failure are assumed4. At low
temperatures subcritical crack growth from preexisting
defects is assumed to be the main cause of failure. At
109
high temperatures failure is assumed to occur as a
consequence of creep, which can either cause the part to
be too long for the engine,
or
can result in rupture from
creep induced damage. A discussion of these two
modes of failure
starts
the paper. The paper ends by
dealing with scatter in lifetime, showing how low
temperature scatter
in
strength determines the maximum
stress that can be applied to a component, while high
temperature scatter establishes the maximum
temperature. All data discussed in this paper were
obtained on current commercial grades of silicon
nitride'.
100
7
10
9
&
r;(
m
1;
FAILURE BY SUBCRITICAL CRACK GROWTH
In ceramics, fracture at low temperatures is usually
preceded by crack growth from flaws
or
cracks present
at surfaces. Crack growth is normally a consequence of
a corrosive environment (water for glass), but can also
occur
in
a vacuum
or
another inert environment'.
Because crack growth precedes catastrophic failure, a
delay to failure is observed in components subjected to
static loads. The delay is the time required for a crack to
grow from the initial to the critical crack size.
Subcritical crack growth also leads to a time
dependence of the strength: the faster a material is
loaded, the stronger it is. A logical framework for
understanding subcritical crack growth and for
designing structural materials is provided by the science
of fracture mechanics, which is summarized in many
excellent texts6*
'.
The principal assumptions behind the lifetime
prediction methodology are:
c
;
0
0
0
Microstructural defects are present from which
cracks grow.
The crack growth velocity is determined by the
crack-tip stress intensity factor,
KI.
Failure occurs when the crack reaches a critical
size, such that
KI=Klc
and
dKJdc>O,
where
c
is the
size of the crack and
KIC
is the critical stress
intensity factor.
The crack tip stress intensity factor is related to the
crack size by
K,=OYC'~,
while
the
crack velocity,
v,
is
related to
Ki
by
v=v,(Ki /KO)"
exp(-Qf /RT).
The
constant,
U,
depends on the geometry of the crack. The
constants
v,
and
K,
are normalization constad.
For any size crack, the strength
or
failure stress of
the material,
S,
can be defined in terms of the size of the
crack:
S=
KI&c'R.
In case of a stress gradient,
the
failure stress is defined at the site of the fracture origin.
The equation also assumes the material has a flat
R-
curve. The failure stress can be measured in an inert
environment
so
that crack growth is negligible prior to
failure. The equation relating failure stress,
S,
and
crack size,
c,
is important since it shows that as the
crack gets longer the failure stress decreases.
*
The use of commercial designations is for purposes of
identification only and does not imply endorsement by
the National Institute of Standards and Technology.
These fracture mechanics relationships can be
combined to give an equation relating the failure stress,
S,
at any time,
t,
to the applied stress,
0,
in the as-
received part':
t/
S"-'
=Sin-'
-[exp(Q f/RT)](l/B)
jo"(t)dt,
(1)
where
B
=
2K
,"
/[(n
-
2)v,
Y
K
c-2
]
is constant for a
given environment. The equation is integrated from the
time at which load is first applied to the time for failure,
q.
The equation demonstrates that failure stress can be
determined if the time dependence of the applied stress,
o,
is known. Equation
1
can be used to determine
lifetime for constant load, constant loading rate and
cyclic load (of various forms). It can also be used to
determine constants,
n
and
B,
which are needed for the
prediction of lifetime. The remainder of this section
discusses the use of equation
1
for
determining the
constant
n
and for evaluating the statistical uncertainty
in predicting lifetime.
The time to failure,
q,
under a constant load is:
where
Q
is the applied stress and
Si
is the initial failure
stress.
The equation also suggests a method of obtaining
these constants. Applying a range of stresses to a
number of tensile
or
flexure specimens the times to
failure are measured. Then, expressing equation
2
in
logarithmic form, a plot of the failure time as a function
of the applied stress yields a straight line
with
a slope of
-n
and an intercept of
BS:-2exp(Qf/RT).
An estimate of
n
for AS800 (AlliedSignal,
Torrance, CA) is given in Fig.
1,
where a constant stress
was applied to tensile specimens at
900
"C and stresses
of 450 MPa, 475 MPa and 500 MPa. The straight line
was fitted to the median value of each set of stress data,
yielding a value for
n of 75. A problem with the use of
static loading for the determination of
n
is the enormous
scatter in lifetime often observed for silicon nitride',
about
6
orders of magnitude in Fig.
1.
To
reduce the
effect
of
scatter, median values of the data are usually
fitted to obtain
n. An advantage of the static fatigue
approach is that real flaws and cracks grow at the rates
likely to be experienced in service failure conditions.
0
tf
=
Ba-"S1-2exp(Qf /RT),
(2)
2s
+
1000
1
400
500
App
bed
Stress,
MPa
600
Fig.
1
Static fatigue of AS800 tested at
900
TI3.
110
The most popular approach to obtaining the crack
growth sensitivity,
n,
is the so-called dynamic fatigue
technique,
in
which specimens are loaded to failure at
several constant-stressing rates. This technique has the
advantage over the constant load technique in that
experiments are relatively rapid and scatter in the
failure stress is relatively small. Furthermore, there
are
no
run-outs or loading failures. Substituting
CJ
=
bt
into
equation
1,
yields an equation for the time to failure
under constant loading rate:
tf
=
(n
-2)Ba-"S;-*exp(Qf/RT).
(3)
+
But for the coefficient, 12-2, equation 2 and
3
are
the same. Thus, the failure time for the same breaking
stress in a constant stressing rate experiment is
substantially shorter than
in
a constant stress
experiment. However, the use of short-term data to
represent a long-term process can be questionable if
long-term processes occur that are undetected by the
short-term test.
Substituting
t
=
d6
into equation 3, yields the
equation that represents failure stress as a function of
stressing rate:
IIIIIIII
From a logarithmic plot of applied stress as a
function of
b
,
the slope of the line fitted to the
stressing rate data is
l/(n+l).
Another approach to obtain
n
is to statistically
analyze the distribution of failure times; we refer to this
technique as the Weibull in Time technique. Because
failure initiates from pre-existing flaws,
the
distribution
of these flaws controls both the times to failure,
q,
and
the distribution of failure stresses,
Si,
when
the failure
stress is measured
in
an inert environment. Failure
stresses are often expressed in terms of a two-parameter
Weibull distribution":
where
rn
is the Weibull modulus and
So
is the
characteristic strength. Substituting equation
5
into
equation 2, gives the failure time in terms of failure
probability:
tf
=to[ln(l-Pi
(6)
The two parameters,
m'
and
to,
are given by
rn'=rn/(n-2) and
t0=BS,"'dnexp(Qf
RT),
respectively.
Equation
6
will be used later to obtain constant times to
failure at a fixed probability level. These are the curves
that are needed for component design. Normally, a
failure probability of one part in ten thousand is the
minimum acceptable level for the design of industrial
gas turbines.
The crack growth parameter,
n,
can now be
determined
if
both the failure stress and the time to
failure are expressed in terms of Weibull distributions.
Once
rn
and
rn'
have been determined,
n
can be
calculated from the relationship rn'=ml(n-2)6v
*,
'Iv
12.
Weibull analyses of the failure times were obtained
for the data shown
in
Fig.
1
and straight lines were
fitted to
the
data to obtain
m',
Fig. 2.13 Values for
m'
are given in Table 1 for AS800 (Honeywell, Torrance,
CA) and SN88 (NGK Insulator, Nagoya, Japan). The
Weibull modulus for AS800 at room temperature was
17,
that
of
SN88 was
9.7.14
Using
rn'=m/(n-2),
values
of
n
are found to range from
60
to 81, for the data
shown in Fig. 1. These compare favorably with the
value for
n
of
75
obtained by a linear regression of the
median values of the times to failure. The parameter,
n,
was determined to be
55
by constant stressing rate
experiments (dynamic fatigue). Values of
n
at the
0.05
and
0.95
confidence level were determined for the
Weibull in time method
(no5=37;
n95=83.
900
"C,
475
MPa) and for the dynamic fatigue method
(no5=40;
n95=88). There is
no
statistical difference between
values of
n
obtained by the techniques.
h
I
m'4.30
In
(Time
to
Failu re, h
)
Fig.
2:
Weibull diagram, failure times for AS800,
900
"C,
475
MPa13.
Table
1:
Static fatigue Data
on
AS800 and SN88I3
T "C Stress, MPa
900
500
475
450
425-475
0.05
-
50
MPdS
700
500
900
525
AS800
0.24 75
Weibull
in
Time
0.30
60
Weibull
in
Time
0.22 81 Weibull in Time
Method m'
n
75
Equation2
55
Equation4
0.19 93
Weibull
in
Time
SN88
0.22
61
Weibull
in
Time
900 500 0.18
55
Weibull
in
Time
FAILURE
BY
CREEP
Two boundary conditions exist for the prediction of
lifetime by creep. The first is that the component
breaks during the creep process. This is an important
mode of failure in ceramic materials, which are
inherently much more brittle that metallic materials.
The second mode of failure is that the dimensions of
part exceed a critical strain during the creep process,
so
that it becomes too large for the particular application.
A complete solution of failure by creep-rupture
requires knowledge of the failure mechanisms and the
relation between the failure mechanism and the creep
rate. Such knowledge of failure modes is not available
111