Fatigue lives at elevated temperatures are often shortened by creep and/or oxidation. Creep causes grain boundary void nucleation and grain boundary cavitation. Grain boundary voids and cavities will accelerate fatigue crack nucleation and propagation, and thereby shorten fatigue life. The functional relationships between the damage rate of fatigue crack nucleation and propagation and the kinetic process of oxygen diffusion depend on the detailed physical processes. The kinetics of grain boundary oxidation penetration was investigated. The statistical distribution of grain boundary penetration depth was analyzed. Its effect on high temperature fatigue life are discussed. A model of intermittent micro-ruptures of grain boundary oxide was proposed for high temperature fatigue crack growth. The details of these studies are reported

Liu, H. W.

Oshida, Yoshiki

English

NASA Technical Reports Server

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Grain Boundary Oxidation
and Its Effects on
High Temperature Fatigue Life*
H.W. Liu and Yoshiki Oshida
Department of Mechanical and Aerospace Engineering
Syracuse University
INTRODUCTION
Fatigue lives at elevated temperatures are often shortened by creep and/or
oxidation. Creep causes grain boundary void nucleation and grain boundary
cavitation. Grain boundary voids and cavities will accelerate fatigue crack
nucleation and propagation, and thereby shorten fatigue life.
Gibb's free energies of metal oxide formation are negative. No metal or alloy is
stable when exposed to an oxidizing environment. Grain boundary is a path of rapid
diffusion. Therefore, grain boundary oxidation rate is higher and grain boundary
oxide penetration is deeper. Oxide is brittle and fractures easily when a tensile
stress is applied. Grain boundary oxide crack may serve as a nucleus of a fatigue
crack and the crack nucleus will grow by the subsequent cyclic fatigue load.
Therefore, grain boundary may shorten fatigue crack nucleation life. Oxidation also
accelerates fatigue crack propagation. Hence, grain boundary oxidation will shorten
fatigue lives at elevated temperatures.
Both oxidation and creep have been shown as possible mechanisms for high
temperature fatigue damage. Grain boundary void formation and cavitation are the
result of surface diffusion and/or grain boundary vacancy diffusion, while grain
boundary oxidation is primarily caused by the diffusion of oxygen. The kinetics of
the diffusions of vacancies and oxygen atoms is shown schematically in Figure (I) .
One mechanism dominates in the high temperature region and the other dominates in the
low temperature region. Therefore, the question is not which one of these two
mechanisms causes high temperature fatigue damage. The problem is to define the
lifferent regions dominated by these two different mechanisms.
The functional relationships between the damage rate of fatigue _rack nucleation
and propagation and the kinetic process of oxygen diffusion depend on the detailed
ohy3ical processes. In this study, the kinetics of grain boundary oxidation
_enetration was invetigated. The statistical distribution of grain boundary
_enetration depth was analyzed. Its effect on high temperature fatigue life will be
ii3scussed. A model of intermittent micro-ruptures of grain boundary oxide was
proposed for high temperature fatigue crack growth. The details of these studies are
_e_orted in references 1 and 2.
?:crk done under NASA Grant NAG3-348
407
https://ntrs.nasa.gov/search.jsp?R=19890003547 2020-03-20T04:34:25+00:00Z
GRAIN BOUNDARY OXIDATION KINETICS AND ITS
EFFECTS ON FATIGUE CRACK NUCLEATION
Cylindrical coupons of a nickel-base superalloy (TAZ-8A) were subjected to
;xidation in air under the stress-free condition. The oxidized disk coupons were
sec<ioned, each sectioned surface was examined under an optical microscope, and the
maximum grain boundary oxide penetration depth, ami of the ith section was measured.
Then a thin layer of coupon approximately 80_m was removed. Then the new surface was
polished, and another ami of the new surface was measured. This process was repeated
12 times for each test coupon to collect enough data for the statistical analysis
Couling and Smoluchowski (ref. 3) and Turnbal and Hoffman (ref. 4) have found that
7rain boundary diffusion penetration is a function of the angle of (I00) tilt
h_undaries. Therefore, it is expected that the grain boundary oxide penetration
!epth, am, is not uniform. It varies from one grain boundary to another. Figure 2
shcws the Weibull plot of 480 data points for oxidation at 800°C for 500 hours. The
data fits the Weibull distribution function very well.
[lami[! - P(ami) ] = exp - an (ami -au)b 1= exp - Ha (i)
?(ami) is the probability of finding an oxide depth less than ami on a sectioned
surface. The probability of finding a depth equal to or deeper than ami i_
[i - P(ami)]. For the data in Figure 2, b = 2.0, a u = 40_m, and a o = 31 _m.
Grain boundary diffusion is several orders of magnitude faster than bulk
!iffusion. If the flux due to bulk diffusion is neglected, grain boundary diffusion
can be considered a channeled one-dimensional flow. With a constant oxygen
concentration C o at the "entrance" of the grain boundary, the oxygen concentration in
the boundary is
C(x, t) = C o [i - erf( _x
24Dgbt)] (2)
where erf is the error function, Dg b is the grain boundary diffusion coefficlent.
"Bulk" oxide will be formed when the oxygen concentration reaches a certain critical
value, C c. According to Equation (2),
x c
C c = C o [i - erf(2--_t) ] (3)
x c is the depth of the oxide penetration, where C = C c. According to Equation (3),
the quantity (Xc/Dgbt) must be a constant, and x c must be proportional to _Dgbt
[herefore, the grain boundary oxide penetration must be proportional to _;t.
However, the model does not take the bulk diffusion and the chemical process
into :onsideration. Perhaps it is reasonable to assume that ami is proportional to
(Dgbt)n. Therefore ami must have the form
_r
ami Dgbt
B B
n
(4a)
nAH n Qami : _i tn exp (- _ ) = [_i t exp(- ) (4b)
is -_he magnitude of the diffusion jumping vector or interatomic spacing.
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The grain boundary oxide penetration depths were measured at the oxidation
temperatures of 600, 800, and I000°C at the exposure time from 100 to i000 hours.
The regression analysis of the data gives the following empirical relation
ami(Cm) = 1.34 × 10 -3 t 0"25 exp(-4.26/RT) (5)
where t is in seconds, the activation energy in kcal/mol, and T in OK. The
coefficient of auto-correlation is 0.96.
Assume the relation between ami, t, and T is deterministic. The deviation of
each measured penetration depth from the empirical relation can be lumped into the
term (_i in Equation (4b) .
_i = ami t-n exp(Q)
(6)
At any temperature T and exposure time t, with the measure ami known, the value of _i
can be calculated from Equation (6). The data of 144 values of _i fit well the
Weibull distribution function as shown in Figure (3).
___ (_ - _u )b[i - Pi(_)] = exp [- ( )b] = exp [ _
] (7)
Pi(_) is the probability of finding an _-value less than _.
are 1.85, 0.53 x 10 -3 and 0.51 x 10 -3 respectively.
The value of b, a u, _o
The maximum _-value along the periphery of the i'th sectioned surface can be
considered as the _i-value of an exposed area of _Sd of a test coupon. 6 is the
coupon diameter and d is the grain size. Another sectioned surface at a distance one
grain diameter away contains an entirely different set of grain boundaries and it is
another independent sample.
If Ps(_) is the probability of finding an a-value less than _ on an exposed area
s. Ps(e) is related to Pi(_)
[I - Ps(_)] = [i - Pi(_)] s/K6d (8)
The value of Ps(_) might be taken as the value of Ps(a), the probability of
finding a penetration depth less than a on an exposed surface area s. Therefore the
_ata measured from the test coupons can be used to extrapolate to a much larger
surface area of an engineering component.
Oxide is brittle and fractures easily under a tensile stress. Once an oxide crack
is formed, the crack will continue to grow under a cyclic fatigue load. The oxide
track can be considered as a precrack. The remaining fatigue life, Nfao of a
orecracked specimen or a precracked engineering component is a function of the
precrack size, a o
Nfao = f(ao ) (9)
Yhe orobability of having fatigue life Nfa ° is also the probability of having an
D:<ide crack size a O . Therefore, the statistical scatter of the fatigue lives at
elevated temperatures may reflect the scatter of the oxide penetration depth.
4O9
A fatigue crack is often nucleated by cyclic plastic deformation. This
nucleation mechanism is cylcle dependent. The damage mechanism by oxide crack
formation is time dependent. Therefore, for a very low cyclic frequency, the oxide
c_ack formation may preceed the fatigue crack nucleation by the cyclic plastic
formation process. Thus the fatigue nucleation life (in terms of number of load
zycles) might be shortened. Perhaps, the shortened fatigue life at elevated
temperatures and the wide scatter of the fatigue life of engineering components are
caused by grain boundary oxidation.
THE INTERMITTENT MICRO-RUPTURE MODEL FOR HIGH TEMPERATURE FATIGUE CRACK GROWTH
Figure (4) shows the frequency effect on fatigue crack growth rate for a number
of high temperature alloys. For each data set, both _K and test temperature were
maintained constant.
In the low frequency region, the fatigue crack growth rate, da/dN, of Inconel
718, Znconel X-750, Astroloy at 700 and 760°C, and Cr-Mo steels, are inversely
proportional to frequency, V. The time rates of the fatigue crack growth, da/dt =
(da/dN) (l/v) are constant. In this region, the fatigue crack growth is
intergranular.
For constant-K tests at elevated temperatures, two crack growth features are
common: (i) the time rate of crack growth is constant, (i.e. da/dt = constant) and
(ii) crack growth is intergranular. Crack growth at constant-K is often referred to
as creep crack growth. Fatigue crack growth in the low frequency region has these
two same features. Therefore, fatigue crack growth in the low frequency region
is often referred to as creep crack growth.
One question can be raised. Do the inverse relation between da/dN and v and the
intergranular crack growth preclude grain boundary oxidation as the underlying cause
of the accelerated fatigue crack growth at elevated temperatures? In this section, a
fatigue crack growth model, based on the fracture of grain boundary oxide, will be
constructed. The model agrees with the inverse relation between da/dN and v. The
fracture path following the grain boundary oxide, is intergranular.
In Figure (4), the cyclic loading patterns are also shown. For Inconel 718 and
Astroloy at 760°C, a hold time, _t H at Kma x was applied. For Inconel X-750, Cr-Mo
steels, and Astroloy at 700°C, a triangular loading pattern was used. The crack
growth with a hold time will be analyzed first.
Uhe oxygen arriving at a crack tip will have to diffuse into the region ahead of
_he zrack tip in order to form oxide along the grain boundary. When the crack tip
_r_in boundary oxide reaches a critical size, 6a, the oxide will rupture and the
_rack will grow by the amount, 6a. The critical size, 6a, depends on the K-level
!uring the hold time. Once the crack tip advances to its new position, this process
_f grain boundary diffusion, grain boundary oxidation, and the micro-rupture of the
_rain boundary oxide will be repeated again. This process of micro-rupture of crack
%!p grain boundary oxide can reoccur intermittently many times during a fatigue
_ycle.
During At H at Kmax, many micro-ruptures will take place. After each micro-
c,i_ture, the penetration of grain boundary oxide will have to start all over again
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from "time" zero.
size 8a is
Therefore, the time interval, 8t necessary to reach the critical
6t = (B/Dg b) (_al_B) i/n
(I0)
The number of micro-ruptures during &t H is
m = AtH/_t = (At H Dgb/B)(_B/_a)I/n
(Ii)
m is linearly proportional to At H and is inversely proportional to v.
Fatigue crack growth per cycle is the sum of the micro-ruptures during At H.
d a = m_a (12)
dN
From Equations (10, ii, and 12), we obtain
da = _,_t H Dg b (B/_a) (1-n)/n = _, (Dgb/V) (B/6a) (1-n)/n (13)
da/dN is inversely proportional to v. For n=0.25, da/dN is inversely proportional to
6a 3. Fatigue crack growth rate increases rapidly as _a becomes small. 6a is smaller
if the oxide is more brittle, if the flow stress of the material is higher, and if
the crack tip stresses are in the state of plane strain•
Figure (5) shows the triangular loading patterns of two different frequencies.
The time interval _t i at K i is inversely proportional to v. We treat _t i as the hold
time at K i. If the crack tip fields at K i are the same at both of these two
frequencies, the number of micro-ruptures during _t i is linearly proportional to _t i
and is inversely proportional to V. This must be true at every Ki-level. Fatigue
crack growth is the sum of all of the micro-ruptures at all the Ki-levels during one
fatigue cycle. Therefore da/dN is inversely proportional to v. Fatigue crack growth
follows the path of grain boundary oxide, therefore, it is intergranular.
We have shown grain boundary oxidation as a possible mechanism of high
temperature damage that shortens fatigue life. Our work is only one of the many
steps toward the construction of a quantitative model based on the physical damage
processes caused by oxidation.
Only after the quantitative models of the physical processes of fatigue damage
due to creep and oxidation are completed, we will be able to predict high temperature
fatigue life accurately and with confidence. The quantitative relations between the
!illusion rates of vacancies and oxygen, the rate of oxide rupture, the rate of
nucleation and growth of voids and cavities, and the rate of fatigue damage have not
yet been established•
without a clear understanding of the underlying physical prbcesses for the
th3erved fatigue behaviors, it is difficult and unsafe to extrapolate a limited
amount of experimental data for fatigue life predictions. For example, to
extrapolate the crack growth rate in Figure (4), from the low frequency region into
_he high frequency region or vise versa will underestimate the growth rate.
Therefore it is unsafe.
411
REFERENCES
I. Oshida, Yoshiki; and Liu, H.W.: Grain Boundary Oxidation and an Analysis of the
Effects of Oxidation on Fatigue Crack Nucleation Life. To be published in the
Proceedings of the ASTM Symposium on Low Cycle Fatigue: Direction for Future
Research, Lake George, NY., Oct. 1985.
2. Liu, H.W.; and Oshida, Yoshiki: Grain Boundary Oxidation and Fatigue Crack Growth
at Elevated Temperatures. To be published in the Jour. of Theoretical and Applied
Fracture Mechanics.
3. C©uling, L; and Smoluchowski, R.: Anisotropy of Diffusion in Grain Boundaries
J. Appl. Phys., 25, p.581, 1954.
4. Turnbull, D; and Hoffman, R.: The Effect of Relative Crystal and Boundary
Orientations of Grain Boundary Diffusion Rates. Acta Met., 2, p.419, 1954.
InR
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Figure i. Schematic illustration of diffusion kinetics of vacancies and oxygen atoms
412
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95
90
80
70
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5O
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I 2 3 4 5
W
A
A
i/
i
,,,,
2 3 4 5 6 7 8910 2 3 4'1 ", 6 7 69 W
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, Oral (_m) 1
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Figure 2. Weibull plot of ami (i = 480)
0
99
95
90
60
7O
6O
50
4O
3O
_ 2o
I0
2 3 4 5 6 7 89 2 3 4 5 6 789
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Figure 3. Weibull plot of _i (i = 144)
413
!0 "1
ld 2(D
(J
10.3
Z
E}
E3 Jd4
'1 ' • JEOMELX-?'JO 6SO 30 /VVVVV (44) I
• ' "_I .... I .... (_ INCONELX-7_JO 6_0 30 _ (4_) I
760 50 /-V-'V- (4_ I
• AST_LOY 6 5 0 _ O /-'V'-V-" (46)
-& ASTROLOY ? 0 0 I 0 A/_VVV (47}
n 3o4s.s 53e 30 /VVV_V (48_
• WIISPALOY 649 30 _ (41)
_, _ v ',.c.-Mo-vsn_L_s 5 ,o A/VVvV (4n
• %."
• _ %... D o _,
" •
%
V V
,I .... I .... I , , ,,I , , , ,I .... ! i
-4
,o ,63 ,62 ,6' _o Io'
Frequenc y (cycle/sec)
Figure 4. Frequency effect on fatigue crack growth
K
\ /
Figure 5. Triangular loading patterns of two different frequencies
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Grain boundary oxidation and its effects on high temperature fatigue life

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