Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep
Holding periods of 300 and 3600 s in a trapezoidal load cycle are shown to increase the crack growth rate dozens of times for alloy EP962 and several-fold for alloy EP742 at a temperature of 973 K. It is demonstrated that in the presence of the first portion on the creep crack growth diagram, whereo...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2009
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irk-123456789-484692013-08-20T06:48:12Z Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep Pokrovskii, V.V. Sidyachenko, V.G. Ezhov, V.N. Kulishov, S.B. Научно-технический раздел Holding periods of 300 and 3600 s in a trapezoidal load cycle are shown to increase the crack growth rate dozens of times for alloy EP962 and several-fold for alloy EP742 at a temperature of 973 K. It is demonstrated that in the presence of the first portion on the creep crack growth diagram, whereon the crack growth rate decreases, the crack growth kinetics for a trapezoidal load cycle can be predicted using the hypothesis of the linear summation of fatigue and creep crack growth rates provided that the peculiarities of the first portion of the creep crack growth diagram are taken into account. Empirical approaches are proposed for determining the mean crack velocity in the first portion of the creep crack growth diagram. Установлено, что наличие участков выдержки 300 и 3600 с в трапецевидном цикле нагружения при температуре 973 К приводит к повышению скорости роста трещины. Показано, что при наличии на диаграмме роста трещины ползучести первого участка, на котором наблюдается снижение скорости роста трещины, можно прогнозировать кинетику ее роста для трапецевидного цикла нагружения на основании гипотезы линейного суммирования скоростей трещин усталости и ползучести. При этом необходимо учитывать особенности первого участка диаграммы роста трещин ползучести. Предложены эмпирические подходы к определению средней скорости роста трещины на первом участке диаграммы. 2009 Article Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep / V.V. Pokrovskii, V.G. Sidyachenko, V.N. Ezhov, S.B. Kulishov // Проблемы прочности. — 2009. — № 1. — С. 105-112. — Бібліогр.: 19 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48469 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Pokrovskii, V.V. Sidyachenko, V.G. Ezhov, V.N. Kulishov, S.B. Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep Проблемы прочности |
| description |
Holding periods of 300 and 3600 s in a trapezoidal load cycle are shown to increase the crack growth rate dozens of times for alloy EP962 and several-fold for alloy EP742 at a temperature of 973 K. It is demonstrated that in the presence of the first portion on the creep crack growth diagram, whereon the crack growth rate decreases, the crack growth kinetics for a trapezoidal load cycle can be predicted using the hypothesis of the linear summation of fatigue and creep crack growth rates provided that the peculiarities of the first portion of the creep crack growth diagram are taken into account. Empirical approaches are proposed for determining the mean crack velocity in the first portion of the creep crack growth diagram. |
| format |
Article |
| author |
Pokrovskii, V.V. Sidyachenko, V.G. Ezhov, V.N. Kulishov, S.B. |
| author_facet |
Pokrovskii, V.V. Sidyachenko, V.G. Ezhov, V.N. Kulishov, S.B. |
| author_sort |
Pokrovskii, V.V. |
| title |
Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep |
| title_short |
Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep |
| title_full |
Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep |
| title_fullStr |
Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep |
| title_full_unstemmed |
Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep |
| title_sort |
theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2009 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/48469 |
| citation_txt |
Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep / V.V. Pokrovskii, V.G. Sidyachenko, V.N. Ezhov, S.B. Kulishov // Проблемы прочности. — 2009. — № 1. — С. 105-112. — Бібліогр.: 19 назв. — англ. |
| series |
Проблемы прочности |
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| first_indexed |
2025-07-04T08:59:21Z |
| last_indexed |
2025-07-04T08:59:21Z |
| _version_ |
1836706233594150912 |
| fulltext |
UDC 539.4
Theoretical-Experimental Model for Predicting Crack Growth Rate
in Structural Alloys under Combined Action of Fatigue and Creep
V. V. P okrovsk ii,a V. G. S idyachenko,a V. N. Ezhov,a and S. B. K ulishovb
a Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine,
Kiev, Ukraine
b Zorya-Mashproekt (State Research and Production Center for Problems of Gas Turbine
Construction), Nikolaev, Ukraine
Holding periods o f 300 and 3600 s in a trapezoidal load cycle are shown to increase the crack
growth rate dozens o f times fo r alloy EP962 and several-fold fo r alloy EP742 at a temperature o f
973 K. It is demonstrated that in the presence o f the first portion on the creep crack growth
diagram, whereon the crack growth rate decreases, the crack growth kinetics fo r a trapezoidal load
cycle can be predicted using the hypothesis o f the linear summation o f fatigue and creep crack
growth rates provided that the peculiarities o f the first portion o f the creep crack growth diagram
are taken into account. Empirical approaches are proposed fo r determining the mean crack velocity
in the first portion o f the creep crack growth diagram.
K e y w o r d s : crack, trapezoidal cycle, creep-fatigue interaction.
In tro d u c tio n . Analysis o f the state o f the problem revealed that at present
the issues concerning prediction o f the crack growth kinetics under high-
tem perature fatigue and long-term static loading are the best elaborated ones
[1-3]. Less well understood are the problems o f creep crack development in
materials that fracture in a brittle mode [4-6]. Also, there is a lack o f experimental
data and theoretical generalization on crack propagation for a trapezoidal load
cycle with various hold periods under m aximum load [7, 8]. The m ajority of
researchers in this case restrict themselves to the use o f the linear damage
summation hypothesis based on the independent damaging effect o f fatigue and
creep [2, 9]. Sometimes, they determine the m aterial susceptibility to a certain
mode o f fracture (fatigue or time-dependent) and, on this basis, choose the
fracture mechanics parameters to describe experimental crack growth rate data
[10, 11]. It is noteworthy that such approaches do not always yield satisfactory
results and require further experimental and physical substantiation.
Earlier [12, 13], on the basis o f the experim ental data obtained and
calculations performed, it was shown that the m ost commonly used approaches
give no way o f predicting the crack growth kinetics in the alloys under study to
sufficient accuracy. In this paper, we will discuss the methods proposed for the
solution o f the above problem.
R esearch Task S ta tem ent. High-temperature nickel-based alloys EP742 and
EP962 for aircraft applications were used as m odel materials. Their mechanical
properties and other characteristics as well as the experimental procedure were
detailed earlier in [12, 14]. The materials under study are used to manufacture
long-life aircraft gas-turbine engine (AGTE) disks. The service conditions (flight
cycle) involve operation o f the material under cyclic loading with long hold
periods at m aximum load in a cycle. The solution o f this problem makes it
© V. V. POKROVSKII, V. G. SIDYACHENKO, V. N. EZHOV, S. B. KULISHOV, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 1 105
V. V. Pokrovskii, V. G. Sidyachenko, V. N. Ezhov, and S. B. Kulishov
possible to determine the num ber o f cycles o f subcritical crack growth, which
should be taken into account when determining the terms and amount of
scheduled maintenance sessions depending on the technical condition, and to
preclude catastrophic failure o f AGTE disks.
To construct a m odel for predicting the influence o f hold time on the crack
growth rate, it is necessary to perform the following experimental investigations:
(i) to study the crack growth behavior under cyclic and long-term static
loading;
(ii) to study the crack growth rate (CGR) under loading w ith a trapezoidal
cycle and w ith holding periods o f 300 and 3600 s at m aximum load.
T h eo re tica l-E x p e rim en ta l M odel. To construct a m odel we used the
experim ental CGR data obtained at a constant load w ith a trapezoidal and
triangular loading cycle shown in Figs. 1-4.
Since the duration o f the first portion o f the CCG diagram at initial K in
values is m uch longer than that o f the flight cycle (by a factor o f 10 and more),
we propose that the equation o f the linear crack growth rate summation should
involve the value o f the m ean CCG rate in the first portion a m instead o f the
conventionally used steady-state CCG rate (Fig. 1).
Aa -103, m
t-10—3,h
Fig. 1. Crack length increment Aa vs. loading time t.
Moreover, during fatigue crack growth (triangular cycle), a transcrystalline
mode o f fracture is m ost often realized in the alloys under study, whereas during
crack growth under creep conditions an intercrystalline m ode o f fracture is
observed [2, 18]. In this case, the presence o f the first portion depends on the
crack initiation technique. In the case o f an initial fatigue crack present, the first
portion did exist on the CCG diagram constructed in the coordinates A a — t. This
was associated with a change in the fracture m echanism in transition from a
fatigue crack to a creep one. In studies o f the creep crack growth directly from a
stress concentrator, the crack propagated at a constant rate, i.e., according to the
mechanism characteristic o f the second portion with the intergranular fracture
mechanism predominant. Since the trapezoidal cycle represents combined loading
(cyclic plus static), the crack growth during holding periods is m ost likely to
occur by the mechanisms responsible for the first portion o f the CCG diagram. In
view o f the aforesaid, we write the hypothesis o f the linear rate summation in the
following form:
106 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 1
Theoretical-Experimental Model fo r Predicting
d a \
d N ) - B ( K max)
CF
( 1)
d a \
where | ~n ) and a m are the crack growth rate for a trapezoidal loading cycle
and the m ean rate in the first portion o f the CCG, respectively, B and m are the
Paris equation coefficients determined from the CGR diagram for a triangular
loading cycle, and th is the hold time.
The m ost reliable m ethod for the a m evaluation is the experimental
determination o f the time (ti_2) when the crack reaches the portion o f constant
growth rate as well as the crack increm ent Aa corresponding to this instant of
time (Fig. 2). However, perform ing such experiments is a cumbersome process
due to certain difficulties involved in visual observation o f the creep crack
increment, particularly at the initial stage o f the experiment, and the necessity of
following the procedure as described in [14, 19]. From Fig. 1 we notice that the
crack increm ent in the first portion is insignificant and is approxim ately 0 .2
0.7 mm. The crack in this case can grow not only on the surface but also in the
bulk o f the specimen and change its front curvature.
t'in ,h
b K in, MPaVm
Fig. 2. Relation tin _ K in for alloys EP962 (a) and EP742 (b).
In accordance w ith [19], t'in is the time from the instant o f load application
to the crack increment by 0.2 mm, w hich can be determined approximately using
the technique described earlier [14]. In addition, this magnitude o f the increment
corresponds to the onset o f the steady-state growth o f the creep crack, as noted by
m any researchers [4, 16, 19].
The dependence o f the conditional incubation period t \n on the stress
intensity factor (SIF) K in is illustrated in Fig. 2 and represented by the empirical
relation
C
4 - K P . (2)
Based on definition o f the conditional incubation period, we determine the
m ean crack growth rate during holding periods by dividing the crack increment,
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V. V. Pokrovskii, V. G. Sidyachenko, V. N. Ezhov, and S. B. Kulishov
A a ~ 0.2 mm, by the time, t 'in, within which this increment occurred. Then, the
formula for the crack growth rate in a trapezoidal loading cycle takes the form
d a \
d N )
= B( K max) ̂ +
0.2-1 0 -3
CF t' l h ■ (3)
From the diagrams in Fig. 3 it follows that for alloy EP962 a satisfactory
agreement is observed between the calculation by formula (3) and experimental
data obtained for the hold times th = 300 and 3600 s. However, for alloy EP742
the calculation by the m odified linear hypothesis (3) fails to give an acceptable
CGR estimate for a holding period o f 300 s.
d a d N , m/cycle
da /dN , m/cycle
K max., MPaVm K max, MPaVm
Fig. 3. Experimental (lines) and calculated (dots) functions (da/dN ) — K max for alloys EP962 (a)
and EP742 (b) under cyclic loading with the hold time th'. (1) f = 0.5 Hz, th = 0; (2) th = 300 s;
(3) th = 3600 s; (■) and ( • ) calculation by (3) with hold times th = 3600 and 300 s, respectively.
To refine the linear hypothesis (1), we analyze the stress state at the tip o f a
quasi-static creep crack in order to determine the m ean crack velocity a m in the
initial portion o f the creep crack growth diagram. W hen a cracked specimen is
loaded w ith a constant load, there occur a crack-tip stress relaxation and the
development o f a creep zone whose size is defined by the following relation [11]:
2 ^
l ( 2 \ 2/(n—1)( n + 1)
(2^ T E A F cr ( ̂ )V2n « n )
K 212/(n—1), (4)r =' cr
where K i s th eS IF , E is the elastic modulus, t is the current time, F cr ( 0 ) is the
geometrical factor, a n+1 ~ 0.69, and n and A are the values o f the coefficients
in the equation that describes the m inimum creep rate for a smooth specimen:
e = A o n. (5)
108 ISSN 0556-171X. npodxeMbi npounocmu, 2009, N9 1
Simultaneously, the process o f damage accumulation starts in the m aterial at
the crack tip (formation o f pores, intergranular cracking, etc.) resulting in the
crack increment and ultim ately in a decrease in the initial creep zone size (4).
Thus, the crack-tip stresses decrease due to relaxation and, at the same time,
increase owing to the crack increment and to the fact that the crack tip approaches
the creep zone boundary. In the first portion o f the CCG diagram the processes
described above are o f transient nature, and as tim e passes the stabilization of
both the CGR and the rate o f displacement along the force action line takes place
(Figs. 1 and 3). Thus, the condition for the crack to reach the portion o f constant
velocity is the equality o f the CCG rate and the creep zone extension rate at the
crack tip:
a s = r c r . (6)
Theoretical-Experimental Model fo r Predicting ...
Differentiation o f relation (4) w ith respect to tim e gives an estimate o f the
time ( t s) at the expiration o f which the condition (6) is satisfied
ft —1
t s =
l K 2
n—1
n—3
(7)
1n
where D is the square-bracketed expression in (4) and a s is the CGR in the
second portion o f the CCG diagram (Fig. 1). Other notations are as described
above.
The size o f the crack-tip creep zone at the time t s is given by
2
s 2 1 2D ̂n—3
r s = D K
cr \ n — 1
i k 2 Nn—3
V )
(8)
2
Assuming that the crack, before reaching the second portion, w ould extend
by the value corresponding to the creep zone size r scr w ithin the time t s , we
estimate its m ean rate in the first portion as
(9)
sr cr
m t s
In order to use relation (1) m odified in view o f (4)-(9), we plotted kinetic
creep crack growth diagrams in the coordinates à s — K . The SIF value in the
linear portion varies but slightly (due to a constant load and small increment in
the crack length).
The diagram in the coordinates à s — K is described by the following
relation:
à s = B ( K ) « . (10)
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 1 109
V. V. Pokrovskii, V. G. Sidyachenko, V. N. Ezhov, and S. B. Kulishov
The a s values were calculated by taking into account only the second
(linear) portion o f each diagram obtained at a constant load (P i = const) and the
SIF value corresponding to this load.
Substitution o f expressions (7) and (8) into (9) with subsequent rearrangement
gives a relation between the m ean CCG rate in the initial portion, a m, and the
rate in the second portion:
n — 1
a m = a s . ( 11)
Verification o f applicability o f the m ethod for determining a m by formulas
(4)—(11) to m odify Eq. (1) is provided in Fig. 4. A satisfactory agreement between
the prediction and experiment is observed at a hold time th = 3600 s, i.e., during
long holding periods, when the processes o f the crack-tip stress redistribution
become less pronounced [as the fulfillment o f condition (6) is approached].
da)dN , m/cycle dafdN , m/cycle
MPaVm
Fig. 4. Experimental (1-3) and calculated (4, 5) functions da/dN — K max for alloys EP962 (a) and
EP742 (b) under cyclic loading with a hold time h (1) th = 0; (2) th = 300 s; (3) th = 3600 s; (4,
5) calculation by (1) in view of (4)-(9) with th = 300 and 3600 s, respectively.
a
However, at th = 300 s the prediction by relation (1) falls short o f being
encouraging owing to the concurrent processes o f the stress relaxation due to
creep and stress increasing through the crack extension increment, w hich are far
from the stabilization condition (6) during short holding periods.
C o n c l u s i o n s
1. Based on generalization o f experimental data, we proposed a m odification
o f the linear hypothesis o f the crack growth rate summation under combined
action o f fatigue and creep. It involves the use o f the value o f the m ean creep
crack growth rate in the initial portion o f the crack growth diagram instead o f the
current creep crack growth rate.
2. The calculation o f the crack growth rate for a trapezoidal cycle using the
m odified linear hypothesis o f the crack growth rate summation has revealed that
in the region o f low SIF values (closer to the threshold ones) the application of
the second m ethod for determining the m ean creep crack growth rate yields a
110 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N9 1
Theoretical-Experimental Model fo r Predicting
somewhat overestim ated value as compared to experimental one, whereas the use
o f the first m ethod gives an underestim ated value. W hen the calculations by the
proposed methods are perform ed for the region o f high SIF values (closer to the
critical ones), ju st an opposite tendency is observed. For this reason, it is
proposed that the creep crack growth rate in the first portion o f the crack growth
diagram should be evaluated by two methods and that the calculated results that
predict higher crack growth rates should be used in the m odified hypothesis o f the
linear rate summation.
3. As a result o f the stress state analysis in the vicinity o f the crack tip, we
have derived an expression relating the m ean crack growth rate in the initial
portion to the steady-state rate in the second portion. The relation obtained
depends solely on the m aterial properties and is invariant to the applied external
load.
1. S. Taira and R. Otani, T h e T h eo ry o f H ig h -T e m p e ra tu re S tren g th o f M a te r ia ls
[Russian translation], Metallurgiya, M oscow (1986).
2. R. P. Skelton (Ed.), H ig h -T e m p e r a tu r e F a tig u e o f M a te r ia l s [Russian
translation], Metallurgiya, M oscow (1988).
3. K. J. Miller, C re e p a n d F ra c tu r e [Russian translation], Metallurgiya, Moscow
(1986).
4. K.-H. S chw albe , R. H. A in sw o rth , A . Saxena, and T. Yokobor i ,
“R ecom m endation fo r a m od ifica tion o f A STM E 1457 to include
creep-brittle m aterials,” E n g . F ra c t. M e c h ., 62, 123-142 (1999).
5. A. Saxena, D. E. Hall, and D. L. McDowell, “A ssessm ent o f the deflection
rate for analyzing creep crack growth data,” E n g . F ra c t. M e c h ., 62, 111-122
(1999).
6 . A. T. Yokobori, Jr., “Difference in the creep and creep crack growth
behavior between creep ductile and creep brittle m aterials,” E n g. F ra c t.
M e c h ., 62, 61-78 (1999).
7. A. Saxena, R. S. W illiams, and T. T. Shih, “A m odel for representing and
predicting the influence o f hold time on fatigue crack growth behavior at
elevated tem perature,” in: F r a c tu r e M e c h a n ic s : Thirteenth Conf., ASTM
STP 743 (1981), pp. 86-99.
8 . Kee Bong Yoon, A. Saxena, and P. K. Liaw, “Characterization o f creep-
fatigue behavior under trapezoidal waveshape using C t -parameter,” Int. J.
F r a c t . , 59, 95-114 (1993).
9. J. P. Perdon and A. Pineau, “Effect o f hold times on the elevated temperature
fatigue crack growth behaviour o f Inconel 718 alloy,” in: Proc. o f the Int.
Conf. on A d v a n c e s in F r a c tu r e R e s e a r c h , ICF 5 (Cannes, France, 1981),
Oxford (1981), p. 2385.
10. S. Mall, E. A. Staubs, and T. Nicholas, “Investigation o f creep/fatigue
interaction on crack growth in a titanium aluminide alloy,” J. E n g. M a te r .
T ech n o l., 112, 435-441 (1990).
11. H. Riedel, F r a c tu r e a t H ig h T e m p e r a tu r e s , Springer-Verlag, Berlin (1987).
ISSN 0556-171X. npodxeMbi npounocmu, 2009, N 1 111
V. V. Pokrovskii, V. G. Sidyachenko, V. N. Ezhov, and S. B. Kulishov
12. V. V. Pokrovskii, V. N. Ezhov, and V. G. Sidyachenko, “Prediction o f crack
growth rate in alloys EP742 and EP962 under combined action o f cyclic and
static loads at a tem perature o f 973 K,” V estn ik K P I . Ser. M a s h in o s tro e n ie ,
41, 221-227 (2001).
13. V. V. Pokrovskii, V. N. Ezhov, and V. G. Sidyachenko, “Prediction o f the
crack growth rate in disc materials taking into account loading conditions,”
in: Proc. Int. Conf. on L ife A s s e s s m e n t a n d M a n a g e m e n t f o r S tr u c tu ra l
C o m p o n e n ts [in Russian], Vol. 2, National Academ y o f Sciences o f Ukraine,
Institute o f Problems o f Strength, K iev (2000), pp. 851-856.
14. V. V. Pokrovskii, V. N. Ezhov, and V. G. Sidyachenko, “Special features of
creep-crack propagation in refractory nickel alloys under static loading,”
S tre n g th M a t e r , 33, No. 5, 438-446 (2001).
15. A. Saxena and J. D. Landes, “Characterization o f creep crack growth in
m etals,” in: Proc. ICF6 , N ew Delhi (1984), pp. 3977-3987.
16. O. Kwon, K. M. Nikbin, G. A. W ebster, and K. V. Jata, “Crack growth in the
presence o f lim ited creep deform ation,” E n g . F ra c t. M e c h ., 62, 33-46
(1999).
17. M. Tabuchi, K. Kubo, K. Yagi, et al., “Results o f a Japanese Round Robin
on creep crack growth evaluation methods for Ni-base superalloys,” Ib id ,
47-60 (1999).
18. A. Fuji, M. Tabuchi, A. T. Yokobori, et al., “Influence o f notch shape and
geometry during creep crack growth testing o f TiAl intermetallic compounds,”
I b id , 23-32 (1999).
19. V. A. Vainshtok, M. V. Baumshtein, I. A. M akovetskaya, and I. A. M an’ko,
“Kinetics and mechanisms o f creep crack growth in a creep-resisting stee1,”
S tre n g th M a t e r , 17, No. 6 , 734-739 (1985).
Received 11. 06. 2008
112 ISSN 0556-171X. npo6xeMbi npounocmu, 2009, N 1
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