Fatigue of NPP Components and Piping under Service Conditions
Empirical equations are proposed for description of fatigue curves (up to 10ˆ12 cycles) of steels employed in NPP equipment and pipelines. Parameters of the obtained equations allow one to take into account the loading cycle asymmetry, corrosive and mechanical interaction between the coolant and pip...
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irk-123456789-470532013-07-09T08:38:57Z Fatigue of NPP Components and Piping under Service Conditions Filatov, V.M. Научно-технический раздел Empirical equations are proposed for description of fatigue curves (up to 10ˆ12 cycles) of steels employed in NPP equipment and pipelines. Parameters of the obtained equations allow one to take into account the loading cycle asymmetry, corrosive and mechanical interaction between the coolant and pipeline metal, and the metal ductilityreduction under service conditions. Предложены эмпирические уравнения для описания кривых усталости (до 10ˆ12 цикл) сталей, используемых для оборудования и трубопроводов АЭС. Параметры представленных уравнений позволяют учитывать влияние асимметрии цикла, коррозионного и механического взаимодействия между охладителем и металлом трубопровода, а также снижения пластичности металла в процессе эксплуатации. Запропоновано емпіричні рівняння для опису кривих утоми (до 10ˆ12 цикл) сталей, що використовуються для обладнання та трубопроводів АЕС. Параметри представлених рівнянь дозволяють враховувати вплив асиметрії циклу, корозійної та механічної взаємодії між охолодником і металом трубопроводу, а також зниження пластичності металу в процесі експлуатації. 2004 Article Fatigue of NPP Components and Piping under Service Conditions / V.M. Filatov // Проблемы прочности. — 2004. — № 1. — С. 131-139. — Бібліогр.: 13 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/47053 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Empirical equations are proposed for description of fatigue curves (up to 10ˆ12 cycles) of steels employed in NPP equipment and pipelines. Parameters of the obtained equations allow one to take into account the loading cycle asymmetry, corrosive and mechanical interaction between the coolant and pipeline metal, and the metal ductilityreduction under service conditions. |
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Filatov, V.M. |
| author_facet |
Filatov, V.M. |
| author_sort |
Filatov, V.M. |
| title |
Fatigue of NPP Components and Piping under Service Conditions |
| title_short |
Fatigue of NPP Components and Piping under Service Conditions |
| title_full |
Fatigue of NPP Components and Piping under Service Conditions |
| title_fullStr |
Fatigue of NPP Components and Piping under Service Conditions |
| title_full_unstemmed |
Fatigue of NPP Components and Piping under Service Conditions |
| title_sort |
fatigue of npp components and piping under service conditions |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2004 |
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Научно-технический раздел |
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| citation_txt |
Fatigue of NPP Components and Piping under Service Conditions / V.M. Filatov // Проблемы прочности. — 2004. — № 1. — С. 131-139. — Бібліогр.: 13 назв. — англ. |
| series |
Проблемы прочности |
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AT filatovvm fatigueofnppcomponentsandpipingunderserviceconditions |
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2025-07-04T06:41:16Z |
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2025-07-04T06:41:16Z |
| _version_ |
1836697546764845056 |
| fulltext |
UDC 539.4
Fatigue of NPP Components and Piping under Service Conditions
V. M. Filatov
ENES, Russia, Moscow
УДК 539.4
К оценке циклической прочности оборудования и трубопроводов
АЭС с учетом эксплуатационных факторов
В. М. Ф илатов
ИЦП МАЭ, Россия, Москва
Предложены эмпирические уравнения для описания кривых усталости (до 1012 цикл) сталей,
используемых для оборудования и трубопроводов АЭС. Параметры представленных урав
нений позволяют учитывать влияние асимметрии цикла, коррозионного и механического
взаимодействия между охладителем и металлом трубопровода, а также снижения плас
тичности металла в процессе эксплуатации.
Ключевые слова : коррозионная усталость, кривая усталости, асимметрия
цикла, легководный ядерный реактор.
The kinetics of fatigue damage suffered by components of nuclear power
facilities with light-water reactors is governed by a number of simultaneous
processes:
a) unsteady-state loading (mechanical and thermal stresses) during transients,
alternating in a general case with steady-state conditions and giving rise to a
series of loading half-cycles with various amplitudes and maximum stresses,
which are separated by steady-state loading conditions with possible coincident
vibrations;
b) in-service variations of metal condition (loss of ductility due to ageing,
coolant effects and irradiation, hardening or softening under cyclic elastic-plastic
loading, radiation hardening, formation of oxide films with properties dissimilar
to those of the metal);
c) corrosive and mechanical interaction between coolant and metal (with
possible deviation of water chemical composition from its nominal parameters
during transients, faults in the water treatment system, local increase in the
coolant corrosivity in stagnant zones, gaps and pockets with accumulation of
sludge).
It appears unrealistic to produce integrated models based on empirical data
for accumulation of fatigue and corrosion fatigue damage in the component metal,
with allowance for all the above processes, operational factors and their
interaction. The equations employed to assess the condition of components in
terms of cumulative fatigue damage [1] are modified fatigue curve equations - of
© V. M. FILATOV, 2004
ISSN 0556-171X. Проблемы прочности, 2004, № 1 131
V. M. Filatov
M anson-Coffin-Langer type - in which the essential data on metal are confined
to mechanical characteristics under static tension. These equations determine the
durability at the time of crack initiation and make allowance for operating
conditions [2-5].
The loading history calculated at the operation stage is based on monitoring
data for pressure, temperature and coolant flow, component displacements, and
vibrations. The calculated tensile (ascending) half-cycles of equivalent stresses,
whose number is equal to the number of full cycles, are used in calculation with
no regard for the chronological sequence of the combined half-cycles or their
parts, in order to obtain the maximum ranges [1]. For cycles fund within the
elasticity limits, it is often impossible to establish the true cycle asymmetry. This
can be explained by the peculiarities of the strength theory in use (the maximum
shear stresses), by the absence of reliable information on the constitutive equation
T .
of metal and its in-service variations (values of the yield stress Rp0 2 , ultimate
T Tstrength R m, and area reduction Z ). Moreover, establishment of the half-cycle
asymmetry for incorporation in calculations is not justified when the actual
loading history is not properly represented by half-cycles formed by the principle
of the maximum range.
This is the reason why fatigue curves with regard to maximum cycle
asymmetry effects are used in the national standards. In this case, it will suffice to
know the stress amplitude to make the calculation.
This issue is also of considerable importance for determining the half-cycle
parameters beyond the elasticity limits as the result of elastic-plastic stress
analysis or rough correction of the elastic analysis result [1, 6], prior to forming
half-cycles of stress ranges, depend on the cyclic proportionality limit, with the
stresses exceeding it, as well as on the strain-hardening exponent. Normally, the
half-cycle parameters are calculated with the use of simplified constitutive
equation based on the specified mechanical properties [1], with the result that the
stress range is underestimated and the strain range is overestimated in elastic-
T
plastic half-cycles. The set of mechanical properties (the yield stress R po 2 and
T . . . .
the ultimate strength R m) specified in [1], is provided for use in the calculations
to choose the basic dimensions (wall thickness of components) at the design stage
and establishes the lower limits of these characteristics.
A higher real value of the initial yield strength or its increase due to, e.g.,
cyclic hardening or irradiation, will lead to a different value of stress range in the
elastic-plastic half-cycle and to a different cycle asymmetry for elastic half-cycle
as compared to the use of the specified parameters Rp02, Rm , and Z T.
Experimental data concerning the effect of water coolant on the cyclic
strength of carbon steels (CS), low-alloy steels (LAS) and austenitic stainless
steels (SS) [3, 7-12] point to the possibility of a considerable decrease in the
number of cycles to failure under certain combined conditions of cyclic loading.
In a general case, these are characterized by coolant temperature T, sulfur content
S (CS, LAS), strain rate e, and oxygen concentration (OC) in the coolant. Static
holds at maximum stresses will also reduce durability of the material in contact
with the coolant [7].
132 ISSN 0556-171X. npo6n.eubi npounocmu, 2004, N 1
Fatigue o f NPP Components and Piping
Low-cycle fatigue in the range of up to 105 cycles is best covered by
available data. Tests were conducted with a fully reversed strain-controlled cycle.
In the region of strain amplitudes ea allowable in nuclear plant components
(ea < 0.3%), results were obtained only for a relatively high strain rate.
No tests have been performed under conditions of unsteady-state loading for
strain amplitude and rate, oxygen concentration and temperature, with holds
under compression and/or tension, during which a damaged oxide film could be
restored on the surface of the stressed metal. The effect of stress asymmetry under
exposure to water in various states (steam, steam-water mixture) has not been
studied in the high-cycle region. This lack of information on corrosion fatigue
dictates a priori some calculation provisions and is explained primarily by the
complexity, high cost and long duration of the required tests.
In a fully reversed strain-controlled cycle, with the number of cycles
exceeding 105, the cyclic strength of specimens is associated with the oxide film
strength at the threshold strain amplitude eath. The strain is expected to cause the
crack to open wide enough to let the fluid enter the crack cavity.
As reported in [7], the threshold value eath, below which no ambient effects
are observed in a fully reversed cycle of the specimen loading, is equal to or is
~ 20% higher than the fatigue limit of metal (CS, LAS) exposed to air.
For SS, eath is estimated by various sources at 0.126 [12], 0.16 [7], and
0.18% [9], which is above the strain of the fatigue limit for SS. It is noteworthy
that the film and metal often have different mean stresses of loading cycles, as
restoration of the oxide film after its rupture in the preceding half-cycle may
occur under conditions of stressed metal.
Initiation of fatigue cracks under the oxide film is not improbable in the
high-cycle region, which is accounted for by the correlation between eath and the
fatigue limit of metal in air under conditions of asymmetrical stress cycling.
The key parameters affecting corrosion-fatigue damage being invariant and
dependant on the steel grade alone, it was deemed possible to use the data [7, 11]
for setting up equations of corrosion fatigue.
In [3], the Langer equation was applied to derive the low-cycle corrosion
fatigue curve for low-alloy steel with the use of ductility Z w and rupture strain of
the oxide film, which were determined for a low strain rate during tensile testing
in water of specified parameters (temperature, OC).
Equations according to [1] for conditions of loading in the air environment
at temperatures typical of light water reactors, were extended to the region of
12
giga-cycle fatigue (up to 10 cycles) with exponent me of power dependence of
the number of cycles, N, on elastic cyclic strain, determined by the stress
R T with N = 1/4 (static tension to strain eTc < e f - true fracture strain and
7 T Tfatigue limit (N = 10 ) in a fully reversed cycle R_ 1 = KRm, where k = 0.4 at
R Tm < 700 MPa and K = (0.54_ 2 - 10_4R Tm )R Tm with 700< R Tm < 1200 MPa.
This assumption certainly adds conservatism to the fatigue analysis with
N > 10 , but allows performing calculations aimed at minimization of vibration
stresses.
ISSN 0556-171X. npoôëeubi npounocmu, 2004, № 1 133
V. M. Filatov
The effect of stress ratio is determined by the modified Goodman diagram,p p
with the maximum mean stress R m replaced by R c .
Inasmuch as the fatigue analysis method applies to components of light
water reactors in which cyclic plastic strains are only allowed in limited areas
making a small part of the component wall thickness (stress concentration zones),
the maximum true stress, R p , including a similar cycle with the ratio of similitude
T Tno (safety margin on stresses), is determined roughly by R m, R m with regard to
cyclic instability of material.
The allowable amplitude of stress [o aF ], which is quasi-elastic stress in the
elastic-plastic area, or the allowable number of cycles [N ] for steels with
12[ N ]< 10 are equal to the least of the two values found from Eqs. (1) and (2), in
which the stress cycle asymmetry factor (stress ratio) is absent in an explicit form,
as distinct from [1]:
[o aF ]= E TeTc (4nN [N ] ) -m + (R TC - [o F max] ia )[(4n n [N ]) m - ia ]- 1 , (1)
where
[o F max ] = R p with [o f max ] — R p ,
i o= 0 with [o aF ] — [of max] or [o aF ] — R Tp ,
io = 1 with [o aF ] < [o F max ] < R P ,
[o aF ]= {ETeTc (4[ N ])-m + ( RTC - П a [o f max] io )[(4[ N ]) me - ia ]- 1 } n - 1, (2)
where
n o [o F max ] = R p with n a [o f max]— R p ,
ia = 0 with [o aF ] — [o f max] or na [o aF ] — Rp ,
io = 1 with n a [o aF ] < n o [o F max ] ~ R p ,
no and n N are safety margins on stresses and on the number of cycles, m , me,
T . . Tand R c are the material characteristics, and e c is the ductility characteristic
dependant on Z c and determined as
eTc = ln[100/(100- Z l ) ] - {(oF )max| - Rp0 .2 }(2 E T ) - 1 , (3)
* t
or with (o f )max < Rp0.2, by the formula
e c = ln [10^(100- Z p )], (4)
*
where (o f )max is the stress of maximum magnitude throughout the loading
history.
134 ISSN 0556-171X. Проблемы прочности, 2004, N2 1
Fatigue o f NPP Components and Piping
Calculation of [ a aF ] or [N ] with regard to the maximum effect of mean
stress in the cycle relies on formulas (1) and (2) with [a F max] = Rp and
satisfaction of the condition for ia .
When using the data from the national standards, material specifications or
T Tregulations (e.g., [1]), which specify the mechanical characteristics, Z c = Z
should be set for Z p < 50%. In case of Z p > 50%, we take Z p = 50%.
T T If the ductility characteristic ec is determined according to Z found from
static tensile tests, the following formulas are to be used:
eTc = 0.005Zp - {(a F )max| - Rp0.2}(2EP )- 1 , (5)
and
e l = ° .°05zP with |( a F )max| < R^0.2. (6)
The characteristics E p , Z p , and R ^ are taken as equal to the minimum
values in the interval of operating temperatures with allowance for ageing. The
safety margin for stress na is set equal to 2, and Hn = 10 for the number of
cycles.
Symbol Rl < 700 MPa 700 < Rl < 1200 MPa
R -i
̂
S
О
(0.54 - 2 • 10-4 R l)R l
m 0.5 0.36+ 2 • 10-4 Rl
me 0.i32log[R l (R-i )- 1 (i + i.4 • i0-2 ZT )]
RTc R l (1+ 1.4 -10-2 ZT )
TThe values of R p for steels are adopted according to the properties at the
minimum temperature of the cycle:
R Tp = 0.5[R + R iTmin)]. (7)
It is acceptable to take Tmin = 20oC.
TAssessment of the cycle asymmetry effect with the use of Rp offsets
T T '
application of the specified R p0 2 and R m which may be lower than the actual
values, but may prove to be too conservative . Whenever justified (in the absence
of residual stresses after manufacture and of elastic-plastic strain during
operation), the Rp value may be reduced according to the stress analysis results .
The regulations [1] contain recommendations for fatigue analysis for cyclic
high-frequency loading, e.g., vibration stresses, coinciding with low-frequency
cycles.
ISSN 0556-171X. Проблемы прочности, 2004, N2 1 135
V. M. Filatov
The fatigue curves according to [1], Eqs. (1), (2) and ASME Code [13],
adopted in French, German, UK and Japanese standards, are compared in [4, 5].
The recommendations for analyses of cases involving exposure to the20
coolant of light water reactors apply to steels with R m < 700 MPa.
The factors affecting the cyclic strength of CS and LAS and their welds are
S, T, and è in the tensile half-cycle as well as OC, while those affecting the cyclic
strength are T, è, and OC.
The recommended analysis involves fatigue equations including the
coefficient of cyclic strength reduction in water environment Fèn (F èn > 1).
12The amplitude [o aF ] or number of cycles [N ] for steels with [N ]< 10
are equal to the least of their values found from Eqs. (8), (9) and (1), (2):
[o aF ] = E T (4nn Fen [N ])-m + R tcf (4nN [N])~MèF , (8)
20
where ec is determined from formulas (3), (4) with the use of specified
T 20values of Z = Z or by formulas (5), (6) when the calculation involves the
actual properties R Tp0 2 , Rm , and Z T
[oaF ]= [ETè f ( 4 F en[N ] ) -m + R TcF (4[N ])~meF ]n - 1. (9)
The values of R cF and mèF in Eqs. (8) and (9) are determined with regard
to the influence of water environment by the formulas:
R Tf = R Tm (1+ 0.014Zf ),
meF = 0.132log(2.5 + 0.035ZF ),
where ZF is calculated with the use of specified values:
Z f = 100[1 - exp(-2èc20F — )],
20or with the use of actual Z values:
20 -m
ZF = Z èn .
The coefficient Fèn is found from formulas involving the data from [7, 11]:
for CS
F en = 2.49/exp(0.101S *T *O * è *),
for LAS
F èn = 2.8/exp(0.101S *T *O * è *),
where %
S = 0.015 with OC > 1.0 ppm,
136 ISSN 0556-171X. Проблемы прочности, 2004, N2 1
Fatigue o f NPP Components and Piping
%
T = 0 with T < 150oC,
5* = 5 % with OC < 1.0 ppm and 0 < 5 < 0.015%,
T* = T -1 5 0 with 150 < T < 3500C,
5 = 0.015 with OC < 1.0 ppm and 5 > 0.015%,
%
O = 0 with OC < 0.05 ppm,
* i
e = 0 with e > 1% s ,
O * = ln(O C/0.04) with 0.05 < OC < 0.5 ppm,
e* = ln e with 10_3 < e < 1 % s - 1 ,
O = ln12.5 with OC > 0.5 ppm,
% _1
e = ln0.001 with e < 0.001% s ,
for annealed SS steels
F en = 2.55/exp(T*O *e*),
where
T = 0 with T < 1500C,
% 1
e = 0 with e > 0.4% s ,
T* = (T - 150)/175 with 150 < T < 3250C,
e* = ln e /0.4 with 4 -10_4 < ^ < 0.4% s - 1 ,
%
O = 0.26 at all OC levels,
e* = ln0.001 with e < 4 - 10_4% s-1 .
S u l^ r content (S) in CS and LAS steels is taken in accordance with the
respective certificates or specifications.
When the component loading half-cycles are formed according to the
maximum stress (strain) range criterion, stress (strain) variation areas associated
with different conditions are combined within one half-cycle, which is why this
half-cycle may show loss of continuity in T, e, and OC.
Temperature T is set equal to the maximum temperature in the half-cycle of
tension in the region of the equivalent stress variation [a f max]_ R_ 1 ; the strain
rate e is taken equal to the minimum value in the tensile half-cycle in the same
region as in determining T ; oxygen concentration OC is set equal to its maximum
value in regimes governing the tensile half-cycle for carbon and low-alloy steels.
The coefficients Fen for CS and LAS steels are taken higher than their
values in [7], where they are determined for the moment of specimen (D ~10m m )
damage by the so-called engineering-size crack (3 mm in depth and ~ 1 0 mm in
length on the surface), which is admissible for thick-walled components. These
higher values of the coefficients are explained by the fact that the low-cycle test
procedure [1] requires allowance for smaller cracks (0.5-2 mm in length and ~ 0.1
mm deep) in plotting the fatigue curves.
ISSN 0556-171X. npoôëeubi npounocmu, 2004, N2 1 137
V. M. Filatov
The effect of water environment as reported in [7], when at least one of the
T , O , and ё values leads to the minimum integral effect of the water
environment, is determined for CS, LAS, and SS steels by coefficients
Fen = 1.74; 2.45 and 2.55, respectively. The correction caused an increase in the
coefficient values to F en = 2.49 and 2.8 for CS and LAS, respectively. For SS,
Fen was left unchanged in the absence of empirical data for its adjustment.
Equations (8) and (9) correspond to the fatigue curve in water environment
and for a fully reversed cycle with exposure to water; the effect of loading
asymmetry is allowed for by equations (1) and (2).
The fully reversed loading cycle in transition from the low-cycle to the
high-cycle region is provisionally adopted for conditions of loading in water
environment as the more damaging to the oxide film formed on the stressed metal
as a result of its restoration during the previous loading. No significant difference
in resistance to corrosion fatigue has been found for SS in cast and deformed
states [7, 11], where coefficient F en was assumed to be identical in both cases.
Conclusions. The procedure for cyclic strength analysis of nuclear plant
components and pipelines performed during design and operation with the aim of
assessing their condition, is based on the empirical equations of fatigue curves.
The analysis takes into account the instability of mechanical properties of
materials, the stress cycle asymmetry, and the influence of the water environment.
The effect of complicated conditions of the actual loading on the fatigue
damage accumulation being still inadequately understood, the evaluation
techniques have to be conservative, especially with allowance made for the
environmental effect, when these techniques are recommended for identifying the
component areas of potentially highest susceptibility to corrosion fatigue damage
and for prescribing periodic inspection of such areas.
Р е з ю м е
12Запропоновано емпіричні рівняння для опису кривих утоми (до 10 цикл)
сталей, що використовуються для обладнання та трубопроводів АЕС. Пара
метри представлених рівнянь дозволяють враховувати вплив асиметрії циклу,
корозійної та механічної взаємодії між охолодником і металом трубопро
воду, а також зниження пластичності металу в процесі експлуатації.
1. PNAE G-7-002-86. Regulations fo r Strength Analysis o fN PP Equipment and
Pipelines [in Russian], Energoatomizdat, Moscow (1989).
2. V. M. Filatov, “Limits to initiation of fatigue macrocracks,” Voprosy
Atomnoi Nauki i Tekhniki. Ser. Nuclear Reactor Physics and Design, I1 (21),
P. 2, 114-123 (1978).
3. V. M. Filatov, “Computational and experimental assessment of cyclic
corrosion resistance,” Zavod. Lab., 9, 66-68 (1991).
4. V. M. Filatov, “Permissible stresses and cyclic strength analysis according to
Russian Regulations and ASME Code,” in: RF-US Workshop “Safety-Life
Extension,” ASME-RAS-Minatom (19-22 May 1997), Moscow (1997).
138 ISSN 0556-171X. Проблемы прочности, 2004, № 1
Fatigue o f NPP Components and Piping
5. V. M. Filatov, “Allowable stresses and design fatigue curves for NPP
components in Russian Strength Standards and ASME Code,” in: 4th Int.
Conf. on Material Behavior Problems o f NPP Equipment. Manufacture and
Operation (16-23 June), St. Petersburg, Russia (1996).
6. V. Yu. Zubov and V. M. Filatov, “Elastic-plastic strain concentration,”
Voprosy Sudostroeniya. Research in Metals, 36, 50-55 (1983).
7. O. K. Chopra and J. Muskara, “Effect of light water reactor coolant
environments on fatigue crack initiation in piping and pressure vessel steels,”
in: Proc. of ICONE 8 (April 2-6, 2000, Baltimore, MD USA) (2000).
8. M. Higuchi and K. Iida, “Evaluations strength correction factors for carbon
and low-allow steels in oxygen-containing high-temperature water,” NED,
129, 293-306 (1991).
9. H. Kanasaki, R. Umehara, H. Mizuta, and T. Suyama, “Fatigue lives of
stainless steels in PWR primary water,” Proc. 14th Int. Conf. on Structural
Mechanics in Reactor Technology (SMIRT 14), v. DO7/1, Aug. 1997, Lyon,
France (1997), p. 473-483.
10. H. Kanasaki, R. Umehara, H. Mizuta, and T. Suyama, “Effects of strain rate
and temperature change on the fatigue lives of stainless steels in PWR
primary water,” Ibid., p. 485-493.
11. O. K. Chopra, “Mechanism and Estimation of Fatigue Crack Initiation in
Austenitic Stainless Steels in LWR Environments,” in: NUREG/CR-6787,
ANL-01/25 (2002).
12. H. S. Mehta and S. R. Gosselin, “Environmental factor approach to account
for reactor water effects in pressure vessel and piping fatigue evaluations,”
NED, 181, 175-197 (1998).
13. ASME BPVC, Sec. III, Appendices (1992).
Received 26. 05. 2003
ISSN 0556-171X. npo6neMU npouHocmu, 2004, № 1 139
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