Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L
На основании результатов испытаний на одноосное растяжение выполнена сравнительная оценка ускоренных эффектов циклической ползучести в условиях переменного и постоянного нагружений для аустенитной нержавеющей стали 304L, широко используемой в энергетике и нефтехимической промышленности из-за ее повы...
Saved in:
| Published in: | Проблемы прочности |
|---|---|
| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2015
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/173399 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L / A.H. Daei-Sorkhabi, F. Vakili-Tahami // Проблемы прочности. — 2015. — № 6. — С. 108-120. — Бібліогр.: 27 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860035812763107328 |
|---|---|
| author | Daei-Sorkhabi, A.H. Vakili-Tahami, F. |
| author_facet | Daei-Sorkhabi, A.H. Vakili-Tahami, F. |
| citation_txt | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L / A.H. Daei-Sorkhabi, F. Vakili-Tahami // Проблемы прочности. — 2015. — № 6. — С. 108-120. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | На основании результатов испытаний на одноосное растяжение выполнена сравнительная оценка ускоренных эффектов циклической ползучести в условиях переменного и постоянного нагружений для аустенитной нержавеющей стали 304L, широко используемой в энергетике и нефтехимической промышленности из-за ее повышенных характеристик сопротивления высокотемпературной ползучести и усталости. Образцы для испытаний получены из холоднотянутых прутков, материал соответствует спецификации ASTM A276-05A. Испытания проводились при температурах 687, 717 и 737°С в условиях знакопеременного и постоянного нагружений. Изучены эффекты переменной нагрузки и времени выдержки нагрузки на механическое поведение материала и характеристики усталости и ползучести.
На основі результатів випробувань на одноосьовий розтяг виконано порівняльну оцінку прискорених ефектів циклічної повзучості в умовах змінного і постійного нагружений для аустенітної нержавіючої сталі 304L, широко використовуваної в енергетиці та нафтохімічної промисловості через її підвищених характеристик опору високотемпературної повзучості і втоми. Зразки для випробувань отримано з холоднотягнутих прутків, матеріал відповідає специфікації ASTM A276-05A. Випробування проводилися при температурах 687, 717 і 737°С в умовах змінного й постійного навантажень. Вивчено ефекти змінного навантаження та часу витримки на механічну поведінку матеріалу і характеристики втоми й повзучості.
|
| first_indexed | 2025-12-07T16:53:58Z |
| format | Article |
| fulltext |
UDC 539.4
Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared
with Constant Load for CD 304L
A. H. Daei-Sorkhabi
a,1
and F. Vakili-Tahami
b
a Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran
b Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
1 amirsorkhabi@gmail.com
ÓÄÊ 539.4
Ñðàâíèòåëüíàÿ îöåíêà óñêîðåííûõ ýôôåêòîâ öèêëè÷åñêîé ïîëçó÷åñòè â
ñòàëè CD-304L â óñëîâèÿõ ïåðåìåííîãî è ïîñòîÿííîãî íàãðóæåíèé
À. Õ. Äàå-Ñîðõàáè
à
, Ô. Âàêèëè-Òàõàìè
á
à Èñëàìñêèé óíèâåðñèòåò Àçàä, Òåáðèç, Èðàí
á Òåáðèçñêèé óíèâåðñèòåò, Òåáðèç, Èðàí
Íà îñíîâàíèè ðåçóëüòàòîâ èñïûòàíèé íà îäíîîñíîå ðàñòÿæåíèå âûïîëíåíà ñðàâíèòåëüíàÿ
îöåíêà óñêîðåííûõ ýôôåêòîâ öèêëè÷åñêîé ïîëçó÷åñòè â óñëîâèÿõ ïåðåìåííîãî è ïîñòîÿííîãî
íàãðóæåíèé äëÿ àóñòåíèòíîé íåðæàâåþùåé ñòàëè 304L, øèðîêî èñïîëüçóåìîé â ýíåðãåòèêå è
íåôòåõèìè÷åñêîé ïðîìûøëåííîñòè èç-çà åå ïîâûøåííûõ õàðàêòåðèñòèê ñîïðîòèâëåíèÿ
âûñîêîòåìïåðàòóðíîé ïîëçó÷åñòè è óñòàëîñòè. Îáðàçöû äëÿ èñïûòàíèé ïîëó÷åíû èç õîëîäíî-
òÿíóòûõ ïðóòêîâ, ìàòåðèàë ñîîòâåòñòâóåò ñïåöèôèêàöèè ASTM A276-05A. Èñïûòàíèÿ
ïðîâîäèëèñü ïðè òåìïåðàòóðàõ 687, 717 è 737�Ñ â óñëîâèÿõ çíàêîïåðåìåííîãî è ïîñòîÿííîãî
íàãðóæåíèé. Èçó÷åíû ýôôåêòû ïåðåìåííîé íàãðóçêè è âðåìåíè âûäåðæêè íàãðóçêè íà ìåõà-
íè÷åñêîå ïîâåäåíèå ìàòåðèàëà è õàðàêòåðèñòèêè óñòàëîñòè è ïîëçó÷åñòè. Ïîëó÷åííûå
ðåçóëüòàòû ïîäòâåðæäàþò ñèëüíîå âçàèìîâëèÿíèå ìåõàíèçìîâ ïîëçó÷åñòè è óñòàëîñòè.
Áûëî óñòàíîâëåíî, ÷òî ïðè âûñîêèõ òåìïåðàòóðàõ ïîâðåæäåíèå ìàòåðèàëà ïî ìåõàíèçìó
ïîëçó÷åñòè äîìèíèðóåò äàæå â ñëó÷àå èñïûòàíèé ñ î÷åíü êîðîòêîé âûäåðæêîé. Êðîìå òîãî,
áûëî ïîêàçàíî, ÷òî ïðè óâåëè÷åíèè âðåìåíè âûäåðæêè óâåëè÷èâàåòñÿ ñêîðîñòü äåôîðìàöèè
ïîëçó÷åñòè è, ñëåäîâàòåëüíî, ñíèæàåòñÿ äîëãîâå÷íîñòü îáðàçöîâ. Ðåçóëüòàòû äîêàçûâàþò,
÷òî ïåðåìåííûå íàãðóçêè ñóùåñòâåííî óâåëè÷èâàþò ñêîðîñòü äåôîðìàöèè ïîëçó÷åñòè è ñíè-
æàþò äîëãîâå÷íîñòü ïî ñðàâíåíèþ ñ ïîñòîÿííûìè íàãðóçêàìè, îáåñïå÷èâàþùèìè òàêîé æå
óðîâåíü ñðåäíèõ íàïðÿæåíèé.
Êëþ÷åâûå ñëîâà: õîëîäíîòÿíóòàÿ ñòàëü 304L, íåðæàâåþùàÿ ñòàëü, ïåðåìåííàÿ íà-
ãðóçêà, ïîëçó÷åñòü, ìàëîöèêëîâàÿ óñòàëîñòü è ïîëçó÷åñòü, âûäåðæêà ïîñòîÿííîé
íàãðóçêè.
Introduction. Many engineering parts, which find applications in power generation
and petrochemical plants, operate at high temperature under mechanical loads. In practice,
level of operating temperature or the mechanical load may vary with time. Therefore,
different mechanisms of failure can occur, which depend on the nature and history of
termomechanical loadings. The important failure mechanisms from this point of view are as
follows:
(i) fatigue, which is usually faced when the engineering part operates at temperatures
below 0.5Tmelt (Tmelt is melting temperature in Kelvin) and at alternating load with low
stresses. Engineering components are often subjected to fatigue loading under stress-
© A. H. DAEI-SORKHABI, F. VAKILI-TAHAMI, 2015
108 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
controlled conditions. The existing models describe the fatigue of engineering components
including the Goodman equation [1, 2], the modified Goodman equations [1, 3], the
Smith–Watson– Topper parameter [4], the Walker parameter [5], and Dowling equation [6];
(ii) creep, which occurs at high temperatures (above 0.5Tmelt ) under mechanical loads.
Creep implies a time-dependant plasticity: after a sufficient elapse of time, either the
viscoplastic strain becomes so large that the original shape of the structure is altered, or the
creep rupture occurs. Creep is critical in a number of applications, for example, components
used in power-generating systems and chemical plants, where the service temperature is
high. Different models have been proposed, which explain creep behavior of materials [7];
(iii) elastic shakedown behavior, in which plastic deformation takes place during
running in (contact between solid surfaces), while the steady state is perfectly elastic due to
residual stresses or strain-hardening. Plastic shakedown behavior is one, in which the
steady state is a closed elastic-plastic loop, with no net accumulation of plastic deformation.
Except for the initial loading cycles, during which plastic strains may occur, no further
deformation increment occurs on the application of loading cycles. Shakedown will occur
when the ratcheting fails to occur [8];
(iv) ratcheting behavior is one in which the steady state is an open elastic-plastic loop,
with the material accumulating a net strain during each cycle. The accumulation of cyclic
deformation is called ratcheting and is defined as a cycle-by-cycle accumulation of plastic
strain with the application of cyclic load characterized by constant stress amplitude with a
nonzero mean stress. After a sufficient number of cycles, the total strain (displacement)
becomes so large that the original shape of the structure is altered, thereby making the
structure unserviceable. The development of cyclic plasticity models for prediction of
ratcheting strain has received a considerable attention in the past decades, and many models
have been suggested. The models by Chaboche and by Ohno and Wang, both based on the
Armstrong and Frederick nonlinear kinematic hardening rule, are among the earlier models
often cited [9–13].
In practice, most of the engineering components are subjected to the combination of
these types of loadings. Therefore, it is important to study the mechanical behavior of
materials or even engineering components and the interaction of these mechanisms under
the combined thermomechanical loadings. Many engineering components, such as gas
turbine blades, operate at high temperature under alternating loads with a low frequency.
This type of loading, which is known as “low cycle fatigue-creep,” is the subject of many
research studies, especially during the last decade [14–17]. Due to the viscoplastic behavior
of the materials at high temperature, shakedown or ratcheting should not be excluded in
these studies.
The interaction of damage mechanisms due to the fatigue and creep is an important
factor that limits the life of engineering parts. Ignoring the mutual interaction between these
mechanisms may lead to erroneous lifetime predictions. Conservative predictions, however,
unnecessarily increase the cost of production and maintenance of such systems. Therefore,
a realistic assessment of lifetime is critical for the prevention of failures. In some studies,
the ASME code method has been used for predicting the creep–fatigue life [14, 15]. This
method is not exact, insofar as it’s basis is strictly phenomenological, with no mechanistic
component [14]. Many investigators have examined creep-fatigue crack initiation and
propagation modes in general. Some of them focused on studying the effect of specific
parameters, such as hold time or creep stress effect, environment, orientation, geometry,
and material parameters [18–21]. For example, Kaae [21] has carried out low-cycle fatigue
tests on alloy 800H in the temperature range of 22–760�C. Alloy 800 is an austenitic
Fe–Ni–Cr alloy with higher Ni and Cr contents than conventional stainless steels. It is
widely used for many high-temperature applications in such areas, as petrochemical
processing, electrical power generation, and solar energy systems. In their tests, the axial
strain was cycled between equal positive and negative values.
Accelerating Effects of Cyclic Creep ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 109
Sabour and Bhat [18] have investigated the creep-fatigue interaction for aircraft
components. They have proposed innovative mathematical models to predict the operating
life of these components, specifically gas turbine blades that are subjected to creep-fatigue
at high temperatures.
Since most of engineering components, which work at high temperature, operate
under alternating load, it is important to know their behavior at this condition. On the other
hand, most of the available data for creep are at constant load or stress. Therefore, it
expedient to estimate the creep life-time and deformation of the parts at alternating load
based on the experimental data obtained at constant stress. This particular issue is the major
aim of the present paper. For this purpose, by using a series of uniaxial creep tests under
alternating load, the behavior of cold-drawn 304L stainless steel (CD 304L SS) at high
temperature has been determined experimentally. Uniaxial creep tests have been carried out
at 687, 717, and 737�C under constant and alternating loads. The effects of alternating load
and the hold time on the mechanical behavior of the material have been studied to
investigate the mutual effect of two damage mechanisms.
1. Creep-Fatigue Damage. The most common method to calculate creep-fatigue
damage is based on the linear superposition of these damages, which leads to the linear
life-fraction rule, which forms the basis of the ASME Boiler and Pressure Vessel Code,
Section III, Code Case N-47 [22]. This approach combines the damage summations of
Robinson for creep and of Miner for fatigue as follows [18]:
N
N
t
t
D
f r
� �� � , (1)
where N N f is the cyclic portion of the life fraction, in which N is the number of cycles
at a given strain (or stress) range and N f is the pure fatigue life at that strain (or stress)
range. The time-dependent creep-life fraction is t t r , where t is the time at a given stress
and temperature, and t r is the time to rupture at that stress and temperature, and D is the
cumulative damage index. Failure is presumed to occur when D� 1. If Eq. (1) is valid, then
a straight line of the type shown in Fig. 1 between the fatigue and creep life fractions
should be expected [18]. The linear behavior shown in Fig. 1 is the ideal type, which can be
depicted by Eq. (1). However, the true behavior of most materials is non-linear which can
be approximated using a bi-linear model as shown in Fig. 1. Most materials manifest a
drastic lifetime reduction under the combined effect of creep and fatigue damages. For
example, as it can be seen in Fig. 1, when the N N f � 0.4, the t t f value calculated via
Eq. (1) is expected to be 0.6. However, due to accumulation of creep damage with loading
cycles, a more realistic lifetime is predicted by the bi-linear model as t t r � 0.35. On the
other hand, when the number of cycles is too low (N N f � 0.2), the fatigue damage is
negligible, and therefore the lifetime becomes closer to the ideal value obtained from the
linear equation.
The life-fraction rule given by Eq. (1) has no mechanistic basis and is therefore,
material-dependent. It also assumes that tensile and compressive hold periods are equally
damaging, whereas most of the experimental results show minor damage levels in
compression. Other effects, such as the strain softening or hardening behavior, the effect of
prior plasticity on subsequent creep, and the order of loading, have not been accounted for
by this rule, which therefore, in general, provides only approximate results. In spite of these
limitations, this rule of damage summation is very popular because it is easy to use and
requires only a standard fatigue S–N diagram and creep stress-rupture curves. To overcome
the above shortcomings, it is necessary to carry out creep tests under alternating load, in
which the specimen is exposed to a high temperature for a long period. This type of tests
has been carried out in this research, in order to obtain results that are more realistic.
A. H. Daei-Sorkhabi and F. Vakili-Tahami
110 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
2. Material and Experimental. Type 304 stainless steel is the most widely used alloy
of the austenitic stainless steel group. It is a variation of the basic 18-8 grade, type 302,
with a higher chromium and lower carbon content. Lower carbon minimizes the chromium
carbide precipitation due to the welding and its susceptibility to intergranular corrosion.
Type 304L is an extra low-carbon variation of type 304 with a 0.03% maximum carbon
content that eliminates carbide precipitation due to the welding. As a result, this alloy can
be used in the “as-welded” condition, even in severe corrosive environment. 304L has
slightly lower mechanical properties than type 304. The maximum temperature to which
304 and 304L can be exposed continuously without appreciable scaling is about 899�C. For
intermittent exposure, the maximum exposure temperature is about 816�C. The hardness of
type 304L does not increase considerably by heat treatment; and it can be annealed by
heating to 1038–1121�C followed byrapid cooling. Cold worked parts can be stress relieved
at 399�C for 1/2 to 2 h [23].
In the current research, creep test specimens have been obtained directly from new
austenitic 304L stainless steel cold drawn bars, which have been solution, annealed at
1050�C. The material conforms to ASTM A276-05A specifications. Chemical composition
of this material is given in Table 1.
Here both the standard values [23] and those, which have been obtained from
quant-metric measurements for the specimens under investigation, are given. The test
specimens have been machined out from the bars according to the ASTM E8M-04 [24]
with gauge length of 100 mm and diameter of 10 mm (see Fig. 2).
2.1. Test Machine. Uniaxial creep tests have been carried out using 5000 kg,
AMSLER creep test machine according to the ASTM E139 [25] standard. Its lever-arm
loading ratio is 25:1 with load accuracy of �0.5%. The temperature range of the furnace or
chamber of the machine is up to 1000�C with the accuracy of �0.5�C. The testing machine
also provides displacement–time graphs with the accuracy of �1.0 �m. The maximum
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 111
Accelerating Effects of Cyclic Creep ...
Fig. 1. Creep rupture/low cycle fatigue damage interaction curve for 1Cr–Mo–V rotor steel at 450�C
[18].
T a b l e 1
Chemical Composition of 304L Stainless Steel in Weight Percent
Composition C Si Mn P S Cr Mo Ni Cu N V
Standard 0.019 0.41 1.75 0.036 0.006 18.28 0.34 8.04 – 0.04 –
Tested (CD 304L SS) 0.025 0.42 1.80 0.035 0.015 17.80 0.27 8.10 0.76 – 0.19
extension of the specimen is 10 mm (see Fig. 3). To apply alternating load, the capability of
this machine is improved by using a moving weight (1000 kg) along the lever-arm (Fig. 4).
The speed and location of this weight, as well as the frequency of the alternating load, can
be pre-programmed using a computer-controlled electronic system. Using this system and
additional alternating axial load of 0 to 10,000 N can be applied to the specimen.
112 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
A. H. Daei-Sorkhabi and F. Vakili-Tahami
Fig. 2. Uniaxial creep test specimen according to the ASTM E8M-04 [24] with gauge length of 100
mm and diameter of 10 mm. (Dimensions are in mm.)
Fig. 3. Uniaxial creep test machine: 5000 kg, AMSLER according to the ASTM E139 standard [25].
Fig. 4. Alternating moving load along the lever-arm of uniaxial creep test machine.
2.2. Test Conditions. In order to investigate the creep and creep-fatigue behavior of
the material, three groups of tests are carried out:
(i) constant load creep, where the uniaxial load and temperature are constant during
the tests;
(ii) creep-fatigue, where the temperature level is constant but the uniaxial load is
alternating with very short hold time;
(iii) alternating load creep, where the temperature level is constant, but the uniaxial
load is alternating with relatively long hold times.
Although the operating temperature for engineering components manufactured from
304L is usually below 650�C in industry, but to reduce the testing times to an achievable
limit, the tests have been carried out at higher temperature levels of 687, 717, and 737�C, in
view that the creep mechanism is the same, since these temperatures are below the
recrystallization level [26]. Also, to avoid the initial plastic deformation, in all tests, the
maximum stress is below the yield stress of the material at the same temperature.
3. Results.
3.1. High Temperature Mechanical Tests. To study the high temperature mechanical
behavior of cold drawn 304L, a series of tensile tests at high temperatures have been
carried out and the results are given in Table 2.
Standard high-cycle fatigue tests at room temperature have been carried out to obtain
the endurance limit of the material. Since the endurance limit of steels are proportionally
related to the ultimate tensile strength [27], by knowing the latter at high temperatures, the
former can be estimated. Hence, the endurance limit at high temperatures ( )S e T have been
estimated using Eq. (2) based on the endurance limit at room temperature ( )S e T � �25 C and
ultimate strength of the material S u at high and room temperatures, which have been
obtained experimentally,
( )
( )
( )
( ) .S
S
S
Se T
u T
u T
e T�
��
�
��
� �
� �
25
25
C
C (2)
3.2. Constant Load Creep Tests. Table 3 presents the experimental data for constant
load creep tests. In this table, the stress � � F A0 0 is obtained using the constant load
(F0) and initial cross section of the specimen (A0). In all tests, the stress is below the yield
stress of the material at the same temperature. Creep failure in engineering components can
be regarded in two ways: when the time to rupture, t r , has been reached or the time,
t creep strain C� % , at which the creep strain reaches a critical level of C%. In most of the
engineering components, the latter condition plays a major role; and therefore, it has been
used in this study. Since the maximum extension of the specimen is 10 mm (total strain of
10%) in the creep-testing-machine, all the tests have been carried out until the true creep
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 113
Accelerating Effects of Cyclic Creep ...
T a b l e 2
Mechanical Properties of CD 304L SS
Test No. T , �C Su ,* MPa S y ,* MPa Se , MPa
1
2
3
4
5
6
25
517
617
687
717
817
675
430
370
300
268
158
425
346
299
252
228
117
310*
198**
170**
138**
123**
72**
* obtained experimentally; ** obtained using Eq. (2).
strain of 3% has been reached or t t creep strain� �3%. At this amount of deformation, most
of engineering components would be regarded as failed. The summary of the creep test
results is given in Table 3.
Also, the minimum creep strain rate, ��ss , for each test has been given in this table.
Figures 5 and 6 show the variation of the creep strain with time at 717 and 687�C,
respectively. The results given in Table 3 and Figs. 5 and 6 show that by increasing the
stress or temperature, time to reach the 3% creep strain decreases significantly.
3.3. Creep Tests at Alternating Loads. Table 4 presents the experimental data for
creep tests at alternating loads. In this table, the following parameters have been used to
define the test conditions:
�
�
� � �
� � �
max max
min min
max min
max
,
,
( ) ,
(
�
�
� �
� �
F A
F A
m
a
0
0
2
min ) ,2
(3)
114 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
A. H. Daei-Sorkhabi and F. Vakili-Tahami
T a b l e 3
Constant Load Creep Test Results for CD 304L SS at High Temperatures
Test No. T , �C �,* MPa tcreep strain�1% ,*
h
tcreep strain�3% ,*
h
� ,�ss %/h
7 737 86.5 27 65 3 65 10 2. � �
8 717 142.0 1.5 4.25 9 36 10 1. � �
9 717 112.0 11 25 9 41 10 2. � �
10 717 86.5 185 327 3 81 10 3. � �
11 717 56.5 3671 NA** 2 65 10 4. � �
12 687 142.0 68 132 131 10 2. � �
13 687 86.5 1390 NA** 5 61 10 4. � �
* obtained experimentally; ** not available (the test has been stopped before reaching 3% strain).
Fig. 5. Creep strain variation of CD 304L SS for constant load creep tests at 717�C.
where Fmax and Fmin refer to the maximum and minimum applied loads also, � m and
� a refer to average and alternating stress. Since, most of the engineering components
operate at tensile stress, and knowing the fact that the creep damage is mostly due to this
type of loading, in all tests the minimum stress is above 1 MPa to avoid any compressive
load. In addition, all tests are load controlled as shown schematically in Fig. 7. In this
figure, definition of parameters such as load-increasing time, t in , load-decreasing time, t d ,
and holding time, t h , are presented. In all tests t ti d� � 60 s.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 115
Accelerating Effects of Cyclic Creep ...
Fig. 6. Creep strain variation of CD 304L SS for constant load creep tests at 687�C.
T a b l e 4
Alternating Load Creep Test Results for CD 304L SS at High Temperatures
Test
No.
T ,
�C
� max ,*
MPa
� min ,*
MPa
th ,
s
Creep strain = 1% Creep strain = 3% � ,�ss
m/(m/s)Total
time (h)
N i ,
cycles
Total
time (h)
N i ,
cycles
14 717 142 31 2 45 1306 115 3338 219 10 2. � �
15 717 112 1 2 292 8477 513 14893 2 07 10 3. � �
16 717 112 1 1800 33.1 32 80.6 78 312 10 2. � �
17 717 112 1 2700 29 19 73.5 54 3 34 10 2. � �
18 717 112 1 3600 25 12 55 27 4 49 10 2. � �
19 687 142 31 2 1332 38670 NA** NA** 134 10 4. � �
* obtained experimentally; ** not available (the test has been stopped before reaching 3% strain).
Fig. 7. Schematic diagram of load–time variation used to apply alternating loads.
Figure 8 shows the variation of the creep strain with time for alternating load tests at
717�C. The stresses for alternating load-tests change between 1 to 112 MPa. This figure
shows that by increasing hold time, creep strain rate increases significantly. To compare
different behaviors of the material, the results for constant load creep tests with 112 MPa
(maximum stress) and 56.5 MPa (average stress) are also included in Fig. 9.
The summary of the test results is given in Table 4. As it can be seen, in all tests, the
specimens reach the creep lifetime limit (creep strain of 1 or 3%) without facing fatigue
fracture. For example, in test No. 14, in spite of the fact that the hold time is very short (two
seconds), even after 3338 cycles, fatigue fracture has not occurred and during this period,
which lapsed 115 h, the creep strain has reached 3% limit. The same trend has been
observed in test No. 15, and after 14,893 cycles, the creep lifetime criterion being satisfied
without facing fatigue fracture.
4. Discussion. To evaluate the level of creep-fatigue damage of the tests, the ASME
Code Case N-47 has been used. This code is based on the use of interaction diagrams such
as that shown in Fig. 1 for the material under consideration. The estimation of the total
damage is also obtained by the use of Eq. (1).
116 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
A. H. Daei-Sorkhabi and F. Vakili-Tahami
Fig. 8. Variation of the creep strain with time for alternating load tests under different hold times.
Fig. 9. Variation of the creep strain with time for constant (average and maximum) and alternating
load.
As it can be seen in Table 4, tests Nos. 14, 15, and 19 have very short hold times (two
seconds) and therefore they can be considered as fatigue tests at high temperature. Based on
the Manson–Coffin equation [16], the pure fatigue damage is related to the number of
cycles and the range of strain change in each cycle or N Bf
m� ( )�� , where B and m are
material constants. Hence, by increasing ��, the fatigue damage will increase. It can be
seen in Fig. 10 (also in Table 5) that the strain range �� at each cycle for tests with t h � 2
s remains almost constant (for example from 0.06 to 0.07% for 687�C, maximum stress of
142 MPa, minimum stress of 31 MPa) but their average values are increased by increasing
temperature (for example compare the strain rang for test No. 14 and 19) or mean stress
� m (compare test No 14 and 15). Therefore, it can be concluded that both increasing
temperature and mean stress level will lead to a shorter fatigue-life. Fatigue-life for each
test can be calculated using either Manson–Coffin equation, or fatigue life diagrams for
304L material [18]. The estimated fatigue-lives given in Table 5 have been obtained using
diagrams provided in ASME Code Case N-47 and for these tests, they are equal or above
106 cycles. Therefore, the fatigue damage value, N Ni f� , is very low. Also in Table 6,
the amount of creep damage, t ti creep strain�� 1%, are given, in which the creep lifetime is
considered to be the life to reach 1% creep strain. It can be seen that due to the high
temperature and stress level for these tests, the creep damage is much higher than the
fatigue one, despite very short hold times. Clearly, by increasing hold time, the role of
creep damage will increase and this failure mechanism will be the dominant one.
Moreover, comparison of the results for tests Nos. 15–18 shows the effect of holding
time on the material creep behavior. Although the stress and temperature levels for these
tests are the same, but due to the increasing hold time, creep strain rate has increased
significantly and therefore the creep lifetime is reduced. For example, for test No. 15 with
t h � 2 s, t creep strain�3% is 513 h, but for test No. 18 with t h � 3600 s, t creep strain�3%
reduces to 55 h.
The test results can be compared using the power law form of constitutive equation to
estimate the steady state creep strain rate:
� ,� �ss
nC� (4)
Accelerating Effects of Cyclic Creep ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 117
Fig. 10. Variation of strains for each cycle with time for three alternating load tests.
where ��ss is the creep strain rate (in h�1), � is stress (in MPa), C and n are material
constants. Comparison of the results for test No. 11 in Table 3 and test No. 15 in Table 4
highlights the significant effect of alternating load on the creep strain rate and lifetime of
the material.
Comparative analysis of the results for tests Nos. 10 and 11 in Table 3 and tests Nos.
14 and 15 in Table 4 also demonstrates the effect of average stress level on the creep
lifetime of the material under alternating load. For example, by increasing the applied
constant stress from 56.5 to 86.5 MPa, creep strain rate increases by a factor of 14.377 and
time for 1% creep strain reduces by factor of 0.05. This trend can also be seen in comparing
the results for tests with alternative stress.
The effect of holding time on creep strain rate can be observed by comparing the
results for tests No. 15 to No. 18. For example by increasing hold time from 2 to 3600 s,
steady state creep strain rate increases by a factor of 21.69 with decrease in time to reach
1% creep strain rate by a factor 0.09.
Conclusions. A set of constant and alternating load creep tests have been carried out
to predict creep behavior of cold-drawn 304L SS. The test results show the difference in
creep behavior of the material under constant and alternating loads.
1. It has been shown that at high temperature and at stress levels below the yield point
at the associated temperature, the specimens have reached creep lifetime limit (creep strain
of 1 or 3%) without facing fatigue fracture. For example, in test No. 14, in spite of the fact
that the hold time is very short (two seconds), even after 3338 cycles, fatigue fracture has
not occurred and during this period which lapsed 115 h, the creep strain has reached 3%
limit.
2. The results highlight the major impact of the alternating loads in increasing creep
strain rate and reducing the creep lifetime when compared with the constant load tests at the
same average stress. For example, in test No. 11, at 717�C and constant stress of 56.5 MPa,
118 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
T a b l e 5
Fatigue Damage Evaluation in Tests with a Short Hold Time of 2 s
Test
No.
T ,
�C
� max ,
MPa
� min ,
MPa
th ,
s
N i ,
cycles
��,
mm/mm
Fatigue
life N f ,
cycles
Fatigue
damage
N Ni f�
14 717 142 31 2 1306 8 64 10 4. � � 106 1306 10 3. � �
15 717 112 1 2 8477 7 54 10 4. � � above 106 8 477 10 3. � �
19 687 142 31 2 38670 6 35 10 4. � � above 106 3 867 10 2. � �
A. H. Daei-Sorkhabi and F. Vakili-Tahami
T a b l e 6
Creep Damage Evaluation in Tests with a Short Hold Time of 2 s
Test
No.
T ,
�C
� max ,
MPa
� min ,
MPa
th ,
s
Creep strain = 1% Creep
damage
t ti creep strain�� 1%
N i ,
cycles
t t Ni h i� ,
h
t f
at max
stress, h
14 717 142 31 2 1306 0.73 1.5 0.49
15 717 112 1 2 8477 4.71 11.0 0.43
19 687 142 31 2 38670 21.48 68.0 0.32
creep life for 1% strain is 3673 h, whereas for test No. 15 with alternating load (56.5 MPa
mean stress and 55.5 MPa alternating stress, two second hold time) creep life for 1% strain
is 292 h or 12.6 times shorter. Hence, estimating creep lifetime for alternating loads based
on the average stress will lead to erroneous result.
3. It has been shown that by increasing the hold time, the creep strain rate increases
and consequently, the creep lifetime is reduced.
4. The results show that due to the high temperature and stress level for these tests, the
creep damage is much higher than the fatigue damage despite very short hold times.
Ð å ç þ ì å
Íà îñíîâ³ ðåçóëüòàò³â âèïðîáóâàíü íà îäíîîñüîâèé ðîçòÿã âèêîíàíî ïîð³âíÿëüíó
îö³íêó ïðèñêîðåíèõ åôåêò³â öèêë³÷íî¿ ïîâçó÷îñò³ â óìîâàõ çì³ííîãî ³ ïîñò³éíîãî
íàãðóæåíèé äëÿ àóñòåí³òíî¿ íåðæàâ³þ÷î¿ ñòàë³ 304L, øèðîêî âèêîðèñòîâóâàíî¿ â
åíåðãåòèö³ òà íàôòîõ³ì³÷íî¿ ïðîìèñëîâîñò³ ÷åðåç ¿¿ ï³äâèùåíèõ õàðàêòåðèñòèê îïîðó
âèñîêîòåìïåðàòóðíî¿ ïîâçó÷îñò³ ³ âòîìè. Çðàçêè äëÿ âèïðîáóâàíü îòðèìàíî ç õîëîäíî-
òÿãíóòèõ ïðóòê³â, ìàòåð³àë â³äïîâ³äຠñïåöèô³êàö³¿ ASTM A276-05A. Âèïðîáóâàííÿ
ïðîâîäèëèñÿ ïðè òåìïåðàòóðàõ 687, 717 ³ 737�Ñ â óìîâàõ çì³ííîãî é ïîñò³éíîãî
íàâàíòàæåíü. Âèâ÷åíî åôåêòè çì³ííîãî íàâàíòàæåííÿ òà ÷àñó âèòðèìêè íà ìåõàí³÷íó
ïîâåä³íêó ìàòåð³àëó ³ õàðàêòåðèñòèêè âòîìè é ïîâçó÷îñò³. Îòðèìàí³ ðåçóëüòàòè
ï³äòâåðäæóþòü ñèëüíèé âçàºìîâïëèâ ìåõàí³çì³â ïîâçó÷îñò³ ³ âòîìè. Áóëî âñòàíîâ-
ëåíî, ùî ïðè âèñîêèõ òåìïåðàòóðàõ ïîøêîäæåííÿ ìàòåð³àëó çà ìåõàí³çìîì ïîâçó-
÷îñò³ äîì³íóº íàâ³òü ó âèïðîáóâàííÿõ ç äóæå êîðîòêîþ âèòðèìêîþ. Êð³ì òîãî, áóëî
ïîêàçàíî, ùî ïðè çá³ëüøåíí³ ÷àñó âèòðèìêè çá³ëüøóºòüñÿ øâèäê³ñòü äåôîðìàö³¿
ïîâçó÷îñò³ ³, îòæå, çíèæóºòüñÿ äîâãîâ³÷í³ñòü çðàçê³â. Ðåçóëüòàòè äîâîäÿòü, ùî çì³íí³
íàâàíòàæåííÿ ³ñòîòíî çá³ëüøóþòü øâèäê³ñòü äåôîðìàö³¿ ïîâçó÷îñò³ ³ çíèæóþòü äîâãî-
â³÷í³ñòü ó ïîð³âíÿíí³ ç ïîñò³éíèìè íàâàíòàæåííÿìè, ùî çàáåçïå÷óþòü òàêèé ñàìèé
ð³âåíü ñåðåäí³õ íàïðóæåíü.
1. C. B. Lim, K. S. Kim, and J. B. Seong, “Ratcheting and fatigue behavior of a copper
alloy under uniaxial cyclic loading with mean stress,” Int. J. Fatigue, 31, No. 3,
501–507 (2009).
2. M. S. Beden, S. Abdullah, A. K. Ariffin, et al., “Fatigue life assessment of different
steel-based shell materials under variable amplitude loading,” Eur. J. Sci. Res., 29,
No. 1, 157–169 (2009).
3. J. Morrow, “Fatigue properties of metals,” in: Fatigue Design Handbook, Section 3.2,
Publ. No. AE-4, Soc. of Automotive Engineers, Warrendale, PA (1968).
4. R. N. Smith, P. Watson, and T. H. Topper, “A stress-strain function for the fatigue of
metal,” J. Mater., 5, No. 4, 767–778 (1970).
5. K. Walker, “The effect of stress ratio during crack propagation for 2024-T3 and
7075-T6 aluminum,” in: Effects of Environment and Complex Load History on
Fatigue Life, ASTM STP 462, Philadelphia (1970), pp. 1–14.
6. N. E. Dowling, “Mean stress effects in stress-life and strain-life fatigue,” in: Proc. of
the Third Int. Sea Fatigue Congress, Sao Paulo, Brazil (2004).
7. J. T. Boyle and J. Spence, Stress Analysis for Creep, Butterworth & Co. Ltd. (1983).
8. K. S. Basaruddin and L. C. Wooi, “Uniaxial ratcheting of mild steel under cyclic
tension,” in: Proc. of Int. Conf. on Applications and Design in Mechanical
Engineering (ICADME), Batu Ferringhi, Penang, Malaysia (2009).
9. J. L. Chaboche, “On some modifications of kinematic hardening to improve the
description of ratcheting effects,” Int. J. Plast., 7, 661–678 (1991).
Accelerating Effects of Cyclic Creep ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 119
10. N. Ohno and J. D. Wang, “Kinematic hardening rules with critical state of dynamic
recovery. Part I: Formulations and basic features for ratcheting behavior,” Int. J.
Plast., 9, 375–390 (1993).
11. X. Chen, R. Jiao, and K. S. Kim, “On the Ohno–Wang kinematic hardening rules for
multiaxial ratcheting modeling of medium carbon steel,” Int. J. Plast., 21, 161–184
(2004).
12. P. J. Armstrong and C. A. Frederick, A Mathematical Representation of the Multiaxial
Bausinger Effect, CEGB Report No. RD/B/N 731 (1966).
13. X. Chen, D.-H. Yu, and K. S. Kim, “Experimental study on ratcheting behavior of
eutectic tin–lead solder under multiaxial loading,” Mater. Sci. Eng. A, 406, 86–94
(2005).
14. D. W. Kim, J. H. Chang, and W. S. Ryu, “Evaluation of the creep-fatigue damage
mechanism of type 316L and type 316LN stainless steel,” Int. J. Press. Vess. Piping,
85, 378–384 (2008).
15. D. W. Kim, H. Y. Lee, Ch. G. Park, and J. H. Lee, “Creep-fatigue test of a SA316SS
structure and comparative damage evaluations based upon elastic and inelastic
approaches,” Int. J. Press. Vess. Piping, 85, 550–556 (2008).
16. S. Holdsworth, “Creep-fatigue interaction in power plant steels,” Mater. High Temp.,
28, No. 3, 197–204 (2011).
17. S. R. Holdsworth, R. P. Skelton, and B. A. Dogan, “Code of practice for the
measurement and analysis of high strain creep-fatigue short crack growth,” Mater.
High Temp., 27, No. 4, 265–283 (2010).
18. M. H. Sabour and R. B. Bhat, “Lifetime prediction in creep-fatigue environment,”
Mater. Sci. Poland, 26, No. 3, 563–584 (2008).
19. R. Valentin, D. Barker, and M. Osterman, “Model for life prediction of fatigue-creep
interaction,” Microelectr. Reliab., 48, 1831–1836 (2008).
20. J. Ewald, S. Sheng, A. Klenk, and G. Schellenberg, “Engineering guide to assessment
of creep crack initiation on components by two-criteria-diagram,” Int. J. Press. Vess.
Piping, 78, 937–949 (2001).
21. J. L. Kaae, “High-temperature low-cycle fatigue of alloy 800H,” Int. J. Fatigue, 31,
332–340 (2009).
22. ASME Boiler and Pressure Vessel Code, Section III, Division 1 – Subsection NH,
Class 1 Components in Elevated Temperature Service, ASME, New York (2001).
23. ASTM A276-05a. Standard Specification for Stainless Steel Bars and Shapes, Vol.
02.04, ASTM International, West Conshohocken, PA (2005).
24. ASTM E8M-04. Standard Test Methods for Tension Testing of Metallic Materials
(Metric), ASTM International, West Conshohocken, PA (2004).
25. ASTM E139-06. Standard Test Methods for Conducting Creep, Creep-Rupture, and
Stress-Rupture Tests of Metallic Materials, ASTM International, West Conshohocken,
PA (2006).
26. A. Le Pécheur, F. Curtit, M. Clavel, et al., “Thermo-mechanical FE model with
memory effect for 304L austenitic stainless steel presenting microstructure gradient,”
Int. J. Fatigue, 45, 106–115 (2012).
27. Y. L. Lee, M. E. Barkey, and H. T. Kang, Metal Fatigue Analysis Handbook:
Practical Problem – Solving Techniques for Computer-Aided Engineering, Chapter 4:
Stress-Based Uniaxial Fatigue Analysis, Butterworth–Heinemann (2011).
Received 09. 04. 2014
A. H. Daei-Sorkhabi and F. Vakili-Tahami
120 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
|
| id | nasplib_isofts_kiev_ua-123456789-173399 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T16:53:58Z |
| publishDate | 2015 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Daei-Sorkhabi, A.H. Vakili-Tahami, F. 2020-12-02T16:35:50Z 2020-12-02T16:35:50Z 2015 Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L / A.H. Daei-Sorkhabi, F. Vakili-Tahami // Проблемы прочности. — 2015. — № 6. — С. 108-120. — Бібліогр.: 27 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173399 539.4 На основании результатов испытаний на одноосное растяжение выполнена сравнительная оценка ускоренных эффектов циклической ползучести в условиях переменного и постоянного нагружений для аустенитной нержавеющей стали 304L, широко используемой в энергетике и нефтехимической промышленности из-за ее повышенных характеристик сопротивления высокотемпературной ползучести и усталости. Образцы для испытаний получены из холоднотянутых прутков, материал соответствует спецификации ASTM A276-05A. Испытания проводились при температурах 687, 717 и 737°С в условиях знакопеременного и постоянного нагружений. Изучены эффекты переменной нагрузки и времени выдержки нагрузки на механическое поведение материала и характеристики усталости и ползучести. На основі результатів випробувань на одноосьовий розтяг виконано порівняльну оцінку прискорених ефектів циклічної повзучості в умовах змінного і постійного нагружений для аустенітної нержавіючої сталі 304L, широко використовуваної в енергетиці та нафтохімічної промисловості через її підвищених характеристик опору високотемпературної повзучості і втоми. Зразки для випробувань отримано з холоднотягнутих прутків, матеріал відповідає специфікації ASTM A276-05A. Випробування проводилися при температурах 687, 717 і 737°С в умовах змінного й постійного навантажень. Вивчено ефекти змінного навантаження та часу витримки на механічну поведінку матеріалу і характеристики втоми й повзучості. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L Сравнительная оценка ускоренных эффектов циклической ползучести в стали CD-304L в условиях переменного и постоянного нагружений Article published earlier |
| spellingShingle | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L Daei-Sorkhabi, A.H. Vakili-Tahami, F. Научно-технический раздел |
| title | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L |
| title_alt | Сравнительная оценка ускоренных эффектов циклической ползучести в стали CD-304L в условиях переменного и постоянного нагружений |
| title_full | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L |
| title_fullStr | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L |
| title_full_unstemmed | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L |
| title_short | Accelerating Effects of Cyclic Creep Due to the Alternative Load Compared with Constant Load for CD 304L |
| title_sort | accelerating effects of cyclic creep due to the alternative load compared with constant load for cd 304l |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/173399 |
| work_keys_str_mv | AT daeisorkhabiah acceleratingeffectsofcycliccreepduetothealternativeloadcomparedwithconstantloadforcd304l AT vakilitahamif acceleratingeffectsofcycliccreepduetothealternativeloadcomparedwithconstantloadforcd304l AT daeisorkhabiah sravnitelʹnaâocenkauskorennyhéffektovcikličeskoipolzučestivstalicd304lvusloviâhperemennogoipostoânnogonagruženii AT vakilitahamif sravnitelʹnaâocenkauskorennyhéffektovcikličeskoipolzučestivstalicd304lvusloviâhperemennogoipostoânnogonagruženii |