Evaluation of the limit state and cyclic life of structural materials under thermal fatigue
The relationship between the cyclic life and reduced stress in half-cycles of heating (compression) has been established, as well as the parameters defining the transition from the quasi-static to fatigue fracture mode and their threshold values. An approach has been proposed for the evaluation of c...
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2009
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| Cite this: | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue / A.P. Gopkalo // Проблемы прочности. — 2009. — № 1. — С. 95-104. — Бібліогр.: 12 назв. — англ. |
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| citation_txt | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue / A.P. Gopkalo // Проблемы прочности. — 2009. — № 1. — С. 95-104. — Бібліогр.: 12 назв. — англ. |
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| description | The relationship between the cyclic life and reduced stress in half-cycles of heating (compression) has been established, as well as the parameters defining the transition from the quasi-static to fatigue fracture mode and their threshold values. An approach has been proposed for the evaluation of cyclic life under thermal fatigue, which involves a preliminary prediction of the fracture mode and the use of calculation relationships corresponding to the predicted mode of fracture.
Установлена зависимость циклической долго вечности от уровня приведенных напряжений в полуциклах нагрева/охлаждения, а также параметры, определяющие переход от квазистатического к усталостному разрушению и соответствующие им пороговые значения. Предложен новый подход к оценке циклической долговечности при термоусталости, который включает в себя предварительный прогноз типа разрушения и использование расчетных зависимостей, соответствующих прогнозируемому типу разрушения.
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UDC 539.4
Evaluation of the Limit State and Cyclic Life of Structural Materials
under Thermal Fatigue
A. P. G opkalo
Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine,
Kiev, Ukraine
The relationship between the cyclic life and reduced stress in half-cycles o f heating (compression)
has been established, as well as the parameters defining the transition from the quasi-static to
fatigue fracture mode and their threshold values. An approach has been proposed fo r the evaluation
o f cyclic life under thermal fatigue, which involves a preliminary prediction o f the fracture mode
and the use o f calculation relationships corresponding to the predicted mode o f fracture.
K e y w o r d s : reduced stress, quasi-static and fatigue fracture, cyclic life.
In tro d u c tio n . A large num ber o f present-day structures in operation are
subject to the action o f variable temperatures and mechanical loads. The experience
o f their operation shows that the limit state o f the whole structure or its individual
elements occurs due to fatigue crack propagation or inadmissible changes in the
initial geometry (a change in the shape). Form ation o f a certain type o f the limit
state occurs by the accumulation o f corresponding types o f damages. Fatigue
crack initiation and propagation are caused by cyclic alternating plastic deformation
while the accumulation o f quasi-static damages is associated with the processes o f
oriented plastic deformation (cyclic creep).
Pecu liarities o f the M ate ria l D am age u n d e r Iso th erm a l an d N on
Iso th erm a l C onditions. The life o f materials under thermal fatigue is generally
determined from the calculation relationships that correspond to a fatigue or
quasi-static fracture mode under low-cycle m echanical loading under isothermal
conditions. Attempts to use the same calculation relationships for thermal fatigue
conditions yield an incorrect result despite the similarity o f m any processes under
low-cycle m echanical fatigue in isothermal conditions and under thermal fatigue,
such as the development o f the local plastic strains and formation o f cracks in the
m ost heavily stressed zones (with the accumulation o f the num ber o f cycles); an
increase in the stress and strain amplitudes leads to a decrease in the num ber of
cycles to fracture; a similar effect o f the stress and strain concentration, stress
state mode, and m any other factors is observed.
A t the same time, there is a fundamental difference between the low-cycle
mechanical fatigue and thermal fatigue. Under conditions o f low-cycle mechanical
loading at constant temperature, the same zones o f the material are in turn subject
to plastic tensile and compressive strains. In this case, the alternating cyclic
elastic-plastic deformation is caused by a change in the resistance to the elastic
and inelastic strains (the Bauschinger effect). Thermal stresses occur due to the
thermal strain constraint, and therefore, they generally decrease rapidly with
increasing tem perature due to an increase in the plastic strain that has a tendency
© A. P. GOPKALO, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 1 95
A. P. Gopkalo
to be concentrated in the m ost heated zones o f the body. In addition, the most
heated zones o f the body “absorb” the elastic-plastic strains that were to have
occurred in the coolest zones due to the tem perature dependence o f the m aterial
m echanical characteristics.
Under thermal fatigue, the effects o f the material hardening m ay not show
depending on the level o f the m aximum temperature. Moreover, in the presence
o f the tem perature gradient, tensile strain concentration can occur in some zones
o f the material, while in other ones the concentration o f compressive strains takes
place. Under thermal fatigue, due to repeated thermal loading, hot and cold
working o f the material is possible that has a great im pact on the m aterial strength
and its subsequent properties. The temperature gradient in a tem perature cycle
that defines the elastic-plastic strain range is also o f great importance here. At the
maximum tem perature in a cycle, the plastic strain value depends essentially on
time and, therefore, the plastic strain is frequently accompanied by a considerable
creep and stress relaxation, whereas at the minimum cycle temperature this
dependence is weaker or absent. I f the maximum cycle tem perature is high
enough, intensive development o f intergranular deformation and fracture can
occur, w hich are typical o f the processes o f creep and long-term fracture, w ith the
development o f diffusion, oxidation and other processes. At the values o f the
cycle m inim um tem perature below 150°C, transgranular deformation and fracture
prim arily occur.
It is reasonable that the differences in the processes o f the m aterial
deform ation under isothermal and non-isotherm al conditions considered here
affect the m aterial ability to resist cyclic deformation. Thus, i f we consider the
lim iting am plitude diagram s for structural heat-resistant steels subjected to
isotherm al and non-isotherm al loading conditions, the difference in the grouping
o f the points, which are representative o f the corresponding mode o f fracture, can
be noted (Fig. 1). U nder non-isotherm al conditions, with the cycle stress ratio R a
varying from 0 to —0.32, fatigue fracture takes place, whereas with R a decreasing
from —0.32 to —1 quasi-static fracture occurs. In contrast to non-isothermal
conditions, under low-cycle loading and isothermal conditions, the fracture mode
is independent o f the cycle stress ratio and is defined by the values o f the cycle
stress amplitude and m ean stress. The noted difference in the grouping o f the
points is due to the peculiarities o f the deformation and fracture o f materials
under non-isotherm al conditions indicated above and in [ 1].
U nder conditions o f therm al fatigue, both the values o f the stresses generated
in the material and the m aterial m echanical characteristics vary during each
thermal cycle. As an example, Fig. 2 illustrates the temperature dependences of
the offset yield stress for some die steels, and Fig. 3 illustrates those o f the
thermal stresses occurring in these steels. Considering the reduced stresses in the
materials (the ratio o f the stress acting in the m aterial to its offset yield stress)
during one thermal cycle (Fig. 4), it should be noted that in the tensile half-cycles,
the differences in the reduced stress values in materials are not as important as in
the compressive half-cycles. The differences in the reduced stresses in materials
during tensile and compressive half-cycles are, to a greater extent, due to the
difference in the m echanical properties (Fig. 2) and, to a lesser extent, to the
difference in the absolute values o f the thermal stresses (Fig. 3).
96 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 1
Evaluation o f the Limit State and Cyclic Life
a a , MPa
200
150
100
50
50 100 150
a
a a , MPa
200 a m, MPa
b
Fig. 1. The limiting amplitude diagrams for loading under non-isothermal [a: (/) steel 15KhML,
(2) steel 20KhML] and isothermal [b: steel 15Kh2NMFA, (/) T = 20°C, (2) T = 400°C] conditions
(open symbols stand for quasi-static fracture, solid symbols for the fatigue fracture).
° a 2> MPa
Fig. 2. Temperature dependence of the offset yield stress for the steels under study: (/) 5KhNM;
(2) 5KhMNAF; (3) Kh4M3AF; (4) 4Kh5MFAS. (The notations in Figs. 3-6 are the same as in
Fig. 2 .)
ISSN 0556-171X. npoôneMU npoHHoemu, 2009, № 1 97
A. P. Gopkalo
a T, MPa
Fig. 3. Temperature dependence of the thermal stresses in a specimen within one thermal cycle at
2a = 370 MPa.
( a 7 a 0.2);
Fig. 4. Temperature dependence of the reduced stress in the steels under study within one thermal
cycle at 2a = 370 MPa.
Generalization o f the results o f experimental investigations into the resistance
o f a num ber o f heat-resistant structural steels to deformation and fracture under
t I tthermal fatigue has shown that for a ^ / a o 2 > 0.8 (the ratio o f the compressive
stress occurring at the maxim um tem perature o f the thermal cycle to the offset
yield stress determined at the same temperature), the m echanism o f quasi-static
T I Tdamage is prevailing, whereas for a mi^ / a 02 < 0.6 , it is the m echanism o f the
fatigue damage [2]. A t the steady-state creep rate V cr = 1-10_5 mm/mm/cycle, a
change in the mechanisms o f damage accumulation occurs. A t V cr > 1 -10_ 5
mm/mm/cycle, quasi-static fracture takes place and at V cr < 1 - 10_5 mm/mm/cycle,
fatigue fracture occurs. In this case, the threshold values o f the steady-state creep
rate, at which the change in the material damage mechanisms is observed, were
98 ISSN 0556-171X. Проблемы прочности, 2009, N 1
Evaluation o f the Limit State and Cyclic Life
confirmed by the test results for more than thirty various materials under
isothermal low-cycle m echanical loading [3].
Traditional presentation o f the fatigue curves in terms o f stresses (Fig. 5a) or
strains (Fig. 5b) shows that for every m aterial there is its own thermal fatigue
curve.
looo loooo N f , cycles
a
b
Fig. 5. Cyclic lifetime of the steels under study as a function of the stress range (a) and plastic strain
range (b) for specimens heated from 150 to 750°C.
I f the same results are presented in the norm alized coordinates (Fig. 6a, b),
y
where o max is the maxim um tensile stress occurring in the material under the
T .
action o f the m inimum tem perature in a thermal cycle, o min is the minimum
(compressive) stress occurring in the material under the action o f the maximumrp
tem perature in a thermal cycle, o 02 is the offset yield stress o f the m aterial at the
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1 99
A. P. Gopkalo
m inim um and m aximum tem perature o f the thermal cycle, respectively, and N f
is the num ber o f cycles to fracture, the thermal fatigue curves differ essentially.
But in the case where the same test results are presented in terms of
T / T
( ° min/ ° 0 2 ) _ N f , the experimental points for the steels under investigation are
described by a single thermal fatigue curve, whereas when the results are presented
T / Tin terms o f ( o ma^ / o 0 2 ) _ N f , every material has its own thermal fatigue curve.
1000 loooo N f , cycles
a
t I t
a min/ a 0.2
1000 10000 N f , cycles
b
Fig. 6. Cyclic lifetime of the steels under study as a function of the reduced stress in tensile
half-cycles (a) and compressive half-cycles (b) for specimens heated from 150 to 750°C.
100 ISSN 0556-171X. Проблемы прочности, 2009, № 1
Evaluation o f the Limit State and Cyclic Life
This circumstance has m ade it possible to conclude that under thermal
fatigue conditions, the most serious damage to the m aterial occurs in the
half-cycles o f heating (compression) under the action o f the maximum temperature
in a therm al cycle, and the lifetime is governed, to a great extent, by the reduced
stress in the m aterial in these half-cycles.
It should be noted that under the action o f the maximum temperature in the
heating half-cycles, the m aterial has lower m echanical characteristics than those
at lower tem perature in the cooling half-cycles. In the half-cycles o f cooling, the
m aximum (tensile) stresses occur in the material; yet, their contribution to the
total damage is not as significant as that o f the half-cycles o f heating (see Fig. 4).
It is this circumstance that determines the availability o f a single thermal fatigue
curve for the m aterials under investigation in terms o f the reduced stress versus
num ber o f cycles to fracture. This indicates that the reduced stress o f the material
in the half-cycles o f heating (compression) is a more generalizing param eter that
allows for the specific character o f the loading conditions and the m aterial
properties.
M ethods o f E s tim a tin g Cyclic L ife o f M ate r ia ls u n d e r Iso th e rm a l
C onditions. As applied to the conditions o f low-cycle m echanical fatigue, of
interest are the C offin-M anson method [4], M anson-H irschberg m ethod of
universal slopes [5], the 10% rule [6 ], the Taira method [7], the m ethod o f strain
amplitude separation, various cumulative damage rules [9, 10], as well as a
num ber o f stress-, strain-, energy-based and other models o f the m aterial damage.
However, the practical use o f the proposed methods for thermal fatigue conditions
is lim ited by the complexity o f obtaining the required data and does not always
yield satisfactory results.
To estimate the cyclic life o f m aterials under isothermal low-cycle loading,
the following calculation relationships are w idely used in the current engineering
practice:
in the case o f quasi-static fracture [11]
where N f is the num ber o f the load cycles to fracture, £ is the reduced
steady-state creep rate, w hich determines the degree o f the material plasticity
realization at the steady-state stage and characterizes the m aterial capability to
accumulate plastic strains at this stage, Vcr is the steady-state creep rate, £ f is
the available plasticity o f the material, £ in is the plastic strain per cycle, and k
and C are material constants.
The reduced steady-state creep rate £, which is determined from the
generalized creep curves in the coordinates ( £ i /£ f ) — ( N t / N f ), is a constant in
the case o f quasi-static fracture and is not such in the case o f fatigue fracture [11].
Vr cr
( 1)
and in the case o f fatigue fracture [12]
(2)
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1 101
A. P. Gopkalo
Figure 7 presents the experim ental data, w hich illustrate the relation
betw een the param eter £ and the reduced stress values a ° 0 2 - From this
t I tfigure it follows that in the region o f quasi-static fracture ( a mi^ / a 0 2 > 0- 8) the
values o f the param eter £ are constant, whereas in the region o f fatigue fracture
7-1 I t
( a mm/ a o.2 < 0. 6) they are not.
K
8
6
4
2
a 'lmml ° 0.2 -1-8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0°
Fig . 7 . Reduced steady-state creep rate versus the level of the reduced stress [(/) steel 15KhML;
(2) steel 20KhML; open symbols - quasi-static fracture, solid symbols - fatigue fracture] .
In view o f the dual character o f the materials fracture under conditions of
thermal fatigue, when estimating cyclic life it is appropriate to perform preliminary
prediction o f the fracture mode (lim it state) with the use o f the threshold values o f
T / Tthe parameters o mi^ / o 0 2 or V cr established earlier [2] with subsequent selection
o f a calculation relationship corresponding to the real prevailing m echanism of
damage accumulation.
The procedure for predicting the limit state and cyclic life o f a material
consists in the following. Based on the analysis o f the service factors and
physical-mechanical properties o f the structure material, the tem perature fields
are determined in the m ost heavily loaded areas o f the structure, and the thermal
stress values are calculated with the use o f a computational method. Then, using
the obtained stress values, a possible lim it state o f the structure material (mode of
fracture) is predicted.
Prediction o f a possible lim it state can also be made using the values o f the
steady-state creep rate. I f the steady-state creep rate exceeds the threshold value,
one should expect a quasi-static fracture (a change in the shape). I f the values of
the steady-state creep rate are below the threshold ones, one should expect a
fatigue fracture (due to fatigue crack propagation).
C o n c l u s i o n s
1. Peculiar features o f the reduced stress o f materials in the half-cycles of
compression and tension under thermal fatigue, which should be taken into
account in engineering practice, have been established.
A "
A
A A
• •
A . O Q n O. i n . <D . lA . O i ...........................
102 ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 1
Evaluation o f the Limit State and Cyclic Life
2. The dependence o f the cyclic life on the reduced stress in the half-cycles
o f heating (compression) has been determined, which, for structures operating
under therm al fatigue, makes it possible to choose the m aterial that w ould be most
appropriate for the specified service conditions w ith a better justification and to
conduct works aimed at creation o f materials with specified properties o f the
resistance to thermal fatigue.
3. For operation under conditions o f thermal loading, it is advisable to
choose the materials whose offset yield stress does not decrease abruptly w ith a
slight increase in temperature. The tem perature range, within which an abrupt
change in the m aterial offset yield stress is possible, should be avoided.
4. Under conditions o f thermal fatigue as well as under isothermal mechanical
low-cycle loading, the param eter £, which enters into relationship (1), is a
constant at quasi-static fracture, and is not a constant at fatigue fracture.
5. Comparison o f the limiting amplitude diagrams obtained under isothermal
and non-isotherm al conditions shows that in the former case the m aterial fracture
m ode is independent o f the cycle stress ratio and is defined by the cyclic stress
amplitude and the m ean stress o f the cycle, whereas in the latter case it depends
on the cycle stress ratio.
6 . To estimate the life o f materials operating under conditions o f cyclic
tem perature variation, it is possible to employ approaches involving a prelim inary
prediction o f the fracture m ode and the use o f calculation relations corresponding
to the predicted fracture mode.
t I t7. Using the generalizing param eter <7 ^ / a 0.2 , it is possible to specify the
in-service conditions for operating structures by decreasing the reduced stress of
the m ost critical elements and to extend the life o f structures that have already
exhausted their assigned service life.
1. A. P. Gopkalo, “An investigation o f the features o f loading in thermal
fatigue,” S tre n g th M a te r . , 26, No. 10, 725-728 (1994).
2. V. T. Troshchenko, D. P. Sinyavskii, and A. P. Gopkalo, “Fracture criteria
for metals under nonisothermal loading. Report No. 2,” Ib id , 13, No. 12,
1450-1455 (1981).
3. A. P. Gopkalo and D. P. Sinyavskii, “On life prediction for structures
operating under conditions o f cyclic tem perature variations,” in: R e lia b il i ty
a n d D u r a b il i ty o f M a c h in e s a n d S tr u c tu re s [in Russian], Issue 2, Kiev
(1982), pp. 40-45.
4. L. F. Coffin, “On the thermal fatigue o f steels,” in: H e a t-R e s is ta n t A llo y s
u n d e r C o n d itio n s o f V a ry in g T e m p e ra tu re s a n d S tr e s se s [Russian translation],
Gosenergoizdat, M oscow (1960), pp. 188-258.
5. S. S. Manson, “Fatigue: A complex subject - some simple approximations,”
E xp. N e c k ., 5, No. 7, 193-226 (1965).
6 . S. S. M anson and G. R. Halford, “A m ethod o f estimating high-temperature
low-cycle fatigue behavior o f m aterials,” in: Proc. Int. Conf. on T h e rm a l a n d
H ig h -S tra in F a tig u e , Metals and M etallurgy Trust, London (1967), pp. 254
270.
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, № 1 103
A. P. Gopkalo
7. S. Taira, “Lifetim e o f structures subjected to varying load and tem perature,”
in: N. J. H off (Ed.), C r e e p in S tr u c tu re s , Academic Press, N ew York (1962),
pp. 96-124.
8 . S. S. Manson, G. R. Halford, and M. H. Hirschberg, “Creep-fatigue analysis
by strain-range partitioning,” in: Proc. Symp. on D e s ig n f o r E le v a te d
T e m p e ra tu re E n v iro n m e n t, ASM E (1971), pp. 12-28 (NASA TM X-67838,
1971).
9. R. A. D ul’nev, “Sum m ation o f static and cyclic effects on strength during
thermocyclic loading,” S tre n g th M a te r . , 3, No. 10, 1234-1237 (1971).
10. V. T. Troshchenko, D. P. Sinyavskii, and A. P. Gopkalo, “Fracture criteria
for metals under nonisothermal loading. Report No. 1,” Ib id , 13, No. 12,
1445-1449 (1981).
11. V. A. Strizhalo, “Study on the regularities o f the transition from quasistatic
to fatigue rupture o f light alloys under a few load cycles,” I b id , 6 , No. 5,
567-573 (1974).
12. V. A. Strizhalo, C y c lic S tr e n g th a n d C r e e p o f M e ta ls u n d e r L o w -C y c le
L o a d in g a t L o w a n d H ig h T e m p e ra tu re s [in Russian], Naukova Dumka, Kiev
(1978).
Received 11. 06. 2008
104 ISSN 0556-171X. npodxeMbi npounocmu, 2009, N 1
|
| id | nasplib_isofts_kiev_ua-123456789-48470 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-02T02:44:51Z |
| publishDate | 2009 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Gopkalo, A.P. 2013-08-20T03:51:13Z 2013-08-20T03:51:13Z 2009 Evaluation of the limit state and cyclic life of structural materials under thermal fatigue / A.P. Gopkalo // Проблемы прочности. — 2009. — № 1. — С. 95-104. — Бібліогр.: 12 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48470 539.4 The relationship between the cyclic life and reduced stress in half-cycles of heating (compression) has been established, as well as the parameters defining the transition from the quasi-static to fatigue fracture mode and their threshold values. An approach has been proposed for the evaluation of cyclic life under thermal fatigue, which involves a preliminary prediction of the fracture mode and the use of calculation relationships corresponding to the predicted mode of fracture. Установлена зависимость циклической долго вечности от уровня приведенных напряжений в полуциклах нагрева/охлаждения, а также параметры, определяющие переход от квазистатического к усталостному разрушению и соответствующие им пороговые значения. Предложен новый подход к оценке циклической долговечности при термоусталости, который включает в себя предварительный прогноз типа разрушения и использование расчетных зависимостей, соответствующих прогнозируемому типу разрушения. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Evaluation of the limit state and cyclic life of structural materials under thermal fatigue Оценка предельного состояния и циклической долговечности конструкционных материалов при термоусталости Article published earlier |
| spellingShingle | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue Gopkalo, A.P. Научно-технический раздел |
| title | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue |
| title_alt | Оценка предельного состояния и циклической долговечности конструкционных материалов при термоусталости |
| title_full | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue |
| title_fullStr | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue |
| title_full_unstemmed | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue |
| title_short | Evaluation of the limit state and cyclic life of structural materials under thermal fatigue |
| title_sort | evaluation of the limit state and cyclic life of structural materials under thermal fatigue |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/48470 |
| work_keys_str_mv | AT gopkaloap evaluationofthelimitstateandcycliclifeofstructuralmaterialsunderthermalfatigue AT gopkaloap ocenkapredelʹnogosostoâniâicikličeskoidolgovečnostikonstrukcionnyhmaterialovpritermoustalosti |