Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading
A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium a...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2008
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| Назва видання: | Проблемы прочности |
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irk-123456789-484602013-08-19T22:48:42Z Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading Shukaev, S. Gladskii, M. Zakhovaiko, A. Panasovskii, K. Научно-технический раздел A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0,6, 0,8, and 1,0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. Предложен новый метод оценки усталостной долговечности в условиях многоосного равномерного и неравномерного нагружения, который основан на модифицированном критерии Писаренко-Лебедева, линейной гипотезе накопления повреждений и нелинейном подходе Мэнсона. Приведены результаты испытаний титанового сплава ВТ9 на малоцикловую усталость при неравномерном пропорциональном и непропорциональном двухосном нагружении. Испытания проводились при трех уровнях деформаций по критерию Мизеса: 0,6; 0,8; 1,0% с различными сочетаниями пропорциональной и непропорциональной траекторий деформации. Все испытания выполнялись при комнатной температуре. Установлено, что предлагаемый метод является эффективным и позволяет учитывать такие факторы, как вид деформированного состояния, тип траектории деформации и неравномерность нагружения. 2008 Article Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading / S. Shukaev, M. Gladskii, A. Zakhovaiko, K. Panasovskii // Проблемы прочности. — 2008. — № 1. — С. 56-59. — Бібліогр.: 3 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48460 539. 4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Shukaev, S. Gladskii, M. Zakhovaiko, A. Panasovskii, K. Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading Проблемы прочности |
| description |
A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0,6, 0,8, and 1,0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. |
| format |
Article |
| author |
Shukaev, S. Gladskii, M. Zakhovaiko, A. Panasovskii, K. |
| author_facet |
Shukaev, S. Gladskii, M. Zakhovaiko, A. Panasovskii, K. |
| author_sort |
Shukaev, S. |
| title |
Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading |
| title_short |
Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading |
| title_full |
Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading |
| title_fullStr |
Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading |
| title_full_unstemmed |
Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading |
| title_sort |
method for low-cycle fatigue life assessment of metallic materials under multiaxial loading |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2008 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/48460 |
| citation_txt |
Method for low-cycle fatigue life assessment of metallic materials under multiaxial loading / S. Shukaev, M. Gladskii, A. Zakhovaiko, K. Panasovskii // Проблемы прочности. — 2008. — № 1. — С. 56-59. — Бібліогр.: 3 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
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| first_indexed |
2025-07-04T08:58:36Z |
| last_indexed |
2025-07-04T08:58:36Z |
| _version_ |
1836706189071613952 |
| fulltext |
UDC 539. 4
A M e th o d fo r L o w - C y c le F a t ig u e L ife A s s e s s m e n t o f M e ta l l ic M a te r ia ls
u n d e r M u lt ia x ia l L o a d in g
S. S h u k aev ,1a M . G lad sk ii,1b A . Z a k h o v a ik o ,1c and K . P a n a so v sk ii1,d
1 National Technical University o f Ukraine “Kiev Polytechnic Institute,” Institute o f Mechanical
Engineering, Department o f Machine Dynamic and Strength o f Materials, Kiev, Ukraine
a shukayev@users.ntu-kpi.kiev.ua, b’d gladsky@gmail.com, c zakhov@users.ntu-kpi.kiev.ua
A new method o f fatigue life assessment under multiaxial low-cycle regular and irregular loading is
proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage
accumulation hypothesis, and the nonlinear Manson approach. The results o f low-cycle fatigue tests
o f titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given.
The tests were carried out at three Mises strain levels (0,6, 0,8, and 1,0%) with various
combinations o f proportional and non-proportional strain paths. All the tests were carried out at
room temperature. The proposed method turned out to be effective and to allow fo r such factors as
strain state type, strain path type and loading irregularity.
K e y w o r d s : m ultiaxial low -cy c le fatigue, irregular loading, titanium alloys, damage
accum ulation, lim it state criteria.
In trod u ction . M achine and construction elem ents often undergo irregular m ultiaxial
cycle loading. Though m ultiaxial fatigue o f materials has been studied for a long tim e and
sufficient experim ental data has been accumulated, the problem o f including a loading
irregularity in a low -cycle fatigue area is still important. N um erous attempts to describe
fatigue damage process have been made, resulting in the developm ent o f a large number
o f damage accum ulation m odels.
The m ost generally em ployed is the linear damage accum ulation concept proposed
b y Miner, w hereby dam ages D per cycle at a variable loading amplitude are added
linearly and the failure happens w hen D = ' ^ . n i / N f = 1, w here n { is the number o f
on e-level loading cycles and N f is number o f cycles to failure under a g iven loading
level. This approach is easy to use but it fails to g ive an adequate estim ation o f life in
m any cases.
There have been m any attempts to develop a m odel based on the nonlinear
accum ulation o f fatigue dam age, but m ost o f them disregarded the com plex influence o f
such factors as the stress state type, loading path, previous stress history in the process o f
fatigue damage accumulation. Fatemi and Yang [1] have carried out a substantial survey
o f the existing m odels, proposed a classification thereof, d iscussed advantages and
disadvantages o f each m odel.
In the paper, the influence o f sequential loading effects is studied on V T9 titanium
alloys under tension-com pression , torsion and 90° out-of-phase non-proportional loading.
The life estim ation m ethod is proposed both for regular and irregular m ultiaxial loading.
A dam age m odel is put forward, w hich considers the nonproportional effects arising at a
change o f the loading regim e.
E xperim enta l Procedure. A high-temperature titanium alloy V T9 o f the T i-A l-M o -
Z r-S i system b elongs to tw o-phase (a + /3) m artensitic alloys. The chem ical com position
(in wt.% ) o f the material is g iven in Table 1. The microstructure o f the material o f the
specim en billets consists o f (a + /3)-phases o f equiaxial structure and corresponds to the
second type in the nine-type scale for bar materials according to Instruction N o. 1054-76
o f the A ll-U n ion Institute o f Aircraft Materials.
© S. SH U K A EV , M. G LA D SK II, A . ZA K H O V A IK O , K. PA N A SO V SK II, 2008
56 ISSN 0556-171X. Проблемы прочности, 2008, № 1
mailto:shukayev@users.ntu-kpi.kiev.ua
mailto:gladsky@gmail.com
mailto:zakhov@users.ntu-kpi.kiev.ua
A Method fo r Low-Cycle Fatigue Life Assessment
T a b l e 1
Chemical Composition of VT9 Alloy
Al Mo Si Fe Zr H2 n 2 C
6.50 3.40 0.30 0.081 1.58 0.006 0.018 0.06
Specim ens w ere m ade from as-delivered rolled bars 25 m m in diameter. The
m echanical properties o f the material, w hich were determ ined by tensile testing o f
125-m m -long solid cylindrical specim ens at room temperature, have the fo llow ing mean
values: proportional lim it 758 MPa, y ield strength 865 MPa, ultimate strength 973 MPa,
elongation 17%, reduction o f the cross-sectional area 45%, and elastic m odulus 118 GPa.
For the purpose o f providing a stress-strain state c lose to a hom ogeneous one,
tubular specim ens w ith an outer diameter o f 11 m m , w all thickness o f 0.5 m m , gauge
length o f 20 m m were used. The realized strain paths are show n in Fig. 1.
/
f
4
\
s "
t
f h Ar\1
\ \
4 V
\
\ \
*4 К N[>
a t o
Fig. 1. Schematics o f strain paths used.
For the V T 9 titanium alloy the test program as g iven in Table 2 w as implemented.
The basic m odes w ere as follow s: tension-com pression , alternating torsion, and 90°
out-of-phase loading. The first stage o f the program w as the b lock axial loading and/or
torsion m om ent test w ith g iven strain ranges. During this test the strain path remained
constant. The second stage o f the program involved testing o f the specim ens w ith
changing o f the strain path. A transition from one strain path to the other w as conducted
w hen the D value reached 0.5 and then the specim en w as cycled to failure. A t the third
stage the test w ith a m ultiple strain path change w as carried out.
P ro p o sed M eth od . It w as prev iously m entioned that the application o f the
Pisarenko-L ebedev m odified criterion for the fatigue life assessm ent o f the V T 1-0
titanium alloy under regular nonproportional loading show s a good agreem ent betw een
the predicted and test data due to the com plex consideration o f the strain state type and
nonproportionality o f loading [3]. Therefore it is recom m ended to apply the P isarenko-
L ebedev m odified criterion as w ell as the chosen damage accum ulation hypothesis for
assessing the V T9 titanium alloy fatigue life. In this study, the tw o damage accumulation
hypotheses w ere analyzed: the linear hypothesis and the M anson approach w ith the
Pisarenko-L ebedev equivalent strain in both cases, according to w hich the damage curve
is a nonlinear function o f the relative fatigue life,
D i = (n t / N fi ) q ,
where q = ( N f i / N f r )a ; a is the material constant to be calculated from the test data for
sequential double-level loading, and N fr is the number o f load cycles to failure at a
“reference” loading level.
A nalyzing Figs. 2 and 3 one can see that during the application o f the P isarenko-
L ebedev m odified criterion and the linear damage accum ulation hypothesis the best
correlation betw een the predicted and test data is obtained for alternating torsion (paths
t_01 and t_ 02 ).
ISSN 0556-171X. Проблемыг прочности, 2008, № l 57
S. Shukaev, M. Gladskii, A. Zakhovaiko, and K. Panasovskii
T a b l e 2
Strain Peak Values and Number o f Cycles to Failure for VT9 Titanium Alloy
Test type £a y J V3 ni N f
% cycle
a_01 a 0.8 - 157 293
a 1.0 - 136
a_02 a 1.0 - 98 245
a 0.8 - 147
a 03 a 0 .6- 0 .8- 1.0- 0.8 - 50 519
a 04 a 1.0- 0 .8- 0 .6- 0.8 - 50 491
oatota — 0.8 1.0 50 475
oa o 1.0 1.0 77 218
a 1.0 - 141
atat 1/5 a 1.0 - 40 423
t - 1.0 130
atat 1/3 a 1.0 — 65 510
t - 1.0 219
t_01 t - 0 .8- 1.0- 1.2- 1.0 50 601
t_02 t - 1.2- 1.0- 0 .8- 1.0 50 528
at a 1.0 - 97 398
t - 1.0 301
ta t - 1.0 398 603
a 1.0 - 205
ao a 1.0 - 98 184
o 1.0 1.0 86
to t - 1.0 282 390
o 1.0 1.0 108
ot o 1.0 1.0 80 384
t - 1.0 304
A s a result, one can com e to a conclusion about the linearity o f damage accumulation
process for a g iven loading type. The com bined application o f the P isarenko-Lebedev
m odified criterion and o f the M anson’s approach show ed a h igh leve l o f correlation
betw een the predicted data and test results for all the loading programs except the
alternating torsion. So, the fo llow in g m odification o f the M anson approach is proposed:
D i = ( n j N f i ) ß( m)
( 1)
w here ß ( « ) = ( V
a
2m
+ — 1- ( V
a
\ N fr> n \ N f r )
m is the strain path orientation angle, w hich
determ ines the dom inating type o f the strain state, m = arctan
/ \
y a £ fs
£ a y fs
£ fs and y fs
58 ISSN 0556-171X. npoôëeMbi npounocmu, 2008, N9 1
A Method fo r Low-Cycle Fatigue Life Assessment
♦ a Q3; a 04
■ i_ p i ; t_D2
■ ADS
o ao
X Dt
. x1o
+ a tat_1/3
-i- a tat 1/5
£>at
' D la
/
/
/
/
, +
*•
/ 4
A
' ♦a_Q3;
a1_01 ;
Aoa
o an
X Dt
x lo
+ ata1_1
+ ata1_1
• DStDta
<-at
. □ la
U4 /
/
/
/
<2 /
1
/
/
p r
A
/
/ *
A
Nobservet
Fig. 2 Fig. 3
Fig. 2. Comparison between the fatigue lives predicted by the modified linear damage rule and the
experimental fatigue lives.
Fig. 3. Comparison between the fatigue lives predicted by the modified damage curve approach and
the experimental fatigue lives.
are the fatigue strength coefficients for a
finite life N f in the uniaxial and torsional
loading cases.
Thus, the damage accum ulation during
the alternating torsion is linear, during the
tension-com pression is calculated using the
M anson approach, and during the biaxial
proportional and non-proportional loading is
assessed by their linear interpolation.
The application o f formula (1) resulted
in the best agreem ent betw een the predicted
and experim ental data as show n in Fig. 4.
C onclusion . The proposed m ethod o f
fatigue life assessm ent under m ultiaxial low -
cycle regular and irregular loading, w hich is
based on the P isarenko-L ebedev m odified
criterion, the linear damage accum ulation
hypothesis, and the nonlinear M anson
approach proved to be effective and to a llow for such factors as the strain state type, strain
path type, and loading irregularity.
♦ a Ü3; a 04
■ t_01 ; t_02
Aoa
o a o
XOt
X t D
+ atat_1/3
+ atat_1ß
* oat ola
Oat
□ ta
/
/
/
Y
/
/ / / / ^ ////̂/
A
Fig. 4. Comparison between the fatigue lives
predicted by the proposed approach and the
experimental fatigue lives.
1. A. Fatemi and L. Yang, “Cumulative fatigue damage and life prediction theories: a survey of
the state o f the art for homogeneous materials,” Int. J. Fatigue, 20, No. 1, 9-34 (1998).
2. T. Itoh, M. Sakane, M. Ohnami, et al., “Dislocation structure and non-proportional hardening
of type 304 stainless steel,” in: Proc. o f the 5th Int. Conf. on Biaxial-Multiaxial Fatigue and
Fracture, Cracow (1997), Vol. 1, pp. 189-206.
3. S. Shukaev, A. Zakhovaiko, M. Gladskii M., and K. Panasovskii, “Estimation o f low-cycle
fatigue criteria under multiaxial loading,” Int. J. Reliab. Life Machin. Struct., 2, 127-135
(2004).
Received 28. 06. 2007
ISSN 0556-171X. npoôneMU npoHHocmu, 2008, № 1 59
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