Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod
The accelerated life test based on the spectrum of fatigue loads was used both in numericalsimulation and bench tests of the push rod. The symmetrical cycling of the push rod was presented asthe positive pulsating load spectrum corresponding to the stress spectrum of the critical node in thefinite e...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2019
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irk-123456789-1883012023-02-23T01:27:17Z Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod Xua, L. Dai, G.Z. Научно-технический раздел The accelerated life test based on the spectrum of fatigue loads was used both in numericalsimulation and bench tests of the push rod. The symmetrical cycling of the push rod was presented asthe positive pulsating load spectrum corresponding to the stress spectrum of the critical node in thefinite element model. As FEM analysis demonstrates, the fatigue crack initiation would occur at theedge of the first-position pin hole with maximum stress and minimum fatigue life. Bench test results show that the fatigue crack initiation and fatigue life of the push rod are in good agreement with FEM data. Спектр усталостного нагружения при ускоренном испытании на долговечность использован как при численном моделировании, так и при стендовых испытаниях толкателя. Симметричный спектр толкателя был упрощен как положительный спектр пульсирующей нагрузки согласно спектру напряжений критического узла в конечноэлементной модели. Результаты анализа, полученные с помощью модели, свидетельствуют о том, что усталостная трещина зарождается на краю точечного отверстия в первом положении с максимальным напряжением и минимальной усталостной долговечностью. Согласно стендовым испытаниям зарождение усталостных трещин и усталостная долговечность толкателя хорошо согласуются с результатами анализа на конечноэлементной модели. Спектр втомного навантаження при прискореному випробуванні на довговічність використаний як при чисельному моделюванні, так і при стендових випробуваннях штовхача. Симетричний спектр штовхача був спрощений як позитивний спектр пульсуючого навантаження згідно спектру напружень критичного вузла в скінченноелементної моделі. Результати аналізу, отримані за допомогою моделі, свідчать про те, що втомна тріщина зароджується на краю точкового отвору в першому положенні з максимальним напруженням і мінімальної втомної довговічністю. Згідно стендовим випробуванням зародження втомних тріщин і втомна довговічність штовхача добре узгоджуються з результатами аналізу на скінченноелементної моделі. 2019 Article Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod / L. Xua, G.Z. Dai // Проблеми міцності. — 2019. — № 1. — С. 39-47. — Бібліогр.: 7 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/188301 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Xua, L. Dai, G.Z. Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod Проблемы прочности |
| description |
The accelerated life test based on the spectrum of fatigue loads was used both in numericalsimulation and bench tests of the push rod. The symmetrical cycling of the push rod was presented asthe positive pulsating load spectrum corresponding to the stress spectrum of the critical node in thefinite element model. As FEM analysis demonstrates, the fatigue crack initiation would occur at theedge of the first-position pin hole with maximum stress and minimum fatigue life. Bench test results show that the fatigue crack initiation and fatigue life of the push rod are in good agreement with FEM data. |
| format |
Article |
| author |
Xua, L. Dai, G.Z. |
| author_facet |
Xua, L. Dai, G.Z. |
| author_sort |
Xua, L. |
| title |
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod |
| title_short |
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod |
| title_full |
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod |
| title_fullStr |
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod |
| title_full_unstemmed |
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod |
| title_sort |
accelerated life test and fem simulation-based fatigue analysis of an aluminum alloy push rod |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2019 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/188301 |
| citation_txt |
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an Aluminum Alloy Push Rod / L. Xua, G.Z. Dai // Проблеми міцності. — 2019. — № 1. — С. 39-47. — Бібліогр.: 7 назв. — англ. |
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2025-07-16T10:18:11Z |
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| fulltext |
UDC 539.4
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis of an
Aluminum Alloy Push Rod
L. Xu
a,1
and G. Z. Dai
b
a School of Material Science and Engineering, Xihua University, Chengdu, China
b School of Material Science and Engineering, Southwest Jiaotong University, Chengdu, China
1 flyagainstwater@163.com
The accelerated life test based on the spectrum of fatigue loads was used both in numerical
simulation and bench tests of the push rod. The symmetrical cycling of the push rod was presented as
the positive pulsating load spectrum corresponding to the stress spectrum of the critical node in the
finite element model. As FEM analysis demonstrates, the fatigue crack initiation would occur at the
edge of the first-position pin hole with maximum stress and minimum fatigue life. Bench test results
show that the fatigue crack initiation and fatigue life of the push rod are in good agreement with
FEM data.
Keywords: high-strength aluminum alloy, push rod, accelerated life test, fatigue life, finite
element analysis.
Introduction. Train’s traction structural parts subjected to the variable loading may
tend to fatigue failure during the high-speed operation. The fatigue failure prevents the
components from functioning properly, and causes the critical problems in vehicle safety
[1, 2]. Therefore, in order to secure the trains components against fatigue failures,
durability test of the components has been performed in the vehicle industries [3]. At
present, analysis of fatigue and durability are used to the most components which is the
basic guarantee of the vehicle secure operation. The fatigue analysis is usually carried out
by theoretical calculation and bench tests [4, 5].
Push rod in the bogie system transmits tractive force between axle box and frame of
bogie which is shown in Fig. 1. In order to evaluate the fatigue life of the push rod
assembly in the bogie and saving testing time, the accelerated fatigue analysis of the push
rod was performed by the finite-element method (FEM) analysis and high-cycle fatigue test
of the Al–Zn–Mg–Cu alloy. Predicted accelerated fatigue life of the push rod was
compared with the bench test determined damage fatigue life to verify the validity of the
FEM results.
© L. XU, G. Z. DAI, 2019
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 39
Fig. 1. Push rod assembly in bogie system of CRH5.
1. Material. The push rod was made from Al–6.2Zn–2.2Mg–1.6Cu alloy. According
to the material micrograph depicted in Fig. 2, a typical microstructure of this aluminum
alloy contains elongated band-like grains aligned in the rod length direction. To research
the mechanical properties of the alloy, cylindrical specimens with a diameter of 8 mm were
taken from the push rod. Material testing machine with 200 kN capability was employed
for the static tensile test. Mechanical properties of the alloy are shown in Table 1.
High-frequency fatigue testing machine was employed for the axial loading fatigue test.
The fatigue life of the aluminum alloy can be described by the Basquin equation as follows:
lg . . lg ,�� � �1 327 012 N f (1)
where ��1 is fatigue stress limit and N f is fatigue life.
2. Numerical Analysis. Fatigue life of each structure depends on the fatigue strength
of material and the operating loads of the components. Fatigue cracking originates in the
weakest region with the maximum stress amplitude. Therefore, in order to analyze the
fatigue cracking behavior and predict the fatigue life of a component, stress analysis at the
critical region is necessary.
As the first step in the numerical fatigue analysis, a finite-element model of the push
rod assembly was created in ANSYS® v12.0 commercial FEM analysis software as shown
in Fig. 3. Solid185 hexahedral elements are used for building the push rod meshed model.
2.1. Stress analysis under Various Tensile and Compressive Loads. The equivalent
stress (assessed via the von Mises strength criterion) in the push rod generated by the
tensile load of 27.2 kN, which is fourfold of the normal service load, is shown in Fig. 4a.
L. Xu and G. Z. Dai
40 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
T a b l e 1
Mechanical Properties of Al–6.2Zn–2.2Mg–1.6Cu Alloy
Elastic modulus E, GPa 71
Poisson’s ratio � 0.33
Yield strength �s , MPa 460
Tensile strength �b , MPa 570
Elongation � , % 9.7
Fig. 2. Metallographic microstructure of Al–Zn–Mg–Cu alloy.
The stress distribution of the both pin holes is different due to the asymmetric structure.
Two inner wall areas of the first location pin hole marked in red in Fig. 4a exhibit a similar
maximum level of equivalent stress of about 142 MPa, while the maximum principal stress
is 149 MPa.
The equivalent stress in the push rod due to a compressive load of 27.2 kN is shown
in Fig. 4b. Inner wall areas of the first location pin hole (which is marked in red) are
subjected to the equivalent stress of about 77.3 MPa, while the maximum principal stress is
6.5 MPa.
The stressed state and stress amplitude are essential to choose the fatigue failure
criterion. Table 2 shows that the intermediate and the minimum principal stress of node
10998 is close to zero, while the maximum principal stress is close to the equivalent stress.
Hence, node 10998 can be considered to be subjected to uniaxial tensile stress of about
147.8 MPa. The stress in node 10998 is close to zero under the compressive load of 27.2 kN.
Thus, the compressive load does not contribute to the fatigue of this node 10998, and the
fatigue analysis can be based on the maximum principal stress criterion.
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis ...
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 41
Fig. 3. FEM model of the push rod.
ba
Fig. 4. The equivalent (von Mises) stress distribution of a push rod under the tensile (a) and
compressive (b) load of 27.2 kN.
T a b l e 2
The Stresses (MPa) of the Node 10998 at the Tensile Load of 27.2 kN
Load type �eq �1 �2 �3 �x
Tensile 142.9 147.8 8.2 3.4 127.8
Compressive 0.5 0.1 �0.1 �0.5 �0.4
Table 3 shows that node 10529 is in the triaxial compressive stressed state under the
tensile loading of 27.2 kN. But since both the maximum and intermediate principal stresses
approach zero, the stress in node 10529 can be reduced to uniaxial compressive stress of
about 24.6 MPa, while this node experiences a biaxial compressive stress under the
compressive load of 27.2 kN.
Connelly and Davis [6] introduced the triaxiality factor (TF) to determine the stressed
state:
TF
I
eq
�
1
�
, (2)
where I1 represents the first stress invariant.
In node 10998 under the tensile load of 27.2 kN, TF � 1.1. Since it approximately
equals to unity, the uniaxial tensile stress criterion can be used for this node. Comparing the
stress amplitude of the maximum stresses in nodes 10998 and 10529, in the case where the
push rod is subjected to cyclic symmetric tension-compression (i.e., with stress ratio
R � �1), node 10998 endures the critical fatigue stress cyclic load. Then, the fatigue analysis
of the push rod can be reduced to the loading scheme shown in Fig. 5, which implies that
node 10998 endures the uniaxial tensile stress with the most critical fatigue stress spectrum.
2.2. ALT Fatigue Testing Spectrum. Accelerated life test (ALT) of products and
materials is used to get information quickly on their life distributions [7]. Such testing
involves subjecting the test units to conditions that are more severe than normal ones and
yields shorter fatigue lives than those under regular conditions. The data obtained at more
severe or accelerated conditions are extrapolated by means of an appropriate model to
obtain an estimate of the life distribution under the normal conditions. ALT provides
savings in time and cost, as compared to testing under the normal conditions. This paper
presents ALT of the push rod, which is used to identify the product weak parts and predict
its fatigue life.
Firstly, it is necessary to study the failure mechanism of the push rod via ALT fatigue
testing loading. The stress of the characteristic nodes 10998 and 10592 changes with a
series of lo as shown in Fig. 6. The stresses in the characteristic nodes are related to loads
by a linear relationship. The stress state of the two nodes remains unchanged with the load
variation. Figure 6a shows that the equivalent stress is primarily constituted by the
maximum principal stress, which direction nearly coincides with the x axis. Figure 6b
42 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
L. Xu and G. Z. Dai
T a b l e 3
The Stresses (MPa) of the Node 10529 at the Compressive Load of 27.2 kN
Load type �eq �1 �2 �3 �y
Tensile 22.0 �2.8 �4.4 �25.8 �24.6
Compressive 77.3 6.5 �19.9 �80.6 6.0
Fig. 5. The critical node 10998 subjected to uniaxial fatigue under a symmetrical cyclic load.
shows that the maximum principal stress approaches zero, so that the equivalent stress is
mainly constituted by the compressive stress. Above all, the fatigue failure mechanism of
the push rod would not change with the load variation from 27.2 to 54.4 kN.
Secondly, it is necessary to simplify the loading spectrum of the bench test, in order to
improve the prediction efficiency. The symmetric sine load spectrum of the rod is shown in
Fig. 7a. The corresponding stress spectrum of node 10998 is the pulsating stress spectrum,
while the push rod is under the symmetric sine load spectrum depicted in Fig. 7b. The
fatigue spectrum of 10998 node in Fig. 7b is equal to that in Fig. 7d, so the load spectrum
of the push rod can be reduced to that in Fig. 7c. Above all, the critical maximum principal
stress amplitude of the rod is at node 10998. To save the fatigue bench test time, the fatigue
load spectrum could be set as a pulsing tensile load, as is shown in Fig. 7c.
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 43
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis ...
a b
Fig. 6. Stress variation for loads ranging from 6.8 to 54.4 kN in nodes 10998 (a) and 10529 (b).
Fig. 7. Load spectrum of the rod and stress spectrum of node 10998: (a) symmetric sine load
spectrum of the rod at 27.2 kN; (b) stress spectrum of node 10998 under symmetric sine load
spectrum of the rod at 27.2 kN; (c) pulsating sine load spectrum of the rod at 27.2 kN; (d) stress
spectrum of node 10998 under pulsating sine load spectrum of the rod at 27.2 kN.
c d
a b
2.3. FEM Fatigue Analysis Results. Fatigue analysis was carried out by the FEM.
The surface and scale factor were set at 1.5, according to the surface processing state.
Figure 8 shows that the crack initiation may occur in the critical zone at the inner wall of
the first pin hole surface. For the maximum stress and minimum fatigue life in Figs. 4 and
8, the crack propagation begins at this area according to the FEM analysis. The respective
fatigue life is assessed as 3 105
� cycles under a pulsing tensile load of 52 kN.
3. Bench Fatigue Test and Failure Analysis. The load capacity and fatigue behavior
of the push rod under dynamic loads are determined by the tractive force fatigue tests
shown in Fig. 9. In these tests, the push rod and pin joint assembly are positioned on a
vertical actuator. The pulsating sine spectrum load of 10 Hz is applied to the first position
pin along the axial direction of the actuator.
In order to verify the static FEM simulation results, local stresses were measured by
the strain gauge testing method, as shown in Fig. 10. The data summarized in Table 4
strongly indicate that the FEM calculated results are in good agreement with strain gauge
testing results with a tensile load of 52 kN. By carrying out the fatigue bench tests with the
44 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
L. Xu and G. Z. Dai
Fig. 8. Calculated stresses in the rod under a pulsing tensile load of 52 kN.
Fig. 9. Electrohydraulic servo used for bench test.
pulsating load of 26 kN, the load life curve of the push rod was determined and used for
assessing the experimental fatigue life.
Figure 11 indicates that a fatigue crack was initiated at the inner pinhole edge of the
push rod, and propagated through the cross-sectional area of the first position pinhole. The
ductile mode of fracture in the final fracture zone can be readily observed in Fig. 12.
The micrograph zone located within the white box in Fig. 12 is enlarged in Fig. 13, to
confirm the fatigue crack propagating path. Thus, Fig. 13 shows the crack propagation
zone, with the fatigue propagation characteristics represented by fatigue striations of a
micron scale. When tensile forces are repeatedly applied to the structure parts, the crack
jumps at a small distance to form the advance striation. With striations perpendicular to the
fatigue crack propagation direction, the fatigue crack direction is shown as a white arrow.
Therefore, the fatigue crack initiated at the inner wall of the pin hole and propagated along
the radial or axial direction, finally resulting in the fracture failure at the pinhole wall.
Figure 14 shows that predicted fatigue life of the push rod by FEM agreed fairly well
with the experimental life within three times.
Comparing the fatigue life results for the first- and second-location pinholes, that the
latter is more than one hundred times longer than that of the former. In order to increase the
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 45
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis ...
T a b l e 4
Local Stresses (MPa) in the Rod under a Tensile Load of 52 kN
Location 1 2 3 4 6 7 8
Experimental 52.6 110 �23.1 35.2 �64.6 109 0.71
FEM 56.1 99.6 �14.2 64.3 �11.5 135 �0.52
Fig. 10. Sensors’ locations on the push rod.
Fig. 11. Fracture appearance of the rod with the load of 52 kN.
fatigue life of the push rod, it is necessary to reduce the stress concentration in the critical
zones.
Conclusions. Fatigue analysis of the push rod was carried out using a comprehensive
combination of the Al–Zn–Mg–Cu alloy characterization, FEM simulation, bench test, and
ALT fatigue life evaluation. It was concluded that:
1. FEM analysis results accurately predict the fatigue crack initiation location, for
which stresses and fatigue life were determined.
2. ALT can be used to get rapid test results on the rod life distribution. The symmetric
sine load spectrum can be reduced to pulsating one, according to the stress spectrum
analysis of the critical node.
3. Fatigue bench test revealed that the fatigue crack initiated from the rod inner edge
and propagated along the cross section of the first pinhole, resulting in the fracture of the
pinhole wall. The predetermined local stress and the fatigue life of the push rod calculated
via FEM analysis agreed fairly well with the fatigue bench test results.
Acknowledgments. This work was partly supported partly by the Scientific Research
Project of Sichuan Province Department of Education (15ZB0137), the Ministry of
Education Chunhui Project (Z2015099), Xihua University Natural Science Fund
(Z1420105), as well as Open Funds of Key Laboratory of High Performance Materials and
Forming Technology of Provincial University (SZJJ2014-057).
46 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
L. Xu and G. Z. Dai
Fig. 12 Fig. 13
Fig. 12. Fracture macrograph of the rod.
Fig. 13. LSCM micrograph showing the crack propagation.
Fig. 14. FEM-calculated life vs. test fatigue life.
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Received 15. 03. 2018
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 47
Accelerated Life Test and FEM Simulation-Based Fatigue Analysis ...
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
/RUS <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>
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|