Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences
The coaxing effect in fatigue refers to an increase in the fatigue strength of material imduced by prior cycling at a stress level below the fatigue limit. In this study, the coaxing effect of multi-level stresses in the fatigue process in the automotive drive shaft material 40Cr was investigated by...
Saved in:
| Published in: | Проблемы прочности |
|---|---|
| Date: | 2017 |
| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2017
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/173583 |
| 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: | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences / L.H. Zhao, J.X. Li, W.Y. Yu, J. Ma, S.L. Zheng // Проблемы прочности. — 2017. — № 1. — С. 66-71. — Бібліогр.: 15 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860094121177251840 |
|---|---|
| author | Zhao, L.H. Li, J.X. Yu, W.Y. Ma, J. Zheng, S.L. |
| author_facet | Zhao, L.H. Li, J.X. Yu, W.Y. Ma, J. Zheng, S.L. |
| citation_txt | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences / L.H. Zhao, J.X. Li, W.Y. Yu, J. Ma, S.L. Zheng // Проблемы прочности. — 2017. — № 1. — С. 66-71. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | The coaxing effect in fatigue refers to an increase in the fatigue strength of material imduced by prior cycling at a stress level below the fatigue limit. In this study, the coaxing effect of multi-level stresses in the fatigue process in the automotive drive shaft material 40Cr was investigated by applying three levels of stress amplitudes below the fatigue limit in different sequences prior to conducting the conventional constant amplitude fatigue test with standard round bar specimens. The existence of coaxing effect under multi-level stress with a load sequence effect was observed and confirmed by the results. The longest fatigue life is achieved through three levels of coaxing load with a step increase sequence, while a decrease sequence will result in the shortest fatigue life. The mechanisms of the coaxing effect which increased the fatigue life at the crack initiation and propagation stages were observed, through fracture morphology analysis, as the regulation ofmicropores, decreasing ofpore density and the narrowed striation spacing. This finding is instrumental for extending the service life of mechanical components.
|
| first_indexed | 2025-12-07T17:25:12Z |
| format | Article |
| fulltext |
UDC 539.4
Experimental Study on the Coaxing Effect of Multi-Level Stresses with
Different Sequences
L. H . Z h ao ,ab1 J . X . L i,a W . Y. Y u ,a J . M a ,a an d S. L . Z hengab
a School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai,
China
b CMIF Key Lab for Automotive Strength and Reliability Evaluation, Shanghai, China
1 Pheigoe@126.com
The coaxing effect in fatigue refers to an increase in the fatigue strength o f material imduced by prior
cycling at a stress level below the fatigue limit. In this study, the coaxing effect o f multi-level stresses
in the fatigue process in the automotive drive shaft material 40Cr was investigated by applying three
levels o f stress amplitudes below the fatigue limit in different sequences prior to conducting the
conventional constant amplitude fatigue test with standard round bar specimens. The existence o f
coaxing effect under multi-level stress with a load sequence effect was observed and confirmed by the
results. The longest fatigue life is achieved through three levels o f coaxing load with a step increase
sequence, while a decrease sequence will result in the shortest fatigue life. The mechanisms o f the
coaxing effect which increased the fatigue life at the crack initiation and propagation stages were
observed, through fracture morphology analysis, as the regulation ofmicropores, decreasing ofpore
density and the narrowed striation spacing. This finding is instrumental fo r extending the service
life o f mechanical components.
K eyw ords: coaxing effect, fatigue strength, load sequence effect, high-cycle fatigue.
In tro d u c tio n . The coaxing effect in fatigue refers to an im provem ent o f fatigue
strength induced by prior cycling at a stress level below the fatigue limit. Early in the
1920s, it was reported that the fatigue lim it o f m ild steel was increased by 28% through
step increasing the stress am plitude from 247 M Pa at an increm ent o f 3 M Pa after every 106
cycles [1]. Since then, m uch research has been conducted to study the coaxing effects in the
fatigue o f materials. Scott-Em uakpor et al. [2] found an im proved fatigue perform ance that
could be attributed to the coaxing effect during vibration-based bending fatigue loading
using the step-test procedure w hen he studied fatigue lives o f aerospace nickel alloys
Inconel 625 and 718. Ishihara and M cEvily [3] reported that the coaxing effect in the small
crack growth regim e can be achieved in S45C steel under a two-step loading w ith low-high
sequence, due to a higher degree o f crack closure inherited at high levels after transitions
from low er levels than w ould be present under constant high am plitude conditions. L u and
Zheng [4, 5] studied coaxing effect o f pre-understressing on carbon steels, and concluded
that the stress am plitudes w hich w ill cause the coaxing effect range from 0.65 to 0.95 o f the
fatigue limit. Coaxing effect in fatigue o f other m aterials have recently been reported,
including alum inum alloys [6-8], m etallic glass [9], fiber glass [10] and carbon com posites
[11, 12]. R ecent research has proposed other possible m echanism s for the coaxing effect
including w ork hardening, strain aging, strain induced phase transform ation, as well as
strengthening at the tip o f non-propagating cracks [13-15].
However, so far, the research into the coaxing effect has been perform ed under simple
load conditions, such as pre-understressing [5-9], step increm ental stress [3, 11] and two
step repeated tests [4]. In practice, m echanical com ponents are usually subject to variable
amplitude loads w ith m ulti-level stresses and differing sequences. There is very little
literature that relates to com plex load conditions. For this paper, the integrated coaxing
effect under a multi-level coaxing load o f 40Cr was investigated by conducting conventional
© L. H. ZHAO, J. X. LI, W. Y. YU, J. MA, S. L. ZHENG, 2017
66 ISSN 0556-Î7ÎX. Проблемы прочности, 2017, № 1
mailto:Pheigoe@126.com
Experimental Study on the Coaxing Effect
fatigue tests and coaxing effect tests on standard round bar specimens. Conventional fatigue
tests were perform ed under constant am plitude above the fatigue limit. Coaxing effect tests
w ere perform ed by applying three levels o f load below the fatigue lim it for certain cycles
prior to the application o f the constant am plitude load used in the conventional fatigue tests.
The sequence effect in the coaxing effect was studied by applying three levels o f load
below the fatigue lim it w ith three sequences. The coaxing effect based on fracture
m orphology and m icrostructure studies w ill also be discussed.
1. C oaxing E ffect Test Setup. The tested material, 40Cr, is a carbon steel consisting
o f 0.37-0.44 C, 0 .17-0 .37 Si, 0 .5-0.8 Mn, 0.8-1.1 Cr, < 0 .3 N i, < 0 .0 3 5 P, < 0 .035 S, and
< 0.03 Cu (in wt.% ) w ith a y ield strength o f 785 M Pa, ultim ate tensile strength o f 980 MPa,
it is tem pered at 520±10°C after being quenched at 850±10°C. Fatigue tests and the
coaxing effect tests were conducted under torsional conditions, on a Sagynom iya TT08 test
m achine utilizing a standard specimen, the shape and dim ension o f the test bed and
specim en are shown in Fig. 1a. The stress ratio R is set to 0.1 to avoid shock and vibration
during testing. A ll specim ens were tested at 30 Hz and room temperature. Prior to testing,
the specim ens were highly polished to diminish the influences brought out by surface
roughness.
b
Fig. 1. Setup of the coaxing effect test: (a) test bed and specimen; (b) sequences of the three levels of
load below the fatigue limit.
Fatigue tests under constant am plitude conditions w ere carried out to determ ine the
S - N curve and fatigue lim it corresponding to a fatigue life at 2-10 cycles. Three stress
levels, 0.75, 0.85, and 0.95 o f the fatigue limit, were selected as the coaxing load for the
coaxing test. The coaxing effect specim ens were first subjected to a block loading o f the
three stress levels below the fatigue lim it for 10 repetitions o f 150,000 cycles, then
fatigue tests were conducted under a stress level above the fatigue limit. In each repetition,
three sequences w ere assessed and the num ber o f cycles o f each stress level w as 5500,
3500, and 1000 respectively. The three block loading and its construction are show n in
Fig. 1b, the coaxing stress o f the fatigue lim it is represented by L = 0.75, M = 0.85, and
H = 0.95.
ISSN 0556-171X. npo6n.eubi 2017, № 1 67
L. H. Zhao, J. X. Li, W. Y. Yu, et al.
2. C oaxing E ffect Test R esults. The results o f conventional constant amplitude
fatigue tests and coaxing effect tests are shown in Fig. 2. Seven specim ens w ere tested
under constant am plitude to determ ine finite life portion o f S - N curve. Two specim ens were
subjected to a m axim um o f 5 - 106 and 107 cycles to ensure the fatigue limit. Coaxing effect
w as observed in the fatigue lives o f the two groups o f specimens. The fatigue life for the
conventional constant amplitude fatigue test group ranged from 102,500 to 250,400 cycles
w ith a m ean value o f 182,175 cycles across the six specimens. The fatigue life for the
coaxing effect group ranged from 296,700 to 556,300 cycles w ith a m ean value o f 404,671
cycles across the seven specimens. The coaxing effect resulted in an average life m ore than
double the constant test average life, and the m inim um life in the coaxing group w as longer
than the m axim um life in the constant test group. The results also indicate that sequence
effect m ay exist in the coaxing effect, as the average lives o f the coaxing group under
sequences o f L -M -H , M -H -L , and H -L - M were 521,290, 377,350, and 345,140 cycles
respectively. The coaxing effect is m ost significant w hen the coaxing load below the fatigue
lim it follows a step increasing sequence L -M -H .
Fig. 2. S -N curves with coaxing effect test results. (Arrows indicate that the specimens were not
broken.)
3. D iscussion. To confirm the coaxing effect, significance testing w as carried out for
the scatter o f fatigue life. H ypotheses for the one-sided test were stated in term s o f the
m ean value i o f the population as follows:
H 0 • 1 constant — 1 coaxed vs H a • 1 constant ^ 1 coaxed •
where H 0 corresponds to the case o f no significant im provem ent in the fatigue life by
coaxing, H a m eans the fatigue life w as increased by coaxing effect on average, and
i constant and i coaxed stand for the average life o f the conventional constant amplitude
fatigue test group and the coaxing group, respectively.
The t -test w as adapted due to the two population variances being unknow n and the
specim en sizes not being equal. The statistic t value is defined by Eq. (1):
t = x1 ~ x2
S ------Xj —X2
1 X1 — x2
1 1
— + —
n 1 n 2 2 x2 — ( 2 X1) n 1 + 2 X2 — ( 2 X2 )
(1)
!n 2
■ 1+ n 2 — 1
68 ISSN 0556-171X. npo6n.eubi 2017, № 1
Experimental Study on the Coaxing Effect
Taking 0.001 as the threshold value for statistical significance, the p -value at the t value
calculated according to Eq. (1) is 0.0002, based on the fatigue lives o f the two specimen
groups. The null hypothesis H 0 is rejected in favor o f the alternative hypothesis H a ,
w hich verifies the coaxing effect.
Fracture m orphology and m icrostructure studies on fatigue striation spacing, pore
characteristics and secondary cracks w ere perform ed using scanning electron m icroscopy
(SEM). Fatigue striation spacing w as m easured at the crack propagation region w ith a
radial distance o f 2.5 m m to crack initiation. Pores and secondary cracks are observed in
the vicinity o f crack initiation. M icrographs w ere taken from both specim en groups for
com parison. Details o f the m icrographs taken using Leica S440i SEM are shown in Fig. 3.
J 200 p m (x 300)
a
15 pm (*1500)
b
J 10jim(x2000)
c
Fig. 3. Comparison of fracture surfaces of specimens under constant amplitude and coaxed under a
sequence L—M—H : (a) fatigue striation spacing; (b) secondary cracks; (c) characteristics of micropores.
ISSN 0556-171X. npoôëeubi 2017, N2 1 69
L. H. Zhao, J. X. Li, W. Y. Yu, et al.
The striations o f the fracture surface are shown in Fig. 3a. Seven striations at a
distance o f 52,051.5 nm, w ith a m ean spacing o f 7.4 ,«m were observed in the specimen
from the constant test group. E leven striations at a distance o f 44,899.2 nm, w ith a mean
spacing o f 4.1 ,am w ere observed in the specim en from the coaxed group, showing that the
coaxing effect results in a reduction o f the crack propagation rate evidenced by the
narrow ed striation spacing.
The secondary cracks on the section perpendicular to the m ain crack are depicted in
Fig. 3b. It can be seen that the secondary cracks on the specim en under constant amplitude
load were coarser and rougher than those on the specim en from the coaxing effect group. In
accordance with pore densities, the density o f secondary cracks on the specim en under
constant amplitude is greater.
Several distinct pore characteristics differences were observed betw een the specimens,
these are shown in Fig. 3c. The pore density is greater in the group under constant
amplitude load than that o f the coaxing effect group. The outlines o f the pores after coaxing
are smoother, and m ore circular. The observable pores w ere interconnected in the specim en
under constant am plitude load, and independent in the specim en from the coaxing effect
group. The im provem ent o f the m icrostructure o f the studied m aterial caused by the
coaxing effect leads to longer fatigue lives at the crack initiation stage.
C onclusions. In summary, the fatigue life o f the m aterial 40Cr can be prolonged
through the coaxing effect o f m ulti-level loads below the fatigue limit, this has been
confirm ed through fatigue tests and coaxing effect tests. This result is due to the
im provem ent o f the m aterial m icrostructure, including the regulation o f m icropores and
reduction o f pore density, which eventually improves the fatigue strength. Additionally, load
sequence effect appears to exist to some extent during the process o f coaxing. The m ean
lives o f the specim ens after being coaxed by three levels o f stress am plitudes below the
fatigue lim it w ith a sequence o f L -M -H , M -H -L , and H -L - M were 521,290, 377,350, and
345,140 cycles, respectively
Though, statistically, the coaxing effect has been dem onstrated by the t-test, according
to the results o f the fatigue test, the statistical nature o f fatigue life cannot be ignored in the
evaluation o f load sequence effect. Since the specim en size is two in each situation, the
variation o f fatigue life o f the coaxed specim ens under different load sequences m ight
sim ply be due to the differences in m icrostructure inherent in the material. M ore tests are
needed in order to cover the scatter o f fatigue life originating from the m aterial
inhom ogeneous microstructure.
A cknow ledgm ents. This w ork w as supported by the N ational N atural Science
Foundation o f China (Grant No. 51375313).
1. J. Schijve, F atigue o f Structures and M aterials, Springer (2009).
2. O. Scott-Emuakpor, J. Schwartz, T. George, et al., “In-situ study on coaxing during
vibration-based bending fatigue o f Inconel 625 and 718,” in: ASM E Turbo Expo
2013: Turbine Technical Conference and Exposition 2013 (June 3-7 , 2013, San
Antonio, TX), Paper No. GT2013-94233, A SM E (2013), pp. V07AT27A003.
3. S. Ishihara and A. M cEvily, “A coaxing effect in the small fatigue crack growth
regim e,” Scripta M ater., 40, No. 5, 617-622 (1999).
4. X. Lu and S. L. Zheng, “ Strengthening and dam aging under low-am plitude loads
below the fatigue lim it,” Int. J. Fatigue, 31, No. 2, 341-345 (2009).
5. X. Lu and S. L. Zheng, “Strengthening o f transm ission gear under low-amplitude
loads,” M ater. Sci. Eng. A , 488, No. 1, 55-63 (2008).
6. T. Shikama, Y. Takahashi, L. Zeng, et al., “D istinct fatigue crack propagation lim it o f
new precipitation-hardened aluminium alloy,” Scripta Mater., 67, No. 1, 49-52 (2012).
70 ISSN 0556-171X. npo6n.eub npouuocmu, 2017, № 1
Experimental Study on the Coaxing Effect
7. Y. Takahashi, H. Yoshitake, R. N akam ichi, et al., “Fatigue lim it investigation of
6061-T6 alum inum alloy in giga-cycle regim e,” M ater. Sci. Eng. A , 614, 243-249
(2014).
8. L. Zeng, Z. Li, R. Che, et al., “M esoscopic analysis o f fatigue strength property o f a
m odified 2618 alum inum alloy,” Int. J. Fatigue, 59, 215-223 (2014).
9. A. B. E l-Shabasy and J. J. Lewandowski, “Fatigue coaxing experim ents on a Zr-based
bulk-m etallic glass,” Scripta M ater., 62, No. 7, 481-484 (2010).
10. M. Tomozawa, P. Lezzi, R. Hepburn, et al., “Surface stress relaxation and resulting
residual stress in glass fibers: A new m echanical strengthening m echanism of
glasses,” J. Non-Cryst. Solids, 358, Nos. 18-19, 2650-2662 (2012).
11. Y. Tanabe, T. Yoshim ura, T. W atanabe, et al., “Fatigue o f C/C com posites in bending
and in shear m odes,” Carbon, 42, Nos. 8-9, 1665-1670 (2004).
12. A. Ozturk, “The influence o f cyclic fatigue dam age on the fracture toughness of
carbon-carbon com posites,” Compos. Part A-Appl. S., 27, No. 8, 641-646 (1996).
13. M. Akita, M. Nakajim a, Y. Uem atsu, et al., “Some factors exerting an influence on
the coaxing effect o f austenitic stainless steels,” Fatigue Fract. Eng. M ., 35, No. 12,
1095-1104 (2012).
14. M. N akajim a, M, Akita, Y. Uem atsu, and K. Tokaji, “Effect o f strain-induced
m artensitic transform ation on fatigue behavior o f type 304 stainless steel,” Proc. Eng.,
2, No. 1, 323-330 (2010).
15. K. Kanazawa and M. Sugimoto, “Increasing behavior o f strength for fatigue fracture
o f austenitic stainless steel during fatigue tests at elevated tem perature,” K ey Eng.
M at., 417-418, 589-592 (2010).
Received 30. 08. 2016
ISSN 0556-171X. npo6n.eubi 2017, № 1 71
|
| id | nasplib_isofts_kiev_ua-123456789-173583 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T17:25:12Z |
| publishDate | 2017 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Zhao, L.H. Li, J.X. Yu, W.Y. Ma, J. Zheng, S.L. 2020-12-12T13:55:04Z 2020-12-12T13:55:04Z 2017 Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences / L.H. Zhao, J.X. Li, W.Y. Yu, J. Ma, S.L. Zheng // Проблемы прочности. — 2017. — № 1. — С. 66-71. — Бібліогр.: 15 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173583 539.4 The coaxing effect in fatigue refers to an increase in the fatigue strength of material imduced by prior cycling at a stress level below the fatigue limit. In this study, the coaxing effect of multi-level stresses in the fatigue process in the automotive drive shaft material 40Cr was investigated by applying three levels of stress amplitudes below the fatigue limit in different sequences prior to conducting the conventional constant amplitude fatigue test with standard round bar specimens. The existence of coaxing effect under multi-level stress with a load sequence effect was observed and confirmed by the results. The longest fatigue life is achieved through three levels of coaxing load with a step increase sequence, while a decrease sequence will result in the shortest fatigue life. The mechanisms of the coaxing effect which increased the fatigue life at the crack initiation and propagation stages were observed, through fracture morphology analysis, as the regulation ofmicropores, decreasing ofpore density and the narrowed striation spacing. This finding is instrumental for extending the service life of mechanical components. This work was supported by the National Natural Science Foundation of China (Grant No. 51375313). en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences Экспериментальное исследование влияния предварительных циклических нагрузок ниже предела выносливости на усталостную долговечность стали 400 Article published earlier |
| spellingShingle | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences Zhao, L.H. Li, J.X. Yu, W.Y. Ma, J. Zheng, S.L. Научно-технический раздел |
| title | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences |
| title_alt | Экспериментальное исследование влияния предварительных циклических нагрузок ниже предела выносливости на усталостную долговечность стали 400 |
| title_full | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences |
| title_fullStr | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences |
| title_full_unstemmed | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences |
| title_short | Experimental Study on the Coaxing Effect of Multi-Level Stresses with Different Sequences |
| title_sort | experimental study on the coaxing effect of multi-level stresses with different sequences |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/173583 |
| work_keys_str_mv | AT zhaolh experimentalstudyonthecoaxingeffectofmultilevelstresseswithdifferentsequences AT lijx experimentalstudyonthecoaxingeffectofmultilevelstresseswithdifferentsequences AT yuwy experimentalstudyonthecoaxingeffectofmultilevelstresseswithdifferentsequences AT maj experimentalstudyonthecoaxingeffectofmultilevelstresseswithdifferentsequences AT zhengsl experimentalstudyonthecoaxingeffectofmultilevelstresseswithdifferentsequences AT zhaolh éksperimentalʹnoeissledovanievliâniâpredvaritelʹnyhcikličeskihnagruzoknižepredelavynoslivostinaustalostnuûdolgovečnostʹstali400 AT lijx éksperimentalʹnoeissledovanievliâniâpredvaritelʹnyhcikličeskihnagruzoknižepredelavynoslivostinaustalostnuûdolgovečnostʹstali400 AT yuwy éksperimentalʹnoeissledovanievliâniâpredvaritelʹnyhcikličeskihnagruzoknižepredelavynoslivostinaustalostnuûdolgovečnostʹstali400 AT maj éksperimentalʹnoeissledovanievliâniâpredvaritelʹnyhcikličeskihnagruzoknižepredelavynoslivostinaustalostnuûdolgovečnostʹstali400 AT zhengsl éksperimentalʹnoeissledovanievliâniâpredvaritelʹnyhcikličeskihnagruzoknižepredelavynoslivostinaustalostnuûdolgovečnostʹstali400 |