Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens
This work deals with fatigue life of plasma-nitrided and virgin specimens made of a low-alloy high strength steel. Specimens were subjected to an in-phase combined bending-torsion loading. The plasma-nitrided specimens exhibited a significantly improved fatigue resistance. The criterion proposed by...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2008
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| Cite this: | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens / S. Major, J. Papuga, J. Hornikova, J. Pokluda // Проблемы прочности. — 2008. — № 1. — С. 73-76. — Бібліогр.: 10 назв. — англ. |
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| author | Major, S. Papuga, J. Hornikova, J. Pokluda, J. |
| author_facet | Major, S. Papuga, J. Hornikova, J. Pokluda, J. |
| citation_txt | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens / S. Major, J. Papuga, J. Hornikova, J. Pokluda // Проблемы прочности. — 2008. — № 1. — С. 73-76. — Бібліогр.: 10 назв. — англ. |
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| description | This work deals with fatigue life of plasma-nitrided and virgin specimens made of a low-alloy high strength steel. Specimens were subjected to an in-phase combined bending-torsion loading. The plasma-nitrided specimens exhibited a significantly improved fatigue resistance. The criterion proposed by McDiarmid was found to be the most precise in the fatigue life prediction fo r virgin specimens. On the other hand, the Matake criterion was the most successful fo r nitrided specimens.
Исследована усталостная долговечность азотированных в плазме образцов и исходных образцов из низколегированной высокопрочной стали. Испытания образцов проводились при синфазном совмещенном изгибе с кручением. Показано, что азотированные в плазме образцы обладают более высокой усталостной стойкостью. Установлено, что для образцов в исходном состоянии наибольшая точность прогнозирования усталостной долговечности обеспечивается при использовании критерия, предложенного Мак-Диармидом. С другой стороны, для азотированных образцов наиболее подходящим оказался критерий Матаке.
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| first_indexed | 2025-11-30T11:22:58Z |
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UDC 539. 4
C o m p a r is o n o f F a t ig u e C r ite r ia fo r C o m b in e d B e n d in g - T o r s io n L o a d in g o f
N itr id e d a n d V ir g in S p e c im e n s
S. M a jo r ,1a J . P ap u ga ,2b J. H orn fk ova ,1c and J . P o k lu d a 1,d
1 Brno University o f Technology, Brno, Czech Republic
2 Czech Technical University, Prague, Czech Republic
a ymajor02@stud.fme.vutbr.cz, b papuga@pragtic.com, c hornikova@fme.vutbr.cz,
d pokluda@fme.vutbr.cz
This work deals with fatigue life o f plasma-nitrided and virgin specimens made o f a low-alloy high
strength steel. Specimens were subjected to an in-phase combined bending-torsion loading. The
plasma-nitrided specimens exhibited a significantly improved fatigue resistance. The criterion
proposed by McDiarmid was found to be the most precise in the fatigue life prediction fo r virgin
specimens. On the other hand, the Matake criterion was the most successful fo r nitrided specimens.
K eyw o rd s : fatigue life, bending-torsion, nitrided layer, high-strength steel.
M otivation o f th e R esearch . M any new stress-based m ultiaxial criteria have been
proposed in recent years [1 -4 ]. However, there is still significant lack o f their experimental
verification. In order to partially fill this gap, in-phase com bined bending-torsion
experim ents w ere perform ed using specim ens made o f a low -a lloy high-strength steel
(virgin specim ens). Similar experim ents were carried out on specim ens containing surface
nitrided layers (nitrided specim ens). A n extended com parison betw een classical and
advanced m ultiaxial criteria as w ell as fatigue life o f virgin and nitrided specim ens was
performed.
M u ltiax ia l C riteria . M ore than ten classical and advanced m ultiaxial criteria were
utilized to predict the fatigue life under com bined bending-torsion. The com plete set o f
criteria can be found elsew here [2]. Hereafter, on ly som e o f them w ill be m entioned in
more detail.
The m ost general form o f fatigue criteria can be g iven as the inequality
a f ( C ) + b g ( N ) < f _ i , ( 1)
w here a and b parameters are set from tw o uniaxial fatigue lim its (e.g ., the fatigue lim it
in the fu lly reversed torsion t _1 and in the fu lly reversed push-pull f_1). The linear
com bination o f shear (C) and normal (N ) stresses in Eq. (1) can be also replaced by a
quadratic version. I f the load data on the left-hand side (LHS) o f Eq. (1) correspond to an
experim entally determ ined fatigue limit, the ideal state o f equality should be achieved.
The fatigue index error I represents the degree o f deviation from the ideal equality,
I = [(L H S _ R H S)/R H S]-100% . (2)
The ideal prediction leads to L H S = RHS, i.e ., I = 0. I f I > 0, the criterion yields
conservative results since it predicts the failure o f the specim en (com ponent) under low er
loads.
Criteria proposed by M cDiarm id, M atake, and Spagnoli can be considered as
classical ones. The M cD iarm id criterion can be written as
C N^ a , max
t — + 1 F “ < , (3)t A, B 2 S u
© S. M A JO R , J. PA PU G A , J. H O R N IK O V A , J. POKLUDA, 2008
ISSN 0556-171X. Проблемы прочности, 2008, № 1 73
mailto:ymajor02@stud.fme.vutbr.cz
mailto:papuga@pragtic.com
mailto:hornikova@fme.vutbr.cz
mailto:pokluda@fme.vutbr.cz
S. Major, J. Papuga, J. Hornikovâ, and J. Pokluda
where S u is the ultimate strength. The subscript a m eans the amplitude and the subscript
m ax denotes the m axim um stress value. The shear fatigue strength t A b for case A or
case B cracking (parallel to the surface or inwards from the surface, respectively). The
relation t a b = t - i is generally fu lfilled for plane bending com bined w ith torsion [5 -6 ].
The Matake criterion can be expressed by the relation
K C a, MSSR + ( 2 - K ) N max, MSSR — f - i . (4)
In this equation the fatigue lim it ratio k = / - 1/ t - i. The subscript M SSR m eans the
critical plane set according to the M axim um Shear Stress Range criterion.
A s an exam ple o f the quadratic form, the Spagnoli criterion [7] can be m entioned,
^ C + N max — f - 1. (5)
The criteria put forward by Papadopoulos (integral approach) [8 ] and G oncalves et
al. [9] are exam ples o f advanced approaches. In the Papadopoulos criterion the input
variables (the shear stress and the normal stress) are integrated over all planes,
f f f (Ta ((P, ^ I ))2 dX s in ipdtpd<p + ( 3 - 3k p h , max < f _ u (6 )
8 '̂ <p=0 ip=0 x=0
where Ta is the amplitude o f resolved stress, f , ty, and % are the Euler angles, and
o h max is a m axim um value o f the hydrostatic stress.
The G oncalves criterion is expressed as
where the parameters d t can be determ ined from m inim um and m axim um values o f the
transformed deviatoric stress tensor
d { = 0.5 ( m a x ( t ) — m in ( t )).
E xp erim en ta l P rocedure. The specim ens were m ade o f the high-strength low -alloy
steel C SN 41 5340. The basic m echanical properties o f the material are o y = 805 MPa
and S u = 930 MPa. One o f the surface treatment m ethods im proving the fatigue life is the
deposition o f nitriding layers by a plasm a discharge [10]. The nitriding process parameters
are show n in Table 1. The experim ents w ere m ade b y m eans o f the m ultiaxial-test
m achine M Z G S-100 at room temperature. The applied loading o f frequency 29 Hz
com prised sym m etric (R = — 1) sinusoidal bending and torsion and their in-phase
com bination.
T a b l e 1
Nitriding Process Parameters
Step Temperature Wall n 2/h 2 Compression U , V Pulse Time
(°C) (°C) (Pa) ( ̂ s) (h)
Refining 510 460 20/2 70 800 100 —
Nitriding 515 455 21/7 260 530 120 32
74 ISSN 0556-171X. npoôëeMbi npounocmu, 2008, N9 1
Comparison o f Fatigue Criteria
T a b l e 2
The Average Iav and Absolute Average Iabs av Values of Error Indices
Criterion Specimens virgin nitrided
Indices (%) 1abs, av I av 1 abs,av I av
Dang Van 7.35 -3 .0 3 8.45 -0 .3 5
Crossland 7.28 -5 .4 2 8.65 -2 .4 7
Sines 11.85 -11 .2 3 12.32 12.82
McDiarmid, Eq. (3) 7.08 -3 .0 2 8.65 1.72
Findley 7.08 -3 .3 8 8.62 -0 .8 7
Matake, Eq. (4) 7.12 -3 .0 4 8.32 -0 .2 3
Spagnoli, Eq. (5) 10.50 4.33 8.56 3.35
Papadopoulos (integral approach), Eq. (6) 7.36 - 3.04 8.46 -0 .3 5
Papadopoulos (critical plane) 11.08 -6 .3 0 16.56 -6 .7 0
Goncalves et al., Eq. (7) 8.62 4.14 13.92 5.20
600-,
500
400
s 3oo-
3L
o ' '
200 -
iOO-
0
0
Na [MPa]
Fig. 1. The constant life diagram (n = 5 • 105 cycles) according to the McDiarmid criterion for virgin
and plasma-nitrided specimen.
C onclusions. Our results show that the fatigue life o f the nitrided specim ens is
significantly higher than that o f the virgin specim ens. The curves are plotted using the
M cDiarm id criterion for the number o f cycles n = 5 • 105 and the experim ental data
correspond to the fatigue life o f ( 5 ± 2) • 10 5. This conclusion can be made even though a
relatively sm all number o f investigated nitrided specim ens w ere tested. The calculated
error indices reveal that the M cDiarm id criterion w as the m ost successfu l in the fatigue
life prediction for virgin specim en and the Matake criterion w as the m ost successfu l for
nitrided ones.
Acknowledgments. This research was supported by the Czech Science Foundation under the
Project No. GA106/05/0550 and the Ministry o f Education and Youth of the Czech Republic under
the Research Plan MSM 0021630518.
v irg in s p e c im e n s
nitrided specimens
- criterion for virgin specimens
- criterion for nitrided specimens
- r ^ —r
100 200 300 400 500 600 700 800 900
ISSN 0556-171X. n poôëeu u npoHHocmu, 2008, № 1 75
S. Major, J. Papuga, J. Hornikovâ, and J. Pokluda
1. D. F. Socie and G. B. Marquis, Multiaxial Fatigue, Warrendale (2000).
2. J. Papuga, Mapping o f Fatigue Damages, PhD Thesis, Czech Technical University in Prague,
Prague (2005).
3. I. V. Papadopoulos, P. Davoli, P. Gorla, et al., Int. J. Fatigue, 19, No. 3, 219-235 (1997).
4. I. V. Papadopoulos, Int. J. Fatigue, 16, 377-384 (1994).
5. D. L. McDiarmid, Fatigue Fract. Eng. Mater. Struct., 14, No. 4, 429-453 (1991).
6 . D. L. McDiarmid, Fatigue Fract. Eng. Mater. Struct., 17, No. 12, 1475-1484 (1994).
7. A. Carpinteri and A. Spagnoli, Int. J. Fatigue, 23, 135-145 (2001).
8 . I. V. Papadopoulos, Fatigue Fract. Eng. Mater. Struct., 21, 269-285 (1998).
9. C. A. Gonçalves, J. A. Araujo, and E. N. Mamiya, Int. J. Fatigue, 27, 177-187 (2005).
10. J. Pokluda, I. Dvorak, S. Major, and H. Horakova, in: W. S. Johnson (Ed.), Fatigue 06,
Elsevier (2006).
Received 28. 06. 2007
76 ISSN 0556-171X. n poôëeu u npouHocmu, 2008, № 1
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| id | nasplib_isofts_kiev_ua-123456789-48456 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-11-30T11:22:58Z |
| publishDate | 2008 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Major, S. Papuga, J. Hornikova, J. Pokluda, J. 2013-08-19T19:04:39Z 2013-08-19T19:04:39Z 2008 Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens / S. Major, J. Papuga, J. Hornikova, J. Pokluda // Проблемы прочности. — 2008. — № 1. — С. 73-76. — Бібліогр.: 10 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48456 539. 4 This work deals with fatigue life of plasma-nitrided and virgin specimens made of a low-alloy high strength steel. Specimens were subjected to an in-phase combined bending-torsion loading. The plasma-nitrided specimens exhibited a significantly improved fatigue resistance. The criterion proposed by McDiarmid was found to be the most precise in the fatigue life prediction fo r virgin specimens. On the other hand, the Matake criterion was the most successful fo r nitrided specimens. Исследована усталостная долговечность азотированных в плазме образцов и исходных образцов из низколегированной высокопрочной стали. Испытания образцов проводились при синфазном совмещенном изгибе с кручением. Показано, что азотированные в плазме образцы обладают более высокой усталостной стойкостью. Установлено, что для образцов в исходном состоянии наибольшая точность прогнозирования усталостной долговечности обеспечивается при использовании критерия, предложенного Мак-Диармидом. С другой стороны, для азотированных образцов наиболее подходящим оказался критерий Матаке. This research was supported by the Czech Science Foundation under the Project No. GA106/05/0550 and the Ministry of Education and Youth of the Czech Republic under the Research Plan MSM 0021630518. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens Сравнение критериев усталости при совместном изгибе и кручении для азотированных образцов и образцов в исходном состоянии Article published earlier |
| spellingShingle | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens Major, S. Papuga, J. Hornikova, J. Pokluda, J. Научно-технический раздел |
| title | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens |
| title_alt | Сравнение критериев усталости при совместном изгибе и кручении для азотированных образцов и образцов в исходном состоянии |
| title_full | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens |
| title_fullStr | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens |
| title_full_unstemmed | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens |
| title_short | Comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens |
| title_sort | comparison of fatigue criteria for combined bending-torsion loading of nitrided and virgin specimens |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/48456 |
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