Crack initiation and endurance limit of hard steels under multiaxial cyclic loads
The endurance limit and the mechanisms o f fatigue crack initiation in the high cycle regime were investigated using round specimens o f the bearing steel 52100 under longitudinal forces and torsional moments and combinations o f these loads. Three specimen types were examined: smooth specimens a...
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| Опубліковано в: : | Проблемы прочности |
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| Дата: | 2008 |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2008
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| Цитувати: | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads / H. Bomas, R. Kienzler, S. Kunow, G. Loewisch, S. Schroeder // Проблемы прочности. — 2008. — № 1. — С. 14-19. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859825527347478528 |
|---|---|
| author | Bomas, H. Kienzler, R. Kunow, S. Loewisch, G. Schroeder, S. |
| author_facet | Bomas, H. Kienzler, R. Kunow, S. Loewisch, G. Schroeder, S. |
| citation_txt | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads / H. Bomas, R. Kienzler, S. Kunow, G. Loewisch, S. Schroeder // Проблемы прочности. — 2008. — № 1. — С. 14-19. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | The endurance limit and the mechanisms o f fatigue crack initiation in the high cycle regime were
investigated using round specimens o f the bearing steel 52100 under longitudinal forces and
torsional moments and combinations o f these loads. Three specimen types were examined: smooth
specimens and specimens with circumferential notches with radii o f 1.0 and 0.2 mm. The influence
ofmean and multiaxial stresses on the endurance limit can be understood by consideration ofcrack
initiation mechanisms and micro-mechanics. Crack initiation took place at oxides, carbonitrides
and at the surface. The mechanisms ofcrack initiation could be related to the load type: Loads with
rotating principal stresses are more damaging fo r nitrides than fo r oxides. Increasing maximum
stresses are more dangerous fo r nitrides than fo r oxides, and introduce more damage to the surface
than to the nitrides. Normal stresses are more damaging fo r oxides than shear stresses. The
endurance limits were calculated by means o f an extended weakest-link model which combines
volume and surface crack initiation with related fatigue criteria. For volume crack initiation the
criterion o f Dang Van was used. For the correct description o f the competing surface crack
initiation, a new criterion was applied. With this concept, a prediction o f the endurance limit is
possible fo r loads which produce critical planes and range within a limited regime ofstress ratios.
Исследованы предел выносливости и механизмы
зарождения усталостных трещин в
многоцикловом режиме, используя круглые
образцы из подшипниковой стали 52100,
подвергаемые действию продольных сил и
крутящих моментов, а также комбинации
этих нагрузок. Использовали гладкие образцы
и образцы с кольцевыми надрезами радиусами
1,0 и 0,2 мм. Влияние средних и
многоосных напряжений на предел выносливости
может быть объяснено с учетом
механизмов зарождения трещин и микромеханики.
Зарождение трещин происходило
на оксидах, карбонитридах и на поверхности.
Механизмы зарождения трещин могут
быть связаны с типом нагрузки: нагрузки
с вращательными главными напряжениями
более деструктивны для нитридов, чем
для оксидов. Возрастающие максимальные
напряжения более опасны для нитридов,
чем для оксидов, и вызывают большие повреждения
поверхности, чем нитридов. Нормальные
напряжения вызывают большее повреждение
оксидов, чем касательные напряжения Пределы выносливости рассчитывали
с помощью модифицированной модели слабого
звена, которая объединяет зарождение
трещин в объеме и на поверхности с соответствующими
критериями усталости. Для
зарождения трещин в объеме был использован
критерий Данг Вана. Для корректного
описания конкурирующего зарождения трещин
на поверхности был применен новый
критерий. С помощью этой концепции можно
предсказать предел выносливости для нагрузок,
которые создают критические плоскости
и диапазон в рамках ограниченного
режима коэффициентов асимметрии цикла.
|
| first_indexed | 2025-12-07T15:28:36Z |
| format | Article |
| fulltext |
UDC 539. 4
C r a c k I n it ia t io n a n d E n d u r a n c e L im it o f H a r d S te e ls u n d e r M u lt ia x ia l
C y c lic L o a d s
H . B o m a s,1a R . K ien z ler ,2 S. K u n ow ,3 G . L oew isch ,4 and R . S ch roed er2
1 Stiftung Institut für Werkstofftechnik, Bremen, Germany
2 University o f Bremen, Bremen, Germany
3 Edelstahlwerke Südwestfalen, Siegen, Germany
4 Universität der Bundeswehr, Neubiberg, Germany
a bomas@iwt-bremen.de
The endurance limit and the mechanisms o f fatigue crack initiation in the high cycle regime were
investigated using round specimens o f the bearing steel 52100 under longitudinal forces and
torsional moments and combinations o f these loads. Three specimen types were examined: smooth
specimens and specimens with circumferential notches with radii o f 1.0 and 0.2 mm. The influence
ofmean and multiaxial stresses on the endurance limit can be understood by consideration ofcrack
initiation mechanisms and micro-mechanics. Crack initiation took place at oxides, carbonitrides
and at the surface. The mechanisms ofcrack initiation could be related to the load type: Loads with
rotating principal stresses are more damaging fo r nitrides than fo r oxides. Increasing maximum
stresses are more dangerous fo r nitrides than fo r oxides, and introduce more damage to the surface
than to the nitrides. Normal stresses are more damaging fo r oxides than shear stresses. The
endurance limits were calculated by means o f an extended weakest-link model which combines
volume and surface crack initiation with related fatigue criteria. For volume crack initiation the
criterion o f Dang Van was used. For the correct description o f the competing surface crack
initiation, a new criterion was applied. With this concept, a prediction o f the endurance limit is
possible fo r loads which produce critical planes and range within a limited regime ofstress ratios.
K eyw ords: endurance limit, bearing steel, crack initiation, m ultiaxial load, w eakest-link
m odel, fatigue criterion.
In trod u ction . This paper describes a calculation m ethod for hard steels w hich
allow s the prediction o f the endurance lim it o f parts o f arbitrary geom etry based on data
that have been gained from tests on a set o f reference specim ens under certain load
conditions. For the developm ent o f this calculation m ethod, the endurance lim its o f
sm ooth and notched specim ens under tension-com pression, repeated tension, alternating
torsion and different superpositions o f cyclic tensile and torsional loads have been
determ ined experimentally. Hereby, the influence o f m ean stresses, m ultiaxial stress
conditions and stress gradients on the fatigue behavior could be evaluated. B ased on the
collected data, a calculation m ethod w as applied w hich is based on the w eakest-link
m odel [1 ] and on suitable h igh-cycle fatigue criteria for surface and volum e crack
initiation [2, 3].
M ater ia l and Specim ens. The experim ents w ere carried out on the bearing steel
SAE 52100 rem elted under vacuum . From this material, sm ooth and notched specim ens
were turned w ith a net diameter o f d = 6 m m (Fig. 1). A fter turning, the specim ens were
heat treated as follow s: 855°C, 25 m in/salt m elt 220°C, 6 h /w ashing 65°C. In this bainitic
condition the material had a hardness o f 715 H V 10 and the fo llow ing tensile properties:
R m = 2467 MPa, R p 0 2 = 2115 MPa, and E = 202 GPa. Finally, the specim ens were
ground in the gauge region, w hich resulted in the fo llow ing residual stresses at the surface
o f the sm ooth specim ens: —479 M Pa in the longitudinal direction and —384 M Pa in the
tangential direction.
© H. B O M A S, R. K IEN Z LE R , S. K U N O W , G. LO EW ISC H , R. SC H R O ED ER , 2008
14 ISSN 0556-171X. Проблемы прочности, 2008, № 1
mailto:bomas@iwt-bremen.de
Crack Initiation and Endurance Limit o f Hard Steels
Fig. 1. Geometry o f the fatigue specimens in the gauge region.
Fig. 2. Loading of a notched specimen and relevant coordinates at the notch root surface, x =
coordinate parallel to the rotation axis, y = tangential coordinate.
E n d u ran ce L im its. The specim ens w ere cycled in a testing system that allow s the
superposition o f longitudinal and torsional loads (Fig. 2). The applied loads can be
described w ith a m ean longitudinal load F m, a corresponding amplitude F a , and an
amplitude M a o f the torsional m om ent. Longitudinal load and torsional m om ent were
cycled w ith the sam e frequency f and com bined in phase or w ith a phase shift d = n / 2 .
The resulting surface load stress tensor at the notch root has the fo llow ing form:
° x = °m + ° a si n ( 2 f ) xxy = x a sin(2Jlfi + (5)
' yx ■■ x a sin(2 f + 5 )
0
( 1)
The endurance lim its under different load types were determ ined by constant
amplitude tests at different amplitudes. Endurance o f a specim en w as defined as reaching
10 cycles w ithout failure. The endurance lim its were assum ed to obey a two-parametric
W eibull distribution:
ISSN 0556-171X. npoöxeMbi npounocmu, 2008, N 1 15
H. Bomas, R. Kienzier, S. Kunow, et al.
F ( S a ) = 1 - 2~ (s J s d ^ , F (T a ) = 1 - 2~{TalTD (2)
Table 1 g ives a survey over the tested variants and the m easured endurance limits.
T a b l e 1
Experimental Variants and Corresponding Endurance Limits
Variant Sa Rs TTa ô Notch radius
[mm]
Endurance limit
[MPa]
m Symbol
in Fig. 4
1 Sa - 1 0 X 866 20 +
2 Sa - 1 0 1.0 631 23 +
3 Sa - 1 0 0.2 373 9 +
4 Sa 0.1 0 X 502 21 +
5 Sa 0.4 0 X 437 48 +
6 Sa 0.5 0 X 419 51 +
7 Sa 0.6 0 X 371 33 +
8 0 TTa X 540 55 X
9 0 Ta 1.0 539 16 X
10 0 Ta 0.2 334 20 X
11 Sa - 1 0.5Sa 0 X 734 19 *
12 Sa - 1 0.5Sa 0 1.0 520 14 *
13 Sa - 1 0.5Sa 0 0.2 345 13 *
14 Sa - 1 0.5Sa n / 2 X 607 45 O
15 Sa - 1 0.5Sa n / 2 1.0 406 25 O
16 Sa - 1 0.5Sa n / 2 0.2 283 6 O
17 Sa - 1 Sa n / 2 X 431 11 O
18 Sa 0.1 0.5Sa n / 2 X 417 31 O
19 Sa - 1 Sa 0 X 477 7 *
F atigu e C rack In itia tion . Three types o f crack initiation w ere observed: crack
initiation at the surface, at aluminum oxides and in titanium carbonitrides. The latter two
types are show n in Fig. 3. Crack initiation at alum inum oxides is due to matrix failure,
since the inclusion is not bonded to the matrix und thus concentrates the stress in the
surrounding matrix. Crack initiation in titanium carbonitrides is due to failure o f the
inclusion itself, since the inclusion is w ell bonded to the matrix and concentrates the stress
in itself. The cracks exhibit cleavage o f the inclusion in w ell defined crystal planes. A ll
notched specim ens exhibited crack initiation at the surface w hich is due to the stress
gradient.
Table 2 show s the crack initiation sites in sm ooth specim ens. Several tendencies can
be observed: Under tensile loads starting from a stress ratio R = — 1, the titanium
carbonitrides get more involved in crack initiation as the stress ratio increases to R = 0.1.
Further increase o f the stress ratio leads to more frequent crack initiation at the surface.
Torsional loads are obviously m ost dangerous for the surface. A comparison o f proportional
loading and non-proportional loading show s that the titanium carbonitrides are m ostly
dam aged by non-proportional loading.
16 ISSN 0556-171X. npoôëeMbi npounocmu, 2008, N 1
Crack Initiation and Endurance Limit o f Hard Steels
T a b l e 2
Observed Crack Initiation Sites in Smooth Specimens
Variant Sa Rs TTa d Crack initiation at S a < S 90
1 Sa - 1 0 33% aluminum oxide
45% titanium carbonitride
22% unknown
4 Sa 0.1 0 100% titanium carbonitride
5 Sa 0.4 0 77% titanium carbonitride
23% surface
6 Sa 0.5 0 11% aluminum oxide
33% titanium carbonitride
56% surface
7 Sa 0.6 0 29% titanium carbonitride
71% surface
8 0 Ta 100% surface
11 Sa - 1 0.5Sa 0C 63% aluminum oxide
32% titanium carbonitride
5% surface
14 Sa - 1 0.5Sa 90c 67% titanium carbonitride
8% surface
25% unknown
a b
Fig. 3. Crack initiation at an aluminum oxide (a) and at a titanium carbonitride (b).
C a lcu la tion o f E n d u ran ce L im its. The endurance lim its were calculated on the
basis o f the w eakest-link concept, as described before [2]. For crack initiation in the
volum e Dang Van’s criterion [3] w as applied, w hich uses the equivalent value r a max +
a v P max. For crack initiation at the surface a criterion o f Bom as, L inkew itz, and M ayr [2]
w as applied, w hich uses the equivalent value r a max + a A p m. The m odel parameters
show n in Table 3 were determ ined by taking the variants 1, 2, 4, 8 , and 9 as references.
Figure 4 show s the calculated and the m easured endurance lim its as nom inal stress
amplitudes S a or Ta . M ost endurance lim its are w ell calculated. Large differences
betw een experim ent and calculation are exhibited by the variants 5, 6 , 7, 14, and 15.
The variants 5, 6 , and 7 exhibit h igh stress ratios o f R = 0 .4, 0.5, and 0.6,
respectively. I f the endurance lim its o f these variants are drawn in the Haigh diagram with
ISSN 0556-171X. npoöxeMbi npounocmu, 2008, N 1 17
H. Bomas, R. Kienzler, S. Kunow, et al.
the values o f the variants 1 and 4, it can be seen that there is a non-linear relation betw een
endurance lim it and m ean stress. This is typical for hard steels, e .g ., [4], but is not
described by the applied fatigue criteria.
T a b l e 3
Model Parameters for Calculation of the Endurance Limits
Reference area or volume TW 0 , MPa a m
Surface A A0 = 213 mm2 551 1.32 10
Volume V V0 = 192 mm3 629 0.59 14
Measured endurance limit [MPa]
Fig. 4. Predicted and measured nominal endurance limits, expressed as nominal longitudinal stress
S a or nominal torsional stress T„.
Fig. 5. Surface shear stress amplitudes in a specimen o f variant 14 normalised with the normal stress
amplitude in x-direction (0 < û < 180°, 0 < p < 360°). An explanation o f the cartesian coordinates
is given in Fig. 2.
18 ISSN 0556-171X. npoôneMbi npoHHoemu, 2008, № 1
Crack Initiation and Endurance Limit o f Hard Steels
The variants 14 and 15 are phase-shifted superpositions o f tension and torsion.
Variant 14 is very special, because it has no critical plane. Figure 5 show s the shear stress
amplitudes in the cutting surface planes norm alised w ith the normal stress amplitude in
x-direction. d and <p indicate the direction o f vector normal to the plane. Since many
planes see the m axim um shear stress amplitude, the damage o f the load is underestimated
b y the applied fatigue criteria. E specially the titanium carbonitrides seem to be victim s o f
the m ulti-plane dam age, since they fail by cleavage fracture in crystal planes. The
specim ens o f variant 15 have a m ild notch, and the stress situation is similar to that o f
variant 14. The specim ens o f variant 16 have a sharp notch, and due to the dom inance o f
the stress concentration factor for tension, the stress situation in the notch root is more
similar to that o f variant 3. It can be seen in Fig. 4 that the endurance lim its o f these
variants are very similar, w hich applies for the experim ental values as w ell as for the
calculated ones.
C on clu sions. In this work, the influence o f notches, stress gradients, m ean stresses
and m ultiaxial loads on the endurance lim it o f ground specim ens m ade o f the bearing steel
SAE 52100 in a bainitic condition w as investigated. The influence o f notches and o f stress
gradients can be described by application o f a w eakest-link concept. A prediction o f the
endurance lim it is possib le for loads w ith —1 < R < 0.1 w hich produce critical planes. The
crack initiation in sm ooth specim ens is very m uch influenced by the load type. Three
crack initiation sites were observed: oxides, carbonitrides and surface. Loads that produce
more than one critical plane lead to further damage o f the titanium carbonitrides. Under
push-pull or repeated-pull condition the m axim um stress is relevant for crack initiation:
W ith increasing m axim um stress, at first titanium carbonitrides and after that the surface
get more and more involved in crack initiation.
1. W. Weibull, “A statistical theory for the strength o f materials,” Royal Swed. Inst. Eng. Res.,
151 (1939).
2. H. Bomas, T. Linkewitz, and P. Mayr, Fatigue Fract. Eng. Mater. Struct., 22, 733 (1999).
3. K. Dang Van, B. Griveau, and O. Message, in: M. W. Brown and K. J. Miller (Eds.), Biaxial
and Multiaxial Fatigue (EGF 3), Mechanical Engineering Publications (1989), p. 479.
4. E. Haibach, Betriebsfestigkeit, Springer (2002).
Received 28. 06. 2007
ISSN 0556-171X. npoöneMbi npoHHocmu, 2008, № 1 19
|
| id | nasplib_isofts_kiev_ua-123456789-48237 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T15:28:36Z |
| publishDate | 2008 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Bomas, H. Kienzler, R. Kunow, S. Loewisch, G. Schroeder, S. 2013-08-17T10:49:10Z 2013-08-17T10:49:10Z 2008 Crack initiation and endurance limit of hard steels under multiaxial cyclic loads / H. Bomas, R. Kienzler, S. Kunow, G. Loewisch, S. Schroeder // Проблемы прочности. — 2008. — № 1. — С. 14-19. — Бібліогр.: 4 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48237 539. 4 The endurance limit and the mechanisms o f fatigue crack initiation in the high cycle regime were investigated using round specimens o f the bearing steel 52100 under longitudinal forces and torsional moments and combinations o f these loads. Three specimen types were examined: smooth specimens and specimens with circumferential notches with radii o f 1.0 and 0.2 mm. The influence ofmean and multiaxial stresses on the endurance limit can be understood by consideration ofcrack initiation mechanisms and micro-mechanics. Crack initiation took place at oxides, carbonitrides and at the surface. The mechanisms ofcrack initiation could be related to the load type: Loads with rotating principal stresses are more damaging fo r nitrides than fo r oxides. Increasing maximum stresses are more dangerous fo r nitrides than fo r oxides, and introduce more damage to the surface than to the nitrides. Normal stresses are more damaging fo r oxides than shear stresses. The endurance limits were calculated by means o f an extended weakest-link model which combines volume and surface crack initiation with related fatigue criteria. For volume crack initiation the criterion o f Dang Van was used. For the correct description o f the competing surface crack initiation, a new criterion was applied. With this concept, a prediction o f the endurance limit is possible fo r loads which produce critical planes and range within a limited regime ofstress ratios. Исследованы предел выносливости и механизмы зарождения усталостных трещин в многоцикловом режиме, используя круглые образцы из подшипниковой стали 52100, подвергаемые действию продольных сил и крутящих моментов, а также комбинации этих нагрузок. Использовали гладкие образцы и образцы с кольцевыми надрезами радиусами 1,0 и 0,2 мм. Влияние средних и многоосных напряжений на предел выносливости может быть объяснено с учетом механизмов зарождения трещин и микромеханики. Зарождение трещин происходило на оксидах, карбонитридах и на поверхности. Механизмы зарождения трещин могут быть связаны с типом нагрузки: нагрузки с вращательными главными напряжениями более деструктивны для нитридов, чем для оксидов. Возрастающие максимальные напряжения более опасны для нитридов, чем для оксидов, и вызывают большие повреждения поверхности, чем нитридов. Нормальные напряжения вызывают большее повреждение оксидов, чем касательные напряжения Пределы выносливости рассчитывали с помощью модифицированной модели слабого звена, которая объединяет зарождение трещин в объеме и на поверхности с соответствующими критериями усталости. Для зарождения трещин в объеме был использован критерий Данг Вана. Для корректного описания конкурирующего зарождения трещин на поверхности был применен новый критерий. С помощью этой концепции можно предсказать предел выносливости для нагрузок, которые создают критические плоскости и диапазон в рамках ограниченного режима коэффициентов асимметрии цикла. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Crack initiation and endurance limit of hard steels under multiaxial cyclic loads Зарождение трещин и предел выносливости твердых сталей при многоосных циклических нагрузках Article published earlier |
| spellingShingle | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads Bomas, H. Kienzler, R. Kunow, S. Loewisch, G. Schroeder, S. Научно-технический раздел |
| title | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads |
| title_alt | Зарождение трещин и предел выносливости твердых сталей при многоосных циклических нагрузках |
| title_full | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads |
| title_fullStr | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads |
| title_full_unstemmed | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads |
| title_short | Crack initiation and endurance limit of hard steels under multiaxial cyclic loads |
| title_sort | crack initiation and endurance limit of hard steels under multiaxial cyclic loads |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/48237 |
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