Area and point approaches in fatigue life evaluation under combined bending and torsion loading
We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction of stresses to representative local ones in the critical plane for fatigue life calculation. The shear and normal stresses are averaged in two overlapping areas of different sizes on the critical plane. The...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2008
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| Cite this: | Area and point approaches in fatigue life evaluation under combined bending and torsion loading / A. Karolczuk, E. Macha // Проблемы прочности. — 2008. — № 1. — С. 69-72. — Бібліогр.: 8 назв. — англ. |
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Karolczuk, A. Macha, E. 2013-08-19T19:11:16Z 2013-08-19T19:11:16Z 2008 Area and point approaches in fatigue life evaluation under combined bending and torsion loading / A. Karolczuk, E. Macha // Проблемы прочности. — 2008. — № 1. — С. 69-72. — Бібліогр.: 8 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48457 539.4 We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction of stresses to representative local ones in the critical plane for fatigue life calculation. The shear and normal stresses are averaged in two overlapping areas of different sizes on the critical plane. The proposed method is compared with the point (in critical distance) method and both are verified by fatigue tests under combined bending and torsion. Verification is done for the experimental and calculated fatigue lives with use of two multiaxial fatigue failure criteria. Представлен новый нелокальный подход к неравномерному распределению напряжений, который заключается в приведении напряжений к представительным локальным напряжениям в критической плоскости при расчете усталостной долговечности. Касательные и нормальные напряжения усредняются по двум перекрывающимся площадям различного размера, находящихся в критической плоскости. Проведено сравнение предлагаемого метода с точечным методом (по критическому расстоянию), выполнена проверка обоих методов при испытаниях на усталость в условиях совместного нагружения при изгибе и кручении. Проверка осуществлялась по полученным экспериментальным и расчетным значениям усталостной долговечности с применением двух критериев усталостного разрушения при сложном напряженном состоянии. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Area and point approaches in fatigue life evaluation under combined bending and torsion loading Объемный и точечный подходы при оценке усталостной долговечности в условиях совместного нагружения при изгибе и кручении Article published earlier |
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Area and point approaches in fatigue life evaluation under combined bending and torsion loading |
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Area and point approaches in fatigue life evaluation under combined bending and torsion loading Karolczuk, A. Macha, E. Научно-технический раздел |
| title_short |
Area and point approaches in fatigue life evaluation under combined bending and torsion loading |
| title_full |
Area and point approaches in fatigue life evaluation under combined bending and torsion loading |
| title_fullStr |
Area and point approaches in fatigue life evaluation under combined bending and torsion loading |
| title_full_unstemmed |
Area and point approaches in fatigue life evaluation under combined bending and torsion loading |
| title_sort |
area and point approaches in fatigue life evaluation under combined bending and torsion loading |
| author |
Karolczuk, A. Macha, E. |
| author_facet |
Karolczuk, A. Macha, E. |
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Научно-технический раздел |
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Научно-технический раздел |
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2008 |
| language |
English |
| container_title |
Проблемы прочности |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Article |
| title_alt |
Объемный и точечный подходы при оценке усталостной долговечности в условиях совместного нагружения при изгибе и кручении |
| description |
We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction of stresses to representative local ones in the critical plane for fatigue life calculation. The shear and normal stresses are averaged in two overlapping areas of different sizes on the critical plane. The proposed method is compared with the point (in critical distance) method and both are verified by fatigue tests under combined bending and torsion. Verification is done for the experimental and calculated fatigue lives with use of two multiaxial fatigue failure criteria.
Представлен новый нелокальный подход к неравномерному распределению напряжений, который заключается в приведении напряжений к представительным локальным напряжениям в критической плоскости при расчете усталостной долговечности. Касательные и нормальные напряжения усредняются по двум перекрывающимся площадям различного размера, находящихся в критической плоскости. Проведено сравнение предлагаемого метода с точечным методом (по критическому расстоянию), выполнена проверка обоих методов при испытаниях на усталость в условиях совместного нагружения при изгибе и кручении. Проверка осуществлялась по полученным экспериментальным и расчетным значениям усталостной долговечности с применением двух критериев усталостного разрушения при сложном напряженном состоянии.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/48457 |
| citation_txt |
Area and point approaches in fatigue life evaluation under combined bending and torsion loading / A. Karolczuk, E. Macha // Проблемы прочности. — 2008. — № 1. — С. 69-72. — Бібліогр.: 8 назв. — англ. |
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| first_indexed |
2025-11-27T00:05:52Z |
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2025-11-27T00:05:52Z |
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1850787283573145600 |
| fulltext |
UDC 539.4
A r e a a n d P o in t A p p r o a c h e s in F a t ig u e L ife E v a lu a t io n u n d e r C o m b in e d
B e n d in g a n d T o r s io n L o a d in g
A . K a ro lczu k 1,a and E. M a ch a 1,b
1 Opole University o f Technology, Opole, Poland
a A.Karolczuk@po.opole.pl, b E.Macha@po.opole.pl
We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction o f
stresses to representative local ones in the critical plane fo r fatigue life calculation. The shear and
normal stresses are averaged in two overlapping areas o f different sizes on the critical plane. The
proposed method is compared with the point (in critical distance) method and both are verified by
fatigue tests under combined bending and torsion. Verification is done fo r the experimental and
calculated fatigue lives with use o f two multiaxial fatigue failure criteria.
K e y w o rd s : nonlocal approach, critical plane approach, stress gradient.
In trod u ction . G eom etry or loading features o f com ponents often causes the
form ation o f nonuniform stress/strain distribution. In case o f fatigue loading, cracks are
form ed under the influence o f a stress/strain w hich undergo changes in tim e and in som e
volum e o f the material. This com plicated process m ust be taken into account in the proper
fatigue life estimation.
On the basis o f experim ental evidences concerning the stress gradient effect on
fatigue life, the fo llow ing phenom ena have been revealed: (i) under equal nom inal
stresses, fatigue lives o f specim ens subjected to reversed bending are higher than fatigue
lives o f the sam e specim ens subjected to reversed push-pull loading [ 1, 2 ]; (ii) the
initiation o f nonpropagating fatigue cracks under loading c lose to the fatigue lim it for
defective materials [3 , 4 ]; (iii) lo w influence o f shear stress gradient on fatigue lives for
specim ens subjected to reversed torsion [ 1, 5 ].
The m ain goal o f the present paper is to develop a m odel o f reduction o f nonuniform
stress distributions around a hot spot in a material to representative loca l stresses.
Representative means taking the above-m entioned (i, ii, iii) phenomena into consideration.
The phenom enon (i) allow s for the averaging o f stresses in som e critical space o f the
material. Fundamental issue is to define the shape and size o f this critical space.
D efin ition o f these geom etrical features is dictated by the other phenom ena - (ii) and (iii).
The phenom enon (ii) accounts for too sm all opening stresses active at a sm all distance
from the stress concentrator. Therefore, it is postulated that an averaged value o f normal
(opening) stresses over the potential crack growth plane, provided that the crack growth
m ust reach the critical value. The phenom enon (iii) is associated on ly w ith the
m acroscopic shear stress gradient w hich arises, e.g., from torsion o f the cylindrical
specim ens. A t the observation scale o f a few m etallic grains, the m acroscopic shear stress
gradient is insignificant and has no influence on the crack initiation and especia lly on the
crack growth. H ow ever, in the case o f a significant shear stress gradient at the m esoscopic
scale, w hich arises, for instance, from notches or defects w ith sizes o f a few m etallic
grains, it is necessary to take this effect into account during an early crack formation
phase. This effect should be considered in the area w here crack is form ed in the m axim um
shear stress plane (stage I). The size o f this area depends m ainly on the material state and
loading (type and test conditions) but for m ost cases this area is very sm all in com parison
to the area w here cracks grow on the m axim um normal stress plane (stage II).
The paper outlines the m odel o f shear and normal stresses reduction over the critical
areas. A new approach is verified using the test results on hour-glass shaped specim ens
© A. K A R O LC ZU K , E. M A C H A , 2008
ISSN 0556-171X. Проблемы прочности, 2008, № 1 69
mailto:A.Karolczuk@po.opole.pl
mailto:E.Macha@po.opole.pl
A. Karolczuk and E. Macha
subjected to com bined cyclic bending and torsion. M oreover, the point approach (the
theory o f critical distance), w hich has been analyzed and developed by Taylor and Susm el
[6 ], has been also verified.
F a tigu e Tests. H our-glass shaped specim ens m ade o f 18G 2A steel (Table 1), w ith a
m inim um diameter o f 6.5 m m , w ere subjected to sinusoidal com binations o f plane
bending and torsion under different m om ent amplitude ratios X M = M t, a / M b, a (torque/
bending) and tw o phase shifts 5 = 0 and d = n / 2 (M b (t ) = M b,a sin (2jzft), M t ( t ) =
M t a sin(2w f — 5 ), f = 20 Hz). Failure o f a specim en is defined by about 30% drop in
bending rigidity. The specim ens w ere cut from a 15.8-m m -diam eter drawn bar, m achine-
turned and conventionally polished w ith progressively finer em ery papers.
T a b l e 1
Cyclic Properties o f the 18G2A Steel
Torsion: r a = r af (N r /N f )1/"r Push-pull: a a = a af (N „ /N f )1/ma £p = (aa ! K ')1/"
r af , MPa mr N r , cycles a af ,M Pa ma N a , cycles K ', MPa n'
157 9.5 1.98 • 106 204 8.2 1.24 • 106 1323 0.207
Indices: a f = fatigue limit, a = amplitude, p = plastic, r = torsion, a = push-pull, N = cycles.
T h e A rea M eth od . The proposed area m ethod for reduction o f nonuniform
distributions o f shear and normal stresses to the uniform ones takes into account the
phenom ena (i), (ii), and (iii) as m entioned above. It is b elieved that the crack growth or
fatigue damage is a loca l process. It m eans that the crack initiation period can be
described also by the crack growth process. A crack grow s from a size o f one or a few
grains up to the size w hich defines the com ponent failure. During this process, the crack
growth could be governed by different m echanism s (M ode I, M ode II, etc.). Under the
conventional uniaxial fatigue tests, the crack grow s through the material over the plane
w hich originally had a uniform stress distribution. In the case o f fatigue tests w ith the
stress gradient effect, a crack grow s over a nonuniform ly stressed plane. The local stresses
w hich vary over the potential crack growth plane have an influence on the loca l crack
growth rate and consequently on the total fatigue life. To avoid the com plicated process o f
iterative m odeling o f the crack growth using the finite elem ent m ethod, it is assum ed that
the averaged stresses over the potential fracture plane reflect the stress gradient effect.
Since the shear crack grow ing process (stage I) is usually lim ited to the area o f a few
grains, the averaging process o f shear stresses r ns is restricted to that area. The tensile
crack growth (stage II) w hich usually leads to the final failure takes place in the area
w hich defines failure by its size or by the beginning o f an unstable crack growth rate. Two
com ponents o f the stress tensor are distinguished for the averaging process, i.e ., shear r ns
and normal o n . The plane orientation w hereby these com ponents are determ ined is
defined by m ultiaxial fatigue failure criterion and is w e ll know n as the critica l p la n e . The
averaged stresses over tw o overlapping areas A nsc and A n c are calculated according to
the fo llow ing relations:
1 r 1 r
r ns ( t ,n , s ) = A------ J r ns ( t ,n , s , ̂ r )dA ns, 0 n ( t ,n ) = A-----J 0 n ( t ,n , ̂ r)dA n , (1)
A ns, c A A n, c A
A n s A n
where n is the normal vector to the critical plane, s is the shear vector on the critical
plane, <p, r are the local coordinates on the critical plane, and t is time. The averaged
stresses r ns and o n w hich are functions o f tim e and the critical plane orientation are
70 ISSN 0556-171X. npoôëeMbi npounocmu, 2008, N 1
Area and Point Approaches in Fatigue Life Evaluation
introduced into the m ultiaxial fatigue failure criterion. B ecause the analyzed data pertain
to the m acroscopic stress gradient, the averaging process over the area o f a few grains is
not necessary. O nly the normal stresses o n are averaged over the area A n c . For
sim plicity, the shape o f the A n c area is assum ed to be semicircular. The failure o f the
specim ens is defined by about 30% drops in bending rigidity. It m eans that the averaging
process in the cross section o f the specim en m ay be reduced to the sem icircular-shaped
area o f 4 .17 m m 2 and this value is taken as A n c .
T h e P o in t M ethod . This m ethod assum es that the stressed state, at som e critical
distance from the hot spot, is responsible for the material failure. I f the equivalent stress at
this point is h igh enough, then the crack w ill propagate and cause the final failure.
R esu lts and D iscussion . Stress and strain histories at an arbitrary point (x, y) o f the
specim en cross section were com puted from bending M b ( t ) and torque M t ( t ) m om ents
by m eans o f a kinem atic hardening m odel as proposed by M roz and m odified by Garud.
M ore details can be found in [7].
Two m ultiaxial fatigue failure criteria have been verified using test results. One o f
them is the w ell know n Matake criterion [8 ],
f +v ns, a 1 f .
7af
\
' af
N T
\ N calc )
(2 )
for w hich the critical plane orientation coincides w ith the m axim um shear stress
amplitude. The other criterion is based on tw o parameters,
N calc : N n N calc (3)
n, max ns, a
The final fatigue life N caic is determined by the minimum fatigue life betw een N ° aic and
N xcaic ; O n max is the m axim um value in tim e o f the averaged normal stress O n ( t ) on a
plane w here this stress reaches its m axim um , f ns a is the amplitude o f the averaged shear
stress f ns (t ) on a plane where this stress is m axim um . Figure 1 g ives the results obtained
by the proposed area method.
N , cycles N 5 cycles
exp
Fig. 1. Comparison o f the experimental and calculated fatigue lives: the area method and (a) Matake
criterion, (b) two-parameter criterion. [Dashed lines represent the maximum experimental scatter
band X3.1 and l o = txz ,a (L = 0)/ o z z ,a (L = °W
ISSN 0556-171X. npoôëeMbi npounocmu, 2008, N9 1 71
A . Karolczuk and E. Macha
The follow ing error parameters w ere applied for the evaluation o f the criteria and
methods:
E (i ) log
N O' )
calc
N (i ) exp
O')
i=1
E std =
(4)
— X (E (i} - Em ) 2 , Ex = V E 2 + E 2d ,
i=1
where k is a number o f specim ens (k = 43).
D ifferent critical distances L were exam ined in the case o f the point method. The
best results used for the Matake criterion were obtained for L = 1.35 m m (Fig. 2a) and for
the two-parameter criterion for L = 0.8 m m (Fig. 2b).
75
&
N , cycles exp J N , cycles e>p J
Fig. 2. Comparison o f the experimental and calculated fatigue lives: the point method and (a) Matake
criterion, (b) two-parameter criterion. [Dashed lines represent the maximum experimental scatter
band X3.1 and x a = XxZ,a (L)/ Oz z ,a (L).]
C on clu sions. Under the investigated test conditions, the experim ental and calculated
fatigue lives can be su ccessfu lly correlated w ith the two-parameter m ultiaxial fatigue
failure criterion based on the critical plane approach and the proposed area m ethod for
nonuniform stress reduction. The proposed area m ethod takes into account the different
effects o f shear and normal stress gradients on the fatigue life. The classical point method
neglects this effect, but the results obtained by this m ethod are on ly a little worse.
1. I. V. Papadopoulos and V. P. Panoskaltsis, Eng. Fract. Mech., 55, No. 4, 513 (1996).
2. F. Morel and T. Palin-Luc, Fatigue Fract. Eng. Mater. Struct., 25, 649 (2002).
3. Y. Murakami and M. Endo, Int. J. Fatigue, 16, 163 (1994).
4. M. Endo and I. Ishimoto, Int. J. Fatigue, IS, 592 (2006).
5. D. McClaflin and A. Fatemi, Int. J. Fatigue, 26, 773 (2004).
6 . L. Susmel and D. Taylor, Int. J. Fatigue, IS, 417 (2006).
7. A. Karolczuk, Eng. Fract. Mech., 13, 1629 (2006).
8 . T. Matake, Bull. JSME, 10 (141), 257 (1977).
Received 28. 06. 2007
12 ISSN 0556-171X. Проблемы прочности, 200S, № 1
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