Abstract
The S–N equation is one of the most important equations in fatigue model investigation. A majority of fatigue models, including multi-axial fatigue model and mean effect models, are established on the basis of the S–N equation. Obviously, an accuracy of the S–N equation is very important. Taking into account that the S–N equation is, in fact, an empirical one in which the material constants are determined by numerical fitting fatigue experimental data, in this study, the S–N equation can be improved, by further processing these fatigue experimental data, to present a new type of S–N equation that is more accurate than the S–N equation. The new type of S–N equation is called a similar S–N equation in this study. By using a large number of experimental data of metallic materials reported in the literature, an accuracy of the similar S–N equation has been proven.
References
1.
Liu
,
B. W.
, and
Yan
,
X. Q.
, 2019
, “
A New Model of Multiaxial Fatigue Life Prediction With Influence of Different Mean Stresses
,” Int. J. Damage Mech.
,
28
(9
), pp. 1323
–1343
.10.1177/10567895188243962.
Liu
,
B. W.
, and
Yan
,
X. Q.
, 2020
, “
A Multi-Axial Fatigue Limit Prediction Equation for Metallic Materials
,” ASME J. Pressure Vessel Technol.
,
142
(3
), p. 034501
.10.1115/1.40462173.
Susmel
,
L.
, 2009
, Multiaxial Notch Fatigue, From Nominal to Stress/Strain Quantities
,
Woodhead Publishing Limited, CRC Press
, Boca Raton, FL
.4.
Gough
,
H. J.
, 1949
, “
Engineering Steels Under Combined Cyclic and Static Stresses
,” Proc. Inst. Mech. Eng.
,
160
(1
), pp. 417
–440
.10.1243/PIME_PROC_1949_160_040_025.
Nishihara
,
T.
, and
Kawamoto
,
M.
, 1941
, “
The Strength of Metals Under Combined Alternating Bending and Torsion
,” Mem. Coll. Eng., Kyoto Imp. Univ.
,
10
, pp. 177
–201
.10.1299/KIKAI1938.7.29-1_856.
Kitaioka
,
S.
,
Chen
,
J.
, and
Seika
,
M.
, 1986
, “
The Threshold of Micro Crack Propagation Under Mixed Mode
,” Bull. Jpn. Soc. Mech. Eng.
,
29
, pp. 214
–237
.10.1299/jsme1958.29.6517.
Frith
,
P. H.
, 1956
, “
Fatigue of Wrought High-Tensile Alloy Steel
,” Proceedings of the Institution of Mechanical Engineers
, pp. 462
–499
.8.
Nishihara
,
T.
, and
Kawamoto
,
M.
, 1945
, “
The Strength of Metals Under Combined Alternating Bending and Torsion With Phase Difference
,” Mem. Coll. Eng., Kyoto Imp. Univ.
,
11
, pp. 85
–112
.https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/280193/1/mcekiu_11_5_85.pdf9.
Achtelik
,
H.
,
Jakubowska
,
I.
, and
Macha
,
E.
, 1983
, “
Actual and Estimated Directions of Fatigue Fracture Plane in ZI250 Grey Cast Iron Under Combined Alternating Bending and Torsion
,” Stud. Geotech. Mech.
,
5
(2
), pp. 9
–30
.10.
Lempp
,
W.
, 1977
, “
Festigkeitsverhalten Von Stählen Bei Mehrachsiger Dauerschwingbeanspruchung Durch Normalspannungen Mit Überlagerten Phasengleichen Und Phasenverschobenen Schubspannungen
,” Dissertation,
Universität Stuttgart
,
Germany
.11.
Zenner
,
H.
,
Heidenreich
,
R.
, and
Richter
,
I.
, 1985
, “
Dauerschwingfestigkeit Bei Nichtsynchroner Mehrachsiger Beanspruchung
,” Z. Werkstofftech.
,
16
, pp. 101
–112
.10.1002/mawe.1985016031012.
Froeschl
,
J.
,
Gerstmayr
,
G.
,
Eichlseder
,
W.
, and
Leitner
,
H.
, 2007
, “
Multiaxial Fatigue of qt-Steels: New Fatigue Strength Criterion for Anisotropic Material Behaviour
,” Proceedings of 8th International Conference on Multiaxial Fatigue and Fracture
,
Sheffield, UK
, Paper No. S3-1.13.
Matake
,
T.
, 1977
, “
An Explanation on Fatigue Limit Under Combined Stress
,” Bull. JSME
,
20
(141
), pp. 257
–263
.10.1299/jsme1958.20.25714.
Altenbach
,
H.
, and
Zolochevsky
,
A.
, 1996
, “
A Generalised Fatigue Limit Criterion and a Unified Theory of Low-Cycle Fatigue Damage
,” Fatigue Fract. Eng. Mater. Struct.
,
19
(10
), pp. 1207
–1219
.10.1111/j.1460-2695.1996.tb00944.x15.
Findley
,
W. N.
,
Coleman
,
J. J.
, and
Hanley
,
B. C.
, 1956
, “
Theory for Combined Bending and Torsion Fatigue With Data for SAE 4340 Steel
,” Proceedings of International Conference on Fatigue of Metals
,
Institution of Mechanical Engineers
,
London
, UK, Sept. 10–14, pp. 150
–157
.https://www.semanticscholar.org/paper/THEORY-FORCOMBINED-BENDING-AND-TORSION-FATIGUE-FOR-Findley-Coleman/0ff6a6dace6bbdf3ed2fe9f3f980fc7a9c3974ce16.
Froustey
,
C.
, 1986
, “
Fatigue Multiaxiale en Endurance de L'acier 30NCD16
,” Ph.D. thesis,
Ecole Nationale Supérieure d'Arts et Métiers
,
Bordeaux, France
.17.
Froustey
,
C.
, and
Lasserre
,
S.
, 1989
, “
Multiaxial Fatigue Endurance of 30NCD16 Steel
,” Int. J. Fatigue
,
11
(3
), pp. 169
–175
.10.1016/0142-1123(89)90436-218.
Froustey
,
C.
,
Lasserre
,
S.
, and
Dubar
,
L.
, 1992
, “
Essais de Fatigue Multiaxiaux et Par Blocs. Validation D'un Critère Pour Les Matériaux Métalliques
,” Proceedings of METTECH 92
,
Grenoble, France
.19.
Fogué
,
M.
, and
Bahuaud
,
J.
, 1985
, “
Fatigue Multiaxiale à Durée de Vie Illimitée
,” Proceedings of Comptes Rendus 7ème Congrès Français de Mécanique
,
Bordeaux, France
, pp. 30
–31
.20.
Delahay
,
T.
, and
Palin-Luc
,
T.
, 2005
, “
Estimation of the Fatigue Strength Distribution in High-Cycle Multiaxial Fatigue Taking Into Account the Stress–Strain Gradient Effect
,” Int. J. Fatigue
,
28
(5–6
), pp. 474
–484
.10.1016/j.ijfatigue.2005.06.04821.
Palin-Luc
,
T.
, and
Lasserre
,
S.
, 1998
, “
An Energy Based Criterion for High Cycle Multiaxial Fatigue
,” Eur. J. Mech.-A/Solids
,
17
(2
), pp. 237
–251
.10.1016/S0997-7538(98)80084-322.
Sonsino
,
C. M.
, 2001
, “
Influence of Load and Deformation-Controlled Multiaxial Tests on Fatigue Life to Crack Initiation
,” Int. J. Fatigue
,
23
(2
), pp. 159
–167
.10.1016/S0142-1123(00)00079-723.
Akrache
,
R.
, and
Lu
,
J.
, 1999
, “
Three-Dimensional Calculations of High Cycle Fatigue Life Under Out-of-Phase Multiaxial Loading
,” Fatigue Fract. Eng. Mater. Struct.
,
22
(6
), pp. 527
–534
.10.1046/j.1460-2695.1999.00172.x24.
Gough
,
H. J.
,
Pollard
,
H. V.
, and
Clenshaw
,
W. J.
, 1951
, Some Experiments on the Resistance of Metals to Fatigue Under Combined Stresses
(Aeronautical Research Council, R and, M),
HMSO
,
London
, UK, p. 2522
.25.
Li
,
B. C.
,
Jiang
,
C.
,
Han
,
X.
, and
Li
,
Y.
, 2015
, “
A New Approach of Fatigue Life Prediction for Metallic Materials Under Multiaxial Loading
,” Int. J. Fatigue
,
78
, pp. 1
–10
.10.1016/j.ijfatigue.2015.02.02226.
Shamsaei
,
N.
,
Fatemi
,
A.
, and
Socie
,
D. F.
, 2011
, “
Multiaxial Fatigue: An Overview and Same Approximation Models for Life Estimation
,” Int. J. Fatigue
,
33
, pp. 948
–958
.10.1016/j.ijfatigue.2011.01.00327.
Crossland
,
B.
, 1956
, “
Effect of Large Hydrostatic Pressures on the Torsional Fatigue Strength of an Alloy Steel
,” Proceedings of the International Conference on Fatigue of Metals
,
The Institution of Mechanical Engineers
,
London
, UK, pp. 138
–149
.28.
Sines
,
G.
,
Waisman
,
J. L.
, and
Dolan
,
T. J.
, 1959
, Metal Fatigue
,
McGraw-Hill
, New York
.29.
Papadopoulos
,
I. V.
,
Davoli
,
P.
,
Gorla
,
C.
,
Filippini
,
M.
, and
Bernasconi
,
A.
, 1997
, “
A Comparative Study of Multiaxial High-Cycle Fatigue Criteria for Metals
,” Int. J. Fatigue
,
19
, pp. 219
–235
.10.1016/S0142-1123(96)00064-330.
Papadopoulos
,
I. V.
, 2001
, “
Long Life Fatigue Under Multiaxial Loading
,” Int. J. Fatigue
,
23
(10
), pp. 839
–849
.10.1016/S0142-1123(01)00059-731.
Gough
,
H. J.
, and
Pollard
,
H. V.
, 1937
, “
Properties of Some Materials for Cast Crankshafts, With Special Reference to Combined Alternating Stresses
,” Proc. Inst. Automob. Eng.
,
31
, pp. 821
–893
.32.
Gough
,
H. J.
, and
Pollard
,
H. V.
, 1935
, “
The Strength of Metals Under Combined Alternating Stress
,” Proc. Inst. Mech. Eng.
,
131
, pp. 3
–18
.10.1243/PIME_PROC_1935_131_008_0233.
Verreman
,
Y.
, and
Guo
,
H.
, 2007
, “
High-Cycle Fatigue Mechanisms in 1045 Steel Under Non-Proportional Axial-Torsional Loading
,” Fatigue Fract. Eng. Mater. Struct.
,
30
(10
), pp. 932
–946
.10.1111/j.1460-2695.2007.01164.x34.
Kardas
,
D.
,
Kluger
,
K.
,
Łagoda
,
T.
, and
Ogonowski
,
P.
, 2004
, “
Fatigue Life of AlCu4Mg1 Aluminium Alloy Under Constant Amplitude Bending With Torsion
,” Proceedings of 7th International Conference on Biaxial and Multiaxial Fatigue and Fracture
,
Berlin, Germany
, June 28–30, pp. 185
–190
.35.
Lee
,
S. B.
, 1985
, “
A Criterion for Fully Reversed Out-of-Phase Torsion and Bending
,” Multiaxial Fatigue
,
K. J.
Miller
, and
M. W.
Brown
, eds.,
ASTM STP
, West Conshohocken, PA
, Vol.
853
, pp. 553
–568
.36.
Chaudonneret
,
M.
, 1993
, “
A Simple and Efficient Multiaxial Fatigue Damage Model for Engineering Applications of Macro-Crack Initiation
,” ASME J. Eng. Mater. Technol.
,
115
(4
), pp. 373
–379
.10.1115/1.290423237.
Kurath
,
P.
,
Downing
,
S. D.
, and
Galliart
,
D. R.
, 1989
, “
Summary of Non-Hardened Notched Shaft – Round Robin Program
,” Multiaxial Fatigue – Analysis and Experiments
,
G. E.
Leese
and
D. F.
Socie
, eds.,
SAE AE-14, Society of Automotive Engineers
,
Warrendale, PA
, pp. 13
–32
.38.
Yan
,
X. Q.
, 2024
, “
Research Into Applicability of Wöhler Curve Method for Low-Cycle Fatigue of Metallic Materials
,” J. Harbin Inst. Technol.
, 31
(2
), pp. 22
–37
.39.
Yan
,
X. Q.
, 2023, “
The Wöhler Curve Method for a Low/Medium/High Cycle Fatigue of Metals
,” Authorea, accessed May 28, 2024, https://doi.org/10.22541/au.167447214.41953886/v140.
Yan
,
X. Q.
, 2021
, “
A Mean Stress Model of Fatigue Life of Metal Materials Under Multiaxial Loading
,” Mater. Sci. Eng. Int. J.
,
5
(2
), pp. 60
–69
.10.15406/mseij.2021.05.0015741.
Yan
,
X. Q.
, 2023
, Multiaxial Notch Fracture and Fatigue
,
CRC Press
,
Boca Raton, London, New York
, p. 367
.42.
Yan
,
X. Q.
, 2021
, “
An Empirical Fracture Equation of Mixed Mode Cracks
,” Theor. Appl. Fract. Mech.
,
116
, p. 103146
.10.1016/j.tafmec.2021.103146
