The purpose of this study is to develop a numerical methodology to simulate the fatigue damage of revolving mechanical parts under cyclic loadings (such as rolling bearings). The methodology is based on the continuum damage mechanics and on a fatigue damage model. The fatigue damage can be caused by numerous loading cycles, even in an elastic state; the damage will then influence the elastoplastic behaviors. The coupling effect of both enfeebles the material strength and leads to the rupture. An important improvement on the Sines fatigue criterion is proposed, which allows the coupling behaviors of damage and plasticity to be described better. This paper deals with the following aspects: (i) the fatigue damage model and the identification of fatigue parameters using S-N curves; (ii) the elastoplastic constitutive behaviors coupled with the fatigue damage; (iii) a cycle jumping algorithm to reduce the computation time; and (iv) an adaptative remeshing to follow the rupture propagation. These mechanical and numerical models are implemented in the framework of ABAQUS software. Two applications are presented in this paper: the fatigue lifetime prediction for a cyclic tension specimen and the fatigue spalling (or chipping) initiation and growth in a thrust roller bearing under a cyclic loading. The present approach is very efficient and helpful for the lifetime prediction of revolving mechanical components.

1.
Bogard
,
F.
,
Debray
,
K.
, and
Guo
,
Y. Q.
, 2002, “
Determination of Sensor Positions for Predictive Maintenance of Revolving Machines
,”
Int. J. Solids Struct.
0020-7683,
39
, pp.
3159
3173
.
2.
Jiang
,
Y.
, and
Sehitoglu
,
H.
, 1999, “
A Model for Rolling Contact Failure
,”
Wear
0043-1648,
224
, pp.
38
49
.
3.
Kapoor
,
A.
, 1994, “
A Re-Evaluation of the Life to Rupture of Ductile Metals by Cyclic Plastic Strain
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
17
, pp.
201
219
.
4.
Saulot
,
A.
,
Descartes
,
S.
,
Desmyter
,
D.
,
Levy
,
D.
, and
Berthier
,
Y.
, 2006, “
A Tribological Characterization of the Damage Mechanism of Low Rail Corrugation on Sharp Curved Track
,”
Wear
0043-1648,
260
, pp.
984
995
.
5.
Ding
,
J.
,
Hall
,
R. F.
,
Byrne
,
J.
, and
Tong
,
J.
, 2007, “
Fatigue Crack Growth From Foreign Object Damage Under Combined Low and High Cycle Loading. Part II: A Two-Parameter Predictive Approach
,”
Int. J. Fatigue
0142-1123,
29
, pp.
1350
1358
.
6.
Spiteri
,
P.
,
Ho
,
S.
, and
Lee
,
Y. L.
, 2007, “
Assessment of Bending Fatigue Limit for Crankshaft Sections With Inclusion of Residual Stresses
,”
Int. J. Fatigue
0142-1123,
29
, pp.
318
329
.
7.
Li
,
B.
,
Reis
,
L.
, and
De Freitas
,
M.
, 2006, “
Simulation of Cyclic Stress/Strain Evolutions for Multiaxial Fatigue Life Prediction
,”
Int. J. Fatigue
0142-1123,
28
, pp.
451
458
.
8.
Guo
,
Y. B.
, and
Barkey
,
M. E.
, 2004, “
FE-Simulation of the Effects of Machining-Induced Residual Stress Profile on Rolling Contact of Hard Machined Components
,”
Int. J. Mech. Sci.
0020-7403,
46
, pp.
371
388
.
9.
De Jesus
,
A. M. P.
,
Ribeiro
,
A. S.
, and
Fernandes
,
A. A.
, 2005, “
Finite Element Modeling of Fatigue Damage Using a Continuum Damage Mechanics Approach
,”
J. Pressure Vessel Technol.
0094-9930,
127
(
2
), pp.
157
164
.
10.
Bouzakis
,
K. D.
, and
Vidakis
,
N.
, 1997, “
Prediction of the Fatigue Behaviour of Physically Vapour Deposited Coatings in the Ball on Rod Rolling Contact Fatigue Test, Using an Elastic-Plastic Finite Element Method Simulation
,”
Wear
0043-1648,
206
, pp.
197
203
.
11.
Gupta
,
V.
,
Bastias
,
P.
,
Hahn
,
G. T.
, and
Rubin
,
C. A.
, 1993, “
Elasto-Plastic Finite-Element Analysis of 2-D Rolling Sliding Contact With Temperature-Dependent Bearing Steel Material Properties
,”
Wear
0043-1648,
169
, pp.
251
256
.
12.
Ekberg
,
K. E.
, 2005, “
Fatigue of Railway Wheels and Rails Under Rolling Contact and Thermal Loading—An Overview
,”
Wear
0043-1648,
258
, pp.
1288
1300
.
13.
Johnson
,
K. L.
, 1989, “
The Strength of Surfaces in Rolling Contact
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
203
, pp.
151
163
.
14.
Ponter
,
R. S.
,
Hearle
,
A. D.
, and
Johnson
,
K. L.
, 1985, “
Application of the Kinematical Shakedown Theorem to Rolling and Sliding Point Contacts
,”
J. Mech. Phys. Solids
0022-5096,
41
, pp.
487
505
.
15.
Kunc
,
R.
,
Zerovnik
,
A.
, and
Prebil
,
I.
, 2007, “
Verification of Numerical Determination of Carrying Capacity of Large Rolling Bearings With Hardened Raceway
,”
Int. J. Fatigue
0142-1123,
29
(
9–11
), pp.
1913
1919
.
16.
Clayton
,
P.
, and
Hill
,
D. N.
, 1987, “
Rolling Contact Fatigue of a Rail Steel
,”
Wear
0043-1648,
117
, pp.
319
334
.
17.
Stone
,
D. H.
, and
Moyar
,
G. J.
, 1989, “
Wheel Shelling and Spalling, An Interpretive Review
,”
Rail Transportation
,
ASME
,
New York
, pp.
19
31
.
18.
ERRI
, 1990, “
Review of Rolling Contact Fatigue in Rails
,” Question D173, Report No. 1, European Rail Research Institute, Utrecht, Netherlands.
19.
Dang Van
,
K.
,
Maitournam
,
M. H.
, and
Prasil
,
B.
, 1996, “
Elastoplastic Analysis of Repeated Moving Contact-Application to Railways Damage Phenomena
,”
Wear
0043-1648,
196
, pp.
77
81
.
20.
Guo
,
Y. B.
, and
Barkey
,
M. E.
, 2004, “
Modelling of Rolling Contact Fatigue for Hard Machined Components With Process-Induced Residual Stress
,”
Int. J. Fatigue
0142-1123,
26
, pp.
605
613
.
21.
Liu
,
Y.
,
Stratman
,
B.
, and
Mahadevan
,
S.
, 2006, “
Fatigue Crack Initiation Life Prediction of Railroad Wheels
,”
Int. J. Fatigue
0142-1123,
28
, pp.
747
756
.
22.
Busquet
,
M.
,
Baillet
,
L.
,
Bordreuil
,
C.
, and
Berthier
,
Y.
, 2005, “
3D Finite Element Investigation on the Plastic Flows of Rolling Contacts-Correlation With Rail Head Microstructural Observations
,”
Wear
0043-1648,
258
, pp.
1071
1080
.
23.
Ringsberg
,
J. W.
,
Franklin
,
J.
,
Josefson
,
B.
,
Kapoor
,
A.
, and
Nielsen
,
C. O.
, 2005, “
Fatigue Evaluation of Surface Coated Railway Rails Using Shakedown Theory, Finite Element Calculations and Lab and Field Trials
,”
Int. J. Fatigue
0142-1123,
27
, pp.
680
694
.
24.
Lemaitre
,
J.
, and
Chaboche
,
J. L.
, 1990,
Mechanics of Solid Materials, Trans, B. Shrivastava
,
Cambridge University Press
,
Cambridge, England
.
25.
ABAQUS Software
, 2006, Documentation v6.6.
26.
Sines
,
G.
, and
Ohgi
,
G.
, 1981, “
Fatigue Criteria Under Combined Stresses or Strains
,”
ASME J. Eng. Mater. Technol.
0094-4289,
103
, pp.
82
90
.
27.
Findley
W. N.
, 1957, “
Fatigue of Metals Under Combinations of Stresses
,”
Trans. ASME
0097-6822,
79
, pp.
1337
1348
.
28.
Matake
,
T.
, 1977, “
An Explanation on Fatigue Limit Under Combined Stress
,”
Bull. JSME
0021-3764,
20
(
141
), pp.
257
263
.
29.
Dang Van
,
K.
,
Griveau
,
B.
, and
Message
,
O.
, 1989, “
On a New Multiaxial Fatigue Limit Criterion: Theory and Applications
,”
Biaxial and Multiaxial Fatigue, EGF3
,
M. W.
Brown
and
K. J.
Mille
, eds.,
Mechanical Engineering Publications
,
London
, pp.
479
496
.
30.
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
, Institute of Mechanical Engineers, London.
31.
Lee
,
S. B.
, 1980, “
Evaluation of Theories on Multiaxial Fatigue With Discriminating Specimens
,” Ph.D. thesis, Stanford University, CA.
32.
Ngargueudedjim
,
K.
, 1998, “
Contribution à l’étude des lois d’endommagement en fatigue
,” Ph.D. thesis, INSA, Lyon, France.
33.
Saanouni
,
K.
, and
Chaboche
,
J. L.
, 2003, “
Computational Damage Mechanics. Application to Metal Forming
,”
Numerical and Computational Methods in Comprehensive Structural Integrity
, Vol.
3
, Chap. 7.
34.
Simo
,
J. C.
, and
Ortiz
,
M.
, 1985, “
A Unified Approach to Finite Deformation Elastoplastic Analysis Based on the Use of Hyperelastic Constitutive Equations
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
49
(
2
), pp.
221
245
.
35.
Saanouni
,
K.
,
Nesnas
,
K.
, and
Hammi
,
Y.
, 2000, “
Damage Modelling in Metal Forming Processes
,”
Int. J. Damage Mech.
1056-7895,
9
(
3
), pp.
196
240
.
36.
Chaboche
,
J. L.
, 1988, “
Continuum Damage Mechanics: Part I and II—General Concepts
,”
ASME J. Appl. Mech.
0021-8936,
55
, pp.
59
72
.
37.
Lestriez
,
P.
, 2003, “
Modélisation numérique du couplage thermo-mécanique-endommagement en transformations finies. Application à la mise en forme
,” Ph.D. thesis, UTT, Troyes.
38.
Bogard
,
F.
,
Lestriez
,
P.
, and
Guo
,
Y. Q.
, 2008, “
Numerical Modeling of Fatigue Damage and Fissure Propagation
,”
Int. J. Damage Mech.
1056-7895,
17
, pp.
173
187
.
39.
Lim
,
J. Y.
,
Hong
,
S. G.
, and
Lee
,
S. B.
, 2005, “
Application of Local Stress-Strain Approaches in the Prediction of Fatigue Crack Initiation Life for Cyclically Non-Stabilized and NON-MASSING STEEL
,”
Int. J. Fatigue
0142-1123,
27
(
10–12
), pp.
1653
1660
.
40.
Wang
,
Y.
, and
Hadfield
,
M.
, 1999, “
Rolling Contact Fatigue Failure Modes of Lubricated Silicon Nitride in Relation to Ring Crack Defects
,”
Wear
0043-1648,
225–229
, pp.
1284
1292
.
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