Rolling contact fatigue of rolling element bearings is a statistical phenomenon that is strongly affected by the heterogeneous nature of the material microstructure. Heterogeneity in the microstructure is accompanied by randomly distributed weak points in the material that lead to scatter in the fatigue lives of an otherwise identical lot of rolling element bearings. Many life models for rolling contact fatigue are empirical and rely upon correlation with fatigue test data to characterize the dispersion of fatigue lives. Recently developed computational models of rolling contact fatigue bypass this requirement by explicitly considering the microstructure as a source of the variability. This work utilizes a similar approach but extends the analysis into a 3D framework. The bearing steel microstructure is modeled as randomly generated Voronoi tessellations wherein each cell represents a material grain and the boundaries between them constitute the weak planes in the material. Fatigue cracks initiate on the weak planes where oscillating shear stresses are the strongest. Finite element analysis is performed to determine the magnitude of the critical shear stress range and the depth where it occurs. These quantities exhibit random variation due to the microstructure topology which in turn results in scatter in the predicted fatigue lives. The model is used to assess the influence of (1) topological randomness in the microstructure, (2) heterogeneity in the distribution of material properties, and (3) the presence of inherent material flaws on relative fatigue lives. Neither topological randomness nor heterogeneous material properties alone account for the dispersion seen in actual bearing fatigue tests. However, a combination of both or the consideration of material flaws brings the model’s predictions within empirically observed bounds. Examination of the critical shear stress ranges with respect to the grain boundaries where they occur reveals the orientation of weak planes most prone to failure in a three-dimensional sense that was not possible with previous models.

References

References
1.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
, 2007,
Rolling Bearing Analysis
,
5th ed.
Essential Concepts of Bearing Technology,
CRC Press
,
Boca Raton, FL
.
2.
Littmann
,
W. E.
and
Widner
,
R. L.
, 1966, “
Propagation of Contact Fatigue From Surface and Sub-Surface Origins
,”
ASME J. Basic Eng.
,
88
, pp.
624
636
.
3.
Littmann
,
W. E.
, 1969, “
The Mechanism of Contact Fatigue
,”
NASA Spec. Rep. No. SP-237.
4.
Tallian
,
T. E.
, 1999,
Failure Atlas for Hertz Contact Machine Elements
,
ASME Press
,
New York, NY
, pp.
179
231
.
5.
Murakami
,
Y.
,
Kodama
,
S.
, and
Konuma
,
S.
, 1989, “
Quantitative Evaluation of Effects of Non-Metallic Inclusions on Fatigue Strength of High Strength Steels. I: Basic Fatigue Mechanism and Evaluation of Correlation Between the Fatigue Fracture Stress and the Size and Location of Non-Metallic Inclusions
,”
Int. J. Fatigue
,
11
(
5
), pp.
291
298
.
6.
Nishioka
,
K.
, 1957, “
On the Effect of Inclusion Upon the Fatigue Strength
,”
J.Soc. Mater. Sci. Jpn.
,
6
, pp.
382
385
.
7.
Tsushima
,
N.
,
Nakashima
,
H.
, and
Maeda
,
K.
, 1993, “
Comparison in Rolling Contact Fatigue Life Between Recent Clean Through-Hardening Steels and Carburizing Steels
,”
Creative Use of Bearing Steels
, ASTM STP 1195,
J. J. C.
Hoo
, Ed.,
ASTM
,
Philadelphia, PA
, pp.
5
20
.
8.
Ringsberg
,
J. W.
, and
Bergkvist
,
A.
, 2003, “
On Propagation of Short Rolling Contact Fatigue Cracks
,”
Fatigue Fract. Eng. Mater. Struct.
,
26
, pp.
969
983
.
9.
Lundberg
,
G.
, and
Palmgren
,
A.
, 1947, “
Dynamic Capacity of Rolling Element Bearings,”
Acta Polytech. Scand., Mech. Eng. Ser.
,
1
(
3
), pp.
1
50
.
10.
Lundberg
,
G.
, and
Palmgren
,
A.
, 1952, “
Dynamic Capacity of Roller Bearings,”
Acta Polytech. Scand., Mech. Eng. Ser.
,
2
(
3
), pp.
1
32
.
11.
Weibull
,
W.
, 1939a, “
A Statistical Theory of the Strength of Materials,” Ingeniors Vetenkaps Akademien
,
Proceedings of the Royal Swedish Academy of Engineering
, No. 151, pp.
1
53
.
12.
Weibull
,
W.
, 1939b, “
On the Phenomenon of Rupture in Solids,” Ingeniors Vetenkaps Akademien,
Proceedings of the Royal Swedish Academy of Engineering
, No. 153, pp.
1
55
.
13.
Sadeghi
,
F.
,
Jalalahmadi
,
B.
,
Slack
,
T.
,
Raje
,
N.
, and
Arakere
,
N. K.
, 2009, “
A Review of Rolling Contact Fatigue
,”
ASME J. Tribol.
,
131
, p.
041403
.
14.
Jalalahmadi
,
B.
, and
Sadeghi
,
F.
, 2009, “
A Voronoi Finite Element Study of Fatigue Life Scatter in Rolling Contacts
,”
ASME J. Tribol.
,
131
, p.
022203
.
15.
Raje
,
N.
,
Sadeghi
,
F.
, and
Rateick
, Jr.,
R. G.
, 2007, “
A Discrete Element Approach to Evaluate Stresses Due to Line Loading on an Elastic Half-Space
,”
Comput. Mech.
,
40
, pp.
513
529
.
16.
Raje
,
N.
,
Sadeghi
,
F.
, and
Rateick
, Jr.,
R. G.
, 2008, “
A Statistical Damage Mechanics Model for Subsurface Initiated Spalling in Rolling Contacts
,”
ASME J. Tribol.
,
130
, p.
042201
.
17.
Raje
,
N.
,
Sadeghi
,
F.
,
Rateick
, Jr.,
R. G.
, and
Hoeprich
,
M. R.
, 2008, “
A Numerical Model for Life Scatter in Rolling Element Bearings
,”
ASME J. Tribol.
,
130
, p.
011011
.
18.
Slack
,
T.
, and
Sadeghi
,
F.
, 2010, “
Explicit Finite Element Modeling of Subsurface Initiated Spalling in Rolling Contacts
,”
Tribol. Int.
,
43
, pp.
1693
1702
.
19.
Weinzapfel
,
N.
,
Sadeghi
,
F.
,
Bakolas
,
V.
, 2010, “
An Approach for Modeling Material Grain Structure in Investigations of Hertzian Subsurface Stresses and Rolling Contact Fatigue
,”
ASME J. Tribol.
,
132
(
4
), p.
041404
.
20.
Dassault Systèmes, 2009, Abaqus 6.9 Documentation,
Dassault Systèmes Simulia Corp
, Providence, RI, USA. http://abaqusdocs.ecn.purdue.edu:2080/v6.9/http://abaqusdocs.ecn.purdue.edu:2080/v6.9/
21.
Mücklich
,
F.
,
Osher
,
J.
, and
Schneider
,
G.
, 1997, “
Die Charakterisierung Homogener Polyedrischer Gefüge mit Hilfe des Räumlichen Poisson-Voronoi-Mosaiks und der Vergleich zur DIN 50 601 (The Characterization of Homogeneous Polyhedral Microstructures Applying the Spatial Poisson-Voronoi Tessellation Compared to the Standard DIN 50 601)
,”
Z. für Metal.
,
88
(
1
), pp.
27
32
.
22.
Okabe
,
A.
,
Boots
,
B.
,
Sugihara
,
K.
, and
Chiu
,
S. N.
, 2000,
Spatial Tessellations: Concepts and Applications of Voronoi Diagrams
,
2nd ed.
,
John Wiley & Sons
,
West Sussex, England
.
23.
Callister
, Jr.,
W. D.
, 2000,
Material Science and Engineering: An Introduction
,
5th ed.
,
John Wiley & Sons
,
New York
, pp.
51
52
.
24.
MathWorks, Inc., 2009, matlab 7.8.0.
25.
Taraf
,
M.
,
Zahaf
,
E. H.
,
Oussouaddi
,
O.
,
Zeghloul
,
A.
, 2010, “
Numerical Analysis for Predicting the Rolling Contact Fatigue Crack Initiation in a Railway Wheel Steel
,”
Tribol. Int.
,
43
, pp.
585
593
.
26.
S˘raml
,
M.
,
Flaîsker
,
J.
, and
Potre˘
,
I.
, 2003, “
Numerical Procedure for Predicting the Rolling Contact Fatigue Crack Initiation
,”
Int. J. Fatigue
,
25
, pp.
585
595
.
27.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University
,
Cambridge, UK
, p.
95
.
28.
Chen
,
L.
,
Chen
,
Q.
, and
Shao
,
E.
, 1989, “
Study on Initiation and Propagation Angles of Sub-Surface Cracks in GCr15 Bearing Steel Under Rolling Contact
,”
Wear
,
133
, pp.
205
213
.
29.
Chen
,
L.
,
Shao
,
E.
,
Zhao
,
D.
,
Guo
,
J.
, and
Fan
,
Z.
, 1991, “
Measurement of the Critical Size of Inclusions Initiating Contact Fatigue Cracks and Its Application in Bearing Steel
,”
Wear
,
147
, pp.
285
294
.
30.
Zaretsky
,
E. V.
,
Parker
,
R. J.
, and
Anderson
,
W. J.
, 1969, “
A Study of Residual Stress Induced During Rolling
,”
ASME J.Lubr. Technol.
,
91
, pp.
314
319
.
31.
Lemaitre
,
J.
, and
Chaboche
,
J. L.
, 1990,
Mechanics of Solid Materials
,
Cambridge University Press
,
Cambridge, UK
.
You do not currently have access to this content.