The paper is devoted to formulation and analysis of a new model of structural fatigue that is a direct extension of the model of contact fatigue developed by Kudish (2000, STLE Tribol. Trans., 43, pp. 711–721). The model is different from other published models of structural fatigue (Collins, J. A., 1993, Failure of Materials and Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley, New York) in a number of aspects such as statistical approach to material defects, stress analysis, etc. The model is based on fracture mechanics and fatigue crack propagation. The model takes into account local stress distribution, initial statistical distribution of defects versus their size, crack location, and orientation, and material fatigue resistance parameters. The assumptions used for the new model derivation are stated clearly and their validity is discussed. The model considers the kinetics of crack distribution by taking into account the fact that the crack distribution varies with the number of applied loading cycles due to crack growth. A qualitative and quantitative parametric analysis of the model is performed. Some analytical formulas for fatigue life as a function of the initial defect distribution, material fatigue resistance, and stress state are obtained. Examples of application of the model to predicting fatigue of beam bending and torsion and contact fatigue for tapered bearings is presented.

1.
Bowles
,
C. Q.
, and
Schijve
,
J.
, 1973, “
The Role of Inclusions in Fatigue Crack Initiation in an Aluminum Alloy
,”
Int. J. Fract.
0376-9429,
9
, pp.
171
179
.
2.
Broek
,
D.
, 1986,
Elementary Fracture Mechanics
,
4th ed.
,
Martinus Nijhoff Publishers
, Boston, pp.
51
55
.
3.
Dudragne
,
G.
,
Fougeres
,
R.
, and
Theolier
,
M.
, 1981, “
Analysis Method for Both Internal Stresses and Microstructural Effect Under Pure Rolling Fatigue Conditions
,”
ASME J. Lubr. Technol.
0022-2305,
103
(
4
), pp.
521
525
.
4.
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
0142-1123,
11
(
5
), pp.
291
298
.
5.
Spektor
,
A. G.
,
Zelbet
,
B. M.
, and
Kiseleva
,
S. A.
, 1980,
Structure and Properties of Bearing Steels
,
“Metallurgia” Publishing
,
Moscow
, pp.
74
88
.
6.
Kudish
,
I. I.
, and
Burris
,
K. W.
, 2000, “
Modern State of Experimentation and Modeling in Contact Fatigue Phenomenon. Part I. Contact Fatigue Versus Normal and Tangential Contact and Residual Stresses. Nonmetallic Inclusions and Lubricant Contamination. Crack Initiation and Crack Propagation. Surface and Subsurface Cracks
,”
STLE Tribol. Trans.
1040-2004,
43
(
2
), pp.
187
196
.
7.
Bokman
,
M. A.
,
Pshenichnov
,
Yu. P.
, and
Pershtein
,
E. M.
, 1984, “
The Microcrack and Non-Metallic Inclusion Distribution in Alloy D16 After a Plastic Strain
,” Plant Laboratory, Moscow,
11
, pp.
71
74
.
8.
Wu
,
H. C.
, and
Yang
,
S. S.
, 1988, “
On the Influence of Strain-Path in Multiaxial Fatigue Failure
,”
ASME J. Eng. Mater. Technol.
0094-4289,
109
, pp.
107
113
.
9.
Nisitani
,
H.
, and
Goto
,
M.
, 1984, “
Effect of Stress Ratio on the Propagation of Small Crack of Plain Specimens Under High and Low Stress Amplitudes
,”
Trans. Jpn. Soc. Mech. Eng., Ser. A
0387-5008,
50
(
453
) pp.,
1090
1096
.
10.
Shao
,
E.
,
Huang
,
X.
,
Wang
,
C.
,
Zhu
,
Y.
, and
Cheng
,
Q.
, 1988, “
A Method of Detecting Rolling Contact Crack Initiation and the Establishment of Crack Propagation Curves
,”
STLE Tribol. Trans.
1040-2004,
31
(
1
), pp.
6
11
.
11.
Clarke
,
T. M.
,
Miller
,
G. R.
,
Keer
,
L. M.
, and
Cheng
,
H. S.
, 1985, “
The Role of Near-Surface Inclusions in the Pitting of Gears
,”
ASLE Trans.
0569-8197,
28
(
1
), pp.
111
116
.
12.
Nélias
,
D.
,
Dumont
,
M. L.
,
Champiot
,
F.
,
Vincent
,
A.
,
Girodin
,
D.
,
Fougéres
,
R.
, and
Flamand
,
L.
, 1999, “
Role of Inclusions, Surface Roughness and Operating Conditions on Rolling Contact Fatigue
,”
ASME J. Tribol.
0742-4787,
121
(
1
), pp.
240
251
.
13.
Murakami
,
Y.
, ed., 1987,
Stress Intensity Factors Handbook
, Vol.
1
,
Pergamon
,
Oxford, UK
, pp.
239
240
,
244
248
.
14.
Newman
,
J. C.
, Jr.
, 1971, “
An Improved Method of Collocation for the Stress Analysis of Cracked Plates With Various Shaped Boundaries
,” NASA TN D-6376, NASA, Washington, D.C., pp.
1
45
.
15.
Kudish
,
I. I.
, 2000, “
A New Statistical Model of Contact Fatigue
,”
STLE Tribol. Trans.
1040-2004,
43
(
4
), pp.
711
721
.
16.
Hasebe
,
N.
, and
Inohara
,
S.
, 1980, “
Stress Analysis of a Semi-Infinite Plate With an Oblique Edge Crack
,”
Ing.-Arch.
0020-1154,
49
, pp.
51
62
.
17.
Isida
,
M.
, 1979, “
Tension of a Half Plane Containing Array Cracks, Branched Cracks and Cracks Emanating From Sharp Notches
,”
Trans. Jpn. Soc. Mech. Eng., Ser. A
0387-5008,
45
(
392
), pp.
306
317
.
18.
Isida
,
M.
, 1966, “
Stress Intensity Factors for the Tension of an Eccentrically Cracked Strip
,”
ASME J. Appl. Mech.
0021-8936,
33
, pp.
674
675
.
19.
Kudish
,
I. I.
, 1987, “
Contact Problem of the Theory of Elasticity for Pre-stressed Bodies with Cracks
,”
J. Appl. Mech. Tech. Phys.
0021-8944,
28
(
2
), pp.
295
303
.
20.
Tallian
,
T.
,
Hoeprich
,
M.
, and
Kudish
,
I. I.
, 2001, “
Author’s Closure
,”
STLE Tribol. Trans.
1040-2004,
44
(
2
), pp.
153
155
.
21.
Yarema
,
S. Ya.
, 1981, “
Determining the Characteristics of the Resistance to Crack Development (Crack Resistance) of Materials in Cyclic Loading
,”
Sov. Mater. Sci.
,
17
(
4
), pp.
371
380
.
22.
Shimizu
,
S.
, 2000, “
P-S-N Curves Model for Rolling Contact Machine Elements
,”
Proceedings of the Intern. Tribol. Conf.
,
Nagasaki
,
3
, pp.
1767
1772
.
23.
Shimizu
,
S.
, 2002, “
Fatigue Limit Concept in Life Prediction Model for Rolling Contact Machine Elements
,”
STLE Tribol. Trans.
1040-2004,
45
(
1
), pp.
39
46
.
24.
Kudish
,
I. I.
, and
Burris
,
K. W.
, 2000, “
Modern State of Experimentation and Modeling in Contact Fatigue Phenomenon. Part II. Analysis of the Existing Statistical Mathematical Models of Bearing and Gear Fatigue Life. New Statistical Model of Contact Fatigue
,”
STLE Tribol. Trans.
1040-2004,
43
(
2
), pp.
293
301
.
25.
Romaniv
,
O. N.
,
Yarema
,
S. Ya.
,
Nikiforchin
,
G. N.
,
Makhutov
,
N. A.
, and
Stadnik
,
M. M.
, 1990, “
Fracture Mechanics and Strength of Materials
,”
Fatigue and Cyclic Crack Resistance of Construction Materials
Vol.
4
,
Naukova Dumka
,
Kiev, USSR
, pp.
354
358
.
26.
Lurye
,
A. I.
, 1970,
Theory of Elasticity
,
Nauka
,
Moscow, USSR
.
27.
Kudish
,
I. I.
, and
Burris
,
K. W.
, 2004, “
Modeling of Surface and Subsurface Crack Behavior Under Contact Load in the Presence of Lubricant
,”
Int. J. Fract.
0376-9429,
125
(
1–2
), pp.
125
147
.
28.
Kudish
,
I. I.
, 2002, “
Lubricant-Crack Interaction, Origin of Pitting, and Fatigue of Drivers and Followers
,”
STLE Tribol. Trans.
1040-2004,
45
(
4
), pp.
583
594
.
29.
Stover
,
J. D.
, and
Kolarik
,
R. V.
, II
, 1987, “
The Evaluation of Improvements in Bearing Steel Quality Using an Ultrasonic Macro-Inclusion Detection Method
,” The Timken Company Technical Note, January, pp.
1
12
.
30.
Stover
,
J. D.
,
Kolarik
,
R. V.
, II
, and
Keener
,
D. M.
, 1990, “
The Detection of Aluminum Oxide Stringers in Steel Using an Ultrasonic Measuring Method
,”
Proceedings of the 31st Mech. Working and Steel Proc. Conference
, Chicago, October 22–25,
Iron and Steel Soc., Inc.
, pp.
431
440
.
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