Abstract

This paper provides a brief summary of life prediction methods for variable amplitude fatigue. Special attention is given to cracks propagating from nominally defect free components in the high cycle regime where a significant portion of the fatigue damage can be attributed to cycles with amplitude less than the fatigue limit observed under constant amplitude loading. Constant and variable amplitude fatigue data for a nodular cast iron are presented. An effective stress method for variable amplitude loaded similar to the Topper model is developed. Most model parameters are derived from constant amplitude S-N curves and the Haigh diagram, but two sets of long life variable amplitude tests are needed to derive the variable amplitude interaction parameters.

References

1.
Schjive
,
J.
Fatigue of Structures and Materials
,
Kluwer Academic Publishers
,
Dordrecht
,
2001
.
2.
Sehitoglu
,
H.
,
Gall
,
K.
, and
Garcia
,
A. M.
, “
Recent Advances in Fatigue Crack Growth Modeling
,”
International Journal of Fracture
, Vol.
80
,
1996
, pp.
165
-
192
.
3.
Lawson
,
L.
,
Chen
,
E. Y.
, and
Meshii
,
M.
, “
Near-Threshold Fatigue: A Review
,”
International Journal of Fatigue
 0142-1123, Vol.
21
,
1999
, pp.
15
-
34
.
4.
Geary
,
W.
, “
A Review of Some Aspects of Fatigue Crack Growth Under Variable Amplitude Loading
,”
International Journal of Fatigue
 0142-1123, Vol.
14
,
1992
, pp.
377
-
386
.
5.
Kumar
,
R.
, “
A Review on Crack Closure for Single Overload, Programmed and Block Loadings
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
42
,
1992
, pp.
151
-
158
.
6.
Forman
,
R. G.
,
Kearny
,
V. E.
, and
Engle
,
R. M.
, “
Numerical Analysis of Crack Propagation in a Cyclic-Loaded Structure
,”
Transactions of the ASME Journal of Basic Engineering
, Vol.
D89
,
1967
, pp.
458
-
464
.
7.
Walker
,
K.
, “
The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T6 Aluminum
,” In:
Effects of Environment and Complex Load History on Fatigue Life
, ASTM STP 462,
ASTM International
,
West Conshohocken, PA
,
1970
.
8.
Barsom
,
J. M.
and
Rolfe
,
S. T.
,
Fracture Control in Structures
,
Prentice-Hall
,
Englewood Cliffs, NJ
,
1977
.
9.
Lal
,
D. N.
, “
The Combined Effects of Stress Ratio and Yield Strength on the LEFM Fatigue Threshold Condition
,”
Fatigue and Fracture of Engineering Materials and Structures
, Vol.
15
,
1992
, pp.
1199
-
1212
.
10.
Wheeler
,
O. E.
, “
Spectrum Loading and Crack Growth
,”
Journal of Basic Engineering
 0021-9223, Vol.
94
,
1972
, pp.
181
-
186
.
11.
Willenborg
,
J.
,
Engle
,
R. M.
, and
Wood
,
H. A.
, “
A Crack Growth Retardation Model Using an Effective Stress Concept
,” AFFDL-TR71-1,
Air Force Flight Dynamic Laboratory, Wright-Patterson Air Force Base
,
OH
,
1971
.
12.
Elber
,
W.
, “
Fatigue Crack Closure Under Cyclic Tension
,”
Engineering Fracture Mechanics
 0013-7944 https://doi.org/10.1016/0013-7944(70)90028-7, Vol.
2
,
1970
, pp.
37
-
45
.
13.
Elber
,
W.
, “
The Significance of Fatigue Crack Closure
,” In:
Damage Tolerant Aircraft Structures
, ASTM STP 486,
ASTM International
,
West Conshohocken, PA
,
1971
, pp.
230
-
242
.
14.
Sadananda
,
K.
,
Vasudevan
,
A. K.
,
Holtz
,
R. L.
, and
Lee
,
E. U.
, “
Analysis of Overload Effects and Related Phenomena
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/S0142-1123(99)00094-8, Vol.
21
,
1999
, pp.
S233
-
S246
.
15.
Sehitoglu
,
H.
and
Sun
,
W.
, “
Modeling of Plane Strain Fatigue Crack Closure
,”
ASME Journal of Engineering Materials and Technology
 0094-4289, Vol.
113
,
1990
, pp.
31
-
40
.
16.
Baudin
,
G.
and
Robert
,
M.
, “
Crack Growth Life Prediction Under Aeronautical Type Loading
,” ECF 5,
Lisbon
,
1984
, pp.
779
-
792
.
17.
de Koning
,
A. U.
, “
A Simple Closure Model for Prediction of Fatigue Crack Growth Rates Under Variable-Amplitude Loading
,” In:
Fracture Mechanics
, ASTM STP 743,
R.
Roberts
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1981
, pp.
63
-
85
.
18.
Topper
,
T. H.
and
Yu
,
M. T.
, “
The Effect of Overloads on Threshold and Crack Closure
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/0142-1123(85)90027-1, Vol.
7
,
1985
, pp.
159
-
164
.
19.
Führing
,
H.
and
Seeger
,
T.
, “
Structural Memory of Cracked Components Under Irregular Loading
,” In:
Fracture Mechanics
, ASTM STP 677,
C. W.
Smith
, Ed.,
ASTM International
,
West Conshohocken, PA
,
1979
, pp.
144
-
167
.
20.
Newman
,
J. C.
 Jr.
, “
A Crack-Closure Model for Predicting Fatigue Crack Growth Under Aircraft Spectrum Loading
,” In:
Methods and Models for Predicting Fatigue Crack Growth Under Random Loading
, ASTM STP 748,
J. B.
Chang
and
C. M.
Hudson
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1981
, pp.
53
-
84
.
21.
Wang
,
G. S.
and
Blom
,
A. F.
, “
A Strip Model for Fatigue Crack Growth Prediction Under General Load Conditions
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
40
,
1991
, pp.
507
-
533
.
22.
Dugdale
,
D. S.
, “
Yielding of Steel Sheets Containing Slits
,”
Journal of Mechanics and Physics of Solids
 0022-5096 https://doi.org/10.1016/0022-5096(60)90013-2, Vol.
8
,
1960
, pp.
100
-
104
.
23.
Pompetzki
,
M. A.
,
Topper
,
T. H.
, and
DuQuesnay
,
D. L.
, “
The Effect of Compressive Underloads and Tensile Overloads on Fatigue Damage Accumulation in SAE 1045 Steel
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/0142-1123(90)90097-X, Vol.
12
,
1990
, pp.
207
-
213
.
24.
Jurcevic
,
R.
,
DuQuesnay
,
D. L.
,
Topper
,
T. H.
, and
Pompetzki
,
M. A.
, “
Fatigue Damage Accumulation in 2024-T351 Aluminium Subjected to Periodic Reversed Overloads
,”
International Journal of Fatigue
 0142-1123, Vol.
12
,
1990
, pp.
259
-
266
.
25.
Conle
,
A.
and
Topper
,
T. H.
, “
Evaluation of Small Cycle Omission Criteria for Shortening of Fatigue Service Histories
,”
International Journal of Fatigue
 0142-1123, Vol.
1
,
1979
, pp.
23
-
28
.
26.
Conle
,
A.
and
Topper
,
T. H.
, “
Overstrain Effects During Variable Amplitude Service History Testing
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/0142-1123(80)90015-8, Vol.
2
,
1980
, pp.
130
-
136
.
27.
DuQuesnay
,
D. L.
,
Topper
,
T. H.
,
Yu.
M. T.
, and
Pompetzki
,
M. A.
, “
The Effective Stress Range as a Mean Stress Parameter
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/0142-1123(92)90153-4, Vol.
14
,
1992
, pp.
45
-
50
.
28.
Varvani-Farahani
,
A.
and
Topper
,
T. H.
, “
Increases in Fatigue Crack Growth Rate and Reductions in Fatigue Strength Due to Periodic Overstrains in Biaxial Fatigue Loading
,” In:
Fatigue Crack Growth Thresholds, Endurance Limits, and Design
, ASTM STP 1372,
J. C.
Newman
, Jr.
, and
R. S.
Piascik
, Eds.,
ASTM International
,
West Conshohocken, PA
,
2000
, pp.
192
-
206
.
29.
MacDougall
,
C.
and
Topper
,
T. H.
, “
The Influence of Variable Amplitude Loading on Crack Closure and Notch Fatigue Behaviour
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/S0142-1123(96)00076-X, Vol.
19
,
1997
, pp.
389
-
400
.
30.
Bonnen
,
J. J. F.
and
Topper
,
T. H.
, “
The Effect of Bending Overloads on Torsional Fatigue in Normalized 1045 Steel
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/S0142-1123(98)00054-1, Vol.
21
,
1999
, pp.
23
-
33
.
31.
Lam
,
T. S.
,
Topper
,
T. H.
, and
Conle
,
F. A.
, “
Derivation of Crack Closure and Crack Growth Rate From Effective-Strain Fatigue Life Data for Fracture Mechanics Fatigue Life Predictions
,”
International Journal of Fatigue
 0142-1123, Vol.
20
,
1998
, pp.
703
-
710
.
32.
Haibach
,
E.
, “
The Allowable Stresses Under Variable Amplitude Loading
,” In:
Proceedings of the Conference on Fatigue of Welded Structures
, Vol.
2
.
Abington, Cambridge
,
The Welding Institute
.
1971
, pp.
328
-
339
.
33.
Gassner
,
E.
and
Lipp
,
W.
, “
Long Life Random Fatigue Behavior of Notched Specimens in Service, in Service Duplication Tests, and in Program Tests
,” In:
Service Fatigue Loads Monitoring, Simulation and Analysis
, ASTM STP 671,
P. R.
Abelkis
and
J. M.
Potter
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1979
, pp.
222
-
239
.
34.
Schütz
,
W.
and
Heuler
,
P.
, “
Miner's Rule Revisited
,” 77,
AGARD-SMP Meeting, Bordeaux
, 27 September-1 October 1993,
Ottobrunn
,
Industrieanlagen-Betriebsgesellshaft GmbH
.
35.
Zenner
,
H.
and
Liu
,
J.
, “
Vorschlag zur Verbesserung der Lebensdauerabschätzung nach dem Nennspannung. Konstruction
,” Vol.
1
,
1992
, pp.
9
-
17
.
36.
Tokaji
,
K.
and
Ando
,
Z.
, “
Small Fatigue Crack Growth Behaviour Under Two Stress Level Multiple Loading
,”
Fatigue and Fracture of Engineering Materials and Structures
, Vol.
7
,
1984
, pp.
109
-
119
.
37.
Yan
,
X.
,
Cordes
,
T. S.
,
Vogel
,
J. H.
, and
Dindinger
,
P. M.
, “
A Property Fitting Approach for Improved Estimates of Small Cycle Fatigue Damage
,”
SAE Transactions Journal of Materials and Manufacturing
, Vol.
101
,
1992
, pp.
544
-
553
.
38.
Stanzl-Tschegg
,
S. E.
,
Mayer
,
H. R.
,
Beste
,
A.
, and
Kroll
,
S.
, “
Fatigue and Fatigue Crack Propagation in AlSi7Mg Cast Alloys Under In-Service Loading Conditions
,”
International Journal of Fatigue
 0142-1123, Vol.
17
,
1995
, pp.
149
-
155
.
39.
Vormwald
,
M.
and
Seeger
,
T.
, “
The Consequences of Short Crack Closure on Fatigue Crack Growth Under Variable Amplitude Loading
,”
Fatigue and Fracture of Engineering Materials and Structures
, Vol.
14
,
1991
, pp.
205
-
225
.
40.
Zhou
,
Z.
and
Zwerneman
,
F. J.
, “
Fatigue Damage Due to Sub-Threshold Load Cycles Between Periodic Overloads
,” In:
Advances in Fatigue Lifetime Predictive Techniques: Second Volume
, ASTM STP 1211,
M. R.
Mitchell
and
R. W.
Landgraf
, Eds.,
ASTM International
,
West Conshohocken, Pa
,
1993
, pp.
45
-
53
.
41.
Hénaff
,
G.
,
Petit
,
J.
, and
Journet
,
B.
, “
Fatigue Crack Propagation Behaviour Under Variable Amplitude Loading in the Near-Threshold Region of a High-Strength Low-Alloy Steel
,”
Fatigue and Fracture of Engineering Materials and Structures
, Vol.
15
,
1992
, pp.
1155
-
1170
.
42.
Kikukawa
,
M.
,
Jono
,
M.
, and
Kondo
,
Y.
, “
An Estimation Method of Fatigue Crack Propagation Rate Under Varying Loading Conditions of Low Stress Intensity Level
,”
Advances in Fracture Research (Fracture '81)
,
Pergamon Press
,
Oxford
,
1982
, pp.
1799
-
1806
.
43.
Koterazawa
,
R.
, “
Fatigue Crack Propagation Under Periodic Overstressing
,”
International Journal of Fracture
, Vol.
12
,
1976
, pp.
169
-
170
.
44.
Koterazawa
,
R.
,
Mudjijana
,
Y.
,
Qinsheng
,
W.
,
Tian-Jian
,
W.
, and
Nosho
,
T.
, “
Acceleration of Fatigue Crack Growth Under Intermittent Overstressing with Different Mean Stress Levels
,”
Fatigue and Fracture of Engineering Materials and Structures
, Vol.
17
,
1994
, pp.
1033
-
1041
.
45.
Sunder
,
R.
, “
Contribution of Individual Spectrum Load Cycles to Damage in Notch Root Crack Initiation, Short and Long Crack Growth
,” In:
Advances in Fatigue Lifetime Predictive Techniques: Second Volume
, ASTM STP 1211,
M. R.
Mitchell
and
R. W.
Landgraf
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1993
, pp.
19
-
29
.
46.
Sunder
,
R.
,
Prakash
,
R. V.
, and
Mitchenko
,
E. I.
, “
Calculation of Spectrum Load Notch Root Crack Growth Rate Under Elastic and Inelastic Conditions
,” In:
Advances in Fatigue Lifetime Predictive Techniques: Second Volume
, ASTM STP 1211,
M. R.
Mitchell
and
R. W.
Landgraf
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1993
, pp.
30
-
44
.
47.
Sunder
,
R.
, “
Near-Threshold Fatigue Crack Growth Prediction Under Spectrum Loading
,” In:
Advances in Fatigue Lifetime Predictive Techniques: Second Volume
, ASTM STP 1122,
M. R.
Mitchell
and
R. W.
Landgraf
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1992
, pp.
161
-
175
.
48.
Marquis
,
G.
,
High Cycle Spectrum Fatigue of Welded Components
, VTT Publications 240,
Technical Research Centre of Finland
,
Espoo, Finland
,
1995
.
49.
Ohta
,
A.
,
Maeda
,
Y.
,
Machida
,
S.
, and
Yoshinari
,
H.
, “
Near Threshold Fatigue Crack Growth in Welded Joints Under Random Loadings
,”
Transactions of the Japan Welding Society
 0385-9282,
19
,
1988
, pp.
69
-
73
.
50.
Palmgren
,
A
, “
Die Ledensdauer von Kugellagern
,”
Verfahrenstechinik
,
Berlin
,
1924
, Vol.
68
,
339
-
341
.
51.
Miner
,
M. A.
, “
Cumulative Damage in Fatigue
,”
ASME Journal of Applied Mechanics
 0021-8936, Vol.
12
,
1945
, pp.
A159
-
164
.
52.
Fatemi
,
A.
and
Yang
,
L.
, “
Cumulative Fatigue Damage and Life Prediction Theories: A Survey of the State of the Art for Homogeneous Materials
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/S0142-1123(97)00081-9, Vol.
20
,
1998
, pp.
9
-
34
.
53.
McClung
,
R. C.
and
Sehitoglu
,
H.
, “
Closure Behavior of Small Cracks Under High Strain Fatigue Histories
,” In:
Mechanics of Fatigue Crack Closure
, ASTM STP 982,
ASTM International
,
West Conshohocken, PA
,
1988
, pp.
279
-
299
.
54.
Marquis
,
G.
and
Karjalainen-Roikonen
,
P.
, “
Long-Life Multiaxial Fatigue of SG Cast Iron
,”
Proceedings of the Sixth International Conference on Biaxial/Multiaxial Fatigue and Fracture
,
M. M.
de Freitas
, Ed.,
2001
, pp.
151
-
159
.
55.
Marquis
,
G.
, “
Mean Stress in Long-Life Torsion Fatigue
,” In:
Proceeding of ECF 13
,
San Sebastian, Spain
, Paper 3m.314,
2000
.
56.
Marquis
,
G.
and
Solin
,
J.
,
Long-Life Fatigue Design of GRP 500 Nodular Cast Iron Components
, VTT Research Notes 2043,
Technical Research Centre of Finland
,
Espoo
,
2000
, p. 70.
57.
Marquis
,
G.
and
Murakami
,
Y.
, “
Scatter in the Fatigue Limit of Nodular Iron
,”
Materials Science Research International, Special Technical Publication
,
T.
Hoshide
, Ed.,
Kyoto
,
2001
, pp.
92
-
96
.
58.
Marquis
,
G.
,
Rabb
,
R.
, and
Siivonen
,
L.
, “
Endurance Limit Design of Spheroidal Graphite Cast Iron Components Based on Natural Defects
,”
Fatigue Crack Growth Thresholds, Endurance Limits, and Design
, ASTM STP 1372,
J. C.
Newman
and
R. S.
Piascik
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1999
, pp.
411
-
426
.
59.
Clement
,
P.
,
Angeli
,
J. P.
, and
Pineau
,
A.
, “
Short Crack Behaviour in Nodular Cast Iron
,”
Fatigue and Fracture of Engineering Materials and Structures
, Vol.
7
,
1984
, pp.
251
-
265
.
60.
Tokaji
,
K.
,
Ogawa
,
T.
, and
Shamoto
,
K.
, “
Fatigue Crack Propagation in Sheroidal-Graphite Cast Irons with Different Microstructures
,”
International Journal of Fatigue
 0142-1123 https://doi.org/10.1016/0142-1123(94)90273-9, Vol.
16
,
1994
, pp.
344
-
350
.
61.
Yaacoub Agha
,
H.
,
Béranger
,
A.-S.
,
Billardon
,
R.
, and
Hild
,
F.
, “
High-Cycle Fatigue Behaviour of Spheroidal Graphite Cast Iron
,”
Fatigue and Fracture of Engineering Materials and Structures
, Vol.
21
,
1998
, pp.
287
-
296
.
62.
Nadot
,
Y.
,
Ranganathan
,
N.
,
Mendez
,
J.
, and
Béranger
,
A.-S.
, “
A Study of Natural Cracks Initiated on Casting Defects by Crack Front Marking
,”
Scripta Materialica
, Vol.
37
,
1997
, pp.
549
-
553
.
63.
Palin-Luc
,
T.
,
Lasserre
,
S.
,
Froustey
,
C.
and
Bérard
,
J. Y.
, “
Experimental Approach of Damage Accumulation in High Cycle Fatigue with Random Loadings in Blocks
,” In:
Mechanisms and Mechanics of Damage and Failure: ECF11
,
J.
Petit
, Ed.,
EMAS
,
UK
,
1996
, pp.
1337
-
1342
.
64.
Nadot
,
Y.
,
Ranganathan
,
N.
,
Mendez
,
J.
, and
Béranger
,
A.-S.
, “
Fatigue Damage in Spheroidal Graphite Cast Iron (SGI)
,” In:
Mechanisms and Mechanics of Damage and Failure: ECF11
,
J.
Petit
, Ed.,
EMAS
,
UK
,
1996
, pp.
1155
-
1160
.
65.
Schleicher
,
M.
,
Bomas
,
H.
, and
Mayr
,
P.
, “
Fatigue Surface Cracks in Cast Iron with Nodular Graphite
,” In:
Fracture from Defects: ECF 12
,
M. W.
Brown
,
E. R.
de los Rios
, and
K. J.
Miller
, Eds.,
EMAS
,
UK
,
1998
, pp.
91
-
96
.
66.
Nadot
,
Y.
,
Ranganathan
,
N.
,
Mendez
,
J.
, and
Béranger
,
A.-S.
, “
Fatigue Limit of Nodular Cast Iron Containing Casting Defects
,” In:
Fracture from Defects: ECF 12
,
M. W.
Brown
,
E. R.
de los Rios
, and
K. J.
Miller
, Eds.,
EMAS
,
UK
,
1998
, pp.
85
-
90
.
67.
Greno
,
G. L.
,
Otegui
,
J. L.
, and
Boeri
,
R. E.
, “
Mechanisms of Fatigue Crack Growth in Austempered Ductile Iron
,”
International Journal of Fatigue
 0142-1123, Vol.
21
,
1999
, pp.
35
-
43
.
68.
Lin
,
C.-K.
and
Lee
,
W.-J.
, “
Effects of Highly Stressed Volume on Fatigue Strength of Austempered Ductile Irons
,”
International Journal of Fatigue
 0142-1123, Vol.
20
,
1998
, pp.
301
-
307
.
69.
Rabb
,
B. R.
,
Fatigue Testing and Its Statistical Evaluation into Design Rules
, Ph.D. thesis,
Tampere University of Technology
, Publication 253, Tampere,
1999
.
70.
Newman
,
J. C.
, Jr.
A Crack Opening Stress Equation for Fatigue Crack Growth
,”
International Journal of Fracture
, Vol.
24
,
1984
,
R131
-
R135
.
71.
Sehitoglu
,
H.
, “
Crack Opening and Closure in Fatigue
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
21
,
1985
, pp.
329
-
339
.
72.
Fukuoka
,
C.
and
Nakagawa
,
Y. G.
, “
Microstructural Evaluation of Cumulative Fatigue Damage Below the Fatigue Limit
,”
Scripta Materialica
, Vol.
34
,
1996
, pp.
1497
-
1502
.
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