Abstract

This investigation examines the variation of the fatigue notch factor with notch size for sharp and blunt notches. Analytical expressions are developed to predict the fatigue notch factor for sharp notches based on short crack fracture mechanics and for blunt notches based on Neuber's rule. Experimental evidence to support these expressions is provided together with fatigue notch factors for circularly center-notched plate specimens of 2024-T351 aluminum and SAE 1045 steel. The notch diameters were varied from 0.24 to 5.0 mm. The specimens were tested in laboratory air under uniaxial constant-amplitude loading at load ratios of R = −1 and R = 0. Further experimental evidence to support the analysis is provided by data from the literature for two low carbon steels and a copper. At the fatigue limit, the fatigue notch factor increases with notch size for sharp notches. However, a notch-size effect does not occur for blunt notches. The observed notch-size effects from this and other investigations are in good agreement with the analytical expressions that are presented.

References

1.
Fenner
,
A. J.
,
Owen
,
N. B.
, and
Phillips
,
C. E.
, “
The Fatigue Crack as a Stress Raiser
,”
Engineering
, Vol.
171
,
1951
, pp.
637
-
638
.
2.
Frost
,
N. E.
, “
Crack Formation and Stress Concentration Effects in Direct Stress Fatigue
,”
The Engineer
, Vol.
200
,
1955
, pp.
464
-
467
and 501–503.
3.
Frost
,
N. E.
, “
Non-Propagating Cracks in Vee-Notched Specimens Subject to Fatigue Loading
,”
The Aeronautical Quarterly
 0001-9259, Vol.
8
,
1957
, pp.
1
-
20
.
4.
Frost
,
N. E.
, “
Studies in the Formation and Propagation of Cracks in Fatigue Speciment
,” in
Proceedings
,
Int. Conf. on Fatigue of Metals
,
Instn. of Mech. Engrs.
,
1956
, Session 6, Paper 2.
5.
Frost
,
N. E.
, “
A Relation Between the Critical Alternating Propagation Stress and Crack Length for Mild Steel
,” in
Proceedings
,
Instn. Mech. Engrs.
, Vol.
173
, No.
35
,
1959
, pp.
811
-
827
.
6.
Frost
,
N. E.
, “
Notch Effects and the Critical Alternating Stress Required to Propagate a Crack in an Aluminum Alloy Subject to Fatigue Loading
,”
Journal of Mechanical Engineering Science
 0022-2542, Vol.
2
, No.
2
,
1960
, pp.
109
-
119
.
7.
Frost
,
N. E.
,
Pook
,
L. P.
, and
Denton
,
K.
, “
A Fracture Mechanics Analysis of Fatigue Crack Growth Data for Various Metals
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
3
,
1971
, pp.
109
-
126
.
8.
Smith
,
R. A.
and
Miller
,
K. J.
, “
Fatigue Cracks at Notches
,”
Journal of Mechanical Engineering Science
 0022-2542, Vol.
19
,
1977
, pp.
11
-
22
.
9.
Smith
,
R. A.
and
Miller
,
K. J.
, “
Prediction of Fatigue Regimes in Notched Components
,”
Journal of Mechanical Engineering Science
 0022-2542, Vol.
20
,
1977
, pp.
201
-
206
.
10.
Hammouda
,
M. M.
,
Smith
,
R. A.
, and
Miller
,
K. J.
,
Fatigue of Engineering Materials and Structures
, Vol.
2
,
1979
, pp.
139
-
154
.
11.
Topper
,
T. H.
and
El Haddad
,
M. H.
, “
Fatigue Strength Prediction of Notches Based on Fracture Mechanics
,” in
Fatigue Thresholds
,
1st Intl. Conf.
,
Stockholm
,
EMAS, Warley
,
U.K.
, Vol.
2
,
1981
, pp.
777
-
797
.
12.
El Haddad
,
M. H.
,
Smith
,
K. N.
, and
Topper
,
T. H.
, “
A Strain-Based Intensity Factor Solution for Short Fatigue Cracks Initiating from Notches
,” in
Fracture Mechanics (Eleventh Conference)
, ASTM STP 677,
American Society for Testing and Materials
,
Philadelphia
,
1979
, pp.
274
-
289
.
13.
El Haddad
,
M. H.
,
Topper
,
T. H.
, and
Smith
,
K. N.
, “
Prediction of Non-Propagating Cracks
,”
Engineering Fracture Mechanics
 0013-7944 https://doi.org/10.1016/0013-7944(79)90081-X, Vol.
11
,
1979
, pp.
573
-
584
.
14.
El Haddad
,
M. H.
,
Smith
,
K. N.
, and
Topper
,
T. H.
, “
Fatigue Crack Propagation of Short Cracks
,”
ASME Journal of Engineering Materials and Technology
 0094-4289, Vol.
101
,
1979
, pp.
42
-
46
.
15.
Dowling
,
N. E.
, “
Fatigue at Notches and the Local Strain and Fracture Mechanics Approaches
,” in
Fracture Mechanics (Eleventh Conference)
, ASTM STP 677,
American Society for Testing and Materials
,
Philadelphia
,
1979
, pp.
247
-
273
.
16.
Lukas
,
P.
and
Klesnil
,
M.
, “
Fatigue Limit of Notched Bodies
,”
Materials Science and Engineering
, Vol.
34
,
1978
, pp.
61
-
66
.
17.
Du Quesnay
,
D. L.
,
Topper
,
T. H.
, and
Yu
,
M. T.
, “
The Effect of Notch Radius on the Fatigue Notch Factor and the Propagation of Short Cracks
,”
The Behaviour of Short Fatigue Crack
, EGF Pub. 1 (Edited by
Miller
J.
and
de los Rios
E. R.
),
Mechanical Engineering Publications
,
London
,
1986
, pp.
323
-
335
.
18.
Weiss
,
B.
,
Stickler
,
R.
,
Lukas
,
P.
, and
Kunz
,
L.
, “
Non-Damaging Notches in Fatigue: A Short Crack Problem?
,”
2nd Intl. Workshop on Small Fatigue Cracks
, 5–10 Jan. 1986,
Santa Barbara, Calif.
19.
Talug
,
A.
and
Reifsnider
,
K.
, “
Analysis and Investigation of Small Flaws
,” in
Cyclic Stress-Strain and Plastic Deformation Aspects of Fatigue Crack Growth
, ASTM STP 637,
American Society for Testing and Materials
,
Philadelphia
,
1977
, pp.
81
-
96
.
20.
Tanaka
,
K.
and
Nakai
,
Y.
, “
Propagation and Non-Propagation of Short Fatigue Cracks at a Sharp Notch
,”
Fatigue of Engineering Materials and Structures
, Vol.
6
, No.
4
,
1983
, pp.
315
-
327
.
21.
Nisitani
,
H.
and
Endo
,
M.
, “
Fatigue Strength of Carbon Steel Specimens Having an Extremely Shallow Notch
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
21
, No.
1
, pp.
215
-
227
.
22.
Murakami
,
Y.
and
Endo
,
T.
, “
Effects of Small Defects on Fatigue Strength of Metals
,”
International Journal of Fatigue
 0142-1123, Vol.
2
, No.
1
,
1980
, pp.
23
-
30
.
23.
Murakami
,
Y.
and
Endo
,
T.
, “
Quantitative Evaluation of Fatigue Strength of Metals Containing Various Small Defects or Cracks
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
17
, No.
1
,
1983
, pp.
1
-
15
.
24.
Dowling
,
N. E.
, “
Crack Growth During Low Cycle Fatigue of Smooth Axial Specimens
,” in
Cyclic Stress-Strain and Plastic Deformation Aspects of Fatigue Crack Growth
, ASTM STP 637,
American Society for Testing and Materials
,
Philadelphia
,
1977
, pp.
97
-
121
.
25.
Salah el din
,
A. S.
and
Lovegrove
,
A. S.
, “
Stress Intensity Factors for Fatigue Cracking of Round Bars
,”
International Journal of Fatigue
 0142-1123, Vol.
3
, No.
3
,
1981
, pp.
117
-
123
.
26.
Cruse
,
T. A.
,
Meyers
,
G. J.
, and
Wilson
,
R. B.
, “
Fatigue Growth of Surface Cracks
,” in
Flaw Growth and Fracture
, ASTM STP 631,
American Society for Testing and Materials
,
Philadelphia
,
1977
, pp.
174
-
189
.
27.
Kitagawa
,
H.
and
Takahashi
,
S.
, “
Application of Fracture Mechanics to Very Small Cracks or Cracks in the Early Stage
,” in
Proceedings
,
2nd Intl. Conf. on Mechanical Behavior
,
Boston, Mass
,
1976
, pp.
627
-
630
.
28.
Neuber
,
H.
, “
Theory of Stress Concentration for Shear Strained Prismatical Bodies with Arbitrary Non-Linear Stress Strain Law
,”
ASME Journal of Applied Mechanics
 0021-8936, Vol.
28
,
1961
, pp.
544
-
550
.
29.
Topper
,
T. H.
,
Wetzel
,
R. M.
, and
Morrow
,
Jo Dean
, “
Neuber's Rule Applied to Fatigue of Notched Specimens
,
Journal of Materials
 0022-2453, Vol.
4
, No.
1
,
1969
, pp.
200
-
209
.
30.
Leis
,
B. N.
,
Gowda
,
C. V. B.
, and
Topper
,
T. H.
, “
Some Studies on the Influence of Localized Gross Plasticity on the Monotonic and Cyclic Concentration Factors
,”
Journal of Testing and Evaluation
 0090-3973, Vol.
1
, No.
4
,
1973
, pp.
341
-
348
.
31.
Leis
,
B. N.
and
Topper
,
T. H.
, “
Cyclic Deformation and Fatigue Analysis for Notched Components
,”
Nuclear Engineering and Design
 0029-5493, Vol.
29
,
1974
, pp.
370
-
383
.
32.
Wetzel
,
R. M.
, “
Smooth Specimen Simulation of Fatigue Behavior of Notches
,”
Journal of Materials
 0022-2453, Vol.
3
, No.
3
,
1968
, pp.
646
-
657
.
33.
Peterson
,
R. E.
,
Stress Concentration Factors
,
Wiley
,
New York
,
1974
.
34.
Neuber
,
H.
,
Theory of Notch Stresses
,
J. S. Edwards, Ann Arbor, Mich.
,
1946
.
35.
Leis
,
B. N.
, “
Fatigue Analyses to Assess Crack Initiation Life for Notched Coupons and Complex Components
,”
University of Waterloo
, Ph.D. thesis, Waterloo, Ontario, Canada,
1976
.
36.
Rooke
,
D. P.
and
Cartwright
,
D. J.
, “
A Compendium of Stress Intensity Factors
,”
H.M.S.O.
,
1974
,
London
.
37.
Smith
,
K. N.
,
Watson
,
P.
, and
Topper
,
T. H.
, “
A Stress Strain Function for the Fatigue of Metals
,”
Journal of Materials
 0022-2453, Vol.
5
, No.
4
,
1970
, pp.
767
-
778
.
38.
Lukas
,
P.
and
Kunz
,
L.
, “
Influence of Notches on High Cycle Fatigue Life
,”
Materials Science and Engineering
, Vol.
47
,
1981
, pp.
93
-
98
.
39.
Yu
,
M. T.
,
Topper
,
T. H.
,
Du Quesnay
,
D. L.
, and
Levin
,
M. S.
, “
The Effect of Compressive Peak Stress on Fatigue Behaviour
,”
International Journal of Fatigue
 0142-1123, Vol.
8
, No.
1
,
1986
, pp.
9
-
15
.
40.
Yu
,
M. T.
and
Topper
,
T. H.
, “
The Effects of Stress Ratio, Compressive Load and Underload on the Threshold Behaviour of a 2024-T351 Aluminum Alloy
,” in
Fatigue '84
(Edited by
Beevers
C. J.
),
Chameleon Press
,
London
, Vol.
1
,
1984
, pp.
179
-
190
.
41.
Yu
,
M T.
and
Topper
,
T. H.
, “
The Effect of Material Strength, Stress Ratio, and Compressive Overload on the Threshold Behavior of a SAE1045 Steel
,”
ASME Journal of Engineering Materials and Technology
 0094-4289, Vol.
107
,
1985
, pp.
19
-
25
.
42.
Du Quesnay
,
D. L.
, “
A Short Crack Fracture Mechanics Analysis of Notch Size Effects in Fatigue
,”
University of Waterloo, M.A.Sc. thesis, Waterloo
,
Ontario, Canada
,
1986
.
43.
Masing
,
G.
in
Proceedings
,
2nd International Congress of Applied Mechanics
,
1929
,
Zurich
.
This content is only available via PDF.
You do not currently have access to this content.