A new method is put forward to predict fatigue life for low cycle nonproportional loading based on the Itoh criterion. The proposed method considers the multi-axiality influence on the reference maximum principal strain path and the calculation of nonproportionality factor Fnp by utilizing a multi-axial fatigue life prediction approach based on the modified Wöhler curve method. Different from the hypothesis of previous integral models for computing factor Fnp where the loading path is considered uniform, a new model using an inhomogeneous integral is presented and a path-dependent weight factor is defined to describe this inhomogeneity. The experimental tests of Itoh on 304 stainless steel with 14 different loading cases are referenced to examine the validity of the new method.

References

References
1.
Sines
,
G.
,
1961
, “
The Prediction of Fatigue Fracture Under Combined Stresses at Stress Concentrations
,”
JSME
,
4
(
15
), pp.
443
453
.
2.
Matake
,
T.
, and
Matake
,
T.
,
1977
, “
An Explanation on Fatigue Limit Under Combined Stress
,”
JSME Int. J.
,
20
(
141
), pp.
257
263
.
3.
McDiarmid
,
D. L.
,
1994
, “
A Shear Stress Based Critical-Plane Criterion of Multiaxial Fatigue Failure for Design and Life
,”
Fatigue Fract. Eng. Mater. Struct.
,
17
(
12
), pp.
1475
1484
.
4.
Brown
,
M. W.
, and
Miller
,
K. J.
,
1973
, “
A Theory for Fatigue Under Multiaxial Stress/Strain Conditions
,”
Proc. Inst. Mech. Eng.
,
187
(
1
), pp.
745
755
.
5.
Shang
,
D. G.
, and
Wang
,
D. J.
,
1998
, “
A New Multiaxial Fatigue Damage Model Based on the Critical Plane Approach
,”
Int. J. Fatigue
,
20
(
3
), pp.
241
245
.
6.
Smith
,
K. N.
,
Topper
,
T. H.
, and
Watson
,
P.
,
1970
, “
A Stress–Strain Function for the Fatigue of Metals
,”
J. Mater.
,
5
(
4
), pp.
767
778
.
7.
Gasiak
,
G.
, and
Pawliczek
,
R.
,
2003
, “
Application of an Energy Model for Fatigue Life Prediction of Construction Steels Under Bending, Torsion and Synchronous Bending and Torsion
,”
Int. J. Fatigue
,
25
(
12
), pp.
1339
1346
.
8.
Kluger
,
K.
, and
Łagoda
,
T.
,
2014
, “
New Energy Model for Fatigue Life Determination Under Multiaxial Loading With Different Mean Values
,”
Int. J. Fatigue
,
66
(
18
), pp.
229
245
.
9.
Grubisic
,
V.
, and
Simbiirger
,
A.
,
1976
, “Fatigue Under Combined Out-of-Phase Multiaxial Stresses,”
International Conference on Fatigue Testing and Design
,
Society of Environmental Engineers, London
, Apr., p.
27
.
10.
Liu
,
J.
, and
Zenner
,
H.
,
1993
, “
Berechnung der Dauerschwingfestigkeit bei mehrachsiger beanspruchung
,”
Materialwiss. Werkstofftech.
,
24
(
7
), pp.
240
249
.
11.
Papadopoulos
,
I. V.
,
1994
, “
A New Criterion of Fatigue Strength for Out-of-Phase Bending and Torsion of Hard Metals
,”
Int. J. Fatigue
,
16
(
6
), pp.
377
384
.
12.
Papadopoulos
,
I. V.
,
1995
, “
A High-Cycle Fatigue Criterion Applied in Biaxial and Triaxial Out-of-Phase Stress Conditions
,”
Fatigue Fract. Eng. Mater. Struct.
,
18
(
1
), pp.
79
91
.
13.
Papadopoulos
,
I. V.
,
1996
, “
Exploring the High-Cycle Fatigue Behaviour of Metals From the Mesoscopic Scale
,”
J. Mech. Behav. Biomed.
,
6
(
2
), pp.
93
118
.
14.
Fatemi
,
A.
, and
Socie
,
D. F.
,
1988
, “
A Critical Plane Approach of Multiaxial Fatigue Damage Including Out of Phase Loading
,”
Fatigue Fract. Eng. Mater. Struct.
,
11
(
3
), pp.
149
165
.
15.
Carpinteri
,
A.
, and
Spagnoli
,
A.
,
2001
, “
Multiaxial High-Cycle Fatigue Criterion for Hard Metals
,”
Int. J. Fatigue
,
23
(
2
), pp.
135
145
.
16.
Sines
,
G.
, and
Ohgi
,
G.
,
1981
, “
Fatigue Criteria Under Combined Stresses or Strains
,”
ASME J. Eng. Mater.
,
103
(2), pp.
81
90
.
17.
Marin
,
J.
,
1956
, “Interpretation of Fatigue Strength for Combined Stresses,”
International Conference on Fatigue of Metals
,
London
, pp.
184
194
.
18.
Crossland
,
B.
,
1956
, “Effect of Large Hydrostatic Pressure on the Torsional Fatigue Strength of an Alloy Steel,”
International Conference on Fatigue of Metals
,
London
, pp.
138
149
.
19.
Shamsaei
,
N.
,
Fatemi
,
A.
, and
Socie
,
D. F.
,
2010
, “
Multiaxial Cyclic Deformation and Non-Proportional Hardening Employing Discriminating Load Paths
,”
Int. J. Plast.
,
26
(
12
), pp.
1680
1701
.
20.
Shamsaei
,
N.
, and
Fatemi
,
A.
,
2010
, “
Effect of Microstructure and Hardness on Non-Proportional Cyclic Hardening Coefficient and Predictions
,”
Mater. Sci. Eng. A
,
527
(
12
), pp.
3015
3024
.
21.
Noban
,
M.
,
Jahed
,
H.
,
Ibrahim
,
E.
, and
Ince
,
A.
,
2012
, “
Load Path Sensitivity and Fatigue Life Estimation of 30CrNiMo8HH
,”
Int. J. Fatigue
,
37
, pp.
123
133
.
22.
Noban
,
M.
,
Jahed
,
H.
,
Winkler
,
S.
, and
Ince
,
A.
,
2011
, “
Fatigue Characterization and Modeling of 30CrNiMo8HH Under Multiaxial Loading
,”
Mater. Sci. Eng. A
,
528
(
6
), pp.
2484
2494
.
23.
Wu
,
Z.-R. R.
,
Hu
,
X.-T. T.
, and
Song
,
Y.-D. D.
,
2014
, “
Multiaxial Fatigue Life Prediction for Titanium Alloy TC4 Under Proportional and Nonproportional Loading
,”
Int. J. Fatigue
,
59
, pp.
170
175
.
24.
Kanazawa
,
K.
,
Miller
,
K. J.
, and
Brown
,
M. W.
,
2010
, “
Cyclic Deformation of 1% Cr–Mo–V Steel Under Out-of-Phase Loads
,”
Fatigue Fract. Eng. Mater. Struct.
,
2
(
2
), pp.
217
228
.
25.
Itoh
,
T.
,
Sakane
,
M.
,
Ohnami
,
M.
, and
Socie
,
D. F.
,
1995
, “
Nonproportional Low-Cycle Fatigue Criterion for Type 304 Stainless Steel
,”
ASME J. Eng. Mater.
,
117
(
3
), pp.
285
292
.
26.
Itoh
,
T.
,
Sakane
,
M.
, and
Ohsuga
,
K.
,
2013
, “
Multiaxial Low Cycle Fatigue Life Under Non-Proportional Loading
,”
Int. J. Pressure Vessels Piping
,
110
, pp.
50
56
.
27.
Mei
,
J.
, and
Dong
,
P.
,
2016
, “
A New Path-Dependent Fatigue Damage Model for Non-Proportional Multi-Axial Loading
,”
Int. J. Fatigue
,
90
, pp.
210
221
.
28.
Meggiolaro
,
M. A.
, and
Castro
,
J. T. P. D.
,
2014
, “
Prediction of Non-Proportionality Factors of Multiaxial Histories Using the Moment of Inertia Method
,”
Int. J. Fatigue
,
61
(
61
), pp.
151
159
.
29.
Susmel
,
L.
, and
Lazzarin
,
P.
,
2002
, “
A Bi-Parametric Wöhler Curve for High Cycle Multiaxial Fatigue Assessment
,”
Fatigue Fract. Eng. Mater. Struct.
,
25
(
1
), pp.
63
78
.
30.
Anes
,
V.
,
Reis
,
L.
,
Li
,
B.
, and
Freitas
,
M. D.
,
2014
, “
New Approach for Analysis of Complex Multiaxial Loading Paths
,”
Int. J. Fatigue
,
62
(
7
), pp.
21
33
.
31.
Freitas
,
M. D.
, and
Reis
,
L.
, and
Li
,
B.
,
2010
, “
Comparative Study on Biaxial Low-Cycle Fatigue Behaviour of Three Structural Steels
,”
Fatigue Fract. Eng. Mater. Struct.
,
29
(
12
), pp.
992
999
.
32.
Li
,
B. C.
,
Jiang
,
C.
,
Han
,
X.
, and
Li
,
Y.
,
2015
, “
A New Approach of Fatigue Life Prediction for Metallic Materials Under Multiaxial Loading
,”
Int. J. Fatigue
,
78
, pp.
1
10
.
33.
Susmel
,
L.
,
Meneghetti
,
G.
, and
Atzori
,
B.
,
2009
, “
A Simple and Efficient Reformulation of the Classical Manson–Coffin Curve to Predict Lifetime Under Multiaxial Fatigue Loading—Part II: Notches
,”
ASME J. Eng. Mater.
,
131
(
2
), pp.
841
846
.
34.
Susmel
,
L.
, and
Taylor
,
D.
,
2008
, “
The Modified Wöhler Curve Method Applied Along With the Theory of Critical Distances to Estimate Finite Life of Notched Components Subjected to Complex Multiaxial Loading Paths
,”
Fatigue Fract. Eng. Mater. Struct.
,
31
(
12
), pp.
1047
1064
.
35.
Cristofori
,
A.
,
Susmel
,
L.
, and
Tovo
,
R.
,
2008
, “
A Stress Invariant Based Criterion to Estimate Fatigue Damage Under Multiaxial Loading
,”
Int. J. Fatigue
,
30
(
9
), pp.
1646
1658
.
36.
Ge
,
J.
,
Sun
,
Y.
, and
Zhou
,
S.
,
2015
, “
Fatigue Life Estimation Under Multiaxial Random Loading by Means of the Equivalent Lemaitre Stress and Multiaxial S–N Curve Methods
,”
Int. J. Fatigue
,
79
, pp.
65
74
.
37.
ASME
,
1978
, “
Case of ASME Boiler and Pressure Vessel Code
,” ASME, New York, Case N-47, Class 1, Section 3, Division 1.
38.
Meggiolaro
,
M. A.
, and
Castro
,
J. T. P. D.
,
2012
, “
An Improved Multiaxial Rainflow Algorithm for Non-Proportional Stress or Strain Histories—Part I: Enclosing Surface Methods
,”
Int. J. Fatigue
,
42
(
4
), pp.
217
226
.
39.
Socie
,
D. F.
,
Kurath
,
P.
, and
Koch
,
J.
,
1989
,
A Multiaxial Fatigue Damage Parameter. Biaxial and Multiaxial Fatigue
,
EGF 3
,
London
, pp.
535
550
.
40.
Lin
,
H.
,
Nayeb-Hashemi
,
H.
, and
Pelloux
,
R. M.
,
1993
, “
A Multiaxial Fatigue Damage Model for Orthotropic Materials Under Proportional Loading
,”
Fatigue Fract. Eng. Mater. Struct.
,
16
(
7
), pp.
723
742
.
41.
Bishop
,
J. E.
,
2000
, “
Characterizing the Non-Proportional and Out-of-Phase Extend of Tensor Paths
,”
Fatigue Fract. Eng. Mater. Struct.
,
23
(
12
), pp.
1019
1032
.
42.
Jiang
,
Y.
, and
Sehitoglu
,
H.
,
1996
, “
Modeling of Cyclic Ratchetting Plasticity—Part I: Development of Constitutive Relations
,”
ASME J. Appl. Mech.
,
63
(
3
), pp.
720
725
.
You do not currently have access to this content.