Abstract

Almost all of the available multiaxial high cycle fatigue (HCF) criteria are proposed based on definition of an equivalent stress expression that is a modified version of a static equivalent stress definition or a static yield function. All the equivalent stress expressions proposed so far in the fatigue analysis field have been expressed in semistationary forms wherein the global cyclic rather than the instantaneous changes are considered. In the present paper, a new technique for instantaneous fatigue equivalent stress definition is introduced based on new concepts of instantaneous (virtual) stress amplitude and instantaneous (virtual) mean stress. Then, new HCF criteria are proposed using two approaches: (1) polynomial approach and (2) integral approach, to overcome the shortcomings of the available criteria. A relevant fatigue life assessment algorithm is also proposed, and results of the available criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are evaluated for components with complicated geometries under proportional, nonproportional, and random nonproportional loadings. Results reveal that predictions of the proposed approaches are more accurate.

1.
Fatemi
,
A.
, and
Yang
,
L.
, 1998, “
Cumulative Fatigue Damage and Life Prediction Theories: A Survey of the State of the Art for Homogeneous Materials
,”
Int. J. Fatigue
0142-1123,
20
(
1
), pp.
9
34
.
2.
Papadopoulos
,
I. V.
,
Davoli
,
P.
,
Gorla
,
C.
,
Filippini
,
M.
, and
Bernasconi
,
A.
, 1997, “
A Comparative Study of Multiaxial High-Cycle Fatigue Criteria for Metals
,”
Int. J. Fatigue
0142-1123,
19
(
3
), pp.
219
235
.
3.
Papadopoulos
,
I. V.
, 1996, “
Invariant Formulation of a Gradient Dependent Multiaxial High-Cycle Fatigue Criterion
,”
Eng. Fract. Mech.
0013-7944,
55
(
4
), pp.
513
528
.
4.
Cristofori
,
A.
,
Susmel
,
L.
, and
Tovo
,
R.
, 2008, “
A Stress Invariant Based Criterion to Estimate Fatigue Damage Under Multiaxial Loading
,”
Int. J. Fatigue
0142-1123,
30
, pp.
1646
1658
.
5.
Sines
,
G.
, 1959, “
Behavior of Metals Under Complex Stresses
,”
Metal Fatigue
,
G.
Sines
and
J. L.
Waisman
, eds.,
McGraw-Hill
,
New York
, pp.
145
169
.
6.
Papadopoulos
,
I. V.
, 1994, “
A New Criterion of Fatigue Strength for Out-of-Phase Bending and Torsion of Hard Metals
,”
Int. J. Fatigue
0142-1123,
16
, pp.
377
384
.
7.
Papadopoulos
,
I. V.
, 2001, “
Long Life Fatigue Under Multiaxial Loading
,”
Int. J. Fatigue
0142-1123,
23
(
10
), pp.
839
849
.
8.
Findley
,
W. N.
, 1959, “
A Theory for Effect of Mean Stress on Fatigue of Metals Under Combined Torsion and Axial Load or Bending
,”
ASME J. Eng. Ind.
0022-0817,
81
(
4
), pp.
301
306
.
9.
Matake
,
T.
, 1977, “
An Explanation of Fatigue Limit Under Combined Stress
,”
Bull. JSME
,
20
, pp.
257
263
. 0021-3764
10.
McDiarmid
,
D. L.
, 1987, “
Fatigue Under Out-of-Phase Bending and Torsion
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
9
, pp.
457
475
.
11.
McDiarmid
,
D. L.
, 1991, “
A General Criterion for High Cycle Multiaxial Fatigue Failure
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
14
(
4
), pp.
429
453
.
12.
McDiarmid
,
D. L.
, 1994, “
A Shear Stress Based Critical-Plane Criterion of Multiaxial Fatigue Failure for Design and Life Prediction
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
17
, pp.
1475
1484
.
13.
Dang Van
,
K.
,
Griveau
,
B.
, and
Message
,
O.
, 1989, “
On a New Multiaxial Fatigue Limit Criterion: Theory and Application
,”
Biaxial and Multiaxial Fatigue
(
European Group on Fracture
),
Mechanical Engineering
,
London
, EGF Publication No. 3, pp.
479
496
.
14.
Dang Van
,
K.
, 1993, “
Marco-Micro Approach in High-Cycle Multiaxial Fatigue
,”
Advances in Multiaxial Fatigue
,
D. L.
McDowell
and
R.
Ellis
, eds.,
American Society for Testing and Materials
,
West Conshohocken, PA
, ASTM STP 1191, pp.
120
130
.
15.
Carpinteri
,
A.
,
Brighenti
,
R.
, and
Spagnoli
,
A.
, 2000, “
A Fracture Plane Approach in Multiaxial High-Cycle Fatigue of Metals
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
23
(
4
), pp.
355
364
.
16.
Carpinteri
,
A.
, and
Spagnoli
,
A.
, 2001, “
Multiaxial High-Cycle Fatigue Criterion for Hard Metals
,”
Int. J. Fatigue
0142-1123,
23
, pp.
135
145
.
17.
Spagnoli
,
A.
, 2001, “
A New High-Cycle Fatigue Criterion Applied to Out-of-Phase Biaxial Stress State
,”
Int. J. Mech. Sci.
,
43
, pp.
2581
95
. 0020-7403
18.
Carpinteri
,
A.
,
Spagnoli
,
A.
, and
Vantadori
,
S.
, 2003, “
A Multiaxial Fatigue Criterion for Random Loading
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
26
, pp.
515
522
.
19.
Dattoma
,
V.
,
Giancane
,
S.
,
Nobile
,
R.
, and
Panella
,
F. W.
, 2006, “
Fatigue Life Prediction Under Variable Loading Based on a New Non-Linear Continuum Damage Mechanics Model
,”
Int. J. Fatigue
0142-1123,
28
, pp.
89
95
.
20.
Ottosen
,
N. S.
,
Stenstrom
,
R.
, and
Ristinma
,
M.
, 2008, “
Continuum Approach to High-Cycle Fatigue Modeling
,”
Int. J. Fatigue
0142-1123,
30
, pp.
996
1006
.
21.
Bernasconi
,
A.
, and
Papadopoulos
,
I. V.
, 2005, “
Efficiency of Algorithms for Shear Stress Amplitude Calculation in Critical Plane Class Fatigue Criteria
,”
Comput. Mater. Sci.
,
34
, pp.
355
368
. 0927-0256
22.
McDiarmid
,
D. L.
, 1985, “
Fatigue Under Out-of-Phase Biaxial Stresses of Different Frequencies
,”
Multiaxial Fatigue
,
K. J.
Miller
and
M. W.
Brown
, eds.,
ASTM
,
Philadelphia, PA
, ASTM STP 853, pp.
606
621
.
23.
McDiarmid
,
D. L.
, 1991, “
Mean Stress Effects in Biaxial Fatigue Where the Stresses Are Out-of-Phase and at Different Frequencies
,”
Fatigue Under Biaxial and Multiaxial Loadings
,
K.
Kussmaul
,
D. L.
McDiarmid
, and
D.
Socie
, eds.,
Mechanical Engineering
,
London
, ESIS 10, pp.
321
335
.
24.
Dietmann
,
H.
,
Bhongbhibhat
,
T.
, and
Schmid
,
A.
, 1991, “
Multiaxial Fatigue Behavior of Steels Under In-Phase and Out-of-Phase Loading, Including Different Wave Forms and Frequencies
,”
Fatigue Under Biaxial and Multiaxial Loadings
,
K.
Kussmaul
,
D. L.
McDiarmid
, and
D.
Socie
, eds.,
Mechanical Engineering
,
London
, ESIS 10, pp.
449
464
.
25.
Liu
,
J.
, and
Zenner
,
H.
, 2003, “
Fatigue Limit of Ductile Metals Under Multiaxial Loading
,”
Biaxial/Multiaxial Fatigue and Fracture
,
A.
Carpinteri
,
M.
de Freitas
, and
A.
Spagnoli
, eds.,
Elsevier
,
Amsterdam
, ESIS 31, pp.
147
163
.
26.
Bernasconi
,
A.
,
Foletti
,
S.
, and
Papadopoulos
,
I. V.
, 2008, “
A Study on Combined Torsion and Axial Load Fatigue Limit Tests With Stresses of Different Frequencies
,”
Int. J. Fatigue
0142-1123,
30
(
8
), pp.
1430
1440
.
27.
Zenner
,
H.
,
Simburger
,
A.
, and
Liu
,
J.
, 2000, “
On the Fatigue Limit of Ductile Metals Under Complex Multiaxial Loading
,”
Int. J. Fatigue
0142-1123,
22
, pp.
137
145
.
28.
Łagoda
,
T.
,
Macha
,
E.
, and
Pawliczek
,
R.
, 2001, “
‘The Influence of the Mean Stress on Fatigue Life of 10HNAP Steel Under Random Loading
,”
Int. J. Fatigue
0142-1123,
23
, pp.
283
291
.
29.
Banvillet
,
A.
,
Łagoda
,
T.
,
Macha
,
E.
,
Niesłony
,
A.
,
Palin-Luc
,
T.
, and
Vittori
,
J. F.
, 2004, “
Fatigue Life Under Non-Gaussian Random Loading From Various Models
,”
Int. J. Fatigue
0142-1123,
26
, pp.
349
363
.
30.
Benasciutti
,
D.
, and
Tovo
,
R.
, 2006, “
Fatigue Life Assessment in Non-Gaussian Random Loadings
,”
Int. J. Fatigue
0142-1123,
28
, pp.
733
746
.
31.
Kang
,
J. Y.
,
Choi
,
B. I.
,
Lee
,
H. J.
,
Kim
,
J. S.
, and
Kim
,
K. J.
, 2006, “
Neural Network Application in Fatigue Damage Analysis Under Multiaxial Random Loadings
,”
Int. J. Fatigue
0142-1123,
28
, pp.
132
140
.
32.
Macha
,
E.
, and
Sonsino
,
C. M.
, 1999, “
Energy Criteria of Multiaxial Fatigue Failure
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
22
, pp.
1053
1070
.
33.
Łagoda
,
T.
, and
Macha
,
E.
, 2000, “
Generalization of Energy-Based Multiaxial Fatigue Criteria to Random Loading
,”
Multiaxial Fatigue and Deformation Testing and Prediction
,
S.
Kalluri
and
P. J.
Bonacuse
, eds.,
American Society for Testing and Materials
,
West Conshohocken, PA
, ASTM STP 1387, pp.
173
190
.
34.
Łagoda
,
T.
, 2001, “
Energy Models for Fatigue Life Estimation Under Uniaxial Random Loading. Part I: The Model Elaboration
,”
Int. J. Fatigue
0142-1123,
23
, pp.
467
480
.
35.
Li
,
B.
, and
De Freitas
,
M.
, 2002, “
A Procedure for Fast Evaluation of High-Cycle Fatigue Under Multiaxial Random Loading
,”
ASME J. Mech. Des.
0161-8458,
124
, pp.
558
563
.
36.
Macha
,
E.
, and
Niesłony
,
A.
, 2005, “
Random Multiaxial Fatigue Loading
,”
Advances in Fatigue, Fracture and Damage Assessment of Materials
,
A.
Varvani-Farahani
, ed.,
WIT
,
Southampton
, Chap. 8, pp.
213
242
.
37.
Łagoda
,
T.
,
Macha
,
E.
, and
Niesłony
,
A.
, 2005, “
Fatigue Life Calculation by Means of the Cycle Counting and Spectral Methods Under Multiaxial Random Loading
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
28
, pp.
409
420
.
38.
Ahmadi
,
A.
, and
Zenner
,
H.
, 2006, “
Lifetime Simulation Under Multiaxial Random Loading With Regard to the Microcrack Growth
,”
Int. J. Fatigue
0142-1123,
28
, pp.
954
962
.
39.
Marciniak
,
Z.
,
Rozumek
,
D.
, and
Macha
,
E.
, 2008, “
Fatigue Lives of 18G2A and 10HNAP Steels Under Variable Amplitude and Random Non-Proportional Bending With Torsion Loading
,”
Int. J. Fatigue
0142-1123,
30
, pp.
800
813
.
40.
Pitoiset
,
X.
,
Rychlik
,
I.
, and
Preumonti
,
A.
, 2001, “
Spectral Methods to Estimate Local Multiaxial Fatigue Failure for Structures Undergoing Random Vibrations
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
24
, pp.
715
727
.
41.
Benasciutti
,
D.
, and
Cristofori
,
A.
, 2008, “
A Frequency-Domain Formulation of MCE Method for Multi-Axial Random Loadings
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
31
, pp.
937
948
.
42.
Liu
,
Y.
,
Stratman
,
B.
, and
Mahadevan
,
S.
, 2006, “
Fatigue Crack Initiation Life Prediction of Railroad Wheels
,”
Int. J. Fatigue
0142-1123,
28
, pp.
747
756
.
43.
Liu
,
Y.
, and
Mahadevan
,
S.
, 2007, “
A Unified Multiaxial Fatigue Damage Model for Isotropic and Anisotropic Materials
,”
Int. J. Fatigue
0142-1123,
29
, pp.
347
359
.
44.
Shariyat
,
M.
, 2008, “
A Fatigue Model Developed by Modification of Gough’s Theory, for Random Non-Proportional Loading Conditions and Three-Dimensional Stress Fields
,”
Int. J. Fatigue
0142-1123,
30
, pp.
1248
1258
.
45.
Brown
,
M. W.
, and
Miller
,
K. J.
, 1973, “
A Theory for Fatigue Failure Under Multiaxial Stress-Strain Conditions
,”
Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
,
187
(
65
), pp.
745
55
. 0954-4119
46.
Karolczuk
,
A.
, and
Macha
,
E.
, 2008, “
Selection of the Critical Plane Orientation in Two-Parameter Multiaxial Fatigue Failure Criterion Under Combined Bending and Torsion
,”
Eng. Fract. Mech.
,
75
, pp.
389
403
. 0013-7944
47.
Davoli
,
P.
,
Bernasconi
,
A.
,
Filippini
,
M.
,
Foletti
,
S.
, and
Papadopoulos
,
I. V.
, 2003, “
Independence of the Torsional Fatigue Limit Upon a Mean Shear Stress
,”
Int. J. Fatigue
0142-1123,
25
, pp.
471
480
.
48.
Lee
,
Y. L.
,
Pan
,
J.
,
Hathaway
,
R.
, and
Barkey
,
M.
, 2005,
Fatigue Testing and Analysis: Theory and Practice
,
Elsevier
,
Amsterdam
.
49.
Haupt
,
P.
, 2002,
Continuum Mechanics and Theory of Materials
,
Springer
,
New York
.
50.
Wu
,
H. C.
, 2005,
Continuum Mechanics and Plasticity
,
Chapman and Hall
,
London
.
51.
Cristescu
,
N. D.
, 2007,
Dynamic Plasticity
,
World Scientific
,
Singapore
.
52.
Socie
,
D.
, and
Marquis
,
G.
, 2000,
Multiaxial Fatigue
, 1st ed.,
Society of Automotive Engineers SAE International
,
Philadelphia, PA
.
53.
Susmel
,
L.
,
Tovo
,
R.
, and
Lazzarin
,
P.
, 2005, “
The Mean Stress Effect on the High-Cycle Fatigue Strength From a Multiaxial Fatigue Point of View
,”
Int. J. Fatigue
0142-1123,
27
, pp.
928
943
.
54.
Park
,
J.
, and
Nelson
,
D.
, 2000, “
Evaluation of an Energy-Based Approach and a Critical Plane Approach for Predicting Constant Amplitude Multiaxial Fatigue Life
,”
Int. J. Fatigue
0142-1123,
22
, pp.
23
39
.
55.
Morel
,
F.
, 2000, “
A Critical Plane Approach for Life Prediction of High Cycle Fatigue Under Multiaxial Variable Amplitude Loading
,”
Int. J. Fatigue
0142-1123,
22
, pp.
101
119
.
56.
Li
,
B.
,
Santos
,
J. L. T.
, and
De Feritas
,
M.
, 2001, “
A Computerized Procedure for Long-Life Fatigue Assessment Under Complex Multiaxial Loading
,”
Fatigue Fract. Eng. Mater. Struct.
8756-758X,
24
, pp.
165
177
.
57.
Liu
,
Y.
, and
Mahadevan
,
B.
, 2005, “
Multiaxial High-Cycle Fatigue Criterion and Life Prediction for Metals
,”
Int. J. Fatigue
0142-1123,
27
, pp.
790
800
.
58.
Carpinteri
,
A.
,
Spagnoli
,
A.
,
Vantadori
,
S.
, and
Viappiani
,
D.
, 2008, “
A Multiaxial Criterion for Notch High-Cycle Fatigue Using a Critical-Point Method
,”
Eng. Fract. Mech.
,
75
, pp.
1864
1874
. 0013-7944
59.
Wright
,
D. H.
, 1993,
Testing Automotive Materials and Components
,
McGraw-Hill
,
New York
.
60.
Collins
,
J. A.
, 2002,
Mechanical Design of Machine Elements and Machines: A Failure Prevention Perspective
,
Wiley
,
New York
.
61.
Shariyat
,
M.
, 2006,
Automotive Body: Design and Analysis
,
KNT University Press
,
Tehran, Iran
.
You do not currently have access to this content.