Abstract

In this paper, a key differential equation is proposed to formulate fatigue damage evolution in metallic alloys under multiaxial, multiblock, proportional loadings in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) regimes. This differential equation possesses two main components: one is a stress function to accommodate the adopted fatigue criterion and the other one is a characteristic damage function that serves to capture the HCF response of alloys. Two distinct characteristic damage functions with three different multiaxial fatigue criteria, namely Sines, Crossland, and Dang Van criteria, are examined to develop six (out of many possible) variants of the presented damage accumulation model. As a validation measure, Chaboche’s HCF damage model is retrieved as a specific case of the developed formalism. For model parameters identification, an ad hoc two-level identification scheme is designed and numerically verified. It is demonstrated that endurance limit, which is determined from fully reversed HCF tests (i.e., R = −1), can be identified from fatigue tests with positive stress ratio (R > 0), thus making our development quite suitable for specimens prone to buckling under compression. Another salient feature of the devised identification scheme is its capability in extracting model parameters from noisy data.

References

References
1.
Wöhler
,
A.
,
1870
,
Über die Festigkeitsversuche mit Eisen und Stahl
,
Ernst & Korn
,
Berlin
.
2.
Basquin
,
O. H.
,
1910
, “
The Exponential Law of Endurance Tests
,”
Proc. ASTM
, pp.
625
630
.
3.
Palmgren
,
A.
,
1924
, “
Die Lebensdauer von Kugellagern
,”
Z. VDI
,
58
(
14
), pp.
339
341
.
4.
Miner
,
M. A.
,
1945
, “
Cumulative Damage in Fatigue
,”
ASME J. Appl. Mech.
,
12
(
3
), pp.
159
164
.
5.
Marco
,
S. M.
, and
Starkey
,
W. L.
,
1954
, “
A Concept of Fatigue Damage
,”
Trans. ASME
,
76
(
4
), pp.
627
632
.
6.
Palin-Luc
,
T.
(
1996
). Fatigue Multiaxiale d’une fonte GS Sous Sollicitations Combinées D’amplitude Variable. ENSAM de Paris. https://www.theses.fr/1996ENAM0029.
7.
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
,
20
(
1
), pp.
9
34
. 10.1016/S0142-1123(97)00081-9
8.
Chaboche
,
J. L.
,
1988
, “
Continuum Damage Mechanics: Part I—General Concepts
,”
ASME J. Appl. Mech.
,
55
(
1
), pp.
59
64
. 10.1115/1.3173661
9.
Chaboche
,
J. L.
,
1988
, “
Continuum Damage Mechanics: Part II—Damage Growth, Crack Initiation, and Crack Growth
,”
ASME J. Appl. Mech.
,
55
(
1
), pp.
65
72
. 10.1115/1.3173662
10.
Lemaitre
,
J.
,
1996
,
A Course on Damage Mechanics
,
Springer Berlin Heidelberg
,
Berlin, Heidelberg
. 10.1007/978-3-642-18255-6
11.
Lemaitre
,
J.
, and
Desmorat
,
R.
,
2005
,
Engineering Damage Mechanics
,
Springer-Verlag
,
Berlin, Heidelberg
. 10.1007/b138882
12.
Murakami
,
S.
,
2012
,
Continuum Damage Mechanics
,
Springer Netherlands
,
Dordrecht
. 10.1007/978-94-007-2666-6
13.
Rabotnov
,
Y.
,
1969
,
Creep Problems in Structural Members
,
North-Holland Pub. Co.
,
Amsterdam
.
14.
Rabotnov
,
Y. N.
,
Leckie
,
F. A.
, and
Prager
,
W.
,
1970
, “
Creep Problems in Structural Members
,”
ASME J. Appl. Mech.
,
37
(
1
), p.
249
. 10.1115/1.3408479
15.
Kachanov
,
L. M.
,
1986
,
Introduction to Continuum Damage Mechanics
,
Springer Netherlands
,
Dordrecht
. 10.1007/978-94-017-1957-5
16.
Rodin
,
G. J.
,
2000
, “
Continuum Damage Mechanics and Creep Life Analysis
,”
ASME J. Appl. Mech.
,
67
(
1
), pp.
193
196
. 10.1115/1.321163
17.
Robinson
,
D. N.
, and
Binienda
,
W. K.
,
2005
, “
A Representation of Anisotropic Creep Damage in Fiber Reinforced Composites
,”
ASME J. Appl. Mech.
,
72
(
4
), pp.
484
492
. 10.1115/1.1875512
18.
Chaboche
,
J. L.
,
1974
, “
Une loi différentielle d’endommagement de fatigue avec cumulation non linéaire
,”
Rev. Française Mécanique
,
50
(
51
), pp.
71
82
.
19.
Chaboche
,
J. L.
, and
Lesne
,
P. M.
,
1988
, “
A non-Linear Continuous Fatigue Damage Model
,”
Fatigue Fract. Eng. Mater. Struct.
,
11
(
1
), pp.
1
17
. 10.1111/j.1460-2695.1988.tb01216.x
20.
Chaudonneret
,
M.
,
1993
, “
A Simple and Efficient Multiaxial Fatigue Damage Model for Engineering Applications of Macro-Crack Initiation
,”
ASME J. Eng. Mater. Technol.
,
115
(
4
), pp.
373
379
. 10.1115/1.2904232
21.
Marmi
,
A. K.
,
Habraken
,
A. M.
, and
Duchene
,
L.
,
2009
, “
Multiaxial Fatigue Damage Modelling at Macro Scale of Ti–6Al–4V Alloy
,”
Int. J. Fatigue
,
31
(
11–12
), pp.
2031
2040
. 10.1016/j.ijfatigue.2009.03.003
22.
Xiao
,
Y.-C.
,
Li
,
S.
, and
Gao
,
Z.
,
1998
, “
A Continuum Damage Mechanics Model for High Cycle Fatigue
,”
Int. J. Fatigue
,
20
(
7
), pp.
503
508
. 10.1016/S0142-1123(98)00005-X
23.
Do Van
,
V. N.
,
Lee
,
C.-H.
, and
Chang
,
K.-H.
,
2015
, “
High Cycle Fatigue Analysis in Presence of Residual Stresses by Using a Continuum Damage Mechanics Model
,”
Int. J. Fatigue
,
70
, pp.
51
62
. 10.1016/j.ijfatigue.2014.08.013
24.
Lee
,
C.-H.
,
Chang
,
K.-H.
, and
Van Do
,
V. N.
,
2016
, “
Modeling the High Cycle Fatigue Behavior of T-Joint Fillet Welds Considering Weld-Induced Residual Stresses Based on Continuum Damage Mechanics
,”
Eng. Struct.
,
125
, pp.
205
216
. 10.1016/j.engstruct.2016.07.002
25.
Gerber
,
W. Z.
,
1874
, “
Calculation of the Allowable Stresses in Iron Structures
,”
Z. Bayer Arch. Ing. Ver.
,
6
(
6
), pp.
101
110
.
26.
Goodman
,
J.
,
1899
,
Mechanics Applied to Engineering
,
Longman, Green and Co
,
London
.
27.
Haigh
,
B. P.
,
1917
, “
Experiments on the Fatigue of Brasses
,”
J. Inst. Met.
,
18
, pp.
55
86
.
28.
Soderberg
,
C. R.
,
1939
, “
Factor of Safety and Working Stress
,”
Trans. ASME
,
52
(
2
), pp.
13
28
.
29.
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
,
19
(
3
), pp.
219
235
. 10.1016/S0142-1123(96)00064-3
30.
Papadopoulos
,
I. V.
,
1998
, “
Critical Plane Approaches in High-Cycle Fatigue: on the Definition of the Amplitude and Mean Value of the Shear Stress Acting on the Critical Plane
,”
Fatigue Fract. Eng. Mater. Struct.
,
21
(
3
), pp.
269
285
. 10.1046/j.1460-2695.1998.00459.x
31.
Carpinteri
,
A.
, and
Spagnoli
,
A.
,
2001
, “
Multiaxial High-Cycle Fatigue Criterion for Hard Metals
,”
Int. J. Fatigue
,
23
(
2
), pp.
135
145
. 10.1016/S0142-1123(00)00075-X
32.
Papuga
,
J.
,
2011
, “
A Survey on Evaluating the Fatigue Limit Under Multiaxial Loading
,”
Int. J. Fatigue
,
33
(
2
), pp.
153
165
. 10.1016/j.ijfatigue.2010.08.001
33.
Mamiya
,
E. N.
,
Castro
,
F. C.
, and
Araújo
,
J. A.
,
2014
, “
Recent Developments on Multiaxial Fatigue: The Contribution of the University of Brasília
,”
Theor. Appl. Fract. Mech.
,
73
, pp.
48
59
. 10.1016/j.tafmec.2014.06.007
34.
Sines
G.
,
1959
, “Behavior of Metals Under Complex Static and Alternating Stresses,”
Metal Fatigue
,
G.
Sines
,
J. L.
Waisman
, and
T. J.
Dolan
, eds., pp.
145
169
,
McGraw-Hill
,
New York
.
35.
Crossland
,
B.
,
1956
, “
Effect of Large Hydrostatic Pressures on the Torsional Fatigue Strength of an Alloy Steel
,”
Proceedings of the International Conference on Fatigue of Metals
,
Institution of Mechanical Engineers
,
London
, pp.
138
149
.
36.
Dang Van
K.
,
Griveau
B.
, and
Message
O.
,
1989
, “On a New Multiaxial Fatigue Limit Criterion: Theory and Application,”
ICBMFF2, Biaxial and Multiaxial Fatigue
, EFG-3,
M. W.
Brown
, and
K. J.
Miller
, eds., pp.
479
496
,
Mechanical Engineering Publications
,
London
.
37.
Dang-Van
K.
,
1993
, “Macro-Micro Approach in High-Cycle Multiaxial Fatigue,”
Advances in Multiaxial Fatigue
, p.
120
,
ASTM International
, 100 Barr Harbor Drive, PO Box C700,
West Conshohocken, PA
19428-2959. 10.1520/STP24799S
38.
Carpinteri
,
A.
,
De Freitas
,
M.
, and
Spagnoli
,
A.
,
2003
, “
Biaxial/Multiaxial Fatigue and Fracture
,”
6th International Conference on Biaxial/Multiaxial Fatigue and Fracture
,
Elsevier
. 10.1016/S1566-1369(03)X8001-2
39.
Lemaitre
,
J.
,
1984
, “
How to Use Damage Mechanics
,”
Nucl. Eng. Des.
,
80
(
2
), pp.
233
245
. 10.1016/0029-5493(84)90169-9
40.
Lemaitre
,
J.
, and
Dufailly
,
J.
,
1987
, “
Damage Measurements
,”
Eng. Fract. Mech.
,
28
(
5–6
), pp.
643
661
. 10.1016/0013-7944(87)90059-2
41.
Lemaitre
,
J.
,
1986
, “
Local Approach of Fracture
,”
Eng. Fract. Mech.
,
25
(
5–6
), pp.
523
537
. 10.1016/0013-7944(86)90021-4
42.
Kintzel
,
O.
,
Khan
,
S.
, and
Mosler
,
J.
,
2010
, “
A Novel Isotropic Quasi-Brittle Damage Model Applied to LCF Analyses of Al2024
,”
Int. J. Fatigue
,
32
(
12
), pp.
1948
1959
. 10.1016/j.ijfatigue.2010.07.001
43.
Patil
,
N.
,
Mahadevan
,
P.
, and
Chatterjee
,
A.
,
2008
, “
A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading
,”
Proc. R. Soc. A Math. Phys. Eng. Sci.
,
464
(
2093
), pp.
1161
1179
. 10.1098/rspa.2007.0109
44.
Chaboche
J.-L.
,
2013
, “Cumulative Damage,”
Fatigue of Materials and Structures
, pp.
47
110
,
John Wiley & Sons, Inc.
,
Hoboken, NJ
. 10.1002/9781118616994.ch2
45.
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
,
28
(
2
), pp.
89
95
. 10.1016/j.ijfatigue.2005.05.001
46.
Kaminski
,
M.
,
Kanouté
,
P.
,
Gallerneau
,
F.
,
Chaboche
,
J. L.
, and
Kruch
,
S.
,
2005
, “
Lifetime Predictions Under Complex Loading for a Car Application
,”
Fatigue Design Conf. on CETIM
,
Senlis
.
47.
Lemaitre
,
J.
, and
Chaboche
,
J.-L.
,
1990
,
Mechanics of Solid Materials
,
Cambridge University Press
,
Cambridge
. 10.1017/CBO9781139167970
48.
Sabirov
,
I.
,
Enikeev
,
N. A.
,
Murashkin
,
M. Y.
, and
Valiev
,
R. Z.
,
2015
,
Multifunctional Properties of Bulk Nanostructured Metallic Materials
,
Springer Cham
,
New York
, pp.
27
100
.
You do not currently have access to this content.