Abstract

The adjustable localization operator (ALO) method allows for the local analytical calculation of complex structures under multiaxial confined plasticity cyclic loadings. This study proposes a theoretical framework for the extension of the method to cover anisotropic yield surface materials. The application is carried out on steel tubes that have been axially compressed beforehand to create a bulge that acts as a stress concentration factor during the fatigue loading process. The ALO method is compared to the reference finite element anisotropic analysis at different steps of the fatigue design chain. Results have shown that although a slight gap on the absolute strain values exists, the strain amplitude and thus the fatigue life are correctly predicted with a reduction of the calculation time by 100.

References

1.
Smith
,
K.
,
Watson
,
P.
, and
Topper
,
T. H.
,
1970
, “
A Stress Strain Function for the Fatigue of Metals
,”
Nl Marls
,
5
(
4
), pp.
767
778
.
2.
Manson
,
S. S.
,
1965
, “
Fatigue: A Complex Subject—Some Simple Approximations
,”
Exp. Mech.
,
5
(
4
), pp.
193
226
.
3.
Coffin
,
L. F. J.
,
1953
, “
A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal
,” Knolls Atomic Power Lab., KAPL-853.
4.
Morrow
,
J.
,
1965
, “
Low Cycle Fatigue Behavior of Quenched and Tempered SAE 1045 Steel
,” TAM R 277 1966-0446, [Online], http://hdl.handle.net/2142/111998
5.
Cojocaru
,
D.
, and
Karlsson
,
A. M.
,
2006
, “
A Simple Numerical Method of Cycle Jumps for Cyclically Loaded Structures
,”
Int. J. Fatigue
,
28
(
12
), pp.
1677
1689
.
6.
Park
,
J. W.
,
Hwang
,
J. W.
, and
Kim
,
Y. H.
,
2003
, “
Efficient Finite Element Analysis Using Mesh Superposition Technique
,”
Finite Elem. Anal. Des.
,
39
(
7
), pp.
619
638
.
7.
Neuber
,
H.
,
1961
, “
Theory of Stress Concentration for Shear-Strained Prismatical Bodies With Arbitrary Nonlinear Stress–Strain Law
,”
ASME J. Appl. Mech.
,
28
(
4
), pp.
544
550
.
8.
Molski
,
K.
, and
Glinka
,
G.
,
1981
, “
A Method of Elastic-Plastic Stress and Strain Calculation at a Notch Root
,”
Mater. Sci. Eng.
,
50
(
1
), pp.
93
100
.
9.
Hoffmann
,
M.
, and
Seeger
,
T.
,
1985
, “
A Generalized Method for Estimating Multiaxial Elastic-Plastic Notch Stresses and Strains, Part 1: Theory
,”
ASME J. Eng. Mater. Technol.
,
107
(
4
), pp.
250
254
.
10.
Moftakhar
,
A.
,
Buczynski
,
A.
, and
Glinka
,
G.
,
1994
, “
Calculation of Elasto-Plastic Strains and Stresses in Notches Under Multiaxial Loading
,”
Int. J. Fract.
,
70
(
4
), pp.
357
373
.
11.
Walker
,
E. K.
,
1977
, “
Multiaxial Stress–Strain Approximations for Notch Fatigue Behaviors
,”
J. Test. Eval.
,
5
(
2
), pp.
106
113
.
12.
Desmorat
,
R.
,
2002
, “
Fast Estimation of Localized Plasticity and Damage by Energetic Methods
,”
Int. J. Solids Struct.
,
39
(
12
), pp.
3289
3310
.
13.
Barkey
,
M. E.
,
Socie
,
D. F.
, and
Hsia
,
K. J.
,
1994
, “
A Yield Surface Approach to the Estimation of Notch Strains for Proportional and Nonproportional Cyclic Loading
,”
ASME J. Eng. Mater. Technol.
,
116
(
2
), pp.
173
180
.
14.
Buczynski
,
A.
, and
Glinka
,
G.
,
2003
, “
An Analysis of Elasto-Plastic Strains and Stresses in Notched Bodies Subjected to Cyclic Non-Proportional Loading Paths
,”
Eur. Struct. Integr. Soc.
,
31
(
C
), pp.
265
283
.
15.
Ye
,
D.
,
Hertel
,
O.
, and
Vormwald
,
M.
,
2008
, “
A Unified Expression of Elastic-Plastic Notch Stress–Strain Calculation in Bodies Subjected to Multiaxial Cyclic Loading
,”
Int. J. Solids Struct.
,
45
(
24
), pp.
6177
6189
.
16.
Singh
,
M. N. K.
,
Glinka
,
G.
, and
Dubey
,
R. N.
,
1996
, “
Elastic–Plastic Stress–Strain Calculation in Notched Bodies Subjected to Non-Proportional Loading
,”
Int. J. Fract.
,
76
(
1
), pp.
39
60
.
17.
McDonald
,
R. J.
, and
Socie
,
D. F.
,
2011
, “
A Technique to Estimate the Local Multiaxial Elastic–Plastic Behavior From a Purely Elastic Solution
,”
Eng. Fract. Mech.
,
78
(
8
), pp.
1696
1704
.
18.
McDonald
,
R. J.
, and
Socie
,
D. F.
,
2010
, “
An Improved Multiaxial Method to Estimate the Elastic–Plastic Behavior From a Purely Elastic Solution
,”
Procedia Eng.
,
2
(
1
), pp.
315
322
.
19.
Glinka
,
G.
,
1985
, “
Energy Density Approach to Calculation of Inelastic Strain–Stress Near Notches and Cracks
,”
Eng. Fract. Mech.
,
22
(
3
), pp.
485
508
.
20.
Glinka
,
G.
,
1985
, “
Calculation of Inelastic Notch-Tip Strain–Stress Histories Under Cyclic Loading
,”
Eng. Fract. Mech.
,
22
(
5
), pp.
839
854
.
21.
Ince
,
A.
, and
Glinka
,
G.
,
2013
, “
A Numerical Method for Elasto-Plastic Notch-Root Stress–Strain Analysis
,”
J. Strain Anal. Eng. Des.
,
48
(
4
), pp.
229
244
.
22.
Antoni
,
N.
,
2019
, “
A Novel Rapid Method of Purely Elastic Solution Correction to Estimate Multiaxial Elastic–Plastic Behavior
,”
J. Comput. Des. Eng.
,
6
(
3
), pp.
269
283
.
23.
Zappalorto
,
M.
, and
Kujawski
,
D.
,
2015
, “
Neuber’s Rules and Other Solutions: Theoretical Differences, Formal Analogies and Energy Interpretations
,”
Theor. Appl. Fract. Mech.
,
79
, pp.
2
13
.
24.
Kilambi
,
S.
, and
Tipton
,
S. M.
,
2013
, “
Numerical Evaluation of the Original ‘Neuber’s Rule’ for Pure Out-of-Plane Shear Loading
,”
J. Strain Anal. Eng. Des.
,
48
(
8
), pp.
522
533
.
25.
Salemi
,
Z.
, and
Kujawski
,
D.
,
2016
, “
A Strain Energy Method for Elastic–Plastic Analysis of Notches Under Shear Loading
,”
Theor. Appl. Fract. Mech.
,
84
, pp.
49
56
.
26.
Darlet
,
A.
,
2014
, “
Estimation Rapide en Surface de la Triaxialité des Contraintes et de la Plasticité : Application aux Disques et aux Aubes de Turbine de Turboréacteurs
,”
Thèse de doctorat
,
Ecole normale supérieure de Cachan
,
Cachan
. http://www.theses.fr/2014DENS0003
27.
Herbland
,
T.
,
2009
, “
Une Méthode de Correction élastoplastique Pour le Calcul en Fatigue des Zones de Concentration de Contraintes Sous Chargement Cyclique Multiaxial non Proportionnel
,”
Thèse de doctorat
,
Ecole des Mines de Paris
,
Paris
. https://tel.archives-ouvertes.fr/tel-00479991/
28.
Sauzay
,
M.
,
2000
, “
Effets de Surface et D’anisotropie en Fatigue Multiaxiale
,”
Thèse de doctorat
,
Paris 6
,
Paris
, https://www.theses.fr/2000PA066429, Accessed April 18, 2019.
29.
Herbland
,
T.
,
Cailletaud
,
G.
, and
Quilici
,
S.
,
2009
, “
Evaluation of Local Stress and Strain State at Notch Root by Means of a New Method Valid for Multiaxial Random Loadings
,”
International Conference on Fracture
,
Ottawa, Canada
,
July 12–17
.
30.
Levieil
,
B.
,
Doudard
,
C.
,
Thevenet
,
D.
,
Bridier
,
F.
,
Ezanno
,
A.
, and
Calloch
,
S.
,
2019
, “
An Original Simplified Method Based on the Use of an Adjustable Localization Operator for Low-Cycle Fatigue Life Predictions in the Case of Confined Plasticity
,”
Theor. Appl. Fract. Mech.
,
104
, p.
102383
.
31.
Levieil
,
B.
,
Bridier
,
F.
,
Doudard
,
C.
,
Thevenet
,
D.
,
Calloch
,
S.
, and
Ezanno
,
A.
,
2017
, “
Numerical Simulation of Low-Cycle Fatigue Behavior of Welded Joints for Naval Applications: Influence of Residual Stresses
,”
Weld. World
,
61
(
3
), pp.
551
561
.
32.
Raujol-Veillé
,
J.
,
Thévenet
,
D.
,
Doudard
,
C.
,
Calloch
,
S.
, and
Minnebo
,
H.
,
2015
, “
Rapid Method for Low Cycle Fatigue Properties: Thickness Effect on the Fatigue Crack Initiation Life of Welded Joints
,”
Fract. Eng. Mater. Struct.
,
38
(
12
), pp.
1492
1506
.
33.
Plessis
,
S.
,
2013
, “
Ingénierie de Modèles Pour la Prévision Rapide de la Tenue en Fatigue Oligocyclique des Assemblages Soudés
,”
Thèse de doctorat
,
ENSTA Bretagne
,
Brest
. http://www.theses.fr/s93910, Accessed April 18, 2019.
34.
Chouman
,
M.
,
Gaubert
,
A.
,
Chaboche
,
J. L.
,
Kanouté
,
P.
,
Cailletaud
,
G.
, and
Quilici
,
S.
,
2014
, “
Elastic-Viscoplastic Notch Correction Methods
,”
Int. J. Solids Struct.
,
51
(
18
), pp.
3025
3041
.
35.
Hill
,
R.
, and
Orowan
,
E.
,
1948
, “
A Theory of the Yielding and Plastic Flow of Anisotropic Metals
,”
Proc. R. Soc. Lond. Ser. Math. Phys. Sci.
,
193
(
1033
), pp.
281
297
.
36.
Darlet
,
A.
, and
Desmorat
,
R.
,
2015
, “
Stress Triaxiality and Lode Angle Along Surfaces of Elastoplastic Structures
,”
Int. J. Solids Struct.
,
67–68
, pp.
71
83
.
37.
Berveiller
,
M.
, and
Zaoui
,
A.
,
1979
, “
An Extension of the Self-Consistent Scheme to Plastically-Flowing Polycrystals
,”
J. Mech. Phys. Solids
,
26
(
5
6
), pp.
325
344
.
38.
Kröner
,
E.
,
1961
, “
Zur Plastischen Verformung des Vielkristalls
,”
Acta Metall.
,
9
(
2
), pp.
155
161
.
39.
Eshelby
,
J. D.
, and
Peierls
,
R. E.
,
1957
, “
The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
,”
Proc. R. Soc. Lond. Ser. Math. Phys. Sci.
,
241
(
1226
), pp.
376
396
.
40.
Munier
,
R.
,
Doudard
,
C.
,
Calloch
,
S.
, and
Weber
,
B.
,
2014
, “
Determination of High Cycle Fatigue Properties of a Wide Range of Steel Sheet Grades From Self-Heating Measurements
,”
Int. J. Fatigue
,
63
, pp.
46
61
.
41.
Voce
,
E.
,
1955
, “
Analysis of Stress Strain Curves
,”
Aeronaut. J.
,
59
(
534
), p.
442
.
42.
Armstrong
,
P. J.
, and
Frederick
,
C. O.
,
1966
,
A Mathematical Representation of the Multiaxial Bauschinger Effect
,
Berkeley Nuclear Laboratories
,
Berkeley, Great Britain
.
43.
Prager
,
W.
,
1949
, “
Recent Developments in the Mathematical Theory of Plasticity
,”
J. Appl. Phys.
,
20
(
3
), pp.
235
241
.
44.
Hauk
,
V.
,
1997
,
Structural and Residual Stress Analysis by Nondestructive Methods
,
Elsevier
,
New York
.
45.
Chen
,
X.
,
Song
,
J.
, and
Kim
,
K. S.
,
2006
, “
Low Cycle Fatigue Life Prediction of 63Sn–37Pb Solder Under Proportional and Non-Proportional Loading
,”
Int. J. Fatigue
,
28
(
7
), pp.
757
766
.
46.
Wormsen
,
A.
,
Sjödin
,
B.
,
Härkegård
,
G.
, and
Fjeldstad
,
A.
,
2007
, “
Non-Local Stress Approach for Fatigue Assessment Based on Weakest-Link Theory and Statistics of Extremes
,”
Fatigue Fract. Eng. Mater. Struct.
,
30
(
12
), pp.
1214
1227
.
47.
Bentachfine
,
S.
,
Pluvinage
,
G.
,
Gilgert
,
J.
,
Azari
,
Z.
, and
Bouami
,
D.
,
1999
, “
Notch Effect in Low Cycle Fatigue
,”
Int. J. Fatigue
,
21
(
5
), pp.
421
430
.
48.
Norberg
,
S.
, and
Olsson
,
M.
,
2007
, “
The Effect of Loaded Volume and Stress Gradient on the Fatigue Limit
,”
Int. J. Fatigue
,
29
(
12
), pp.
2259
2272
.
49.
Härkegård
,
G.
, and
Halleraker
,
G.
,
2010
, “
Assessment of Methods for Prediction of Notch and Size Effects at the Fatigue Limit Based on Test Data by Böhm and Magin
,”
Int. J. Fatigue
,
32
(
10
), pp.
1701
1709
.
50.
Skallerud
,
B.
,
Ås
,
S. K.
, and
Ottosen
,
N. S.
,
2018
, “
A Gradient-Based Multiaxial Criterion for Fatigue Crack Initiation Prediction in Components With Surface Roughness
,”
Int. J. Fatigue
,
117
, pp.
384
395
.
51.
le Roux
,
P. A.
,
Laubscher
,
R. F.
, and
Schubert
,
A.
,
2020
, “
Machining for an Increased Fatigue Life for a Ti–6Al–4V ELI Component
,”
Procedia CIRP
,
87
, pp.
462
468
.
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