Abstract

This research tackles the fundamental issue of computational fatigue studies by developing an effective approach that combines the crystal plasticity finite element method (CPFEM) with the Tanaka–Mura–Wu (TMW) model for crack nucleation and the Tomkins model for fatigue crack propagation, to provide Class-A predictions of the total coupon-fatigue life (crack initiation and growth lives) for a nickel-based superalloy, Haynes 282. To gain a statistical significance accounting for the microstructure inhomogeneity, 11 3D Representative Volume Elements (RVEs) are created utilizing Dream.3d to represent the polycrystalline material with different grain structures and orientations in equivalence to the experimental microstructure data. The CPFEM model is calibrated to the material's hysteresis behavior, and then, the microstructural plastic strain from the RVE is taken to calculate the fatigue life. The prediction is found in good agreement with the fatigue test data, validating the effectiveness of the proposed approach in predicting the fatigue life and scatter due to microstructural variability for Haynes 282 alloy. In addition, the effects of local grain attributes including grain orientation and adjacent grain arrangement on fatigue crack nucleation are analyzed quantitatively. It is suggested that grain orientation influences plastic deformation by inducing the active slip systems, and the slip transfer across grain boundaries also contributes to fatigue crack nucleation.

References

1.
Bowles
,
C. Q.
,
1996
, “Industrial Significance of Fatigue Problems,”
ASM Handbook, Volume 19: Fatigue and Fracture
,
ASM International
,
Materials Park, OH
, pp.
10
13
.
2.
Basquin
,
O. H.
,
1910
, “
The Exponential Law of Endurance Test
,”
Am. Soc. Test. Mater. Proc.
,
10
, pp.
625
630
.
3.
Manson
,
S. S.
,
1954
, “
Behaviour of Materials Under Conditions of Thermal Stress
,”
NACA Technical Note No. 1170, National Advisory Committee for Aeronautics
, pp.
1
34
.
4.
Coffin
,
L. F.
, Jr.
,
1954
, “
A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal
,”
Trans. ASME.
,
76
(
6
), pp.
931
949
.
5.
Morrow
,
J.
,
1965
, “
Cyclic Plastic Strain Energy and Fatigue of Metals
”, ASTM STP No. 378,
International Friction, Damping and Cyclic Plasticity, American Society for Testing and Materials, Philadelphia
, pp.
45
84
.
6.
Sines
,
G.
,
1955
, “
Failure of Materials Under Combined Repeated Stresses with Superimposed Static Stress
,” NACA Technical Note No. 3495, National Advisory Committee for Aeronautics, pp.
1
69
.
7.
Sines
,
G.
,
1959
, “Behavior of Metals Under Complex Static and Alternating Stresses,”
Metal Fatigue
,
G.
Sines
and
J. L.
Waisman
, eds.,
McGraw-Hill
,
New York
, pp.
145
169
.
8.
Crossland
,
B.
,
1956
, “
Effect of Large Hydrostatic Pressure on the Torsional Fatigue Strength of An Alloy Steel
,”
Proceedings of the Third International Conference on Fatigue of Metals
,
London, UK
,
Sept. 10–14
, Vol.
138
, pp.
1
12
.
9.
Findley
,
W. N.
,
1959
, “
A Theory for the Effect of Mean Stress on Fatigue of Metals Under Combined Torsion and Axial Load or Bending
,”
ASME J. Eng. Ind.
,
81
(
4
), pp.
301
305
.
10.
McDiarmid
,
D.
,
1991
, “
A General Criterion for High Cycle Multiaxial Fatigue Failure
,”
Fatigue Fract. Eng. Mater. Struct.
,
14
(
4
), pp.
429
453
.
11.
McDiarmid
,
D.
,
1994
, “
A Shear Stress Based Critical-Plane Criterion of Multiaxial Fatigue Failure for Design and Life Prediction
,”
Fatigue Fract. Eng. Mater. Struct.
,
17
(
12
), pp.
1475
1484
.
12.
Brown
,
M.
, and
Miller
,
K. J.
,
1973
, “
A Theory for Fatigue Failure Under Multiaxial Stress-Strain Conditions
,”
Proc. Inst. Mech. Eng.
,
187
(
1
), pp.
745
755
.
13.
Kandil
,
F.
,
Brown
,
M.
, and
Millaer
,
K. J.
,
1981
, “
Biaxial Low-Cycle Fatigue Fracture of 316 Stainless Steel at Elevated Temperatures
,”
Proceedings of International Conference on Mechanical Behaviour and Nuclear Applications of Stainless Steel at Elevated Temperatures
,
Varese, Italy
,
May 20–22
, Vol.
14
, pp.
203
209
.
14.
Wang
,
C. H.
, and
Brown
,
M. W.
,
1993
, “
A Path Independent Parameter for Fatigue Under Proportional and Non Proportional Loading
,”
Fatigue Fract. Eng. Mater. Struct.
,
16
(
12
), pp.
1285
1297
.
15.
Lefebvre
,
D.
,
Neale
,
K. W.
, and
Ellyin
,
F.
,
1981
, “
A Criterion for Low-Cycle Fatigue Failure Under Biaxial States of Stress
,”
ASME J. Eng. Mater. Technol.
,
103
(
1
), pp.
1
6
.
16.
Letcher
,
T.
,
Shen
,
M.-H. H.
,
Scott-Emuakpor
,
O.
,
George
,
T.
, and
Cross
,
C.
,
2012
, “
An Energy-Based Critical Fatigue Life Prediction Method for AL6061-T6
,”
Fatigue Fract. Eng. Mater. Struct.
,
35
(
9
), pp.
861
870
.
17.
Glinka
,
G.
,
Shen
,
G.
, and
Plumtree
,
A.
,
1988
, “
A Multiaxial Fatigue Strain Energy Density Parameter Related to The Critical Fracture Plane
,”
Fatigue Fract. Eng. Mater. Struct.
,
11
(
3
), pp.
149
165
.
18.
Glinka
,
G.
,
Wang
,
G.
, and
Plumtree
,
A.
,
1995
, “
Mean Stress Effects in Multi-Axial Fatigue
,”
Fatigue Fract. Eng. Mater. Struct.
,
18
(
7–8
), pp.
755
764
.
19.
Golos
,
K.
, and
Ellyin
,
F.
,
1987
, “
Generalization of Cumulative Damage Criterion to Multilevel Cyclic Loading
,”
Theor. Appl. Fract. Mech.
,
7
(
3
), pp.
169
176
.
20.
Smith
,
K. N.
,
Watson
,
P.
, and
Topper
,
T. H.
,
1970
, “
A Stress-Strain Function for the Fatigue of Metals
,”
J. Mater.
,
5
(
4
), pp.
767
778
.
21.
Fatemi
,
A.
, and
Socie
,
D. F.
,
1988
, “
A Critical Plane to Multiaxial Fatigue Damage Including Out-of-Phase Loading
,”
Fatigue Fract. Eng. Mater. Struct.
,
11
(
3
), pp.
149
165
.
22.
Chen
,
B.
,
Jiang
,
J.
, and
Dunne
,
F. P. E.
,
2018
, “
Is Stored Energy Density the Primary Meso-Scale Mechanistic Driver for Fatigue Crack Nucleation
,”
Int. J. Plast.
,
101
, pp.
213
229
.
23.
Korsunsky
,
A. M.
,
Dini
,
D.
,
Dunne
,
F. P. E.
, and
Walsh
,
M. J.
,
2007
, “
Comparative Assessment of Dissipated Energy and Other Fatigue Criteria
,”
Int. J. Fatigue
,
29
(
9–11
), pp.
1990
1995
.
24.
Bandyopadhyay
,
R.
,
Prithivirajan
,
V.
,
Peralta
,
A. D.
, and
Sangid
,
M. D.
,
2020
, “
Microstructure-Sensitive Critical Plastic Strain Energy Density Criterion for Fatigue Life Prediction Across Various Loading Regimes
,”
Proc. R. Soc. A: Math. Phys. Eng. Sci.
,
476
(
2236
), pp.
1
23
.
25.
Prithivirajan
,
V.
, and
Sangid
,
M. D.
,
2020
, “
Examining Metrics for Fatigue Life Predictions of Additively Manufactured IN718 via Crystal Plasticity Modeling Including the Role of Simulation Volume and Microstructural Constraints
,”
Mater. Sci. Eng. A
,
783
(
5
), p.
139312
.
26.
Yuan
,
G. J.
,
Zhang
,
X. C.
,
Chen
,
B.
,
Tu
,
S. T.
, and
Zhang
,
C. C.
,
2020
, “
Low-Cycle Fatigue Life Prediction of a Polycrystalline Nickel-Base Superalloy Using Crystal Plasticity Modelling Approach
,”
J. Mater. Sci. Technol.
,
38
, pp.
28
38
.
27.
Manonukul
,
A.
, and
Dunne
,
F. P. E.
,
2004
, “
High- and Low-Cycle Fatigue Crack Initiation Using Polycrystal Plasticity
,”
Mater. Sci. Eng. A
,
460
(
2047
), pp.
1881
1903
.
28.
Wan
,
V. V. C.
,
Jiang
,
J.
,
Maclachlan
,
D. W.
, and
Dunne
,
F. P. E.
,
2016
, “
Microstructure-Sensitive Fatigue Crack Nucleation in a Polycrystalline Ni Superalloy
,”
Int. J. Fatigue
,
90
, pp.
181
190
.
29.
Zhang
,
L.
,
Zhao
,
L. G.
,
Jiang
,
R.
, and
Bullough
,
C.
,
2020
, “
Crystal Plasticity Finite-Element Modelling of Cyclic Deformation and Crack Initiation in a Nickel-Based Single Crystal Superalloy Under Low-Cycle Fatigue
,”
Fatigue Fract. Eng. Mater. Struct.
,
43
(
8
), pp.
1769
1783
.
30.
Li
,
K. J.
,
Cheng
,
L. Y.
,
Xu
,
Y. L.
,
Wang
,
R. Z.
,
Zhang
,
Y.
,
Zhang
,
X. C.
,
Tu
,
S. T.
, and
Miura
,
H.
,
2022
, “
A Dual-Scale Modelling Approach for Creep-Fatigue Crack Initiation Life Prediction of Holed Structure in a Nickel-Based Superalloy
,”
Int. J. Fatigue
,
154
, p.
106522
.
31.
Shen
,
J. B.
,
Fan
,
H. D.
,
Wang
,
J.
,
Zhang
,
G. Q.
,
Pan
,
R.
, and
Huang
,
Z. Y.
,
2023
, “
Stored Energy Density Research on the Fatigue Crack Initiation at Twin Boundary and Life Prediction of Inconel718 Superalloy
,”
Int. J. Fatigue
,
171
, p.
107590
.
32.
Tanaka
,
K.
, and
Mura
,
T.
,
1981
, “
Tanaka-Mura a Dislocation Model for Fatigue Crack Initiation
,”
ASME J. Appl. Mech.
,
48
(
1
), pp.
97
103
.
33.
Wu
,
X. J.
,
2018
, “
On Tanaka-Mura's Fatigue Crack Nucleation Model and Validation
,”
Fatigue Fract. Eng. Mater. Struct.
,
41
(
4
), pp.
894
899
.
34.
Wu
,
X. J.
,
2019
, “Microscopic Crack Nucleation ANF Growth,”
Deformation and Evolution of Life in Crystalline Materials: An Integrated Creep-Fatigue Theory
,
X. J.
Wu
, ed.,
CRC Press, Taylor & Francis
,
Milton Park, UK
, pp.
229
257
.
35.
Li
,
S. Q.
,
Liu
,
R.
,
Wu
,
X. J.
, and
Zhang
,
Z.
,
2021
, “
Full-Range Fatigue Life Prediction of Metallic Materials Using Tanaka-Mura-Wu Model
,”
SAE Int. J. Mater. Manuf.
,
15
(
2
), pp.
133
153
.
36.
Li
,
S. Q.
,
Zhang
,
Z.
,
Liu
,
R.
, and
Wu
,
X. J.
,
2023
, “
Microstructure-Based Computational Fatigue Life Prediction of Haynes 282 Alloy
,”
J. Mater. Eng. Perform.
,
32
(
11
), pp.
5150
5166
.
37.
Hill
,
R.
,
1981
, “
A Theory of the Yielding and Plastic Flow of Anisotropic Metals
,”
Proc. R. Soc. A: Math. Phys. Eng. Sci.
,
193
(
1033
), pp.
281
297
. http://dx./doi.org/10.1098/rspa.1948.0045
38.
Huang
,
Y. G.
,
1991
, “
A User-Material Subroutine Incorporating Single Crystal Plasticity in the Abaqus Finite Element Program
.”
39.
Owolabi
,
G. M.
, and
Whitworth
,
H. A.
,
2014
, “
Modeling and Simulation of Microstructurally Small Crack Formation and Growth in Notched Nickel-Base Superalloy Component
,”
J. Mater. Sci. Technol.
,
30
(
3
), pp.
203
212
.
40.
Harren
,
S. V.
,
Dève
,
H. E.
, and
Asaro
,
R. J.
,
1988
, “
Shear Band Formation in Plane Strain Compression
,”
Acta Metall.
,
36
(
9
), pp.
2435
2480
.
41.
Peirce
,
D.
,
Asaro
,
R. J.
, and
Needleman
,
A.
,
1983
, “
Material Rate Dependence and Localized Deformation in Crystalline Solids
,”
Acta Metall.
,
31
(
12
), pp.
1951
1976
.
42.
Frederick
,
C. O.
, and
Armstrong
,
P. J.
,
2007
, “
A Mathematical Representation of the Multiaxial Bauschinger Effect
,”
Mater. High Temp.
,
24
(
1
), pp.
1
26
.
43.
Groeber
,
M. A.
, and
Jackson
,
M. A.
,
2014
, “
DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D
,”
Integr. Mater. Manuf. Innov.
,
3
(
1
), pp.
56
72
.
44.
Brommesson
,
R.
,
Ekh
,
M.
, and
Persson
,
C.
,
2016
, “
Experimental Observations and Modelling of Cyclic and Relaxation Behaviour of the Ni-Based Superalloy Haynes 282
,”
Int. J. Fatigue
,
87
, pp.
180
191
.
45.
Charles
,
K.
,
1996
, “Dislocations,”
Introduction to Solid State Physics
,
C.
Kittel
, eds.,
John Wiley and Sons
,
Hoboken, NJ
, pp.
597
618
.
46.
Tyson
,
W. R.
, and
Miller
,
W. A.
,
1977
, “
Surface Free Energies of Sold Metals Estimation From Liquid Surface Tension Measurements
,”
Surf. Sci.
,
62
(
1
), pp.
267
276
.
47.
Shiraiwa
,
T.
,
Briffod
,
F.
, and
Enoki
,
M.
,
2018
, “
Development of Integrated Framework for Fatigue Life Prediction in Welded Structures
,”
Eng. Fract. Mech.
,
198
, pp.
158
170
.
48.
Sweeney
,
C. A.
,
Vorster
,
W.
,
Leen
,
S. B.
,
Sakurada
,
E.
,
McHugh
,
P. E.
, and
Dunne
,
F. P. E.
,
2013
, “
The Role of Elastic Anisotropy, Length Scale and Crystallographic Slip in Fatigue Crack Nucleation
,”
J. Mech. Phys. Solids
,
61
(
5
), pp.
1224
1240
.
49.
Han
,
Q. N.
,
Qiu
,
W. H.
,
He
,
Z. W.
,
Su
,
Y.
,
Ma
,
X. F.
, and
Shi
,
H. J.
,
2018
, “
The Effect of Crystal Orientation on Fretting Fatigue Crack Formation in Ni-Based Single-Crystal Superalloys: In-Situ SEM Observation and Crystal Plasticity Finite Element Simulation
,”
Tribol. Int.
,
125
, pp.
209
219
.
50.
Tomkins
,
B.
,
1975
, “
The Development of Fatigue Crack Propagation Models for Engineering Applications at Elevated Temperatures
,”
ASME J. Eng. Mater. Technol.
,
97
(
4
), pp.
289
297
.
51.
Ramberg
,
G.
, and
Osgood
,
W. R.
,
1943
, “
Description of Stress–Strain Curves by Three Parameters
,” NACA Technical Note No. 902, National Advisory Committee for Aeronautics, pp.
1
13
.
52.
Sneddon
,
I. N.
,
1946
, “
The Distribution of Stress in Neighborhood of a Crack in a Elastic Solid
,”
Integr. Mater. Manuf. Innov.
,
187
(
1009
), pp.
229
260
. http://dx.doi.org/doi.org/10.1098/rspa.1946.0077
53.
Saha
,
D.
,
2015
, “Task 3: Materials for Non-Welded Rotors, Buckets, and Bolting,”
Materials for Advanced Ultrasupercritical Steam Turbines
,
Energy Industries of Ohio Incorporated
, OH,
USA
, pp.
23
109
.
54.
Stinville
,
J. C.
,
Charpagne
,
M. A.
,
Cervellon
,
A.
,
Hemery
,
S.
,
Wang
,
F.
,
Callahan
,
P. G.
,
Valle
,
V.
, and
Pollock
,
T. M.
,
2022
, “
On the Origins of Fatigue Strength in Crystalline Metallic Materials
,”
Science
,
377
(
6610
), pp.
1065
1071
.
55.
American Society for Testing and Materials E739
,
2015
,
Standard Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (ε−N) Fatigue Data
,
ASTM International
,
West Conshohocken, PA
. pp.
1
7
.
56.
Reid
,
C. N.
,
1973
, “Slip on More Than Two Systems–Multiple Slip,”
Deformation Geometry for Materials Scientists—A Volume in International Series on Materials Science and Technology
,
Pergamon Press
,
Oxford, UK
, pp.
145
178
.
57.
Luster
,
J.
, and
Morris
,
M. A.
,
1995
, “
Compatibility of Deformation in Two-Phase Ti-Al Alloys: Dependence on Microstructure and Orientation Relationships
,”
Metall. Mater. Trans. A
,
26
(
7
), pp.
1745
1756
.
58.
Bieler
,
T. R.
,
Eisenlohr
,
P.
,
Zhang
,
C.
,
Phukan
,
H. J.
, and
Crimp
,
M. A.
,
2014
, “
Grain Boundaries and Interfaces in Slip Transfer
,”
Curr. Opin. Solid State Mater. Sci.
,
18
(
4
), pp.
212
226
.
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