The aim of this paper is to investigate different factors, including dwell time, strain range, and strain ratio on creep-fatigue endurances in nickel-based Inconel 718 and GH4169 superalloys. We also summarize classic approaches for life assessments based on the generalizations of Coffin–Manson equation, linear damage summation (LDS), and strain-range partitioning (SRP) method. Each approach does have some degree of success in dealing with a specific set of creep–fatigue data. In order to evaluate the prediction capabilities of the validated approaches, a Bayesian information criterion (BIC) allowing for maximum likelihood and principle of parsimony is used to select the best performing model.

References

References
1.
Zhu
,
S.-P.
,
Yang
,
Y.-J.
,
Huang
,
H.-Z.
,
Lv
,
Z.
, and
Wang
,
H.-K.
,
2017
, “
A Unified Criterion for Fatigue–Creep Life Prediction of High Temperature Components
,”
Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng.
,
231
(
4
), pp.
677
688
.
2.
Zhang
,
X.-C.
,
Tu
,
S.-T.
, and
Xuan
,
F.-Z.
,
2014
, “
Creep–Fatigue Endurance of 304 Stainless Steels
,”
Theor. Appl. Fract. Mech.
,
71
, pp.
51
66
.
3.
Yan
,
X.-L.
,
Zhang
,
X.-C.
,
Tu
,
S.-T.
,
Mannan
,
S.-L.
,
Xuan
,
F.-Z.
, and
Lin
,
Y.-C.
,
2015
, “
Review of Creep–Fatigue Endurance and Life Prediction of 316 Stainless Steels
,”
Int. J. Pressure Vessels Piping
,
126–127
, pp.
17
28
.
4.
Hales
,
R.
,
1980
, “
A Quantitative Metallographic Assessment of Structural Degradation of Type 316 Stainless Steel During Creep-Fatigue
,”
Fatigue Fract. Eng. Mater. Struct.
,
3
(
4
), pp.
339
356
.
5.
Zhu
,
S.-P.
,
Huang
,
H.-Z.
,
He
,
L.-P.
,
Liu
,
Y.
, and
Wang
,
Z.
,
2012
, “
A Generalized Energy-Based Fatigue–Creep Damage Parameter for Life Prediction of Turbine Disk Alloys
,”
Eng. Fract. Mech.
,
90
, pp.
89
100
.
6.
Zhu
,
S. P.
,
Lei
,
Q.
, and
Wang
,
Q. Y.
,
2017
, “
Mean Stress and Ratcheting Corrections in Fatigue Life Prediction of Metals
,”
Fatigue Fract. Eng. Mater. Struct.
,
40
(
9
), pp.
1343
1354
.
7.
Ghonem
,
H.
, and
Zheng
,
D.
,
1992
, “
Frequency Interactions in High-Temperature Fatigue Crack Growth in Superalloys
,”
Metall. Trans. A
,
23
(
11
), pp.
3067
3072
.
8.
McDowell
,
D. L.
, and
Miller
,
M. P.
,
1981
, “
Physically Based Microcrack Propagation Laws for Creep-Fatigue-Environment Interaction
,”
ASME Winter Annual Meeting
, Washington, DC, Nov. 15–20, pp.
19
30
.
9.
Wang
,
R.-Z.
,
Chen
,
B.
,
Zhang
,
X.-C.
,
Tu
,
S.-T.
,
Wang
,
J.
, and
Zhang
,
C.-C.
,
2017
, “
The Effects of Inhomogeneous Microstructure and Loading Waveform on Creep-Fatigue Behaviour in a Forged and Precipitation Hardened Nickel-Based Superalloy
,”
Int. J. Fatigue
,
97
, pp.
190
201
.
10.
Takahashi
,
Y.
,
2008
, “
Study on Creep-Fatigue Evaluation Procedures for High Chromium Steels—Part II: Sensitivity to Calculated Deformation
,”
Int. J. Pressure Vessels Piping
,
85
(
6
), pp.
423
440
.
11.
Fournier
,
B.
,
Sauzay
,
M.
,
Caes
,
C.
,
Noblecourt
,
M.
,
Mottot
,
M.
,
Bougault
,
A.
,
Rabeau
,
V.
, and
Pineau
,
A.
,
2008
, “
Creep-Fatigue-Oxidation Interactions in a 9Cr–1Mo Martensitic Steel—Part II: Effect of Compressive Holding Period on Fatigue Lifetime
,”
Int. J. Fatigue
,
30
(
4
), pp.
663
676
.
12.
Skelton
,
R. P.
,
2003
, “
Creep-Fatigue Interactions (Crack Initiation)
,”
Compr. Struct. Integrity
,
5
, pp.
25
112
.
13.
Kalluri
,
S.
,
Manson
,
S.
, and
Halford
,
G. R.
,
1987
, “
Exposure Time Considerations in High Temperature Low Cycle Fatigue
,” NASA Lewis Research Center, Cleveland, OH, NASA Technical Memorandum TM 88934.
14.
Challenger
,
K. D.
,
Miller
,
A. K.
, and
Brinkman
,
C. R.
,
1981
, “
An Explanation for the Effects of Hold Periods on the Elevated Temperature Fatigue Behavior of 2 1/4 Cr–1 Mo Steel
,”
ASME J. Eng. Mater. Technol.
,
103
(
1
), pp.
7
14
.
15.
François
,
D.
,
Pineau
,
A.
, and
Zaoui
,
A.
,
2012
,
Mechanical Behaviour of Materials: Volume II: Fracture Mechanics and Damage
, Vol. 191,
Springer Science & Business Media
, Berlin.
16.
Aoto
,
K.
,
Komine
,
R.
,
Ueno
,
F.
,
Kawasaki
,
H.
, and
Wada
,
Y.
,
1994
, “
Creep-Fatigue Evaluation of Normalized and Tempered Modified 9Cr-1Mo
,”
Nucl. Eng. Des.
,
153
(
1
), pp.
97
110
.
17.
Tong
,
J.
,
Dalby
,
S.
,
Byrne
,
J.
,
Henderson
,
M.
, and
Hardy
,
M.
,
2001
, “
Creep, Fatigue and Oxidation in Crack Growth in Advanced Nickel Base Superalloys
,”
Int. J. Fatigue
,
23
(
10
), pp.
897
902
.
18.
Deng
,
G.-J.
,
Tu
,
S.-T.
,
Zhang
,
X.-C.
,
Wang
,
Q.-Q.
, and
Qin
,
C.-H.
,
2015
, “
Grain Size Effect on the Small Fatigue Crack Initiation and Growth Mechanisms of Nickel-Based Superalloy GH4169
,”
Eng. Fract. Mech.
,
134
, pp.
433
450
.
19.
Leo Prakash
,
D. G.
,
Walsh
,
M. J.
,
Maclachlan
,
D.
, and
Korsunsky
,
A. M.
,
2009
, “
Crack Growth Micro-Mechanisms in the IN718 Alloy Under the Combined Influence of Fatigue, Creep and Oxidation
,”
Int. J. Fatigue
,
31
(
11–12
), pp.
1966
1977
.
20.
Bhattacharyya
,
A.
,
Sastry
,
G.
, and
Kutumbarao
,
V.
,
1997
, “
On the Dual Slope Coffin-Manson Relationship During Low Cycle Fatigue of Ni-Base Alloy in 718
,”
Scr. Mater.
,
36
(
4
), pp.
411
415
.
21.
Andrews
,
R. G.
,
1992
, “
High Temperature Fatigue Crack Initiation and Propagation Behaviour in Inconel 718 Turbine Discs
,”
National Library of Canada
, Gatineau, QC, Canada.
22.
Brinkman
,
C. R.
,
1985
, “
High-Temperature Time-Dependent Fatigue Behaviour of Several Engineering Structural Alloys
,”
Int. Met. Rev.
,
30
(
1
), pp.
235
258
.
23.
Thakker
,
A. B.
, and
Cowles
,
B. A.
,
1983
, “
Low Strain, Long Life Creep Fatigue of AF2-1DA and INCO 718
,” National Aeronautics and Space Administration, Springfield, VA, Technical Report No.
NASA CR-167989
.
24.
Shahani
,
V.
, and
Popp
,
H. G.
,
1978
, “
Evaluation of Cyclic Behavior of Aircraft Turbine Disk Alloys
,” National Aeronautics and Space Administration, Washington, DC, Technical Report No.
NASA-CR-159433
.
25.
Prasad
,
K.
,
Sarkar
,
R.
,
Ghosal
,
P.
, and
Kumar
,
V.
,
2013
, “
Simultaneous Creep–Fatigue Damage Accumulation of Forged Turbine Disc of in 718 Superalloy
,”
Mater. Sci. Eng. A
,
572
, pp.
1
7
.
26.
Zhang
,
X.-C.
,
Li
,
H.-C.
,
Zeng
,
X.
,
Tu
,
S.-T.
,
Zhang
,
C.-C.
, and
Wang
,
Q.-Q.
,
2017
, “
Fatigue Behavior and Bilinear Coffin-Manson Plots of Ni-Based GH4169 Alloy With Different Volume Fractions of δ Phase
,”
Mater. Sci. Eng. A
,
682
, pp.
12
22
.
27.
Wei
,
D.-S.
, and
Yang
,
X.-G.
,
2009
, “
Investigation and Modeling of Low Cycle Fatigue Behaviors of Two Ni-Based Superalloys Under Dwell Conditions
,”
Int. J. Pressure Vessels Piping
,
86
(
9
), pp.
616
621
.
28.
Wang
,
R.-Z.
,
Zhang
,
X.-C.
,
Gong
,
J.-G.
,
Zhu
,
X.-M.
,
Tu
,
S.-T.
, and
Zhang
,
C.-C.
,
2017
, “
Creep-Fatigue Life Prediction and Interaction Diagram in Nickel-Based GH4169 Superalloy at 650 °C Based on Cycle-by-Cycle Concept
,”
Int. J. Fatigue
,
97
, pp.
114
123
.
29.
Chen
,
G.
,
Zhang
,
Y.
,
Xu
,
D. K.
,
Lin
,
Y. C.
, and
Chen
,
X.
,
2016
, “
Low Cycle Fatigue and Creep-Fatigue Interaction Behavior of Nickel-Base Superalloy GH4169 at Elevated Temperature of 650 °C
,”
Mater. Sci. Eng. A
,
655
, pp.
175
182
.
30.
Shang
,
D.
,
Sun
,
G.
,
Yan
,
C.
,
Chen
,
J.
, and
Cai
,
N.
,
2007
, “
Creep-Fatigue Life Prediction Under Fully-Reversed Multiaxial Loading at High Temperatures
,”
Int. J. Fatigue
,
29
(
4
), pp.
705
712
.
31.
Yu
,
Z.-Y.
,
Zhu
,
S.-P.
,
Liu
,
Q.
, and
Liu
,
Y.
,
2017
, “
A New Energy-Critical Plane Damage Parameter for Multiaxial Fatigue Life Prediction of Turbine Blades
,”
Materials
,
10
(
5
), p.
E513
.
32.
Manson
,
S. S.
,
1954
, “
Behavior of Materials Under Conditions of Thermal Stress
,” National Advisory Committee for Aeronautics, Washington, DC, Technical Report No.
NACA-TR-1170
.
33.
Ostergren
,
W. J.
,
1976
, “
A Damage Function and Associated Failure Equations for Predicting Hold Time and Frequency Effects in Elevated Temperature, Low Cycle Fatigue
,”
J. Test. Eval.
,
4
(
5
), pp.
327
339
.
34.
Halford
,
G. R.
, 1991, “
Evolution of Creep-Fatigue Life Prediction Models
,”
112th ASME Winter Annual Meeting
, Atlanta, GA, Dec. 1–6, pp.
43
57
.
35.
Coffin
,
L. F.
,
1973
, “
Fatigue at High Temperature
,”
Fatigue at Elevated Temperatures
,
ASTM International
, West Conshohocken, PA, Paper No. STP 520.
36.
Coffin
,
L. F.
,
1969
, “
A Generalized Equation for Predicting High-Temperature, Low-Cycle Fatigue, Including Hold Times
,” GE Research and Development Center, Shanghai, China, Report No. AFFDL TR 70-144.
37.
Coffin
,
L. F.
,
1976
, “
Concept of Frequency Separation in Life Prediction for Time-Dependent Fatigue
,”
General Electric
,
Schenectady, NY
.
38.
Robinson
,
E. L.
,
1952
, “
Effect of Temperature Variation on the Long-Time Rupture Strength of Steels
,”
Trans. ASME
,
74
(
5
), pp.
777
781
.
39.
Miner
,
M. A.
,
1945
, “
Cumulative Damage in Fatigue
,”
ASME J. Appl. Mech.
,
12
(
3
), pp.
159
164
.
40.
Priest
,
R. H.
, and
Ellison
,
E. G.
,
1981
, “
A Combined Deformation Map-Ductility Exhaustion Approach to Creep-Fatigue Analysis
,”
Mater. Sci. Eng.
,
49
(
1
), pp.
7
17
.
41.
Hales
,
R.
,
1983
, “
A Method of Creep Damage Summation Based on Accumulated Strain for the Assessment of Creep‐Fatigue Endurance
,”
Fatigue Fract. Eng. Mater. Struct.
,
6
(
2
), pp.
121
135
.
42.
Spindler
,
M. W.
,
2005
, “
The Prediction of Creep Damage in Type 347 Weld Metal—Part I: The Determination of Material Properties From Creep and Tensile Tests
,”
Int. J. Pressure Vessels Piping
,
82
(
3
), pp.
175
184
.
43.
Spindler
,
M. W.
, and
Payten
,
W. M.
,
2011
, “
Advanced Ductility Exhaustion Methods for the Calculation of Creep Damage During Creep-Fatigue Cycling
,”
J. ASTM Int.
,
8
(
7
), pp.
1
19
.
44.
Manson
,
S. S.
, and
Halford
,
G. R.
,
2009
,
Fatigue and Durability of Metals at High Temperatures
,
ASM International
, Materials Park, OH.
45.
Manson
,
S. S.
,
Halford
,
G. R.
, and
Hirschberg
,
M. H.
,
1971
, “
Creep-Fatigue Analysis by Strain-Range Partitioning
,” ASME Symposium on Design for Elevated Temp-Environment, San Francisco, CA, May 10–12.
46.
He
,
J.
,
Duan
,
Z.
,
Ning
,
Y.
, and
Zhao
,
D.
, 1983, “
Strain Energy Partitioning and Its Application to GH33A Nickel-Base Superalloy and 1Cr–18Ni–9Ti Stainless Steel
,” ASME International Conference on Advances in Life Prediction Methods, Albany, NY, Apr. 18–20.
47.
Wong
,
E. H.
,
van Driel
,
W. D.
,
Dasgupta
,
A.
, and
Pecht
,
M.
,
2016
, “
Creep Fatigue Models of Solder Joints: A Critical Review
,”
Microelectron. Reliab.
,
59
, pp.
1
12
.
48.
Wang
,
R.-Z.
,
Zhang
,
X.-C.
,
Tu
,
S.-T.
,
Zhu
,
S.-P.
, and
Zhang
,
C.-C.
,
2016
, “
A Modified Strain Energy Density Exhaustion Model for Creep–Fatigue Life Prediction
,”
Int. J. Fatigue
,
90
, pp.
12
22
.
49.
Manson
,
S. S.
,
1965
, “
Fatigue: A Complex Subject—Some Simple Approximations
,”
Exp. Mech.
,
5
(
4
), pp.
193
226
.
50.
ASME,
1996
, “
ASME and Boiler Pressure Vessel Code Section III, Subsection-NH 2005
,” American Society of Mechanical Engineers, New York.
51.
Ainsworth
,
R. A.
,
2006
, “
R5 Procedures for Assessing Structural Integrity of Components Under Creep and Creep–Fatigue Conditions
,”
Int. Mater. Rev.
,
51
(
2
), pp.
107
126
.
52.
Halford
,
G. R.
, and
Saltsman
,
J. F.
,
1983
, “
Strainrange Partitioning: A Total Strain Range Version
,” NASA Lewis Research Center, Cleveland, OH, Technical Report No.
NASA TM-83023
.
53.
Takahashi
,
Y.
,
2008
, “
Study on Creep-Fatigue Evaluation Procedures for High-Chromium Steels—Part I: Test Results and Life Prediction Based on Measured Stress Relaxation
,”
Int. J. Pressure Vessels Piping
,
85
(
6
), pp.
406
422
.
54.
Takahashi
,
Y.
,
Dogan
,
B.
, and
Gandy
,
D.
, “
Systematic Evaluation of Creep-Fatigue Life Prediction Methods for Various Alloys
,”
ASME
Paper No. PVT-11-1141.
55.
Andrieu
,
E.
,
Molins
,
R.
,
Ghonem
,
H.
, and
Pineau
,
A.
,
1992
, “
Intergranular Crack Tip Oxidation Mechanism in a Nickel-Based Superalloy
,”
Mater. Sci. Eng. A
,
154
(
1
), pp.
21
28
.
56.
Pineau
,
A.
, and
Antolovich
,
S. D.
,
2009
, “
High Temperature Fatigue of Nickel-Base Superalloys—A Review With Special Emphasis on Deformation Modes and Oxidation
,”
Eng. Failure Anal.
,
16
(
8
), pp.
2668
2697
.
57.
Shankar
,
V.
,
Valsan
,
M.
,
Rao
,
K. B. S.
,
Kannan
,
R.
,
Mannan
,
S. L.
, and
Pathak
,
S. D.
,
2006
, “
Low Cycle Fatigue Behavior and Microstructural Evolution of Modified 9Cr–1Mo Ferritic Steel
,”
Mater. Sci. Eng. A
,
437
(
2
), pp.
413
422
.
58.
Dyson
,
B. F.
,
1976
, “
Constraints on Diffusional Cavity Growth Rates
,”
Met. Sci.
,
10
(
10
), pp.
349
353
.
59.
Skelton
,
R. P.
,
2014
, “
The Energy Density Exhaustion Method for Assessing the Creep-Fatigue Lives of Specimens and Components
,”
Mater. High Temp.
,
30
(
3
), pp.
183
201
.
60.
Spera
,
D. A.
,
1973
, “
Comparison of Experimental and Theoretical Thermal Fatigue Lives for Five Nickel-Base Alloys
,”
Fatigue at Elevated Temperatures
,
ASTM International
, West Conshohocken, PA, pp. 648–657.
61.
Schwarz
,
G.
,
1978
, “
Estimating the Dimension of a Model
,”
Ann. Stat
,
6
(
2
), pp.
461
464
.
62.
Biem
,
A.
,
2003
, “
A Model Selection Criterion for Classification: Application to Hmm Topology Optimization
,”
IEEE
Seventh International Conference on Document Analysis and Recognition,
Edinburgh, UK, Aug. 3–6, pp.
104
108
.
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