The creep deformation and damage evolution of nickel base superalloy (Waspaloy) at 700 °C are studied using the classic Kachanov–Rabotnov (KR) and a recently developed Sin-hyperbolic (Sinh) model. Uniaxial creep deformation and Bridgman rupture data collected from literature are used to determine the model constants and to compare the KR and the Sinh solutions. Finite-element (FE) simulations on a single eight-node element are conducted to validate the accuracy of the FE code. It is observed that KR cannot predict the creep deformation, damage, and rupture life of nickel base superalloys accurately using one set of constants for all the stress levels. The Sinh model exhibits a superior ability to predict the creep behavior using one set of constants for all the stress levels. Finite-element analysis (FEA) on 3D Bridgman notched Waspaloy specimen using the Sinh model is conducted. The results show that the Sinh model when combined with a representative stress equation and calibrated with experimental data can accurately predict the “notch effect” observed in the rupture life of notched specimen. Contour plots of damage evolution and stress redistribution are presented. It is demonstrated that the Sinh model is less stress sensitive, produces unconditional critical damage equal to unity at rupture, exhibits a more realistic damage distribution around the crack tip, and offers better crack growth analysis than KR.
Issue Section:
Materials and Fabrication
References
1.
Stewart
, C. M.
, and Gordon
, A. P.
, 2011
, “Strain and Damage-Based Analytical Methods to Determine the Kachanov-Rabotnov Tertiary Creep Damage Constants
,” Int. J. Damage Mech.
, 21
(8
): pp. 1186
–1201
.2.
Hyde
, T. H.
, Becker
, A. A.
, Sun
, W.
, Yaghi
, A.
, Williams
, J. A.
, and Concari
, S.
, 2006
, “Determination of Creep Properties for P91 Weldment Materials at 625 °C
,” 5th International Conference on Mechanics and Materials in Design
, University of Porto, Porto, Portugal, Vol. 1, pp. 1
–13
.3.
Goodall
, I. W.
, and Skelton
, R. P.
, 2004
, “The Importance of Multiaxial Stress in Creep Deformation and Rupture
,” Fatigue Fract. Eng. Mater. Struct.
, 27
(4
), pp. 267
–272
.4.
Ha
, J.
, Tabuchi
, M.
, Hongo
, H.
, Yokobori
, A. T.
, and Fuji
, A.
, 2004
, “Creep Crack Growth Properties for 12CrWCoB Rotor Steel Using Circular Notched Specimens
,” Int. J. Pressure Vessels Piping
, 81
(5
), pp. 401
–407
.5.
Lukáš
, P.
, Preclı́k
, P.
, and Čadek
, J.
, 2001
, “Notch Effects on Creep Behaviour of CMSX-4 Superalloy Single Crystals
,” Mater. Sci. Eng. A
, 298
(1
), pp. 84
–89
.6.
Hosseini
, E.
, Holdsworth
, S. R.
, and Mazza
, E.
, 2013
, “Stress Regime-Dependent Creep Constitutive Model Considerations in Finite Element Continuum Damage Mechanics
,” Int. J. Damage Mech.
, 22
(8
), pp. 1186
–1205
.7.
Yao
, H. T.
, Xuan
, F. Z.
, Wang
, Z.
, and Tu
, S. T.
, 2007
, “A Review of Creep Analysis and Design Under Multi-Axial Stress States
,” Nucl. Eng. Des.
, 237
(18
), pp. 1969
–1986
.8.
Yu
, T.
, Yatomi
, M.
, and Shi
, H. J.
, 2009
, “Numerical Investigation on the Creep Damage Induced by Void Growth in Heat Affected Zone of Weldments
,” Int. J. Pressure Vessels Piping
, 86
(9
), pp. 578
–584
.9.
Rouse
, J. P.
, Sun
, W.
, Hyde
, T. H.
, and Morris
, A.
, 2013
, “Comparative Assessment of Several Creep Damage Models for Use in Life Prediction
,” Int. J. Pressure Vessels Piping
, 108
, pp. 81
–87
.10.
Dyson
, B.
, 2000
, “Use of CDM in Materials Modeling and Component Creep Life Prediction
,” ASME J. Pressure Vessel Technol.
, 122
(3
), pp. 281
–296
.11.
Hyde
, T. H.
, Becker
, A. A.
, Sun
, W.
, and Williams
, J. A.
, 2006
, “Finite-Element Creep Damage Analyses of P91 Pipes
,” Int. J. Pressure Vessels Piping
, 83
(11
), pp. 853
–863
.12.
Stewart
, C. M.
, 2013
, “A Hybrid Constitutive Model for Creep, Fatigue, and Creep-Fatigue Damage
,” Ph.D. dissertation, University of Central Florida, Orlando, FL.13.
Haque
, M. S.
, and Stewart
, C. M.
, 2015
, “Comparison of a New Sin-Hyperbolic Creep Damage Constitutive Model With the Classic Kachanov-Rabotnov Model Using Theoretical and Numerical Analysis
,” TMS2015 Supplemental Proceedings
, pp. 937
–945
.14.
Yatomi
, M.
, Nikbin
, K. M.
, and O'Dowd
, N. P.
, 2003
, “Creep Crack Growth Prediction Using a Damage Based Approach
,” Int. J. Pressure Vessels Piping
, 80
(7
), pp. 573
–583
.15.
Cocks
, A. C. F.
, and Ashby
, M. F.
, 1980
, “Intergranular Fracture During Power-Law Creep Under Multiaxial Stresses
,” Metal Sci.
, 14
(8–9
), pp. 395
–402
.16.
Bernstein
, H. L.
, 1998
, “Materials Issues for Users of Gas Turbines
,” 27th Turbomachinery Symposium
, Turbomachinery Laboratory, Texas A&M University, College Station, TX, pp. 129
–179
.17.
Yu
, Q. M.
, Wang
, Y.
, Wen
, Z. X.
, and Yue
, Z. F.
, 2009
, “Notch Effect and Its Mechanism During Creep Rupture of Nickel-Base Single Crystal Superalloys
,” Mater. Sci. Eng. A
, 520
(1
), pp. 1
–10
.18.
Hyde
, T. H.
, Xia
, L.
, and Becker
, A. A.
, 1996
, “Prediction of Creep Failure in Aero Engine Materials Under Multi-Axial Stress States
,” Int. J. Mech. Sci.
, 38
(4
), pp. 385
–403
.19.
Jiang
, Y. P.
, Guo
, W. L.
, Yue
, Z. F.
, and Wang
, J.
, 2006
, “On the Study of the Effects of Notch Shape on Creep Damage Development Under Constant Loading
,” Mater. Sci. Eng., A
, 437
(2
), pp. 340
–347
.20.
Yu
, Q. M.
, Yue
, Z. F.
, and Liu
, Y. S.
, 2005
, “Numerical Study on the Creep Damage Development in Circumferential Notched Specimens Under Cyclic Loading
,” Mater. Sci. Eng., A
, 406
(1
), pp. 166
–171
.21.
Hayhurst
, D. R.
, Dimmer
, P. R.
, and Morrison
, C. J.
, 1984
, “Development of Continuum Damage in the Creep Rupture of Notched Bars
,” Philos. Trans. R. Soc., A
, 311
(1516
), pp. 103
–129
.22.
Ng
, S. E.
, Webster
, G. A.
, and Dyson
, B. F.
, 1981
, “Notch Weakening and Strengthening in Creep of 05Cr 05Mo 025 Steel
,” ICF5, Cannes, France, pp. 1275
–1283
.23.
Fuji
, A.
, Tabuchi
, M.
, Yokobori
, A. T.
, and Yokobori
, T.
, 1999
, “Influence of Notch Shape and Geometry During Creep Crack Growth Testing of Ti-Al Intermetallic Compounds
,” Eng. Fract. Mech.
, 62
(1
), pp. 23
–32
.24.
Webster
, G. A.
, Holdsworth
, S. R.
, Loveday
, M. S.
, Nikbin
, K.
, Perrin
, I. J.
, Purper
, H.
, and Spindler
, M. W.
, 2004
, “A Code of Practice for Conducting Notched Bar Creep Tests and for Interpreting the Data
,” Fatigue Fract. Eng. Mater. Struct.
, 27
(4
), pp. 319
–342
.25.
Liu
, Y.
, and Murakami
, S.
, 1998
, “Damage Localization of Conventional Creep Damage Models and Proposition of a New Model for Creep Damage Analysis
,” JSME Int. J., Ser. A
, 41
(1
), pp. 57
–65
.26.
Hayhurst
, D. R.
, 1972
, “Creep Rupture Under Multi-Axial States of Stress
,” J. Mech. Phys. Solids
, 20
(6
), pp. 381
–382
.27.
Othman
, A. M.
, and Hayhurst
, D. R.
, 1993
, “Determination of Large Strain Multi-Axial Creep Rupture Criteria Using Notched-Bar Data
,” Int. J. Damage Mech.
, 2
(1
), pp. 16
–52
.28.
Stewart
, C. M.
, 2009
, “Tertiary Creep Damage Modeling of a Transversely Isotropic Ni-Based Superalloy
,” M.Sc. thesis
, University of Central Florida, Orlando, FL.29.
Hill
, R.
, 1948
, “A Theory of the Yielding and Plastic Flow of Anisotropic Metals
,” Proc. R. Soc. London A
, 193
(1033
), pp. 281
–297
.30.
Kachanov
, L. M.
, 1958
, “Time of the Rupture Process Under Creep Conditions
,” Isv. Akad. Nauk SSR Otd Tekh. Nauk
, 8
, pp. 26
–31
.31.
Rabotnov
, Y. N.
, 1969
, Creep Problems in Structural Members
, Wiley-VCH Verlag GmbH and Co. KGaA
, Weinheim, Germany
.32.
McVetty
, P. G.
, 1943
, “Creep of Metals at Elevated Temperatures–Hyperbolic-Sine Relation Between Stress and Creep Rate
,” Trans. ASME
, 65
(7
), pp. 761
–767
.33.
Haque
, M. S.
, 2015
, “An Improved Sin-Hyperbolic Constitutive Model for Creep Deformation and Damage
,” Dissertation
, The University of Texas, El Paso, TX.34.
Spindler
, M. W.
, Hales
, R.
, and Skelton
, R. P.
, 2001
, “The Multiaxial Creep Ductility of an Ex-Service Type 316H Stainless Steel
,” Book-Inst. Mater.
, 769
, pp. 679
–690
.35.
Hayhurst
, D. R.
, Brown
, P. R.
, and Morrison
, C. J.
, 1984
, “The Role of Continuum Damage in Creep Crack Growth
,” Philos. Trans. R. Soc., A
, 311
(1516
), pp. 131
–158
.36.
Spindler
, M. W.
, 2004
, “The Multiaxial Creep Ductility of Austenitic Stainless Steels
,” Fatigue Fract. Eng. Mater. Struct.
, 27
(4
), pp. 273
–281
.37.
Chellapandi
, P.
, Srinivasan
, R.
, Chetal
, S. C.
, and Raj
, B.
, 2006
, “Experimental Creep Life Assessment of Tubular Structures With Geometrical Imperfections in Welds With Reference to Fast Reactor Plant Life
,” Int. J. Pressure Vessels Piping
, 83
(7
), pp. 556
–564
.38.
Al-Abed
, B.
, Timmins
, R.
, Webster
, G. A.
, and Loveday
, M. S.
, 1999
, “Validation of a Code of Practice for Notched Bar Creep Rupture Testing: Procedures and Interpretation of Data for Design
,” Mater. High Temp.
, 16
(3
), pp. 143
–158
.39.
Hyde
, T. H.
, Jones
, I. A.
, Peravali
, S.
, Sun
, W.
, Wang
, J. G.
, and Leen
, S. B.
, 2005
, “Anisotropic Creep Behaviour of Bridgman Notch Specimens
,” Proc. Inst. Mech. Eng., Part L
, 219
(3
), pp. 163
–175
.40.
Lin
, G.
, 1999
, ANSYS User Material Subroutine USERMAT
, ANSYS, Inc.
, Canonsburg, PA
.41.
ANSYS Academic Research
, Mechanical APDL
, Release 15.0, ANSYS, Inc.
, Canonsburg, PA
.42.
Becker
, A. A.
, Hyde
, T. H.
, Sun
, W.
, and Andersson
, P.
, 2002
, “Benchmarks for Finite Element Analysis of Creep Continuum Damage Mechanics
,” Comput. Mater. Sci.
, 25
(1
), pp. 34
–41
.43.
Murakami
, S.
, and Liu
, Y.
, 1995
, “Mesh-Dependence in Local Approach to Creep Fracture
,” Int. J. Damage Mech.
, 4
(3
), pp. 230
–250
.44.
Wisniewski
, A.
, and Beddoes
, J.
, 2009
, “Influence of Grain-Boundary Morphology on Creep of a Wrought Ni-Base Superalloy
,” Mater. Sci. Eng., A
, 510
, pp. 266
–272
.45.
Yao
, Z.
, Zhang
, M.
, and Dong
, J.
, 2013
, “Stress Rupture Fracture Model and Microstructure Evolution for Waspaloy
,” Metall. Mater. Trans. A
, 44
(7
), pp. 3084
–3098
.46.
Hong
, H. U.
, Kim
, I. S.
, Choi
, B. G.
, Kim
, M. Y.
, and Jo
, C. Y.
, 2009
, “The Effect of Grain Boundary Serration on Creep Resistance in a Wrought Nickel-Based Superalloy
,” Mater. Sci. Eng., A
, 517
(1
), pp. 125
–131
.47.
Soula
, A.
, Renollet
, Y.
, Boivin
, D.
, Pouchou
, J. L.
, Locq
, D.
, Caron
, P.
, and Bréchet
, Y.
, 2009
, “Analysis of High-Temperature Creep Deformation in a Polycrystalline Nickel-Base Superalloy
,” Mater. Sci. Eng., A
, 510
, pp. 301
–306
.48.
Floreen
, S.
, 1975
, “The Creep Fracture of Wrought Nickel-Base Alloys by a Fracture Mechanics Approach
,” Metall. Trans. A
, 6
(9
), pp. 1741
–1749
.49.
Floreen
, S.
, and Kane
, R. H.
, 1976
, “A Critical Strain Model for the Creep Fracture of Nickel-Base Superalloys
,” Metall. Trans. A
, 7
(8
), pp. 1157
–1160
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