Additive creep rate model has been developed to predict creep strain-time behavior of materials important to engineering creep design of components for high temperature applications. The model has two additive formulations: the first one is related to sine hyperbolic rate equation describing primary and secondary creep deformation based on the evolution of internal stress with strain/time, and the second defines the tertiary creep rate as a function of tertiary creep strain. In order to describe creep data accurately, tertiary creep rate relation based on MPC-Omega methodology has been appropriately modified. The applicability of the model has been demonstrated for tempered martensitic plain 9Cr-1Mo steel for different applied stresses at 873 K. Based on the observations, a power law relationship between internal stress and applied stress has been established for the steel. Further, a higher creep damage accumulation with increasing life fraction has been observed at low stresses than those obtained at high stresses.
Issue Section:
Materials and Fabrication
References
1.
Evans
, M.
, 2013
, “The Potential United Kingdom Energy Gap and Creep Life Prediction Methodologies
,” Metall. Mater. Trans. A
, 44
(S1
), pp. 109
–127
.2.
Li
, J. C. M.
, 1963
, “A Dislocation Mechanism for Transient Creep
,” Acta Metall.
, 11
(11
), pp. 1269
–1270
.3.
Akulov
, N. S.
, 1964
, “On the Dislocation Kinetics
,” Acta Metall.
, 12
(10
), pp. 1195
–1196
.4.
Evans
, R. W.
, and Wilshire
, B.
, 1985
, Creep of Metals and Alloys
, Institute of Metals
, London
.5.
Kloos
, K.
, Granacher
, J.
, and Monsees
, M.
, 1998
, “Creep Equations for Heat Resistant Steels
,” Steel Res. Int.
, 69
(10–11
), pp. 446
–456
.6.
Stouffer
, D. C.
, and Dame
, L. T.
, 1996
, Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy
, Wiley Interscience
, New York
.7.
Sasikala
, G.
, Ray
, S. K.
, and Mannan
, S. L.
, 2004
, “Evolution of Damage in Tertiary Creep of Type 316 L(N) Weld Metal
,” Acta Mater.
, 52
(19
), pp. 5677
–5686
.8.
Kachanov
, L. M.
, 1960
, The Theory of Creep
, Wetherby
, Boston, MA
.9.
Rabotnov
, Y. N.
, 1969
, Creep Problems in Structural Members
, North-Holland
, Amsterdam, The Netherlands
.10.
Murakami
, S.
, 2012
, Continuum Damage Mechanics: A Continuum Mechanics Approach to the Analysis of Damage and Fracture
, Springer
, New York
.11.
Dyson
, B.
, 2000
, “Use of CDM in Materials Modelling and Component Creep Life Prediction
,” ASME J. Pressure Vessel Technol.
, 122
(3
), pp. 281
–296
.12.
Semba
, H.
, Dyson
, B.
, and McLean
, M.
, 2008
, “Microstructure-Based Creep Modelling of a 9% Cr Martensitic Steel
,” Mater. High. Temp.
, 25
(3
), pp. 131
–137
.13.
Hore
, S.
, and Ghosh
, R. N.
, 2011
, “Computer Simulation of the High Temperature Creep Behaviour of Cr–Mo Steels
,” Mater. Sci. Eng. A
, 528
(19–20
), pp. 6095
–6102
.14.
Christopher
, J.
, and Choudhary
, B. K.
, 2016
, “Constitutive Description of Primary and Steady State Creep Deformation Behaviour of Tempered Martensitic 9Cr-1Mo Steel
,” Philos. Mag.
, 96
(21
), pp. 2256
–2279
.15.
Prager
, M.
, 2000
, “The Omega Method—An Engineering Approach to Life Assessment
,” ASME J. Pressure Vessel. Technol.
, 122
(3
), pp. 273
–280
.16.
Orowan
, E.
, 1940
, “Problems of Plastic Gliding
,” Proc. Phys. Soc.
, 52
(1
), pp. 8
–22
.17.
Gibbs
, G. B.
, 1969
, “Thermodynamic Analysis of Dislocation Glide Controlled by Dispersed Local Obstacles
,” Mater. Sci. Eng.
, 4
(6
), pp. 313
–328
.18.
Friedel
, J.
, 1964
, Dislocations
, Pergamon Press
, Oxford, UK
.19.
Estrin
, Y.
, and Mecking
, H.
, 1984
, “A Unified Phenomenological Description of Work Hardening and Creep Based on One Parameter Models
,” Acta Metall.
, 32
(1
), pp. 57
–70
.20.
Orlova
, A.
, and Milicka
, K.
, 1996
, “Constitutive Description of Creep in Silicon Iron at High Temperatures
,” J. Mater. Sci.
, 31
(12
), pp. 3325
–3330
.21.
Estrin
, Y.
, 1996
, “Dislocation Density Related Constitutive Modelling
,” Unified Constitutive Laws of Plastic Deformation
, A. S.
Krausz
, and K.
Krausz
, eds., Academic Press
, San Diego, CA
, pp. 69
–104
.22.
Abe
, F.
, 2011
, “Creep Life Estimation of Gr. 91 Based on Creep Strain Analysis
,” Mater. High. Temp.
, 28
(2
), pp. 75
–84
.23.
Nocedal
, J.
, and Wright
, S. J.
, 2006
, Numerical Optimization, Springer Series in Operation Research
, Springer
, New York
.24.
Nakajima
, T.
, Spigarelli
, S.
, Evangelista
, E.
, and Endo
, T.
, 2003
, “Strain Enhanced Growth of Precipitates During Creep of T91
,” Mater. Trans.
, 44
(9
), pp. 1802
–1808
.25.
Abe
, F.
, 2008, “Strengthening Mechanisms in Steel for Creep and Creep Rupture
,” Creep-Resistant Steels.
, F.
Abe
, T. U.
Kern
, and R.
Viswanathan
, ed., Woodhead Publishing
, Cambridge, UK
, pp.279
–304
.26.
Wang
, L.
, Li
, M.
, and Almer
, J.
, 2014
, “Investigation of Deformation and Microstructural Evolution in Grade 91 Ferritic-Martensitic Steel by In-Situ High-Energy X-Rays
,” Acta Mater.
, 62
, pp. 239
–249
.27.
Choudhary
, B. K.
, 2013
, “Tertiary Creep Behaviour of 9Cr-1Mo Ferritic Steel
,” Mater. Sci. Eng. A
, 585
, pp. 1
–9
.28.
Choudhary
, B. K.
, and Christopher
, J.
, 2016
, “Comparative Tensile Flow and Work Hardening Behaviour of 9 Pct Chromium Ferritic-Martensitic Steels in the Framework of Estrin-Mecking Internal-Variable Approach
,” Metall. Mater. Trans. A
, 47
(6
), pp. 2642
–2655
.29.
Ahlquist
, C. N.
, and Nix
, W. D.
, 1971
, “The Measurement of Internal Stresses During Creep of Al and Al–Mg Alloys
,” Acta Metall.
, 19
(4
), pp. 373
–385
.30.
Orlova
, A.
, 2004
, “Relation Between the Internal Stress Measured in Creep and the Stress Generated by the Dislocation Structure in the FCC Metals
,” Philos. Mag.
, 84
(32
), pp. 3419
–3426
.31.
Esposito
, L.
, and Bonora
, N.
, 2012
, “Primary Creep Modeling Based on the Dependence of the Activation Energy on the Internal Stress
,” ASME J. Pressure Vessel Technol.
, 134
(6
), p. 061401
.32.
Sandstrom
, R.
, 2012
, “Basic Model for Primary and Secondary Creep in Copper
,” Acta Mater.
, 60
(1
), pp. 314
–332
.33.
Groisbock
, F.
, and Jeglitsch
, F.
, 1992
, “Internal and Effective Stresses in High-Temperature Creep Evaluated From Transient Dip Tests and Dislocation Bowing
,” J. Mater. Sci.
, 27
(16
), pp. 4365
–4372
.34.
Argon
, A. S.
, and Takeuchi
, S.
, 1981
, “Internal Stresses in Power-Law Creep
,” Acta Metall.
, 29
(11
), pp. 1877
–1884
.35.
Northwood
, D. O.
, and Smith
, I. O.
, 1985
, “Steady State Creep and Strain Transients for Stress Change Tests in an Al-0.4% Li Solid-Solution Alloy
,” Phys. Status Solidi A
, 88
(1
), pp. 181
–191
.36.
Northwood
, D. O.
, and Smith
, I. O.
, 1984
, “Steady State Creep and Strain Transients for Stress-Dip Tests in Polycrystalline Magnesium at 300 °C
,” Phys. Status Solidi A
, 85
(1
), pp. 149
–158
.37.
Northwood
, D. O.
, and Smith
, I. O.
, 1986
, “Internal and Effective Stresses in the Steady State Creep of Polycrystalline Cadmium at 0.5 Tm
,” Phys. Status Solidi A
, 98
(1
), pp. 163
–169
.38.
Polcik
, P.
, Straub
, S.
, Henes
, D.
, and Blum
, W.
, 1998
, “Simulation of the Creep Behaviour of 9-12% CrMo-V Steels on the Basis of Microstructural Data
,” Microstructural Stability of Creep Resistant Alloys for High Temperature Plant Application
, A.
Strang
, J.
Cawley
, and G. W.
Greenwood
, eds., Institute of Materials
, London
, pp. 405
–429
.39.
Choudhary
, B. K.
, Saroja
, S.
, Rao
, K. B. S.
, and Mannan
, S. L.
, 1999
, “Creep-Rupture Behavior of Forged, Thick Section 9Cr-1Mo Ferritic Steel
,” Metall. Mater. Trans. A
, 30
(11
), pp. 2825
–2834
.40.
Phaniraj
, C.
, Choudhary
, B. K.
, Rao
, K. B. S.
, and Raj
, B.
, 2003
, “Relationship Between Time to Reach Monkman–Grant Ductility and Rupture Life
,” Scr. Mater.
, 48
(9
), pp. 1313
–1318
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