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.

References

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
.
You do not currently have access to this content.