In the pressure vessel and piping and power industries, creep deformation has continued to be an important design consideration. Directionally solidified components have become commonplace. Creep deformation and damage is a common source of component failure. A considerable effort has gone into the study and development of constitutive models to account for such behavior. Creep deformation can be separated into three distinct regimes: primary, secondary, and tertiary. Most creep damage constitutive models are designed to model only one or two of these regimes. In this paper, a multistage creep damage constitutive model is developed and designed to model all three regimes of creep for isotropic materials. A rupture and critical damage prediction method follows. This constitutive model is then extended for transversely isotropic materials. In all cases, the influence of creep damage on general elasticity (elastic damage) is included. Methods to determine material constants from experimental data are detailed. Finally, the isotropic material model is exercised on tough pitch copper tube and the anisotropic model on a Ni-based superalloy.

References

References
1.
Andrade
,
E. N.
, 1910, “
The Viscous Flow in Metals and Allied Phenomena
,”
Proc. R. Soc., A
,
84
, pp.
1
12
.
2.
Norton
,
F. H.
, 1929,
The Creep of Steel at High Temperatures
,
McGraw-Hill
,
London
.
3.
Kachanov
,
L. M.
, 1967,
The Theory of Creep
,
National Lending Library for Science and Technology, Boston Spa
,
England
.
4.
Rabotnov
,
Y. N.
, 1969,
Creep Problems in Structural Members
,
North Holland
,
Amsterdam
.
5.
Yatomi
,
M.
,
Bettinson
,
A. D.
,
O’Dowd
,
N. P.
, and
Nikbin
,
K. M.
, 2004, “
Modelling of Damage Development and Failure in Notched-Bar Multiaxial Creep Tests
,”
Fatigue Fract. Eng. Mater. Struct.
,
27
(
4
), pp.
283
295
.
6.
Stewart
C. M.
,
Gordon
A. P.
,
Ma
,
Y. W.
, and
Neu
,
R. W.
, 2011, “
An Anisotropic Tertiary Creep-Damage Constitutive Model for Anisotropic Materials
,”
Int. J. Pressure Vessel Piping
,
88
(
8-9
), pp.
356
364
.
7.
Stewart
C. M.
,
Gordon
A. P.
,
Ma
,
Y. W.
, and
Neu
,
R. W.
, 2011, “
An Improved Anisotropic Tertiary Creep Damage Formulation
,”
J. Pressure Vessel Technol.
,
133
(
5
),
051201
.
8.
Stewart
,
C. M.
, and
Gordon
,
A. P.
, 2011, “
A Multistage Creep Damage Constitutive Model for Isotropic and Anisotropic Materials With Elastic Damage
,”
ASME 2011 Pressure Vessel and Piping Conference
, PVP2011-57049, Baltimore, MD, July 17–21.
9.
Betten
,
J.
, 1989, “
Generalization of nonlinear material laws found in experiments to multiaxial states of stress
,”
Eur. J. Mech. A/Solids
,
8
, pp.
325
339
.
10.
McVetty
,
P. G.
, 1934, “
Creep Under Non-Steady Temperatures and Stresses
,”
Mechanical Behavior of Materials at Elevated Temperatures
,
J. E.
Dorn
, ed.,
McGraw-Hill
,
London
.
11.
Penny
,
R. K.
, and
Marriott
,
D. L.
, 1995,
Design for Creep
,
Springer
,
New York
.
12.
Murakami
,
S.
, 1987, “
Progress of Continuum Damage Mechanics
,”
JSME Int. J.
,
30
(
263
), pp.
701
710
.
13.
Sidoroff
,
F.
, 1981, “
Description of Anisotropic Damage Application to Elasticity
,”
IUTAM Colloqium on Physical Nonlinearities in Structural Analysis
,
Springer-Verlag
,
Germany
, pp.
237
244
.
14.
Skrzypek
,
J.
, and
Ganczarski
,
A.
, 1999,
Modeling of Material Damage and Failure of Structures
,
Springer
,
New York
.
15.
Hill
,
R.
, 1950,
The Mathematical Theory of Plasticity
,
Oxford University
,
New York
.
16.
Stewart
,
C. M.
, and
Gordon
,
A. P.
, 2010, “
Modeling the Tertiary Creep Damage Behavior of a Transversely-Isotropic Material Under Multiaxial and Periodic Loading Conditions
,”
ASME Pressure Vessel and Piping Conference 2010
,
Bellevue
,
Washington
, July
18
22
.
17.
Stewart
,
C. M.
, and
Gordon
,
A. P.
, 2011, “
Anisotropic Creep Damage and Elastic Damage of Notched Directionally Solidified Materials
,”
ASME Turbo Expo 2011
,
Vancouver, BC
,
Canada
, June
6
10
.
18.
Rabotnov
,
Y.
, 1968, “
Creep Rupture
,”
Applied Mechanics Conference
,
Stanford University
,
Palo Alto
, pp.
342
349
.
19.
Stewart
,
C. M.
, 2009, “
Tertiary Creep Damage Modeling of a Transversely Isotropic Ni-Based Superalloy
” Master’s thesis, University of Central Florida, Orlando, FL.
20.
Stewart
,
C. M.
, and
Gordon
,
A. P.
, 2010, “
Analytical Method to Determine the Tertiary Creep Damage Constants of the Kachanov-Rabotnov Constitutive Model
,”
Proceedings of the 2010 ASME International Mechanical Engineering Congress & Exposition
,
Vancouver, BC
, Nov.
12
18
.
21.
Stewart
C. M.
,
Gordon
A. P.
,
Hogan
,
E. A.
, and
Saxena
,
A.
, 2011, “
Characterization of the Creep Deformation and Rupture Behavior of DS GTD-111 Using the Kachanov-Rabotnov Constitutive Model
,”
J. Eng. Mater. Technol.
,
133
(
2
),
021013
.
22.
Drefahl
,
K.
,
Kleniau
,
M.
, and
Steinkamp
,
W.
, 1985, “
Creep Behavior of Copper and Copper Alloys as Design Criteria in Pressure Vessel Manufacture
,”
J. Test. Eval
,
13
(
5
), pp.
1
15
.
23.
Murakami
,
S.
,
Sanomura
,
Y.
, and
Saitoh
,
K.
, 1986, “
Formulation of Cross-Hardening in Creep and its Effect on the Creep Damage Process of Copper
,”
J. Eng. Mater. Technol.
,
108
(
2
), pp.
167
173
.
24.
Yaguchi
,
M.
,
Yamamoto
M.
, and
Ogata
,
T.
, 2007, “
A Unified Anisotropic Constitutive Model for a Ni Base Directionally Solidified Superalloy
,”
Eighth International Conference on Creep and Fatigue at Elevated Temperatures
,
San Antonio, TX
, July
22
26
.
You do not currently have access to this content.