Directionally solidified (DS) Ni-base superalloys are commonly used as gas turbine materials to primarily extend the operational lives of components under high load and temperature. The nature of DS superalloy grain structure facilitates an elongated grain orientation, which exhibits enhanced impact strength, high temperature creep and fatigue resistance, and improved corrosion resistance compared with off-axis orientations. Of concern to turbine designers are the effects of cyclic fatigue, thermal gradients, and potential stress concentrations when dealing with orientation-dependent materials. When coupled with a creep environment, accurate prediction of crack initiation and propagation becomes highly dependent on the quality of the constitutive damage model implemented. This paper describes the development of an improved anisotropic tertiary creep damage model implemented in a general-purpose finite element analysis software. The creep damage formulation is a tensorial extension of a variation in the Kachanov–Rabotnov isotropic tertiary creep damage formulation. The net/effective stress arises from the use of the Rabotnov second-rank symmetric damage tensor. The Hill anisotropic behavior analogy is used to model secondary creep and tertiary creep damage behaviors. Using available experimental data for a directionally solidified Ni-base superalloy, the improved formulation is found to accurately model intermediate oriented specimen.

1.
Suzuki
,
K.
,
Ito
,
H.
,
Inoue
,
T.
, and
Miura
,
H.
, 2009, “
Creep Damage Process of Ni-Base Superalloy Caused by Stress-Induced Anisotropic Atomic Diffusion
,”
JSME Int. J., Ser. A
1340-8046,
3
(
3
), pp.
487
497
.
2.
Kawai
,
M.
, 1997, “
Coupled Inelasticity and Damage Model for Metal Matrix Composites
,”
Int. J. Damage Mech.
1056-7895,
6
(
4
), pp.
453
478
.
3.
Peravali
,
S.
,
Hyde
,
T. H.
,
Cliffe
,
K. A.
, and
Leen
,
S. B.
, 2009, “
An Anisotropic Creep Damage Model for Anisotropic Weld Metal
,”
ASME J. Pressure Vessel Technol.
0094-9930,
131
(
2
), p.
021401
.
4.
Stewart
,
C. M.
, and
Gordon
,
A. P.
, 2009, “
A Novel Anisotropic Tertiary Creep Damage Model for Transversely Isotropic Materials
,”
Proceedings of the 12th International Conference on Pressure Vessel Technology
, Jeju Island, South Korea, pp.
20
23
.
5.
Hill
,
R.
, 1950,
The Mathematical Theory of Plasticity
,
Oxford University
,
New York
.
6.
Stewart
,
C. M.
,
Hogan
,
E.
, and
Gordon
,
A. P.
, 2009, “
Modeling the Temperature-Dependence of Tertiary Creep Damage of a Directionally Solidified Ni-Base Superalloy
,”
Proceedings of the 2009 ASME International Mechanical Engineering Congress and Exposition
, Lake Buena Vista, FL, Nov. 13–19.
7.
ANSYS, Inc
, ANSYS® User Manual, Release 12.0.
8.
Dyson
,
B. F.
,
Loveday
,
M. S.
, and
Rodgers
,
M. J.
, 1976, “
Grain Boundary Cavitation Under Various States of Applied Stress
,”
Proc. R. Soc. London, Ser. A
0950-1207,
349
(
1657
), pp.
245
259
.
9.
Altenbach
,
H.
,
Huang
,
C.
, and
Naumenko
,
K.
, 2002, “
Creep Damage Predictions in Thin-Walled Structures by Use of Isotropic and Anisotropic Damage Models
,”
J. Strain Anal. Eng. Des.
0309-3247,
37
(
3
), pp.
265
275
.
10.
Murakami
,
S.
, and
Sanomura
,
Y.
, 1985, “
Creep and Creep Damage of Copper Under Multiaxial States of Stress
,”
Plasticity Today
,
A.
Sawczuk
and
G.
Bianchi
, eds.,
Elsevier
,
New York
, pp.
535
551
.
11.
Murakami
,
S.
, and
Ohno
,
N.
, 1981, “
A Continuum Theory of Creep and Creep Damage
,”
Creep in Structures
,
A. R. S.
Ponter
and
D. R.
Hayhurst
, eds.,
Springer
,
Berlin
, pp.
422
443
.
12.
Skrzypek
,
J.
, and
Ganczarski
,
A.
, 1999,
Modeling of Material Damage and Failure of Structures
,
Springer
,
New York
.
13.
Trampczynski
,
W. A.
,
Hayhurst
,
D. R.
, and
Leckie
,
F. A.
, 1981, “
Creep Rupture of Copper and Aluminum Under Non-Proportional Loading
,”
J. Mech. Phys. Solids
0022-5096,
29
(
5–6
), pp.
353
374
.
14.
Betten
,
J.
,
El-Magd
,
E.
,
Meydanli
,
S.
, and
Palmen
,
P.
, 1995, “
Bestimmung der Materialkennwerte einer dreidimensionalen Theorie zur Beschreibung des tertiären Kriechverhaltens austenitischer Stähle auf der Basis der Experimente
,”
Arch. Appl. Mech.
0939-1533,
65
(
2
), pp.
110
120
.
15.
Murakami
,
S.
, 1990, “
A Continuum Mechanics Theory of Anisotropic Damage
,”
Yielding, Damage and Failure of Anisotropic Solids
,
J. P.
Boehler
, ed.,
Mechanical Engineering
,
London
, pp.
465
482
.
16.
Hayhurst
,
D. R.
, 1972, “
Creep Rupture Under Multi-Axial States of Stress
,”
J. Mech. Phys. Solids
0022-5096,
20
(
6
), pp.
381
382
.
17.
Stewart
,
C. M.
,
Gordon
,
A. P.
, and
Nicholson
,
D. W.
, 2009, “
Numerical Simulation of Temperature-Dependent, Anisotropic Tertiary Creep Damage
,”
47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
, Orlando, FL, Jan 5–8.
18.
Radayev
,
Y. N.
, 1996, “
Thermodynamical Model of Anisotropic Damage Growth. Part I. Canonical Dynamic State Variables of Continuum Damage Mechanics and Thermodynamical Functions of Three-Dimensional Anisotropic Damage State
,”
J. Non-Equilib. Thermodyn.
0340-0204,
21
(
2
), pp.
129
152
.
19.
Radayev
,
Y. N.
, 1996, “
Thermodynamical Model of Anisotropic Damage Growth. Part II. Canonical Damage Growth Rate Equations and Theory Of Damage Invariants
,”
J. Non-Equilib. Thermodyn.
0340-0204,
21
(
3
), pp.
197
222
.
20.
Murakami
,
S.
, 1987, “
Progress of Continuum Damage Mechanics
,”
JSME Int. J.
0913-185X,
30
(
263
), pp.
701
710
.
21.
Rabotnov
,
Y.
, 1968, “
Creep Rupture
,”
Applied Mechanics Conference
, Stanford University, Palo Alto, CA, pp.
342
349
.
22.
Murakami
,
S.
, 1988, “
Mechanical Modeling of Material Damage
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
55
, pp.
280
286
.
23.
Cordebois
,
J. P.
, and
Sidoroff
,
F.
, 1982, “
Damage Induced Elastic Anisotropy
,”
Mechanical Behavior of Anisotropic Solids
,
J. P.
Boehler
, ed.,
Martinus Nijhoff
,
The Hague
, pp.
761
774
.
24.
Cordebois
,
J. P.
, and
Sidoroff
,
F.
, 1982, “
Endommagement Anistrope en Elasticite et Plasticite
,”
J. Mec. Theor. Appl.
0750-7240, Special number,
45
60
.
25.
Chow
,
C.
, and
Wang
,
J.
, 1987, “
An Anisotropic Theory of Elasticity for Continuum Damage Mechanics
,”
Int. J. Fract.
0376-9429,
33
, pp.
3
16
.
26.
Murakami
,
S.
, and
Imaizumi
,
T. J.
, 1982, “
Mechanical Description of Creep Damage State and Its Experimental Verification
,”
J. Mec. Theor. Appl.
0750-7240,
1
(
5
), pp.
743
761
.
27.
Murakami
,
S.
,
Sanomura
,
Y.
, and
Saitoh
,
K.
, 1986, “
Formulation of Cross-Hardening in Creep and Its Effect on the Creep Damage Process of Copper
,”
ASME J. Eng. Mater. Technol.
0094-4289,
108
(
2
), pp.
167
173
.
28.
Murakami
,
S.
, and
Sanomura
,
Y.
, 1986, “
Analysis of the Coupled Effect of Plastic Damage and Creep Damage in Nimonic 80A at Finite Deformation
,”
Eng. Fract. Mech.
0013-7944,
25
(
5–6
), pp.
693
704
.
29.
Lemaitre
,
J.
, and
Chaboche
,
J. L.
, 1978, “
Aspect Phénoménologique de la Rupture par Endommagement
,”
J. Mec. Appl.
,
2
(
3
), pp.
317
365
.
30.
Chaboche
,
J. L.
, 1982, “
Le Concept de Contrainte Effective Appliquée À L'élasticité Et À La Viscoplasticité en Présence d'un Endommagement Anisotrope
,”
Mechanical Behavior of Anisotropic Solids, Proceedings of Euromech Colloquium 115
, Villars de Lans, France, editions du CNRS, Paper No. 295, pp.
737
760
.
31.
Ohno
,
N.
,
Mizuno
,
T.
,
Kawaji
,
H.
, and
Okada
,
I.
, 1992, “
Multiaxial Creep of a Nickel-Base Directionally Solidified Alloy: Anisotropy and Simulation
,”
Acta Metall. Mater.
0956-7151,
40
(
3
), pp.
559
567
.
32.
Shesterikov
,
S. A.
,
Lokochtchenko
,
A. M.
, and
Mjakotin
,
E. A.
, 1998, “
Creep Rupture of Anisotropic Pipes
,”
ASME J. Pressure Vessel Technol.
0094-9930,
120
(
3
), pp.
223
225
.
33.
Liu
,
X. B.
,
Ma
,
L. Z.
,
Chang
,
K. M.
, and
Barbero
,
E.
, 2005, “
Fatigue Crack Propogation of Ni-Base Superalloys
,”
Acta Metall. Sin.
0412-1961,
18
(
1
), pp.
55
64
.
34.
McEvily
,
A. J.
, 2002,
Metal Failures: Mechanisms, Analysis, Prevention
,
Wiley
,
New York
.
35.
Ibanez
,
A. R.
, 2003, “
Modeling Creep Behavior in a Directionally-Solidified Nickel Base Superalloy
,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
36.
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
1464-4207,
219
(
3
), pp.
163
175
.
37.
Norton
,
F. H.
, 1929,
The Creep of Steel at High Temperatures
,
McGraw-Hill
,
London
.
38.
Kachanov
,
L. M.
, 1967,
The Theory of Creep
,
National Lending Library for Science and Technology
,
Boston Spa, UK
, p.
X
.
39.
Rabotnov
,
Y. N.
, 1969,
Creep Problems in Structural Members
,
North-Holland
,
Amsterdam
.
40.
Schur
,
I.
,
Joseph
,
A.
,
Melnikov
,
A.
, and
Rentschler
,
R.
, 2003,
Studies in Memory of Issai Schur
,
Springer
,
New York
.
41.
Bernstein
,
D. S.
, 2005,
Matrix Mathematics
,
Princeton University
,
Princeton, NJ
.
42.
Stewart
,
C. M.
, and
Gordon
,
A. P.
, 2010, “
A Creep Rupture Time Model for Anisotropic Creep-Damage of Transversely-Isotropic Materials
,”
ASME Turbo Expo 2010
, Glasglow, UK, Jun. 14–18.
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