Abstract

This study presents an irradiation-dependent internal state variable (ISV) elastoviscoplasticity-damage constitutive model that accounts for nuclear irradiation hardening and embrittlement of the irradiated polycrystalline materials. The irradiation effects were added to the coupled plasticity-damage kinetics with consideration of the structure–property relationships. The present irradiation-dependent elastoviscoplasticity-damage model was compared with the lab deformation experimental data of irradiated oxygen-free high conductivity (OFHC) copper, modified 9Cr-1Mo steel, and Ti-5Al-2.5Sn. The results show excellent agreement over the entire stress–strain curves at various irradiation doses. Because the ISV model, before the irradiation plasticity-damage addition, had been used on over 80 different metal alloys, it is anticipated that this nuclear irradiation supplement will also allow for application to many more irradiated metal alloys.

References

1.
Landes
,
J. D.
,
1990
, “
Fracture Mechanics and the Nuclear Industry
,”
Metall. Trans. A
,
21
(
4
), pp.
1097
1104
.
2.
Stiegler
,
J. O.
, and
Mansur
,
L. K.
,
1979
, “
Radiation Effects in Structural Materials
,”
Ann. Rev. Mater. Sci.
,
9
(
1
), pp.
405
454
.
3.
Spencer
,
B. W.
,
Hoffman
,
W. M.
, and
Backman
,
M. A.
,
2019
, “
Modular System for Probabilistic Fracture Mechanics Analysis of Embrittled Reactor Pressure Vessels in the Grizzly Code
,”
Nucl. Eng. Des.
,
341
, pp.
25
37
.
4.
Seeger
,
A.
,
1958
, “
Theory of Radiation Damage and Hardening
,”
Proceedings of the 2nd UN International Conference of Peaceful Uses of Atomic Energy
,
, Geneva, Switzerland
,
Sept. 1–13
, pp.
250
273
.
5.
Orowan
,
E.
,
1954
,
Dislocations in Metals
,
The American Institute of Mining and Metallurgical Engineers
,
New York
.
6.
Orowan
,
E.
,
1940
, “
Problems of Plastic Gliding
,”
Proc. Phys. Soc.
,
52
(
1
), pp.
8
22
.
7.
Singh
,
B. N.
,
Foreman
,
A. J. E.
, and
Trinkaus
,
H.
,
1997
, “
Radiation Hardening Revisited: Role of Intracascade Clustering
,”
J. Nucl. Mater.
,
249
(
2–3
), pp.
103
115
.
8.
Khraishi
,
T. A.
,
Zbib
,
H. M.
,
De La Rubia
,
T. D.
, and
Victoria
,
M.
,
2002
, “
Localized Deformation and Hardening in Irradiated Metals: Three-Dimensional Discrete Dislocation Dynamics Simulations
,”
Metall. Mater. Trans. B Process Metall. Mater. Process. Sci.
,
33B
(
2
), pp.
285
296
.
9.
Diaz De La Rubla
,
T.
,
Zbib
,
H. M.
,
Khralshl
,
T. A.
,
Wirth
,
B. D.
,
Victoria
,
M.
, and
Caturia
,
M. J.
,
2000
, “
Multiscale Modelling of Plastic Flow Localization in Irradiated Materials
,”
Nature
,
406
(
6798
), pp.
871
874
.
10.
Bacon
,
D. J.
,
Kocks
,
U. F.
, and
Scattergood
,
R. O.
,
1973
, “
The Effect of Dislocation Self-Interaction on the Orowan Stress
,”
Philos. Mag.
,
28
(
6
), pp.
1241
1263
.
11.
Bammann
,
D. J.
,
1984
, “
An Internal Variable Model of Viscoplasticity
,”
Int. J. Eng. Sci.
,
22
(
8–10
), pp.
1041
1053
.
12.
Bammann
,
D. J.
,
1990
, “
Modeling Temperature and Strain Rate Dependent Large Deformations of Metals
,”
ASME Appl. Mech. Rev.
,
43
(
5
), pp.
S312
S319
.
13.
Bammann
,
D. J.
,
Chiesa
,
M. L.
, and
Johnson
,
G. C.
,
1996
, “
Modeling Large Deformation and Failure
in
Manufacturing Processes
,”
Proceedings of the XIXth International Congress Theoretical and Applied Mechanics
,
Kyoto, Japan
,
Aug. 25–31
,, pp.
359
375
.
14.
Horstemeyer
,
M. F.
, and
Gokhale
,
A. M.
,
1999
, “
A Void-Crack Nucleation Model for Ductile Metals
,”
Int. J. Solids Struct.
,
36
(
33
), pp.
5029
5055
.
15.
Horstemeyer
,
M. F.
,
Lathrop
,
J.
,
Gokhale
,
A. M.
, and
Dighe
,
M.
,
2000
, “
Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy
,”
Theor. Appl. Fract. Mech.
,
33
(
1
), pp.
31
47
.
16.
Horstemeyer
,
M. F.
, and
Bammann
,
D. J.
,
2010
, “
Historical Review of Internal State Variable Theory for Inelasticity
,”
Int. J. Plast.
,
26
(
9
), pp.
1310
1334
.
17.
Cho
,
H. E.
,
Hammi
,
Y.
,
Bowman
,
A. L.
,
Karato
,
S.
,
Baumgardner
,
J. R.
, and
Horstemeyer
,
M. F.
,
2019
, “
A Unified Static and Dynamic Recrystallization Internal State Variable (ISV) Constitutive Model Coupled With Grain Size Evolution for Metals and Mineral Aggregates
,”
Int. J. Plast.
,
112
, pp.
123
157
.
18.
Peterson
,
L. A.
,
Horstemeyer
,
M. F.
,
Lacy
,
T. E.
, and
Moser
,
R. D.
,
2020
, “
Experimental Characterization and Constitutive Modeling of an Aluminum 7085-T711 Alloy Under Large Deformations at Varying Strain Rates, Stress States, and Temperatures
,”
Mech. Mater.
,
151
, p.
103602
.
19.
Horstemeyer
,
M. F.
,
2012
,
Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design With Science
,
John Wiley & Sons
,
New York
.
20.
Horstemeyer
,
M. F.
,
2018
,
Integrated Computational Materials Engineering (ICME) for Metals: Concepts and Case Studies
,
John Wiley & Sons
,
New York
.
21.
Bammann
,
D. J.
, and
Johnson
,
G. C.
,
1987
, “
On the Kinematics of Finite-Deformation Plasticity
,”
Acta Mech.
,
70
(
1–4
), pp.
1
13
.
22.
Bammann
,
D. J.
, and
Aifantis
,
E. C.
,
1989
, “
A Damage Model for Ductile Metals
,”
Nucl. Eng. Des.
,
116
(
3
), pp.
355
362
.
23.
Bammann
,
D. J.
, and
Solanki
,
K. N.
,
2010
, “
On Kinematic, Thermodynamic, and Kinetic Coupling of a Damage Theory for Polycrystalline Material
,”
Int. J. Plast.
,
26
(
6
), pp.
775
793
.
24.
Ruggeri
,
T.
,
2008
, “
The Entropy Principle From Continuum Mechanics to Hyperbolic Systems of Balance Laws: The Modern Theory of Extended Thermodynamics
,”
Entropy
,
10
(
3
), pp.
319
333
.
25.
Coleman
,
B. D.
, and
Gurtin
,
M. E.
,
1967
, “
Thermodynamics With Internal State Variables
,”
J. Chem. Phys.
,
47
(
2
), pp.
597
613
.
26.
Malvern
,
L. E.
,
1969
,
Introduction to the Mechanics of a Continuous Medium
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
27.
Singh
,
B. N.
,
Horsewell
,
A.
,
Toft
,
P.
, and
Edwards
,
D. J.
,
1995
, “
Temperature and Dose Dependencies of Microstructure and Hardness of Neutron Irradiated OFHC Copper
,”
J. Nucl. Mater.
,
224
(
2
), pp.
131
140
.
28.
Victoria
,
M.
,
Baluc
,
N.
,
Bailat
,
C.
,
Dai
,
Y.
,
Luppo
,
M. I.
,
Schaublin
,
R.
, and
Singh
,
B. N.
,
2000
, “
Microstructure and Associated Tensile Properties of Irradiated FCC and BCC Metals
,”
J. Nucl. Mater.
,
276
(
1
), pp.
114
122
.
29.
Chaouadi
,
R.
, and
Gérard
,
R.
,
2011
, “
Neutron Flux and Annealing Effects on Irradiation Hardening of RPV Materials
,”
J. Nucl. Mater.
,
418
(
1–3
), pp.
137
142
.
30.
Fabritsiev
,
S. A.
, and
Pokrovsky
,
A. S.
,
2007
, “
Effect of Irradiation Temperature on Microstructure, Radiation Hardening and Embrittlement of Pure Copper and Copper-Based Alloy
,”
J. Nucl. Mater.
,
367–370
(
B
), pp.
977
983
.
31.
Odette
,
G. R.
,
Yamamoto
,
T.
, and
Klingensmith
,
D.
,
2005
, “
On the Effect of Dose Rate on Irradiation Hardening of RPV Steels
,”
Philos. Mag.
,
85
(
4–7
), pp.
779
797
.
32.
Li
,
D.
,
Zbib
,
H. M.
,
Garmestani
,
H.
,
Sun
,
X.
, and
Khaleel
,
M.
,
2011
, “
Modeling of Irradiation Hardening of Polycrystalline Materials
,”
Comput. Mater. Sci.
,
50
(
8
), pp.
2496
2501
.
33.
Fabritsiev
,
S. A.
, and
Pokrovsky
,
A. S.
,
2011
, “
Effect of Irradiation Temperature and Dose on Radiation Hardening of Some Pure Metals
,”
J. Nucl. Mater.
,
417
(
1–3
), pp.
940
943
.
34.
Cho
,
H. E.
,
Hammi
,
Y.
,
Francis
,
D. K.
,
Stone
,
T.
,
Mao
,
Y.
,
Sullivan
,
K.
,
Wilbanks
,
J.
,
Zelinka
,
R.
, and
Horstemeyer
,
M. F.
,
2018
, “
Microstructure-Sensitive, History-Dependent Internal State Variable Plasticity-Damage Model for a Sequential Tubing Process
,”
Integr. Comput. Mater. Eng. Met. Concepts Case Stud.
, pp.
199
234
.
35.
Horstemeyer
,
M. F.
,
2000
, “
A Numerical Parametric Investigation of Localization and Forming Limits
,”
Int. J. Damage Mech.
,
9
(
3
), pp.
255
285
.
36.
Dai
,
Y.
,
Henry
,
J.
,
Tong
,
Z.
,
Averty
,
X.
,
Malaplate
,
J.
, and
Long
,
B.
,
2011
, “
Neutron/Proton Irradiation and He Effects on the Microstructure and Mechanical Properties of Ferritic/Martensitic Steels T91 and EM10
,”
J. Nucl. Mater.
,
415
(
3
), pp.
306
310
.
37.
Chandler
,
M. Q.
,
Bammann
,
D. J.
, and
Horstemeyer
,
M. F.
,
2013
, “
A Continuum Model for Hydrogen-Assisted Void Nucleation in Ductile Materials
,”
Model. Simul. Mater. Sci. Eng.
,
21
(
5
), p.
055028
.
38.
McClintock
,
F. A.
,
1964
, “
A Criterion for Ductile Fracture by the Growth of Holes
,”
ASME J. Appl. Mech.
,
35
(
2
), pp.
363
371
.
39.
Jordon
,
J. B.
,
Horstemeyer
,
M. F.
,
Solanki
,
K.
, and
Xue
,
Y.
,
2007
, “
Damage and Stress State Influence on the Bauschinger Effect in Aluminum Alloys
,”
Mech. Mater.
,
39
(
10
), pp.
920
931
.
40.
Garofalo
,
F.
,
1963
, “
An Empirical Relation Defining the Stress Dependence of Minimum Creep Rate in Metals
,”
Trans. Metall. Soc. AIME
,
227
, p.
351
.
41.
Singh
,
B. N.
,
Edwards
,
D.
,
Eldrup
,
M.
, and
Toft
,
P.
,
1997
,
Pre- and Post-Irradiation Properties of Copper Alloys at 250 Deg C Following Bonding and Bakeout Thermal Cycles
, Risoe National Lab., RISO-R–937(EN), Denmark.
42.
Fabritsiev
,
S. A.
,
Pokrovsky
,
A. S.
, and
Ostrovsky
,
S. E.
,
2004
, “
Effect of the Irradiation–Annealing–Irradiation Cycle on the Mechanical Properties of Pure Copper and Copper Alloy
,”
J. Nucl. Mater.
,
324
(
1
), pp.
23
32
.
43.
Robach
,
J. S.
,
Robertson
,
I. M.
,
Wirth
,
B. D.
, and
Arsenlis
,
A.
,
2003
, “
In-Situ Transmission Electron Microscopy Observations and Molecular Dynamics Simulations of Dislocation-Defect Interactions in Ion-Irradiated Copper
,”
Philos. Mag.
,
83
(
8
), pp.
955
967
.
44.
Meulbroek Fick
,
J. P.
,
Ramesh
,
K. T.
, and
Swaminathan
,
P. K.
,
2015
, “
Modeling of Ductile Fragmentation That Includes Void Interactions
,”
J. Mech. Phys. Solids
,
85
, pp.
54
73
.
45.
Wright
,
T. W.
, and
Ramesh
,
K. T.
,
2008
, “
Dynamic Void Nucleation and Growth in Solids: A Self-Consistent Statistical Theory
,”
J. Mech. Phys. Solids
,
56
(
2
), pp.
336
359
.
46.
Ashby
,
M. F.
,
2005
,
Materials Selection in Mechanical Design
,
Elsevier
,
New York
.
47.
Fan
,
Z.
,
Velisa
,
G.
,
Jin
,
K.
,
Crespillo
,
M. L.
,
Bei
,
H.
,
Weber
,
W. J.
, and
Zhang
,
Y.
,
2019
, “
Temperature-Dependent Defect Accumulation and Evolution in Ni-Irradiated NiFe Concentrated Solid-Solution Alloy
,”
J. Nucl. Mater.
,
519
, pp.
1
9
.
48.
Yang
,
T.
,
Xia
,
S.
,
Guo
,
W.
,
Hu
,
R.
,
Poplawsky
,
J. D.
,
Sha
,
G.
,
Fang
,
Y.
,
Yan
,
Z.
,
Wang
,
C.
,
Li
,
C.
,
Zhang
,
Y.
,
Zinkle
,
S. J.
, and
Wang
,
Y.
,
2018
, “
Effects of Temperature on the Irradiation Responses of Al0.1CoCrFeNi High Entropy Alloy
,”
Scr. Mater.
,
144
, pp.
31
35
.
49.
Kumar
,
N. A. P. K.
,
Li
,
C.
,
Leonard
,
K. J.
,
Bei
,
H.
, and
Zinkle
,
S. J.
,
2016
, “
Microstructural Stability and Mechanical Behavior of FeNiMnCr High Entropy Alloy Under Ion Irradiation
,”
Acta Mater.
,
113
, pp.
230
244
.
50.
Patra
,
A.
, and
McDowell
,
D. L.
,
2013
, “
Continuum Modeling of Localized Deformation in Irradiated BCC Materials
,”
J. Nucl. Mater.
,
432
(
1–3
), pp.
414
427
.
51.
Schastlivtsev
,
V. M.
,
Rodionov
,
D. P.
,
Khlebnikova
,
Y. V.
, and
Yakovleva
,
I. L.
,
1999
, “
Peculiarity of Structure and Crystallography of Plastic Deformation of Lath Martensite in Structural Steels
,”
Mater. Sci. Eng. A
,
273–275
, pp.
437
442
.
52.
Maloy
,
S. A.
,
James
,
M. R.
,
Willcutt
,
G.
,
Sommer
,
W. F.
,
Sokolov
,
M.
,
Snead
,
L. L.
,
Hamilton
,
M. L.
, and
Garner
,
F.
,
2001
, “
The Mechanical Properties of 316L/304L Stainless Steels, Alloy 718 and Mod 9Cr–1Mo After Irradiation in a Spallation Environment
,”
J. Nucl. Mater.
,
296
(
1–3
), pp.
119
128
.
53.
Barrett
,
R. A.
,
O’Donoghue
,
P. E.
, and
Leen
,
S. B.
,
2018
, “
A Physically-Based High Temperature Yield Strength Model for 9Cr Steels
,”
Mater. Sci. Eng. A
,
730
, pp.
410
424
.
54.
Li
,
Y.
,
Du
,
J.
,
Li
,
L.
,
Gao
,
K.
,
Pang
,
X.
, and
Volinsky
,
A. A.
,
2020
, “
Mechanical Properties and Phases Evolution in T91 Steel During Long-Term High-Temperature Exposure
,”
Eng. Fail. Anal.
,
111
, p.
104451
.
55.
Edwards
,
D. J.
,
Singh
,
B. N.
, and
Toft
,
P.
,
2001
, “Radiation Hardening in HCP Titanium Alloys,”
Fusion Materials: Semi-Annual Report for Period Ending December 31, 2000
,
S.
Berk
, ed.,
US Department of Energy Office of Fusion Energy Sciences
,
Washington, DC
, pp.
214
220
.
56.
Griffiths
,
M.
,
1993
, “
Evolution of Microstructure in HCP Metals During Irradiation
,”
J. Nucl. Mater.
,
205
(
C
), pp.
225
241
.
57.
Leguey
,
T.
,
Baluc
,
N.
,
Schäublin
,
R.
, and
Victoria
,
M.
,
2002
, “
Structure–Mechanics Relationships in Proton Irradiated Pure Titanium
,”
J. Nucl. Mater.
,
307–311
(
1
), pp.
696
700
.
58.
Leguey
,
T.
,
Baluc
,
N.
,
Schäublin
,
R.
, and
Victoria
,
M.
,
2005
, “
Temperature Dependence of Irradiation Effects in Pure Titanium
,”
Philos. Mag.
,
85
(
4–7
), pp.
689
695
.
59.
Leguey
,
T.
,
Schäublin
,
R.
,
Marmy
,
P.
, and
Victoria
,
M.
,
2002
, “
Microstructure of Ti5Al2.5Sn and Ti6Al4V Deformed in Tensile and Fatigue Tests
,”
J. Nucl. Mater.
,
305
(
1
), pp.
52
59
.
60.
Fukuhara
,
M.
, and
Sanpei
,
A.
,
1993
, “
Elastic Moduli and Internal Frictions of Inconel 718 and T I-6 A I-4V as a Function of Temperature
,”
J. Mater. Sci. Lett.
,
12
(
14
), pp.
1122
1124
.
You do not currently have access to this content.