In this study, a crystal plasticity finite element model (CPFEM) has been revisited to study the microstructure effects on macroscopic mechanical behavior of ultrafine-grained (UFG) nickels processed by severe plastic deformation (SPD). The microstructure characteristics such as grain size and dislocation density show a strong influence on the mechanical behavior of SPD-processed materials. We used a modified Hall–Petch relationship at grain level to study both grain size and dislocation density dependences of mechanical behavior of SPD-processed nickel materials. Within the framework of small strain hypothesis, it is quite well shown that the CPFEM predicts the mechanical behavior of unimodal nickels processed by SPD methods. Moreover, a comparison between the proposed model and the self-consistent approach will be shown and discussed.

References

References
1.
Sanders
,
P.
,
Youngdahl
,
C.
, and
Weertman
,
J.
,
1997
, “
The Strength of Nanocrystalline Metals With and Without Flaws
,”
Mater. Sci. Eng. A
,
234–236
, pp.
77
82
.10.1016/S0921-5093(97)00185-8
2.
Atkinson
,
H. V.
, and
Davies
,
S.
,
2000
, “
Fundamental Aspects of Hot Isostatic Pressing: An Overview
,”
Metall. Mater. Trans. A
,
31
(
12
), pp.
2981
3000
.10.1007/s11661-000-0078-2
3.
Champion
,
Y.
,
Bernard
,
F.
,
Guigue-Millot
,
N.
, and
Perriat
,
P.
,
2003
, “
Sintering of Copper Nanopowders Under Hydrogen: An In Situ X-Ray Diffraction Analysis
,”
Mater. Sci. Eng. A
,
360
(
1–2
), pp.
258
263
.10.1016/S0921-5093(03)00446-5
4.
Segal
,
V.
,
1995
, “
Materials Processing by Simple Shear
,”
Mater. Sci. Eng. A
,
197
(
2
), pp.
157
164
.10.1016/0921-5093(95)09705-8
5.
Valiev
,
R.
,
Islamgaliev
,
R.
, and
Alexandrov
,
I.
,
2000
, “
Bulk Nanostructured Materials From Severe Plastic Deformation
,”
Prog. Mater. Sci.
,
45
(
2
), pp.
103
189
.10.1016/S0079-6425(99)00007-9
6.
Valiev
,
R.
,
Estrin
,
Y.
,
Horita
,
Z.
,
Langdon
,
T.
,
Zechetbauer
,
M.
, and
Zhu
,
Y.
,
2006
, “
Producing Bulk Ultrafine-Grained Materials by Severe Plastic Deformation
,”
JOM
,
58
(
4
), pp.
33
39
.10.1007/s11837-006-0213-7
7.
Dubravina
,
A.
,
Zehetbauer
,
M.
,
Schafler
,
E.
, and
Alexandrov
,
I.
,
2004
, “
Correlation Between Domain Size Obtained by X-Ray Bragg Profile Analysis and Macroscopic Flow Stress in Severely Plastically Deformed Copper
,”
Mater. Sci. Eng. A
,
387–389
, pp.
817
821
.10.1016/j.msea.2004.03.093
8.
Kapoor
,
R.
,
Kumar
,
N.
,
Mishra
,
R.
,
Huskamp
,
C.
, and
Sankaran
,
K.
,
2010
, “
Influence of Fraction of High Angle Boundaries on the Mechanical Behavior of an Ultrafine Grained Al–Mg Alloy
,”
Mater. Sci. Eng. A
,
527
(
20
), pp.
5246
5254
.10.1016/j.msea.2010.04.086
9.
Segal
,
V.
,
1999
, “
Equal Channel Angular Extrusion: From Macromechanics to Structure Formation
,”
Mater. Sci. Eng. A
,
271
(
1–2
), pp.
322
333
.10.1016/S0921-5093(99)00248-8
10.
Valiev
,
R.
, and
Langdon
,
T.
,
2006
, “
Principles of Equal-Channel Angular Pressing as a Processing Tool for Grain Refinement
,”
Prog. Mater. Sci.
,
51
(
7
), pp.
881
981
.10.1016/j.pmatsci.2006.02.003
11.
Bridgman
,
P.
,
1943
, “
On Torsion Combined With Compression
,”
J. Appl. Phys.
,
14
(
6
), pp.
273
283
.10.1063/1.1714987
12.
Jiang
,
H.
,
Zhu
,
Y. T.
,
Butt
,
D.
,
Alexandrov
,
I.
, and
Lowe
,
T.
,
2000
, “
Microstructural Evolution, Microhardness and Thermal Stability of HPT-Processed Cu
,”
Mater. Sci. Eng. A
,
290
(
1–2
), pp.
128
138
.10.1016/S0921-5093(00)00919-9
13.
Alexandrov
,
I.
,
Dubravina
,
A.
,
Kilmametov
,
A.
,
Kazykhanov
,
V.
, and
Valiev
,
R.
,
2003
, “
Textures in Nanostructured Metals Processed by Severe Plastic Deformation
,”
Met. Mater. Int.
,
9
(
2
), pp.
151
156
.10.1007/BF03027271
14.
Stolyarov
,
V.
,
Zhu
,
Y.
,
Lowe
,
T.
,
Islamgaliev
,
R.
, and
Valiev
,
R.
,
2000
, “
Processing Nanocrystalline Ti and Its Nanocomposites From Micrometer-Sized Ti Powder Using High Pressure Torsion
,”
Mater. Sci. Eng. A
,
282
(
1–2
), pp.
78
85
.10.1016/S0921-5093(99)00764-9
15.
Zhilyaev
,
A.
,
McNelley
,
T.
, and
Langdon
,
T.
,
2007
, “
Evolution of Microstructure and Microtexture in fcc Metals During High-Pressure Torsion
,”
J. Mater. Sci.
,
42
(
5
), pp.
1517
1528
.10.1007/s10853-006-0628-0
16.
Jahedi
,
M.
,
Paydar
,
M. H.
,
Zheng
,
S.
,
Beyerlein
,
I. J.
, and
Knezevic
,
M.
,
2014
, “
Texture Evolution and Enhanced Grain Refinement Under High-Pressure-Double-Torsion
,”
Mater. Sci. Eng. A
,
611
, pp.
29
36
.10.1016/j.msea.2014.05.081
17.
Tsuji
,
N.
,
Ueji
,
R.
, and
Minamino
,
Y.
,
2002
, “
Nanoscale Crystallographic Analysis of Ultrafine Grained IF Steel Fabricated by ARB Process
,”
Scr. Mater.
,
47
(
2
), pp.
69
76
.10.1016/S1359-6462(02)00088-X
18.
Pérez-Prado
,
M.
,
del Valle
,
J. A.
, and
Ruano
,
O.
,
2004
, “
Grain Refinement of Mg–Al–Zn Alloys Via Accumulative Roll Bonding
,”
Scr. Mater.
,
51
(
11
), pp.
1093
1097
.10.1016/j.scriptamat.2004.07.028
19.
Heason
,
C.
, and
Prangnell
,
P.
,
2002
, “
Texture Evolution and Grain Refinement in Al Deformed to Ultra-High Strains by Accumulative Roll Bonding (ARB)
,”
Mater. Sci. Forum
,
408–412
, pp.
733
738
.10.4028/www.scientific.net/MSF.408-412.733
20.
Kamikawa
,
N.
,
Tsuji
,
N.
,
Huang
,
X.
, and
Hansen
,
N.
,
2006
, “
Quantification of Annealed Microstructures in ARB Processed Aluminum
,”
Acta Mater.
,
54
(
11
), pp.
3055
3066
.10.1016/j.actamat.2006.02.046
21.
Jiang
,
L.
,
Prado
,
M. P.
,
Gruber
,
P.
,
Arzt
,
E.
,
Ruano
,
O.
, and
Kassner
,
M.
,
2008
, “
Texture, Microstructure and Mechanical Properties of Equiaxed Ultrafine-Grained Zr Fabricated by Accumulative Roll Bonding
,”
Acta Mater.
,
56
(
6
), pp.
1228
1242
.10.1016/j.actamat.2007.11.017
22.
Saito
,
Y.
,
Utsunomiya
,
H.
, and H
Suzuki
,
T. S.
,
2008
, “
Improvement in the R-Value of Aluminum Strip by a Continuous Shear Deformation Process
,”
Scr. Mater.
,
42
(
12
), pp.
1139
1144
.10.1016/S1359-6462(00)00349-3
23.
Okamura
,
Y.
,
Utsunomiya
,
H.
,
Sakai
,
T.
, and
Saito
,
Y.
,
2003
, “
Texture and Microstructure of Ultra-Low Carbon IF Steel Strip Processed by Conshearing
,”
J. Iron Steel Inst. Jpn.
,
89
(
6
), pp.
666
672
.
24.
Utsunomiya
,
H.
,
Hatsuda
,
K.
,
Sakai
,
T.
, and
Saito
,
Y.
,
2004
, “
Continuous Grain Refinement of Aluminum Strip by Conshearing
,”
Mater. Sci. Eng. A
,
372
(
1–2
), pp.
199
206
.10.1016/j.msea.2003.12.014
25.
Hall
,
E. O.
,
1951
, “
The Deformation and Aging of Mild Steel. III: Discussion of Results
,”
Proc. Phys. Soc. London B
,
64
(
9
), pp.
747
753
.10.1088/0370-1301/64/9/303
26.
Petch
,
N.
,
1953
, “
The Cleavage Strength of Polycrystals
,”
J. Iron Steel Inst.
,
174
(
1
), pp.
25
28
.
27.
Krasilnikov
,
N.
,
Lojkowski
,
W.
,
Pakiela
,
Z.
, and
Valiev
,
R.
,
2005
, “
Tensile Strength and Ductility of Ultra-Fine-Grained Nickel Processed by Severe Plastic Deformation
,”
Mater. Sci. Eng. A
,
397
(
1–2
), pp.
330
337
.10.1016/j.msea.2005.03.001
28.
Jiang
,
B.
, and
Weng
,
G.
,
2004
, “
A Generalized Self-Consistent Polycrystal Model for the Yield Strength of Nanocrystalline Materials
,”
J. Mech. Phys. Solids
,
52
(
5
), pp.
1125
1149
.10.1016/j.jmps.2003.09.002
29.
Ramtani
,
S.
,
Bui
,
H.
, and
Dirras
,
G.
,
2009
, “
A Revisited Generalized Self-Consistent Polycrystal Model Following an Incremental Small Strain Formulation and Including Grain-Size Distribution Effect
,”
Int. J. Eng. Sci.
,
47
(
4
), pp.
537
553
.10.1016/j.ijengsci.2008.09.005
30.
Ramtani
,
S.
,
Dirras
,
G.
, and
Bui
,
H.
,
2010
, “
A Bimodal Bulk Ultra-Fine-Grained Nickel: Experimental and Micromechanical Investigations
,”
Mech. Mater.
,
42
(
5
), pp.
522
536
.10.1016/j.mechmat.2010.02.001
31.
Bui
,
Q. H.
, and
Pham
,
X. T.
,
2011
, “
Modeling of Microstructure Effects on the Mechanical Behavior of Ultrafine-Grained Nickels Processed by Hot Isostatic Pressing
,”
Int. J. Mech. Sci.
,
53
(
10
), pp.
812
826
.10.1016/j.ijmecsci.2011.06.012
32.
Weng
,
G. J.
,
1983
, “
A Micromechanical Theory of Grain Size Dependence in Metal Plasticity
,”
J. Mech. Phys. Solids
,
31
(
3
), pp.
193
203
.10.1016/0022-5096(83)90021-2
33.
Berbenni
,
S.
,
Favier
,
V.
, and
Berveiller
,
M.
,
2007
, “
Impact of the Grain Size Distribution on the Yield Stress of Heterogeneous Materials
,”
Int. J. Plast.
,
23
(
1
), pp.
114
142
.10.1016/j.ijplas.2006.03.004
34.
Raeisinia
,
B.
, and
Sinclair
,
C.
,
2009
, “
A Representative Grain Size for the Mechanical Response of Polycrystals
,”
Mater. Sci. Eng. A
,
525
(
1–2
), pp.
78
82
.10.1016/j.msea.2009.06.045
35.
Nicaise
,
N.
,
Berbenni
,
S.
,
Wagner
,
F.
,
Berveiller
,
M.
, and
Lemoine
,
X.
,
2011
, “
Coupled Effects of Grain Size Distributions and Crystallographic Textures on the Plastic Behaviour of IF Steels
,”
Int. J. Plast.
,
27
(
2
), pp.
232
249
.10.1016/j.ijplas.2010.05.001
36.
Lebensohn
,
R. A.
, and
Tomé
,
C. N.
,
1993
, “
A Study of the Stress State Associated With Twin Nucleation and Propagation in Anisotropic Materials
,”
Philos. Mag. A
,
67
(
1
), pp.
187
206
.10.1080/01418619308207151
37.
Clausen
,
B.
,
Tomé
,
C.
,
Brown
,
D.
, and
Agnew
,
S.
,
2008
, “
Reorientation and Stress Relaxation Due to Twinning: Modeling and Experimental Characterization for Mg
,”
Acta Mater.
,
56
(
11
), pp.
2456
2468
.10.1016/j.actamat.2008.01.057
38.
Barai
,
P.
, and
Weng
,
G. J.
,
2008
, “
The Competition of Grain Size and Porosity in the Viscoplastic Response of Nanocrystalline Solids
,”
Int. J. Plast.
,
24
(
8
), pp.
1380
1410
.10.1016/j.ijplas.2007.09.010
39.
Lebensohn
,
R.
,
Solas
,
D.
,
Canova
,
G.
, and
Brechet
,
Y.
,
1996
, “
Modelling Damage of Al–Zn–Mg Alloys
,”
Acta Mater.
,
44
(
1
), pp.
315
325
.10.1016/1359-6454(95)00163-7
40.
Kurzydlowsky
,
K.
,
1990
, “
A Model for the Flow Stress Dependence on the Distribution of Grain Size in Polycrystals
,”
Scr. Metall. Mater.
,
5
(
24
), pp.
879
883
.10.1016/0956-716X(90)90129-5
41.
Kadkhodapour
,
J.
,
Ziaei-Rad
,
S.
, and
Karimzadeh
,
F.
,
2009
, “
Finite-Element Modeling of Rate Dependent Mechanical Properties in Nanocrystalline Materials
,”
Comput. Mater. Sci.
,
45
(
4
), pp.
1113
1124
.10.1016/j.commatsci.2009.01.014
42.
Wei
,
Y.
, and
Anand
,
L.
,
2004
, “
Grain-Boundary Sliding and Separation in Polycrystalline Metals: Application to Nanocrystalline fcc Metals
,”
J. Mech. Phys. Solids
,
52
(
11
), pp.
2587
2616
.10.1016/j.jmps.2004.04.006
43.
Wei
,
Y.
,
Su
,
C.
, and
Anand
,
L.
,
2006
, “
A Computational Study of the Mechanical Behavior of Nanocrystalline fcc Metals
,”
Acta Mater.
,
54
(
12
), pp.
3177
3190
.10.1016/j.actamat.2006.03.007
44.
Fu
,
H.-H.
,
Benson
,
D. J.
, and
Meyers
,
M. A.
,
2004
, “
Computational Description of Nanocrystalline Deformation Based on Crystal Plasticity
,”
Acta Mater.
,
52
(
15
), pp.
4413
4425
.10.1016/j.actamat.2004.05.036
45.
Wu
,
B.
,
Liang
,
L.
,
Ma
,
H.
, and
Wei
,
Y.
,
2012
, “
A Trans-Scale Model for Size Effects and Intergranular Fracture in Nanocrystalline and Ultra-Fine Polycrystalline Metals
,”
Comput. Mater. Sci.
,
57
, pp.
2
7
.10.1016/j.commatsci.2011.03.045
46.
Péron-Lührs
,
V.
,
Jérusalem
,
A.
,
Sansoz
,
F.
,
Stainier
,
L.
, and
Noels
,
L.
,
2013
, “
A Two-Scale Model Predicting the Mechanical Behavior of Nanocrystalline Solids
,”
J. Mech. Phys. Solids
,
61
(
9
), pp.
1895
1914
.10.1016/j.jmps.2013.04.009
47.
Aoyagi
,
Y.
,
Kobayashi
,
R.
,
Kaji
,
Y.
, and
Shizawa
,
K.
,
2013
, “
Modeling and Simulation on Ultrafine-Graining Based on Multiscale Crystal Plasticity Considering Dislocation Patterning
,”
Int. J. Plast.
,
47
, pp.
13
28
.10.1016/j.ijplas.2012.12.007
48.
Aoyagi
,
Y.
,
Tsuru
,
T.
, and
Shimokawa
,
T.
,
2014
, “
Crystal Plasticity Modeling and Simulation Considering the Behavior of the Dislocation Source of Ultrafine-Grained Metal
,”
Int. J. Plast.
,
55
, pp.
43
57
.10.1016/j.ijplas.2013.09.009
49.
Dobosz
,
R.
,
Lewandowska
,
M.
, and
Kurzydlowski
,
K. J.
,
2012
, “
The Effect of Grain Size Diversity on the Flow Stress of Nanocrystalline Metals by Finite-Element Modelling
,”
Scr. Mater.
,
67
(
4
), pp.
408
411
.10.1016/j.scriptamat.2012.05.043
50.
Peirce
,
D.
,
Asaro
,
R. J.
, and
Needleman
,
A.
,
1982
, “
An Analysis of Nonuniform and Localized Deformation in Ductile Single Crystals
,”
Acta Mater.
,
30
(6), pp.
1087
1119
.10.1016/0001-6160(82)90005-0
51.
Huang
,
Y.
,
1991
, “
A User-Material Subroutine Incorporating Single Crystal Plasticity in the Abaqus Finite Element Program
,” Division of Applied Sciences, Harvard University, Cambridge, MA, Mechanical Report No. 178.
52.
Ting
,
T.
,
1996
, “
Anisotropy Elasticity: Theory and Applications
,” Oxford University Press, Oxford, UK.
53.
Hutchinson
,
J. W.
,
1976
, “
Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials
,”
Proc. R. Soc. London A.
,
348
(1652), pp.
101
127
.10.1098/rspa.1976.0027
54.
Asaro
,
R. J.
,
1983
, “
Micromechanics of Crystals and Polycrystals
,”
Adv. Appl. Mech.
,
23
, pp.
1
15
.10.1016/S0065-2156(08)70242-4
55.
Asaro
,
R. J.
,
1983
, “
Crystal Plasticity
,”
ASME J. Appl. Mech.
,
50
(4b), pp.
921
934
.10.1115/1.3167205
56.
Simulia, 2012, “Abaqus 6.12: Abaqus/CAE User's Manual,” Dassault Systemes, Providence, RI.
57.
Peirce
,
D.
,
Shih
,
C. F.
, and
Needleman
,
A.
,
1984
, “
A Tangent Modulus Method for Rate Dependent Solids
,”
Comput. Struct.
,
18
(
5
), pp.
875
887
.10.1016/0045-7949(84)90033-6
58.
Böhlke
,
T.
,
Risy
,
G.
, and
Bertram
,
A.
,
2006
, “
Finite Element Simulation of Metal Forming Operations With Texture Based Material Models
,”
Modell. Simul. Mater. Sci. Eng.
,
14
(
3
), pp.
365
387
.10.1088/0965-0393/14/3/003
59.
Phan
,
V. T.
,
Jöchen
,
K.
, and
Böhlke
,
T.
,
2012
, “
Simulation of Sheet Metal Forming Incorporating EBSD Data
,”
J. Mater. Process. Technol.
,
212
(
12
), pp.
2659
2668
.10.1016/j.jmatprotec.2012.07.015
60.
Glavas
,
V.
,
Böhlke
,
T.
,
Daniel
,
D.
, and
Leppin
,
C.
,
2012
, “
Texture Based Finite Element Simulation of a Two-Step Can Forming Process
,”
Key Eng. Mater.
,
504–506
, pp.
655
660
.10.4028/www.scientific.net/KEM.504-506.655
61.
Bui
,
Q.
,
Pham
,
X.
, and
Fafard
,
M.
,
2013
, “
Modelling of Microstructure Effects on the Mechanical Behavior of Aluminium Tubes Drawn With Different Reduction Areas
,”
Int. J. Plast.
,
50
, pp.
127
145
.10.1016/j.ijplas.2013.04.005
62.
Schwartz
,
A. J.
,
Kumar
,
M.
,
Adams
,
B.
, and
Field
,
D. P.
,
2009
,
Electron Backscatter Diffraction in Materials Science
, 2nd ed.,
Springer
,
New York
.
63.
Zhang
,
C.
,
Enomoto
,
M.
,
Suzuki
,
A.
, and
Ishimaru
,
T.
,
2004
, “
Characterization of Three-Dimensional Grain Structure in Polycrystalline Iron by Serial Sectioning
,”
Metall. Mater. Trans. A
,
35
(
7
), pp.
1927
1933
.10.1007/s11661-004-0141-5
64.
Rowenhorst
,
D.
,
Lewis
,
A.
, and
Spanos
,
G.
,
2010
, “
Three-Dimensional Analysis of Grain Topology and Interface Curvature in a β-Titanium Alloy
,”
Acta Mater.
,
58
(
16
), pp.
5511
5519
.10.1016/j.actamat.2010.06.030
65.
Cailletaud
,
G.
,
Forest
,
S.
,
Jeulin
,
D.
,
Feyel
,
F.
,
Galliet
,
I.
,
Mounoury
,
V.
, and
Quilici
,
S.
,
2003
, “
Some Elements of Microstructural Mechanics
,”
Comput. Mater. Sci.
,
27
(
3
), pp.
351
374
.10.1016/S0927-0256(03)00041-7
66.
Diard
,
O.
,
Leclercq
,
S.
,
Rousselier
,
G.
, and
Cailletaud
,
G.
,
2005
, “
Evaluation of Finite Element Based Analysis of 3D Multicrystalline Aggregates Plasticity: Application to Crystal Plasticity Model Identification and the Study of Stress and Strain Fields Near Grain Boundaries
,”
Int. J. Plast.
,
21
(
4
), pp.
691
722
.10.1016/j.ijplas.2004.05.017
67.
Aurenhammer
,
F.
,
1991
, “
Voronoi Diagrams—A Survey of a Fundamental Geometric Data Structure
,”
ACM Comput. Surv.
,
23
(
3
), pp.
345
405
.10.1145/116873.116880
68.
CEA
,
2003
, “Cast3M,” CEA, Saclay, France, http://www-cast3m.cea.fr/
69.
Knezevic
,
M.
,
Drach
,
B.
,
Ardeljan
,
M.
, and
Beyerlein
,
I. J.
,
2014
, “
Three Dimensional Predictions of Grain Scale Plasticity and Grain Boundaries Using Crystal Plasticity Finite Element Models
,”
Comput. Methods Appl. Mech. Eng.
,
277
, pp.
239
259
.10.1016/j.cma.2014.05.003
70.
Furukawa
,
M.
,
Horita
,
Z.
,
Nemoto
,
M.
, and
Langdon
,
T. G.
,
2002
, “
The Use of Severe Plastic Deformation for Microstructural Control
,”
Mater. Sci. Eng. A
,
324
(
1–2
), pp.
82
89
.10.1016/S0921-5093(01)01288-6
71.
Bui
,
Q.
,
Dirras
,
G.
,
Ramtani
,
S.
, and
Gubicza
,
J.
,
2010
, “
On the Strengthening Behavior of Ultrafine-Grained Nickel Processed From Nanopowders
,”
Mater. Sci. Eng. A
,
527
(
13–14
), pp.
3227
3235
.10.1016/j.msea.2010.02.003
72.
Ebrahimi
,
F.
,
Bourne
,
G.
,
Kelly
,
M.
, and
Matthews
,
T.
,
1999
, “
Mechanical Properties of Nanocrystalline Nickel Produced by Electrodeposition
,”
Nanostruct. Mater.
,
11
(
3
), pp.
343
350
.10.1016/S0965-9773(99)00050-1
73.
Xiao
,
C.
,
Mirshams
,
R.
,
Whang
,
S.
, and
Yin
,
W.
,
2001
, “
Tensile Behavior and Fracture in Nickel and Carbon Doped Nanocrystalline Nickel
,”
Mater. Sci. Eng. A
,
301
(
1
), pp.
35
43
.10.1016/S0921-5093(00)01392-7
74.
Hughes
,
D.
, and
Hansen
,
N.
,
2000
, “
Microstructure and Strength of Nickel at Large Strains
,”
Acta Mater.
,
48
(
11
), pp.
2985
3004
.10.1016/S1359-6454(00)00082-3
75.
Neighbours
,
J. R.
,
Bratten
,
F. W.
, and
Smith
,
C. S.
,
1952
, “
The Elastic Constants of Nickel
,”
J. Appl. Phys.
,
23
(
4
), pp.
389
393
.10.1063/1.1702218
76.
Bui
,
Q.
, and
Nguyen-Thê
,
D.
,
2013
, “
Elasto-Plastic Self-Consistant Model for Nano Metal Fabricated by Top-Down Method
,”
Proceedings of the 11th National Congress on Mechanics of Deformable Bodies
, Vol.
1
, Hanoi, Vietnam, December, 8–9, 2012, Vietnam Association for Mechanics, Vietnam, pp.
455
461
.
77.
Wu
,
P.
,
Huang
,
Y.
, and
Lloyd
,
D.
,
2006
, “
Studying Grain Fragmentation in ECAE by Simulating Simple Shear
,”
Scr. Mater.
,
54
(
12
), pp.
2107
2112
.10.1016/j.scriptamat.2006.03.016
78.
Fromm
,
B. S.
,
Adams
,
B. L.
,
Ahmadi
,
S.
, and
Knezevic
,
M.
,
2009
, “
Grain Size and Orientation Distributions: Application to Yielding of α-Titanium
,”
Acta Mater.
,
57
(
8
), pp.
2339
2348
.10.1016/j.actamat.2008.12.037
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