Abstract
A self-consistent scheme is used to describe the behavior of nanocrystalline F.C.C. materials. The material is approximated as a composite with two phases. The inclusion phase represents the grain cores while the matrix phase represents both grain boundaries and triple junctions. The dislocation glide mechanism is incorporated in the constitutive law of the inclusion phase while a thermally activated mechanism accounting for the penetration of dislocations in the grain boundaries is incorporated in the constitutive law of the matrix phase. The model is applied to pure Cu and the results are compared with various experimental data.
1.
Arzt
,
E.
,
1998, “Size Effect in
Materials Due to Microstructural and Dimensional Constraints: a Comparative
Review
,” Acta Mater.
1359-6454, 46
, pp.
5611
–5626
.2.
Hall
, E.
O.
, 1951,
“The Deformation and Aging of Mild Steel
,”
Proc. Phys. Soc. London, Sect. B
0370-1301, B64
, pp.
747
.3.
Petch
, N.
J.
, 1953,
“The Cleavage Strength of Polycrystals
,”
J. Iron Steel Inst., London
0021-1567, 174
, pp.
25
–28
.4.
Ashby
, M.
F.
, 1970,
“The Deformation of Plastically Nonhomogeneous
Materials
,” Philos. Mag.
0031-8086, 21
, pp.
399
–424
.5.
Taylor
, G.
I.
, 1934,
“The Mechanism of Plastic Deformation of Crystals: Part I
Theoretical
,” Proceeedings of the Royal
Society
, A, CXLV
, pp.
362
–387
.6.
Li
, J. C.
M.
, 1963,
“Petch Relation and Grain Boundary Sources
,”
Trans. Metall. Soc. AIME
0543-5722, 227
, pp.
239
–247
.7.
Gao
,
H.
,
Huang
,
Y.
,
Nix
, W.
D.
, and Hutchinson
,
J. W.
, 1999,
“Mechanism Based Strain Gradient Plasticity I.
Theory
,” J. Mech. Phys. Solids
0022-5096, 47
, pp.
1239
–1263
.8.
Gao
,
H.
,
Huang
,
Y.
,
Nix
, W.
D.
, and Hutchinson
,
J. W.
, 1999,
“Mechanism Based Strain Gradient Plasicity II
Analysis
,” J. Mech. Phys. Solids
0022-5096, 47
, pp.
1239
–1263
.9.
Conrad
,
H.
, and
Narayan
,
J.
,
2000, “On the Grain Size
Softening in Nanocrystalline Materials
,” Scr.
Mater.
1359-6462, 42
, pp.
1025
–1030
.10.
Schuh
, C.
A.
, Nieh
, T.
G.
, and Yamasaki
,
T.
,
2002, “Hall–Petch
Breakdown Manifested in Abrasive Wear Resistance of Nanocrystalline
Nickel
,” Scr. Mater.
1359-6462, 46
, pp.
735
–740
.11.
Birringer
,
R.
,
1989, “Nanocrystalline
Materials
,” Mater. Sci. Eng., A
0921-5093, 117
, pp.
33
–43
.12.
Van Swygenhoven
,
H.
,
Caro
,
A.
, and
Farkas
,
D.
,
2001, “Grain Boundary
Structure and its Influence on Plastic Deformation of Polycrystalline FCC
Metals at the Nanoscale: a Molecular Dynamics Study
,”
Scr. Mater.
1359-6462, 44
, pp.
1513
–1516
.13.
Kumar
, K.
S.
, Suresh
,
S.
,
Chislom
, M.
F.
, Horton
, J.
A.
, and Wang
,
P.
,
2003, “Deformation of
Nanocrystalline Nickel
,” Acta Mater.
1359-6454, 51
, pp.
387
–405
.14.
Konstantinidis
, D.
A.
, and Aifantis
,
E. C.
, 1998,
“On the Anomalous Hardness of Nanocrystalline
Materials
,” Acta Metallurgica, 10
, pp.
1111
–1118
.15.
Kim
, H.
S.
, Estrin
,
Y.
, and
Bush
, M.
B.
, 2000,
“Plastic Deformation Behavior of Fine Grained
Materials
,” Acta Mater.
1359-6454, 48
, pp.
493
–504
.16.
Carsley
, J.
E.
, Ning
,
J.
,
Milligan
, W.
W.
, Hackney
, S.
A.
, and Aifantis
,
E. C.
, 1995,
“A Simple Mixture Based Model for the Grain Size Dependence
of Strength in Nanophase Metals
,” Nanostruct.
Mater.
0965-9773, 5
, pp.
441
–448
.17.
Stokes
, R.
J.
, and Cottrel
, A.
H.
, 1954,
“Work Softening in Aluminium Crystals
,”
Acta Metall.
0001-6160, 2
, pp.
341
–342
.18.
Kocks
, U.
F.
, 1976,
“Laws for Work Hardening and Low Temperature
Creep
,” Trans. ASME
0097-6822,98
1
pp.
76
–85
. 19.
Mecking
,
H.
, and
Kocks
, U.
F.
, 1981,
“Kinetics of Flow Stress and Strain
Hardening
,” Acta Metall.
0001-6160, 29
, pp.
1865
–1875
.20.
Van Swygenhoven
,
H.
,
Spaczer
,
M.
, and
Caro
,
A.
,
1999, “Microscopic
Description of Plasticity in Computer Generated Metallic Nanophase Samples:
a Comparison Between Cu and Ni
,” Acta Metall.
Sin.
0412-1961, 47
, pp.
3117
–3126
.21.
Yamakov
,
V.
,
Wolf
,
D.
,
Salazar
,
M.
,
Phillpot
, S.
R.
, and Gleiter
,
H.
,
2001, “Length Scale
Effects in the Nucleation of Extended Dislocations in Nanocrystalline Al by
Molecular Dynamics Simulation
,” Acta Mater.
1359-6454, 49
, pp.
2713
–2722
.22.
Froseth
,
A.
,
Van Swygenhoven
,
H.
, and
Derlet
, P.
M.
, 2004,
“The Influence of Twins on the Mechanical Properties of
nc-Al
,” Acta Mater.
1359-6454, 52
, pp.
2259
–2268
.23.
Malis
,
T.
, and
Tangri
,
K.
,
1979, “Grain Boundaries
as Dislocation Sources in the Premacroyield Strain Region
,”
Acta Metall.
0001-6160, 27
, pp.
25
–32
.24.
Ranganathan
,
S.
,
Divakar
,
R.
, and
Raghunathan
, V.
S.
, 2000,
“Interface Structures in Nanocrystalline
Materials
,” Scr. Mater.
1359-6462, 44
, pp.
1169
–1174
.25.
Hirth
, J.
P.
, and Lothe
,
J.
,
1982, Theory of
Dislocations
, Krieger Publishing
Co.
, p. 760
.26.
Murr
, L.
E.
, 1981,
“Strain Induced Dislocation Emission from Grain Boundaries in
Stainless Steel
,” Mater. Sci. Eng.
0025-5416, 51
, pp.
71
–79
.27.
Murr
, L.
E.
, and Venkatesh
,
E.
,
1978, “Contrast
Phenomena and the Identification of Grain Bounday Ledges
,”
Metallography
0026-0800, 11
, pp.
61
–79
.28.
Nazarov
, A.
A.
, Shenderova
, O.
A.
, and Brenner
, D.
W.
, 2000,
“On the Dislcination Structural Unit Model of Grain
Boundaries
,” Mater. Sci. Eng., A
0921-5093, 281
, pp.
148
–155
.29.
Gutkin
, M.
Y.
, Ovid’ko
, I.
A.
, and Skiba
, N.
V.
, 2003,
“Transformation of Grain Boundaries Due to Disclination
Motion and Emission of Dislocation Pairs
,” Mater.
Sci. Eng., A
0921-5093, 339
, pp.
73
–80
.30.
Yamakov
,
V.
,
Wolf
,
D.
,
Phillpot
, S.
R.
, and Gleiter
,
H.
,
2002, “Deformation
Twinning in Nanocrystalline Al by Molecular Dynamics
Simulation
,” Acta Mater.
1359-6454, 50
, pp.
5005
–5020
.31.
Karaman
,
I.
,
Sehitoglu
,
H.
,
Beaudoin
, A.
J.
, Chumlyakov
, Y.
I.
, Maier
, H.
J.
, and Tome
, C.
N.
, 2000,
“Modeling the Deformation Behavior of Hadfield Steel Single
and Polycrystals due to Twinning and Slip
,” Acta
Mater.
1359-6454, 48
, pp.
2031
–2047
.32.
Ke
,
M.
,
Hackney
, S.
A.
, Milligan
, W.
W.
, and Aifantis
,
E. C.
, 1995,
“Observation and Measurement of Grain Rotation and Plastic
Strain in Nanostructured Metal Thin Films
,”
Nanostruct. Mater.
0965-9773, 5
, pp.
689
–697
.33.
Van Swygenhoven
,
H.
, and
Caro
,
A.
,
1997, “Molecular
Dynamics Computer Simulation of Nanophase Ni: Structure and Mechanical
Properties
,” Nanostruct. Mater.
0965-9773, 9
, pp.
669
–672
.34.
Cai
,
B.
,
Kong
, Q.
P.
, Lu
,
L.
, and
Lu
,
K.
,
1999, “Interface
Controlled Diffusional Creep of Nanocrystalline Pure
Copper
,” Scr. Mater.
1359-6462, 41
, pp.
755
–759
.35.
Sanders
, P.
G.
, Rittner
,
M.
,
Kiedaisch
,
E.
,
Weertman
, J.
R.
, Hung
,
H.
, and
Lu
, Y. C.
, 1997,
“Creep of Nanocrystalline Cu, Pd, and Al–Zr
,”
Nanostruct. Mater.
0965-9773, 9
, pp.
433
–440
.36.
Coble
, R.
L.
, 1963,
“A Model for Boundary Diffusion Controlled Creep in
Polycrystalline Materials
,” J. Appl. Phys.
0021-8979,
34
, pp.
1679
–1682
.37.
Wang
,
N.
,
Wang
,
Z.
,
Aust
, K.
T.
, and Erb
,
U.
,
1997, “Room Temperature
Creep Behavior of Nanocrystalline Nickel Produced by an Electrodeposition
Technique
,” Mater. Sci. Eng., A
0921-5093, 237
, pp.
150
–158
.38.
Jiang
,
B.
, and
Weng
, G.
J.
, 2003,
“A Composite Model for the Grain Size Dependence of Yield
Stress of Nano-Grained Materials
,” Metall. Mater.
Trans. A
1073-5623, 34A
, pp.
765
–772
.39.
Jiang
,
B.
, and
Weng
, G.
J.
, 2004,
“A Theory of Compressive Yield Strength of Nanograined
Ceramics
,” Int. J. Plast.
0749-6419, 20
, pp.
2007
–2026
.40.
Jiang
,
B.
, and
Weng
, G.
J.
, 2004,
“A Generalized Self Consistent Polycrystal Model for the
Yield Strength of Nanocryatslline Materials
,” J.
Mech. Phys. Solids
0022-5096, 52
, pp.
1125
–1149
.41.
Zhou
,
Y.
,
Erb
,
U.
,
Aust
, K.
T.
, and Palumbo
,
G.
,
2003, “The Effects of
Triple Junctions and Grain Boundaries on Hardness and Young’S Modulus in
Nanostructured Ni-P
,” Scr. Mater.
1359-6462, 48
, pp.
825
–830
.42.
Ovid’ko
, I.
A.
, and Reizis
, A.
B.
, 2001,
“Grain Boundary Dislocation Climb and Diffusion in
Nanocrystalline Solids
,” Phys. Solid State
1063-7834,
43
, pp.
35
–38
.43.
Kocks
, U.
F.
, Argon
, A.
S.
, and Ashby
, M.
F.
, 1975,
Prog. Mater. Sci.
0079-6425, 19
, pp.
110
–170
.44.
Estrin
,
Y.
,
1998, “Dislocation
Theory Based Constitutive Modelling: Foundations and
Applications
,” J. Mater. Process. Technol.
0924-0136, 80–81
, pp.
33
–39
.45.
Eshelby
, J.
D.
, 1957,
“The Determination of an Ellipsoidal Inclusion and Related
Problems
,” Proc. R. Soc. London, Ser. A
1364-5021, 241
, pp.
376
–396
.46.
Cherkaoui
,
M.
,
Sun
, Q.
P.
, and Song
, G.
Q.
, 2000,
“Micromechanics Modeling of Composite with Ductile Matrix and
Shape Memory Alloy Reinforcement
,” Int. J. Solids
Struct.
0020-7683, 37
, pp.
1577
–1594
.47.
Hirth
, J.
P.
, and Lothe
,
J.
,
1982, Theory of
dislocations
, John Wiley and Sons
,
New York.48.
Youngdahl
, C.
J.
, Sanders
, P.
G.
, and Eastman
, J.
R.
, 1997,
“Compressive Yield Strengths of Nanocrystalline Cu and
Pd
,” Scr. Mater.
1359-6462, 37
, pp.
809
–813
.49.
Sanders
, P.
G.
, Eastman
, J.
A.
, and Weertman
,
J. R.
, 1996,
Processing and Properties of Nanocrystalline Materials
,
TMS
, Warrendale, PA.50.
Nieman
, G.
W.
, Weertman
, J.
R.
, and Siegel
, R.
W.
, 1991,
“Mechanical Behavior of Nanocrystalline Cu and
Pd
,” J. Mater. Res.
0884-2914, 6
, p.
1012
.51.
Surayanarayana
,
R.
,
Frey
,
R.
,
Sastry
, S. M.
L.
, Waller
, B.
E.
, Bates
, S.
E.
, and Buhro
, W.
E.
, 1996,
“Deformation, Recovery, and Recrystallization Behavior of
Nanocrystalline Copper Produced From Solution-Phase Synthesized
Nanoparticles
,” J. Alloys Compd.
0925-8388, 11
, pp.
449
–457
.52.
Kumar
, K.
S.
, Van Swygenhoven
,
H.
, and
Suresh
,
S.
,
2003, “Mechanical
Behavior of Nanocrystalline Metals and Alloys
,” Acta
Mater.
1359-6454, 51
, pp.
5743
–5774
.Copyright © 2005
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