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,
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
.
You do not currently have access to this content.