This paper deals with an analysis of the size effect on the flow strength of metal-matrix composites due to the presence of geometrically necessary dislocations. The work is based upon a cell model of uniaxial deformation. The deformation field is analyzed based on a requirement of the deformation compatibility along the interface between the particle and the matrix, which in turn is completed through introducing an array of geometrically necessary dislocations. The results of modelling show that the overall stress-strain relationship is dependent not only on the particle volume fraction but also on the particle size. It has been found that the material length scale in the strain gradient plasticity is dependent on the particle volume fraction, or in other words, on the relative ratio of the particle spacing to the particle size. The strain gradient is, besides the macro-strain and the particle volume fraction, inversely proportional to the particle size.

1.
Kelly
,
A.
,
1985
, “
Composites in context
,”
Combust. Sci. Technol.
,
23
, pp.
171
199
.
2.
Lloyd
,
D. J.
,
1994
, “
Particle-reinforced aluminum and magnesium matrix composites
,”
Int. Mater. Rev.
,
39
, No.
1
, pp.
1
23
.
3.
McDanels
,
D. L.
,
1985
, “
Analysis of stress-strain, fracture and ductility behavior of alumunum composites containing discontinuous silicon carbide reinforcement
,”
Metall. Trans.
,
16A
, pp.
1105
1115
.
4.
Lloyd, D. J., 1991, “Metal matrix composites—processing, microstructure and properties,” 12th Riso Int. Symp. On Metallurgy and Materials Science, Riso National Laboratory, Roskilde, Denmark, pp. 81–99.
5.
Humphreys, F. J., Basu, H., and Djazeb, M. R., 1991, “Metal matrix composites—processing, microstructure and properties,” 12th Riso Int. Symp. On Metallurgy and Materials Science, Riso National Laboratory, Roskilde, Denmark, pp. 81–99.
6.
Christman
,
T.
,
Needleman
,
A.
, and
Suresh
,
S.
,
1989
, “
An experimental and numerical study of deformation in metal-matrix composites
,”
Acta Metall.
,
37
, pp.
3029
3050
.
7.
Tvergaad, V., 1991, “Metal matrix composites—processing, microstructure and properties,” 12th Riso Int. Symp. On Metallurgy and Materials Science, Riso National Laboratory, Roskilde, Denmark, pp. 81–99.
8.
Brown, L. M., 1980, “Precipitation and dispersion hardening,” Strength of metals and alloys, Hassen, P. Gerold, V. and Kostortz, G., eds., Pergamon Press, New York, pp. 1551–1571.
9.
Ashby, M. F., 1971, Strengthening Methods in Crystals A. Kelly and R. B. Nicholson, eds., Chapter 3, Applied Science Publishers, London, pp. 137–192.
10.
Rhee
,
M.
,
Hirth
,
J. P.
,
Zbib
,
H. M.
,
1994
, “
A superdislocation model for the strengthening of metal matrix composites and the initiation and propagation of shear bands
,”
Acta Metall. Mater.
,
42
, pp.
2645
2655
.
11.
Rhee
,
M.
,
Hirth
,
J. P.
,
Zbib
,
H. M.
,
1994
, “
On the bow-out tilt wall model of flow stress and size effect in metal matrix composites
,”
Scr. Metall. Mater.
,
31
, pp.
1321
1324
.
12.
Dillon
,
O. W.
,
Kratochivil
,
J. A.
,
1970
, “
A strain gradient theory of plasticity
,”
Int. J. Solids Struct.
,
6
, pp.
1513
1533
.
13.
Bao
,
G.
,
Hutchinson
,
J. W.
, and
McMeeking
,
R. M.
,
1991
, “
Particle reinforcement of ductile matrices against plastic flow and creep
,”
Acta Metall. Mater.
,
39
, pp.
1871
1882
.
14.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
,
1993
, “
A phenomenological theory for strain gradient effects in plasticity
,”
J. Mech. Phys. Solids
,
41
, No.
12
, pp.
1825
1857
.
15.
Fleck, N. A., and Hutchinson, J. W., 1997, “Strain gradient plasticity,” Advances in Applied Mechanics, J. W. Hutchinson and T. Y. Wu, eds., Academic Press, New York, pp. 295–361.
16.
Stelmashenko, N. A., Walls, M. G., Brown, L. M., and Milman, Y. V., 1993, Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, M. Nastasi, D. M. Parkin and H. Gleiter, eds., NATO ASI Series E 233, pp. 605–610.
17.
Ma
,
Q.
, and
Clarke
,
D. R.
,
1995
, “
Size dependent hardness of silver single crystal
,”
J. Mater. Res.
,
10
, No.
4
, pp.
853
863
.
18.
Poole
,
W. J.
,
Ashby
,
M. F.
, and
Fleck
,
N. A.
,
1996
, “
Micro-hardness of annealed and work-hardened copper polycrystals
,”
Scr. Metall. Mater.
,
34
, No.
41
, pp.
559
564
.
19.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
,
1994
, “
Strain gradient plasticity-theory and experiment
,”
Acta Metall. Mater.
,
42
, No.
2
, pp.
475
487
.
20.
Zbib, H. M., and Zhu, H. T., 1994, “On the mechanics of plastic deformation in metal-matrix composites,” Inelasticity and micromechanics of metal matrix composites, Voyjadjis, G. Z., and Ju, J. W., eds., Elsever, Amsterdam, pp 97–118.
21.
Zhu
,
H. T.
, and
Zbib
, I,
H. M.
,
1995
, “
A macroscopic model for plastic flow in metal-matrix composites
,”
Int. J. Plast.
,
II
, pp.
471
499
.
22.
Zhu
,
H. T.
, and
Zbib
,
H. M.
,
1997
, “
Strain gradients and continuum modeling of size effect in metal matrix composites
,”
Acta Mech.
,
121
, pp.
165
176
.
23.
Ashby
,
M. F.
,
1970
, “
The deformation of plastically non-homogeneous materials
,”
Philos. Mag.
,
21
, pp.
399
424
.
24.
Brown
,
L. M.
, and
Stobbs
,
W. M.
,
1976
, “
The worl-hardening of copper-silica, V. Equilibrium plastic relaxation by secondary dislocations
,”
Philos. Mag.
,
34
, No.
3
, pp.
351
372
.
25.
Nix
,
W. D.
, and
Gao
,
H.
,
1998
, “
Indentation size effects in crystalline materials: A law for strain gradient plasticity
,”
J. Mech. Phys. Solids
,
46
, pp.
411
425
.
26.
Duan
,
D-M.
,
Wu
,
N. Q.
,
Slaughter
,
W. S.
, and
Mao
,
S. X.
,
2001
, “
Length scale effect on mechanical behavior due to strain gradient plasticity
,”
Mater. Sci. Eng., A
,
303
, No.
1–2
, pp.
241
249
.
27.
Tvergaard
,
V.
,
1990
, “
Analysis of tensile properties for a whisker-reinforced metal-matrix composites
,”
Acta Metall. Mater.
,
38
, pp.
185
194
.
28.
Dragone, T. and Nix, W. D., 1990, Metal and Ceramic Matrix Composites: Processing, Modelling and Mechanical Behaviour, R. B. Bhagat, A. H. Clauer, P. Kumar and A. M. Ritter, eds., Anaheim, California, The Minerals, Metals & Materials Society, pp. 367–380.
29.
Papazian
,
J. M.
, and
Adler
,
P. N.
,
1990
, “
Tensile properties of short-fiber reinforced SiC/Al composites, Part I: effect of matrix precipitates, Part II: finite-element analysis
,”
Metall. Mater. Trans. A
,
21A
, pp.
401
420
.
You do not currently have access to this content.