α-brass and aluminum microhardness and deep nanoindentation data when fitted to the Taylor dislocation-hardening (TDH) model produced a straight-line behavior consistent with the model. Literature data, including copper, silver, and tungsten when also fitted to TDH model, exhibited results similar to the ones produced by the α-brass and aluminum data. The nanohardness data obtained at shallower depths also exhibited straight-line behavior but with a shallower slope. Taken together, the nano-microindentation data constituted what we term a “bilinear behavior,” and we shall discuss possible mechanisms for this behavior.

1.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
,
1994
, “
Strain Gradient Plasticity: Theory and Experiment
,”
Acta Metall. Mater.
,
42
(
2
), pp.
475
487
.
2.
Stolken
,
J. S.
, and
Evans
,
A. G.
,
1998
, “
A Microbend Test Method for Measuring the Plasticity Length Scale
,”
Acta Metall. Mater.
,
46
, pp.
5109
5115
.
3.
Poole
,
W. J.
,
Ashby
,
M. F.
, and
Fleck
,
N. A.
,
1996
, “
Micro-hardness of Annealed and Work-hardened Copper Polycrystals
,”
Acta Metall.
,
34
(
4
), pp.
559
564
.
4.
McElhaney
,
K. W.
,
Vlassak
,
J. J.
, and
Nix
,
W. D.
,
1998
, “
Determination of Indenter Tip Geometry and Indentation Contact Area for Depth-sensing Indentation Experiments
,”
J. Mater. Res.
,
13
(
5
), pp.
1300
1306
.
5.
Ma
,
Q.
, and
Clarke
,
D. R.
,
1995
, “
Size Dependent Hardness of Silver Single Crystals
,”
J. Mater. Res.
,
10
(
4
), pp.
853
863
.
6.
Stelmashenko
,
N. A.
,
Walls
,
M. G.
,
Brown
,
L. M.
, and
Milman
,
Yu. V.
,
1993
, “
Microindentation on W and Mo Oriented Single Crystals: An STM Study
,”
Acta Metall.
,
41
(
10
), pp.
2855
2865
.
7.
Hutchinson
,
J. W.
,
2000
, “
Plasticity at the Micron Scale
,”
Int. J. Solids Struct.
,
37
(
1–2
), pp.
225
238
.
8.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
,
1993
, “
A Phenomenological Theory for Strain Gradient Effects in Plasticity
,”
J. Mech. Phys. Solids
,
41
(
12
), pp.
1825
1857
.
9.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
,
2001
, “
A Reformulation of Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
49
(
10
), pp.
2245
2271
.
10.
Nix
,
W. D.
, and
Gao
,
H.
,
1998
, “
Indentation Size Effect in Crystalline Materials: A Law for Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
46
(
3
), pp.
411
425
.
11.
Fleck, N. A., and Hutchinson, and J. W., 1997, “Strain Gradient Plasticity,” in Advances in Applied Mechanics, J. W. Hutchinson and T. Y. Wu, eds., Academic Press, New York, Vol. 33, p. 295.
12.
Gao
,
H.
,
Huang
,
Y.
,
Nix
,
W. D.
, and
Hutchison
,
J. W.
,
1999
, “
Mechanism-based Strain Gradient Plasticity–I. Theory
,”
J. Mech. Phys. Solids
,
47
(
6
), pp.
1239
1263
.
13.
Huang
,
Y.
,
Gao
,
H.
,
Nix
,
W. D.
, and
Hutchinson
,
J. W.
,
2000
, “
Mechanism-based Strain Gradient Plasticity–II. Analysis
,”
J. Mech. Phys. Solids
,
48
(
1
), pp.
99
128
.
14.
Duan
,
D.-M.
,
Wu
,
N. Q.
,
Slaughter
,
W. S.
, and
Mao
,
S. X.
,
2000
, “
Length Scale Effect on Mechanical Behavior Due to Strain Gradient Plasticity
,”
Mater. Sci. Eng., A
,
303
(
1–2
), pp.
241
249
.
15.
Weertman
,
J.
,
2002
, “
Anomalous Work Hardening, Non-redundant Screw Dislocations in a Circular Bar Deformed in Torsion, and Non-redundant Edge Dislocations in a Bent Foil
,”
Acta Mater.
,
50
, pp.
673
689
.
16.
Elmustafa, A. A., and Stone, D. S., 1999, “Indentation Size Effect: A Kinetic Perspective,” in Advanced Materials for the 21st Century, 1999 Julia Weertman Symp., Y.-W. Chung, and D. C. Dunand, eds., Cincinnati, OH, pp. 311–321.
17.
Elmustafa
,
A. A.
, and
Stone
,
D. S.
,
2003
, “
Nanoindentation and the Indentation Size Effect: Kinetics of Deformation and Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
51
(
2
), pp.
357
381
.
18.
Joslin
,
D. L.
, and
Oliver
,
W. C.
,
1990
, “
A New Method for Analyzing Data from Continuous Depth-Sensing Microindentation Tests
,”
J. Mater. Res.
,
5
(
1
), pp.
123
126
.
19.
Stone
,
D. S.
,
Yoder
,
K. B.
, and
Sproul
,
W. D.
,
1991
, “
Hardness and Elastic Modulus of TiN Based on Continuous Indentation Technique and New Correlation
,”
J. Vac. Sci. Technol.
,
9
(
4
), pp.
2543
2547
.
20.
Lim
,
Y. Y.
, and
Chaudhri
,
M. M.
,
1999
, “
The Effect of Indenter Load on the Nanohardness of Ductile Metals: An Experimental Study on Polycrystalline Workhardened and Annealed Oxygen-free Copper
,”
Philos. Mag. A
,
79
, pp.
2979
3000
.
21.
Swadener
,
J. G.
,
George
,
E. P.
, and
Pharr
,
G. M.
,
2002
, “
The Correlation of the Indentation Size Effect Measured With Indenters of Various Shapes
,”
J. Mech. Phys. Solids
,
50
, pp.
681
694
.
22.
Xin
,
X. J.
,
Daehn
,
G. S.
, and
Wagoner
,
R. H.
,
1997
, “
Equilibrium Configuration of Coaxial Prismatic Dislocation Loops and Related Size-dependent Plasticity
,”
Acta Mater.
,
45
, pp.
1821
1836
.
23.
Kassner
,
M. E.
,
Perez-Prado
,
M.-T.
,
Vecchio
,
K. S.
, and
Wall
,
M. A.
,
2000
, “
Determination of Internal Stresses in Cyclically Deformed Copper Single Crystals Using Convergent-Beam Electron Diffraction and Dislocation Dipole Separation Measurements
,”
Acta Mater.
,
48
, pp.
4247
4254
.
24.
Tippelt
,
B.
,
Bretschneider
,
J.
, and
Ha¨hner
,
P.
,
1997
, “
The Dislocation Microstructure of Cyclically Deformed Nickel Single Crystals at Different Temperatures
,”
Phys. Status Solidi A
,
163
, pp.
11
26
.
25.
Verecky
,
S.
,
Kratochvil
,
J.
, and
Kroupa
,
F.
,
2002
, “
The Stress Field of a Rectangular Prismatic Dislocation Loops
,”
Phys. Status Solidi A
,
191
, pp.
418
426
.
26.
Elmustafa
,
A. A.
, and
Stone
,
D. S.
,
2002
, “
Indentation Size Effect in Polycrystalline F.C.C. Metals
,”
Acta Metall. Mater.
,
50
(
14
), pp.
3641
3650
.
27.
Taylor
,
G.
,
1992
, “
Thermally-activated Deformation of bcc Metals and Alloys
,”
Prog. Mater. Sci.
,
36
, pp.
29
61
.
28.
Conrad, H., 1965, in High Strength Materials, V. F. Zackay, ed., Wiley, New York, p. 436.
29.
Briggs
,
T. L.
, and
Campbell
,
J. D.
,
1972
, “
The Effect of Strain Rate and Temperature on the Yield and Flow Stress of Polycrystalline Niobium and Molybdenum
,”
Acta Metall.
,
20
, pp.
711
724
.
30.
Boyer, H. E., and Gall, T. L., 1985, Metals Handbook, Desk Edition, American Society for Metals, Metals Park, Ohio.
31.
Stone, D. S., and Yoder, K. B., 1993, in Load and Depth-Sensing Indentation Tester for Properties Measurement at Non-Ambient Temperatures: Thin Films, Stresses and Mechanical Properties IV, Mat. Res. Soc. Proc. Vol. 308, P. H. Townsend, T. Weihs, J. E. Sanchez, Jr., and P. Borgensen, eds., Pittsburgh, Mat. Res. Soc., p. 121.
32.
Yoder, K. B., and Stone, D. S., 1993, “Load-and-depth-sensing Indentation Tester for Properties Measurement at Non-ambient Temperatures,” in Mat. Res. Soc. Proc., Mat. Res. Soc., Pittsburgh, p. 308.
33.
Elmustafa
,
A. A.
, and
Stone
,
D. S.
,
2003
, “
Stacking Fault Energy and Dynamic Recovery: Do They Impact the Indentation Size Effect
,”
Mater. Sci. Eng., A
,
238
, pp.
1
8
.
34.
Kramer
,
D.
,
Juang
,
H.
,
Kriese
,
M.
,
Robach
,
J.
,
Nelson
,
J.
,
Wright
,
A.
,
Bahr
,
D.
, and
Gerberich
,
W. W.
,
1999
, “
Yield Strength Predictions From the Plastic Zone Around Nanocontacts
,”
Acta Metall. Mater.
,
47
(
1
), pp.
333
343
.
35.
Gao
,
H.
,
Huang
,
Y.
, and
Nix
,
W. D.
,
1999
, “
Modeling Plasticity at the Micrometer Scale
,”
Naturwissenschaften
,
86
, pp.
507
515
.
36.
Kroupa
,
F.
,
1960
, “
Circular Edge Dislocation Loop
,”
Czech. J. Phys., Sect. B
,
10
, pp.
284
293
.
37.
Khraishi
,
T. A.
,
Zbib
,
H. M.
,
Hirth
,
J. P.
, and
de La Rubia
,
T. D.
,
2000
, “
The Stress Field of a General Volterra Dislocation Loop
,”
Philos. Mag. A
,
80
, pp.
95
105
.
38.
Elmustafa, A. A., Ananda, A. A., and Elmahboub, W. I., “Dislocation Mechanics Simulation of the Bilinear Behavior in Micro and Nanoindentations,” J. Mater. Res., 19(3), pp. 768–779.
You do not currently have access to this content.