Abstract

Strain gradient plasticity theories that have emerged during recent years to provide an explanation for size dependent behavior exhibited by some materials have also created a need for additional material parameters. In this study on PbSn solder alloys’ material length scale, which is needed for use in strain gradient plasticity type constitutive models, is determined. The value of length scale is in agreement with values available in literature for different materials like copper, nickel, and aluminum.

1.
Fleck
,
N.
,
Muller
,
G.
,
Ashby
,
M.
, and
Hutchinson
,
J.
, 1994, “
Strain Gradient Plasticity: Theory and Experiment
,”
Acta Metall. Mater.
0956-7151,
42
(
2
), pp.
475
487
.
2.
McElhaney
,
K.
,
Vlassak
,
J.
, and
Nix
,
W.
, 1998, “
Determination of Indenter Tip Geometry and Indentation Contact Area for Depth-Sensing Indentation Experiment
,”
J. Mater. Res.
0884-2914,
13
, pp.
1300
1306
.
3.
Stolken
,
J.
, and
Evans
,
A.
, 1998, “
A Microbend Test Method For Measuring the Plasticity Length Scale
,”
Acta Mater.
1359-6454,
46
, pp.
5109
5115
.
4.
Xue
,
Z.
,
Huang
,
Y.
, and
Li
,
M.
, 2001, “
Particle Size Effect in Metallic Materials: A Study by the Theory of Mechanism-Based Strain Gradient Plasticity
,”
Acta Mater.
1359-6454,
50
, pp.
149
160
.
5.
Stelemashenko
,
N. A.
,
Walls
,
M. G.
,
Brown
,
L. M.
, and
Milman
,
Y. V.
, 1993, “
Microindentation on W and Mo Oriented Single Crystals: An STM Study
,”
Acta Metall. Mater.
0956-7151,
41
, pp.
2855
2865
.
6.
Ma
,
Q.
, and
Clarke
,
D. R.
, 1995, “
Size Dependent Hardness in Silver Single Crystals
,”
J. Mater. Res.
0884-2914,
10
, pp.
853
863
.
7.
Arselinis
,
A.
, and
Parks
,
D.
, 1999, “
Crystallographic Aspects of Geometrically-Necessary and Statistically-Stored Dislocation Density
,”
Acta Mater.
1359-6454,
47
, pp.
1597
1611
.
8.
Gomez
,
J.
, and
Basaran
,
C.
, 2006, “
Nanoindentation of Pb∕Sn Solder Alloys; Experimental and Finite Element Simulation Results
,”
Int. J. Solids Struct.
0020-7683,
43
(
6
), pp.
1505
1527
.
9.
Gomez
,
J.
, and
Basaran
,
C.
, 2006, “
Damage Mechancis Constitutive Model for Pb∕Sn Solder Joints Incorporating Nonlinear Kineamtic Hardening and Rate Dependent Effects Using a Return Mapping Integration Algorithm
,”
Mech. Mater.
0167-6636,
38
(
7
), pp.
585
589
.
10.
Fleck
,
N.
, and
Hutchinson
,
J.
, 1993, “
A Phenomenological Theory for Strain Gradient Effects in Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
41
(
12
), pp.
1825
1857
.
11.
Kroner
,
E.
, 1962, “
Dislocations and Continuum Mechanics
,” Appl. Mater. Res., 15(
8
), pp.
599
606
.
12.
Ashby
,
M.
, 1970, “
The deformation of Plastically Non-Homogenous Materials
,”
Philos. Mag.
0031-8086,
21
, pp.
399
424
.
13.
Fleck
,
N.
, and
Hutchinson
,
J.
, 1997, “
Strain Gradient Plasticity
,”
Adv. Appl. Mech.
0065-2156,
33
, pp.
295
361
.
14.
Gao
,
H.
,
Huang
,
Y.
, and
Nix
,
W.
, 1999, “
Modeling Plasticity at the Micrometer Scale
,”
Naturwiss.
0028-1042,
86
, pp.
507
515
.
15.
Aifantis
,
E.
, 1998, “
Recent Progress on Gradient Theory and Applications
,”
Material Instabilities in Solids
.
R.
deBorst
, ed., pp.
533
.
16.
Aifantis
,
E.
, 2003, “
Update on a Class of Gradient Theories
,”
Mech. Mater.
0167-6636,”
35
, p.
259
.
17.
Begley
,
M.
, and
Hutchinson
,
J. W.
, 1998, “
The Mechanics of Size Dependent Indentation
,”
J. Mech. Phys. Solids
0022-5096,
46
(
10
), pp.
2049
2068
.
18.
Nix
,
W.
, and
Gao
,
H.
, 1998, “
Indentation Size Effects in Crystalline Materials: A Law for Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
46
(
3
), p.
411
.
19.
Abu Al-Rub
,
R.
, and
Voyiadjis
,
G.
, 2004, “
Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory
,”
Int. J. Multiscale Comp. Eng.
1543-1649, in press.
20.
Abu Al-Rub
,
R.
, and
Voyiadjis
,
G.
, 2004, “
Analytical and Experimental Determination of the Material Intrinsic Length Scale of Strain Gradient Plasticity Theory From Micro- and Nano-Indentation Experiments
,”
Int. J. Plast.
0749-6419,
20
, pp.
1139
1182
.
21.
De Guzman
,
M. S.
,
Neubauer
,
G.
,
Flinn
,
P.
, and
Nix
,
W. D.
, 1993, “
The Role of Indentation Depth on the Measured Hardness of Materials
,”
Mater. Res. Soc. Symp. Proc.
0272-9172,
308
, pp.
613
618
.
22.
Pharr
,
G. M.
, 1998, “
Measurement of Mechanical Properties by Ultra-low Load Indentation
,”
Mater. Sci. Eng., A
0921-5093,
253
, pp.
51
159
.
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