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 Pb/Sn solder alloys the 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 the literature for different materials like copper, nickel and aluminum.
Volume Subject Area:
Applied Mechanics
Topics:
Alloys,
Aluminum,
Constitutive equations,
Copper,
Nickel,
Plasticity,
Solder joints,
Solders,
Strain gradient,
Tin
1.
Abu Al-Rub
R
Voyiadjis
G.
2004
). Analytical and Experimental Determination of the Material Intrinsic Length Scale of Strain Gradient Plasticity Theory From Micro- And Nano-Indentation experiments
. International Journal of Plasticity.
, 20
., pp 1139
–1182
.2.
Abu Al-Rub, R and Voyiadjis, G. (2004). Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory. International Journal of Multiscale Computational Engineering. (in press).
3.
Arselinis
A.
Parks
D.
1999
). Crystallographic Aspects of Geometrically-necessary and Statistically-stored Dislocation Density
. Acta Materialia.
, 47
., pp 1597
–1611
.4.
Begley
M.
Hutchinson
J. W.
1998
) The mechanics of size dependent indentation
. J. Mech. Phys. Solids
, Vol 46
, No. 10
, 2049
–2068
.5.
Fleck
N.
Hutchinson
J.
1993
) A Phenomenological Theory for Strain Gradient Effects in Plasticity
. J. Mech. Phys. Solids.
, Vol 41
, 12
, pp 1825
–1857
.6.
Fleck
N.
Hutchinson
J
1997
). Strain Gradient Plasticity
. In Advances in Applied mechanics
, 33
., pp 295
–361
.7.
Fleck
N.
Muller
G
Ashby
M.
Hutchinson
J.
1994
). Strain gradient plasticity: Theory and experiment
. Acta. Metall. Mater.
, 42
(2)
., pp 475
–487
.8.
Gao
H.
Huang
Y.
Nix
W.
1999
). Modeling Plasticity at the Micrometer Scale
. Natur Wissenschaften
., 86
, pp 507
–515
.9.
Gomez
J.
Basaran
C.
2006
a) Nanoindentation of Pb/Sn Solder Alloys; Experimental and Finite Element Simulation Results
,” Int. J. Of Soldis and Structures
, 43
(6)
, 1505
–1527
, March 2006.10.
Gomez
J.
Basaran
C.
2006
b) Damage Mechancis Constitutive Model for Pb/Sn Solder Joints Incorporating nonlinear Kineamtic Hardening and Rate Dependent Effects Using A return Mapping Integration Algorithm
, Mechancis of Materials
, 38
(7)
: 585
–589
July 2006.11.
McElhaney
K.
Vlassak
J.
Nix
W.
1998
). Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiment
. J Mater Res.
, 13
, pp 1300
–1306
.12.
Nix
W.
Gao
H.
1998
). Indentation size effects in crystalline materials: a law for strain gradient plasticity
. J. Mech. Phys. Solids
, Vol 46
, NO 3
, pp 411
411
.13.
Stolken
J.
Evans
A.
1998
). A Microbend Test Method For Measuring The Plasticity Length Scale
. Acta. mater.
, 14
, pp 5109
–5115
.14.
Xue
Z.
Huang
Y.
Li
M.
2001
). Particle size effect in metallic materials: a study by the theory of mechanism-based strain gradient plasticity
. Acta Materialia.
, 50
, pp 149
–160
.15.
Stelemashenko
N. A.
Walls
M. G.
Brown
L. M.
Milman
Y. V.
1993
). Microindentation on W and Mo oriented single crystals: an STM study
. Acta Metallurgica et Materialia.
41
, pp 2855
–2865
.16.
Ma
Q
Clarke
D. R.
1995
). Size dependent hardness in silver single crystals
. J Mater Res.
10
, pp 853
–863
.17.
Kroner
E.
1962
). Dislocations and continuum mechanics
. Appl. Mech. Rev.
15
(8)
., pp 599
–606
.18.
Ashby
M.
1970
). The deformation of plastically non-homogenous materials
. Phil Mag.
, 21
, pp 399
–424
.19.
Aifantis
E
2003
). Update on a class of gradient theries
. Mechanics of Materials.
Vol 35
. pp 259
259
.20.
Aifantis, E (1998). Recent progress on gradient theory and applications. Material Instabilities in Solids. Ed Rene deBorst., pp 533.
21.
De Guzman
M. S.
Neubauer
G
Flinn
P.
Nix
W. D.
1993
). The role of indentation depth on the measured hardness of materials
. Materials Research Symposium Proceedings
, 308
, pp 613
–618
.22.
Pharr
GM
1998
). Measurement of Mechanical Properties by Ultra-low Load Indentation. Mater
. Sci. Eng. A
, Vol 253
, pp 51
–159
.
This content is only available via PDF.
Copyright © 2006
by ASME
You do not currently have access to this content.