An analytical and computational model of a novel bending stage is presented. The stage applies bending moments on micro/nanoscale beam specimens using a nanoindenter. In uniaxial tests, any flaw within the entire volume of the specimen may lead to fracture before material yields. The new stage minimizes the volume of material under a uniaxial state of stress in the specimen, but maximizes bending stress over a small volume such that high stresses can be reached within a small volume on the specimen without a premature failure by fracture. The analytical model of the stage accounts for the geometric nonlinearity of the sample, but assumes simplified boundary conditions. It predicts the deflection and stresses in the specimen beam upon loading. The numerical model of the stage and the specimen employing a finite element (FE) package tests the validity of the analytical model. Good agreement between analytical and numerical results shows that the assumptions in the analytical model are reasonable. Therefore, the analytical model can be used to optimize the design of the stage and the specimen. A design of the stage is presented that results in axial/bending stress < 2% in the sample. In order to test the feasibility of the proposed design, a 3D printed stage and a sample are fabricated using the Polyamide PA2200. Bending test is then carried out employing an indenter. Elastic modulus of PA2200 is extracted from the load-deflection data. The value matches closely with that reported in the literature.

References

References
1.
Guénolé
,
J.
,
Godet
,
J.
, and
Brochard
,
S.
,
2011
, “
Deformation of Silicon Nanowires Studied by Molecular Dynamics Simulations
,”
Modell. Simul. Mater. Sci. Eng.
,
19
(
7
), p.
074003
.
2.
Tang
,
D.-M.
,
Ren
,
C.-L.
,
Wang
,
M.-S.
,
Wei
,
X.
,
Kawamoto
,
N.
,
Liu
,
C.
,
Bando
,
Y.
,
Mitome
,
M.
,
Fukata
,
N.
, and
Golberg
,
D.
,
2012
, “
Mechanical Properties of Si Nanowires as Revealed by In Situ Transmission Electron Microscopy and Molecular Dynamics Simulations
,”
Nano Lett.
,
12
(
4
), pp.
1898
1904
.
3.
Han
,
X. D.
,
Zheng
,
K.
,
Zhang
,
Y. F.
,
Zhang
,
X. N.
,
Zhang
,
Z.
, and
Wang
,
Z. L.
,
2007
, “
Low-Temperature In Situ Large-Strain Plasticity of Silicon Nanowires
,”
Adv. Mater.
,
19
(
16
), pp.
2112
2118
.
4.
Sohn
,
Y.-S.
,
Park
,
J.
,
Yoon
,
G.
,
Song
,
J.
,
Jee
,
S.-W.
,
Lee
,
J.-H.
,
Na
,
S.
,
Kwon
,
T.
, and
Eom
,
K.
,
2009
, “
Mechanical Properties of Silicon Nanowires
,”
Nanoscale Res. Lett.
,
5
(
1
), pp.
211
216
.
5.
Kang
,
K.
, and
Cai
,
W.
,
2010
, “
Size and Temperature Effects on the Fracture Mechanisms of Silicon Nanowires: Molecular Dynamics Simulations
,”
Int. J. Plast.
,
26
(
9
), pp.
1387
1401
.
6.
Qin
,
Q.
, and
Zhu
,
Y.
,
2011
, “
Static Friction Between Silicon Nanowires and Elastomeric Substrates
,”
ACS Nano
,
2011
(
9
), pp.
7404
7410
.
7.
Gordon
,
M. J.
,
Baron
,
T.
,
Dhalluin
,
F.
,
Gentile
,
P.
, and
Ferret
,
P.
,
2009
, “
Size Effects in Mechanical Deformation and Fracture of Cantilevered Silicon Nanowires
,”
Nano Lett.
,
9
(
2
), pp.
525
529
.
8.
Kim
,
Y.
,
Son
,
K.
, and
Choi
,
I.
,
2011
, “
Exploring Nanomechanical Behavior of Silicon Nanowires: AFM Bending Versus Nanoindentation
,”
Adv. Funct. Mater.
,
21
(
2
), pp.
279
286
.
9.
Hoffmann
,
S.
,
Utke
,
I.
,
Moser
,
B.
,
Michler
,
J.
,
Christiansen
,
S. H.
,
Schmidt
,
V.
,
Senz
,
S.
,
Werner
,
P.
,
Gösele
,
U.
, and
Ballif
,
C.
,
2006
, “
Measurement of the Bending Strength of Vapor-Liquid-Solid Grown Silicon Nanowires
,”
Nano Lett.
,
6
(
4
), pp.
622
625
.
10.
Korte
,
S.
,
Barnard
,
J. S.
,
Stearn
,
R. J.
, and
Clegg
,
W. J.
,
2011
, “
Deformation of Silicon—Insights From Microcompression Testing at 25–500 °C
,”
Int. J. Plast.
,
27
(
11
), pp.
1853
1866
.
11.
Rabier
,
J.
,
Renault
,
P. O.
,
Eyidi
,
D.
,
Demenet
,
J. L.
,
Chen
,
J.
,
Couvy
,
H.
, and
Wang
,
L.
,
2007
, “
Plastic Deformation of Silicon Between 20 °C and 425 °C
,”
Phys. Status Solidi
,
4
(
8
), pp.
3110
3114
.
12.
Mook
,
W.
,
Nowak
,
J.
,
Perrey
,
C.
,
Carter
,
C.
,
Mukherjee
,
R.
,
Girshick
,
S.
,
McMurry
,
P.
, and
Gerberich
,
W.
,
2007
, “
Compressive Stress Effects on Nanoparticle Modulus and Fracture
,”
Phys. Rev. B
,
75
(
21
), p.
214112
.
13.
Erk
,
C.
,
Brezesinski
,
T.
,
Sommer
,
H.
,
Schneider
,
R.
, and
Janek
,
J.
,
2013
, “
Toward Silicon Anodes for Next-Generation Lithium Ion Batteries: A Comparative Performance Study of Various Polymer Binders and Silicon Nanopowders
,”
ACS Appl. Mater. Interfaces
,
5
(
15
), pp.
7299
7307
.
14.
Kang
,
W.
, and
Saif
,
M. T. A.
,
2013
, “
In Situ Study of Size and Temperature Dependent Brittle-to-Ductile Transition in Single Crystal Silicon
,”
Adv. Funct. Mater.
,
23
(
6
), pp.
713
719
.
15.
Nakao
,
S.
,
Ando
,
T.
,
Shikida
,
M.
, and
Sato
,
K.
,
2008
, “
Effect of Temperature on Fracture Toughness in a Single-Crystal-Silicon Film and Transition in Its Fracture Mode
,”
J. Micromech. Microeng.
,
18
(
1
), p.
015026
.
16.
Namazu
,
T.
,
Isono
,
Y.
, and
Tanaka
,
T.
,
2000
, “
Evaluation of Size Effect on Mechanical Properties of Single Crystal Silicon by Nanoscale Bending Test Using AFM
,”
J. Microelectromech. Syst.
,
9
(
4
), pp.
450
459
.
17.
Stan
,
G.
,
Krylyuk
,
S.
,
Davydov
,
A. V.
,
Levin
,
I.
, and
Cook
,
R. F.
,
2012
, “
Ultimate Bending Strength of Si Nanowires
,”
Nano Lett.
,
12
(
5
), pp.
2599
2604
.
18.
Östlund
,
F.
,
Rzepiejewska-Malyska
,
K.
,
Leifer
,
K.
,
Hale
,
L. M.
,
Tang
,
Y.
,
Ballarini
,
R.
,
Gerberich
,
W. W.
, and
Michler
,
J.
,
2009
, “
Brittle-to-Ductile Transition in Uniaxial Compression of Silicon Pillars at Room Temperature
,”
Adv. Funct. Mater.
,
19
(
15
), pp.
2439
2444
.
19.
Rabier
,
J.
,
Montagne
,
A.
,
Wheeler
,
J. M.
,
Demenet
,
J. L.
,
Michler
,
J.
, and
Ghisleni
,
R.
,
2013
, “
Silicon Micropillars: High Stress Plasticity
,”
Phys. Status Solidi
,
10
(
1
), pp.
11
15
.
20.
Rubanov
,
S.
, and
Munroe
,
P. R.
,
2004
, “
FIB-Induced Damage in Silicon
,”
J. Microsc.
,
214
(
Pt 3
), pp.
213
221
.
21.
Furmanchuk
,
A.
,
Isayev
,
O.
,
Dinadayalane
,
T. C.
,
Leszczynska
,
D.
, and
Leszczynski
,
J.
,
2012
, “
Mechanical Properties of Silicon Nanowires
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
,
2
(
6
), pp.
817
828
.
22.
Florando
,
J. N.
, and
Nix
,
W. D.
,
2005
, “
A Microbeam Bending Method for Studying Stress–Strain Relations for Metal Thin Films on Silicon Substrates
,”
J. Mech. Phys. Solids
,
53
(
3
), pp.
619
638
.
23.
Weihs
,
T.
,
Hong
,
S.
,
Bravman
,
J. C.
, and
Nix
,
W. D.
,
1988
, “
Mechanical Deflection of Cantilever Microbeams: A New Technique for Testing the Mechanical Properties of Thin Films
,”
J. Mater. Res.
,
3
(
5
), pp.
931
942
.
24.
Baker
,
S. P.
, and
Nix
,
W. D.
,
1994
, “
Mechanical Properties of Compositionally Modulated Au-Ni Thin Films: Nanoindentation and Microcantilever Deflection Experiments
,”
J. Mater. Res.
,
9
(
12
), pp.
3131
3144
.
25.
Heinzelmann
,
M.
, and
Petzold
,
M.
,
1994
, “
FEM Analysis of Microbeam Bending Experiments Using Ultra-Micro Indentation
,”
Comput. Mater. Sci.
,
3
(
2
), pp.
169
176
.
26.
Saif
,
M.
,
2000
, “
On a Tunable Bistable MEMS-Theory and Experiment
,”
J. Microelectromech. Syst.
,
9
(
2
), pp.
157
170
.
27.
Finlayson
,
B.
,
1972
,
The Method of Weighted Residuals and Variational Principles
,
Academic Press
,
New York
.
28.
Coy
,
J. A.
,
Kuball
,
C.-M.
,
Roppenecker
,
D. B.
, and
Lueth
,
T. C.
,
2013
, “
Flexural Modulus of Laser Sintered PA 2200
,”
ASME
Paper No. IMECE2013-64696.
You do not currently have access to this content.