In this paper, the effective strength and elastic properties of carbon nanotube reinforced composites are evaluated using a representative volume element with a number of carbon nanotubes embedded in the matrix. This concept is used to predict the mechanical properties of multiple, unidirectional, aligned, and also randomly dispersed carbon nanotube reinforced composites. To characterize these nanocomposites, a continuum model has been developed for large-scale analysis. The effective Young’s and shear moduli of the composites are determined using finite element analysis under the effect of elastic deformation. The role of design parameters like length and volume fraction of carbon nanotubes, tensile and shear strength as well as type of loading conditions are analyzed for multiple carbon nanotubes based composites. The discontinuous and continuous types of carbon nanotubes, with aligned and random distribution, are evaluated. The results show that the continuous and aligned carbon nanotubes produce the largest tensile modulus, compared to the discontinuous and aligned as well as discontinuous and randomly oriented carbon nanotubes along the longitudinal direction.

References

References
1.
Iijima
,
S.
, 1991, “
Helical Microtubules of Graphitic Carbon
,”
Nature
,
354
, pp.
56
58
.
2.
Thostenson
,
E. T.
,
Ren
,
Z. F.
, and
Chou
,
T. W.
, 2001, “
Advances in the Science and Technology of Carbon Nanotubes and Their Composites: A Review
,”
Compos. Sci. Technol.
,
61
, pp.
1899
1912
.
3.
Endo
,
M.
,
Kim
,
Y. A.
,
Hayashi
,
T.
,
Nishimura
,
K.
,
Matushita
,
T.
,
Miyashita
,
K.
, and
Dresselhaus
,
M.S
., 2001, “
Vapor-Grown Carbon Fibers (VGCFs): Basic Properties and Their Battery Applications
,”
Carbon
,
39
, pp.
1287
1297
.
4.
Ruoff
,
R. S.
, and
Lorents
,
D. C.
, 1995, “
Mechanical and Thermal Properties of Carbon Nanotubes
,”
Carbon
,
33
(
7
), pp.
925
930
.
5.
Lu
,
J. P.
, 1997, “
Elastic Properties of Single and Multilayered Nanotubes
,”
J. Phys. Chem. Solids
,
58
(
11
), pp.
1649
1652
.
6.
Ren
,
Z. F.
,
Huang
,
Z. P.
,
Xu
,
J. W.
,
Wang
,
J. H.
,
Bush
,
P.
,
Siegal
,
M. P.
, and
Provencio
,
P. N.
,1998, “
Synthesis of Large Arrays of Well-Aligned Carbon Nanotubes on Glass
,”
Science
,
282
(
5391
), pp.
1105
1107
.
7.
Li
,
C. Y.
, and
Chou
,
T. W.
, 2003, “
A Structural Mechanics Approach for the Analysis of Carbon Nanotubes
,”
Int. J. Solids Struct.
,
40
, pp.
2487
2499
.
8.
Chang
,
T.
, and
Gao
,
H.
, 2003, “
Size-Dependent Elastic Properties of a Single-Walled Carbon Nanotube via a Molecular Mechanics Model
,”
J. Mech. Phys. Solids
,
51
, pp.
1059
1074
.
9.
Krishnan
,
A.
,
Dujardin
,
E.
,
Ebbesen
,
T. W.
,
Yianilos
,
P. N.
, and
Treacy
,
M. M. J.
, 1998, “
Young’s Modulus of Single-Walled Nanotubes
,”
Phys. Rev. B
,
58
, pp.
14013
14019
.
10.
Yao
,
N.
, and
Lordi
,
V.
, 1998, “
Young’s Modulus of Single-Walled Carbon Nanotubes
,”
J. Appl. Phys.
,
84
, pp.
1939
1943
.
11.
Qian
,
D.
,
Liu
,
W. K.
, and
Ruoff
,
R. S.
, 2001, “
Mechanics of C60 in Nanotubes
,”
J. Phys. Chem. B
,
105
, pp.
10753
10758
.
12.
Bower
,
C.
,
Rosen
,
R.
,
Jin
,
L.
,
Han
,
J.
, and
Zhou
,
O.
,1999, “
Deformation of Carbon Nanotubes in Nanotube-Polymer Composites
,”
Appl. Phys. Lett.
,
74
, pp.
3317
3319
.
13.
Chen
,
X. L.
, and
Liu
,
Y. J.
, 2004, “
Square Representative Volume Elements for Evaluating the Effective Material Properties of Carbon Nanotube-Based Composites
,”
Comput. Mater. Sci.
,
29
, pp.
1
11
.
14.
Liu
,
Y. J.
, and
Chen
,
X. L.
, 2003, “
Evaluations of the Effective Materials Properties of Carbon Nanotube-Based Composites Using a Nanoscale Representative Volume Element
,”
Mech. Mater.
,
35
, pp.
69
81
.
15.
Ruoff
,
R. S.
,
Qian
,
D.
, and
Liu
,
W. K.
, 2003, “
Mechanical Properties of Carbon Nanotubes: Theoretical Predictions and Experimental Measurements
,”
C. R. Phys.
,
4
, pp.
993
1008
.
16.
Joshi Unnati
,
A.
,
Harsha
,
S. P.
, and
Sharma Satish
,
C.
, 2011, “
Effect of Pinhole Defects on the Elasticity of Carbon Nanotube Based Nanocomposites
,”
ASME J. Nanotechnol. Eng. Med.
,
2
, p.
011003
.
17.
Joshi Unnati
,
A.
,
Harsha
,
S. P.
, and
Sharma Satish
,
C.
, 2011, “
Effect of Waviness on the Mechanical Properties of Carbon Nanotube Based Composites
,”
Physica E: Low Dimensional systems & Nanostructures.
,
43
, pp.
1453
1460
.
18.
Xie
,
J.
,
Aatre
,
K. A.
,
Varadan
,
V. K.
,
Veetil
,
J. V.
, and
Ye
,
K.
, 2008, “
Synthesis of Aligned Carbon Nanotubes by Microwave Chemical Vapor Deposition and Investigation of Their Covalent Bonding With Antibodies for Biomedical Applications
,”
Int. J. Nanopart.
,
1
, pp.
119
135
.
19.
Liu
,
Y. J.
,
Nishimura
,
N.
, and
Otani
,
Y.
, 2005, “
Large-Scale Modeling of Carbon Nanotube Composites by a Fast Multipole Boundary Element Method
,”
Comput. Mater. Sci.
,
34
, pp.
173
187
.
20.
Yu
,
M. F.
,
Lourie
,
O.
, and
Ruoff
,
R. S.
, 2000, “
Strength and Breaking Mechanism of Multiwalled Carbon Nano Rubes Under Tensile Load
,”
Science
,
287
, pp.
637
640
.
21.
Govindjee
,
S.
, and
Sackman
,
J. L.
, 1999, “
On the Use of Continuum Mechanics to Estimate the Properties of Nanotubes
,”
Solid State Commun.
,
110
, pp.
227
230
.
22.
Sohlberg
,
K.
,
Sumpter
,
B. G.
,
Tuzun
,
R. E.
, and
Noid
,
D. W
.,1998, “
Continuum Methods of Mechanics as a Simplified Approach to Structural Engineering of Nanostructures
,”
Nano- 390 technology
,
9
, pp.
30
36
.
23.
Schadler
,
L. S.
,
Giannaris
,
S. C.
, and
Ajayan
,
P. M.
, 1998, “
Load Transfer in Carbon Nanotube Epoxy Composites
,”
Appl. Phys. Lett.
,
73
(
26
), pp.
3842
3844
.
24.
Fisher
,
F. T.
,
Bradshaw
,
R. D.
, and
Brinson
,
L. C.
, 2002, “
Effects of Nanotube Waviness on the Modulus of Nanotube-Reinforced Polymers
,”
Appl. Phys. Lett.
,
80
(
24
), pp.
4647
4649
.
25.
Lau
,
K. T.
, 2003, “
Interfacial Bonding Characteristics of Nanotubes/Polymer Composites
,”
Chem. Phys. Lett.
,
370
, pp.
399
405
.
26.
Joshi Unnati
,
A.
,
Preeti
,
J.
,
Harsha
,
S. P.
, and
Sharma
,
S. C.
, 2010, “
Evaluation of the Mechanical Properties of CNT Based Composites Using Hexagonal RVE
,”
ASME J. Nanotechnol. Eng. Med.
,
1
, p.
031006
.
27.
Chen
,
X. L.
, and
Liu
,
Y. J.
, 2003, “
Continuum Models of Carbon Nanotube-Based Composites by the BEM
,”
Electron. J. Boundary Elem.
,
1
(
2
), pp.
316
335
.
28.
Hyer
,
M. W.
, 1998,
Stress Analysis of Fiber-Reinforced Composite Materials
,
1st ed.
,
McGraw-Hill
,
Boston
.
29.
Halpin
,
J. C.
, and
Kardos
,
J. L.
, 1976, “
The Halpin-Tsai Equations: A Review
,”
Polym. Eng. Sci.
,
16
(
5
), pp.
344
352
.
30.
Franklanda
,
S. J. V.
,
Harikb
,
V. M.
,
Odegarda
,
G. M.
,
Brennerc
,
D. W.
, and
Gatesd
,
T. S.
, 2003, “
The Stress–Strain Behavior of Polymer–Nanotube Composites From Molecular Dynamics Simulation
,”
Compos. Sci. Technol.
,
63
, pp.
1655
1661
.
You do not currently have access to this content.