In order to fully harness the outstanding mechanical properties of carbon nanotubes (CNT) as fiber reinforcements, it is essential to understand the nature of load transfer in the fiber matrix interfacial region of CNT-based composites. With controlled experimentation on nanoscale interfaces far off, molecular dynamics (MD) is evolving as the primary method to model these systems and processes. While MD is capable of simulating atomistic behavior in a deterministic manner, the extremely small length and time scales modeled by MD necessitate multiscale approaches. To study the atomic scale interface effects on composite behavior, we herein develop a hierarchical multiscale methodology linking molecular dynamics and the finite element method through atomically informed cohesive zone model parameters to represent interfaces. Motivated by the successful application of pullout tests in conventional composites, we simulate fiber pullout tests of carbon nanotubes in a given matrix using MD. The results of the pullout simulations are then used to evaluate cohesive zone model parameters. These cohesive zone models (CZM) are then used in a finite element setting to study the macroscopic mechanical response of the composites. Thus, the method suggested explicitly accounts for the behavior of nanoscale interfaces existing between the matrix and CNT. The developed methodology is used to study the effect of interface strength on stiffness of the CNT-based composite.

1.
Treacy
,
M. M. J.
,
Ebbesen
,
T. W.
, and
Gibbson
,
J. M.
,
1996
, “
Exceptionally High Young’s Modulus Observed for Individual Carbon Nanotubes
,”
Nature (London)
,
381
, pp.
678
680
.
2.
Robertson
,
D. H.
,
Brenner
,
D. W.
, and
Mintmire
,
J. W.
,
1992
, “
Energetics of Nanoscale Graphitic Tubules
,”
Phys. Rev. B
,
45
, p.
12592
12592
.
3.
1987, Engineered Materials Handbook, ASM International, Metals Park, OH, Vol. 1, Composites.
4.
Demczyk
,
B. G.
,
Wang
,
Y. M.
,
Cumings
,
J.
,
Hetman
,
M.
,
Han
,
W.
,
Zettl
,
A.
, and
Ritchie
,
R. O.
,
2002
, “
Direct Mechanical Measurement of the Tensile Strength and Elastic Modulus of Multiwalled Carbon Nanotubes
,”
Mater. Sci. Eng., A
,
334
, pp.
173
178
.
5.
Yakobson
,
B. I.
,
Brabec
,
C. J.
, and
Bernholc
,
J.
,
1996
, “
Nanomechanics of Carbon Tubes: Instabilities Beyond Linear Response
,”
Phys. Rev. Lett.
,
76
, pp.
2511
2515
.
6.
Belytschko
,
T.
,
Xiao
,
S. P.
,
Schatz
,
G. C.
, and
Ruoff
,
R. S.
,
2002
, “
Atomistic Simulations of Nanotube Fracture
,”
Phys. Rev. B
,
65
, p.
235430
235430
.
7.
Pan
,
Z. W.
,
Xie
,
S. S.
,
Lu
,
L.
,
Chang
,
B. H.
,
Sun
,
L. F.
,
Zhou
,
W. Y.
,
Wang
,
G.
, and
Zhang
,
D. L.
,
1999
, “
Tensile Tests of Ropes of Very Long Aligned Multiwalled Carbon Nanotubes
,”
Appl. Phys. Lett.
,
74
(
21
), pp.
3152
3155
.
8.
Qian
,
D.
,
Dickey
,
E. C.
,
Andrews
,
R.
, and
Rantell
,
T.
,
2000
, “
Load Transfer and Deformation Mechanisms in Carbon Nanotube-Polystyrene Composites
,”
Appl. Phys. Lett.
,
76
, pp.
2868
2871
.
9.
Wang
,
Q. H.
,
Setlur
,
A. A.
,
Lauerhaas
,
J. M.
,
Dai
,
J. Y.
,
Seelig
,
E. W.
, and
Chang
,
R. P. H.
,
1998
, “
A Nanotube-Based Field-Emission Flat Panel Display
,”
Appl. Phys. Lett.
,
72
, pp.
2912
2194
.
10.
Jia
,
Z.
,
Wang
,
Z.
,
Xu
,
C.
,
Liang
,
J.
,
Wei
,
B.
,
Wu
,
D.
, and
Zhu
,
S.
,
1999
, “
Study on Poly(methly methacrylate)Carbon Nanotube Composites
,”
Mater. Sci. Eng., A
,
271
, pp.
395
400
.
11.
Wagner
,
H. D.
,
Lourie
,
O.
,
Feldman
,
Y.
, and
Tenne
,
R.
,
1998
, “
Stress-Induced Fragmentation of Multiwall Carbon Nanotubes in a Polymer Matrix
,”
Appl. Phys. Lett.
,
72
, pp.
188
190
.
12.
Andrews
,
R.
,
Jacques
,
D.
,
Minot
,
M.
, and
Rantell
,
T.
,
2002
, “
Fabrication of Carbon Multiwalled Nanotube/Polymer Composites by Shear Mixing
,”
Macromol. Mater. Eng.
,
287
, pp.
395
403
.
13.
Ajayan
,
M. P.
,
Stephan
,
O.
,
Colliex
,
C.
, and
Trauth
,
D.
,
1994
, “
Aligned Carbon Nanotube Arrays Formed by Cutting a Polymer Resin-Nanotube Composite
,”
Science
,
265
, pp.
1212
1214
.
14.
McCarthy
,
B.
,
Coleman
,
J. N.
,
Czerw
,
R.
,
Dalton
,
A. B.
,
Caroll
,
D. L.
, and
Blau
,
W. J.
,
2001
, “
Microscopic Study of Nanotube-Conjugated Polymer Interactions
,”
Synth. Met.
,
121
, pp.
1225
1229
.
15.
Dong
,
S. R.
,
Tu
,
J. P.
, and
Zhang
,
X. B.
,
2001
, “
An Investigation of the Sliding Wear Behavior of Cu-Matrix Composite Reinforced by Carbon Nanotubes
,”
Mater. Sci. Eng., A
,
313
, pp.
83
87
.
16.
Kuzumaki
,
T.
,
Miyazawa
,
K.
,
Ichinose
,
H.
, and
Ito
,
K.
,
1998
, “
Processing of Carbon Nanotube Reinforced Aluminum Composite
,”
J. Mater. Res.
,
13
, pp.
2445
2449
.
17.
Kuzumaki
,
T.
,
Ujiie
,
O.
,
Ichinose
,
H.
, and
Ito
,
K.
,
2000
, “
Mechanical Characteristics and Preparation of Carbon Nanotube Fiber-Reinforced Ti Composite
,”
Adv. Eng. Mater.
,
2
, pp.
416
418
.
18.
Ning
,
J.
,
Zhang
,
J.
,
Pan
,
Y.
, and
Guo
,
J.
,
2003
, “
Fabrication and Mechanical Properties of SiO2 Matrix Composites Reinforced by Carbon Nanotube
,”
Mater. Sci. Eng., A
,
357
, pp.
392
396
.
19.
Kamalakaran
,
R.
,
Lupo
,
F.
,
Grobert
,
N.
,
Lozano-Castello
,
D.
,
Jin-Phillipp
,
N. Y.
, and
Ruhle
,
M.
,
2003
, “
In-Situ Formation of Carbon Nanotubes in an Alumina-Nanotube Composite by Spray Pyrolysis
,”
Carbon
,
41
, pp.
2737
2740
.
20.
Cooper
,
C. A.
,
Young
,
R. J.
, and
Halsall
,
M.
,
2001
, “
Investigation Into the Deformation of Carbon Nanotubes and Their Composites Through the Use of Raman Spectroscopy
,”
Composites, Part A
,
32
, pp.
401
411
.
21.
Wood
,
J. R.
,
Zhao
,
Q.
, and
Wagner
,
H. D.
,
2001
, “
Orientation of Carbon Nanotubes in Polymers and Its Detection by Raman Spectroscopy
,”
Composites, Part A
,
32
, pp.
391
399
.
22.
Cooper
,
C. A.
,
Cohen
,
S. R.
,
Barber
,
A. H.
, and
Wagner
,
H. D.
,
2002
, “
Detachment of Nanotubes From a Polymer Matrix
,”
Appl. Phys. Lett.
,
81
, pp.
3873
3875
.
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.
Ajayan
,
P. M.
,
Schadler
,
L. S.
,
Giannaris
,
C.
, and
Rubio
,
A.
,
2000
, “
Single-Walled Carbon Nanotube-Polymer Composites: Strength and Weakness
,”
Adv. Mater. (Weinheim, Ger.)
,
12
, pp.
750
753
.
25.
Namilae, S., 2004, Ph.D. Dissertation, Florida State University.
26.
Tadmor
,
E. B.
,
Philips
,
R.
, and
Ortiz
,
M.
,
1996
, “
Quasicontinuum Analysis of Defects in Solids
,”
Philos. Mag. A
,
73
, pp.
1529
1563
.
27.
Rudd
,
R. E.
, and
Broughton
,
J. Q.
,
2000
, “
Concurrent Coupling of Length Scales in Solid State Systems
,”
Phys. Status Solidi B
,
217
, pp.
251
291
.
28.
Lidorikis
,
E.
,
Bachlechner
,
M. E.
,
Kalia
,
R. K.
,
Nakano
,
A.
,
Vashishta
,
P.
, and
Voyiadjis
,
G. J.
,
2001
, “
Coupling Length Scales for Multiscale Atomistics-Continuum Simulations: Atomistically Induced Stress Distributions in Si/Si3N4 Nanopixels
,”
Phys. Rev. Lett.
,
87
, p.
086104
086104
.
29.
Qian
,
D.
,
Liu
,
W. K.
, and
Ruoff
,
R. S.
,
2001
, “
Mechanics of C60 in Nanotubes
,”
J. Phys. Chem. B
,
105
, p.
10753
10753
.
30.
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
.
31.
Thostenson
,
E. T.
, and
Chou
,
T. W.
,
2003
, “
On the Elastic Properties of Carbon Nanotube-Based Composites: Modeling and Characterization
,”
J. Phys. D
,
36
, pp.
573
582
.
32.
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
, pp.
4647
4649
.
33.
Ananth
,
C. R.
, and
Chandra
,
N.
,
1995
, “
Numerical Modeling of Fiber Pushout Testing Metallic Ceramic and Intermetallic Matrix Composites—Mechanics of the Failure Processes
,”
J. Compos. Mater.
,
29
, pp.
1488
1514
.
34.
Mukherjee
,
S.
,
Ananth
,
C. R.
, and
Chandra
,
N.
,
1997
, “
Effect of Residual Stresses on the Interfacial Fracture Behavior of Metal-Matrix Composites
,”
Compos. Sci. Technol.
,
57
, pp.
1501
1512
.
35.
Chandra
,
N.
, and
Ananth
,
C. R.
,
1995
, “
Analysis of Interfacial Behavior in MMCS and IMCS Using Thin-Slice Push-Out Tests
,”
Compos. Sci. Technol.
,
54
, pp.
87
100
.
36.
Carman
,
G. P.
,
Averill
,
R. C.
,
Reifsnider
,
K. L.
, and
Reddy
,
J. N.
,
1993
, “
Optimization of Fiber Coatings to Minimize Stress-Concentrations in Composite-Materials
,”
J. Compos. Mater.
,
27
, pp.
589
597
.
37.
Chandra
,
N.
,
Li
,
H.
,
Shet
,
C.
, and
Ghonem
,
H.
,
2002
, “
Some Issues in the Application of Cohesive Zone Models for Metal Ceramic Interfaces
,”
Int. J. Solids Struct.
,
39
, pp.
2827
2855
.
38.
Shet
,
C.
, and
Chandra
,
N.
,
2002
, “
Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Processes
,”
ASME J. Eng. Mater. Technol.
,
124
, pp.
440
450
.
39.
Mukherjee
,
S.
,
Ananth
,
C. R.
, and
Chandra
,
N.
,
1997
, “
Evaluation of Fracture Toughness of MMC Interfaces Using This-Slice Push Out Tests
,”
Scr. Mater.
,
36
, pp.
1333
1339
.
40.
Barrenblatt
,
G. I.
,
1959
, “
The Formation of Equilibrium Cracks in Brittle Fracture: General Ideas and Hypothesis, Axially-Smmetric Cracks
,”
Prikl. Mat. Mekh.
,
23
, pp.
434
441
.
41.
Dugdale
,
D. S.
,
1959
, “
Yielding of Steel Sheets Containing Silts
,”
J. Mech. Phys. Solids
,
8
, pp.
100
104
.
42.
Hillerborg
,
A.
,
Modeer
,
M.
, and
Petersson
,
P. E.
,
1976
, “
Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements
,”
Cem. Concr. Res.
,
6
, pp.
773
777
.
43.
Chandra
,
N.
,
Namilae
,
S.
, and
Shet
,
C.
,
2004
, “
Local Elastic Properties of Carbon Nanotubes in the Presence of Stone-Wales Defects
,”
Phys. Rev. B
,
69
, p.
094101
094101
.
44.
Frankland
,
S. J. V.
,
Caglar
,
A.
,
Brenner
,
D. W.
, and
Griebel
,
M.
,
2002
, “
Molecular Simulation of the Influence of Chemical Cross-Links on the Shear Strength of Carbon Nanotube-Polymer Interfaces
,”
J. Phys. Chem. B
,
106
, pp.
3046
3048
.
45.
Lourie
,
O.
, and
Wagner
,
H.
,
1999
, “
Evidence of Stress Transfer and Formation of Fracture Clusters in Carbon Nanotube-Based Composites
,”
Compos. Sci. Technol.
,
59
, pp.
975
977
.
46.
Sun
,
Y. P.
,
Fu
,
K.
,
Lin
,
Y.
, and
Huang
,
W.
,
2002
, “
Functionalized Carbon Nanotubes: Properties and Applications
,”
Acc. Chem. Res.
,
35
, pp.
1096
1102
.
47.
Eitan
,
A.
,
Jiang
,
K.
,
Dukes
,
D.
,
Andrews
,
R.
, and
Schadler
,
L. S.
,
2003
, “
Surface Modification of Multiwalled Carbon Nanotubes: Toward the Tailoring of the Interface in Polymer Composites
,”
Chem. Mater.
,
15
, pp.
3198
3201
.
48.
Namilae
,
S.
,
Chandra
,
N.
, and
Shet
,
C.
,
2004
, “
Mechanical Behavior of Functionalized Nanotubes
,”
Chem. Phys. Lett.
,
387
, pp.
247
252
.
49.
Lordi
,
V.
, and
Yao
,
N.
,
2000
, “
Molecular Mechanics of Binding in Carbon-Nanotube-Polymer Composites
,”
J. Mater. Res.
,
15
, pp.
2770
2773
.
50.
Liao
,
K.
, and
Li
,
S.
,
2001
, “
Interfacial Characteristics of a Carbon Nanotube-Polystyrene Composite System
,”
Appl. Phys. Lett.
,
79
, pp.
4225
4227
.
51.
Brenner
,
D. W.
,
1991
, “
Emperical Potential for Hydrocarbon for Use in Simulating the Chemical Vapor Deposition of Diamond Films
,”
Phys. Rev. B
,
42
,
9458
9471
.
52.
Williams
,
E. R.
,
Jones
, Jr.,
G. C.
,
Fang
,
L.
,
Zare
,
R. N.
,
Garrison
,
B. J.
, and
Brenner
,
D. W.
,
1992
, “
Ion Pickup of Large, Surface-Adsorbed Molecules—A Demonstration of the Eley—Rideal Mechanism
,”
J. Am. Chem. Soc.
,
114
, pp.
3207
3210
.
53.
Zhang
,
L.
, and
Tanaka
,
H.
,
1997
, “
Towards a Deeper Understanding of Wear and Friction on the Atomic Scale—A Molecular Dynamics Analysis
,”
Wear
,
211
, pp.
44
53
.
54.
Buldum
,
A.
, and
Lu
,
J. P.
,
2003
, “
Modeling and Simulations of Carbon Nanotubes and Their Junctions on Surfaces
,”
Appl. Surf. Sci.
,
219
, pp.
123
128
.
55.
Wagner
,
H. D.
,
Aronhime
,
J.
, and
Marom
,
G.
,
1990
,
Proc. R. Soc. London, Ser. A
,
428
, pp.
493
500
.
56.
ABAQUS, 2003 Manual, Version 6.3, Habbit, Karlsson & Sorensen Inc. USA.
You do not currently have access to this content.