A fuzzy fiber reinforced composite (FFRC) reinforced with wavy zig-zag single-walled carbon nanotubes (CNTs) and carbon fibers is analyzed in this study. The distinct constructional feature of this composite is that the wavy CNTs are radially grown on the surface of carbon fibers. To study the effect of the waviness of CNTs on the elastic properties of the FFRC, analytical models based on the mechanics of materials (MOM) approach is derived. Effective elastic properties of the FFRC incorporating the wavy CNTs estimated by the MOM approach have been compared with those predicted by the Mori–Tanaka (MT) method. The values of the effective elastic properties of this composite are estimated in the presence of an interphase between the CNT and the polymer matrix which models the nonbonded van dar Waals interaction between the CNT and the polymer matrix. The effect of waviness of CNTs on the effective properties of the FFRC is investigated when the wavy CNTs are coplanar with two mutually orthogonal planes. The results demonstrate that the axial effective elastic properties of the FFRC containing wavy CNTs can be improved over those of the FFRC with straight CNTs.
Issue Section:
Research Articles
References
1.
Iijima
, S.
, 1991
, “Helical Microtubules of Graphitic Carbon
,” Nature
, 354
, pp. 56
–58
.10.1038/354056a02.
Treacy
, M. M. J.
, Ebbesen
, T. W.
, and Gibson
, J. M.
, 1996
, “Exceptionally High Young's Modulus Observed for Individual Carbon Nanotubes
,” Nature
, 381
, pp. 678
–680
.10.1038/381678a03.
Li
, C.
, and Chou
, T. W.
, 2003
, “A Structural Mechanics Approach for the Analysis of Carbon Nanotubes
,” Int. J. Solids Struct.
, 40
(10
), pp. 2487
–2499
.10.1016/S0020-7683(03)00056-84.
Shen
, L.
, and Li
, J.
, 2004
, “Transversely Isotropic Elastic Properties of Single-Walled Carbon Nanotubes
,” Phys. Rev. B
, 69
, p. 045414
.10.1103/PhysRevB.69.0454145.
Xiao
, J. R.
, Gama
, B. A.
, and Gillespie
, J. W.
, 2005
, “An Analytical Molecular Structural Mechanics Model for the Mechanical Properties of Carbon Nanotubes
,” Int. J. Solids Struct.
, 42
, pp. 3075
–3092
.10.1016/j.ijsolstr.2004.10.0316.
Batra
, R. C.
, and Sears
, A.
, 2007
, “Uniform Radial Expansion/Contraction of Carbon Nanotubes and Their Transverse Elastic Moduli
,” Modell. Simul. Mater. Sci. Eng.
, 15
, pp. 835
–844
.10.1088/0965-0393/15/8/0017.
Batra
, R. C.
, and Gupta
, S. S.
, 2008
, “Wall Thickness and Radial Breathing Modes of Single-Walled Carbon Nanotubes
,” ASME J. Appl. Mech.
, 75
, p. 061010
.10.1115/1.29653708.
Cheng
, H. C.
, Liu
, Y. L.
, Hsu
, Y. C.
, and Chen
, W. H.
, 2009
, “Atomistic-Continuum Modeling for Mechanical Properties of Single-Walled Carbon Nanotubes
,” Int. J. Solids Struct.
, 46
, pp. 1695
–1704
.10.1016/j.ijsolstr.2008.12.0139.
Tsai
, J. L.
, Tzeng
, S. H.
, and Chiu
, Y. T.
, 2010
, “Characterizing Elastic Properties of Carbon Nanotube/Polyimide Nanocomposites Using Multi-Scale Simulation
,” Composites, Part B
, 41
(1
), pp. 106
–115
.10.1016/j.compositesb.2009.06.00310.
Thostenson
, E. T.
, and Chow
, T. W.
, 2003
, “On the Elastic Properties of Carbon Nanotube-Based Composites: Modeling and Characterization
, J. Phys. D Appl. Phys.
, 36
(5
), pp. 573
–582
.10.1088/0022-3727/36/5/32311.
Liu
, Y. J.
, and Chen
, X. L.
, 2003
, “Evaluations of the Effective Material Properties of Carbon Nanotube-Based Composites Using a Nanoscale Representative Volume Element
,” Mech. Mater.
, 35
, pp. 69
–81
.10.1016/S0167-6636(02)00200-412.
Gao
, X. L.
, and Li
, K.
, 2005
, “A Shear-Lag Model for Carbon Nanotube-Reinforced Polymer Composites
,” Int. J. Solids Struct.
, 42
, pp. 1649
–1667
.10.1016/j.ijsolstr.2004.08.02013.
Jiang
, B.
, Liu
, C.
, Zhang
, C.
, Liang
, R.
, and Wang
, B.
, 2009
, “Maximum Nanotube Volume Fraction and its Effect on Overall Elastic Properties of Nanotube-Reinforced Composites
,” Composites, Part B
, 40
(3
), pp. 212
–217
.10.1016/j.compositesb.2008.11.00314.
Esteva
, M.
, and Spanos
, P. D.
, 2009
, “Effective Elastic Properties of Nanotube Reinforced Composites With Slightly Weakened Interfaces
,” J. Mech. Mater. Struct.
, 4
, pp. 887
–900
.10.2140/jomms.2009.4.88715.
Mathur
, R. B.
, Chatterjee
, S.
, and Singh
, B. P.
, 2008
, “Growth of Carbon Nanotubes on Carbon Fiber Substrates to Produce Hybrid/Phenolic Composites With Improved Mechanical Properties
,” Compos. Sci. Technol.
, 68
, pp. 1608
–1615
.10.1016/j.compscitech.2008.02.02016.
Garcia
, E. J.
, Wardle
, B. L.
, Hart
, A. J.
, and Yamamoto
, N.
, 2008
, “Fabrication and Multifunctional Properties of a Hybrid Laminate With Aligned Carbon Nanotubes Grown In Situ
,” Compos. Sci. Technol.
, 68
(9
), pp. 2034
–2041
.10.1016/j.compscitech.2008.02.02817.
Lin
, Y.
, Gregory
, E.
, and Sodano
, H. A.
, 2009
, “Increased Interface Strength in Carbon Fiber Composites Through a ZnO Nanowire Interphase
,” Adv. Funct. Mater.
, 19(16)
, 2654
–2660
.10.1002/adfm.20090001118.
Ray
, M. C.
, Guzman de Villoria
, R.
, and Wardle
, B. L.
, 2009
, “Load Transfer Analysis in Short Carbon Fibers With Radially-Aligned Carbon Nanotubes Embedded in a Polymer Matrix
,” J. Adv. Mater.
, 41
(4
), pp. 82
–94
.19.
Ray
, M. C.
, 2010
, “Concept for a Novel Hybrid Smart Composite Reinforced With Radially Aligned Zigzag Carbon Nanotubes on Piezoelectric Fibers
,” Smart Mater. Struct.
, 19
, p. 035008
.10.1088/0964-1726/19/3/03500820.
Kundalwal
, S. I.
, and Ray
, M. C.
, 2011
, “Micromechanical Analysis of Fuzzy Fiber Reinforced Composites
,” Int. J. Mech. Mater. Des.
, 7
(2
), pp. 149
–166
.10.1007/s10999-011-9156-421.
Shaffer
, M. S. P.
, and Windle
, A. H.
, 1999
, “Fabrication and Characterization of Carbon Nanotube/Poly(Vinyl Alcohol) Composites
,” Adv. Mater.
, 11
(11
), pp. 937
–941
.10.1002/(SICI)1521-4095(199908)11:11<937::AID-ADMA937>3.0.CO;2-922.
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
(20
), pp. 2868
–2870
.10.1063/1.12650023.
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
.10.1063/1.148790024.
Berhan
, L.
, Yi
, Y. B.
, and Sastry
, A. M.
, 2004
, “Effect of Nanorope Waviness on the Effective Moduli of Nanotube Sheets
,” J. Appl. Phys.
, 95
(9
), pp. 5027
–5034
.10.1063/1.168798925.
Shi
, D. L.
, Feng
, X. Q.
, Huang
, Y. Y.
, Hwang
, K. C.
, and Gao
, H.
, 2004
, “The Effect of Nanotube Waviness and Agglomeration on the Elastic Property of Carbon Nanotube-Reinforced Composites
,” ASME J. Eng. Mater. Technol.
, 126
(3
), pp. 250
–257
.10.1115/1.175118226.
Anumandla
, V.
, and Gibson
, R. F.
, 2006
, “A Comprehensive Closed Form Micromechanics Model for Estimating the Elastic Modulus of Nanotube-Reinforced Composites
,” Composites, Part A
, 37
(12
), pp. 2178
–2185
.10.1016/j.compositesa.2005.09.01627.
Shao
, L. H.
, Luo
, R. Y.
, Bai
, S. L.
, and Wang
, J.
, 2009
, “Prediction of Effective Moduli of Carbon Nanotube-Reinforced Composites With Waviness and Debonding
,” Composite Struct.
, 87
(3
), pp. 274
–281
.10.1016/j.compstruct.2008.02.01128.
Smith
, W. A.
, and Auld
, B. A.
, 1991
, “Modeling 1-3 Composite Piezoelectrics: Thickness Mode Oscillations
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
, 38
(1
), pp. 40
–47
.10.1109/58.6783329.
Benveniste
, Y.
, and Dvorak
, G. J.
, 1992
, “Uniform Fields and Universal Relations in Piezoelectric Composites
,” J. Mech. Phys. Solids
, 40
(6
), pp. 1295
–1312
.10.1016/0022-5096(92)90016-U30.
Hsiao
, H. M.
, and Daniel
, I. M.
, 1996
, “Elastic Properties of Composites With Fiber Waviness
,” Composites, Part A
, 27
(10
), pp. 931
–941
.10.1016/1359-835X(96)00034-631.
Dunn
, M. L.
, and Ledbetter
, H.
, 1995
, “Elastic Moduli of Composites Reinforced by Multiphase Particles
,” ASME J. Appl. Mech.
, 62
(4
), pp. 1023
–1028
.10.1115/1.289603832.
Qui
, Y. P.
, and Weng
, G. J.
, 1990
, “On the Application of Mori-Tanaka's Theory Involving Transversely Isotropic Spheroidal Inclusions
,” Int. J. Eng. Sci.
, 28
(11
), pp. 1121
–1137
.10.1016/0020-7225(90)90112-V33.
Mori
, T.
, and Tanaka
, K.
, 1973
, “Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions
,” Acta Metall.
, 21
(5
), pp. 571
–574
.10.1016/0001-6160(73)90064-334.
Li
, J. Y.
, and Dunn
, M. L.
, 1998
, “Anisotropic Coupled-Field Inclusion and Inhomogeneity Problems
,” Philos. Mag. A
, 77
(5
), pp. 1341
–1350
.10.1080/0141861980821425635.
Honjo
, K.
, 2007
, “Thermal Stresses and Effective Properties Calculated for Fiber Composites Using Actual Cylindrically-Anisotropic Properties of Interfacial Carbon Coating
,” Carbon
, 45
(4
), pp. 865
–872
.10.1016/j.carbon.2006.11.00736.
Odegard
, G. M.
, Clancy
, T. C.
, and Gates
, T. S.
, 2005
, “Modeling of the Mechanical Properties of Nanoparticle/Polymer Composites
,” Polymer
, 46
(2
), pp. 553
–562
.10.1016/j.polymer.2004.11.022Copyright © 2013 by ASME
You do not currently have access to this content.
