The Effect of Nanotube Waviness and Agglomeration on the Elastic Property of Carbon Nanotube-Reinforced Composites

[+] Author and Article Information
Dong-Li Shi, Xi-Qiao Feng

Key Lab of Failure Mechanics of Education Ministry of China, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China

Yonggang Y. Huang

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Keh-Chih Hwang

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China

Huajian Gao

Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569 Stuttgart, Germany

J. Eng. Mater. Technol 126(3), 250-257 (Jun 29, 2004) (8 pages) doi:10.1115/1.1751182 History: Received June 30, 2003; Revised March 01, 2004; Online June 29, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Iijima,  S., 1991, “Helical Microtubles of Graphitic Carbon,” Nature (London), 354, pp. 56–58.
Qian,  D., Wagner,  G. J., Liu,  W. K., Yu,  M. F., and Ruoff,  R. S., 2002, “Mechanics of Carbon Nanotubes,” Appl. Mech. Rev., 55(6), pp. 495–533.
Saito, R., Dresselhaus, G., and Dresselhaus, M. S., 1998, Physical Properties of Carbon Nanotubes, Imperial College Press, London.
Treacy,  M. M. J., Ebbesen,  T. W., and Gibson,  J. M., 1996, “Exceptionally High Young’s Modulus Observed for Individual Carbon Nanotubes,” Nature (London), 381, pp. 678–680.
Yakobson,  B. I., Brabec,  C. J., and Bernholc,  J., 1996, “Nanomechanics of Carbon Tubes: Instability Beyond Linear Response,” Phys. Rev. Lett., 76(14), pp. 2511–2514.
Yu,  M. F., Files,  B. S., Arepalli,  S., and Ruoff,  R. S., 2000, “Tensile Loading of Ropes of Single Wall Carbon Nanotubes and Their Mechanical Properties,” Phys. Rev. Lett., 84, pp. 5552–5555.
Yu,  M. F., Lourie,  O., Dyer,  M. J., Moloni,  K., and Ruoff,  R. S., 2000, “Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load,” Science, 287, pp. 637–640.
Zhang,  P., Huang,  Y., Gao,  H., and Hwang,  K. C., 2002, “Fracture Nucleation in Single-Wall Carbon Nanotubes Under Tension: A Continuum Analysis Incorporating Interatomic Potentials,” ASME J. Appl. Mech., 69(3), pp. 454–458.
Zhang,  P., Huang,  Y., Geubelle,  P. H., Klein,  P. A., and Hwang,  K. C., 2002, “The Elastic Modulus of Single-Wall Carbon Nanotubes: A Continuum Analysis Incorporating Interatomic Potentials,” Int. J. Solids Struct., 39, pp. 3893–3906.
Cornwell,  C. F., and Wille,  L. T., 1997, “Elastic Properties of Single-Walled Carbon Nanotubes in Compression,” Solid State Commun., 101(8), pp. 555–558.
Yao,  Z. H., Zhu,  C. C., Cheng,  M., and Liu,  J., 2001, “Mechanical Properties of Carbon Nanotube by Molecular Dynamics Simulation,” Comput. Mater. Sci., 22, pp. 180–184.
Ebbesen,  T. W., Lezec,  H. J., and Hiura,  H., 1996, “Electrical Conductivity of Individual Carbon Nanotubes,” Nature (London), 382, pp. 54–56.
Wei,  J. H., Xie,  S. J., Wang,  S. G., and Mei,  M. L., 2001, “Dimensional Model of Carbon Nanotubes,” Phys. Lett. A, 292, pp. 207–211.
Calvert,  P., 1999, “Nanotube Composites: A Recipe for Strength,” Nature (London), 399, pp. 210–211.
Thostenson,  E. T., Ren,  Z., 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.
Haggenmueller,  R., Gommans,  H. H., Rinzler,  A. G., Fischer,  J. E., and Winey,  K. I., 2000, “Aligned Single-Wall Carbon Nanotubes in Composites by Melt Processing Methods,” Chem. Phys. Lett., 330, pp. 219–225.
Bower,  C., Rosen,  R., Jin,  L., Han,  J., and Zhou,  O., 1999, “Deformation of Carbon Nanotubes in Nanotube-Polymer Composites,” Appl. Phys. Lett., 74(22), pp. 3317–3319.
Lourie,  O., Cox,  D. M., and Wagner,  H. D., 1998, “Buckling and Collapse of Embedded Carbon Nanotubes,” Phys. Rev. Lett., 81(8), pp. 1638–1641.
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(2), pp. 188–190.
Lourie,  O., and Wagner,  H. D., 1998, “Transmission Electron Microscopy Observations of Single-Wall Carbon Nanotubes Under Axial Tension,” Appl. Phys. Lett., 73(24), pp. 3527–3529.
Jia,  Z. J., Wang,  Z., Xu,  C., Liang,  J., Wei,  B., Wu,  D., and Zhu,  S., 1999, “Study on Poly(methyl methacrylate)/Carbon Nanotube Composites,” Mater. Sci. Eng., A, 271, pp. 395–400.
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. 2868–2870.
Pötschke,  P., Fornes,  T. D., and Paul,  D. R., 2002, “Rheological Behavior of Multiwalled Carbon Nanotube/Polycarbonate Composites,” Polymer, 43(11), pp. 3247–3255.
Andrews,  R., Jacques,  D., Rao,  A. M., Rantell,  T., Derbyshire,  F., Chen,  Y., Chen,  J., and Haddon,  R. C., 1999, “Nanotube Composite Carbon Fibers,” Appl. Phys. Lett., 75(9), pp. 1329–1331.
Odegard,  G. M., Gates,  T. S., Wise,  K. E., Park,  C., and Siochi,  E. J., 2002, “Constitutive Modeling of Nanotube-Reinforced Polymer Composites,” Compos. Sci. Technol., 63(11), pp. 1671–1687.
Ajayan,  P. M., Schadler,  L. S., Giannaris,  C., and Rubio,  A., 2000, “Single-Walled Nanotube-Polymer Composites: Strength and Weaknesses,” Adv. Mater. (Weinheim, Ger.), 12(10), pp. 750–753.
Nardelli,  M. B., Fattebert,  J. L., Orlikowski,  D., Roland,  C., Zhao,  Q., and Bernholc,  J., 2000, “Mechanical Properties, Defects and Electronic Behavior of Carbon Nanotubes,” Carbon, 38, pp. 1703–1711.
Nemat-Nasser, S., and Hori, M., 1993, Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland, New York.
Mori,  T., and Tanaka,  K., 1973, “Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions,” Acta Metall., 21, pp. 571–574.
Hill,  R., 1965, “A Self-Consistent Mechanics of Composite Materials,” J. Mech. Phys. Solids, 13, pp. 213–222.
Mura, T., 1987, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, Dordrecht.
Popov,  V. N., Doren,  V. E., and Balkanski,  M., 2000, “Elastic Properties of Crystals of Single-Walled Carbon Nanotubes,” Solid State Commun., 114, pp. 395–399.
Andrews,  R., Jacques,  D., Minot,  M., and Rantell,  T., 2002, “Fabrication of Carbon Multiwall Nanotube/Polymer Composites by Shear Mixing,” Macromolecular Materials and Engineering,287, pp. 395–403.
Shaffer,  M. S. P., and Windle,  A. H., 1999, “Fabrication and Characterization of Carbon Nanotube/Poly(vinyl alcohol) Composites,” Adv. Mater. (Weinheim, Ger.), 11, pp. 937–941.
Vigolo,  B., Penicaud,  A. P., Couloun,  C., Sauder,  S., Pailler,  R., Journet,  C., Bernier,  P., and Poulin,  P., 2000, “Macroscopic Fibers and Ribbons of Oriented Carbon Nanotubes,” Science, 290, pp. 1331–1334.
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.
Fisher,  F. T., Bradshaw,  R. D., and Brinson,  L. C., 2003, “Fiber Waviness in Nanotube-Reinforced Polymer Composites: I. Modulus Predictions Using Effective Nanotube Properties,” Compos. Sci. Technol., 63(11), pp. 1689–1703.
Bradshaw,  R. D., Fisher,  F. T., and Brinson,  L. C., 2003, “Fiber Waviness in Nanotube-Reinforced Polymer Composites: II. Modeling via Numerical Approximation of the Dilute Strain Concentration Tensor,” Compos. Sci. Technol., 63(11), pp. 1705–1722.
Curtin, W. A., 2002, private communication with Y. Huang.
Stephan,  C., Nguyen,  T. P., Chapelle,  M. L., and Lefrant,  S., 2000, “Characterization of Single-Walled Carbon Nanotubes-PMMA Composite,” Synth. Met., 108, pp. 139–149.
Jones, R. M., 1999, Mechanics of Composite Materials, Taylor & Francis, Philadelphia.
Shi,  D. L., Feng,  X. Q., Huang,  Y., and Hwang,  K. C., 2004, “Critical evaluation of the stiffening effect of carbon nanotubes in composites,” Key Eng. Mater., 261–263, pp. 1487–1492.


Grahic Jump Location
A CNT with a global and a local coordinate system
Grahic Jump Location
Effective elastic moduli of a composite reinforced with aligned straight CNTs
Grahic Jump Location
Effective elastic moduli of a composite reinforced with randomly orientated straight CNTs
Grahic Jump Location
The spring model of a curved CNT
Grahic Jump Location
Calculation model of the strain in a curved CNT: (a) a curved CNT in the RVE; (b) a slice of infinitesimal thickness; and (c) the approximate model for calculating the strain in the slice
Grahic Jump Location
Effect of CNT waviness on the effective elastic modulus in the longitudinal direction
Grahic Jump Location
Effect of CNT waviness on the effective elastic modulus in the transversal direction
Grahic Jump Location
Eshelby inclusion model of agglomeration of CNTs
Grahic Jump Location
Effect of CNT agglomeration on the effective elastic modulus with ζ=1, in which the CNTs are assumed to be: (a) isotropic; and (b) transversely isotropic
Grahic Jump Location
The effective elastic modulus of a CNT-reinforced composite with agglomeration effect with ξ=0.5, in which the CNTs are assumed to be: (a) isotropic; and (b) transversely isotropic




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In