The recently developed distinct element method for mesoscale modeling of carbon nanotubes is extended to account for energy dissipation and then applied to characterize the constitutive behavior of crystalline carbon nanotube bundles subjected to simple tension and to simple shear loadings. It is shown that if these structures are sufficiently long and thick, then they become representative volume elements. The predicted initial stiffness and strength of the representative volumes are in agreement with reported experimental data. The simulations demonstrate that energy dissipation plays a central role in the mechanical response and deformation kinematics of carbon nanotube bundles.
Issue Section:
Research Papers
References
1.
Thostenson
, E.
, Li
, C.
, and Chou
, T.-W.
, 2005
, “Nanocomposites in Context
,” Compos. Sci. Technol.
, 65
(3-4), pp. 491
–516
.10.1016/j.compscitech.2004.11.0032.
Tahhan
, M.
, Truong
, V.-T.
, Spinks
, G. M.
, and Wallace
, G. G.
, 2003
, “Carbon Nanotube and Polyaniline Composite Actuators
,” Smart Mater. Struct.
, 12
(4), pp. 626
–632
.10.1088/0964-1726/12/4/3133.
Hobbie
, E. K.
, Simien
, D. O.
, Fagan
, J. A.
, Huh
, J. Y.
, Chung
, J. Y.
, Hudson
, S. D.
, and Obrzut
, J.
, 2010
, “Wrinkling and Strain Softening in Single-Wall Carbon Nanotube Membranes
,” Phys. Rev. Lett.
, 104
(12
), p. 125505
.10.1103/PhysRevLett.104.1255054.
Suhr
, J.
, Kotakar
, N.
, Keblinski
, P.
, and Ajayan
, P.
, 2005
, “Viscoelasticity in Carbon Nanotube Composites
,” Nature Mater.
, 4
, pp. 134
–137
.10.1038/nmat12935.
Xu
, M.
, Futaba
, D. N.
, Yamada
, T.
, Yumura
, M.
, and Hata
, K.
, 2010
, “Carbon Nanotubes With Temperature-Invariant Viscoelasticity From −196° to 1000 °C
,” Science
, 330
(6009), pp. 1364
–1368
.10.1126/science.11948656.
Thess
, A.
, Lee
, R.
, Nikolaev
, P.
, Dai
, H.
, Petit
, P.
, Robert
, J.
, Xu
, C.
, Lee
, Y. H.
, Kim
, S. G.
, Rinzler
, A. G.
, Colbert
, D. T.
, Scuseria
, G.
, Tomanek
, D.
, Fischer
, J. E.
, and Smalley
, R. E.
, 1996
, “Crystalline Ropes of Metallic Carbon Nanotubes
,” Science
, 273
(5274), pp. 483
–487
.10.1126/science.273.5274.4837.
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
(24
), pp. 5552
–5555
.10.1103/PhysRevLett.84.55528.
Vigolo
, B.
, Penicaud
, A.
, Coulon
, C.
, Sauder
, C.
, Pailler
, R.
, Journet
, C.
, Bernier
, P.
, and Poulin
, P.
, 2000
, “Macroscopic Fibers and Ribbons of Oriented Carbon Nanotubes
,” Science
, 290
(5495), pp. 1331
–1334
.10.1126/science.290.5495.13319.
Zhu
, H. W.
, Xu
, C. L.
, Wu
, D. H.
, Wei
, B. Q.
, Vajtai
, R.
, and Ajayan
, P. M.
, 2002
, “Direct Synthesis of Long Single-Walled Carbon Nanotube Strands
,” Science
, 296
(5569), pp. 884
–886
.10.1126/science.106699610.
Foroughi
, J.
, Spinks
, G. M.
, Wallace
, G. G.
, Oh
, J.
, Kozlov
, M. E.
, Fang
, S.
, Mirfakhrai
, T.
, Madden
, J. D. W.
, Shin
, M. K.
, Kim
, S. J.
, and Baughman
, R. H.
, 2011
, “Torsional Carbon Nanotube Artificial Muscles
,” Science
, 334
(6055), pp. 494
–497
.10.1126/science.121122011.
Beese
, A. M.
, Sarkar
, S.
, Nair
, A.
, Naraghi
, M.
, An
, Z.
, Moravsky
, A.
, Loutfy
, R. O.
, Buehler
, M. J.
, Nguyen
, S. T.
, and Espinosa
, H. D.
, 2013
, “Bio-Inspired Carbon Nanotube Polymer Composite Yarns With Hydrogen Bond-Mediated Lateral Interactions
,” ACS Nano
, 7
(4
), pp. 3434
–3446
.10.1021/nn400346r12.
Dalton
, A. B.
, Collins
, S.
, Munoz
, E.
, Razal
, J. M.
, Ebron
, V. H.
, Ferraris
, J. P.
, Coleman
, J. N.
, Kim
, B. G.
, and Baughman
, R. H.
, 2003
, “Super-Tough Carbon-Nanotube Fibers
,” Nature
, 423
(6941), pp. 703
.10.1038/423703a13.
Behabtu
, N.
, Young
, C. C.
, Tsentalovich
, D. E.
, Kleinerman
, O.
, Wang
, X.
, Ma
, A. W. K.
, Bengio
, E. A.
, Waarbeek
, R. F.
, Jong
, J. J.
, Hoogerwerf
, R. E.
, Fairchild
, S. B.
, Ferguson
, J. B.
, Maruyama
, B.
, Kono
, J.
, Talmon
, Y.
, Cohen
, Y.
, Otto
, M. J.
, and Pasquali
, M.
, 2013
, “Strong, Light, Multifunctional Fibers of Carbon Nanotubes With Ultrahigh Conductivity
,” Science
339
(6116
), pp. 182
–186
.10.1126/science.122806114.
Dumitrică
, T.
, Hua
, M.
, and Yakobson
, B.
, 2006
, “Symmetry-, Time-, and Temperature-Dependent Strength of Carbon Nanotubes
,” Proc. Natl. Acad. Sci. U.S.A.
, 103
(16
), pp. 6105
–6109
.10.1073/pnas.060094510315.
Zhang
, D.-B.
, and Dumitrică
, T.
, 2008
, “Elasticity of Ideal Single-Walled Carbon Nanotubes Via Symmetry-Adapted Tight-Binding Objective Modeling
,” Appl. Phys. Lett.
, 93
, p. 031919
.10.1063/1.296546516.
Zhang
, D.-B.
, James
, R.
, and Dumitrică
, T.
, 2009
, “Electromechanical Characterization of Carbon Nanotubes in Torsion Via Symmetry Adapted Tight-Binding Objective Molecular Dynamics
,” Phys. Rev. B
, 80
(11
), p. 115418
.10.1103/PhysRevB.80.11541817.
Nikiforov
, I.
, Zhang
, D.-B.
, James
, R.
, and Dumitrică
, T.
, 2010
, “Wavelike Rippling in Multiwalled Carbon Nanotubes Under Pure Bending
,” Appl. Phys. Lett.
, 96
(12), p. 123107
.10.1063/1.336870318.
Berhan
, L.
, Yi
, Y. B.
, Sastrya
, A. M.
, Munoz
, E.
, Selvidge
, M.
, and Baughman
, R.
, 2004
, “Mechanical Properties of Nanotube Sheets: Alterations in Joint Morphology and Achievable Moduli in Manufacturable Materials
,” J. Appl. Phys.
, 95
(8
), pp. 4335
–4345
.10.1063/1.168799519.
Buehler
, M. J.
, 2006
, “Mesoscale Modeling of Mechanics of Carbon Nanotubes: Self-Assembly, Self-Folding, and Fracture
,” J. Mater. Res.
, 21
(11
), pp. 2855
–2869
.10.1557/jmr.2006.034720.
Cranford
, S. W.
, and Buehler
, M. J.
, 2010
, “In Silico Assembly and Nanomechanical Characterization of Carbon Nanotube Buckypaper
,” Nanotechnology
, 21
(26), p. 265706
.10.1088/0957-4484/21/26/26570621.
Hahm
, M. G.
, Wang
, H.
, Jung
, H.
, Hong
, S.
, Lee
, S. G.
, Kim
, S. R.
, Upmanyu
, M.
, and Jung
Y. J.
, 2012
, “Bundling Dynamics Regulates the Active Mechanics and Transport in Carbon Nanotube Networks and Their Nanocomposites
,” Nanoscale
, 4
(11
), pp. 3584
–3590
.10.1039/c2nr30254c22.
Xie
, B.
, Liu
, Y.
, Ding
, Y.
, Zheng
, Q.
, and Xu
, Z.
, 2011
, “Mechanics of Carbon Nanotube Networks: Microstructural Evolution and Optimal Design
,” Soft Matter
, 7
(21), pp. 10039
–10047
.10.1039/c1sm06034a23.
Li
, Y.
, and Kroger
, M.
, 2012
, “A Theoretical Evaluation of the Effects of Carbon Nanotube Entanglement and Bundling on the Structural and Mechanical Properties of Buckypaper
,” Carbon
, 50
(5), pp. 1793
–1806
.10.1016/j.carbon.2011.12.02724.
Li
, Y.
, and Kroger
, M.
, 2012
, “Viscoelasticity of Carbon Nanotube Buckypaper: Zipping–Unzipping Mechanism and Entanglement Effects
,” Soft Matter
, 8
(30), pp. 7822
–7830
.10.1039/c2sm25561h25.
Zhigilei
, L. V.
, Wei
, C.
, and Srivastava
, D.
, 2005
, “Mesoscopic Model for Dynamic Simulations of Carbon Nanotubes
,” Phys. Rev. B
, 71
(16), p. 165417
.10.1103/PhysRevB.71.16541726.
Volkov
, A. N.
, and Zhigilei
, L. V.
, 2010
, “Mesoscopic Interaction Potential of Carbon Nanotubes of Arbitrary Length and Orientation
,” J. Phys. Chem. C
, 114
(12), pp. 5513
–5531
.10.1021/jp906142h27.
Volkov
, A. N.
, and Zhigilei
, L. V.
, 2010
, “Structural Stability of Carbon Nanotube Films: The Role of Bending Buckling
,” ACS Nano
, 4
(10
), pp. 6187
–6195
.10.1021/nn101590228.
Jacobs
, W. M.
, Nicholson
, D. A.
, Zemer
, H.
, Volkov
, A. N.
, and Zhigilei
, L. V.
, 2012
, “Acoustic Energy Dissipation and Thermalization in Carbon Nanotubes: Atomistic Modeling and Mesoscopic Description
,” Phys. Rev. B
, 86
(16), p. 165414
.10.1103/PhysRevB.86.16541429.
Anderson
, T.
, Akatyeva
, E.
, Nikiforov
, I.
, Potyondy
, D.
, Ballarini
, R.
, and Dumitrică
, T.
, 2010
, “Toward Distinct Element Method Simulations of Carbon Nanotube Systems
,” ASME J. Nanotechnol. Eng. Med.
, 1
(4), p. 041009
.10.1115/1.400260930.
Ostanin
, I.
, Ballarini
, R.
, Potyondy
, D.
, and Dumitrică
, T.
, 2013
, “A Distinct Element Method for Large Scale Simulations of Carbon Nanotube Assemblies
,” J. Mech. Phys. Solids
, 61
(3
), pp. 762
–782
.10.1016/j.jmps.2012.10.01631.
Filleter
, T.
, Yockel
, S.
, Naraghi
, M.
, Paci
, J. T.
, Compton
, O. C.
, Mayes
, M. L.
, Nguyen, S-B. T.
, Schatz
, G. C.
, and Espinosa
, H. D.
, 2012
, “Experimental-Computational Study of Shear Interactions Within Double-Walled Carbon Nanotube Bundles
,” Nano Lett.
, 12
(2), pp. 732
–742
.10.1021/nl203686d32.
Zhang
, Q.
, Lu
, Y. C.
, Du
, F.
, Dai
, L.
, Baur
, J.
, and Foster
, D. C.
, 2010
, “Viscoelastic Creep of Vertically Aligned Carbon Nanotubes
,” J. Phys. D: Appl. Phys.
, 43
(31), p. 315401.10.1088/0022-3727/43/31/31540133.
Carlson
, A.
, and Dumitrică
, T.
, 2007
, “Extended Tight-Binding Potential for Modeling Intertube Interactions in Carbon Nanotubes
,” Nanotechnology
, 18
(6
), p. 065706
.10.1088/0957-4484/18/6/06570634.
Johnson
, S. M.
, Williams
, J. R.
, and Cook
, B. K.
, 2007
, “Quaternion-Based Rigid Body Rotation Integration Algorithms for Use in Particle Methods
,” Int. J. Numer. Meth. Eng.
, 74
(8), pp. 1303
–1313
.10.1002/nme.221035.
Itasca Consulting Group Inc.
, 2008
, “PFC3D (Particle Flow Code in 3 Dimensions)
,” Version 4.0, Itasca Consulting Group Inc., Minneapolis, MN.36.
Tang
, Y.
, Ballarini
, R.
, Buehler
, M. J.
, and Eppell
, S. J.
, 2010
, “Deformation Micromechanisms of Collagen Fibrils Under Uniaxial Tension
,” J. R. Soc. Interface
, 7
(46), pp. 839
–850
.10.1098/rsif.2009.039037.
Li
, C.
, Liu
, Y.
, Yao
, X.
, Ito
, M.
, Noguchi
, T.
, and Zheng
, Q.
, 2010
, “Interfacial Shear Strengths Between Carbon Nanotubes
,” Nanotechnology
, 21
(11), p. 115704
.10.1088/0957-4484/21/11/11570438.
Moore
, D. F.
, Ding
, Y.
, and Wang
, Z. L.
, 2004
, “Crystal Orientation-Ordered ZnS Nanowire Bundles
,” J. Am. Chem. Soc.
, 126
(44), pp. 14372
–14373
.10.1021/ja045105739.
Ma
, J.
, Liu
, X.
, Cao
, X.
, Feng
, S.
, and Fleet
, E. M.
, 2006
, “Bundle of Nanobelts Up to 4 cm in Length: One-Step Synthesis and Preparation of Titanium Trisulfide (TiS3) Nanomaterials
,” Eur. J. Inorganic Chem.
, 2006
(3
), pp. 519
–522
.10.1002/ejic.200500805Copyright © 2014 by ASME
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