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Research Papers

Distinct Element Method Modeling of Carbon Nanotube Bundles With Intertube Sliding and Dissipation

[+] Author and Article Information
Igor Ostanin

Department of Civil Engineering,
University of Minnesota,
500 Pillsbury Drive SE,
Minneapolis, MN 55455
e-mail: ostan002@umn.edu

Roberto Ballarini

Mem. ASME
Department of Civil Engineering,
University of Minnesota,
500 Pillsbury Drive SE,
Minneapolis, MN 55455
e-mail: broberto@umn.edu

Traian Dumitrică

Mem. ASME
Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: dtraian@me.umn.edu

It was assumed that an average CNT in a bundle has three slipped nearest neighbors. Critical strain εc is used to calculate stress and its terms in Eq. (13).

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 27, 2013; final manuscript received January 9, 2014; accepted manuscript posted February 3, 2014; published online February 3, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(6), 061004 (Feb 03, 2014) (10 pages) Paper No: JAM-13-1487; doi: 10.1115/1.4026484 History: Received November 27, 2013; Revised January 09, 2014; Accepted February 03, 2014

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.

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Figures

Grahic Jump Location
Fig. 1

(a) Coarse graining of a CNT into a chain of cylindrical segments, representing inertial properties of a CNT. Segments are linked with parallel bond interfaces, representing elastic properties of a CNT surface, arising from covalent bonds between C atoms within the CNT surface. Segments of neighboring CNTs interact via mesoscopic vdW contact model, acting in parallel with viscous forces that damp relative translational motion of CNT segments. (b) Illustration of definition of generalized coordinates r, θ, φ for two interacting cylindrical segments of neighboring CNTs. n1 and n2 are axial directions of first and second cylinder.

Grahic Jump Location
Fig. 2

(a) Schematics of a crystalline CNT bundle (N = 2). (b) Geometry of the prerelaxed bundle (N = 4, M = 4). Color legend gives x-component of displacements developing during the relaxation. (c) Changes in different terms of CNT bundle energy during prerelaxation. The change in strain energy ΔUstr, vdW adhesion energy ΔUvdw, total energy ΔUtot, and kinetic energy Ukin are presented. (d) Gage and grip regions of a CNT bundle specimen.

Grahic Jump Location
Fig. 3

(a), (b) SSCs of bundles of different length, containing 37 tubes on a cross section (N = 4), for LCNT = 0.068μm (specimens 1–9, (a)) and LCNT = 0.136μm (specimens 10–18, (b)). (c) Uniaxial tensile strength of a bundle σuts as a function of the length factor M for LCNT = 0.068μm and LCNT = 0.136μm. (d), (e) SSCs of bundles of different thickness, with length factor M = 4, and LCNT = 0.068μm (specimens 19–24, (d)) and LCNT = 0.136μm (specimens 25–30, (e)). (f) Uniaxial tensile strength of a bundle σuts as a function of the thickness factor N for LCNT = 0.068μm and LCNT = 0.136μm. The slope of reference lines given in figures (a), (b), (d), (e) corresponds to Young's modulus E0 estimated for hexagonal arrangement of stretched noninteracting CNTs.

Grahic Jump Location
Fig. 4

(a) Work of external force Aext, as compared to changes in elastic strain energy ΔUstr, vdW adhesion energy ΔUvdw, and dissipated energy ΔQ during the test. (b) Terms of decomposition (Eq. (13)) during the simulation. Total stress response σtot is calculated as a sum of derivatives of traced energy terms (dashed line) and directly from force balance (solid line). (c) Development of a localized deformation in a CNT bundle. Visualization of CNT bundle geometry and magnitude of a slip vector (on the surface of a bundle and on a horizontal axial cross section of a bundle).

Grahic Jump Location
Fig. 5

Low damping (α = 0.2,β = 0.0) mechanical tests on CNT bundles. (a) Stress-strain curves for specimen 12 and specimen 16 in Table 2 indicate the absence of an RVE. (b) Magnitude of slip vector, visualized on a horizontal axial cross-section, indicates immediate localization of the deformation and brittle fracture of a specimen. (c) Magnitude of a slip vector, averaged over thin slices of a bundle (specimen 16) along the length for few different values of viscous and local damping.

Grahic Jump Location
Fig. 6

Large deformation of a CNT bundle. (a) Work of external force Aext, as compared to changes in elastic strain energy ΔUstr, vdW adhesion energy ΔUvdw, and dissipated energy ΔQ during the test. (b) Terms of decomposition (Eq. (13)) during the simulation. (c) CNT bundle geometry and magnitude of a slip vector on the surface of a bundle and on a horizontal axial cross section of a bundle.

Grahic Jump Location
Fig. 7

Shear test on a close-packed CNT assembly. (a) Problem geometry and boundary conditions. (b) Definition of the cross-sectional area of a specimen for given values of B and H. (c) Displacement field (x component of displacement) observed in a simple shear test. (d) External work as compared to potential energy terms and dissipation during the test. (e) Decomposition of stress into vdW adhesive, elastic, and dissipative terms. (f) The influence of specimen length on its shear modulus. Red circles are simulation results, and blue crosses are theoretical predictions for the shear modulus due to surface tension. On the inset—the effect of cross section size (B and H) on the shear modulus.

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