Atomistic simulation and continuum modeling of graphene nanoribbons under uniaxial tension

Modelling and Simulation in Materials Science and Engineering (Impact Factor: 2.17). 06/2011; 19(5):054006. DOI: 10.1088/0965-0393/19/5/054006


Atomistic simulations are performed to study the nonlinear mechanical behavior of graphene nanoribbons under quasistatic uniaxial tension, emphasizing the effects of edge structures (armchair and zigzag, without and with hydrogen passivation) on elastic modulus and fracture strength. The numerical results are analyzed within a theoretical model of thermodynamics, which enables determination of the bulk strain energy density, the edge energy density and the hydrogen adsorption energy density as nonlinear functions of the applied strain based on static molecular mechanics simulations. These functions can be used to describe mechanical behavior of graphene nanoribbons from the initial linear elasticity to fracture. It is found that the initial Young's modulus of a graphene nanoribbon depends on the ribbon width and the edge chirality. Furthermore, it is found that the nominal strain to fracture is considerably lower for graphene nanoribbons with armchair edges than for ribbons with zigzag edges. Molecular dynamics simulations reveal two distinct fracture nucleation mechanisms: homogeneous nucleation for the zigzag-edged graphene nanoribbons and edge-controlled heterogeneous nucleation for the armchair-edged ribbons. The modeling and simulations in this study highlight the atomistic mechanisms for the nonlinear mechanical behavior of graphene nanoribbons with the edge effects, which is potentially important for developing integrated graphene-based devices.

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    • "MD simulations have also demonstrated that the mechanical response of graphene nanoribbons (GNRs) is nonlinear elastic and their size and chirality have significant influences on their mechanical properties [13]. It has been reported that 8 nm constitutes a critical width for GNRs beyond which the size effect largely disappears and their elastic properties converge to the values for bulk/infinite graphene [13] [14]. In addition, MD simulations have shown that while the Young's modulus of graphene remains fairly insensitive to the temperature up to 1200 K, the values of its failure strength and strain undergo a steady fall as temperature is increased from the absolute zero [15] [16]. "
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    ABSTRACT: Molecular dynamics simulations are carried out in order to develop a failure criterion for infinite/bulk graphene in biaxial tension. Stresses along the principal edge configurations of graphene (i.e. armchair and zigzag directions) are normalized to the corresponding uniaxial ultimate strength values. The combinations of normalized stresses resulting in the failure of graphene are used to define failure envelopes (limiting stress ratio surfaces). Results indicate that a bilinear failure envelope can be used to represent the tensile strength of graphene in biaxial loading at different temperatures with reasonable accuracy. A circular failure envelope is also introduced for practical applications. Both failure envelopes define temperature-independent upper limits for the feasible combinations of normalized stresses for a graphene sheet in biaxial loading. Predicted failure modes of graphene under biaxial loading are also shown and discussed.
    Modelling and Simulation in Materials Science and Engineering 07/2015; 23(6):14p. DOI:10.1088/0965-0393/23/6/065004 · 2.17 Impact Factor
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    • "The second-generation reactive empirical bondorder potential (REBO) is used to describe the C–C interactions in graphene [31]. Previous studies [32] [33] [34] [35] [36] have shown that the REBO potential provides reasonable predictions of the mechanical properties of monolayer graphene. For the a-SiO 2 substrate, we use the Tersoff potential [37], with a parameter set developed by Munetoh et al. [38] for the Si–O systems. "
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    ABSTRACT: Interfacial adhesion between graphene and various substrate materials is essential for practical applications of graphene. To date, most of the studies on adhesion of graphene have assumed dry adhesion of van der Waals type. In this paper, we conduct molecular dynamics simulations to study the traction–separation behaviors for wet adhesion of graphene on amorphous silicon oxide covered by a thin layer of water. Three stages of the traction–separation relations are identified and they are analyzed by simple, approximate continuum models. The work of separation is found to be close to the theoretical value dictated by the interaction potential between graphene and water. The maximum traction is found to be set by the critical stress for cavitation at the water/graphene interface. With morphological evolution of water from cavitation to capillary bridging, the range of interaction extends to about 3 nm before complete separation of graphene. Compared to van der Waals interactions for dry adhesion of graphene, the work of separation for wet adhesion is smaller, the maximum traction is lower, but the interaction range is longer. It is noted that the properties of wet adhesion depend sensitively on the graphene–water interactions, which may vary considerably from hydrophobic to hydrophilic interactions.
    Extreme Mechanics Letters 04/2015; 3. DOI:10.1016/j.eml.2015.04.003
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    • "However, this equation is only applicable in simulations of nanoindentation experiments, whereas ours is more general. Nonlinear strain energy functions have been similarly developed for graphene nanoribbons, for which the effect of the surface energy of free edges is important (Lu et al., 2011). A general continuum description of graphene sheets based on calculations using the Tersoff-Brenner potential that accounts for inplane and bending elasticity has also been developed (Lu and Huang, 2009). "
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    ABSTRACT: An anisotropic strain energy function is proposed for tensile loading in graphene that provides a nonlinear, hyperelastic constitutive equation. In the proposed function, the energy depends on the principal invariants of the right Cauchy–Green tensor and the strains in the zigzag and armchair directions. The use of the zigzag and armchair strains gives the model the ability to account for anisotropic behavior at moderate deformations. The constitutive law parameters are determined by a least squares fit to the energies predicted by density functional theory (DFT) calculations, and a good match is obtained to the DFT results for zigzag and armchair graphene sheets with various loading combinations. The law is applied in a continuum calculation of nanoindentation of a graphene membrane. The force–deflection predicted with this model show excellent agreement with analogous experimental results, thus providing a strong link between DFT calculations and nanoexperiments.
    International Journal of Solids and Structures 09/2012; 49(18):2582–2589. DOI:10.1016/j.ijsolstr.2012.05.019 · 2.21 Impact Factor
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