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Nanoindentation models and Young's modulus of monolayer graphene: A molecular dynamics study
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Image of FIG. 1.
FIG. 1.

Morphologies of indented circular graphene monolayer with a rigid boundary. δ is the deflection. R and a are the radius of the indenter and the monolayer graphene, respectively (a). Structural profile (b). Equilibrium state (c). Ruptured graphene with large deflection.

Image of FIG. 2.
FIG. 2.

Force (F)-deflection (δ) plot on log-log scale coordinates with R = 1.6 nm and a = 9.0 nm. The green dotted-dashed lines are obtained by fitting the data in the entire deflection range to Eq. (2) and the fitting coefficients are (c,d). The blue-dashed lines and the red solid lines are the curves obtained by fitting the data in the small and large deflection ranges to Eq. (2) , respectively, the fitting coefficients of which are and , respectively. The inset plots the fitting curves obtained in one range and their extensions to another range, showing that the extended part disagrees with the simulated indentation data appreciably. The vertical dashed lines indicate the point separating the small and large deflection range, which is 2.0, 2.3, and 2.6 nm for pretensions with C–C bond length of 0.146, 0.144, and 0.142 nm, respectively.

Image of FIG. 3.
FIG. 3.

Force-deflection data at 300 K for different sizes of indenter and the circular monolayer graphene. The pretension corresponds to an initial C–C bondlength of 0.144 nm. The curves are obtained by least-square method.


Generic image for table
Table I.

Young's modulus (TPa) obtained by different models in small and large deflection ranges with different initial pretensions (C–C bondlength), R and a.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nanoindentation models and Young's modulus of monolayer graphene: A molecular dynamics study