Comment on “Nanoindentation models and Young's modulus of monolayer graphene: A molecular dynamics study” [Appl. Phys. Lett. 102, 071908 (2013)]

The interpretation of the measured load-deflection characteristics from spherical indentation tests on graphene has been a complex issue. In 2013, Tan et al. studied the nanoindentation of monolayer graphene by molecular dynamics simulations, and they found that the response of graphene to indentation is deflection dependent: in small deflection range, the response obeys the point load model developed by Wan et al. and Komaragiri et al., while large-deflection indentation follows the sphere load model developed by Begley and Mackin. The calculated Young’s modulus is about 1.00 TPa, which is in good agreement with the experimental results. In the molecular dynamics simulations performed by Tan et al., a monolayer graphene with an elastic modulus E, Poisson’s ratio ν, thickness h, and radius a is clamped at the perimeter before indentation. A frictionless rigid spherical indenter of radius R is brought into contact with the graphene sheet by applying a transverse load F at the center of the sheet. The centerline displacement of sheet is denoted by δ. The simulations were performed using graphene sheets and spherical indenters of different sizes, and in the case of zero pre-tension, the typical load-deflection curves are shown in Fig. 1. According to the sphere model developed by Begley and Mackin, the relationship between load and central deflection is shown below (see, e.g., Eq. (24) in Ref. 4 and Eq. (5) in Ref. 5):