Mechanical characterization of nanoindented graphene via molecular dynamics simulations
© Fang et al; licensee Springer. 2011
Received: 16 January 2011
Accepted: 3 August 2011
Published: 3 August 2011
The mechanical behavior of graphene under various indentation depths, velocities, and temperatures is studied using molecular dynamics analysis. The results show that the load, elastic and plastic energies, and relaxation force increased with increasing indentation depth and velocity. Nanoindentation induced pile ups and corrugations of the graphene. Resistance to deformation decreased at higher temperature. Strong adhesion caused topological defects and vacancies during the unloading process.
Keywordsmolecular dynamics nanoindentation graphene mechanical properties
Graphene has received a lot of attention due to its good mechanical and electromagnetic properties [1–3], including a zero electron bandgap, a high electron emission rate, and elastic scattering [4–6]. Atomic-scale graphene can be fabricated using micro-mechanical chop crack , thermal expansion , and extension growth  techniques. Studies [10–13] have found that the band-field effect of a 10-nm-thick graphene sheet is similar to that of a small (less than 1.2 nm in diameter) nanographite particle.
Novoselov and Geim  used graphene to fabricate a small crystal tube. Monolayer graphene is considered a suitable material for investigating two-dimensional quantization phenomena, such as temperature-trigger plasma , quantization absorption spectrum , and the fractional quantum Hall effect . In addition, the hexagonal symmetric structure of graphene makes it a candidate material for nano devices.
Many studies [17–25] have focused on the chemical functionalization of graphene, especially on the effect of absorbed atoms on the electronic and chemical properties of graphene. However, the mechanical properties of graphene under indentation, which are important for developing sensors, resonators, and impermeable membranes, have yet to be investigated.
In this study, the effects of nanoindentation depth and velocity on the mechanical properties and contact behavior of graphene at various temperatures are investigated using molecular dynamics (MD) simulations. Adhesion, relaxation, defects, and deformation are discussed.
The Lennard-Jones potential function is employed to describe the interaction between the diamond tip and the graphene atoms. The Tersoff empirical potential energy function  is generally used to simulate the interaction between graphene carbon atoms.
Results and discussion
The tip then indented the graphene. The absorptive force gradually turns into a repulsive force. As the indentation depth increased, the stress wave spread out farther from the center, inducing ripples and corrugations. Figure 2b shows the tip at its maximum indentation depth. During the subsequent packing stage, the substrate releases the indentation-induced energy, as shown in Figure 2c. Finally, the tip moves up at a constant velocity (the same as that used for the indentation). Some substrate atoms beneath the tip move up during the unloading process to create a peak, as shown in Figure 2d.
The affected area, load, elastic and plastic energies, and relaxation force increased with increasing indentation depth.
Nanoindentation-induced pile ups and corrugations of graphene were observed. Strong adhesion causes topological defects and vacancies.
The average contact stiffnesses of the graphene at temperatures of 0, 200, 300, and 400 K are 58.7, 58.1, 49.48, and 36.6 N/m, respectively.
At higher temperature, the kinetic energy among atoms increases, which weakens covalent bonds and thus decreases resistance to deformation. The load, elastic and plastic energies, and relaxation force decrease with increasing temperature.
With a fast indentation, the graphene has insufficient time to respond, which leads to a high load, elastic and plastic energies, and relaxation force.
The authors would like to thank the National Science Council of Taiwan for financially supporting this research under grant NSC 96-2628-E-151-004-MY3.
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