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Research Papers

On the Fracture of Supported Graphene Under Pressure

[+] Author and Article Information
Zhiping Xu

e-mail: xuzp@tsinghua.edu.cn
Department of Engineering Mechanics and Center for Nano and Micro Mechanics,
Tsinghua University,
Beijing 100084, China

Ji-Yeun Kim

Samsung Advanced Institute of Technology China,
Beijing 100028, China

Quanshui Zheng

Department of Engineering Mechanics and Center for Nano and Micro Mechanics,
Tsinghua University,
Beijing 100084, China;
State Key Laboratory of Tribology and Applied Mechanics Laboratory,
Tsinghua University,
Beijing 100084, China;
Institute of Advanced Study,
Nanchang University,
Nanchang 330031, China
e-mail: zhengqs@tsinghua.edu.cn

1To whom correspondence should be addressed.

Manuscript received January 31, 2013; final manuscript received April 10, 2013; accepted manuscript posted April 13, 2013; published online May 31, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 040911 (May 31, 2013) (4 pages) Paper No: JAM-13-1054; doi: 10.1115/1.4024198 History: Received January 31, 2013; Revised April 10, 2013; Accepted April 13, 2013

We explore here the structural stability and fracture of supported graphene sheets under pressure loadings normal to the sheets by performing molecular dynamics simulations. The results show that, in absence of defects, supported graphene deforms into an inverse bubble shape and fracture is nucleated at the supported edges. The critical pressure decreases from ideal tensile strength of graphene in biaxial tension as the size of supporting pores increases. When nanoscale holes are created in the suspended region of graphene, the critical pressure is further lowered with the area of nanoholes, with additional dependence on their shapes. The results are explained by analyzing the deformed profile of graphene sheets under pressure and the stress state.

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Figures

Grahic Jump Location
Fig. 1

(a) Illustration of the system setup, including a graphene sheet supported on a substrate with hexagonal pores with size D. (b) Displacement profiles of the graphene sheet under pressure for D = 19.9 and 2.7 nm, respectively, that are fitted into the solutions of membrane and nonlinear plate models (i.e., Eqs. (1) and (2)). Panels (c) and (d) show the amplitudes of maximum principal stress in the graphene sheet, suggesting the peak values localized at the contact with the substrate for a perfect graphene (c) and at the edges of the nanoholes due to the presence of stress concentration (d).

Grahic Jump Location
Fig. 2

(a) The critical pressure defined by the suspended size of graphene membrane D. (b) The critical pressure of a porous graphene with size of nanohole d, defined by the diagonal length of the hexagon, while D is kept at 19.9 nm in the simulations. Panels (c) and (d) show the nucleation and fracture pattern of perfect graphene and nanoholed graphene with pressure beyond the critical value Pcr. The color represents amplitude of maximum principal component of the stress tensor.

Grahic Jump Location
Fig. 3

Finite element analysis of the maximum principal stress component in supported (a) perfect graphene and (b) nanoholed graphene sheet under pressure, using the membrane model that is fitted into stress-strain relations calculated by molecular dynamics simulations. The dimensions of graphene sheets and the nanoholed are the same as those shown in Figs. 2(c) and 2(d).

Grahic Jump Location
Fig. 4

Critical pressure of a nanoholed graphene with size and shape of nanoholes

Grahic Jump Location
Fig. 5

Comparison of the strength (a) and strain to failure (b) of graphene sheets with triangular, rectangular, and hexagonal nanoholes of different sizes, obtained from biaxial tensile loading simulations

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