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Proceedings of the 11th International Conference on Frontiers of Design and Manufacturing
May 23~25, 2014, Nanjing, China
Anisotropic Mechanical Properties of Graphene Sheets from Molecular Dynamics
1
Zhonghua Ni1a, Hao Bu1b, Min Zou2c
Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, Southeast University,
Nanjing 211189, China
2
Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR 72701, USA
E-mail: anzh2003@seu.edu.cn, b hao.bu@hotmail.com, cmzou@uark.edu
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Abstract: Anisotropic mechanical properties are observed for a
sheet of graphene along different load directions.
Keywords: Anisotropic mechanical property, Graphene, Young’s
modulus
1 Introduction
Since graphene holds great promise as a building
block in nano-electromechanical systems (NEMS) [1, 2],
nanoelectronics [3, 4] and nanocomposites [5, 6],
fundamental understanding of its nanomechanical
behavior is of primary importance in achieving the
desired mechanical performance for its applications.
Despite the high anisotropy of bulk graphite, Blakslee et
al. [7] obtained its five independent elastic constants
with the assumption of in-plane mechanical isotropy.
Similarly, the isotropic assumption was adopted in the
calculation of elastic properties for carbon nanotubes [8]
and a finite-sized sheet of garphene [9] due to the
six-fold rotational symmetry of graphene atomic lattice.
2 Molecular dynamics models
For comparison of the two modes, a square-shaped
graphene sheet with the edge length of 4.15 nm is selected
as a specimen, as shown in Fig. 1.
Figure 1. The tensile model for (a) longitudinal mode and (b)
transverse mode.
3 Results and discussion
3.1 Young’s modulus and third-order modulus
Due to the anharmonic terms of the C–C interatomic
potential, the second-order elastic modulus, i.e., the
Young’s modulus, denoted by E, and the third-order
modulus ,denoted by D, are adopted to describe the
nonlinear elastic behavior [20, 21].
3.2 Rupture process
The fundamental mechanism can be explained for the
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force analysis diagrams in Fig. 1(c) and (d). Assuming
each unit cell bears equivalent forces applied by its
neighboring unit cells, according to the force-balance
principle, the force equations can be acquired as follows:
2 FL 0 sin  L  FL1
(1)
2FT 0 sin T  FT 1
(2)
A set of graphene sheets with different edge lengths
ranged from 2.0 to 8.4nm are simulated to investigate the
size and edge effects on the mechanical properties, as
shown in Table 1.
Table 1 Graphene sheets with Different edge lengths
4 Conclusions
In conclusion, we have confirmed the mechanical
anisotropy of graphene sheets. The averaged Young’s
moduli for the longitudinal and transverse modes are 1.13
and 1.05 TPa, respectively. The two modes have distinctly
different fracture mechanisms. For a unit cell in the LM,
the two bond angles symmetrical about the load direction
become small under the tensile load while the other four
bond angles increase with the tensile load. These changes
of the bond angles in one unit cell for the LM induce the
topological defect growth once the load exceeds a critical
value.
Acknowledgements
The authors acknowledge the financial support from
the National Basic Research Program of China
(2006CB300404) and Natural Science Foundation of
China (50875047, 50776017 and 50676019).
References
[1] Y. H. Zhang, H. H. Liu and D. C. Wang, Spring handbook,
Mechanical Industry Press, Beijing, PRC (1999).
[2] G. A. Costello and J. W. Philips, Static response of
strandedwire helical springs, International Journal of
Mechanical Sciences, 21 (1979) 171-178.
[3] H. H. Clark, Spring design and application, McGraw-Hill
Book Company, New York, USA (1961).
[4] S. L. Wang, S. Lei and J. Zhou, Mathematical model for
determination of strand twist angle and diameter in stranded
wire helical springs, Journal of Mechanical Science and
Technology, 24 (6) (2010) 1203-1210.
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