﻿ 含缺陷双层石墨烯的纳米压痕模拟研究
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 力学学报  2016, Vol. 48 Issue (4): 917-925  DOI: 10.6052/0459-1879-15-427 0

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Hua Jun , Wu Xiaxia , Duan Zhirong . NUMERICAL STUDY ON NANOINDENTATION OF DEFECTIVE BILAYER GRAPHENE[J]. Chinese Journal of Ship Research, 2016, 48(4): 917-925. DOI: 10.6052/0459-1879-15-427.
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2015-11-30 收稿
2016-03-23网络版发表

0 引言

1 力学模型及模拟方法 1.1 模型建立

 图 1 缺陷示意图 (A、B、C、D分别为邻、对、间、单空位缺陷，E和F分别为STW、圆孔缺陷) Fig. 1 Sketch of defect (A,B,C and D are the adjacent,registration,interval,single vacancy defect,E and F are the STW, hole defect,respectively)
 图 2 双层石墨烯薄膜的纳米压痕模型图 Fig. 2 Atomic configuration of bilayer graphene model
1.2 模拟方法

Lenard-Jones (L-J)势函数

 ${\Phi _{ij}}\left( {{r_{ij}}} \right) = 4\varepsilon \left[ {{{\left( {{{{r_{ij}}} \over \sigma }} \right)}^{ - m}} - {{\left( {{{{r_{ij}}} \over \sigma }} \right)}^{ - n}}} \right]$ (1)

2 结果分析及讨论

 图 3 LJ势函数的截断半径与临界载荷关系曲线 Fig. 3 The relationship between critical load and LJ potential's cut-off radius
2.1 缺陷在压头正下方时的影响分析

 图 4 缺陷石墨烯载荷-位移曲线 Fig. 4 Load-depth curves of defective graphene films

 $F = \sigma _0^{{\rm{2D}}}\left( {\pi Rd} \right)\left( {{h \over R}} \right){\left( {{r \over R}} \right)^{{\textstyle{3 \over 4}}}} + {E^{2D}}\left( {{q^3}Rd} \right){\left( {{h \over R}} \right)^3}{\left( {{r \over R}} \right)^{{\textstyle{1 \over 4}}}}$ (2)

 $\sigma _{{\rm{MAX}}}^{{\rm{2D}}} = \sqrt {{{{F_{{\rm{cr}}}}{E^{{\rm{2D}}}}} \over {4\pi r}}}$ (3)

2.2 缺陷在不同位置时的影响分析

 图 5 缺陷到薄膜圆心的距离与临界载荷关系曲线 Fig. 5 The relationship between critical load and distance (from defect to the film's center)
2.3 缺陷数目的影响分析

(1) 空位缺陷数目的影响

 图 6 缺陷石墨烯初始构型图 Fig. 6 Model of single vacancy defect
 图 7 多个单空位缺陷下的石墨烯薄膜载荷-位移曲线 Fig. 7 Load-depth curves of graphene with multiple single vacancy defects

 图 8 不同数目空位缺陷与临界载荷关系曲线 Fig. 8 The relationship between the critical loads and multiple vacancy defects
 图 9 空位缺陷位于压头下方时缺陷数目与临界载荷关系曲线 Fig. 9 The relationship between the critical loads and multiple vacancy defects located in the region covered by the indenter

(2) 圆孔缺陷数目的影响分析

 图 10 不同数目圆孔缺陷与临界载荷关系曲线 Fig. 10 The relationship between the critical loads with multiple hole defects
3 结论

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NUMERICAL STUDY ON NANOINDENTATION OF DEFECTIVE BILAYER GRAPHENE
Hua Jun, Wu Xiaxia, Duan Zhirong
Department of Mechanics, School of Science, Xi'an University of Architecture & Technology, Xi'an 710055, China
Abstract: Comparing with pristine graphene, graphene with various defects produced by the current technology still has a certain application value. Therefore it is necessary to investigate the influence of defects on graphene properties. In this paper, interaction between carbon atoms that forms the covalent bonds of graphene is modeled with Tersoffff potential, the long range interactions of carbon atoms are characterized by Lennard-Jones potential. The nanoindentation of spherical diamond indenter into defective bilayer graphene is studied by molecular dynamics simulations. The Lernnard-Jones potential function optimal value of cut-o radius is discussed and typical load-depth curves are obtained. The effects including Stone-Thrower-Wales (STW) defect, vacancy (single and double vacancy defects) and hole defect in different positions and numbers on the mechanical properties of graphene are studied. The results show that when defect is in the film's center, it makes intensity decrease significantly; when vacancy defect is in the region covered by indenter, the critical load increases linearly with the increase of distance which is from the defect to the film's center; The more vacancy defect, the lower Young's modulus and intensity. The number of hole defects reaching a certain concentration outside the region covered by indenter radius which makes the mechanical properties of graphene decrease apparently. It is concluded that graphene with the stable structure is not sensitive to small defects and defective graphene still has good performance and practical value.
Key words: bilayer graphene    defect    nanoindentation    molecular dynamics    thin film