DOI QR코드

DOI QR Code

분자역학을 사용한 단층 그래핀 시트의 모드 III 파괴인성

Mode III Fracture Toughness of Single Layer Graphene Sheet Using Molecular Mechanics

  • 웬민키 (울산대학교 기계공학부) ;
  • 염영진 (울산대학교 기계공학부)
  • 투고 : 2013.07.25
  • 심사 : 2013.12.02
  • 발행 : 2014.02.01

초록

단층 그래핀 시트(Single layer graphene sheet, SLGS)의 찢어짐 모드(모드 III) 파괴 예측을 위한 원자 기반 미세결합요소모델이 개발되었다. 이 모델은 그래핀 시트의 최대 변형률 관계를 예측하기 위해 수정된 모스포텐셜을 사용한다. 면외 전단하중 조건에서 그래핀의 모드 III 파괴를 광범위한 분자역학(Molecular mechanics, MM) 시뮬레이션으로 조사하였다. 분자역학은 원자의 균열선단 근처 원자의 변위를 설명하기 위해 사용되었고, 선형탄성파괴역학은 이 영역 바깥의 영역을 설명하기 위해 사용되었다. 해석 결과 분자역학 방법이 SLGS의 전단 물성 계산뿐만 아니라 armchair 및 zigzag 방향 모드 III 파괴인성 연구에도 단순하면서도 신뢰할만하다는 것을 보여준다. SLGS 의 모드 III 파괴인성은 zigzag 방향에 대해 $0.86MPa{\sqrt{m}}$, armchair 방향에 대해 $0.93MPa{\sqrt{m}}$로 예측되었다.

An atomistic-based finite bond element model for predicting the tearing mode (mode III) fracture of a single-layer graphene sheet (SLGS) is developed. The model uses the modified Morse potential for predicting the maximum strain relationship of graphene sheets. The mode III fracture of graphene under out-of-plane shear loading is investigated with extensive molecular mechanics simulations. Molecular mechanics is used for describing the displacements of atoms in the area near a crack tip, and linear elastic fracture mechanics is used outside this area. This work shows that the molecular mechanics method can provide a reliable and yet simple method for determining not only the shear properties of SLGS but also its mode III fracture toughness in the armchair and the zigzag directions; the determined mode III fracture toughness values of SLGS are $0.86MPa{\sqrt{m}}$ and $0.93MPa{\sqrt{m}}$, respectively.

키워드

참고문헌

  1. Xiao, J.-R and Gillespie, J.-W., 2011, "Fracture Behaviors of Graphene Sheets and Carbon Nanotubes," Physics and Applications of Graphene - Theory, ISBN 978-953-307-152-7.
  2. Han, M.-Y, Ozyilmaz, B. and Zhang Y., Kim P., 2007, "Energy Band-Gap Engineering of Graphene Nanoribbons," Phys Rev Lett, 98 20,206805. https://doi.org/10.1103/PhysRevLett.98.206805
  3. Jeon, S.-C and Kim, Y.-S., 2010, "Fabrication of a Graphene Nanoribbon with Electron Beam Lithography Using a XR-1541/PMMA Lift-Off Process," Transactions on Electrical and Electronic Materials, Vol. 11, No. 4, pp. 190-193. https://doi.org/10.4313/TEEM.2010.11.4.190
  4. Zhou, X., Qi, X.-Y., Wu, S., Li, H., Boey, F. and Zhang, H., 2009, "A Method for Fabrication of Graphene Oxide Nanoribbons from Graphene Oxide Wrinkles," J Phys Chem C, 113:19119. https://doi.org/10.1021/jp9079298
  5. Li, L.-X., Liu, R.-P., Chen, Z.-W., Wang, Q., Ma, M.-Z., Jing Q., Li, G. and Tian, Y., 2006, "Tearing, Folding and Deformation of a Carbon-Carbon sp2-Bonded Network," Carbon 44, 8, pp. 1544-1547. https://doi.org/10.1016/j.carbon.2005.12.031
  6. Belytschko, T., Xiao, S.-P., Schatz, G.C. and Ruoff, R.S., 2002, "Atomistic Simulations of Nanotube Fracture," Phys. Rev. B 65, 235430. https://doi.org/10.1103/PhysRevB.65.235430
  7. Xiao, J.-R., Gama, B.-A. and Gillespie, J.-W., 2005, "An Analytical Molecular Structural Mechanics Model for the Mechanical Properties of Carbon Nanotubes," Int. J. Solids Struct, 42, pp. 3075-3092.. https://doi.org/10.1016/j.ijsolstr.2004.10.031
  8. Xiao, J.-R., Staniszewski, J. and Gillespie, J.-W., 2009, "Fracture and Progressive Failure of Defective Graphene Sheets and Carbon Nanotubes," Comp Struct, 88, pp. 602-609. https://doi.org/10.1016/j.compstruct.2008.06.008
  9. Dipanjan, S., Kostya, S., Novoselov., Pedro, M.-R, and Markus, J.-B., 2010, "Tearing Graphene Sheets From Adhesive Substrates Produces Tapered Nanoribbons," Small, 6, No. 10, pp. 1108-1116. https://doi.org/10.1002/smll.201000097
  10. Shen, L. and Li, J., 2005, "Equilibrium Structure and Strain Energy of Single-Walled Carbon Nanotubes," Physical Review B 71, 165427. https://doi.org/10.1103/PhysRevB.71.165427
  11. Haddo, R.-C., 1988, "${\pi}$-Electrons in Three Dimensions," Acc. Chem. Res, 21, pp. 243-249. https://doi.org/10.1021/ar00150a005
  12. Takazumi, K., Susumu, O., Yoshiyuki, M. and Hidefumi, H., 2009, "Self-Redirection of Tearing Edges in Graphene: Tight-Binding Molecular Dynamics Simulations," Physical Review B, 80, 033401.
  13. Huang, X., Yang, H, Adri, C.-T., Jimmy, H. and Zhang, S., 2012, "Chemomechanics Control of Tearing Paths in Graphene," Physical Review B, 85, 195453. https://doi.org/10.1103/PhysRevB.85.195453
  14. Shi, W., Mu, G. and Li, H., 2008, "Relationship Between the Stress Intensity Factors and Bond $\sigma$ in Graphene Sheet," Int J Fract, 149, pp. 105-111. https://doi.org/10.1007/s10704-008-9237-z
  15. Rappe, A.-K. and Casewit, C.-J., 1997, "Molecular Mechanics Across Chemistry," University Science Books.
  16. Zhang, H.-W., Wang, J.-B. and Ye, H.-F., 2007, "Influence of Inversion Energy on Elastic Properties of Single-Walled Carbon Nanotubes," Materials Science and Engineering A, 467, pp. 78-88. https://doi.org/10.1016/j.msea.2007.02.106
  17. Tserpes, K.-I. and Papanikos, P., 2007, "The Effect of Stone-Wales Defect on the Tensile Behavior and Fracture of Single-Walled Carbon Nanotubes," Composite Structures 79, pp. 581-589. https://doi.org/10.1016/j.compstruct.2006.02.020
  18. Kundu, T., 2008, "Fundamentals of Fracture Mechanics," CRC Press Taylor & Francis Group.
  19. Khare, R., Mielke, S.L., Paci, J.T., Zhang, S., Ballarini, R., Schatz, G.C. and Belytschko, T., 2007, "Coupled Quantum Mechanical/Molecular Mechanical Modeling of the Fracture of Defective Carbon Nanotubes and Graphene Sheets," Physical Review B 75, 075412. https://doi.org/10.1103/PhysRevB.75.075412