×

Strength of graphene in biaxial tension. (English) Zbl 1348.82093

Summary: A simple analytical study of a single-atom-thick sheet of graphene under biaxial tension is presented. It is based on the combination of the approaches of continuum and molecular mechanics. On the molecular level the Tersoff-Brenner potential with a modified cut-off function is used as an example. Transition to a continuum description is achieved by employing the Cauchy-Born rule. In this analysis the graphene sheet is considered as a crystal composed of two simple Bravais lattices and the mutual atomic relaxation between these lattices is taken into account. Following this approach a critical failure surface is produced for strains in biaxial tension. The adopted methodology is discussed in the context of the alternative approaches.

MSC:

82D60 Statistical mechanics of polymers
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Admal, N. C.; Tadmor, E. B., A unified interpretation of stress in molecular systems, J. Elast., 100, 63-143 (2010) · Zbl 1260.74005
[2] Arroyo, M.; Belytschko, T., An atomistic-based finite deformation membrane for single layer crystalline films, J. Mech. Phys. Solids, 50, 1941-1977 (2002) · Zbl 1006.74061
[3] Arroyo, M.; Belytschko, T., Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule, Phys. Rev. B, 69, 115415 (2004)
[4] Beatty, M. F.; Hayes, M. A., Mechanics and Mathematics of Crystals (2005), World Scientific: World Scientific Singapore, Selected Papers of J.L. Ericksen · Zbl 1172.74002
[5] Born, M.; Huang, K., Dynamical Theory of the Crystal Lattices (1954), Oxford University Press: Oxford University Press Oxford · Zbl 0057.44601
[6] Brenner, D. W., A second generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys. Condens. Matter, 14, 783-802 (2002)
[7] Brenner, D. W., Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Phys. Rev. B, 42, 9458-9471 (1990)
[8] Geim, A. K.; Novoselov, K. S., The rise of graphene, Nat. Mater., 6, 183-191 (2007)
[9] Huang, Y.; Wu, J.; Hwang, K. C., Thickness of graphene and single-wall carbon nanotubes, Phys. Rev. B, 74, 245413 (2006)
[10] Khare, R.; Mielke, S. L.; Paci, J. T.; Zhang, S. L.; Ballarini, R.; Schatz, G. C.; Belytschko, T., Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets, Phys. Rev. B, 75, 075412 (2007)
[11] Lee, C.; Wei, X.; Kysar, J. W.; Hone, J., Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science, 321, 385-388 (2008)
[12] Liu, F.; Ming, P. M.; Li, J., Ab initio calculation of ideal strength and phonon instability of graphene under tension, Phys. Rev. B, 76, 064120 (2007)
[13] Lu, Q.; Huang, R., Nonlinear mechanics of single-atomic-layer graphene sheets, Int. J. Appl. Mech., 3, 443-467 (2009)
[14] Marianetti, C. A.; Yevick, H. G., Failure mechanisms of graphene under tension, Phys. Rev. Lett., 105, 245502 (2010)
[15] Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K., Two-dimensional atomic crystals, Proc. Natl. Acad. Sci. U. S. A., 102, 10451-10453 (2005)
[16] Reddy, C. D.; Rajendran, S.; Liew, K. M., Equilibrium configuration and continuum elastic properties of finite sized graphene, Nanotechnology, 17, 864-870 (2006)
[17] Tadmor, E. B.; Ortiz, M.; Phillips, R., Quasicontinuum analysis of defects in solids, Phil. Mag. A, 73, 1529-1563 (1996)
[18] Tadmor, E. B.; Smith, G. S.; Bernstein, N.; Kaxiras, E., Mixed finite element and atomistic formulation for complex crystals, Phys. Rev. B, 59, 235-245 (1999)
[19] Tersoff, J., New empirical approach for the structure and energy of covalent systems, Phys. Rev. B, 37, 6991-7000 (1988)
[20] Volokh, K. Y., On the strength of graphene, J. Appl. Mech., 79, 064501 (2012)
[21] Wei, X.; Fragneaud, B.; Marianetti, C. A.; Kysar, J. W., Nonlinear elastic behavior of graphene: ab initio calculations to continuum description, Phys. Rev. B, 80, 205407 (2009)
[22] Weiner, J. H., Statistical Mechanics of Elasticity (1983), Wiley: Wiley New York · Zbl 0616.73034
[23] Wu, J.; Hwang, K. C.; Huang, Y., An atomistic-based finite-deformation shell theory for single-wall carbon nanotubes, J. Mech. Phys. Solids, 56, 279-292 (2008) · Zbl 1162.74397
[24] Zhang, P.; Jiang, H.; Huang, Y.; Geubelle, P. H.; Hwang, K. C., An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation, J. Mech. Phys. Solids, 52, 977-998 (2004) · Zbl 1112.74311
[25] Zhao, H.; Aluru, N. R., Temperature and strain-rate dependent fracture strength of graphene, J. Appl. Phys., 108, 064321 (2010)
[26] Zhou, J.; Huang, R., Internal lattice relaxation of single-layer graphene under in-plane deformation, J. Mech. Phys. Solids, 56, 1609-1623 (2008) · Zbl 1171.74334
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.