Abstract




 
   

IJE TRANSACTIONS C: Aspects Vol. 31, No. 3 (March 2018) 456-463    Article in Press

PDF URL: http://www.ije.ir/Vol31/No3/C/8-2718.pdf  
downloaded Downloaded: 41   viewed Viewed: 638

  STUDY OF STONE-WALES DEFECT ON ELASTIC PROPERTIES OF SINGLE-LAYER GRAPHENE SHEETS BY AN ATOMISTIC BASED FINITE ELEMENT MODEL
 
S. Safarian and M. Tahani
 
( Received: August 13, 2017 – Accepted in Revised Form: October 12, 2017 )
 
 

Abstract    In this paper, an atomistic based finite element model is developed to investigate the influence of topological defects on mechanical properties of graphene. The general in-plane stiffness matrix of the hexagonal network structure of graphene is found. Effective elastic modulus of a carbon ring is determined from the equivalence of molecular potential energy related to stretch and angular deformation. A hexagonal carbon ring as a unit cell of graphene sheets is modeled by four-node elements and by applying three-node triangular elements, Stone-Wales (SW) defect as an important topological defect which leads to the formation of two heptagons and pentagons is modeled. In this method, both pristine structure of graphene and graphene with SW defect are considered and to get more real structure, an atomistic model of a small part of graphite sheet around the defect site, is modeled in Gaussian software and new arrangement around SW defect are obtained by minimizing its energy. Young’s modulus, shear modulus and Poisson’s ratio of the pristine single-layered graphene sheet (SLGS) and the effect of topological defects on the elastic properties of SLGS is examined. The numerical results from this new model show good agreement with data available in the literature.

 

Keywords    Graphene sheet, Defects, Atomistic model, Finite element method, Elastic properties

 

چکیده    عیوب ساختاری که پیدایش آن ها در طی فرآیندهای سنتز و خالص­سازی اجتناب ناپذیر بوده، بر روی خواص گرافن تاثیر می گذارند. در این مقاله مدل جدید هیبریدی اتمی – پیوسته به منظور مطالعه اثرات عیوب ساختاری بر روی خواص مکانیکی گرافن معرفی شده است. طی یک تحلیل محیط پیوسته ماتریس سختی برای ساختار شبکه ای گرافن محاسبه شده است. از این رو حلقه شش گوشه­ای کربن به عنوان نماینده گرافن با یک مدل جدید شامل المان­های چهار نقطه­ای و در قسمت عیب با المان­های مثلثی مدل شده است. این ترکیب کمک می­کند که بتوان هر ساختاری شامل المان­های شش گوشه­ای کربن را شبیه سازی کرد. با وجود در نظر گرفتن تمامی اندرکنش­های پیوندی و غیرپیوندی حجم محاسبات و تعداد المان­ها کم شده است. در تحقیقات گذشته تغییر شکل­های موضعی اتمی در اطراف محل عیب در نظر گرفته نشده که این در واقع نمی­تواند درست باشد چراکه آرایش اتمی در اطراف عیب بهم می­ریزد. برای این منظور از نرم افزار Gaussian برای پیدا کردن موقعیت دقیق اتم­های اطراف عیب استفاده شده است. در نهایت مدول الاستیسته، مدول برشی و نسبت پواسون برای ساختارگرافن کامل و معیوب محاسبه شده است.

References    1              Cranford, S.W. and Buehler, M.J. (2011) Mechanical properties of graphyne. Carbon 49 (13), 4111-4121 2              Xiao, J.R. et al. (2010) Tensile behaviors of graphene sheets and carbon nanotubes with multiple Stone–Wales defects. Materials Science and Engineering: A 527 (3), 715-723 %@ 0921-5093 3              Cho, J. et al. (2007) Mechanical characterization of graphite/epoxy nanocomposites by multi-scale analysis. Composites science and technology 67 (11), 2399-2407 4              Odegard, G.M. and Gates, T.S. (2006) Modeling and testing of the viscoelastic properties of a graphite nanoplatelet/epoxy composite. Journal of intelligent material systems and structures 17 (3), 239-246 5              Shen, L. et al. (2010) Temperature-dependent elastic properties of single layer graphene sheets. Materials & Design 31 (9), 4445-4449 6              Kudin, K.N. et al. (2001) C 2 F, BN, and C nanoshell elasticity from ab initio computations. Physical Review B 64 (23), 235406 7              Huang, Y. et al. (2006) Thickness of graphene and single-wall carbon nanotubes. Physical review B 74 (24), 245413 8              Reddy, C.D. et al. (2006) Equilibrium configuration and continuum elastic properties of finite sized graphene. Nanotechnology 17 (3), 864 9              Hemmasizadeh, A. et al. (2008) A method for developing the equivalent continuum model of a single layer graphene sheet. Thin Solid Films 516 (21), 7636-7640 10            Reddy, C.D. et al. (2005) Equivalent continuum modeling of graphene sheets. International Journal of Nanoscience 4 (04), 631-636 11            Sakhaee-Pour, A. (2009) Elastic properties of single-layered graphene sheet. Solid State Communications 149 (1–2), 91-95 12            Scarpa, F. et al. (2009) Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology 20 (6), 065709 13            Lee, C. et al. (2008) Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321 (5887), 385-388 14            Ni, Z. et al. (2010) Anisotropic mechanical properties of graphene sheets from molecular dynamics. Physica B: Condensed Matter 405 (5), 1301-1306 15            Talukdar, K. and Mitra, A.K. (2010) Comparative MD simulation study on the mechanical properties of a zigzag single-walled carbon nanotube in the presence of Stone-Thrower-Wales defects. Composite structures 92 (7), 1701-1705 16            Shokrieh, M.M. and Rafiee, R. (2010) Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach. Materials & Design 31 (2), 790-795 17            Bu, H. et al. (2009) Atomistic simulations of mechanical properties of graphene nanoribbons. Physics Letters A 373 (37), 3359-3362 18            Tsai, J.-L. and Tu, J.-F. (2010) Characterizing mechanical properties of graphite using molecular dynamics simulation. Materials & Design 31 (1), 194-199 19            Georgantzinos, S.K. et al. (2010) Numerical investigation of elastic mechanical properties of graphene structures. Materials & Design 31 (10), 4646-4654 20            Van Lier, G. et al. (2000) Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene. Chemical Physics Letters 326 (1–2), 181-185 21            Samaroo, K.J. (2005) Stiffness matrices of carbon nanotube structures. 22            Mohammadiana, M. and Fereidoonb, A. (2014) Young\'s Modulus of Single and Double Walled Carbon Nanocones Using Finite Element Method. International Journal of Engineering-Transactions C: Aspects 27 (9), 1467 23            Moshrefzadeh-Sani, H. et al. (2015) A continuum model for stone-wales defected carbon nanotubes. International Journal of Engineering-Transactions C: Aspects 28 (3), 433 24            Nardelli, M.B. et al. (2000) Mechanical properties, defects and electronic behavior of carbon nanotubes. Carbon 38 (11), 1703-1711 25            Sadrnejad, S.A. et al. (2007) Inelastic Continuum Modeling Of Carbon Nanotube\'s Behavior Using Finite Element Method. INTERNATIONAL JOURNAL OF ENGINEERING TRANSACTIONS A BASICS 20 (2), 129 26            Ebbesen, T.W. and Takada, T. (1995) Topological and sp 3 defect structures in nanotubes. Carbon 33 (7), 973-978 27            Pozrikidis, C. (2009) Effect of the Stone–Wales defect on the structure and mechanical properties of single-wall carbon nanotubes in axial stretch and twist. Archive of Applied Mechanics 79 (2), 113-123 28            Khare, R. et al. (2007) Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Physical Review B 75 (7), 075412 29            Tserpes, K.I. et al. (2006) A progressive fracture model for carbon nanotubes. Composites Part B: Engineering 37 (7), 662-669 30            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 (4), 581-589 31            Xiao, J.R. et al. (2009) Fracture and progressive failure of defective graphene sheets and carbon nanotubes. Composite Structures 88 (4), 602-609 32            Nguyen-Tuong, D. et al. Local Gaussian process regression for real time online model learning. pp. 1193-1200 33            Jiang, H. et al. (2004) Defect nucleation in carbon nanotubes under tension and torsion: Stone–Wales transformation. Computer Methods in Applied Mechanics and Engineering 193 (30), 3419-3429 34            Odegard, G.M. et al. (2002) Equivalent-continuum modeling with application to carbon nanotubes, Citeseer


Download PDF 



International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir