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Grain boundaries (GBs) are known to have an important influence on material properties, so understanding how GBs in graphene change its physical properties is important both scientifically and technologically. In this paper, we perform a series of molecular dynamics simulations to investigate the energies, mechanical properties and fracture process of 29 graphene GBs (symmetric and nonsymmetric) under tensile strains. With different arrangements of the pentagonal and heptagonal rings, the misorientation angle () ranges from 3.5 to 27.8. The GBs defects in graphene can produce a pre-strain that will lead to an increase of the energy of GBs. We study the atomic energy distribution around GBs and define a new parameter: single defect energy (Esingle) to calculate the average energy per GBs defect. It is found that Esingle shows a clear linear relation between and defect density (), because pre-strain filed can be cancelled out locally with the increase of defect density. And this pre-stain can reduce the strength of the C-C bond contained in GBs defects. Hence, with very few exceptions, mechanical failure always starts from the defective region. Furthermore, the energy of GBs can be used to reflect the strength of GBs indirectly. The simulated results show that the tensile strength of GBs is linearly related to the highest atomic energy (Emax), and it also depends on Esingle monotonically. Owing to the pre-strain, load distribution along GBs is uneven. Because some bonds are stretched while others are compressed, that is, the real number of bearing carbon bonds is less than the nominal number. Therefore, at the beginning of tension, the Young's modulus of polycrystalline graphene is significantly lower than that of the monocrystal one. But with the increase of strain, it becomes comparable to that of the monocrystal graphene at sufficiently large strain. The results of fracture process indicate that formation and propagation of crack are both dependent on strength GBs. For low GB strength, the fracture mechanism is transgranular fracture in the form of direct fracture of C-C bonds. When stress reaches a critical value, the weakest C-C bonds in GBs will breakdown and form a fracture site. Because of the uneven bearing condition, the C-C bonds in front of the crack possess considerable residual strength and could prevent crack from propagating. As a result, many other fracture sites in the GBs defect can be produced with the increase of strain, and finally, these sites emerge gradually along GBs and form a sawtooth crack. In contrast, the fracture process of high strength GBs is always accompanied with the variations of Stone-Wales (S-W) transformation and direct fracture of C-C bonds. Once the fracture site forms, the crack will propagate rapidly predominantly along armchair or zigzag direction and finally could cross GBs, this process can be called intergranular fracture. Our present work provides fundamental guidance for understanding how defects affect the mechanical behaviour, which is important for further research and application of graphene devices.
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Keywords:
- polycrystalline graphene /
- tensile /
- fracture /
- mechanical properties
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[2] Miao T, Yeom S, Wang P, Standley B, Bockrath M 2014 Nano Lett. 14 2982
[3] Zhao J, Zhang G Y, Shi D X 2013 Chin. Phys. B 22 57701
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[9] An J, Voelkl E, Suk J W, Li X, Magnuson C W, Fu L, Tiemeijer P, Bischoff M, Freitag B, Popova E, Ruoff R S 2011 ACS Nano 5 2433
[10] Wang M C, Yan C, Ma L, Hu N, Chen M W 2012 Comput. Mater. Sci. 54 236
[11] Xiao J R, Staniszewski J, Gillespie J W 2010 Mater. Sci. Eng. A 527 715
[12] Lee G H, Cooper R C, An S J, Lee S, van der Zande A, Petrone N, Hammerberg A G, Lee C, Crawford B, Oliver W, Kysar J W, Hone J 2013 Science 340 1073
[13] Grantab R, Shenoy V B, Ruoff R S 2010 Science 330 946
[14] Wei Y, Wu J, Yin H, Shi X, Yang R, Dresselhaus M 2012 Nat. Mater. 11 759
[15] Wu J, Wei Y 2013 J. Mech. Phys. Solids 61 1421
[16] Yi L, Yin Z, Zhang Y, Chang T 2013 Carbon 51 373
[17] Liu T H, Pao C W, Chang C C 2012 Carbon 50 3465
[18] Rasool H I, Ophus C, Klug W S, Zettl A, Gimzewski J K 2013 Nat. Commun. 4 2811
[19] Cao A, Yuan Y 2012 Appl. Phys. Lett. 100 211912
[20] Han J, Ryu S, Sohn D, Im S 2014 Carbon 68 250
[21] Zhang J, Zhao J, Lu J 2012 ACS Nano 6 2704
[22] Kotakoski J, Meyer J C 2012 Phys. Rev. B 85 195447
[23] Zhang T, Li X, Kadkhodaei S, Gao H 2012 Nano Lett. 12 4605
[24] Ansari R, Ajori S, Motevalli B 2012 Superlattices Microstruct. 51 274
[25] Jhon Y I, Zhu S E, Ahn J H, Jhon M S 2012 Carbon 50 3708
[26] Kim K, Artyukhov V I, Regan W, Liu Y, Crommie M F, Yakobson B I, Zettl A 2012 Nano Lett. 12 293
[27] Ruiz-Vargas C S, Zhuang H L, Huang P Y, van der Zande A M, Garg S, McEuen P L, Muller D A, Hennig R G, Park J 2011 Nano Lett. 11 2259
[28] Wang B, Puzyrev Y, Pantelides S T 2011 Carbon 49 3983
[29] Wang W D, Hao Y, Ji X, Yi C L, Niu X Y 2012 Acta. Phys. Sin. 61 200207 (in Chinese) [王卫东, 郝跃, 纪翔, 易成龙, 牛翔宇 2012 物理学报 61 200207]
[30] Brenner D W, Shenderova O A, Harrison J A, Stuart S J, Ni B, Sinnott S B 2002 J. Phys. Condens. Matter 14 783
[31] Ni Z, Bu H, Zou M, Yi H, Bi K, Chen Y 2010 Phys. B: Condens. Matter 405 1301
[32] Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385
[33] Liu F, Ming P, Li J 2007 Phys. Rev. B 76 064120
[34] Xiang L, Wu J, Ma S Y, Wang F, Zhang K W 2015 Chin. Phys. Lett. 32 096801
[35] Liu Y, Yakobson B I 2010 Nano Lett. 10 2178
[36] Chen S, Chrzan D C 2011 Phys. Rev. B 84 214103
[37] Yazyev O V, Louie S G 2010 Phys. Rev. B 81 195420
[38] Li L, Reich S, Robertson J 2005 Phys. Rev. B 72 184109
[39] Frank O, Tsoukleri G, Riaz I, Papagelis K, Parthenios J, Ferrari A C, Geim A K, Novoselov K S, Galiotis C 2011 Nat Commun. 2 255
[40] Sakhaee-Pour A, Ahmadian M T, Vafai A 2008 Solid State Commun. 147 336
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[1] Ramanathan T, Abdala A A, Stankovich S, Dikin D A, Herrera-Alonso M, Piner R D, Adamson D H, Schniepp H C, Chen X, Ruoff R S, Nguyen S T, Aksay I A, Prud'homme R K, Brinson L C 2008 Nat. Nanotechnol. 3 327
[2] Miao T, Yeom S, Wang P, Standley B, Bockrath M 2014 Nano Lett. 14 2982
[3] Zhao J, Zhang G Y, Shi D X 2013 Chin. Phys. B 22 57701
[4] Li X, Cai W, An J, Kim S, Nah J, Yang D, Piner R, Velamakanni A, Jung I, Tutuc E, Banerjee S K, Colombo L, Ruoff R S 2009 Science 324 1312
[5] Yang H, Shen C M, Tian Y, Wang G Q, Lin S X, Zhang Y, Gu C Z, Li J J, Gao H J 2014 Chin. Phys. B 23 096803
[6] Zhang T, Li X, Gao H 2015 Int. J. Fract. 196 1
[7] Yazyev O V, Louie S G 2010 Phys. Rev. B 81 195420
[8] Huang P Y, Ruiz-Vargas C S, van der Zande A M, Whitney W S, Levendorf M P, Kevek J W, Garg S, Alden J S, Hustedt C J, Zhu Y, Park J, McEuen P L, Muller D A 2011 Nature 469 389
[9] An J, Voelkl E, Suk J W, Li X, Magnuson C W, Fu L, Tiemeijer P, Bischoff M, Freitag B, Popova E, Ruoff R S 2011 ACS Nano 5 2433
[10] Wang M C, Yan C, Ma L, Hu N, Chen M W 2012 Comput. Mater. Sci. 54 236
[11] Xiao J R, Staniszewski J, Gillespie J W 2010 Mater. Sci. Eng. A 527 715
[12] Lee G H, Cooper R C, An S J, Lee S, van der Zande A, Petrone N, Hammerberg A G, Lee C, Crawford B, Oliver W, Kysar J W, Hone J 2013 Science 340 1073
[13] Grantab R, Shenoy V B, Ruoff R S 2010 Science 330 946
[14] Wei Y, Wu J, Yin H, Shi X, Yang R, Dresselhaus M 2012 Nat. Mater. 11 759
[15] Wu J, Wei Y 2013 J. Mech. Phys. Solids 61 1421
[16] Yi L, Yin Z, Zhang Y, Chang T 2013 Carbon 51 373
[17] Liu T H, Pao C W, Chang C C 2012 Carbon 50 3465
[18] Rasool H I, Ophus C, Klug W S, Zettl A, Gimzewski J K 2013 Nat. Commun. 4 2811
[19] Cao A, Yuan Y 2012 Appl. Phys. Lett. 100 211912
[20] Han J, Ryu S, Sohn D, Im S 2014 Carbon 68 250
[21] Zhang J, Zhao J, Lu J 2012 ACS Nano 6 2704
[22] Kotakoski J, Meyer J C 2012 Phys. Rev. B 85 195447
[23] Zhang T, Li X, Kadkhodaei S, Gao H 2012 Nano Lett. 12 4605
[24] Ansari R, Ajori S, Motevalli B 2012 Superlattices Microstruct. 51 274
[25] Jhon Y I, Zhu S E, Ahn J H, Jhon M S 2012 Carbon 50 3708
[26] Kim K, Artyukhov V I, Regan W, Liu Y, Crommie M F, Yakobson B I, Zettl A 2012 Nano Lett. 12 293
[27] Ruiz-Vargas C S, Zhuang H L, Huang P Y, van der Zande A M, Garg S, McEuen P L, Muller D A, Hennig R G, Park J 2011 Nano Lett. 11 2259
[28] Wang B, Puzyrev Y, Pantelides S T 2011 Carbon 49 3983
[29] Wang W D, Hao Y, Ji X, Yi C L, Niu X Y 2012 Acta. Phys. Sin. 61 200207 (in Chinese) [王卫东, 郝跃, 纪翔, 易成龙, 牛翔宇 2012 物理学报 61 200207]
[30] Brenner D W, Shenderova O A, Harrison J A, Stuart S J, Ni B, Sinnott S B 2002 J. Phys. Condens. Matter 14 783
[31] Ni Z, Bu H, Zou M, Yi H, Bi K, Chen Y 2010 Phys. B: Condens. Matter 405 1301
[32] Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385
[33] Liu F, Ming P, Li J 2007 Phys. Rev. B 76 064120
[34] Xiang L, Wu J, Ma S Y, Wang F, Zhang K W 2015 Chin. Phys. Lett. 32 096801
[35] Liu Y, Yakobson B I 2010 Nano Lett. 10 2178
[36] Chen S, Chrzan D C 2011 Phys. Rev. B 84 214103
[37] Yazyev O V, Louie S G 2010 Phys. Rev. B 81 195420
[38] Li L, Reich S, Robertson J 2005 Phys. Rev. B 72 184109
[39] Frank O, Tsoukleri G, Riaz I, Papagelis K, Parthenios J, Ferrari A C, Geim A K, Novoselov K S, Galiotis C 2011 Nat Commun. 2 255
[40] Sakhaee-Pour A, Ahmadian M T, Vafai A 2008 Solid State Commun. 147 336
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