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Atomistic simulation study on the crack growth stability of graphene under uniaxial tension and indentation

  • Mechanics of Extreme Materials
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Abstract

Combining a series of atomistic simulations with fracture mechanics theory, we systematically investigate the crack growth stability of graphene under tension and indentation, with a pre-existing crack made by two methods: atom removal and (artificial) bonding removal. In the tension, the monotonically increasing energy release rate \(G\) is consistent with the unstable crack growth. In contrast, the non-monotonic \(G\) with a maximum for indentation explains the transition from unstable to stable crack growth when the crack length is comparable to the diameter of the contact zone. We also find that the crack growth stability within a stable crack growth regime can be significantly affected by the crack tip sharpness even down to a single atom scale. A crack made by atom removal starts to grow at a higher indentation force than the ultimately sharp crack made by bonding removal, which leads to a large force drop at the onset of the crack growth that can cause unstable crack growth under indentation with force control. In addition, we investigate the effect of the offset distance between the indenter and the crack to the indentation fracture force and find that the graphene with a smaller initial crack is more sensitive. The findings reported in this study can be applied to other related 2D materials because crack growth stability is determined primarily by the geometrical factors of the mechanical loading.

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References

  1. Bunch JS, van der Zande AM, Verbridge SS, Frank IW, Tanenbaum DM, Parpia JM, Craighead HG, McEuen PL (2007) Electromechanical resonators from graphene sheets. Science 315(5811):490–493

    ADS  Google Scholar 

  2. Lee C, Wei XD, Kysar JW, Hone J (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321(5887):385–388

    ADS  Google Scholar 

  3. Koenig SP, Boddeti NG, Dunn ML, Bunch JS (2011) Ultrastrong adhesion of graphene membranes. Nat Nanotechnol 6(9):543–546

    ADS  Google Scholar 

  4. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA (2004) Electric field effect in atomically thin carbon films. Science 306(5696):666–669

    ADS  Google Scholar 

  5. Zhang YB, Tan YW, Stormer HL, Kim P (2005) Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438(7065):201–204

    ADS  Google Scholar 

  6. Balandin AA, Ghosh S, Bao WZ, Calizo I, Teweldebrhan D, Miao F, Lau CN (2008) Superior thermal conductivity of single-layer graphene. Nano Lett 8(3):902–907

    ADS  Google Scholar 

  7. Balandin AA (2011) Thermal properties of graphene and nanostructured carbon materials. Nat Mater 10(8):569–581

    ADS  Google Scholar 

  8. Zaman I, Phan TT, Kuan HC, Meng QS, La LTB, Luong L, Youssf O, Ma J (2011) Epoxy/graphene platelets nanocomposites with two levels of interface strength. Polymer 52(7):1603–1611

    Google Scholar 

  9. Rafiee MA, Rafiee J, Srivastava I, Wang Z, Song HH, Yu ZZ, Koratkar N (2010) Fracture and Fatigue in Graphene Nanocomposites. Small 6(2):179–183

    Google Scholar 

  10. Yang XW, Cheng C, Wang YF, Qiu L, Li D (2013) Liquid-mediated dense integration of graphene materials for compact capacitive energy storage. Science 341(6145):534–537

    ADS  Google Scholar 

  11. Raccichini R, Varzi A, Passerini S, Scrosati B (2015) The role of graphene for electrochemical energy storage. Nat Mater 14(3):271–279

    ADS  Google Scholar 

  12. Li XS, Zhu YW, Cai WW, Borysiak M, Han BY, Chen D, Piner RD, Colombo L, Ruoff RS (2009) Transfer of large-area graphene films for high-performance transparent conductive electrodes. Nano Lett 9(12):4359–4363

    ADS  Google Scholar 

  13. Gomez H, Ram MK, Alvi F, Villalba P, Stefanakos E, Kumar A (2011) Graphene-conducting polymer nanocomposite as novel electrode for supercapacitors. J Power Sources 196(8):4102–4108

    Google Scholar 

  14. Berciaud S, Ryu S, Brus LE, Heinz TF (2009) Probing the intrinsic properties of exfoliated graphene: Raman spectroscopy of free-standing monolayers. Nano Lett 9(1):346–352

    ADS  Google Scholar 

  15. Garcia-Sanchez D, van der Zande AM, Paulo AS, Lassagne B, McEuen PL, Bachtold A (2008) Imaging mechanical vibrations in suspended graphene sheets. Nano Lett 8(5):1399–1403

    ADS  Google Scholar 

  16. Cao HL, Yu QK, Jauregui LA, Tian J, Wu W, Liu Z, Jalilian R, Benjamin DK, Jiang Z, Bao J, Pei SS, Chen YP (2010) Electronic transport in chemical vapor deposited graphene synthesized on Cu: quantum Hall effect and weak localization. Appl Phys Lett 96(25):122106

    ADS  Google Scholar 

  17. Reina A, Jia XT, Ho J, Nezich D, Son HB, Bulovic V, Dresselhaus MS, Kong J (2009) Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano Lett 9(1):30–35

    ADS  Google Scholar 

  18. Han J, Pugno NM, Ryu S (2015) Nanoindentation cannot accurately predict the tensile strength of graphene or other 2D materials. Nanoscale 7(38):15672–15679

    ADS  Google Scholar 

  19. Grantab R, Shenoy VB, Ruoff RS (2010) Anomalous strength characteristics of tilt grain boundaries in graphene. Science 330(6006):946–948

    ADS  Google Scholar 

  20. Han J, Ryu S, Sohn D, Im S (2014) Mechanical strength characteristics of asymmetric tilt grain boundaries in graphene. Carbon 68:250–257

    Google Scholar 

  21. Wei YJ, Wu JT, Yin HQ, Shi XH, Yang RG, Dresselhaus M (2012) The nature of strength enhancement and weakening by pentagon-heptagon defects in graphene. Nat Mater 11(9):759–763

    ADS  Google Scholar 

  22. Liu TH, Pao CW, Chang CC (2012) Effects of dislocation densities and distributions on graphene grain boundary failure strengths from atomistic simulations. Carbon 50(10):3465–3472

    Google Scholar 

  23. Yi LJ, Yin ZN, Zhang YY, Chang TC (2013) A theoretical evaluation of the temperature and strain-rate dependent fracture strength of tilt grain boundaries in graphene. Carbon 51:373–380

    Google Scholar 

  24. Lee G-H, Cooper RC, An SJ, Lee S, van der Zande A, Petrone N, Hammerberg AG, Lee C, Crawford B, Oliver W, Kysar JW, Hone J (2013) High-strength chemical-vapor–deposited graphene and grain boundaries. Science 340(6136):1073

    ADS  Google Scholar 

  25. Meyer JC, Geim AK, Katsnelson MI, Novoselov KS, Booth TJ, Roth S (2007) The structure of suspended graphene sheets. Nature 446(7131):60–63

    ADS  Google Scholar 

  26. Kim K, Lee Z, Regan W, Kisielowski C, Crommie MF, Zettl A (2011) Grain boundary mapping in polycrystalline graphene. ACS Nano 5(3):2142–2146

    Google Scholar 

  27. Rasool HI, Ophus C, Klug WS, Zettl A, Gimzewski JK (2013) Measurement of the intrinsic strength of crystalline and polycrystalline graphene. Nat Commun 4:2811

    ADS  Google Scholar 

  28. Han J, Ryu S, Sohn D (2016) A feasibility study on the fracture strength measurement of polycrystalline graphene using nanoindentation with a cylindrical indenter. Carbon 107:310–318

    Google Scholar 

  29. Zhang P, Ma LL, Fan FF, Zeng Z, Peng C, Loya PE, Liu Z, Gong YJ, Zhang JN, Zhang XX, Ajayan PM, Zhu T, Lou J (2014) Fracture toughness of graphene. Nat Commun 5:3782

    Google Scholar 

  30. Pugno N, Carpinteri A, Ippolito M, Mattoni A, Colombo L (2008) Atomistic fracture: QFM vs. MD. Eng Fract Mech 75(7):1794–1803. https://doi.org/10.1016/j.engfracmech.2007.01.028

    Article  Google Scholar 

  31. Pugno NM, Ruoff RS (2004) Quantized fracture mechanics. Philos Mag 84(27):2829–2845

    ADS  Google Scholar 

  32. Han J, Sohn D, Woo W, Kim DK (2017) Molecular dynamics study of fracture toughness and trans-intergranular transition in bi-crystalline graphene. Comp Mater Sci 129:323–331

    Google Scholar 

  33. Yin HQ, Qi HJ, Fan FF, Zhu T, Wang BL, Wei YJ (2015) Griffith criterion for brittle fracture in graphene. Nano Lett 15(3):1918–1924

    ADS  Google Scholar 

  34. Zhao H, Aluru NR (2010) Temperature and strain-rate dependent fracture strength of graphene. J Appl Phys 108(6):064321

    ADS  Google Scholar 

  35. Meng FC, Chen C, Song J (2017) Lattice trapping and crack decohesion in graphene. Carbon 116:33–39

    Google Scholar 

  36. Plimpton S (1995) Fast parallel algorithms for short-range molecular-dynamics. J Comput Phys 117(1):1–19

    ADS  MATH  Google Scholar 

  37. Stuart SJ, Tutein AB, Harrison JA (2000) A reactive potential for hydrocarbons with intermolecular interactions. J Chem Phys 112(14):6472–6486

    ADS  Google Scholar 

  38. Shenderova OA, Brenner DW, Omeltchenko A, Su X, Yang LH (2000) Atomistic modeling of the fracture of polycrystalline diamond. Phys Rev B 61(6):3877–3888

    ADS  Google Scholar 

  39. Costescu BI, Grater F (2014) Graphene mechanics: II. Atomic stress distribution during indentation until rupture. Phys Chem Chem Phys 16(24):12582–12590

    Google Scholar 

  40. Umeno Y, Yachi Y, Sato M, Shima H (2019) On the atomistic energetics of carbon nanotube collapse from AIREBO potential. Physica E 106:319–325

    ADS  Google Scholar 

  41. Dilrukshi KGS, Dewapriya MAN, Puswewala UGA (2015) Size dependency and potential field influence on deriving mechanical properties of carbon nanotubes using molecular dynamics. Theor Appl Mech Lett 5(4):167–172. https://doi.org/10.1016/j.taml.2015.05.005

    Article  Google Scholar 

  42. Zhang T, Li X, Gao H (2014) Designing graphene structures with controlled distributions of topological defects: a case study of toughness enhancement in graphene ruga. Extrem Mech Lett 1:3–8. https://doi.org/10.1016/j.eml.2014.12.007

    Article  Google Scholar 

  43. Ni ZH, Wang HM, Kasim J, Fan HM, Yu T, Wu YH, Feng YP, Shen ZX (2007) Graphene thickness determination using reflection and contrast spectroscopy. Nano Lett 7(9):2758–2763

    ADS  Google Scholar 

  44. Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO-the open visualization tool. Mod Simul Mater Sc 18(1):015012

    ADS  Google Scholar 

  45. Anderson TL (2017) Fracture mechanics: fundamentals and applications. CRC Press, Boca Raton

    MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the Basic Science Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT (NRF-2019R1A2C4070690). NMP is supported by the European Commission under the Graphene Flagship Core 2 Grant No. 785219 (WP14 “Composites”) and FET Proactive “Neurofibres” Grant No. 732344 as well as by the Italian Ministry of Education, University and Research (MIUR) under the “Departments of Excellence” Grant L.232/2016 and ARS01-01384-PROSCAN Grant.

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Authors and Affiliations

  1. Department of Mechanical Engineering and KI for the NanoCentury, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Republic of Korea

    Sangryun Lee & Seunghwa Ryu

  2. Laboratory of Bio-Inspired & Graphene Nanomechanics, Department of Civil Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123, Trento, Italy

    Nicola M. Pugno

  3. School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Nicola M. Pugno

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  1. Sangryun Lee
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Correspondence to Seunghwa Ryu.

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Appendices

Appendix 1: force-depth and stress–strain curve of all pre-cracked graphene

We draw the results for all the indentation testing and uniaxial testing for all pre-cracked graphene (see Fig. 6). For the armchair (zigzag) crack, the shortest and longest initial crack lengths are 1.56 nm (0.984 nm) and 12.6 nm (9.33 nm), respectively, and the interval between the crack lengths is 0.85 nm(0.49 nm).

Fig. 6
figure 6

a force-depth and b stress–strain curve for all pre-cracked graphene

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Appendix 2: nonlinear stress–strain curve of the pristine graphene

We plot the stress–strain curves of the pristine graphene for two different loading directions to show that the graphene is an anisotropic material with a nonlinear response. As shown in Fig. 7, the graphene has a high stretchability with a maximum elongation limit of 20%. Accordingly, the energy release rate is more suitable than the stress intensity factor (which is only valid for linear elastic materials) for accurately predicting the crack growth stability.

Fig. 7
figure 7

stress-strain curve of the pristine graphene under two different loading directions, \(x\) (zigzag) and \(y\) (armchair)

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Lee, S., Pugno, N.M. & Ryu, S. Atomistic simulation study on the crack growth stability of graphene under uniaxial tension and indentation. Meccanica 54, 1915–1926 (2019). https://doi.org/10.1007/s11012-019-01027-x

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