Grain size effects on dynamic fracture instability in polycrystalline graphene under tear loading

Abstract

The stability of dynamic fracture is a fundamental and challenging problem in the field of materials science. The grain size effect on dynamic fracture instability in polycrystalline graphene under tear loading is explored via theoretical analysis and molecular dynamics simulations. The fracture stability phase diagram in terms of grain size and crack propagation velocity is obtained, and three regions of crack propagation are identified: stable, metastable, and unstable. For grain size above 2 nm, there exists a critical velocity beyond which fracture instability occurs, and this critical velocity depends linearly on grain size. Decreasing grain size leads to reduced characteristic time for correction of crack path deflection, which plays a dominant role in dynamic fracture instabilities. However, when grain size is below 2 nm, there does not exist a critical velocity for steady propagation of cracks due to discontinuous effects. Our results also provide a valuable insight into dynamic fracture of polycrystalline graphene as well as other 2D and quasi-2D materials.

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References

  1. 1.

    M.J. Buehler and H. Gao: Dynamical fracture instabilities due to local hyperelasticity at crack tips. Nature 439, 307 (2006).

    CAS  Article  Google Scholar 

  2. 2.

    J. Swadener, M. Baskes, and M. Nastasi: Molecular dynamics simulation of brittle fracture in silicon. Phys. Rev. Lett. 89, 085503 (2002).

    CAS  Article  Google Scholar 

  3. 3.

    T. Belytschko, S. Xiao, G. Schatz, and R. Ruoff: Atomistic simulations of nanotube fracture. Phys. Rev. B 65, 235430 (2002).

    Article  CAS  Google Scholar 

  4. 4.

    L.B. Freund: Dynamic Fracture Mechanics (Cambridge university Press, Cambridge, U.K., 1998).

    Google Scholar 

  5. 5.

    K.B. Broberg: Cracks and Fracture (Elsevier, San Diego, California, 1999).

    Google Scholar 

  6. 6.

    E.H. Yoffe: The moving Griffith crack. Philos. Mag. 42, 739–750 (1951).

    Article  Google Scholar 

  7. 7.

    H. Gao: Surface roughening and branching instabilities in dynamic fracture. J. Mech. Phys. Solids 41, 457–486 (1993).

    Article  Google Scholar 

  8. 8.

    H. Gao: A theory of local limiting speed in dynamic fracture. J. Mech. Phys. Solids 44, 1453–1474 (1996).

    CAS  Article  Google Scholar 

  9. 9.

    H. Gao: Elastic waves in a hyperelastic solid near its plane-strain equibiaxial cohesive limit. Philos. Mag. Lett. 76, 307–314 (1997).

    CAS  Article  Google Scholar 

  10. 10.

    S. Rezaei, S. Wulfinghoff, and S. Reese: Prediction of fracture and damage in micro/nano coating systems using cohesive zone elements. Int. J. Solids Struct. 121, 62–74 (2017).

    Article  Google Scholar 

  11. 11.

    R. Daniel, M. Meindlhumer, W. Baumegger, J. Zalesak, B. Sartory, M. Burghammer, C. Mitterer, and J. Keckes: Grain boundary design of thin films: Using tilted brittle interfaces for multiple crack deflection toughening. Acta Mater. 122, 130–137 (2017).

    CAS  Article  Google Scholar 

  12. 12.

    A. Tehranchi and W. Curtin: Atomistic study of hydrogen embrittlement of grain boundaries in nickel: I. Fracture. J. Mech. Phys. Solids 101, 150–165 (2017).

    CAS  Article  Google Scholar 

  13. 13.

    K. Leitner, D. Scheiber, S. Jakob, S. Primig, H. Clemens, E. Povoden-Karadeniz, and L. Romaner: How grain boundary chemistry controls the fracture mode of molybdenum. Mater. Des. 142, 36–43 (2018).

    CAS  Article  Google Scholar 

  14. 14.

    D. Hull and D. Rimmer: The growth of grain-boundary voids under stress. Philos. Mag. 4, 673–687 (1959).

    CAS  Article  Google Scholar 

  15. 15.

    T.L. Anderson: Fracture Mechanics: Fundamentals and Applications (CRC Press, Boca Raton, 2017).

    Google Scholar 

  16. 16.

    D. Holland and M. Marder: Ideal brittle fracture of silicon studied with molecular dynamics. Phys. Rev. Lett. 80, 746 (1998).

    CAS  Article  Google Scholar 

  17. 17.

    B.L. Holian and R. Ravelo: Fracture simulations using large-scale molecular dynamics. Phys. Rev. B 51, 11275 (1995).

    CAS  Article  Google Scholar 

  18. 18.

    T. Bittencourt, P. Wawrzynek, A. Ingraffea, and J. Sousa: Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng. Fract. Mech. 55, 321–334 (1996).

    Article  Google Scholar 

  19. 19.

    H. Rafii-Tabar, L. Hua, and M. Cross: A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate. J. Phys.: Condens. Matter 10, 2375 (1998).

    CAS  Google Scholar 

  20. 20.

    R. Mas-Balleste, C. Gomez-Navarro, J. Gomez-Herrero, and F. Zamora: 2D materials: To graphene and beyond. Nanoscale 3, 20–30 (2011).

    CAS  Article  Google Scholar 

  21. 21.

    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, and A.A. Firsov: Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    CAS  Article  Google Scholar 

  22. 22.

    K.I. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer: Ultrahigh electron mobility in suspended graphene. Solid State Commun. 146, 351–355 (2008).

    CAS  Article  Google Scholar 

  23. 23.

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

    CAS  Article  Google Scholar 

  24. 24.

    K.S. Kim, Y. Zhao, H. Jang, S.Y. Lee, J.M. Kim, K.S. Kim, J-H. Ahn, P. Kim, J-Y. Choi, and B.H. Hong: Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457, 706 (2009).

    CAS  Article  Google Scholar 

  25. 25.

    B. Özyilmaz, P. Jarillo-Herrero, D. Efetov, D.A. Abanin, L.S. Levitov, and P. Kim: Electronic transport and quantum hall effect in bipolar graphene p-n-p junctions. Phys. Rev. Lett. 99, 166804 (2007).

    Article  CAS  Google Scholar 

  26. 26.

    J.S. Bunch, A.M. Van Der Zande, S.S. Verbridge, I.W. Frank, D.M. Tanenbaum, J.M. Parpia, H.G. Craighead, and P.L. McEuen: Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007).

    CAS  Article  Google Scholar 

  27. 27.

    I. Frank, D.M. Tanenbaum, A.M. van der Zande, and P.L. McEuen: Mechanical properties of suspended graphene sheets. J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.–Process., Meas., Phenom. 25, 2558–2561 (2007).

    CAS  Article  Google Scholar 

  28. 28.

    T. Zhang, X. Li, and H. Gao: Fracture of graphene: A review. Int. J. Fract. 196, 1–31 (2015).

    Article  Google Scholar 

  29. 29.

    D. Akinwande, C.J. Brennan, J. Scott Bunch, P. Egberts, J.R. Felts, H. Gao, R. Huang, J-S. Kim, T. Li, Y. Li, K.M. Liechti, N. Lu, H.S. Park, E.J. Reed, P. Wang, B.I. Yakobson, T. Zhang, Y-W. Zhang, Y. Zhou, and Y. Zhu: A review on mechanics and mechanical properties of 2D materials—Graphene and beyond. Extreme Mech. Lett. 13, 42–77 (2017).

    Article  Google Scholar 

  30. 30.

    A. Gupta, T. Sakthivel, and S. Seal: Recent development in 2d materials beyond graphene. Prog. Mater. Sci. 73, 44–126 (2015).

    CAS  Article  Google Scholar 

  31. 31.

    M-Q. Le and R.C. Batra: Single-edge crack growth in graphene sheets under tension. Comput. Mater. Sci. 69, 381–388 (2013).

    CAS  Article  Google Scholar 

  32. 32.

    E. Orowan: Fracture and strength of solids. Rep. Prog. Phys. 12, 185 (1949).

    Article  Google Scholar 

  33. 33.

    H. Yin, H.J. Qi, F. Fan, T. Zhu, B. Wang, and Y. Wei: Griffith criterion for brittle fracture in graphene. Nano Lett. 15, 1918–1924 (2015).

    CAS  Article  Google Scholar 

  34. 34.

    X. Liu, F. Wang, and H. Wu: Anisotropic propagation and upper frequency limitation of terahertz waves in graphene. Appl. Phys. Lett. 103, 071904 (2013).

    Article  CAS  Google Scholar 

  35. 35.

    X. Liu, F. Wang, and H. Wu: Anisotropic growth of buckling-driven wrinkles in graphene monolayer. Nanotechnology 26, 065701 (2015a).

    CAS  Article  Google Scholar 

  36. 36.

    X. Liu, F. Wang, and H. Wu: Anomalous twisting strength of tilt grain boundaries in armchair graphene nanoribbons. Phys. Chem. Chem. Phys. 17, 31911–31916 (2015b).

    CAS  Article  Google Scholar 

  37. 37.

    A.K. Geim: Graphene: Status and prospects. Science 324, 1530–1534 (2009).

    CAS  Article  Google Scholar 

  38. 38.

    G-H. Lee, R.C. Cooper, S.J. An, S. Lee, A. Van Der Zande, N. Petrone, A.G. Hammerberg, C. Lee, B. Crawford, W. Oliver, J.W. Kysar, and J. Hone: High-strength chemical-vapor–deposited graphene and grain boundaries. Science 340, 1073–1076 (2013).

    CAS  Article  Google Scholar 

  39. 39.

    R. Grantab, V.B. Shenoy, and R.S. Ruoff: Anomalous strength characteristics of tilt grain boundaries in graphene. Science 330, 946–948 (2010).

    CAS  Article  Google Scholar 

  40. 40.

    M. Wang, C. Yan, L. Ma, N. Hu, and M. Chen: Effect of defects on fracture strength of graphene sheets. Comput. Mater. Sci. 54, 236–239 (2012).

    CAS  Article  Google Scholar 

  41. 41.

    G. López-Polín, J. Gómez-Herrero, and C. Gómez-Navarro: Confining crack propagation in defective graphene. Nano Lett. 15, 2050–2054 (2015).

    Article  CAS  Google Scholar 

  42. 42.

    M-Q. Le and R.C. Batra: Crack propagation in pre-strained single layer graphene sheets. Comput. Mater. Sci. 84, 238–243 (2014).

    CAS  Article  Google Scholar 

  43. 43.

    P.R. Budarapu, B. Javvaji, V. Sutrakar, D. Roy Mahapatra, G. Zi, and T. Rabczuk: Crack propagation in graphene. J. Appl. Phys. 118, 064307 (2015).

    Article  CAS  Google Scholar 

  44. 44.

    D. Sen, K.S. Novoselov, P.M. Reis, and M.J. Buehler: Tearing graphene sheets from adhesive substrates produces tapered nanoribbons. Small 6, 1108–1116 (2010).

    CAS  Article  Google Scholar 

  45. 45.

    M.J. Moura and M. Marder: Tearing of free-standing graphene. Phys. Rev. E 88, 032405 (2013).

    CAS  Article  Google Scholar 

  46. 46.

    R. Khare, S.L. Mielke, J.T. Paci, S. Zhang, R. Ballarini, G.C. Schatz, and T. Belytschko: Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Phys. Rev. B 75, 075412 (2007).

    Article  CAS  Google Scholar 

  47. 47.

    P. Zhang, L. Ma, F. Fan, Z. Zeng, C. Peng, P.E. Loya, Z. Liu, Y. Gong, J. Zhang, X. Zhang, P.M. Ajayan, T. Zhu, and J. Lou: Fracture toughness of graphene. Nat. Commun. 5, 3782 (2014).

    CAS  Article  Google Scholar 

  48. 48.

    L. Priester: Grain Boundaries: From Theory to Engineering, Vol. 172 (Springer Science & Business Media, Dordrecht, 2012).

    Google Scholar 

  49. 49.

    T. Zhang, X. Li, S. Kadkhodaei, and H. Gao: Flaw insensitive fracture in nanocrystalline graphene. Nano Lett. 12, 4605–4610 (2012).

    CAS  Article  Google Scholar 

  50. 50.

    P. Hirvonen, M.M. Ervasti, Z. Fan, M. Jalalvand, M. Seymour, S.M.V. Allaei, N. Provatas, A. Harju, K.R. Elder, and T. Ala-Nissila: Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models. Phys. Rev. B 94, 035414 (2016).

    Article  CAS  Google Scholar 

  51. 51.

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

    CAS  Article  Google Scholar 

  52. 52.

    M. Hossain, T. Hao, and B. Silverman: Stillinger–weber potential for elastic and fracture properties in graphene and carbon nanotubes. J. Phys.: Condens. Matter 30, 055901 (2018a).

    CAS  Google Scholar 

  53. 53.

    M.Z. Hossain, T. Ahmed, B. Silverman, M.S. Khawaja, J. Calderon, A. Rutten, and S. Tse: Anisotropic toughness and strength in graphene and its atomistic origin. J. Mech. Phys. Solids 110, 118–136 (2018b).

    CAS  Article  Google Scholar 

  54. 54.

    A. Stukowski: Visualization and analysis of atomistic simulation data with ovito–the open visualization tool. Modell. Simul. Mater. Sci. Eng. 18, 015012 (2009).

    Article  Google Scholar 

  55. 55.

    S. Xiao and T. Belytschko: A bridging domain method for coupling continua with molecular dynamics. Comput. Methods Appl. Mech. Eng. 193, 1645–1669 (2004).

    Article  Google Scholar 

  56. 56.

    S.S. Terdalkar, S. Huang, H. Yuan, J.J. Rencis, T. Zhu, and S. Zhang: Nanoscale fracture in graphene. Chem. Phys. Lett. 494, 218–222 (2010).

    CAS  Article  Google Scholar 

  57. 57.

    K.A. Brakke: Statistics of Random Plane Voronoi Tessellations (Department of Mathematical Sciences, Susquehanna University, Pennsylvania, 1987). (Manuscript 1987a).

    Google Scholar 

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Acknowledgments

This work was partially supported by the National Key R&D Program of China (Grant No. 2017YFB0702002), the Scientific Challenge Project of China (No. TZ2018001), and the National Natural Science Foundation of China (No. 11627901). The numerical calculations were performed at the Supercomputing Center of the Peac Institute of Multiscale Sciences.

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Correspondence to Jun Zhu or Sheng-Nian Luo.

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Zhao, Y., Xu, Y., Liu, X. et al. Grain size effects on dynamic fracture instability in polycrystalline graphene under tear loading. Journal of Materials Research 34, 2209–2217 (2019). https://doi.org/10.1557/jmr.2019.76

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