13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- and zigzag sheets, respectively. The value of Ef is given by E(εf), where εf is the failure strain of a sheet with a particular crack length. A comparison of strength of graphene sheets with various crack lengths is given in Fig. 6. The strength of graphene sheets obtained from MD is between the values given by Inglis' and Griffith's approaches. The strength at 300 K shows slight fluctuations due to kinetic energy of atoms. The strength of zigzag graphene sheets given by Griffith and MD simulations agrees quite well with each other. However, both Inglis' and Griffith's theories have been derived for a flat structure, whereas graphene with a crack does not remain flat as shown in Fig. 2. The continuum theories also assume the continuity of material, which is not the case in graphene. Therefore, a perfect agreement between continuum theories and MD simulations cannot be expected. Figure 6. Comparison of Griffith’s and Inglis’ theories with MD simulations. 5. Conclusions The crack tips of graphene show out-of-plane deformations at equilibrium configuration. These deformations propagate with the applied strain and eventually generate ripples in the sheet. A crack with the length of 2.5 nm reduces the strength of both armchair and zigzag graphene sheet by around 55%. Strength obtained from molecular dynamics simulations shows inverse square-root proportionality with crack length as in continuum fracture mechanics theories. Strength of graphene sheet given by Griffith's theory reasonably agrees with strength obtained from molecular dynamics simulations. Acknowledgements This research was supported by Natural Sciences and Engineering Research Council (NSERC) of Canada.
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