13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Another experiment [36] also confirmed that the zigzag edge is more stable than the armchair edge, although the opposite has been predicted theoretically by ab initio calculations which depend strongly on the choice of the density functional among different DFT calculations yielding dramatically different values in quantitative scattering. During our simulations, total energy at each strain level is minimized for each equilibrium lattice structure. The kinematic energy changes slightly while potential energy increases gradually since the temperature is coupled with a thermostat. Energy jumps are infrequently observed, thus lattice-trapping effects are negligibly small for long-range potentials we used. Undoubtedly, temperature and strain rate can quantitatively affect Kc that increases slightly with increase of strain rates while decreases with temperature. At high temperature beyond 1000K, fracture shows plastic behaviors opposite to brittle at room temperature, the crack edges are reconstructed, fresh surfaces are bridged with carbon chains, and formation and motion of defects and vacancies appear frequently. 4. Concluding remarks In summary, graphene embedded with pre-existing zigzag or armchair crack under complex mechanical stresses is studied by extensive molecular dynamics simulations based on the modified REBO potential. An asymptotic expansion of the displacement field in the region of crack tip is adopted to apply loading combined with in-plane opening and shear stresses. The critical effective stress intensity factors are obtained in the range of 2.63 nN Å-3/2 to 3.38 nN Å-3/2 varied with the phase angle of far-field loading, the predicted low toughness indicates that strong graphene is absolutely brittle at room temperature. The direction of crack initiation is also dependent on the phase angle, and changes by 30°(or multiples of 30°) to the original crack line. Straight cracks with zigzag edges grow self-similarly when opening loading is dominant, or else kinking occurred. Torn edges of fresh cracks are along either zigzag or armchair edge, while zigzag edges are more preferable. Fresh armchair edges are formed occasionally under particular stress conditions. Our theoretical results show that graphene cracking prefers along zigzag edges concerning with its lower toughness and complex mechanical stress in dynamic fracture. Acknowledgements The author gratefully acknowledges supports from Newton International Fellowship (NF080039) and Newton Alumni Follow-On of UK’s Royal Society hosted by University of Glasgow and Newcastle University, and Aeronautical Science Foundation of China (2012ZF52074), NSFCs (10602023 and 11232007), the Fundamental Research Funds for the Central Universities, the Program for Changjiang Scholars and Innovative Research Team (IRT0968) and National Basic Research Program (973, 2011CB707602) of China. References [1]. 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(5696) ( 2004) 666 -669. [2]. C. Lee, X. Wei, J.W. Kysar, and J. Hone, Measurement of the elastic properties and intrinsic strength of
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