Our recent molecular dynamics study shows that edge energy induces ripples in graphene sheets with a central crack. The sheets are allowed to relax over a time period of 30 ps before applying the strain. It is noticed that the crack tips come out of the plane of sheet during relaxation. The crack tips are free edges. Deformation of free edges of graphene arises from the difference of the energy stored in edge atoms and interior atoms [1]. As shown in the following figure and the video, the out-of-plane deformation of a crack tip at equilibrium configuration is localized around the tip. However, when the strain increases up to 0.018, the deformed shape of the crack tip changes to a localized ripple. As strain further increases up to 0.0235, this localized ripple spreads throughout the sheet. This behaviour prevails both at 1 K and 300 K. Therefore temperature is not a significant factor in the observed rippling behaviour. We explained this behaviour in our recent paper “Atomistic and continuum modelling of temperature-dependent fracture of graphene ” published in International Journal of Fracture.

Fig. Ripples in a garphene sheet at various strain levels. Size of the sheet is 27 nm × 27 nm. Strain is applied along y-direction. Colours of the atoms indicate the out of plane (z) coordinate.

Video: Crack induced ripples and fracture of an armchair graphene sheet with a central crack.

Reference

[1] Lu Q, Huang R (2010) Excess energy and deformation along free edges of graphene nanoribbons. Phys Rev B 81:155410

Q. Lu and R. Huang, Excess energy and deformation along free edges of graphene nanoribbons. Posted online at arXiv:0910.0912, October 2009.

Change of the bonding environment at the free edges of graphene monolayer leads to excess edge energy and edge force, depending on the edge morphology (zigzag or armchair). By using a reactive empirical bond-order potential and atomistic simulations, we show that the excess edge energy in free-standing graphene nanoribbons can be partially relaxed by both in-plane and out-of-plane deformation. The excess edge energy and edge force are calculated for graphene nanoribbons with parallel zigzag or armchair edges. Depending on the longitudinal constraint, the compressive edge force leads to either in-plane elongation of the ribbon or out-of-plane buckling deformation. In the former case, the longitudinal strain is inversely proportional to the ribbon width. In the latter case, energy minimization predicts an intrinsic wavelength for edge buckling to be 6.2 nm along the zigzag edge and 8.0 nm along the armchair edge. For graphene nanoribbons of width less than the intrinsic wavelength, interaction between the two free edges becomes significant, leading to anti-phase correlation of the buckling waves.