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

Surface rippling may appear in ductile polymer nanofibers under axial stretching. Such rippling phenomenon has been detected in as-electrospun polyacrylonitrile (PAN) in recent single-fiber tension tests and in electrospun polyimide (PI) nanofibers after imdization. We herein propose a simple one-dimensional (1D) nonlinear elastic model to take into account the combined effect of surface tension and nonlinear elasticity during the rippling initiation and its evolution in compliant polymer nanofibers. The polymer nanofiber is modeled as incompressible, isotropically hyperelastic Mooney-Rivlin solid. The fiber geometry prior to rippling is considered as a long circular cylinder. The governing equation of surface rippling is established through linear perturbation of the static equilibrium state of the nanofiber subjected to finite axial pre-stretching. Critical stretch and ripple wavelength are determined in terms of surface tension, elastic property, and fiber radius. Numerical examples are demonstrated to examine these dependencies. Besides, a critical fiber radius is determined, below which the polymer nanofibers are intrinsically unstable. The present model, therefore, is capable of predicting the rippling condition in compliant nanofibers, and can be further used as continuum mechanics approach for the study of surface instability and nonlinear wave propagation in compliant fibers and wires at nanoscale.