Graphene mechanics: II. Atomic stress distribution during indentation until rupture

Abstract

Previous Atomic Force Microscopy (AFM) experiments found single layers of defect-free graphene to rupture at unexpectedly high loads in the micronewton range. Using molecular dynamics simulations, we modeled an AFM spherical tip pressing on a circular graphene sheet and studied the stress distribution during the indentation process until rupture. We found the graphene rupture force to have no dependency on the sheet size and a very weak dependency on the indenter velocity, allowing a direct comparison to experiment. The deformation showed a non-linear elastic behavior, with a two-dimensional elastic modulus in good agreement with previous experimental and computational studies. In line with theoretical predictions for linearly elastic sheets, rupture forces of non-linearly elastic graphene are proportional to the tip radius. However, as a deviation from the theory, the atomic stress concentrates under the indenter tip more strongly than predicted and causes a high probability of bond breaking only in this area. In turn, stress levels decrease rapidly towards the edge of the sheet, most of which thus only serves the role of mechanical support for the region under the indenter. As a consequence, the high ratio between graphene sheets and sphere radii, hitherto supposed to be necessary for reliable deformation and rupture studies, could be reduced to a factor of only 5-10 without affecting the outcome. Our study suggests time-resolved analysis of forces at the atomic level as a valuable tool to predict and interpret the nano-scale response of stressed materials beyond graphene.

Mechanical properties of atomically thin boron nitride and the role of interlayer interactions

“…In this regard, the mechanical properties of monolayer (1L) graphene have been systematically studied. Although the reported experimental values of the elastic modulus of high-quality graphene vary between 0.5 and 2.4 TPa (refs 1, 2, 3, 4, 5), most studies obtained a value of ∼1 TPa, that is, an effective Young’s modulus ( E 2D ) of ∼342 N m −1 with an effective thickness of 0.335 nm, consistent with many theoretical calculations678. The theoretical and experimental fracture strengths of graphene are in the range of 70–130 GPa, and the intrinsic strain is between 14 and 33% (refs 1, 7, 8, 9).…”

“…Although the reported experimental values of the elastic modulus of high-quality graphene vary between 0.5 and 2.4 TPa (refs 1, 2, 3, 4, 5), most studies obtained a value of ∼1 TPa, that is, an effective Young’s modulus ( E 2D ) of ∼342 N m −1 with an effective thickness of 0.335 nm, consistent with many theoretical calculations678. The theoretical and experimental fracture strengths of graphene are in the range of 70–130 GPa, and the intrinsic strain is between 14 and 33% (refs 1, 7, 8, 9). It has been found that although low levels of defects do not have a negative influence on the elastic modulus of graphene1011, their presence can greatly deteriorate its strength10121314.…”

Mechanical Strength of Nanoporous Graphene as a Desalination Membrane

“…22 Prior to fracture, the entire membrane is in a state of plane stress with regions away from nanopores experiencing less stress than atoms located in the immediate vicinity of a nanopore. Carbon−carbon bonds colored red have buckled earlier in the simulation and are therefore in a lower state of stress.…”

A Review Ba(OH)2 : Transpor Ionik pada Barium Hidroksida di dalam Air dengan Konsep Termodinamika

“…Tabel 2. Jari-jari atom (78)(79)(80)(81)(82)(83)(84)(85)(86)(87)(88)(89) masing-masing unsur penyusun senyawa barium hidroksida (90) https://en.wikipedia.org/wiki/Barium…”