No abstract

A methodology is presented here for deriving true experimental axial stress-strain curves in both tension and compression for monolayer graphene through the shift of the 2D Raman peak (Δω) that is present in all graphitic materials. The principle behind this approach is the observation that the shift of the 2D wavenumber as a function of strain for different types of PAN-based fibres is a linear function of their Young's moduli and, hence, the corresponding value of Δω over axial stress is, in fact, a constant. By moving across the length scales we show that this value is also valid at the nanoscale as it corresponds to the in-plane breathing mode of graphene that is present in both PAN-based fibres and monolayer graphene. Hence, the Δω values can be easily converted to values of σ in the linear elastic region without the aid of modelling or the need to resort to cumbersome experimental procedures for obtaining the axial force transmitted to the material and the cross-sectional area of the two-dimensional membrane.

Wrinkles in supported graphenes can be formed either by uniaxial compression or uniaxial tension beyond a certain critical load depending on the mode of loading. In the first case, the wrinkling direction is normal to the compression axis whereas in tension, wrinkles of the same pattern are formed parallel to the loading direction due to Poisson's (lateral) contraction. Herein we show by direct AFM observations that in simply-supported graphenes such instabilities appear as periodic wrinkles over existing stochastic undulations caused by the underlying-substrate-roughness. The critical strain for the generation of these wrinkles in both tension and compression is less than 1% which particularly for the former is far lower than the predicted tensile strain to fracture of suspended graphene estimated at ∼30%. Based on these findings, a constitutive model that provides the critical tensile strain for induced buckling in the lateral direction is proposed that depends only on the graphene-support interaction and not on the nature of the substrate. Understanding the wrinkling failure of graphenes under strain is of paramount importance as it leads to new threshold limits beyond which the physical-mechanical properties of graphene are impaired.