Avoiding lateral failure of 2D materials subjected to large axial deformations

The axial tensile deformation of exfoliated monolayer graphene in air is always accompanied by the formation of lateral wrinkles, or buckles, due to the extremely low bending stiffness. When supported or embedded in polymer matrices, the resistance to buckling significantly increases, but for large irregular flakes, out-of-plane wrinkling occurs at axial strains below similar to 1 %, leading to interfacial failure. However, Poisson's driven lateral strains are generated by shear and, therefore, for small widths (less than twice the transfer length) the material is expected to remain flat under axial deformation. In this work, we have tested this assertion by performing uniaxial tensile testing combined with in-situ Atomic Force Microscopy, in order to observe the onset of lateral wrinkling in simply-supported monolayer graphene flakes having different widths. We have provided evidence that the onset of wrinkle formation can be eliminated or pushed back to high strains (i.e. >2 %), if graphene is shaped as a narrow micro-ribbon. We also implemented a theoretical model based on shear-lag theory to predict the critical tensile strain for the initiation of lateral wrinkling, and demonstrated that for ribbons of width <800 nm the lateral wrinkling is fully eliminated. We argue that this is the only route possible for the exploitation of graphene as a strong and tough material in a multitude of applications.