Graphene-Induced Surface Stiffening of Copper Studied by Nanoindentation

We report on the surface mechanical behavior of graphene-covered copper foils measured by nanoindentation. We observe a significant elastic modulus increase of the surface when it is covered by graphene after chemical vapor deposition, around 8-12% higher than that in graphene-free regions. This is a remarkable increase given that only a single layer of atoms is added to the surface and that the resistance of a single atomic layer to normal compression is not expected to strongly affect indentation measurements. We explain these results using a finite element analysis (FEA) and a theoretical equal-displacement model based on total elastic energy, combining the Oliver-Pharr method with free-standing membrane indentation (FSI) models to explain the limiting case of the results. The increase in modulus is due to in-plane stretching of graphene under large indentation depths, graphene-induced stress redistribution, and pile-up suppression manifested by the reduction of the contact area during indentation. We discuss the critical importance of considering these effects in order to understand the mechanics of graphene indentation on metal substrates with neat interfaces. We examine cross-sectional TEM samples of indented regions and compare the plastic behavior of graphene-covered and graphene-free regions, where more spatially distributed plasticity is observed in the former as opposed to more tip-localized plasticity in the latter.