Graphene-Induced Surface Stiffening of Copper Studied by Nanoindentation

Graphene, a 2D material, has been rapidly gaining steam for material strengthening and protection applications at the nanoscale. Despite its single atomic thinness, it is thought to improve pre-existing desirable mechanical, electrical or optical properties, among numerous others. It is therefore highly desirable to accurately measure and understand the structure and properties of graphene commensurate on other materials.<br/>For mechanical property characterization, nanoindentation has been widely adopted for measuring modulus and hardness of thin and thick films, and more recently for measuring the stiffness and strength of suspended 2D materials. In both cases, a measured load-displacement response must be fitted to an analytical model for extraction of mechanical properties. The Oliver-Pharr method, for example, is one of the most widely used for elastic modulus and hardness extraction using load-displacement for bulk materials supported on rigid substrates. In contrast, the mechanical properties of 2D materials are extracted using free-standing indentation techniques (FSI), where classical solutions for suspended clamped membranes are adopted for modeling their load-displacement behavior. However, the existing indentation models can not currently capture atomically thin materials on a substrate, hence the urgent need for new models capable of explaining the behavior of such systems.<br/>In this study, we report on the mechanical property enhancement of graphene-covered copper (Cu) foils through nanoindentation and subsequent high-resolution transmission electron microscopy (TEM) techniques. We observe a clear enhancement of elastic modulus of copper when it is covered by graphene, in the range of 5 to 10% compared to graphene-free regions. No significant enhancement of hardness was measured. We present an equal-displacement model explaining the nanoindentation behavior observed for the graphene-copper system. Our simplified model takes the limit of frictionless sliding of the graphene within the indented region due to shear lag, a concept inspired by the mechanics of composite materials. It uses of both the Oliver-Pharr method for the behavior of copper in addition to the FSI model based on classical clamped membrane solutions for graphene. We also take cross sectional TEM samples of indented regions and compare the plastic behavior of graphene-covered and graphene-free regions. We observe more scattered plastic activity in the former, as opposed to the more tip-localized plasticity observed in the latter.