Incipient plasticity and fully plastic contact behavior of copper coated with a graphene layer

Cu coated with a graphene layer increases the elastic modulus from 163.4 GPa to 176.7 GPa, as analyzed for the initial elastic loading during nanoindentation by the Hertzian contact theory. This is attributed to stiffening, due to the ultra-high elastic modulus of the graphene layer, and the compressive in-plane residual stresses in the Cu surface volume introduced by the lattice mismatch between graphene and Cu. The graphene layer induces incipient plasticity, manifested by pop-in events during nanoindentation loading, at shallower indentation depths. This could be due to the compressive in-plane residual stress in the Cu surface volume; however, this compressive stress does not significantly change the critical resolved shear stress for the incipient plasticity. Even in the fully plastic contact region, at an indentation depth of 100 nm, the graphene layer affects the stress distribution underneath the indenter, resulting in a lower pile-up height. When considering this reduced pile-up height, the graph...