Engineering size-scaling of plastic deformation in nanoscale asperities

Size-dependent plastic flow behavior is manifested in nanoindentation, microbending, and pillar-compression experiments and plays a key role in the contact mechanics and friction of rough surfaces. Recent experiments using a hard flat plate to compress single-crystal Au nano-pyramids and others using a Berkovich indenter to indent flat thin films show size scaling into the 100-nm range where existing mechanistic models are not expected to apply. To bridge the gap between single-dislocation nucleation at the 1-nm scale and dislocation-ensemble plasticity at the 1-μm scale, we use large-scale molecular dynamics (MD) simulations to predict the magnitude and scaling of hardness H versus contact size ℓ_c in nano-pyramids. Two major results emerge: a regime of near-power-law size scaling H ≈ ℓ_c -η exists, with ηMD ≈ 0.32 compared with ηexpt ≈ 0.75, and unprecedented quantitative and qualitative agreement between MD and experiments is achieved, with HMD ≈4 GPa at ℓ_c =36 nm and Hexpt ≈ 2.5 GPa at ℓ_c = 100 nm. An analytic model, incorporating the energy costs of forming the geometrically necessary dislocation structures that accommodate the deformation, is developed and captures the unique magnitude and size scaling of the hardness at larger MD sizes and up to experimental scales while rationalizing the transition in scaling between MD and experimental scales. The model suggests that dislocation-dislocation interactions dominate at larger scales, whereas the behavior at the smallest MD scales is controlled by nucleation over energy barriers. These results provide a basic framework for understanding and predicting size-dependent plasticity in nanoscale asperities under contact conditions in realistic engineered surfaces.