Engineering size-scaling of plastic deformation in nanoscale asperities

Abstract

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-m scale, we use large-scale molecular dynamics (MD) simulations to predict the magnitude and scaling of hardness H versus contact size ഞ c in nano-pyramids. Two major results emerge: a regime of near-power-law size scaling H Ϸ ഞ c ؊ exists, with MD Ϸ 0.32 compared with expt Ϸ 0.75, and unprecedented quantitative and qualitative agreement between MD and experiments is achieved, with H MD Ϸ 4 GPa at ഞc ‫؍‬ 36 nm and Hexpt Ϸ 2.5 GPa at ഞ 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.atomistics ͉ dislocation interactions ͉ plasticity ͉ size-effects ͉ surfaces I t is now well established that plastic flow behavior in metallic materials is size dependent, with flow stress (1, 2) or hardness (3) increasing with decreasing volume of material under load. Experimental studies of nanoindentation (4-6) and wire and thin-film bending (7-10) and tension (11-17) clearly elucidate the size effects at micrometer scales. The rational for size-dependent plasticity has been attributed to the need for ''geometrically necessary'' defect structures, typically dislocations, which accommodate the rapid strain gradients that must exist in many small-scale deformation conditions and the influence of these dislocations in hardening the material. Phenomenological strain-gradient-plasticity theories (18-21) and discrete dislocation models (22) both qualitatively exhibit the observed size effects under varying conditions. However, the conceptual bases of these models typically rely on interactions between preexisting, statistically generated, and geometrically necessary dislocations that are not thought to be applicable at nanometer scales where relatively few dislocations exist. Atomistic studies using molecular dynamics (MD) at the nanometer scale can exhibit size effects (23-26), but they are usually ass...

Size-dependent hardness of nanoscale metallic contacts from molecular dynamics simulations

“…10 Prior MD simulations of Au pyramids indenting a flat surface led to exponent of 0.32. 9 The good agreement between our exponents for sinusoidal asperities contacting a flat surface and experiments represents an important validation of our simulations. We note that we use a power law to describe our data in order to be able to compare with prior work, and it is not our objective to establish whether a power law describes the scaling of contact hardness with size or not.…”

“…The asperity hardness is described by the contact stress-contact length relationship after the first local maximum. 9,10 Our results predict both increasing and decreasing hardness with decreasing contact length and that the aspect ratio of the asperities controls these size effects. Flat/asperity contacts with A = 1 nm with the highest aspect ratio of all cases studied exhibit the steepest hardening with decreasing contact size.…”

Conductivity of an atomically defined metallic interface

“…For comparison, the values measured here are similar to the macroscopic hardness of quartz (11). This finding is an instance of the well-documented size effect, where plastic deformation is constrained when the stressed volume is small, dramatically increasing the hardness (10,(12)(13)(14)(15)(16)(17)(18)(19). The slight increase of hardness with increasing force in Fig.…”

Nanoscale Metal-Metal Contact Physics from Molecular Dynamics: The Strongest Contact Size

“…More recently, size effects in strength have been observed in micropillars [5,6], thin films [7], and nanoindentation [8]. In the case of polycrystals, Hall-Petch strengthening exhibits a maximum at a finite size (typically in the tens of nanometers) and further reduction in grain size leads to weakening [9,10].…”