The hardness measured by the nanosize indenter under atomic indentation is examined for the cases of nanocrystalline nickel by means of molecular dynamics (MD) simulations. The grain size effect observed is different from the one by uniform deformation or deep indentation. The results show that hardness can only show inverse Hall–Petch (H-P) effect, no H-P effect is observed with the grain size up to 40nm. Grain boundary (GB) absorption of the localized strain is the main deformation mechanism when the indenter size and the depth both come to nano size. The area of plastic zone generated beneath the tip is strongly dependent on the GB density, sample with small grain size results in larger plastic area, which leads to the softer response of hardness

The work by Greenwood and Williamson (GW) has initiated a simple but effective method of contact mechanics: statistical modeling based on the mechanical response of a single asperity. Two main assumptions of the original GW model are that the asperity response is purely elastic and that there is no interaction between asperities. However, as asperities lie on a continuous substrate, the deformation of one asperity will change the height of all other asperities through deformation of the substrate and will thus influence subsequent contact evolution. Moreover, a high asperity contact pressure will result in plasticity, which below tens of microns is size dependent, with smaller being harder. In this paper, the asperity interaction effect is taken into account through substrate deformation, while a size-dependent plasticity model is adopted for individual asperities. The intrinsic length in the strain gradient plasticity (SGP) theory is obtained by fitting to two-dimensional discrete dislocation plasticity simulations of the flattening of a single asperity. By utilizing the single asperity, response in three dimensions and taking asperity interaction into account, a statistical calculation of rough surface contact is performed. The effectiveness of the statistical model is addressed by comparison with full-detail finite element simulations of rough surface contact using SGP. Throughout the paper, our focus is on the difference of contact predictions based on size-dependent plasticity as compared to conventional size independent plasticity. (C) 2017 Elsevier Ltd. All rights reserved

From a microscopic point of view, the real contact area between two rough surfaces is the sum of the areas of contact between facing asperities. Since the real contact area is a fraction of the nominal contact area, the real contact pressure is much higher than the nominal contact pressure, which results in plastic deformation of asperities. As plasticity is size dependent at size scales below tens of micrometers, with the general trend of smaller being harder, macroscopic plasticity is not suitable to describe plastic deformation of small asperities and thus fails to capture the real contact area and pressure accurately. Here we adopt conventional mechanism-based strain gradient plasticity (CMSGP) to analyze the contact between a rigid platen and an elasto-plastic solid with a rough surface. Flattening of a single sinusoidal asperity is analyzed first to highlight the difference between CMSGP and J2 isotropic plasticity. For the rough surface contact, besides CMSGP, pure elastic and J2 isotropic plasticity analysis is also carried out for comparison. In all cases, the contact area A rises linearly with the applied load, but with a different slope which implies that the mean contact pressures are different. CMSGP produces qualitative changes in the distributions of local contact pressures compared with pure elastic and J2 isotropic plasticity analysis, furthermore, bounded by the two