Correcting for Tip Geometry Effects in Molecular Simulations of Single-Asperity Contact

Abstract

Molecular simulation is a powerful tool for studying the nanotribology of single-asperity contacts, but computational limits require that compromises be made when choosing tip sizes. To assess and correct for the finite size effects, complementary finite element (FE) and molecular statics (MS) simulations examining the effects of tip size (height and radius) on contact stiffness and stress were performed. MS simulations of contact between paraboloidal tips and a flat, rigid diamond substrate using the 2B-SiCH reactive empirical bond-order potential were used to generate force–displacement curves and stress maps. Tips of various radii and heights, truncated by a rigid boundary, were formed from carbon- and silicon-containing materials so that they possessed differing elastic properties. Results were compared to FE simulations with matching geometries and elastic properties. FE analysis showed that the rigid boundary at the back of the tip influences the contact stiffness strongly, deviating from the Hertz model for small tip heights and radii. By examining the relationships between force, tip height, tip radii, and elastic properties obtained with FE simulations, a map interpolation method is presented that accounts for the effect of tip size and enables the extraction of Young’s modulus from MS force–displacement data. Furthermore, the FE results show that the effect of the finite size of the tip on contact stress is less pronounced than its effect on stiffness. The MS simulations also demonstrate that stress propagation within the tip is significantly impacted by the structure of the tip.