A semi-analytical model for the scale-dependent friction of nanosized asperity

TL;DR

This paper develops a semi-analytical model for nanoscale asperity friction, revealing a scale-dependent local friction coefficient that varies within the contact and differs from traditional models, supported by molecular dynamics simulations.

Contribution

The paper introduces a new semi-analytical model capturing the scale-dependent friction behavior of nanosized asperities, extending beyond conventional constant-coefficient assumptions.

Findings

Local friction coefficient decreases with distance from contact center.

Slip zone expands inward with increasing lateral force.

Model accurately predicts size-dependent static friction.

Abstract

The friction of a nanosized sphere in commensurate contact with a flat substrate is investigated by performing molecular dynamics simulations. Particular focus is on the distribution of shear stress within the contact region. It is noticed that within the slip zone, the local friction coefficient defined by the ratio of shear stress to normal pressure declines monotonically as the distance to contact center increases. With the lateral force increasing, the slip zone expands inwards from the contact edge. At the same time, the local friction coefficient at the contact edge decreases continuously, while at the dividing between the slip and stick zones keeps nearly invariant. These characteristics are distinctly different from the prediction of the conventional Cattaneo-Mindlin model assuming a constant local friction coefficient within the slip zone. An analytical model is advanced in view of such new features and generalized based on numerous atomic simulations. This model not only accurately characterizes the interfacial shear stress, but also explains the size-dependence of static friction of single nanosized asperity.