Breakdown of Reye's theory in nanoscale wear

TL;DR

This paper challenges traditional linear models of nanoscale wear debris formation, proposing a fracture mechanics-based super-linear relation between debris volume and work, validated by molecular dynamics simulations.

Contribution

It introduces a fracture mechanics model for nanoscale wear debris that predicts a super-linear scaling relation, improving understanding of wear particle formation.

Findings

Debris volume scales as W_t^{3/2} in 3D

Debris volume scales as W_t^{2} in 2D

Model validated by molecular dynamics simulations

Abstract

Building on an analogy to ductile fracture mechanics, we quantify the size of debris particles created during adhesive wear. Earlier work suggested a linear relation between tangential work and wear debris volume, assuming that the debris size is proportional to the micro contact size multiplied by the junction shear strength. However, the present study reveals deviations from linearity. These deviations can be rationalized with fracture mechanics and imply that less work is necessary to generate debris than what was assumed. Here, we postulate that the work needed to detach a wear particle is made of the surface energy expended to create new fracture surfaces, and also of plastic work within a fracture process zone of a given width around the cracks. Our theoretical model, validated by molecular dynamics simulations, reveals a super-linear scaling relation between debris volume ($V_d$) and tangential work ($W_t$): $V_d \sim W_t^{3/2}$ in 3D and $V_d \sim W_t^{2}$ in 2D. This study provides a theoretical foundation to estimate the statistical distribution of sizes of fine particles emitted due to adhesive wear processes.