Breakdown of Reye's theory in nanoscale wear

Building on an analogy to ductile fracture mechanics, we investigate the energetic cost of debris particle creation during adhesive wear. Macroscopically, Reye proposed in 1860 that there is a linear relation between frictional work and wear volume at the macroscopic scale. Earlier work suggested a linear relation between tangential work and wear debris volume also exists at the scale of a single asperity, 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 at the microscopic scale. 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 similar to W-t(3/2) in 3D and V-d similar to 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.