Elastic shakedown and roughness evolution in repeated elastic-plastic contact

TL;DR

This study uses continuum simulations to analyze how surface roughness evolves under repeated elastic-plastic contact, revealing a steady-state roughness profile and a dynamic model for its spectral density.

Contribution

It introduces a simple dynamic collapse model for the power-spectral density of roughness, highlighting the multi-scale features encoded in initial contact cycles.

Findings

Roughness approaches a steady-state before complete elastic recovery.

Small-scale roughness and skewness do not reach steady-state, vanishing asymptotically.

The first few contact cycles encode the multi-scale roughness features.

Abstract

Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither Gaussian nor self-affine emerges from repeated elastic-plastic contact of rough and rigid surfaces on a flat elastic-plastic substrate. Roughness profiles change with each contact cycle, but appear to approach a steady-state long before the substrate stops deforming plastically and has hence "shaken-down" elastically. We propose a simple dynamic collapse for the emerging power-spectral density, which shows that the multi-scale nature of the roughness is encoded in the first few indentations. In contrast to macroscopic roughness parameters, roughness at small scales and the skewness of the height distribution of the resulting roughness do not show a steady-state, with the latter vanishing asymptotically with contact cycle.