The steady-state Archard adhesive wear problem revisited based on the phase field approach to fracture

Abstract

The problem of adhesive wear is herein investigated in relation to periodic asperity junction models in the framework of the Archard interpretation suggesting that wear debris formation is the result of asperity fracture. To this aim, the phase field model for fracture is exploited to simulate the crack pattern leading to debris formation in the asperity junction model. Based on dimensional analysis considerations, the effect of the size of the junction length, the lateral size of the asperity, and the amplitude of the re-entrant corner angles $\gamma$ and $\beta$ defined by the junction geometry is examined in the parametric analysis. Results show that two failure modes are expected to occur, one with a crack nucleated at the re-entrant corner $\gamma$, and another with a crack nucleated at the re-entrant corner $\beta$, depending on the dominant power of the stress-singularity at the two re-entrant corner tips. Steady-state adhesive wear, where the initial asperity junction geometry is reproduced after debris formation, is observed for asperity junctions with $\gamma = 45^\circ$, almost independently of the lateral size of the asperity and of the horizontal projection of the junction length.