Some Remarks on a Recent Wear Theory

Persson et al. in (Rubber wear: experiment and theory. arXiv:2411.07332, 2024) and Xu and Persson in (Sliding wear: role of plasticity. arXiv: abs/2412.13129, 2024) have recently proposed an interesting theory of wear which is based on particle formation due to fatigue crack growth at different scales of roughness. The theory perhaps is the first one to take into account of a full characterization of the roughness, and obtains semi-quantitative prediction of wear coefficients for rubber and PMMA, but in the original form, many details of actual roughness features and the material properties do not permit to elucidate general simple trends. We attempt to make general comments to show the main effects of the various macroscopic parameters in the theory, with qualitative comparisons having in mind the case of metals wear for which we found experimental trends, at least for the dependence on friction coefficient. It is found that wear rate in the elastic theory very strongly depends on friction coefficient and on rms roughness, showing even a regime of wearless behaviour below friction coefficient of about 0.2-which may indicate transition to other mechanisms, like adhesive wear. It is shown that an elasto-plastic theory probably mitigates these effects, as a fully plastic one depends only quadratically on friction coefficient, and has no dependence at all on any feature of roughness. However, the present oversimplistic perfectly plastic model truncating the elastic prediction, and the use of a crack propagation theory which is irrespective of large plastic flow can make the theory more hardly quantitative in general. In addition, hardness at asperity scale may increase due to size effect, so the elastic model may be the most appropriate choice in many cases. Along with many other complex effects known in wear (even limiting attention to fatigue wear), it remains, therefore, to be investigated how generally the Persson theory can result in quantitative predictions.