Multiscale characteristic lengths of abraded surfaces: Three stages of the grit-size effect

The abrasion mechanisms in polishing titanium-alloy samples with different grades of silicon carbide-coated abrasives were characterized using a novel multiscale analysis of the extreme amplitudes of the peaks and valleys (EAPV) of surface roughness. Two stages of roughness were found: a fractal stage (l∈10–160 μm), where EAPV values versus the observation length l were linked to the fractal dimension D (EAPV∝l2−D), and a stochastic stage (l>160 μm), where EAPV was modeled by the extreme-value theory, allowing the prediction of EAPV values versus observation length. Three regimes of abrasion were found: for grit particles of diameter d>100 μm, EAPV values did not depend on the observation scale and were consistent with Archard’s model. For particle sizes 10 μm<d<100 μm, the EAPV diminished with d regardless of scale, representing the “grit-size effect”. For particles of diameter d<10 μm, the EAPV dramatically decreased at all scales and was independent of d because of adhesive wear. We show that Regimes one and three were dominated by the valleys due to cutting and adhesive wear, respectively, whereas Regime two (the grit-size effect) was dominated by wear peaks due to clogging and deterioration of the abrasive surface, which led to a lower indentation of the abrasive. This contribution proves that the bifractal characteristic previously observed in abrasion can be explained by a single fractal power law and, above a threshold of l>160 μm, by a cumulative-damage model, with a probability proportional to the length of the sample but always uncorrelated with scale.