The multi-scale roughness analyses and modeling of abrasion with the grit size effect on ground surfaces

This paper is focused on the study of abrasion using a multi-scale roughness analysis of Extreme Amplitude of Peaks to Valleys (EAPV) on stainless steel (316L) surfaces polished with different grit abrasive papers. In order to examine the different abrasive mechanisms at all scales, roughness measurements are carried out. From the log–log plot of the maximum peaks height or maximum valleys depth amplitude versus the evaluation length, an “apparent” bi-fractal structure is assumed based on the observed break in the plotted curve. Such break may refer to a transition in the abrasive mechanism giving two distinct fractal ranges. However, other mechanisms not completely understood may also explain such break. Using the multiscale approach proposed here, the log–log plot is indeed consistent with a succession of a genuine fractal range (i.e. linear in log–log) and an “ergodic” range above the autocorrelation length, where the “real” amplitude becomes actually stationary, independent of the evaluation length. This means there is no more coupling between the vertical height distribution and the horizontal spread, hence, “the higher scale does not show a fractal structure” above 160 μm. In this situation, the continued growth of roughness amplitudes is due to a sampling effect and accurately modeled by the Extreme Value Theory. Then, three regimes of abrasion are recognized. (1) For coarse abrasive particles d > 125 μm, where d is the size of the abrasive particles, EAPV seems not to depend on d whatever the scale of observation, (2) for intermediate size particles 10 μm < d < 125 μm, EAPV decreases with d for all scales which represent the “grit size effect”, and (3) for fine particles d < 10 μm, EAPV drastically decreases at all scales and becomes independent of the particle size due to the occurrence of the adhesive process. It is shown that regimes 1 and 3 are governed by valleys generation due to respectively cutting process for regime 1 and adhesive process on peaks for regime 3. The regime 2 (where grit size effect is observed) results in peaks arrangement associated to clogging and deterioration of the abrasive surface leading to a lower indentation of the abrasive. The proposed work clearly shows that the bi-fractal structure observed in abrasion can be indeed explained using a single fractal structure.