OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Ta b l e 4 “Shape factor” and erosion rate (ER) Shape factor ER 0.25 0.00349 0.5 0.0055466 0.75 0.0061866 It can be mentioned that more stretched particles having lower SF (0.25–0.5) give a qualitatively different profile compared to particles having a shape closer to spherical (1–0.75). It is also quantitatively reflected on the relative dimensionless erosion rate presented in table 4. Evidently, the same behavior would be observed for other empirical erosion models. Obviously, such a behavior is due to the change of particle velocity profile and the redistribution of particles having different sizes along the crater radii. The distributions of particle velocities and sizes, cellaveraged, for SF 0.25; 0.5; 0.75 are shown in fig. 15 and fig. 16. It can be seen that while SF decreases, the absolute velocity along the crater radii decreases slowly for SF=0.5 and more rapidly for SF=0.25, which follows the decrease of dimensionless erosion rate. Notable is also the change in profile shape: a drastic velocity decrease can be seen for SF=0.25 along the first 0.25 mm of crater radii. To the opposite, a smooth velocity decay is observed for SF=0.75 (having even a local increase). Decreasing SF leads to increase of the cell averaged diameter in the crater center vicinity, also followed by the growth of the cell-averaged diameters difference between the central and peripheral crater area. This also leads to the influence of averaged diameter local maximums for SF 0.75 and 0.5. Fig. 17 shows the abrasive powder. The shape factor is obviously depending on the surface area of a particle and, therefore, some relation between the sides and/or perimeter of a particle. It can be supposed that for most particles, despite angularities and some coagulated large structures, such relation, if expressed as an aspect ratio, would be no higher than 0.4–0.5. An estimate made using free ImageJ software [40] for the relation of a circle with area equivalent to the summary area of particles to the summary perimeter of particles showed a value of ≈ 0.35. Also, a qualitative similarity can be observed between the calculated erosion rate profile and experimental crater profile for shape factor 0.5 and lower. Therefore, using dimensionless erosion rate (table 2) and erosion rate profiles (fig. 13) the best agreement with experimental data is reached for SF ≈ 0.25 and Oka erosion model with E90 = 0.004, n1 = 0.613; n2 = 6.439; k2 = 2.21; k3 = 0.19. Fig. 15. Particle velocity near the sample wall along its length
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