# The Influence of Grain Size on the Abrasive Wear Resistance of Hardox 500 Steel
## 3 Results and Discussion
### Abrasive Wear Resistance
Heat treatment starting from 900 \({}^{\circ}\)C reduces this parameter, with the greatest decrease (17% compared to the reference state) recorded for the sample austenitized at 850 \({}^{\circ}\)C and the smallest (4%) for samples austenitized at 900 \({}^{\circ}\)C and 1000 \({}^{\circ}\)C. Moreover, all surfaces exhibit considerable groove width variability, evidenced by relatively high coefficients of variation. Figure 13: Microstructure of sample cross-sections subjected to wear testing, longitudinal to abrasive movement direction: (**a**) as-delivered state; (**b**) T\({}_{\rm A}\) = 850 \({}^{\circ}\)C; (**c**) T\({}_{\rm A}\) = 900 \({}^{\circ}\)C; (**d**) T\({}_{\rm A}\) = 1000 \({}^{\circ}\)C; (**e**) T\({}_{\rm A}\) = 1100 \({}^{\circ}\)C; and (**f**) T\({}_{\rm A}\) = 1200 \({}^{\circ}\)C. SEM, etched with reagent No. 3 per ASTM E407. Figure 14: Surface roughness parameters of samples subjected to wear testing: (**a**) \(Ra\) and \(Rq\); (**b**) \(Rz\), \(Rp\), and \(Rv\); (**c**) \(RSm\). DS, as-delivered state. In tribological surface property analysis, the literature often explores additional parameters to enable a more comprehensive topographical description [49; 50]. One of the key factors influencing the tribological behavior of a surface is the shape of surface irregularities, which can significantly affect wear mechanisms and surface interactions during friction. [PERSON] [50] proposed using dimension of standard vertical roughness parameters to differentiate two primary types of topography: surfaces with sharp indentations and surfaces with sharp protrusions. These shape indices provide precise characterization of both depressions and protrusions, which is crucial for assessing surface behavior under frictional conditions. These indices respond to various aspects of surface irregularities:  
\(\frac{Rt}{Rp}\) indicates the symmetry of irregularity distribution. Higher values suggest a profile dominated by distinct protrusions. \(\frac{Rt}{Ra}\) reflects both peaks and valleys in the surface profile. High values indicate a diverse profile with prominent peaks and valleys, which may significantly affect tribological properties. \(\frac{Rp}{Ra}\), \(\frac{Rt-Ra}{Rp^{2}}\), and \(\frac{Rt-Rp}{Ra^{2}}\) are particularly sensitive to sharp peaks. Higher values suggest a surface with sharp, well-defined protrusions, potentially leading to accelerated wear due to intense contact on limited surface areas. Table 7 presents combinations of [PERSON]'s roughness shape indices calculated from measured roughness values. The \(\frac{Rt}{Rp}\) ratio in this study ranges from 1.83 to 2.29, suggesting a profile with numerous moderate-amplitude protrusions. These values, close to 2.0, indicate a relatively symmetrical distribution of surface irregularities regardless of the heat treatment condition. The \(\frac{Rt-Ra}{Rp^{2}}\) ratio, ranging from 7.65 to 11.41, reflects surface profile variability in terms of height versus average deviation. The highest value, 11.41, is observed for the sample ausentitized at 850 \({}^{\circ}\)C, indicating significant protrusions, while lower values, such as 7.65 for the as-delivered state and 7.76 for the 1000 \({}^{\circ}\)C-treated state, suggest a more even profile compared to other states. The \(\frac{Rp}{Ra}\) ratio, ranging from 1.01 to 1.76, and particularly the \(\frac{Rt-Rp}{Ra^{2}}\) ratio for the 1200 \({}^{\circ}\)C austenitized sample (1.76), indicate the presence of distinct protrusions. Additionally, high \(\frac{Rt}{Ra}\), values, between 6.49 and 7.73, suggest the presence of sharp peaks. Comparing the ratio values reveals similarities within each index, regardless of austenitizing temperature. The \(\frac{Rp}{Rp}\) ratio, consistently around 0.11-0.14 for all samples, indicates that protrusions predominate over indentations in the surface topography. This consistency across heat treatment states suggests a recurring profile character irrespective of austenitizing temperature.