## 3 Results and Discussion
### Surface Evolution Mechanism during Polishing
Scratches of varying depth appear on the surface, and the Rz value of the line profile (corresponding to the red line in Figure 8d) shown in Figure 9d even exceeds 30 \(\upmu\)m.  
The experimental results show that the surface quality and consistency of marbles did not continue to increase with increasing polishing time, which is very different from the case in the polishing of single-crystal hard-brittle materials. This is mainly because natural marble is composed of a variety of soft and hard materials, and the surface shows a characteristic of inconsistent hardness distribution, which causes great difficulties in polishing marble. To maximize the quality of the polished surface of marble, the optimal polishing time must be selected according to the hardness distribution characteristics of various types of marble. Otherwise, the inconsistent removal of different soft and hard materials on the marble during polishing would take place, and the material of the surface will have incomplete ductile flow, which will seriously affect the surface quality and quality consistency. This phenomenon of incomplete ductile flow caused by the uneven removal of materials is called the orange peel effect in industry and academia [5; 26; 27]. This orange peel effect was discovered very early, and some scholars have qualitatively analyzed the reasons for this phenomenon. However, thus far, there are few works to quantitatively analyze the mechanism for this phenomenon, and no corresponding theoretical model has been established to avoid this phenomenon. To quantitatively reveal the cause of the orange peel effect during the polishing of marble tile, the hardnesses of the smooth and rough zones of the surface were measured with a microhardness tester, as shown in Figure 10. The average hardness value of the rough zone is HV = 373 \(\pm\) 15, and the average hardness value of the smooth zone is HV = 406 \(\pm\) 8. This shows that the zone where the surface remains smooth is harder, while the rough zone is relatively soft. Figure 9: Surface profile at different polishing times: (**a**) 4 min polishing, (**b**) 8 min polishing, (**c**) 12 min polishing, and (**d**) 16 min polishing. Figure 11 shows the surface evolution mechanism of marble tile during polishing. The exposure height of the abrasive particles on the SG pads is inconsistent during the polishing process because of the rough and uneven marble tile surface. Each abrasive grain appears to have a different degree of yield, which leads to different yield pressures for each abrasive grain [14; 21], as shown by the blue arrow in Figure 11. This yield force directly affects the polishing pressure of abrasive grains on the surface of marble. At the beginning of the polishing stage, due to the rough and uneven marble tile surface, a lot of material must be removed. The material removal mainly occurs via brittle fracture. The contact area between the marble tile and the abrasive particles is relatively large, and the contact pressure is relatively small, as shown in Figure 11. When polishing, to a certain extent, the rough and uneven stone surface is almost removed, and the surface tends to become smooth. The material removal occurs mainly by ductile flow, which spreads over the entire surface to obtain a smooth plane. At this time, the contact area between the marble tile surface and the abrasive particles decreases, resulting in increased contact pressure, as shown in Figure 11. Since natural marble tile is composed of a variety of materials with uneven degrees of hardness and softness, there are hard zones and soft zones on the stone surface, as shown in Figure 11. As the polishing process continues, this phenomenon of inconsistent yield pressure leads to different degrees of material removal by abrasive particles on the marble tile surface with inconsistent hardness. Abrasive particles pass over the hard zones and cut into the soft zones to expose the rough surface, resulting in incomplete ductile flow, poor surface quality, and quality consistency, as shown in Figures 10 and 11.