**4. Conclusions**

The results of nanoindentation experiments under static sti ffness showed that the hardness of C and Si faces of single crystal SiC under 500 mN loads was 38.596 Gpa and 36.246 Gpa, and the elastic moduli of the C and Si faces were 563.019 Gpa and 524.839 Gpa, respectively. According to the experimental results, the theoretical critical loads for the plastic transition of C and Si faces of single crystal SiC were calculated as 1.941 mN and 1.77 mN and the theoretical loads for their brittle fractures were 366.8 mN and 488.67 mN, respectively. These results basically coincided with the experimental results of nanoindentation.

In grinding based on the rotation of workpieces using fixed abrasives, the critical grit cutting depth of abrasives on the C and Si faces of single crystal 6H-SiC were 5.3 nm and 6.1 nm, separately. When the maximum thickness of undeformed substrate relating to the processing parameters was less than the critical grit cutting depth, single crystal SiC material was removed by plastic deformation, and when the maximum thickness of undeformed substrate was larger than the critical grit cutting depth, the removal mode changed to brittle removal. Moreover, as the maximum thickness of undeformed substrate increased the proportion of brittle removal on the surfaces gradually increased.

The forces of lapping materials on C and Si faces by using free abrasives (W14) were 1723 mN and 1782 mN, while those obtained using free abrasives (W1.5) were 569 mN and 588 mN, respectively. These forces were larger than the theoretical critical loads for the brittle fractures of single crystal SiC substrates. With the three-body friction motion of abrasives, single crystal SiC material was rolled, broken, and removed under pure brittle fracture.

In the cluster MR finishing experiments where semi-fixed abrasives were used, the theoretical pressure of abrasives at the entrance and exit of the polishing belts were 1514.27 μN and 3.47 μN, respectively. These pressures were in the range for elastic-plastic and elastic deformation of single crystal SiC. The elastic-plastic removal grooves at the entrance of the polishing belts were deeper while the surface at the exit was flatter and smoother; this coincided with the mechanical calculation and nanoindentation experiment.

This study applied the experimental results of nanoindentation to the mechanical analysis of abrasives under di fferent fixation methods and the removal and deformation analysis of single crystal SiC material. These research results are significant for the ultra-precision machining of single crystal SiC substrates.

**Author Contributions:** Conceptualization, J.P. and Q.Y.; Formal analysis, X.Z.; Funding acquisition, Q.Y.; Writing—original draft, J.P.; Writing—review & editing, W.L.

**Funding:** The authors would like to thank the NSFC-Guangdong Joint Fund Project (No. U1801259), the Guangdong Graduate Education Innovation Project (No. 2018JGXM35) and the Foshan Science and Technology Innovation Project for their financial support.

**Conflicts of Interest:** The authors declare no conflict of interest.
