In-depth investigations into nano-indentation play an important role in the full understanding of the deformation mechanisms of materials subjected to ultra-precision machining on the nanometer scale. This paper developed a reliable molecular dynamics model for simulating the nano-indentation of monocrystalline silicon carbide by some diamond hemispherical indenters that have different radii sizes. The research shows the size effect of indenter radius for deformation mechanisms. A phase transformation from its crystal structure to amorphous and a crack generation and propagation are observed with the smaller indenter radius, while a phase transformation to amorphous on a thin plane, stacking faults and crack generation and propagation are observed with the larger indenter radius.