Fractal analysis of surface topography in ground monocrystal sapphire

The surface characterization of ground monocrystal sapphire is investigated by fractal analysis method. A serial of ground sapphire surfaces in ductile removal and brittle removal mode are obtained by grinding experiments, and their three dimensional (3D) and two dimensional (2D) fractal dimensions are calculated and analyzed by box-counting methods. The 3D surface fractal dimension Ds shows a negative correlation with the surface roughness parameter Ra and is sensitive to the ground surface defects. For the ground surface with larger fractal dimension Ds, its micro-topography is more exquisite with minor defects. Once the fractal dimension Ds become smaller, deep cracks and pronounced defects are exhibited in ground surface. Moreover, the material removal mode can be implied from the distribution of 2D cross-sectional profile fractal dimension DL. The workpiece surface generated in ductile removal mode has high surface quality with high 2D and 3D fractal dimensions. This study indicates that the box-counting fractal analysis is an effective method to evaluate ground sapphire surface comprehensively.