Reliability of measured fractal dimension and roughness exponent as materials dimensionless parameters for fracture surfaces

The effects of accuracy of measured fractal dimension D and roughness exponent H are investigated in this paper with a view to examine the reliability of D and H as materials dimensionless parameters of fracture surfaces. D and H are different from general physical quantity, because they are dimensionless quantities and often appear as exponents in a theoretical function or formula. In many cases, the error of the physical quantity related to D or H may far exceed 10%, if D or H has error around 10%. The required accuracy of fractal dimension and roughness exponent should be higher, but it depends on the specific material, the associated physical quantity and the scale of measurement.