Fractal Characteristics of Steel Surface Profilograms

The roughness of the steel surface before and after corrosion has been examined. The analysis of surface profilograms of steel plates is usually made by traditional methods, using average characteristics where R_a is an arithmetic mean deviation of a profile, R_z is a height of irregularities for ten points, R_max is the highest profile height and others. In the present work, fractal parameters are used to describe the characteristics of roughness. At the initial stage of the experiment, a sample was subjected to corrosion. After removing the corrosion products, roughness values of the sample surface were removed and profilograms representing nonsmooth curves were analyzed. When analyzing time series, the fractality index is calculated—the Hurst index. The Hurst index (0 < H < 1) sets a measure of persistence—the tendency of the process to trends. If H > 0.5, the sequence of ordinates of the profile is characterized by the effect of long-term memory. If H < 0.5, there is no memory effect in the sequence of ordinates of the profile. The intermediate case H = 0.5 (random Gaussian process) means uncertainty. Autocorrelation functions of roughness as a random process have been obtained. Fractan computer programs were used for calculations. A comparison was made with generalized Brownian motion, which is characterized by the Hurst exponent. Profilograms are considered as curves belonging to the class of fractal curves. For visual confirmation, a graph of a self–affine curve, continuous but nowhere differentiable is presented, which is set by the classical Weierstrass–Mandelbrot function. The possibility of using the Hurst index to evaluate the microgeometry of surfaces is shown. The Hurst indices H and the fractal dimension D before and after corrosion differ by about 10%. The possibility of using the characteristics of fractal geometry to study the problems of corrosion of metal surfaces is shown. Based on the theoretical calculations presented in this paper, it is planned to conduct a series of laboratory experiments with statistical processing of results for the development of nondestructive testing methods.