FRACTAL APPROACH TO THE CHARACTERIZATION OF METAL SURFACE PROPERTIES

Hanna Samar

doi:10.36074/grail-of-science.20.02.2026.123

FRACTAL APPROACH TO THE CHARACTERIZATION OF METAL SURFACE PROPERTIES

Authors

Hanna Samar National Technical University « Igor Sikorsky Kyiv Polytechnic Institute», Ukraine https://orcid.org/0000-0002-6142-2552

DOI:

https://doi.org/10.36074/grail-of-science.20.02.2026.123

Keywords:

fractal dimension, metal surfaces, fracture analysis, microstructure

Summary

The article reviews the application of fractal analysis to characterize complex hierarchical structures of metal surfaces formed by machining, corrosion, or wear, which traditional parameters like inadequately describe. It examines fractal dimension D as a scale-invariant metric of surface roughness and complexity, correlating with adhesion, wear resistance, and mechanical properties. Examples are provided for fracture surfaces - distinguishing brittle and ductile failures - and grain boundaries for fatigue prediction. The Minkowski box-counting method on binary REM images is described, enabling quantitative forecasts of material durability.

Downloads

PDF

Downloads

Download data is not yet available.

License

References

Evaluating the fractal dimension of surfaces. (1989). Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 425(1868), 113–127. https://doi.org/10.1098/rspa.1989.0101 DOI: https://doi.org/10.1098/rspa.1989.0101

Feng, X., & Gu, B. Q. (2007). Fractal Characterization of Sealing Surface Topography and Leakage Model of Metallic Gaskets. Key Engineering Materials, 353-358, 2977–2980. https://doi.org/10.4028/www.scientific.net/kem.353-358.2977 DOI: https://doi.org/10.4028/www.scientific.net/KEM.353-358.2977

Hotar, V. H., & Salac, P. (2014). Surface evaluation by estimation of fractal dimension and statistical tools. ScientificWorldJournal. https://doi.org/10.1155/2014/435935 DOI: https://doi.org/10.1155/2014/435935

Mandelbrot, B. B. (1983). Self-affine fractals and fractal dimension. Phys. Scr.,

(32), 257–260.

Shyofel, O. O. (2019). Application of the method of fractal analysis to the study of metal structure. Metaloznavstvo ta obrobka metalìv, 91(3), 40–46. https://doi.org/10.15407/mom2019.03.040 DOI: https://doi.org/10.15407/mom2019.03.040