| 2026 №03 (05) | 2026 №03 (01) |
The Paton Welding Journal, 2026, #3, 45-50 pages
Possibilities of fractal analysis methods for welded metal microstructure metallographic research (Review)
V.V. Holovko1, O.O. Shtofel1,2
1E.O. Paton Electric Welding Institute of the NASU. 11 Kazymyr Malevych Str., 03150, Kyiv, Ukraine. Е-mail: vicholow@gmail.com2National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” 37 Prosp. Beresteiskyi, 03056, Kyiv, Ukraine
Abstract
The metal of welded joints, which is characterized by increased stochasticity of structural components, requires taking into account a certain number of indicators when analyzing in the “composition–structure–properties” system. Such analysis complexity is associated with both the modern metallographic analysis methods imperfection and the difference in measurement units. The non-metallic inclusions content in the metal is determined in percent, the intergrain boundaries branching — in micrometers, the grains orientation — in degrees. It is shown that when performing metallographic research based on fractal parameterization methods of analysis of low alloyed steels weld metal structure, it is possible to obtain measurement results in numerical form, which should be the basis for creating programs for describing the interaction in the “structure–properties” system.
Keywords: welding, metallurgy, metal structure, fractal analysis, microstructure, non-metallic inclusions, grain boundaries
Received: 29.12.2025
Received in revised form: 05.02.2026
Accepted: 18.03.2026
References
1. Li, X.C., Zhao, J.X., Cong, J.H. et al. (2021) Machine learning guided automatic recognition of crystal boundaries in bainitic/martensitic alloy and relationship between boundary types and ductile-to-brittle transition behavior. J. Mater. Sci. Technol., 84, 49–58. DOI: https://doi.org/10.1016/j.jmst.2020.12.0242. Lehto, P., Remes, H. (2022) EBSD characterisation of grain size distribution and grain sub‑structures for ferritic steel weld metals. Welding in the World, 66, 363–377. DOI: https://doi.org/10.1007/s40194-021-01225-w
3. Svensson, L.E. (2000) Control of microstructures and properties in steel arc welds. CRC Press, Inc., Corporate Blvd., N.W., Boca Raton, Florida.
4. DSTU ISO 4967:1998: Steel — Determination of content of nonmetallic inclusions — Micrographic method using standard diagrams. 5. Dubrov, U., Bolshakov, V., Volchuk, V. (2015) Ways of identification of periodic multi-criteria technologies: monograph. Saarbrücken, Palmarium Academic Publishing [in Russian]. 6. Bolshakov, V., Volchuk, V., Dubrov, U. (2017) Topological and fractal structure invariants for assessing metal quality. Reports of the NASU, 4, 42‒48 [in Russian]. DOI: https://doi.org/10.15407/dopovidi2017.04.042
7. Volchuk, V. (2014) Regarding the application of the multifractal theory to the evaluation of the mechanical properties of metal. Metallurgy and heat treatment of metals, 3, 12–19 [in Russian].
8. Liu, S., Olson, D.L. (1986) The role of inclusions in controlling HSLA steel weld microstructures. Welding J., 6, 139s‒149s. DOI: https://doi.org/doi.org/10.1007/BF02834144
9. Li, H.G., Zheng, S.B., Xie, S.J. et al. (2009) Influence of liquid steel cooling rate during directional solidification on titanium oxide precipitation. Ironmaking and Steelmaking, 36(1), 29‒32. DOI: https://doi.org/10.1179/174328107X167977
10. Kikuchi, N., Nabeshima, S., Yamashita, T. et al. (2011) Microstructure refinement in low carbon high manganese steels through Ti-deoxidation, characterization and effect of secondary deoxidation particles. ISIJ Inter., 51(12), 2019‒2028. DOI: https://doi.org/10.2355/isijinternational.51.2019
11. Sarma, D.S., Karasev, A.V., Jonsson, P.G. (2009) On role of non-metallic inclusions in the nucleation of acicular ferrite in steels. ISIJ Inter., 46(6), 1063–1074. DOI: https://doi.org/10.2355/isijinternational.49.1063
12. A.L.V. da Costa e Silva (2019) The effects of non-metallic inclusions on properties relevant to the performance of steel in structural and mechanical applications. Review Article. J. of Materials Research and Technology, 8(2), April, 2408‒2422.
13. DOI: https://doi.org/10.1016/j.jmrt.2019.01.009
14. Pidhaetskii, V. (1970) Pores, inclusions, cracks in the metal of welds. Kyiv, Tekhnika.
15. Holovko, V., Shtofel, O., Krasikov, I. (2023) Fractal measurements of the weld metal structure. In: Proc. of II Inter. Scientific and Practical Conf. on Topical Aspects of Modern Scientific Research, Tokyo, Japan 26‒28 October, 2023.
16. ISO 643:2012: Steel — Micrographic determination of the apparent grain size.
17. ISO 9042:1988: Steels — Manual point counting method for statistically estimating the volume fraction of a constituent with a point grid.
18. Jorge, J.C.F., de Souza, L.F.G., Mendes, M.C. et al. (2021) Microstructure characterization and its relationship with impact toughness of C‒Mn and high strength low alloy steel weld metals — A review. J. of Materials Research and Technology, 10, 471‒501. DOI: https://doi.org/10.1016/j.jmrt.2020.12.006
19. Niu, Y., Jia, S., Liu, Q. et al. (2019) Influence of effective grain size on low temperature toughness of high-strength pipeline steel. Materials, 12, 3672. DOI: https://doi.org/10.3390/ma12223672
20. Carneiro, Í., Simões, S. (2020) Recent advances in EBSD characterization of metals. Metals, 10, 1097. DOI: https://doi.org/10.3390/met10081097
21. Holovko, V., Shtofel, О., Korolenko, D. (2025) Fractal analysis methodology of the structural component orientation. Avtomatychne Zvaryuvannya, 5, 25‒30. DOI: https://doi.org/10.5281/zenodo.15266778
