The fractal analysis of fractographic surfaces employing digital processing of scanning electron microscope (SEM) images is considered. Mathematical tools for digital photogrammetry, particularly in stereological or stereometric options, are proposed. The mathematical formalism for processing SEM images is employed. The fractal analysis of SEM images is analyzed for correctness.
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V. V. Polyakov, S. V. Kucheryavski, and A. V. Egorov, “Investigation of fractal properties of porous metal materials,” in: D. Jouffrey and J. Svejcar (eds.), Proc. Eur. Conf. Euromat–99. Microstructural Investigation and Analysis, Wiley–VCH, Weinheim, Germany (2000), Vol. 4, pp. 7–10.
R. Williford, “Multifractal fracture,” Scripta Metall., 22, 1749–1754 (1988).
J. Stampfl, S. Scherer, M. Gruber, and O. Kolednik, “Determination of the fracture toughness with automatic image processing,” Int. J. Fract., 78, 35–44 (1996).
D. G. Tigetov and Yu. A. Goritskii, “Markovian model for mechanical interaction of rough surfaces in the friction process,” Tren. Smaz. Mash. Mech., No. 3, 4–13 (2010).
B. Mandelbrot, The Fractal Geometry of Nature, San Francisco, USA (1984), p. 468.
J. Feder, Fractals, Plenum Press, New York (1988).
I. M. Zhuravel, “Texture analysis of fractographic images based on Rényi fractal dimensions,” Iskusstv. Intell., No. 1, 204–208 (2013).
I. G. Grabar, O. I. Grabar, O. A. Gutnichenko, and Yu. O. Kubrak, Percolation Fractal Materials: Properties, Technologies, Applications: Research Monograph [in Ukrainian], Zhytomyr Derzh. Tekh. Univ., Zhytomyr (2007), p. 370.
V. Mel’nik, O. Piskunova, and L. Vakulyuk, “Fractal analysis of SEM images using wavelets,” Nat. Tech. Sci.: Sci. Educ. New Dimens., IV (10), Issue 91, 50–54 (2016).
Yu. A. Fadin and Yu. P. Kozyrev, “Fractal features of wear particles,” Pis’ma Zh. Tekh. Fiz., 26, No. 13, 46–50 (2000).
V. M. Mel’nik and A. V. Shostak, Quantitative Stereomicrofractography: Monograph [in Ukrainian], Tverdynya, Lutsk (2010), p. 460.
V. M. Mel’nik, V. D. Rud’, and Yu. A. Mel’nik, “Mathematical formalism of pore stereology of powder materials,” Powder Metall. Met. Ceram., 53, No. 1–2, 107–112 (2014).
A. V. Shostak and Yu. A. Mel’nik, “Application of fractal geometry principle in metallurgical and materials science problems,” Nauk. Visn. Novi Tekhnol., No. 1, 68–73 (2012).
Yu. A. Mel’nik, “Three-dimensional fractographic characterization of regular-shaped and randomized surfaces,” in: Resource-Saving Materials, Structures, and Buildings (Collected Scientific Papers) [in Ukrainian], Issue 24, 356–365 (2012).
K. S. Chernyavskii, Stereology in Metallurgical Science [in Russian], Metallurgiya, Moscow (1977), p. 384.
M. G. Kendall and P. A. P. Moran, Geometrical Probability, Griffin, London (1963).
B. N. Grudin, V. S. Plotnikov, A. V. Kirilov, et al., “Fractal analysis and filtration of electron microscopy images of nanostructures,” in: Proc. 24th All-Russ. Conf. Electron Microscopy [in Russian], Chernogolovka (2010), p. 53.
R. L. Legotkin, Study of Fractal Analysis Methods for Thematic Interpretation of Aerial Photographs [in Russian], Author’s Abstract of PhD Thesis in Technical Sciences, 25.00.34, Mosk. Gov. Univ. Geodez. Kartograf., Moscow (2002), p. 22.
J. M. Keller, S. Chen, and R. Crownover, “Texture description through fractal geometry,” Comput. Vis. Graphics Image Process., 45, No. 1, 150–166 (1989).
N. Yokoya, K. Yamamoto, and N. Funakubo, “Fractal-based analysis and interpolation of 3D natural surface shapes and their application to terrain modeling,” Comput. Vis. Graphics Image Process., 46, No. 3, 284–302 (1989).
S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple resolution texture analysis and classification,” IEEE Trans. Pattern Anal. Mach. Intell., 6, Issue III (4), 518–552 (1984).
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Translated from Poroshkova Metallurgiya, Vol. 57, Nos. 5–6 (521), pp. 134–143, 2018.
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Melnyk, V.M., Rud, V.D. & Melnyk, Y.A. Correctness of Fractal Analysis of Fractographic Surface Microstructure According to Digital SEM Photogrammetry. Powder Metall Met Ceram 57, 353–360 (2018). https://doi.org/10.1007/s11106-018-9991-z
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DOI: https://doi.org/10.1007/s11106-018-9991-z