Topological and fractal invariants of a structure to assess the quality of a metal

Authors

  • V.I. Bol’shakov Prydneprovs’ka State Academy of Civil Engineering and Architecture, Dnipro
  • V.M. Volchuk Prydneprovs’ka State Academy of Civil Engineering and Architecture, Dnipro
  • Yu.I. Dubrov Prydneprovs’ka State Academy of Civil Engineering and Architecture, Dnipro

DOI:

https://doi.org/10.15407/dopovidi2017.04.042

Keywords:

class of a structure, forecast of properties, fractal theory, metal, topology

Abstract

An efficacious method of evaluating the mechanical properties of a metal with the application of a composition of the topological and fractal approaches for the cellular, lamellar, granular, and needle-grade classes of a structure is proposed. It is based on four new criteria for the evaluation of new structures and allows one to reduce the error in the prediction of strength characteristics of a metal by 1.24—2.16 times depending on its class.

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References

Russ, J.C., & Dehoff, R.T. (2000) Practical Stereology. New-York: McGraw-Hill. https://doi.org/10.1007/978-1-4615-1233-2

Underwood, E.E. (1970) Quantitative Stereology. Boston: Addision-Wesley.

Saltykov, S.A. (1976) Stereometric Metallography. Moscow: Metallurgy (in Russian).

Sokolov, V. N. (1997). Quantitative microstructure analysis of rocks by the processing of their scanning-electron microscope (SEM) images. Sorosov. obrazovateln. zhurn., No. 8, pp. 72-78 (in Russian).

Bol'shakov, V. I., Dubrov, Yu. I. & Kasian, O. S. (2010). Steel microstructure as a defining parameter in the prediction of its mechanical properties. Dopov. Nac. akad. nauk Ukr., No. 6, pp. 89-96 (in Russian).

Grinchenko, V.T., Matsypura, V.T., & Snarskiy, A.A. (2005) Introduction to nonlinear dynamics. Chaos and Fractals. Kyiv: Nauk. Dumka (in Russian).

Bulat, A.F., Dyrda, V.I. (2005) Fractals in geomechanics. Kyiv: Nauk. Dumka (in Russian).

Mandelbrot, B. B. (2006). Fractal Analysis and Synthesis of Fracture Surface Roughness and Related Forms of Complexity and Disorder. Int. J. Fract., 138, No. 1, pp, 13-17. https://doi.org/10.1007/s10704-006-0037-z

Lung, C.W., March, N.H. (1999) Mechanical Properties of Metals. Atomistic and Fractal Continuum Approaches. Singapore: World Scientific. https://doi.org/10.1142/3064

Sabirov, I., Yang, C., Mullins, J. & Hodgson, P. D. (2013). A theoretical study of the structure-property relations in ultrafine metallic materials with fractal microstructures. Materials Science & Engineering A., 559, pp. 543-548. https://doi.org/10.1016/j.msea.2012.08.139

Balankin, A. S. (2013). Stresses and strains in a deformable fractal medium and in its fractal continuum model. Phys. Lett. A., 377, No. 38, pp. 2535-2541. https://doi.org/10.1016/j.physleta.2013.07.029

Bolshakov, V. I. & Dubrov, Yu. I. (2002). An estimate of the applicability of fractal geometry to describe the language of qualitative transformation of materials. Reports of the National Academy of Sciences of Ukraine, No. 4, pp. 116-121 (in Russian).

Hausdorff, F. (1919). Dimension und äußeres Maß. Mathematische Annalen, 79, pp. 157-179. https://doi.org/10.1007/BF01457179

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Published

01.07.2024

How to Cite

Bol’shakov, V., Volchuk, V., & Dubrov, Y. (2024). Topological and fractal invariants of a structure to assess the quality of a metal . Reports of the National Academy of Sciences of Ukraine, (4), 42–48. https://doi.org/10.15407/dopovidi2017.04.042

Issue

No. 4 (2017): Reports of the National Academy of Sciences of Ukraine

Section

Materials Science

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