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

1Bol'shakov, VI, 2Volchuk, VM, 1Dubrov, Yu.I
1Prydniprovska State Academy of Civil Engineering and Architecture, Dnipropetrovsk
2Prydniprovska State Academy of Civil Engineering and Architecture, Dnipro
Dopov. Nac. akad. nauk Ukr. 2017, 4:42-48
https://doi.org/10.15407/dopovidi2017.04.042
Section: Materials Science
Language: Russian
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.

Keywords: class of a structure, forecast of properties, fractal theory, metal, topology
References: 
  1. Russ, J.C., & Dehoff, R.T. (2000) Practical Stereology. New-York: McGraw-Hill.
  2. Underwood, E.E. (1970) Quantitative Stereology. Boston: Addision-Wesley.
  3. Saltykov, S.A. (1976) Stereometric Metallography. Moscow: Metallurgy (in Russian).
  4. 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).
  5. 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).
  6. Grinchenko, V.T., Matsypura, V.T., & Snarskiy, A.A. (2005) Introduction to nonlinear dynamics. Chaos and Fractals. Kyiv: Nauk. Dumka (in Russian).
  7. 7Bulat, A.F., Dyrda, V.I. (2005) Fractals in geomechanics. Kyiv: Nauk. Dumka (in Russian).
  8. 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.
  9. Lung, C.W., March, N.H. (1999) Mechanical Properties of Metals. Atomistic and Fractal Continuum Approaches. Singapore: World Scientific.
  10. 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.
  11. 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.
  12. 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).
  13. Hausdorff, F. (1919). Dimension und äußeres Maß. Mathematische Annalen, 79, pp. 157-179.