Main stages of fractal modeling in material science

Authors

  • V. Y. Bolshakov Department of Materials Science and Materials Processing, State HigherEducation Establishment “Pridniprovsk State Academy of Civil Engineering and Architecture”, 24-а, Chernyshevskogo str., Dnipro 49600, Ukraine https://orcid.org/0000-0003-0790-6473
  • V. N. Volchuk Department of Materials Science and Materials Processing, State HigherEducation Establishment “Pridniprovsk State Academy of Civil Engineering and Architecture”, 24-а, Chernyshevskogo str., Dnipro 49600, Ukraine https://orcid.org/0000-0001-7199-192X
  • Yu. Y. Dubrov Department of Materials Science and Materials Processing, State HigherEducation Establishment “Pridniprovsk State Academy of Civil Engineering and Architecture”, 24-а, Chernyshevskogo str., Dnipro 49600, Ukraine https://orcid.org/0000-0002-3213-4893

DOI:

https://doi.org/10.30838/J.PMHTM.2413.230419.244.289

Keywords:

fractal, modeling, quality criteria, sensitivity criterion, structure

Abstract

Introduction. The complexity of identifying fractal objects initiates a search for algorithms for their description. These objects  include  the  structure  of  metals,  determines  a  number  of  their  basic  properties,  and  is  usually  described  by  traditional techniques. These techniques are based on the use of Euclidean geometry (length, area, volume). This leads to the incompleteness of the formal axiom that arises when identifying the elements of the structure. The use of fractal geometry allows to partially eliminate the incompleteness of formal axiomatics, but for this it is necessary to develop algorithms for its implementation. The technique. The authors have proposed an algorithm for describing the structure and properties of metals, which includes the main stages of fractal modeling. Results and its discussion. Separate stages of fractal modeling are given for roller iron. For their realization, the region of self-similarity  of  the  structure  elements,  the  sensitivity  of  the  mechanical  properties  of  cast  iron  in  the  fractal  dimension  of  the structure, are determined, the research results are formalized. Conclusions. The regularities of the influence of the fractal dimension of the Ст3 structure elements on the mechanical properties are established. The developed models make it possible to predict the properties of mild steel depending on the transformations of its microstructure due to the effects of heat treatment.

Author Biographies

V. Y. Bolshakov, Department of Materials Science and Materials Processing, State HigherEducation Establishment “Pridniprovsk State Academy of Civil Engineering and Architecture”, 24-а, Chernyshevskogo str., Dnipro 49600

Dr. Sc. (Tech.), Prof.

V. N. Volchuk, Department of Materials Science and Materials Processing, State HigherEducation Establishment “Pridniprovsk State Academy of Civil Engineering and Architecture”, 24-а, Chernyshevskogo str., Dnipro 49600

Dr. Sc. (Tech.), As. Prof.

Yu. Y. Dubrov, Department of Materials Science and Materials Processing, State HigherEducation Establishment “Pridniprovsk State Academy of Civil Engineering and Architecture”, 24-а, Chernyshevskogo str., Dnipro 49600

Dr. Sc. (Tech.), Prof.

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Published

2019-04-23

Issue

No. 2 (2019): Metal Science and Heat Treatment of Metals

Section

Technical science

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