Determining the sensitivity of the multifractal characteristics of metals

V. Volchuk


Raising of problem. Recently, some articles devoted to the issues of materials, are examples of objects which are used to describe the language of fractal geometry. However, such an approach must be rigorously justified, as it should be based on the fact that the fractal dimension is inherent in the test material can be characterized by its high- quality properties. Until now, this problem was proposed to solve using the criterion of F. Takens. The prerequisites for satisfying this criterion is reduced to measuring any one characteristic of the system under study at different times at intervals Dt . As a result of these measurements are obtained by a bounded sequence {ai },  0 £ i < ¥ . If this sequence r is possible to construct a smooth deterministic model of the form [1], then we are dealing with a complex deterministic process and apply the language of fractal geometry is meaningless. An approach based on the use of multi-fractal theory [2, 3] to quantify the elements of the structure, allows the spectrum by comparing the statistical dimensions of its elements, identify sensitive indicators of qualitative characteristics, in particular the mechanical properties, describing the one-to-one correspondence data dimensional structures and these properties. This in turn reduces the incompleteness of formal axiomatic that occurs in the description of the elements of the metal structure through the traditional figures of Euclidean geometry by identifying structurally sensitive to the quality criteria of dimensional ratings.

Purpose. To determine the sensitivity between the dimensional assessments of the structural elements of roll-iron and mechanical properties.

Conclusion. To predict the mechanical properties of cast iron plate roll form graphite is advisable to use it with an increase in the dimensional assessment framework ´200. Dimension assessment graphite, due to their low sensitivity to mechanical properties, applied to their forecast of the investigated large-scale representation of the range of structure (´100, ´1000) correctly.


sensitivity; multifractal structure; mechanical properties; dimension


Bol'shakov V.I. and Dubrov Yu.I. Ob otsenke primenimosti yazyka fraktal'noy geometrii dlya opisaniya kachestvennykh transformatsiy materialov [An estimate of the applicability of the language of fractal geometry to describe quality transformation of materials]. Dopovіdі Nacіonal'noї akademії nauk Ukraїni. [Reports of National Academy of Sciences of Ukraine]. 2002, no. 4, pp. 116-121. Available at:

Ivanova V.S., Balankin A.S., Bunin I.Z. and Oksogoyev A.A. Sinergetika i fraktaly v materialovedenii [Synergy and fractals in material]. Moscow: Science, 1994. 383 p. Available at:

Bolshakov V.I., Volchuk V.N. and Dubrov Yu.I. Osobennosti primeneniya mul'tifraktal'nogo formalizma v materialovedenii [Features of the multifractal formalism in materials science]. Dopovіdі Nacіonal'noї akademії nauk Ukraїni [Reports of the National Academy of Sciences of Ukraine]. 2008, no. 11, pp 99-107. Available at:

Bolshakov V.I. and Volchuk V.N. Materialovedcheskiye aspekty primeneniya veyvletno-mul'tifraktal'nogo podkhoda dlya otsenki struktury i svoystv malouglerodistoy stali [Materials aspects of wavelet-multifractal approach for assessing the structure and properties of low-carbon steel]. Metallofizika i novejshie tehnologii [Metal Physics and Advanced Technologies]. 2011, vol. 33, no. 3, pp. 347-360. Available at:

GOST Style Citations

Большаков В. И. Об оценке применимости языка фрактальной геометрии для описания качественных тран- сформаций материалов / В. И. Большаков, Ю. И. Дубров // Доповіді Національної академії наук України. - № 4. - 2002. - С. 116-121.


Синергетика и фракталы в материаловедении / В. С. Иванова, А. С. Баланкин, И. Ж. Бунин, А. А. Оксогоев. - Москва : Наука, 1994. - 383 с.


Большаков В. И.    Особенности    применения  мультифрактального    формализма    в    материаловедении / В. И. Большаков, В. Н. Волчук, Ю. И. Дубров // Доповіді Національної академії наук України. - 2008. - № 11. - С. 99-107.


Большаков В. И.  Материаловедческие  аспекты  применения  вейвлетно-мультифрактального  подхода  для оценки структуры и свойств малоуглеродистой стали / В. И. Большаков, В. Н. Волчук // Металлофизика и новейшие технологии. - 2011. – Т. 33, вып. 3. - С. 347–360.