Abstract
. Introduction . The incompleteness of formal axiomatics in identifying the structure of many materials is a consequence of the complex geometric shape of its elements. For adequate approximation of the structure elements, it is not enough to use standard techniques that are based on Euclidean geometry. The use of the language of fractal geometry allows to partially eliminate the incompleteness of formal axiomatics through the use of fractal (fractional) dimensions. Materials and techniques . The object of the study was Ст3пс mild steel. The composition, structure and properties of steel are given. A method for calculating the fractal dimension developed by the authors is described. Results and its discussion . An algorithm is proposed for fractal modeling of the structure and properties of Ст3 low carbon steel, which is based on establishing the limits of self-similarity of the structure; calculation of the spectrum of dimensions of the elements of the structure; determining the sensitivity between the quality criteria of the metal and the dimensional characteristics of the structure; formalization of the results. 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.
Highlights
The incompleteness of formal axiomatics in identifying the structure of many materials is a consequence of the complex geometric shape of its elements
For adequate approximation of the structure elements, it is not enough to use standard techniques that are based on Euclidean geometry
A method for calculating the fractal dimension developed by the authors is described
Summary
Неполнота формальной аксиоматики при идентификации структуры многих материалов является следствием сложной геометрической формы ее элементов. Для адекватной аппроксимации элементов структуры недостаточно использовать стандартные методики, которые основаны на геометрии Евклида. Применение языка фрактальной геометрии позволяет частично устранить неполноту формальной аксиоматики благодаря использованию фрактальной (дробной) размерности. Предложен алгоритм фрактального моделирования структуры и свойств малоуглеродистой стали Ст3, который базируется на установлении границ самоподобия структуры; вычислении спектра размерностей элементов структуры; определении чувствительности между критериями качества металла и размерностными характеристиками структуры; формализации полученных результатов. Установлены закономерности влияния фрактальной размерности элементов структуры Ст3 на механические свойства. Разработанные модели позволяют прогнозировать свойства малоуглеродистой стали в зависимости от трансформаций ее микроструктуры вследствие воздействия термической обработки. Ключевые слова: металл; механические свойства, микроструктура; фрактальная размерность; модель; критерий чувствительности
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