Regularization of One Conditionally Ill-Posed Problem of Extractive Metallurgy

Bolshakov, V. I.; Architecture, a Chernyshevs’ky Str.; Volchuk, V. M.; Dubrov, Yu. I.

doi:10.15407/mfint.40.09.1165

Cited by 14 publications

(4 citation statements)

References 6 publications

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“…Отримані коефіцієнти кореляції R Отримані рівняння (1-3) відображають комплексний вплив елементів хімічного складу на механічні властивості у встановлених межах експерименту. Залежно від зміни вмісту елементів хімічного складу чавуну механічні властивості будуть змінюватися в більш широкому інтервалі у зв'язку з багатопараметричністю технології його виготовлення [34][35][36].…”

Section: Introductionunclassified

Evaluation of Material Quality by Non-Destructive Method

Kurazhenko,

Tiutieriev,

Chaikovska

2022

PM&HTM

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Introduction. Different approaches are used to assess the quality of metal by non-destructive methods. These include ultrasound, X-ray, optical and electron microscopy, and mathematical prediction. The latter differ in the ability to improve the obtained models by adjusting the arguments (in this case, the studied parameters of technology). This problem is especially acute when assessing the quality criteria for solid metal castings, which include cast iron rolls. Materials and methods. As a material for the study, high-grade rolled cast iron of СПХН was selected to study the effect of its chemical composition on mechanical properties (HB hardness; tensile strength σB; flexural strength σзгин). The structure of the working layer of cast iron barrels (up to 50 mm from the surface) consisted of a pearlite matrix (70… 85 %), ledeburite eutectic cementite (13… 28 %) and plate-shaped graphite (up to 2,5 %). The results of the experiment. Using the matrix of experimental planning, mathematical models of forecasting the selected quality criteria of cast iron depending on the influence of elements of chemical composition on them are obtained. In order to increase the results of the forecast of mechanical properties, a symbiosis of expert and experimental evaluations was used in the work. The application of this approach has made it possible to reduce the cost of conducting mechanical examinations, which is relevant for the considered periodic technology. The values of the rows of the planning matrix, where there were not enough experimental estimates of mechanical properties, were replaced by expert estimates. Rows 6 and 13−16 of the matrix provide expert assessments. The pairwise correlation coefficients of the obtained regression equations vary in the range of 0,71…0,83, which allows them to be used for practical purposes to predict and adjust the mechanical characteristics in the process of manufacturing cast iron rolls. Conclusions. The influence of elements of chemical composition (carbon, silicon, manganese, phosphorus, sulfur, chromium and nickel) of rolled cast iron of SPHN performance on its mechanical properties: σB, σзгин and HB is investigated. It is recommended to apply the obtained equations of estimation of mechanical properties at the enterprise ДЗПВ of Dnipro for their operative forecast.

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Section: Introductionunclassified

Evaluation of Material Quality by Non-Destructive Method

Kurazhenko,

Tiutieriev,

Chaikovska

2022

PM&HTM

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“…In order to take into account influence of "deformity" of grain structure in thin-walled tubes of structurally sensitive 026Сr16Ni15Mo3Nb steel after cold rolling on their mechanical characteristics, it was proposed to apply the Mandelbrot's fractal formalism [8]. Practical implementation of this formalism allows one to regularize conditionally incorrect problems of metal science [9]. The use of fractal (fractional) dimensions in materials science has made it possible to determine average grain size in metals [10], predict mechanical properties of low-carbon steel after heat treatment [11], estimate residual life of aircraft structures [12], develop a fractal accelerator based on a corrugated plasma waveguide [13], etc.…”

Section: Introductionmentioning

confidence: 99%

Fractal Model of Estimating Quality of Cold Worked Fuel Cladding Tubes

Vakhrusheva¹,

Volchuk²,

Hruzin³

et al. 2021

Problems of Atomic Science and Technology

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A possibility was considered concerning estimation of grain anisomery in the structure of fuel cladding tubes of corrosion-resistant 026Cr16Ni15Mo3Nb steel of austenitic class rolled according to two flow charts: regular and intensive technologies using fractal formalism. Role of grain boundary hardening during cold plastic deformation was analyzed by studying the effect of the fractal dimension of grains D and their boundaries Dg on 0.2, w, and 5. The best correlation among those that were considered was observed between relative elongation and fractal dimensions of the grain structure (R2 = 0.90). The smallest correlation was observed with the yield stress (R2 = 0.64). It is because of variation of plastic flow processes towards a decrease in the degree of hardening in the material rolled according to the intensive technology. Cold deformation results in refining of the average grain size from 15.50 to 15.42 µm. In this case, extent of the grain boundary length L increased by 17.62% at an iteration step  commensurate with the average grain size which is indicated by a change in the fractal dimension according to L ~ δ1-D. Degree of the grain structure inhomogeneity was estimated using ratios of self-similarity of regions of fractal dimensions of the structure. The obtained results on the level of mechanical properties of fuel cladding tubes made of austenitic steel indicate advantage of the intensive technology over regular one that was confirmed by results of fractal modeling.

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“…For example, increase in the hardness of metal causes the decrease of its plasticity etc. Therefore, this task of keeping the desired complex of various by nature properties in a so-called region of compromise, according to J. Hadamard [4], can be referred to conditionally correct ones [5]. B. Mandelbrot fractal formalism [6] can be applied for partial regularisation of the given problem.…”

Section: Introductionmentioning

confidence: 99%

Search for the Evaluation of ‘strength-plasticity’ Relation in Constructional Steel

Volchuk

Ivantsov

Tiutieriev

et al. 2020

KEM

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The work considers the approach determining suboptimal relation of strength and plasticity by the example of low-carbon constructional steel 3 (0.14...0.22 % С), which is widely used in metal structures. As parameters for the research, the elements of chemical composition and properties of ferrite-pearlite structure of steel were taken. For the reliability of the obtained results for the evaluation of structure, its quantitative analysis was carried out either by traditional methods or by fractal approach. Combining operating regions of the values of steel properties depending on the chemical composition and area and fractal dimension of pearlite, we got the diagram of the region of compromise for indices of strength limit σВ, σ0,2 and specific elongation δ. Areas with suboptimal relations σВ/δ and σ0.2/δ were defined in the region of compromise for quality criteria. The application of the given approach allows (while adhering to steel production process) to predict areas with stable suboptimal relations for strength and plasticity indices by selecting value range for the elements of chemical composition and analysis of structure.

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Regularization of One Conditionally Ill-Posed Problem of Extractive Metallurgy

Cited by 14 publications

References 6 publications

Evaluation of Material Quality by Non-Destructive Method

Evaluation of Material Quality by Non-Destructive Method

Fractal Model of Estimating Quality of Cold Worked Fuel Cladding Tubes

Search for the Evaluation of ‘strength-plasticity’ Relation in Constructional Steel

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