Оцінка граничного стану двокомпонентного матеріалу з кулястими включеннями та прогнозування надійності конструкції методами комп'ютерного і математичного моделювання

Abstract

Thesis for obtaining the philosophy doctor scientific degree on the specialty 113 “Applied mathematics”. – National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, 2021. The PhD work devoted to the creation of mathematical methods for assessing the strength of structural elements based on the analysis of the elastic material parameters, taking into account the features of its internal microstructure; determining the dependence of the inclusions distribution from their concentration on the sample plane using computer vision and image processing technology of the material structure; application of developed approaches to the estimation of the probabilistic features of material characteristics. The object of research is the deformation process of two-component materials with spherical inclusions. The subject of research is the probabilistic characteristics of elastic parameters, the limiting state, as a yield surface, at various concentrations of the internal components of the material; statistical forecast of the reliability of structures made of two-component materials. The theoretical basis of the PhD work is the following methods: image processing (filtration, segmentation, normalization, and object recognition); solid mechanics, probability theory, theory of random processes. The calculation of the stress-strain state is carried out using the finite element method. The scientific novelty of the dissertation work consists of the following ones: – a new computational approach is proposed for assessing the probabilistic parameters of the boundary state of a two-component material with spherical inclusions. This approach is based on the Monte Carlo method and, in contrast to the existing ones, is based on the analysis of statistically equivalent microstructures. It allows predicting the residual life of structural elements, determining its probabilistic characteristics; – algorithms (based on methods of computer image processing) have been developed for the automated determination of the probabilistic characteristics of the size, spatial distribution, and concentration of spherical inclusions of a two-component material; – for the first time, using the created algorithms, the distribution density functions of the radii of the inclusions were determined depending on their concentration for cast iron (microstructures of the ShG2-ShG12 type). This made it possible to develop an algorithm for the synthesis of statistically equivalent structures; – for the first time, the regularities of the influence of the concentration of inclusions on the distribution density functions (and their parameters) of the components of the stiffness tensor (including the coefficients of mutual influence of the first and second-order) are established for cast iron (microstructures of the ShG2-ShG12 type); – for the first time, concentration dependences of the mathematical expectation, dispersion, and confidence intervals of the flow boundaries under compression and tension are established for cast iron (microstructures of the ShG2-ShG12 type). The introduction contains the relevance of the chosen topic, objectives, subject and research methods, scientific novelty, and the practical significance of the work. The first section of the work contains the analysis of modern approaches to determining the influence of the material microstructure on its mechanical properties and a review of scientific publications on the topic of work. The analysis of experimental and analytical methods of the material microstructure influence on its strength characteristics is carried out. The machine learning and computer vision methods for metallographic images classification, prediction, and statistical assessment of the internal structure influence on material properties are considered. The current state of strength criteria and data-driven methods in problems of solid mechanics is described. It is determined that the most common numerical method, that used to study the stress-strain state of models is the finite element method (FEM). The analysis of scientific directions and approaches related to the task of identifying the strength parameters of materials based on their microstructure, including the determination of the yield surface, contributed to the formulation of research tasks and the description of ways of building a calculation method. The second section describes the theoretical basis for solving the problem of identifying strength parameters using data obtained from material microstructure images. Including consideration of techniques used in image processing. Approaches and methods of input image pre-processing, segmentation, normalization, and filtering with further object recognition are described. A general mathematical statement is formulated for analyzing the elastic properties of a material based on plane stress elasticity theory. The finite element method is used to determine the stress-strain state of the model. This is a numerical variation-difference method for analyzing technical structures, which is a standard research method due to its versatility and ability to work on computing systems. Attention is paid to the formation of a finite-element approach for solving the problem of the classical theory of elasticity. The mechanical properties of the material are determined through the stiffening tensor coefficients. Strength assessment is implemented by the construction of material yield surface. To determine the limit state of material existing hypotheses of the strength of the composite material are considered and modified to take into account different resistance to tensile and compressive stresses. The third section describes the process of artificially generating a statistically equivalent microstructure, which is based on metallographic images of high-strength cast iron. An algorithm for obtaining the function of inclusion distribution in-plane and process of artificial microstructure construction based on mathematical expectation and dispersion of inclusion radii depending on their concentration is described. Based on the obtained models, a series of virtual experiments is used to calculate the complex stress state with the simultaneous action of tensile and compressive loads. Elastic material constants are determined using FEM from the series of tests for uniaxial stretching along with X coordinates, Y coordinates, simultaneous stretching along X and Y coordinate axes, and displacement in the XY plane. Probabilistic characteristics of elasticity modulus, Poisson coefficient, and shear modulus are obtained. The obtained results of the study are verified for reliability. For testing the hypotheses about the normal distribution of the inclusion parameters on the plane the Shapiro-Wilk test is used. The fourth section is aimed to determine the yield parameters of the material. Materials research is carried out in a complex stress state using the finite element method on plane models. The yield surfaces for the test series have been determined. The research of the transition of a material from an elastic to a plastic state based on the entire set of probabilistic characteristics of the yield surfaces is used. The statistical parameters of the yield stress are determined by the mathematical expectation, variance, and coefficient of variation. Analysis of the obtained data shows the effect of the inclusions concentration on the strength characteristics of the material. In the fifth section, the reliability parameters of the centrifugal pump are evaluated (under normal operating conditions and during hydro tests), taking into account the decrease in wall thickness of the housing parts from erosion-corrosion wear. Based on the developed mathematical model, the yield surface of the parts of the pump is evaluated using the material properties data obtained in the previous section. Structural analysis is carried out at the macro- and micro-levels. The occurrence of plastic deformations at the micro-level can lead to the development of a crack and structural damage at the macro level. As a result of the study, the probability of plastic deformation at control points is determined, and areas that require careful control during the entire life of the equipment are established. The conclusion indicates the scientific and practical problems that are solved in the work, outlines the most important scientific and practical results provided by the information on the implementation of the research results.