Expressions are obtained for operators of the concentration of the electric field strength and displacement on the surface of inclusions in a matrix composite depending on the shape and volume fraction of inclusions in the material. These operators relate the fields on the inclusion surface on the matrix side with the average values of the electric field strength and displacement in the composite sample.

The work solves the problem of multi-parameter optimization of vacuum ion-plasma coatings based on the use of a database, which was formed by the authors over several years of experimental and applied work in the field of increasing the antifriction properties of engineering products. Three types of monolayer vacuum ion-plasma coatings (thin films) with a thickness of 0.5–3.5 μm were considered as the object of study: coatings of two nitride systems TiAlN and CrAlSiN, as well as a diamond-like carbon coating (DLC) with a gradient distribution of carbon electronic configurations sp2 and sp3 in depth. The coatings were applied to a substrate made of structural steel 12Cr2Ni4, subjected to carburization with a followed hardening and low tempering. Wear-resistant cemented surface layers of steel products are widely used in mechanical engineering as a contact surface in loaded friction units. Therefore, when conducting a comparative analysis, the mechanical and tribological properties of the cemented surface of the samples (without coatings) were used as a standard and were considered in the optimization process along with coatings. The work used a multi-parameter optimization technique in the form of an integral assessment of each material by constructing radial (ray) diagrams, which were based on a complex of eight characteristics, combining 4 physical-mechanical and 3 tribological properties, as well as the coating thickness parameter. The results of the analysis showed a consistent pattern: in terms of a complex of eight parameters, all coatings are significantly superior to the reference cemented layer. The CrAlSiN coating has the highest integral property indicator.

One of the options for solving the scientific and applied problem of the predicted formation of ion-plasma coating tribological characteristics is presented. The problem is solved by creating and analyzing a carbon coating database. The object of research in this work is ion-plasma diamond-like coatings (DLCs) deposited on a steel substrate. It is shown that the use of nitrogen instead of hydrogen to stabilize carbon coatings not only ensures stable thicknesses of DLCs at the level of 1.0–1.5 μm, but also serves as an important and convenient technological parameter for regulating the tribological coating characteristics during deposition. Based on the predicted and experimental values of friction coefficient μ and data on sample path length L, the intervals of optimal values of technological parameters

This work discusses the predictable control of coating deposition by vacuum ion plasma technology. The multiple technological parameters and the instability of the nonequilibrium ion plasma system create substantial obstacles to the wide industrial application of promising multicomponent functional coatings. Here we propose a solution to this problem, which includes: creation of a database of diamond-like carbon coatings (DLC) in order to identify a limited number of adjustable control parameters of the technology, determination of how these parameters affect the coating properties, analysis of the revealed effects using statistical methods and neural network algorithms, and use of the results for the predictable tuning of specified coating properties. The object of research is original DLC coatings whose structure is stabilized with nitrogen instead of conventionally used hydrogen. The experimental database of DLC coatings is created based on our previous studies and includes structural, morphological and architectural characteristics of coatings, various types of substrates and sublayers, physical, mechanical and tribological properties, and various combinations of coating deposition parameters. A specific problem is solved to determine the influence of deposition parameters such as chamber pressure P, stabilizer content (% nitrogen), ion flow rate (coil current λ) and deposition time t on hardness H and elastic modulus E of coatings. Based on the results obtained, the deposition parameters are optimized so as to obtain predictable strength values of the formed carbon coating. The optimization procedure is developed using both classical statistical methods and modern algorithms of ridge regression, randomized trees (ExtraTrees), and a fully connected neural network (multilayer perceptron MLP).

Films of the CrMnFeCoNiCu high-temperature alloy have been deposited onto a steel substrate by vacuum sputtering in the magnetron evaporation mode. The local atomic structure and phase composition are studied. The structural state of the CrMnFeCoNiCu alloy is determined by the superposition of contributions of equiatomic simple cubic lattices with lattice parameters of the P1 space group. Reflexes from the S1 and S2 phases contribute to the integral intensity; the contribution is 65.7 and 28.9

The work examines the conditions of tribological tests of steel samples with nitride ion-plasma coatings. A calculation and analytical model is proposed for quantitative assessment of contact and wear parameters during sliding friction tests: the size of the contact area, the depth of contact approach, the depth of the plastic zone, stresses in the coating, fatigue limit, and the critical thickness of the coating, which excludes its deflection. It has been shown that coatings with a thickness above critical realize their potential for physical, mechanical, and tribological properties regardless of the substrate. If the coating thickness is insufficient, the result of tribological tests is determined by the behavior of the “coating–substrate” system, a high-hard nitride coating on a ductile steel substrate experiences deflection and premature brittle failure. To assess the wear of coatings in this case, it is recommended to use fatigue failure models with construction of the Wöhler fatigue curve and determination of the fatigue limit based on the Murakami–Endo theory. The implementation of the recommended approach was carried out for the studied nitride coatings using a database of our own experimental data.

In this work, the structure of a CrMnFeCoNiCu high-entropy alloy (HEA) film deposited by magnetron evaporation on a steel substrate is studied. It is established that the phase content of the CrMnFeCoNiCu HEAs is determined by a superposition of contributions from equiatomic simple cubic lattices of the CrMnFeCoNiCu composition (Struct-26 and Struct-278) with space group P1. It is found that the contributions of the diffraction patterns from the reference lattices to the integral intensity are 0.66 and 0.29, respectively. For simple cubic lattices Struct-26 and Struct-278, the full structural information (the lattice parameters, coordinates of atoms, spatial groups, and occupancies) is derived. It is established that the CrMnFeCoNiCu HEA is a stable compound, which is confirmed by calculations of the mixing energy for the convex Hull model.

A three-cathode arc-based evaporation system has been used to obtain vacuum ion-plasma high-entropy CrTiZrNbHf coatings. The statistically averaged concentration of components in the coating corresponds to Cr0.30Ti0.35Zr0.25Nb0.08Hf0.01. The kinetics of the coating deposition and the process of its structure self-organization have been studied by constructing a diagram of the Movchan–Demchishin–Thornton structure zone. Technological parameters such as the substrate temperature, vacuum chamber pressure, coating deposition rate, ion current density, bias voltage, etc., were combined into the form calculated. It is shown that, for the CrTiZrNbHf system under study, the critical value of the Ebi parameter amounts to about100 MJ/cm3. Exceeding this threshold leads to degeneration of the coating structure in the form of a nuclei-like or droplet-like morphology.

The present paper aims to analyze the wear of TiAlN and CrAlSiN vacuum ion-plasma coatings applied as thin films to carburized and nitrided steel samples, with thicknesses ranging from 0.8 to 4.0 μm. Both dynamic and continuous indentation techniques were used to determine the mechanical and adhesive properties of the coatings. The wear properties of the coatings were defined through tribological sliding friction tests employing the “pin-plate” scheme. The experimental data also include the results of elemental composition detection of coatings and electron microscopic investigations of their structure, morphology, and wear mechanisms, as defined during tribological testing when examining friction tracks. We have found that the wear of coatings during friction does not exhibit stable correlations with any mechanical characteristic, such as hardness H, elastic modulus E, or their ratios H/2, H3/E2, or the adhesion criterion F_N^c , which is the coating's critical shear load as determined by scratch testing. To predict the amount of wear of the ion-plasma nitride coatings, it was suggested to use the G-parameter, the reciprocal value of peeling the coating off the substrate. G is a function of the adhesion parameter F_N^c and significantly depends on the physical and mechanical parameters, including the elastic modulus E and the coating resistance to plastic deformation H3/E2. Experimental results revealed an acceptable correlation with the specific volumetric wear of TiAlN and CrAlSiN coatings.

Methods of predicting how temperature affects the physical and mechanical properties of polymer composites used in LED lamps are considered. By differential scanning calorimetry, the specific heat and phase changes of the polymers and samples of lamp housings are determined. In filler selection, the optimal polymer composition is taken into account.

The work sets the task of determining the conditions for tribological testing of coatings in which the coating realizes its potential of physical, mechanical, and tribological properties regardless of the substrate. A standard method of tribological testing was used on a friction machine according to the pin–disk scheme with a circular motion of a spherical indenter pin. Experimental data are presented on the study of the structure and properties of vacuum ion-plasma nitride coatings of TiN, TiAlN, and CrAlSiN. The coatings had a thickness of 0.8–4.0 μm and were applied to plate steel samples intended for testing in a friction machine. The wear process of coatings is considered from the perspective of contact fracture mechanics and fatigue theories. A calculation and analytical model is proposed for quantitative assessment of contact and wear parameters during friction tests: the size of the contact area; the depth of contact approach; the depth of the plastic zone; stresses in the coating; fatigue limit; and critical thickness of the coating, which excludes its deflection. To assess the wear of coatings in this case, it is recommended to use fatigue failure models with the construction of a Woehler fatigue curve and determination of the fatigue limit based on the Murokami–Endo theory. The implementation of the recommended approach was carried out for the nitride coatings using a database of the authors’ experimental data.

High-entropy coatings based on 3D metals have a unique combination of strength and ductility over a wide temperature range and can be obtained using vacuum ion-plasma magnetron sputtering technology. However, the model calculations of the thermomechanical properties of such alloys are complicated by a lack of stable and equilibrium lattices with complete structural information. This article implements prediction of the stability of the phases of an equiatomic high-entropy coating of CrMnFeCoNi by the inverse convex hull method. The thermodynamic and mechanical properties were determined. It was found that, up to room temperature, the medium-entropy, 4-element alloy of composition MnFeCoNi also belongs to the stable phases.

Introduction. Modern tribology solves the problems of increasing the reliability of friction units through applying vacuum wear-resistant coatings by the physical vapor deposition (PVD) method. More than five thousand scientific papers are devoted to high-entropy alloys (HEA). However, an urgent question about the possibility of obtaining wear-resistant and antifriction high-entropy coatings (HEC) using the PVD method remains unsolved. Its solution opens up the possibility of using HEC in mechanical engineering. The presented article is intended to fill this gap. Research objectives are as follows: to identify the key results on the creation of HEC by such PVD methods as vacuum arc evaporation and magnetron sputtering, to establish tribological characteristics of PVD coatings.Materials and Methods. From November 2023 to February 2024, the authors analyzed materials published in the Web of Science, Elibrary, Scopus, Medline, CINAHL databases in the Russian and English languages.Results. At the first stage, the literature on the vacuum arc coating method was considered. The issues of creating a vacuum arc discharge, its technological features, disadvantages, as well as processes in the cathode region of the arc were studied. The conditions of existence of cathode spots, the influence of temperature on the erosion coefficient, and processes on the anode and substrate were noted. The dependence of the deposition rate on the value of the potential on the substrate was shown. Nitride and combined coatings obtained by vacuum-arc method were analyzed: TiN, TiCN, TiAlN, TiMoS, TiSiN, TiN/VN, TiAlN/DLC-Ti. At the second stage, the history of the magnetron sputtering method was presented; technological features, types of magnetrons and nitride coatings obtained in this way were described. The third stage was devoted to the five-stage process of forming the coating structure. Island, layer-by-layer, and mixed growth modes of coating were considered. A schematic representation of the fundamental processes of structure formation was given. Defects in vacuum coatings were noted. At the fourth stage, the HEC based on the HEA were presented. Parameters predicting the formation of a HEA solid solution were indicated. Six families of high-entropy alloys were considered. Modern high-entropy coatings obtained by vacuum arc and magnetron methods were evaluated. The results of studies of structural-phase and physico-mechanical properties were summarized in the form of a table. The data of tribological studies of high-entropy coatings were presented.Discussion and Conclusion. The literature on HEC describes the coating structure, physical and mechanical properties, and thermal stability. The authors of the presented article found a gap in the research of tribology of high-entropy coatings. From the known results, it can be concluded that these coatings are frictional. However, due to their high hardness and ductility, they exhibit high wear resistance. In addition, it is difficult to talk about their tribological purpose. To solve the issue of the possibility of using PVD coatings in mechanical engineering, attention should be paid to the development of compositions with high hardness, wear resistance, and low coefficient of friction. They can be operated in tribo-loaded nodes.

Решается задача построения модели прогнозирования значений локальных упругих характеристик антифрикционных полимерных композитов, определяемых оператором концентрации напряжений (тензором четвертого ранга). Указанный тензор связывает значения локальных (внутренних) напряжений в каждом элементе неоднородности композита со значениями средних (внешних)напряжений в материале. Построенная модель опирается на обобщенное сингулярное приближение теории случайных полей, используемое при решении стохастического дифференциального уравнения равновесия упругой среды. С помощью указанного приближения возможен анализ изменения значений компонент оператора концентрации напряжений в зависимости от состава, структуры и объемного содержания наполнителей композита. Объектом моделирования являются многокомпонентные трибокомпозиты на основе эпоксидного связующего ЭД-20, армированные волокнами бесщелочного стекла и политетрафторэтилена. Полагается, что стеклянные волокна ориентированы вдоль осей х и у прямоугольной системы координат, а волокна политетрафторэтилена - только в направлении оси х. Это соответствует армированию материала стеклотканью, в которую вплетены политетрафторэтиленовые волокна. Опираясь на разработанную модель, авторы провели численные модельные расчеты значений компонент 3333, 1313 и 2323оператора концентрации напряжений, учитывающие изменения объемных содержаний наполнителей неоднородных материалов. Данные компоненты наиболее полно характеризуют перераспределение напряжений между элементами неоднородности композита при приложении к нему сжимающих и сдвиговых нагрузок. Приведены графики изменения значений указанных компонент оператора концентрации напряжений при увеличении объемных долей как волокон политетрафторэтилена, так и волокон бесщелочного стекла. При вычислении значений локальных упругих характеристик модельных трибо-композитов использовался метод самосогласования.

A model is considered for predicting the operational elastic characteristics of polymer composites based on ED-20 epoxy resin with microcapsules (polyester shells) containing vegetable oil and magnetite nanoparticles. The model is based on the generalized singular approximation of random field theory and takes account of the qualitative and quantitative composition of the frictional materials and also the characteristic size of the microcapsules and nonuniformity of their distribution over the polymer thickness.

In this paper, the study of the tribological properties of self-lubricating composites is based on a mathematical model taking into account experimental data. We considered self-lubricating composite materials based on phenylone, which is modified with ultrafine PTFE powder. Theoretical studies were carried out on the basis of a numerical solution of the quasi-static contact problem on the sliding of a punch with a spherical base along the boundary of a microinhomogeneous medium. It was assumed that the coefficient of friction depends on the path traveled by the punch. The microstructure of the base was taken into account within the framework of the concept of equivalent homogeneity. The numerical solution of the contact problem was carried out in the finite element complex Ansys. The stress state of the composite depending on the variable coefficient of friction and the mechanical properties of the medium was investigated. The dependence of the coefficient of friction on the distance traveled was determined on the basis of laboratory experiments. Functional dependences of stresses in the contact area, internal stresses in the projection of the contact area, maximum shear stresses depending on the mechanical properties of the heterogeneous medium and the variable coefficient of friction are established.

Attempts to solve interrelated tasks by specifying materials for coatings and developing a methodology for monitoring the friction unit operation have been tried previously. The importance and originality of this study is that it examines the distribution of elements in the CrAlSiN coating, as well as their comparative physical, mechanical, and tribological properties. Besides, we have found that surface modification with a coating of the CrAlSiN system increases the strength and resistance to plastic deformation, which ensures high-quality deposition of thin vacuum ion-plasma coatings and leads to an increase in wear resistance. To control friction units with such coatings, it was decided to develop a monitoring technology using a dimensionless damping coefficient of friction-mechanical bonds in sub-octave band frequency ranges of forced vibrations. It makes it possible to identify natural vibration frequencies, which manifest the properties of the coatings and modifiers used for friction or anti-friction purposes. Our findings should make a significant contribution to tribology. Alongside observations of variations in the elastic-dissipative and inertial properties of the interaction between contact surfaces, the analysis of the generalized dynamic criteria on heavily loaded friction units that operate in the boundary lubrication mode allowed determining adhesion stability of contact friction bodies for friction subsystems. Furthermore, we have defined the effectiveness of lubricants, transition to boundary friction, and non-lubricated friction for antifriction subsystems. The use of the technologies developed by the authors for heavy-loaded tribosystems makes it possible to increase the wear resistance, reliability, and safety of operation of railway and air transport.

Three types of vacuum ion-plasma coatings were chosen as the object of study: two nitride systems TiAlN, CrAlSiN and a carbon diamond-like coating (DLC). All coatings had a monolayer structural morphology with a thickness of 1.0–1.5 µm. Nitride coatings were obtained by arc deposition simultaneously from two cathodes; however, they had different microstructures, single-phase (TiAlN) and heterophase (CrAlSiN), and the DLC coating was characterized by a gradient distribution of the electronic configurations of sp2 and sp3 carbon in depth. Coatings were applied to samples of steel 38Cr2MoAl with a nitrided surface and a sorbite structure, which is widely used in mechanical engineering as a contact surface in loaded friction units. The database of our own experimental data obtained by the authors in previous studies was used. On its basis, using the method of radial (beam) diagrams, a multi-parameter optimization of coatings (including a nitrided substrate layer as a comparative standard) was performed in the work according to eight properties that combine 4 physical-mechanical and 3 tribological characteristics, as well as the coating thickness parameter. The results of the analysis show that all coatings outperform the reference nitrided layer in terms of a set of eight properties. At the same time, the nitride coating of the CrAlSiN system has the highest set of properties. It is noted that it is very promising to combine coatings of different systems, for example, a wear-resistant CrAlSiN nitride coating and a DLC carbon coating, which significantly reduces the coefficient of friction during dry friction.

The original derivation of the formula for the mean free path of an electron in a conductive multiply connected domain in three-dimensional space, for which the Ostrogradsky–Gauss theorem is valid, is given, subject to scattering from the boundary of the domain according to Lambert’s law. The result can be used to predict the optical characteristics of nanocomposites with metal-coated inclusions.

Thin film-composed coatings can significantly improve the mechanical and tribological properties of spacecraft friction units. In this regard, protection by ion-plasma coatings has become one of the most used options and well-established technologies. However, design of coatings that remain effective over multiple usages, is a challenge. Improving their production requires a large number of parameters to be optimized and many verification experiments to be set up. We exploited machine learning algorithm to solve the problem of double layer coatings optimization with respect to a set of mechanical properties (hardness, Young's modulus, Poisson's ratio, and yield stress). The training dataset was constructed using the adaptive sampling algorithm and numerical simulation of indentation in ANSYS for coatings of different compositions and thicknesses. The machine learning approximation provided significant accuracy (R2 > 0.96) in predicting the coating hardness based on the mechanical properties of its individual layers. The feature importance analysis of the Extra Trees algorithm was used to define the parts of the indentation curve that carry information about the properties of individual coating layers. We have also addressed the inverse problem of coatings design in terms of the required hardness. Our findings demonstrate that only tandem approach to the cross-validation task permitted correct estimation of error in the presence of multiple ambiguous solutions. The value of error was smaller than 0.15 GPa. Being comprehensive, the proposed methodology can be applied to design optimal multilayer coatings in terms of their mechanical properties for friction units in aviation and rocketry-astronautics.