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The reprint under the permission of the “Bulletin of the Belarusian State University of Transport. Science and Transport”. – 2010. – No. 1. Also published in the Journal “Mechanics of Machines, Tools and Materials”. -2010. - No 3 (12). - P. 98-100 (abridged version)

Abstract

The paper presents a curriculum vitae of Professor, Doctor (Engineering) Leonid Sosnovskiy on the occasion of his jubilee.

Leonid Sosnovskiy was born on July 25, 1935 in the village of Polesie of the Chechersk district of the Gomel region. He graduated from the Shilovichi Secondary School with a silver medal, then the G.V. Plekhanov Leningrad Mining Institute, and received the profession of mechanical engineer. He worked at a machine-building factory, as well as at research institutes and higher education institutions of Russia, Ukraine, and Belarus. He obtained his Ph. D. at the Central Research Institute of Machine Building Technology in Moscow and Doctor’s degree at the Kiev Polytechnic Institute. At present, Leonid A. Sosnovskiy is Professor of the Belarusian State University of Transport, Director of the TRIBO-FATIGUE, Ltd., and the scientific supervisor of the Interdepartmental Laboratory “TRIBO-FATIGUE” that was founded according to the protocol signed by President of the National Academy of Sciences of Belarus, Chief of the State Committee on Science and Technology of Belarus, and by Ministers of Education and Industry of Belarus in 2004. The Laboratory was organized on the proposal of P.A. Vityaz, L.G. Krasnevskii, V.I. Senko, V.A. Zhmailik, and L.A. Sosnovskiy in effort to solve interdisciplinary problems in the spheres of science, production, and education.

Professor Leonid A. Sosnovskiy is Doctor in Engineering, a State Prize Winner of Ukraine, a Honoured Scientist of Belarus, a member of the Russian National Commettee on Theoretical and Applied Mechanics, as well as Co-Chair (along with V.T. Troschenko, N.A. Makhutov, and Gao Wanzhen) of the International Coordination Council on Tribo-Fatigue created by the Academies of Sciences of Belarus, Russia, and Ukraine in 1993. Leonid A. Sosnovskiy is a Honorary citizen of Chechersk and an author of more than 700 research papers and inventions. He is an expert in the field of mechanics of materials and structures, and of movable and deformable systems.

He developed methodological, experimental, and theoretical fundamentals of tribo-fatigue – a new part of mechanics that is defined as mechanics of wear-fatigue damage and fracture (the State Standardian GOST 30638-99). In this field the direct effect of Sosnosvkiy–Serensen was revealed, according to which the fatigue strength of tribo-fatigue systems can decrease sharply (by a factor of 2-3 or more) and increase considerably (by 30–60% or more) depending on friction and wear conditions. The back Sosnovskiy–Sharay effect was been established, according to which friction and wear strength characteristics can both reduce and rise considerably (by ±70% or more in the both cases). The both effects were described analytically and their experimental regularities were studied. The multiple microshearing dissipated effect scattered multiple microshear effect, namely, the Sosnovskiy–Makhutov–Chizhik effect, was found experimentally. It allowed these authors to understand and study regularities of complex damage formation and development in difficult conditions. L.A. Sosnovskiy together with K.V. Frolov formulated the principle of L-interactions of irreversible damages due to different-nature loads (cyclic, frictional, thermodynamic, etc.). This principle was widely confirmed experimentally and became a basis for transition from the analysis of factors in solid mechanics (mechanical fatigue, friction and wear mechanics, etc.) to that of phenomena in tribo-fatigue. It permitted the authors to establish and explain four tribo-fatigue surprises: S1 – unexpected drop of steel fatigue strength due to the interaction of mechanical-physical-chemical phenomena at friction against a polymer (tribo-fatigue paradox); S2 – effective control of friction and wear processes by exciting cyclic stresses resulted from off-contact load (back effect); S3 – anomalously low failure strength at fretting-fatigue due to a strong interaction of a set of small damages (tribo-fatigue, or Makhutov’s bomb); S4 – abnormally high failure strength at contact-mechanical fatigue due to spontaneous hardening (tribo-fatigue’s gift). These surprises are studied experimentally and described analytically. They have yielded effective ways for optimal control of wear-fatigue damage of deformable solid/solid systems.

As applied to deformed solid/radiation systems, it is found that if the direct effect characterizes the irradiation influence on variations in long-term strength characteristics, then the back effect represents the force stimulation of radiation damage. Its influence is stronger for loaded specimens, whereas it is much weaker for those irradiated with the same dose without loading. A model of radiation damage is proposed, on the basis of which an equation is derived for calculatation of equivalent stress with account for the irradiation behavior and parameters (dose, fast and thermal neutron intensity, etc.). The equation is in a fair agreement with experimental results. As applied to solid/fluid systems. L.A. Sosnovskiy in cooperation with V.V. Vorobyov developed a model of corrosion-erosion fatigue, according to which erosion processes can decrease and increase mechano-corrosion fatigue strength (direct effect). The back effect at corrosion fatigue involves changes in the rate of chemical processes due to cyclic stresses.

To date, over 500 research papers, including 20 books, have been published in the field of tribo-fatigue with participation of L.A. Sosnovskiy. Six International Symposia on Tribo-Fatigue have been organized (1993 – Gomel, 1996 – Moscow, 2000 – Beijing, 2002 – Ternopol, 2005 – Irkutsk, 2010 – Minsk). When supported by V. N. Koreshkov, 7 state standards have been developed, including 3 Interstate standards. 150 scientists from various countries have been awarded with the Honorary Diploma “For Contribution to Tribo-Fatigue” among them are 16 scientists from Belarus. Over the past five years, 6 candidates and one doctor of science have been prepared, and the economic effect of over 3 mln USD has been achieved. With the support of V.I. Senko, A.S. Shaginyan, M.A. Zhuravkov, B.M. Khrustalev, E.A. Rovba, A.V. Bogdanovich, P.S. Poita, V.I. Dragan, and D.G. Medvedev, the training courses of five universities in Belarus have been added with the subjects “Fundamentals of Tribo-Fatigue” and “Fundamental and Applied Tribo-Fatigue Problems” with full scientific and methodological provision. Fundamental tribo-fatigue studies are conducted, in particular, in the framework of several state research programs (“Priority”, “Machine Building”, “Reliability”, “Mechanics”, etc.) organized and headed by M.S. Vysotskiy, P.A. Vityaz, O.V. Berestnev, V.A. Marchenko, A.V. Kukharev, L.A. Sosnovskiy et al.

Tribo-fatigue has been created at the junction of such well-developed disciplines as the theory of mechanical fatigue, tribology, the theory of reliability of mechanical systems, materials science, and the theory of corrosion. So, its development is based on methods and advantages of mechanics of solids, applied mechanics (mechanics of materials and structures), damage mechanics, contact mechanics, the theory of elasticity, mechanics of continua, dynamics of mechanical systems, etc. It is natural that the generalized methods and the results obtained in tribo-fatigue are useful and enrich classical mechanics.

The evolution of traditional solid mechanics is made: mechanical states of not an individual loaded solid, but of a movable and deformable system as a whole are investigated; the system comprises two interacting elements. Such systems are called tribo-fatigue systems. In cooperation with K.V. Frolov, M.S. Vysotskiy, N.A. Makhutov, V.T. Troschenko, M.A. Zhuravkov, P.A. Vityaz, and S.S. Sherbakov, the methodology and the mechanical-mathematical models for comprehensive investigation of the mechanical states of such a system and its elements are developed. It includes a sequential formulation and solution of generalized problems on their stress-strain state, damage states, and the limiting state. This methodology has been adopted to study roller/shaft systems, roller/ring systems, etc. A general solution to the problem on the joint stress-strain state of tribo-fatigue systems has been obtained. Its analysis has allowed one to make the following conclusions: а) changes in the local field of contact stresses or deformations as superimposed by a field of stresses or deformations due to volume deformation are, in essence, a special class of problems in contact mechanics; b) study of the field of stresses or deformations due to volume deformation as excited in a local region where the field of contact stresses or deformations is simultaneously excited. In essence, it is a special part of the theory of elasticity. For engineering solutions of the above problems, L.A. Sosnovskiy in cooperation with S.S. Sherbakov proposed the hypothesis on the separation (in tribo-fatigue system) of contact load into contact and bending components. The equation of equilibrium is written in the energy and phenomenological formulations, and the experimental confirmation of the hypothesis is obtained. Unlike the known approaches, according to which damage is estimated only at dangerous surface points or in the dangerous deformable solid section, in this case a general solution is derived for the problem on the volumetric damage state. It opens the possibility of predicting zones of possible appearance and development of initial (original) crack formation. Unlike the known approaches, for which the material limiting state is estimated, in this case in cooperation with S.S. Sherbakov, as a rule, in terms of one criterion the generalized energy theory of limiting states of tribo-fatigue systems affected by volume, frictional, and thermodynamic loads and operating in the corrosive environment is proposed. It allows one to predict the fail of system elements through various criteria of reaching the limiting state (volume fracture – separation into parts; critical surface fracture – limiting wear and others). In cooperation with N.A. Makhutov, A.V. Bogdanovich, and S.A. Tyurin, a method for constructing a multicriterion diagram of limiting states is developed. It is experimentally verified. Unlike the known approaches, for which characteristics of friction (in a friction pair) are found only under the contact load action, in this case in cooperation with S.S. Sherbakov a general solution to the problem on the friction force coefficient in a tribo-fatigue system is derived. It is based on the analysis of displacements and strains in the contact region. It allows one to take into account the effect not only of contact load and strains resulted from off-contact loads on changes in friction characteristics. It is shown that the friction force in a tribo-fatigue system is cyclic (repeated or alternating depending on loading conditions) and does not correspond to the direction of the conventional friction force in a similar friction pair. The friction coefficient can be varied by changing the magnitude and sign of cyclic stresses up to ±(30–70)% or more.

In mechanics of damage, L.A. Sosnovskiy proposed a generalized idea of damage: it is any change in composition, structure, dimensions, mass, volume, and continuity, hence, mechanical-physical-chemical properties of material. Fracture (in the traditional understanding) is treated as one of the modes of damage (critical damage). Numerically, generalized damage can be characterized by any number within the range 0 ? ? ? ?. If ? ? ?, then the characteristic dimension of decomposition products of a solid is d? ? 0, that is, the solid is decomposed into indefinitely small particles, atoms, etc. In the general case, two different types of damage states are considered. These are the subcritical state (0 ? ? ? 1 in the traditional understanding) and the supercritical state or the decomposition of a solid into a great number of parts: 1 < ? ? ?. In contact mechanics and tribo-fatigue, L.A. Sosnovskiy in cooperation with M.A. Zhuravkov and S.S. Sherbakov proposed several types of measures of volumetric damage under static and dynamic loading and presented the classification of the stress-strain state (component, octahedron, deviator, tensor, energy and others). A method for estimating asymmetry parameters of damage processes is proposed. Their analysis allows one to describe the ratio of mechanical and thermal or force and frictional damages of tribo-fatigue system elements in specified operating (testing) conditions. The development of mechanics of local damages is made on the basis of the experimental and theoretical methods developed in cooperation with O.M. Elovoi, A.V. Bogdanovich, V.V. Komissarov, and S.S. Scherbakov. Methods for measurement and analysis of local wear and local deformations on the friction track of systems with main rotational motion per each shaft revolution (up to 64 measuring points) during the whole testing period (107 loading cycles) are developed. Procedures of constructing diagrams of local wear, local deformation, and the fatigue curve through the local damage criterion are proposed. The mechanical and mathematical model is based on the analysis of dangerous volume intersections and union due to all stress tensor components (when acted by contact and off-contact loads).

In continuum mechanics, the problem on the effect of near-wall friction and geometric discontinuity of channel turbulent fluid on changes in the tube stress-strain state is formulated and solved in cooperation with S.S. Sherbakov. A model for interactions between continua is formulated in cooperation with S.S. Sherbakov and M.A. Zhuravkov, and the governing relations of their states are being sought.

In dynamics of mechanical systems, L.A. Sosnovskiy in cooperation with S.S. Sherbakov discovered and described analytically the troppy phenomenon – formation of irregular residual wavy damages due to the unsteady process of cyclic elastoplastic deformation in the contact zone at rolling friction (surprise S5 in tribo-fatigue). This phenomenon is really observed under certain conditions of movement of carriages (trains, trams) along the rails. In cooperation with S.A. Tyurin, this phenomenon has been reproduced in laboratory conditions of testing small-size models of a rail/wheel system and its basic regularities have been studied. L.A. Sosnovskiy formulated and substantiated the problem on optimization of a dynamic system and indicated tf-channels (tribo-fatiue channels) of control of its life. As applied to movable and deformable solid/solid systems, he discovered the effect of interrelation of the processes of movement, information, and damage (surprise S6 in tribo-fatigue triade); the analytical description is made in cooperation with О.Т. Vavilov. According to this effect, the motion yields new information in the system if the index of its damage is non-zero. Information will be positive when the system is hardened and negative when it is softened. As a result, L.A. Sosnovskiy formulated the basic principles and developed an algorithm of automatic control of a smart system.

In the field of mechanical fatigue, L.A. Sosnovskiy in cooperation with V.T. Troschenko developed the statistical theory of fatigue fracture in an arbitrary stress state. Its advantage is a possibility to calculate fatigue strength of machine parts simultaneously in terms of three criteria: fatigue fracture probability, equvalent stress, and safety factor. The latter are estimated from the probabilistic viewpoint. A condition of static equivalency of various stress states, which is independent of the principal stress ratio, is proposed: the complex stress state of a solid is equivalent to a uniform or nonuniform linear stress state of the same solid or a solid with other dimensions and shape if the probabilities of their fracture during the identical life period are equal. A representation of the equivalent stress function is introduced, which predicts the same damage probability as the assigned values of the principal stresses do. Its limiting surface under the assigned fatigue damage probability can be interpreted as a cube, ellipsoid (particular cases) or other higher-order surfaces. A method of calculating the critical safety factor value, which divides dangerous and safety (in terms of the damage probability) zones of stresses, is presented. A model of joining particular damage probabilities due to fatigue cracks in the corresponding linear stress states is developed and approved in effort to estimate the damage probability in an arbitrary complex stress state. An idea of a determinant or tensor of fatigue fracture probabilities due to the principal stresses is introduced. Its invariants are similar to those of the stress tensor. A procedure is proposed and a comparative analysis is made of the danger of various stress states in terms of the fracture probability. Fatigue strength criteria for the typical cases of linear and biaxial stress states are obtained. Calculation formulas for estimating the fatigue fracture probability, the equivalent stress, and the safety factor are obtained with account for the efect of various factors, including material properties, size and shape of parts, surface state, etc. The distribution function of longevity limits of parts with regard to the effect of a complex of design, technology, and operating factors on the fatigue strength is constructed analytically. It is shown that it has a permissible error. L.A. Sosnovskiy developed a statistical model of a deformable solid with a dangerous volume (SDV model) that became a basis both for the joint theory of the scale effect in fatigue strength (allowing for the influence of the governing factors such as temperature, surface state, etc.) and for the proposed similarity criterion of fatigue fracture.

For complex stress state conditions, L.A. Sosnovskiy introduced a concept of a second-order damage tensor whose components are either absolute (dangerous volumes) or relative (relative dangerous volumes) measures of damage. A problem of optimization through fatigue strength criteria is formulated and solved to the first approximation with account for economic and other importance of mechanical system parts. A kinetic function of damage accumulation is proposed and is applicable for cyclic-stable, hardenable and softenable materials, as well as for materials of complex behavior in time. Based on this function L.A. Sosnovskiy in cooperation with A.V. Bogdanovich and N.A. Makhutov constructed power-law models and derived the formulas for calculating the longevity in regular and block loading regimes. Equations for the fatigue curve are proposed with regard to damage processes proceeding in time according to exponential or power laws. A database of basic fatigue strength characteristics of metals and structure elements with account for the effect of the main factors affecting their fatigue fracture is created and published in cooperation with V.T. Troschenko. It is approved by the State Service for Reference Data and comproses over 10,000 entries for over 400 grades of metals and alloys.

In the field of crack mechanics, L. A. Sosnovskiy developed one of the concepts of cyclic fracture toughness applicable to plastic materials since it is based on the plasticity correction which he proposed. In cooperation with A.V. Bogdanovich, the latter is used when constructing the diagram of cyclic elastoplstic fracture of a cracked specimen (CEPFCS) in the coordinates “stress intensity factor – transverse component of plastic strain (cross section residual contraction)”. The CEPFCS diagram is used to find several characteristics of cyclic crack resistance for plastic steels. This simple and clear diagram is of the same significance in engineering applications as the tensile test diagram. In cooperation with A.V. Bogdanovich, he proposed a procedure of similarity transformation and, based on it, a method of constructing a generalized CEPFCS diagram for different-type specimens. In cooperation with I.V. Kudryavtsev, he found basic residual deformation redistribution regularities at low-cycle loading because of the crack motion and the formation of a zone with a limiting dangerous cross section contraction. In cooperation with A.V. Bogdanovich and A.M. Bordovskii, he proposed the engineering formulas for calculating the longevity of objects at the stage of developing a main fatigue crack and the model for predicting the longevity of oil pipelines with crack-like defects. In cooperation with I.V. Kudryavtsev, it is found experimentally that during cyclic elastoplastic deformation, metal micro- and macroparticles are removed from the cracking area and their shape and dimension classification is given. In cooperation with A.V. Bogdanovich et al., Professor L.A. Sosnovskiy studied the radiation effect on crack resistance of stainless steel. It is shown that after 100,000 hours of operation (in the conditions of the first loop of the primary circulating pipeline of an atomic power-plant), cracks are initiated at loads approx. twice as low as those required for the original material. They are growing with a rate that is 6 or 7 times higher than that of the material before irradiation since its deformation reduces by 15–25%.

In friction and wear mechanics or tribology, L.A. Sosnovskiy established an energy analog of the friction law: the deformation friction-to-contact energy ratio is a constant equal to the energy friction parameter. A method for estimating this parameter is presented. In cooperation with S.S. Sherbakov and V.V. Komissarov, he formulated the friction law in a tribo-fatigue system: the generalized friction force is proportional to both contact and off-contact loads. The law is verified experimentally. It is shown that the friction coefficient is presented as a linear dependence of the conventional friction coefficient (in a friction pair) and the friction index in a tribo-fatigue system that is governed by the cyclic stress amplitude-to-contact pressure ratio. In cooperation with N.A. Makhutov, he showed theoretically and experimentally that in the general case, a full friction fatigue curve can be constructed in terms of the limiting wear criterion. It has characteristic portions similar to the corresponding portions of the full mechanical fatigue curve and transitions from one portion to another result from changes in the wear modes. The equations for portions are similar in form, but different in governing parameter values. Based on these results, the condition for wear strength similar to that for material strength is proposed. Its use allows one to formulate requirements on the friction coefficient in effort to provide assigned wear strength. The applicability and the effectiveness of the SDV model, as well as the similarity criterion to analyze damage and the friction limiting state are shown and a generalized formula for calculating wear strength or wear is derived. In cooperation with V.V. Komissarov, a noncontradictory theory of the scale effect at rolling friction is developed, according to which contact fatigue strength decreases as the dangerous volume increases; the latter is found by the stress intensity criterion. A phenomenological model for variations in a friction parameter at a scale transition from the macro- to nanolevel and at a reverse transition is proposed; this parameter is a function of physical surface roughness and incorporates deformation and molecular components, whose sum is constatnt (equals unity). Possible ways for the above transition are analyzed. They are governed by physical-mechanical properties of materials, from which system elements are manufactured. A modified Hersy–Stribek–Sosnovskiy curve is constructed and a kinematic friction model (in motion) is developed. It reflects the effect of both the conventional parameters (contact load, velosity, lubricant dynamic viscosity) and the parameters of interaction of irreversible damages due to different-nature loads (surface, volume, thermodynamic) on friction coefficient variations. The analysis of the model is performed. Sosnovskiy–Komarovs’ effect – the effect of local plasticization of high-strength steel in given rolling friction conditions is established. Conditions of transfer of polymer to steel or of steel to polymer at sliding friction for a metal/polymer pair are found. Based on extensive experimental studies, in cooperation with A.V. Marchenko, he proposed a classification of types of wear kinetic curves by changes in friction conditions within a wide time interval (up to 80 million loading cycles). Roscoe-Rehbinder’s parameter is proposed, which characterizes numerically the hardening and softening process ratio at friction. In cooperation with V.V. Komissarov, V.V. Vorobyov, and A.A. Kebikov, he found experimentally the basic regularities of the effect of cyclic compressive or tensile stresses induced in the friction zone on variations in wear, axis approach, and friction coefficient. Generally, it is shown that the study of the back effect, in essence, opens a way for construction of “parallel” tribology in which the known regularities of friction and wear processes are corrected with account for the effect of volume or off-contact loads.

In the theory of probability, L.A. Sosnovskiy proposed a one-dimensional L-function of distribution of random values within the interval (0; 1). This funcion is not reduced to any known distribution law and has found application in damage mechanics. He introduced the r-statistics in the form of the complementary event probability ratio that is useful in applications (technology and humanities). In the theory of reliability of mechanical systems, he established a two-dimensional S-function of distribution of limiting stresses at bending and contact loading and used it to develop the model for calculation of the system failure probability at complex loading, as well as he systematized generalized reliability conditions. As applied to conditions and the damage degree of tribo-fatigue systems in the supercritical region, he introduced a concept of the reliable failure probability, whose values are over the range (1; ?); they are the so-called tribo-fatigue probabilities. He developed a concept of L-risk and Sr-safety. It is based on the generalized concept of risk as a portion of “bad in good” or r-statistics. This concept has turned to be effective for the analysis and prediction of the safety of reliable systems in terms of fatigue fracture and wear criteria. In cooperation with V.A. Zhmailik, he proposed and implemented the QRR (quality-risk-reliability) approach to predict the performance of tribo-fatigue systems. The three interrelated characteristics are introduced, i. e., the indicators of quality, quality fail, and risk, for which three caterogies are established and normalized – highest, first, and second. A method of constructing the operation characteristic and circular risk diagrams are developed. A relation between the probability of operational damage of parts and the risk and quality characteristics is found.

In applied mechanics or mechanics of materials and structures, L.A. Sosnovskiy in cooperation with K.V. Frolov, M.S. Vysotskiy, V.T. Troschenko, and N.A. Makhutov developed the principles of designing tribo-fatigue systems by the criteria of strength, wear strength, reliability, risk and safety, and longevity. The implementation of these principles allows one to formulate and solve the following main problems: the determination of required dimensions of elements of tribo-fatigue systems and their contact area; the selection of materials for their fabrication; the determination of required friction coefficient to provide the preset operation wear strength of a system; the prediction of the longevity and reliability by the fatigue strength and wear rate criteria; the estimation of the operation risk or safety. The design principles are based on the generalized energy theory of limiting states of tribo-fatigue systems, whose versions are developed by L.A. Sosnovskiy in cooperation with A.V. Bogdanovich, S.S. Sherbakov, and N.A. Makhutov. The following problems have been formulated and practically solved: the selection of an effective part from the total (supplied to a system) energy spent for generation and development of irreversible damages; the substantiation of a limiting effective energy characteristic independent of both the loading mode and damage mechanisms; the calculated ectimate of the function of L-interactions in a tribo-fatigue system; a method of consideration of stress corrosion, frictional corrosion, and temperature corrosion at the assessment of the limiting state of such a system. In the general case, in cooperation with V.V. Vorobyov and A.A. Kostyuchenko, an engineering model of mechano-corrosion strength is proposed; its general regularity is as follows: the product of the actual normal stress and the corrosion rate function is a constant value for a given material and various loading conditions. A method for calculating the longevity in corrosion effect conditions is developed, if the parameters of the curve for fatigue in air are known. Methods for predicting the longevity at irregular loading developed in cooperation with A.V. Bogdanovich and N.A. Makhutov are based on the theory of the fatigue curve and the hypothesis of fatigue damage accumulation which considers cyclic hardening and softening processes.

In experimental mechanics, in cooperation with M.S. Vysotskiy, N.A. Makhutov, A.V. Bogdanovich, V.A. Zhmailik, V.I. Senko, O.M. Elovoi, A.M. Bordovskii, S.A. Tyurin, V.V. Vorobyov, V.A. Andriyashin et al., Professor L.A. Sosnovskiy developed innnovation methods for wear-fatigue testing, including accelerated ones. They are based on modeling the governing conditions for operation of real structures, friction units, and tribo-fatigue systems and are implemented using testing elements of unified sizes. This allows one to compare the testing results at different loading and to reduce sharply the time of tests. For example, as applied to the mechanisms of motion of harvesters, it is shown that 125 units under testing (sizes of their elements are varied from 10 to 1500 mm) are reduced to four typical models. In cooperation with V.I. Senko, V.A. Zhmailik, V.V. Komissarov, V.V. Vorobyov, and S.A. Tyurin, he modeled such systems as rail/wheel, gearings, liquid flow at pressure / tube, etc. As a rule, laboratory tests reproduce the main types of operation damage of the corresponding objects, which confirms the correctness of the testing methods. The main testing methods are implemented in standard form (five state standards are developed), and it is possible to obtain experimentally characteristics of fatigue strength, friction and wear, complex wear-fatigue damage and fracture to be used in calculations. To implement the developed methods, Professor L.A. Sosnovskiy in cooperation with N.L. Indman, G.P. Ozhigar, M.S. Vysotskiy, O.M. Elovoi, A.V. Bogdanovich, N.A. Makhutov, V.A. Shurinov, V.V. Komissarov, V.O. Zamyatnin, S.A. Tyurin, S.A. Goman, V.N. Shkarubo, O.D. Zholyd et al. created a special class of testing equipment based on a number of inventions. To date, 11 modifications of SI machines for wear-fatigue tests are developed. These machines made as desktop units are designed in accordance with the unit-module principle, provide wide ranges of loads (bending and contact) and testing frequency, and are equipped with a PC-based information and control system. The processes of testing, measurement, and data processing are automated. In cooperation with V.A. Zhmailik, a concept of testing agricultural machines was developed to solve problems of providing their required quality by strength and tribological reliabilty characteristics in order to reduce the operational damage risk. It implies seven levels of testing at three scale steps (mechanical properties of materials; longevity properties of units, tribo-fatigue systems, and aggregates; machine service characteristics). In cooperation with V.V. Vorobyov, he carried out a unique statistical experiment on loading of pipes of the linear portion of the “Druzhba” oil pipeline in regular operation conditions for eight years. The analysis of over 400,000 pressure values has shown that the pipe / oil flow system under pressure is a tribo-fatigue system and operates at low-frequency high-cycle fatigue and loading process parameters are determined. This is an initial prerequisite for development and introduction (in cooperation with А.М. Bordovskiy) of a complex of methods for keeping and partial recovery of the performance of the oil pipeline (the pipe diameter is 600 mm) after the service life. This has allowed increasing its output due to a pressure rise by ~5%) and providing its practically trouble-free operation during nine years; the oil pipeline continues operating. In cooperation with A.M. Bordovskiy, he developed a method and technology for hydraulic testing of a full-scale portion (16 km in length) of the oil pipeline that operates over the service life at the internal pressure being by 25% higher than the working pressure. It is found experimentally that due to elastoplastic deformation of metal in hydraulic tests, a considerable recovery of fatigue strength of pipes occurs: the longevity limit of base metal recovers up to ~90% of the initial level and that of welded joints – up to almost 100%. In cooperation with V.V. Vorobyov, A.A. Kostyuchenko, and A.N. Kozik, Professor L Sosnovskiy developed a method and technology for comparative fracture testing of full-scale long pipes (length exceeds diameter more than ten times) with corrosion damages and without them by the method of stepwise pressure increase. The test results have shown that after long-term operation at underwater transitions, zones with local corrosion damages of base metal become dangerous rather than heated-affected zones of longitudinal welded pipes. Therefore, the prediction of their residual longevity is made using the mechano-corrosion fatigue strength criterion. In cooperation with V.V. Vorobyov and N.V. Kovalenko, he found deformation regularities of full-scale pipes with local corrosion damages: at low pressures some zones show compression instead of expected tension. At low pressures corresponding to the material yield, there occurs sharp localization of strains: they are 3–8 times as much as total strain. With account for the experimental data obtained, methods and technologies of recovering the strength reliability of underwater transitions of the “Druzhba” oil pipeline are developed and introduced. A paradox (Sosnovskiy–Komissarov–Sherbakov paradox) of results of testing a roller (100 mm in diameter)/ shaft (10 mm in diameter) system at console bending with rotation (at contact loading): though the path of friction to reach the limiting state is the same for a roller and a shaft, the average radial residual deformation of the roller has turned to be 3-5 times (depending on load and longevity) higher than that of the shaft, despite the fact that the number of loading cycles of the roller is, on the contrary, ten times less than that of the shaft. The analysis of this paradox is made.

In materials science for machine building, Professor L.A. Sosnovskiy in cooperation with A.A. Kebikov and with participation of V.V. Komissarov developed a diagram of mechanical state of steels that illustrates stable correlations between the main characteristics of material mechanical properties determined at static, cyclic, and contact loading: tensile strength, relative elongation and contraction at rupture, hardness, and endurance limits at bending and rolling friction (contact fatigue limit). A relationship between complex fracture characteristics of elements of tribo-fatigue systems and materials is established with account for the proposed index of steel resistance at contact and mechanical fatigue. In cooperation with A.V. Bogdanovich and S.A. Tyurin, he proposed and substantiated experimentally the systematization of characteristics of wear-fatigue damage and fracture, and a noncontradictory system of their designations is developed. Using a complex of wear-fatigue damage and fracture strength characteristics as an estimation system of performance characteristics of such an important object as a rail, he developed (in cooperation with and with participation of V.A. Zhmailik, V.N. Psyrkov, V.A. Gapanovich, V.V. Komissarov, V.O. Zamyatnin et al.) a chemical composition and technologies of melting and heat treatment of high-strength cast iron with globular graphite of grade VChTG. Cast iron shows a specific diagram of mechanical states: strength increase within a certain interval leads to a plasticity rise. Since the main characteristics of this cast iron by bending and contact fatigue criteria are not practically worser than those of high-strength steel, a technology for producing full-scale portions of heavy rails of R65 type has been developed and implemented. The manufacturing of rails made of high-strength cast iron instead of steel is a promising and economically efficient for railway transport. VChTG cast iron is also used to fabricate a pilot batch of large (about 500 mm in diameter) gears for final drives of harvesters; first full-scale tests have been succsessfully completed. The use of special heat treatment provides VChTG cast iron with high cutting ability at impact-cyclic loading. This iron is used to fabricate a pilot batch of blades for harvester cutting aggregates. During full-scale testing, the blades have shown the resistance comparable with that of imported blades made of special steel; cast iron blades are much cheaper than steel ones. In physical material sciences, Professor L.A. Sosnovskiy proposed a thermomechanical constatnt of material that characterizes theoretical strength loss per 1 K. It is established on the basis of the known physical-mechanical and thermodynamical ideas of the fracture process.

In the field of interaction of natural and engineering sciences, and humanities, L.A. Sosnovskiy works in three directions developed on the basis of the methodology and achievements of tribo-fatigue.

The fist direction is the development (with participation of S.S. Sherbakov) of the basic principles of mechano-thermodynamics of systems (surprise S9 in tribo-fatigue). It is based on the idea of tribo-fatigue entropy (surprise S7) defined as a measure of irreversible adsorption of (effective) energy in a dangerous volume of a deformable (solid-state) element of a mechanothermodynamic system. It is shown that the thermodynamic and tribo-fatigue entropies are not additive and interact in a complex matter, thus determining (forming) A-evolution of the system in terms of damage. This serves as a basis for the following postulate: the damage degree of solids can be infinitely large up to decomposition into atoms, etc. In essense, it is a thesis about the never-ending (in time) evolution, if one takes into account that decomposition products of any system become construction material for new systems. From this the global sequence follows: the production of internal mechanothermodynamic entropy is also forever as motion and damage. This means that the entropy of the Universe increases. These ideas do not contradict up-to-date physical views. A thesis about the objective function of A-evolutionis is proposed and substantiated: to maintain the necessary balance between the damage risk and the system safety so that their existence in time would obey golden relations. In general, the formation of mechanothermodynamics of systems as a united physical discipline is based on the following two principles: 1) damage of entire matter has no conceivable boundaries and 2) flows of effective energy (entropy) resulting from different-nature sources interact dialectically rather than sum up. These studies are under development with participation of P.A. Vityaz and S.S. Sherbakov.

The second direction relates to biomechanics of living and intellectual organisms. It is based on the fundamental idea of tribo-fatigue life (surprise S8 in tribo-fatigue) as a specific way to accumulate damages. Ideas of the field of life (damages – time) and the field of fate (living loads – time) are introduced. Models of the main types of life (genetic and real) are developed and analyzed. It is shown that the death of any organism is inevitable because of the imminence of achieving the limiting damage value. This gives the following conclusion: really there exists the only one right way to prolong life, i. e., to reduce a rate of damage accumulation. Eight classes of life loads are proposed (mechanical, energy, ecological, moral-psychological or emotional, intellectual, etc.) that to a considerable extent govern the life of homo sapiens. A procedure of their experiment-calculated estimation is proposed. A method and a model for consideration of force-majeure circumstances as accelerators of the damage accumulation process are developed. All the analysises are, as a rule, based on quantitative estimates of characteristic parameters and governing functions. Further studies in this direction will be carried out with participation of specialists in biochemical and other sciences.

The third direction is the development of quantitative methods in dialectics. The main laws (negation of negation, unity and struggle of opposites, and transition of quantity to quality) are formalized in the simplest equations (formulas) that can be comparatively simply analyzed. Such an analysis does not contradict philosophical views, but it allows one to elucidate novel regularities of evolution processes. It has opened ways for studying such phenomena as the ratio good and evil in human society, evolution of diseases in regions, etc. Thus, the tribo-fatigue methodology turns to be useful in humanities for purposes of concretization and numerical analysis of society phenomena (effect of crowd, relationship between discord and well-being in the state, life quality changes, etc.). Further development of this direction is connected with involving scientists in social sciences and humanities.

L. A. Sosnovskiy is the author not only of scientific publications, but also of verses. They have been written at different times and reflect wide mosaic of the author’s senses and thoughts, as well as his rich spirit of this original and interesting man. Many of his works are saturated with philosophic thinkings that invite a reader to reflect.

We would like to congratulate Professor L.A. Sosnovskiy on occasion of his seventy-fifth anniversary and wish him new success in science.

References:

1. “Some words about tribo-fatigue” (Devoted to the decade of evolution of tribo-fatigue studies and the 60th anniversary of Prof. L.A. Sosnovskiy), edited and compiled by A.V. Bogdanovich, Authors: Strazhev, V.I., Frolov, K.V., Vysotsky, V.S., Troshchenko, V.T., Sosnovskiy, L.A., Makhutov, N.A., Kukharev, A. V., Gruntov, P.S., Starovoytov, E.I., Marchenko, V.A., Koreshkov, V.N., Shurinov, V. A., Botvina, L.R., Drozdov, Yu.N., Gorbatsevich, M.I., Pavlov, V.G., Efros, D.G., Gomel·Minsk·Moscow·Kiev, Remika, 1996. 132 p.
2. “Leonid A. Sosnovskiy”, Who is Who in the Republic of Belarus. People of Matter, ed. by I.V. Chekalov, Minsk, Entsiklopediks, 1999. 330.
3. Sosnovskiy L.А. “Memory”, in 2 books, Minsk, BELTA, 1999, Book 2, 380 p.
4. “Trybafatika”, Belarus Encyclopedia, Minsk, Belarus Encyclopedia, 2002, vol. 15, 542.
5. “Leonid A. Sosnovskiy”, Belarus Encyclopedia, Minsk, Belarus Encyclopedia, 2002, vol. 14, 191.
6. Bogdanovch А.V. “Tribo-fatigue – it is serious…”, Professors of the Belarus State University of Transport, Gomel, 2003, 227-235.
7. “About Tribo-Fatigue”, Materials of Scientific Workshop Devoted to Two Decades of Evolution of Tribo-Ftigue Studies and the 70th Anniversary of Prof. L. A. Sosnovskiy, Minsk, July 28, 2005, Foreword by Academician М.S. Vysotskiy, ed. by L.G. Krasnevskii, Minsk, NIRUP “Belavtotraktorostroyeniye”, 2005, 84 p.
8. Kukharev А.V. “To History of Tribo-Fatigue: First Two Decades”, ISTF 2005 (Proc. 5th International Symposium on Tribo-Fatigue, October 3-7, 2005, Irkutsk, Russia), Irkutsk, Irkutsk State University of Communications, 2005, vol. 1, 7-14.
9. Voschula М. “Laws Formulated by Life”, Science and Innovations, 2006, No 10, 48-51.
10. Chernyak S.S. “Leonid A. Sosnovskiy”, Metals Science Researchers, vol. II, Irkutsk State University of Communications, 2009, 436-437.
11. * Vysotsky M.S. The new word in the mechanics // Science and Innovation. -2010. - No 9 (91). P. 17-19.
12. * Leonid Sosnovskiy, “Tribo-Fatigue is innovation in science, education, technology,” / The newspaper “Zvezda”. – 27 August 2010 – No 167 (26775). – P. 1-2. (see also Proc. VI International Symposium on Tribo-Fatigue (ISTF 2010), October 25 – November 1, 2010, Minsk (Belarus) / Eds. М.А. Zhuravkov (Chairman) [et al.]. – Minsk: BSU, 2010. – Vol. 2. – P. 711-718.)

Main Books Published by L. A. Sosnovskiy and in Co-Authorship

1. Sosnovskiy L.А. “Statistical Mechanics of Fatigue Fracture”, Minsk, Navuka i Tehknika, 1987, 288 p.
2. Troschenko V.Т. and Sosnovskiy L.А. “Fatigue Resistance of Metals and Alloys” (Handbook in 2 Volumes), Kiev, Naukova Dumka, 1987, vol. 1, 510 p., vol.2, 825 p.
3. Troschenko V.Т., Krasovskii А. Ya., Pokrovskii V. V., Sosnovskiy L.А., and Strizhalo V. А. “Resistance of Materials to Deformation and Fracture” (Handbook), in 2 parts, Kiev, Naukova Dumka, 1993. Pt. 1, 288 p., Pt. 2, 701 p.
4. Sosnovskiy L.А. “Mechanics of Fatigue Fracture” (Dictionary-handbook in Two Volumes), Gomel, NPO TRIBO-FATIGUE, 1994, vol.1, 328 p., vol.2, 340 p.
5. Sosnovskiy L.А. “Elements of Theory of Probability, Mathematical Statistics, and Theory of Reliability” (Textbook), Gomel, Belarus State University of Transport, 1994, 147 p.
6. Sosnovskiy L.А. “Tribo-Fatigue: on Dialectics of Life”, 2nd edition, NPO TRIBO-FATIGUE, 1999, 116 p.
7. Sosnovskiy L.А. and Bogdanovich А.V. “Theory of Accumulation of Wear-Fatigue Damage”, Gomel, NPO TRIBO-FATIGUE, 2000, 60 p.
8. Sosnovskiy L.А. and Makhutov N.А. “Tribo-Fatigue: Wear-Fatigue Damages in Problems of Life and Safety of Machines”, Moscow-Gomel, FTsNTP “Safety”-NPO TRIBO-FATIGUE”, 2000, 304 p.
9. Sosnovskiy L.А., Troschenko V.Т., Makhutov N.А., Gao Wanchzhen, Bogdanovich А.V., and Scherbakov S.S. “Wear-Fatigue Damages and Their Prediction (Tribo-Fatigue)”, Gomel?Kiev?Moscow?Uhan, 2001, 170 p.
10. Sosnovskiy L.А. “Fundamentals of Tribo-Fatigue” (Textbook for Higher Educational Institutions), Gomel, Belarus State University of Transport, 2003, vol.1, 246 p., vol.2, 234 p.
11. Sosnovskiy L.А. “L-Risk (Mechanothermodynamics of Irreversible Damages)”, Gomel, Belarus State University of Transport, 2004, 317 p.
12. Senko V.I. and Sosnovskiy L.А. “Basic Ideas of Tribo-Fatigue and Their Study at Technical Universities”, Gomel, Belarus State University of Transport, 2005, 187 p.
13. Sosnovskiy L.А. and Sherbakov S.S. “Tribo-Fatigue Surprises”, Gomel, Belarus State University of Transport, 2005, 192 p.
14. Sosnovskiy L.A. “Tribo-Fatigue. Wear-Fatigue Damage and Its Prediction (Fundamentals of Engineering Mechanics)”, Series: Foundations of Engineering Mechanics, Springer, 2005, 424 p.
15. Sosnovskiy L.A. “Mechanics of Wear-Fatigue Damage”, Gomel, BelSUT, 2007, 434 p.
16. Sosnovskiy L.A., Sherbakov S.S. “Surprises of Tribo-Fatigue”, Magic book, 2009, 200 p.
17. Sosnovskiy L.A. “Scattering of Senses” (Verses), Gomel, JSC “Polespechat”, 2008, 208 p.
18. Sosnovskiy L.A. “Embracing a Dawn with Love” (Verses), Minsk, 2010, 104 p.
19. * L.A. Sosnovskiy, M.A. Zhuravkov, and S.S. Sherbakov. Introduction to Tribo-Fatigue: Textbook for Students of Mechanical-Mathematical Department (Speciality 1-31 03 02 “Mechanics” (in directions)). – Minsk: BSU, 2010,77 p.
20. * S.S. Sherbakov and L.A. Sosnovskiy. Mechanics of Tribo-Fatigue Systems. –Minsk: BSU, 2010, 407 p.
21. * L.A. Sosnovskiy, M.A. Zhuravkov, and S.S. Sherbakov. Fundamental and Applied Problems of Tribo-Fatigue: A Course of Lectures. Minsk: BSU, 2010, 488 p.
22. * L.A. Sosnovskiy, A.V. Bogdanovich, Crack Resistance. Gomel: BelSUT, 2011, 366 p.

* Added by the editor

Pyotr A. Vityaz Academician of the National Academy of Sciences of Belarus, Academician of the International Academy of Eurasia, D. Sci. (Eng.), Professor, Honoured Science Worker of BSSR, First Deputy of Chief of Presidium of the National Academy of Sciences of Belarus Scientific Interests: nanotechnologies, new porous materials and articles based on metal powders; technologies of hardening and recovering of parts by gas-thermal deposition of coatings. The author of over 500 scientific publications and inventions and 14 monographs. e-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

Mikhail S. Vysotskii Academician of the National Academy of Sciences of Bel-arus, D. Sci. (Eng.), Professor, Hero of Belarus, Winner of State Prizes of USSR and BSSR, Honoured Science Worker of BSSR, Honoured Industrial Worker of USSR, Director General of the Joint Institute of Machine Building of the National Academy of Sciences of Belarus Scientific Interests: theory, calculation, and testing of mobile machines. The author of over 450 scientific publications and inventions and 19 monographs. e-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

Valerii A. Zhmailik Cand. Sci. (Eng.), Honoured Science Worker of the Repub-lic of Belarus, Winner of State Prize of the Republic of Bela-rus, Director General of the PA «GOMSELMASH» Scientific Interests: reliability and durability of agricultural machinery; tribo-fatigue The author of over 40 scientific publications. e-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it