The effect of hydrogen on contact stresses in a roller bearing fitted with interference on a shaft is investigated. The hydrogen-induced damage to the material of the inner bearing ring is described by the introduction of a weakened layer. It is found out that hydrogen released from the lubricant causes additional expansion of the ring, which reduces the working radial clearance in the bearing and redistributes the axial load between the rolling elements, in some cases increasing the clamping force to the most loaded rolling element. The problem of contact between a cylindrical roller and a bearing ring is solved in terns of the elastic half-space problem. Dimensionless expressions for the stress tensor components in the ring under the contact surface are obtained and the distribution by depth is investigated. It is shown that the equivalent stresses reach maximum at a certain depth. Based on the constructed graphs, a simple method for calculating these values and the depth of their location is proposed. It is shown that with an increase in the pressing force, the dangerous region of high stresses shifts deep into the ring and facilitate the initiation of fatigue subsurface defects.

We study the effect of stabilization of a pendulum with internal degree of freedom in the upper inverted equilibrium position subject to vertical vibration of the support. A small amplitude parameter of support vibration is introduced. The method of two-scale expansions is used to obtain the averaged motion equation of the pendulum. Stability conditions for the upper equilibrium position are found depending on the parameters of the elastic element of the pendulum. Critical values of the pendulum deflection angle are obtained, which control the boundary of the stable oscillation zone.

The object of study. The upper upward position of the pendulum subjected to vibration of the pendulum base is known to be stable for some parameters of the base vibration. The research is devoted to dynamics of the model of a two-link inverted pendulum in a general nonlinear formulation. The goal. The boundaries of the parameters of a given base vibration, under which the inverted mode is stable, are assumed to be known. The goal is to find the regions of the initial conditions of the problem, namely, the initial non-small angles of deviation of the pendulum links from the vertical that result in stable oscillation in the inverted position. We intend to reveal the impact of the rod compressibility on the oscillation mode, as well as the influence of the resonance on stability in the framework of more complex formulation of the problem which involves account for small elastic axial deformation in the rods. Methods. By applying the laws of dynamics to the moving elements of the structure, we derive the complete nonlinear system of equations of the pendulum motion in two formulations: (i) for a system with two and (ii) four degrees of freedom, respectively. The equations include the parameter of small base vibration amplitude, which makes it possible to apply the two-scale asymptotic expansion method. The method leads to a system of averaged equations of motion which is convenient for the benchmark study of parameters. Results. The modes and eigenfrequencies of small oscillations of the pendulum are found depending on the dimensionless parameter of the problem. In the nonlinear for-mulation, the maximum deviations of the pendulum links are calculated which ensure a stable solution to the problem for zero initial angular velocities. Depending on the initial phase of vibration of the base, the boundaries of absolute and partial zones of stability of vibrations are obtained. In the absolute zone, stable oscillations are realized for any value of the initial phase of the base vibration. In the partial region, stable oscillation occurs at least for one set of initial condition. The dynamics of the pendulum is compared with and without account for rod the compressibility. The results are presented in the graphs.

Influence of the skin effect caused by the hydrogen charging of the samples on the thermal desorption spectra and the values of the hydrogen binding energy are critically analyzed. For the study, the experimental data and the McNab–Foster model are used. It is shown that an artificially formed specific inhomogeneity in the distribution of hydrogen concentrations significantly affects the shape of thermal desorption spectra and in turn the results of their interpretation based on the Choo–Lee plot and the Kissinger formula. Large errors are possible in the binding energies determined by means of the thermal desorption spectra, provided that the skin layer is formed artificially when the samples are charged with hydrogen. It is shown that the standard description of thermal desorption of hydrogen based upon the one-dimensional model leads to errors. The three-dimensional formulation of problem of hydrogen diffusion in cylindrical sample results in a broken line in the Choo–Lee plot rather than a straight line obtained in the framework of one-dimensional formulation. Comparison of experimental data with the 3D simulation data convinces that effect of the skin layer on the thermal desorption spectra is associated only with the diffusion of hydrogen at the sites of the crystal lattice in the McNab–Foster model.

The article is concerned with finite element solution of hydrogen-induced brittle fracture of a metal cylindrical specimen with a semicircular groove. The study is based on the HEDE model of hydrogen brittleness and considers the skin effect of charging the samples with hydrogen. The results showed that taking into account the skin effect leads to the changes in the mechanisms of destruction of samples, and it can be the true cause of the experimentally observed dual fracture pattern.

In this paper, we study the distribution of the hydrogen concentration in a rotating cylindrical elastic body compressed by two concentrated forces. This problem is relevant for diagnostics of bearing failure due to the influence of hydrogen on the mechanical properties of structures. During the study, the plane stress state of a loaded cylindrical elastic body is determined by means of the theory of functions of a complex variable. We used the transition to a rotating coordinate system to obtain the static problem of hydrogen diffusion in a body loaded by the known stresses. The solution of the problem includes the methods of asymptotic analysis for the simplification of partial differential equation, the expansion in a Fourier series and the Galerkin approach for finding the expansion coefficients for several harmonics. The results can be useful for calculating the hydrogen concentration distribution in roller bearings.

One of the main methods of protecting pipelines and machine parts against stress corrosion and hydrogen embrittlement is to test metals for hydrogen-induced cracking. The hydrogen-induced cracking test is a standard procedure for testing steels and titanium alloys and for studying hydrogen resistance. The experimentally revealed phenomenon of nonuniform hydrogen distribution after hydrogen charging of specimens is called the skin effect. Here we study the influence of the skin effect after hydrogen charging on the crack growth under mechanical stresses and the influence of a 50-μm-thick skin layer on the durability of bulk specimens. A corset-type cylindrical specimen with a circumferential notch is considered. The Oriani decohesion model is chosen as a hydrogen embrittlement model. The investigation is performed using our data on the real nonuniform hydrogen distribution and the literature data on hydrogen diffusion coefficients, diffusion activation energy, steel parameters, cohesive law parameters, as well as other parameters of the hydrogen embrittlement model proposed by Serebrinsky. Hydrogen redistribution is described by the diffusion law taking into account mechanical stresses. Modeling is carried out with the original finite volume code in the axisymmetric setting. Crack propagation parameters are determined. The fracture pattern is complex. Cracking first occurs by the hydrogen-enhanced decohesion mechanism and then by the conventional mechanism, which explains the experimentally observed brittle-ductile fracture behavior in tensile hydrogen-charged specimens.

The chapter provides an overview of the results of studying the effect of hydrogen in mixtures with gases on strength, ductility, fatigue crack growth rate, and fracture morphology of the most commonly used pipeline steels X70, X80. The main methods of testing susceptibility of pipeline steels to hydrogen following the standards are briefly discussed. The results obtained by various authors show that there is a strong influence of partial hydrogen in mixtures with gases. Fatigue crack growth rate increases many times, the fracture morphology changes, and a quasi-cleavage fracture mode is observed. At the same time, tensile strength and yield strength of smooth tensile specimens made of the base metal practically do not change. This, in turn, can lead to an incorrect interpretation of the results of testing.

The problem of active vibration suppression of the distributed elastic system is considered in the example of a slender metal beam undergoing bending vibrations. Control systems include piezoelectric sensors and actuators. Three different strategies for vibration suppression are considered: local, modal and shape control strategy. The local approach means that each feedback loop includes only one sensor–actuator pair placed at specific location on the beam, while the modal strategy implies that each feedback loop corresponds to a specific vibration mode of the object. The shape control method is based on the compensation of known distribution of the external excitation using only one feedback loop with all available sensors and actuators. First, experimental results are obtained for the local and the modal control systems using the same two sensor–actuator pairs, and then the transfer functions in feedback loops for these systems are improved as the result of numerical modeling. After that, the modal method is compared numerically with the shape control strategy. The results show that the modal method is the most effective if it is needed to suppress several vibration modes of the object.

Hydrogen charging is widely used in industry for testing metals intended for natural gas pipelines and hydrogen energetics. Here we study the distribution of mechanical damage in a specimen resulting from hydrogen charging in a neutral solution based on hydrogen-induced cracking tests according to NACE standard TM0284. The investigation is carried out by acoustoelasticity (acoustic damage detection). The basic relationships are derived for the time delay in acoustic sounding and for damage tensor components. The dependences of the principal damage tensor components on the hydrogen charging time are plotted. The volume distribution of hydrogen concentrations after hydrogen charging is measured. It is found that the skin effect due to hydrogen charging is closely related to a similar effect of damage concentration in a 100-µm-thick surface layer. This means that hydrogen embrittlement induced by artificial hydrogen charging in aqueous electrolytes can be considered as a surface phenomenon. This conclusion allows us to verify the adequacy of hydrogen-induced cracking tests for metals, mechanical models of hydrogen embrittlement, and methods for evaluating and predicting the effect of the hydrogen-containing corrosive environment on the mechanical properties of metals and metal structures. The test results will surely differ considerably from the field evidence due to different hydrogen charging times. It needs to be ascertained if this difference is significant for the fracture mechanism of the specimens. The strong surface effect observed in the experiments on artificial hydrogen charging of metals requires further investigation and comparison.

The classical Kapitsa's problem of stability of an inverted pendulum subjected to vertical vibration of the support and some generalizations are investigated. The asymptotic method of two-scale expansions allows one to determine the level of vibrations that stabilizes the vertical position of the rod. The cases of inextensible and extensible rod are studied, and a benchmark of results is carried out. An attraction basin of the stable vertical position of the rod is found. Both harmonic and random stationary vibrations of the support are considered, too. Stability and attraction basin of the vertical position for a flexible rod are studied in detail. A single-mode approximation is used for the approximate solution to the nonlinear problem of stability of a flexible rod.

The main organizer of the congress was the Russian National Committee for Theoretical and Applied Mechanics established in 1956 to promote joining the International Union of Theoretical and Applied Mechanics (IUTAM) and organization of various scientific events in Russia.The XII Russian Congress of Theoretical and Applied Mechanics was held in the city of Ufa, the capital of the Republic of Bashkortostan, on August 19-24, 2019.In order to get an idea about the scope and scientific level of the Congress it is worth mentioning the following fact.Altogether 1517 scientists from 70 cities of Russian Federation and other countries attended the Congress.The list of attendees included 32 members of Russian Academy of Sciences, about 1000 scientists of the PhD and Dr.Sci level and more than 300 young researchers.The Congress became the key scientific event bringing together fundamental researchers and leading specialists in aerospace, aviation, and oil&gas industry.During the Congress 1362 lectures were presented, among them 11 plenary lectures, 42 keynote lectures at different sections, 652 oral presentations, and 973 posters.

Aluminum alloys are very popular in a variety of technical applications. The strong influence of hydrogen on the properties of aluminum alloys is known, however, as in the case of steels; it is continuously increasing as new alloys with extreme properties are developed and introduced. Scientific research in the field of the hydrogen effect on the properties of aluminum alloys is mainly focused on the fundamental aspects such as the diffusion coefficients of hydrogen in aluminum, possible types of hydrogen traps, and their effect on the microstructure of alloys. At the same time, the industry has a problem of cracking ingots and semi-finished products (sheets, pipes, and plates), including their further processing and welding. In contrast to the high-strength steels, scientific research does not actually provide specific values for critical hydrogen concentration. The problem of separating the hydrogen adsorbed on the surface and dissolved during measurements has not been solved. There are only a few types of aluminum alloy reference specimens. The article is intended to partially fill this gap. It provides specific examples of the study of technological problems and proposes the measurement methods that allow the separation of hydrogen dissolved and adsorbed on the surface.

The bending stiffness of a multilayer plate with alternating soft and hard layers is considered under the assumption that the deformation wavelength is substantially greater than the plate thickness. We discuss the approximate methods for determining the shear compliance required for replacing a multilayer plate with an equivalent single-layer Timoshenko–Reissner plate. A comparison is made with the exact solution of the three-dimensional problem of the theory of elasticity. The dependence of shear compliance on the ratio of Young's moduli of layers and on their location is investigated.

The classical problem of buckling of a thin rod subjected to axial compressive force is studied. Two cases are studied in detail: (i) case of short loading and (ii) case of long-lasting loading. Dynamic buckling of a thin rod subjected to a continuously acting longitudinal load at the initial stage of the movement is studied. If the applied static load significantly exceeds the critical Euler force, one of the higher buckling modes has the maximum rate of amplitude growth at the initial stage of the motion. This result is obtained in the framework of a linear statement of the problem, and an explanation of the paradoxical result by Lavrentyev and Ishlinsky is provided. A possibility of the appearance of buckling due to a suddenly applied longitudinal load which is smaller than the Euler critical force is found out. This buckling can occur only for the rod length from a certain range and is caused by the parametric resonance. In the linear approximation, the amplitude increases unboundedly while a small resistance leads to a significant increase in the amplitude. Introduction of nonlinear terms into consideration results in beats with energy exchange between longitudinal and transverse vibrations. Axial impact on the rod by an impactor is considered as a way of reproduction of the jump force in the experiment. The contact force is determined analytically and by means of finite element analysis. The results of these two approaches are confirmed by test results on the example of the impact time.

This chapter presents the classic results by Euler on nonlinear static deformation of the axially compressed rod, the results of the work by M.A. Lavrentiev and A.Yu. Ishlinsky on rod buckling under dynamic axial compression and the recent results mainly related to the study of interaction of longitudinal and transverse vibrations. The chapter introduces readers to the basic research methods which are the D’Alembert and Fourier methods, the methods of studying parametric resonances, the asymptotic method of two-scale expansion.

Investigations of hydrogen concentrations and acoustic anisotropy in single-crystal nickel-based specimens were carried out. The growth of creep and thermal fatigue cracks for different modes of thermomechanical loading was studied. Experimental data and theoretical estimates of acoustic anisotropy in specimens with crystallographic direction $$ \langle 011 \rangle $$ of face-centered cubic lattice were obtained. It was found that anisotropy of elastic modulus provides a main contribution to acoustic anisotropy in the case of single-crystal alloys. Measurements of hydrogen concentrations revealed its accumulation after thermomechanical loading in a weakly bound state along edges of specimens to the level of 4 ppm. It indicates a significant degradation of mechanical properties and the presence of developed hydrogen embrittlement. The obtained results allow one to develop an integrated approach for estimating the residual life of single-crystal structures by analyzing hydrogen concentrations and acoustic anisotropy parameters.

A linear static problem of bending of a multilayer plate with homogeneous isotropic layers is considered. The deflection is assumed to have harmonic shape in the tangential directions. For calculation of the bending stiffness we introduce two dimensionless parameters: a small thickness parameter equal to the ratio of the thickness to the deformation wavelength in the tangential directions, and a large inhomogeneity parameter equal to the ratio of the maximum and minimum Young’s moduli of the layers. The plane of these parameters is split into four regions, in which different models are available for calculating the bending stiffness. The first of these is the Kirchhoff - Love model based on the hypothesis of straight non-deformable normal. In the second region, the Timoshenko - Reissner model with a shear parameter is used, calculated by an asymptotic formula of the second order of accuracy. The third region is based on assumptions on inextensible normal fiber and large heterogeneity. Finally, in the fourth region, compression of the normal is taken into account, and an approximate formula for bending stiffness is proposed for a three-layer plate. Error estimation of the models is carried out on test examples by comparison with the exact numerical solution of the three-dimensional problem of the elasticity theory. The possibility of suitability of the bending stiffness for calculating the plate eigenfrequencies is discussed.

The study of influence of the skin effect, which occurs when charging metal samples with hydrogen, on the thermal desorption spectra (TDS) is carried out. The main goal of the study was to identify the causes of possible errors in determining the binding energies of hydrogen. The effects arising at different rates of the increase TDS temperature are investigated. The study was carried out analytically and numerically by means of FEM modeling. The standard Fick model is taken for modeling the hydrogen transport model in order to gain a simple explanation of the effects. The skin effect was found to lead to appearance of an extra peak on the TDS. Deciphering the TDS using the Choo-Lee plot results in dependence of the activation energy or hydrogen binding energy calculated by the Kissenger formula on the range of temperature rates in which the TDS experiment was performed.