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The contact between an infinitely extended plane indentor and a viscoelastic layer is considered within the Derjaguin self-consistent approach with the surface (traditional formulation) and bulk (refined formulation) application of intermolecular interaction forces. Some analytical expressions are derived for the stress-strain state. Using the first law of thermodynamics, the energy dissipation in a viscoelastic layer is calculated. It is shown that the traditional and refined problem formulations may lead to essentially different results of calculation for the characteristics of contact between an indentor and a viscoelastic layer.

A number of deformation models are considered for a wear coating. They are used as a basis to perform the calculations of coating wear kinetics within the two-dimensional formulation of the wear contact problem. It is shown that the use of refined deformation models for a coating with consideration for its shape transformation may have a significant effect on the results of calculating the coating wear kinetics.

An elastic inhomogeneous coating is considered for which a simplified deformation model is proposed in the framework of the concept of an asymptotically thin layer. Based on such a model for an inhomogeneous coating, a solution of the contact problem in the presence of intermolecular interaction is constructed and the wear kinetics for the thrust sliding bearing is calculated. It is shown that the pattern of the inhomogeneity of the coating can have a significant effect on its stress-strain state and wear kinetics.

One of the predicted disruptions in the normal functioning of steam generators in a lead-cooled reactor over a long period of operation is depressurization of the heat-exchange tubes. The most likely tube failure sites are the tube–spacer comb interfacing zones. The oscillatory motion of the tubes in the lead coolant makes it necessary to study the fretting of the tube material. We describe the structural features of the setup modeling the interaction of the heat-exchange tubes and the spacer comb provided that the heatengineering properties of the lead coolant are the same and the material and structure features of the interfacings are the same. The experimental data on the wear of heat-exchange tubes that serve as the basis for theoretical modeling of their fretting are presented.

Although the contact theory between rough surfaces is designed for adhesion energies ≳100mJ/m2, microsystems are controlled by much weaker adhesion ≲100μJ/m2, which is critical for their operation. The weakest adhesion is related to the omnipresent fluctuation-induced dispersion forces. We develop a theory for such a weak adhesion emphasizing that the adhesion energy as a function of the average distance separating the bodies is almost entirely defined by the dispersion interaction. This dependence can be evaluated using the Lifshitz theory, but the effects of contact interaction or plastic deformations give only small contribution to the adhesion. Such a behavior is explained by a specific roughness of the deposited thin films used in microtechnologies. The films deposited on cold substrates have a much larger number of high asperities than is predicted by the Gaussian distribution and the contact occurs over a few asperities with heights much larger than the root-mean-square roughness. Finally, we discuss application of the effect for more precise determination of the distance upon contact, which is crucial for precise measurements of the dispersion forces especially at short separations in the range 5

A study has been conducted on the wear resistance of the tread rubber of an all-metal radial truck tire at various temperatures: –25, 23, and 80°C. Sandpaper of various grains is used as a counterbody. The tests were carried out at a constant sliding rate of 2 cm/s and a normal pressure of 0.7 MPa. This paper presents the results of assessing the effect of temperature on the intensity and mechanism of wear for rubber. A contactless 3D gauge was used to study the evolution of the surface microgeometry and changes in the size of wear particles. The rubber wear resistance parameter was determined by processing experimental data on mass wear using a simplified solution of the corresponding wear contact problem.

In the present study, the structure, microrelief and optical properties of the iron films deposited onto silica and silicon substrates by thermal evaporation have been evaluated. The film top surface layer is a textured iron polycrystal, as it has been verified by RHEED. When iron is deposited onto silicon, the microrelief magnitude is below 12–15 nm, as measured by AFM. The dispersive optical constants n(λ) and k(λ) of the iron films have been defined over the spectral range of λ = 250–1100 nm by spectroscopic ellipsometry. The n(λ) and k(λ) parameters open a possibility of precise thin semi-transparent iron film thickness measurement by laser ellipsometry.

The formulation of the contact problem is considered in the presence of bulk-applied intermolecular interaction forces between the contacting bodies. A method for contact gap evaluation is proposed to simplify to a significant extent the calculation of contact interaction in the scope of a self-consistent approach. Using the estimate of the contact gap, subsurface stresses in an elastic half-space that is in contact with a spherical indenter have been calculated.

A mechanical model of friction and wear of an elastic coating against a wavy punch under forced oscillations (vibrations) is proposed. The model allows predicting reduction in the effective coefficients of friction and wear depending on the parameters of forced vibrations and waviness of the punch. Qualitative agreement between the obtained theoretical dependences and known experimental results is demonstrated. The proposed model can be used for correct interpretation of the results of tribological experiments.

In this paper, we consider a contact problem for an elastic half-space that is nonuniform over depth in the presence of applied bulk intermolecular interaction forces. Our attention is focused on constructing an influence function for this problem. A solution of the Mindlin problem on the action of a concentrated vertical force in an elastic half-space that is inhomogeneous over depth is obtained by using the perturbation method. The influence function is analyzed and some of its features are revealed.

The parameter of the wear law of bronze coupled with steel under dry friction is identified by comparing the results of mathematical modeling with experimental data. The wear tests were carried out according to the steel-ball–flat-bronze sample scheme under relative reciprocal sliding of the tested samples. The modeling of the wear of the sample was based on asymptotic behavior of the solution of the corresponding wear-contact problem. The effectiveness of using this asymptotic behavior to identify the wear law based on the tribological test results has been demonstrated.

The problem of the non-uniform sliding of an indenter over a viscoelastic foundation, whose deformation properties are described by a simplified Kelvin model, is considered. An analytical solution is obtained, and it is established that it has a hereditary character, i.e., it depends on the past history of the interaction of the indenter with the foundation. The solution obtained is used to calculate the sliding dynamics of a massive body, i.e., the problem of braking of a massive indenter as it slides over a viscoelastic foundation and the problem of grasping a massive viscoelastic body by a pair of indenters sliding over its sides. The influence of the viscoelastic parameters and the shape of the indenter on the dynamic characteristics of the massive body is studied. In particular, it is shown that the type of dependence of the deformation friction force on the sliding velocity has a significant influence on the braking mode of the indenter. The possibility of controlling the braking process is demonstrated.

The contact problem is considered for a system of bodies subject to wear on a common base. The deformation properties of the bodies and the base are described by the Winkler model. The problem is reduced to a system of ordinary differential equations and an integral equation of hereditary type with difference kernel. The solution of the problem is constructed with the use of the Laplace transform. The asymptotics of the solution at large times is studied. The continuity conditions for the contact of each of the bodies with the base are derived.

An analytical solution of the problem on the wear of a punch sliding on a thin elastic strip under the condition that they are in complete contact is given for variable friction and wear coefficients. The particular case of a wavy punch (periodic problem) is considered. Some distinguishing features of the process of wear in the transient regime are revealed. It is established, for example, that the contact pressure distribution curve can have a narrow local maximum (peak), significantly exceeding the average level of the contact pressure in magnitude.

The formulation of the contact problem in the presence of bulk forces of intermolecular interaction of contacting bodies is examined. Principal attention is paid to the construction and analysis of the properties of the influence function (Green's function) for an elastic base consisting of a half-space and a layer adhered to it. The behaviour of this function with small and large values of the argument is studied. A numerical analysis of the dependence of the influence function on certain parameters of contact is carried out.

A three-dimensional problem on the contact interaction between a thin elastic layer and an absolutely rigid body sliding over it is considered where wear of both bodies is assumed. The solution is represented by a Fourier series, the coefficients of which are found in an explicit form. The asymptotics of the contact pressure for large times are investigated. The importance of taking the factor of the mutual wear of the contacting bodies into account is demonstrated.

The formulation of the contact problem is considered for the bulk application of intermolecular interaction forces between the contacting bodies as applied to the contact between an absolutely rigid body (an indentor) and an elastic half space. The subsurface stresses and, in particular, the shear stress intensity associated with the fracture of the material are analysed.

By comparing the calculation results with the experimental data, the wear law of bronze against steel counterbody under dry sliding friction is identified. The bronze sample was a block in three configurations, i.e., block–bar and block–pad with and without clearance. The calculation of wear of the sample was carried out based on a wear model of rigid bodies. Quite close values of the power wear law parameters were obtained for the different configurations of the sample. This demonstrates the effectiveness of using the rigid body wear model to identify the wear law of friction units in case of developed wear.

Relations between the boundary stresses and displacements are derived for an elastic half-plane with a weakly distorted boundary. To do this, the stress-strain state of the half-plane is expressed by means of two harmonic functions using the general Papkovich–Neuber solution and the distorted half-plane is conformally mapped onto a canonical (flat) half-plane. As a result, a system of boundary value problems for the harmonic functions is obtained from which the required deformation relations follow using a Fourier transform. The effect of the distortion of the boundary on its deformation is analysed.

The spatial (three-dimensional) problem of the wear of a wavy punch sliding over an elastic layer bonded to a rigid base, assuming there is complete contact between the punch and the layer, is considered. It is assumed that there is Coulomb friction and wear of the punch. An analytical expression for the contact pressure is constructed using the general Papkovich–Neuber solution, the harmonic functions in which are represented in the form of double Fourier integrals, after which the problem reduces to a linear system of differential equations. It is established that the harmonics constituting the shape of the punch and the contact pressure are shifted with respect to one another in time along the sliding line of the punch. The velocity of this shift depends on the longitudinal and transverse frequencies of the harmonic, that is, dispersion of the waves is observed.

The stress state of the carpometacarpal joint (CMJ)was studied in sound and pathologic states by methods of continuum mechanics. The CMJ geometric model was constructed according to the results of computer processing of the data of tomographic investigations in the extension position, which were obtained at Cheng Kung Medical University (Taiwan). The study of contact interactions in the CML region for a given geometry were performed numerically in the ABAQUS program code. The obtained numerical solutions of contact problems permit comparatively analyzing the stress distribution in the bone tissue for various thumb positions and study the stress state dependence on the bone tissue porosity (osteoporosis), which varies with human age.

A solution of the plane problem of the contact interaction of a periodic system of convex punches with an elastic half-plane is given for two forms of boundary conditions: 1) sliding of the punches when there is friction and wear, and 2) the indentation of the punches when there is adhesion. The problem is reduced to a canonical singular integral equation on the arc of a circle in the complex plane. The solution of this equation is expressed in terms of simple algebraic functions of a complex variable, which considerably simplifies its analysis. Asymptotic expressions are obtained for the solution of the problem in the case when the size of the contact area is small compared with the distance between the punches.

A refined formulation of the contact problem when there are intermolecular interaction forces between the contacting bodies is considered. Unlike the traditional formulation, it is assumed that these forces are applied to points within the body, rather than to the surface of the deformable body as a contact pressure, and that the body surface is load-free. Solutions of the contact problems for a thin elastic layer attached to an absolutely rigid substrate and for an elastic half-space are analysed. The refined and traditional formulations of the problem when there is intermolecular interaction are compared. ©2013

The contact of indenters with an elastic composition consisting of a coating and a substrate when there is intermolecular interaction (adhesion) is considered. The method of successive approximations is used to solve the non-linear integral equation of the problem. The verification of the convergence of this method, as applied to the case of an intermolecular interaction described by the Lennard-Jones potential, is given. The results of a numerical solution of the problem for an indenter of rectangular cross section with a contact surface of parabolic-wave shape are presented.

The plane problem of the sliding contact of a punch with an elastic half-plane is considered. The deformation force resisting the sliding of the punch, caused by the asymmetry of the contact pressure curve, is calculated. It is established that, in order to satisfy the law of conservation of energy, it is necessary to take account of additional tangential forces applied to the end corners of the punch.

The problem of frictional interaction between a wavy punch subjected to wear and an elastic strip is discussed. The contact of the punch and strip is assumed to cover the whole its lengths (complete contact). An analytic solution of the problem is presented, based on which the formula for the deformation component of the friction force is derived. Analysis of this formula enables us to represent visually certain features of the deformation component of the friction force, particularly in relation to its behavior in time.

The paper describes the theoretical model of contact between a spherical indentor and a rotating disc made of a viscoelastic material. Numerical analysis of the effect of the load and velocity conditions on the disc wear rate is carried out. It is shown that it is important to select an adequate contact model which considers the rheological behavior of the disc material when identifying the wear law from the corresponding test results.

The plane problem of the mutual wear of a wavy punch and an elastic strip, bonded to an undeformable foundation under the condition of complete contact between the punch and the strip is considered. An analytical expression for the contact pressure is constructed using the general Papkovich–Neuber solution, the two harmonic functions in which are represented in the form of Fourier integrals after which the problem reduces to a non-linear system of differential equations. In the case of a small degree of wear of the strip, this system becomes linear and admits of a solution in explicit form. The harmonics, constituting the profile of the punch and the contact pressure, move along the strip with respect to one another and are shifted in time. Conditions are obtained that ensure the hermetic nature of the contact between the wavy punch and the strip when there is friction and wear.

The paper deals with a model of the wear process of journal bearings in outer space when they are exposed to significant temperature oscillations. Derived equations and experimental data are used to calculate the kinetics of wear of the bearings.

A wear-contact problem for a Winkler foundation is considered in the case when the rate of wear depends nonlinearly on the contact pressure and the contact area increases. The corresponding integral and differential equations are obtained. A successive approximation procedure is proposed which enables an exact solution of the problem in the space of continuous functions to be found. The property of non-negativity of the contact pressure when it has non-negative initial values is established. It is shown, using a qualitative analysis and calculations, that the non-linearity of the wear law can have a considerable effect on the behaviour of the contact pressure during the wear process.

The deformation component of the force of friction is determined for the standard elastoviscous base using the energy approach. The obtained formula served to calculate the force of friction of a punch with extreme points. It is established that the friction coefficient grows as the punch becomes rougher. When the sliding velocity of the flat punch with the left angle tends to zero, the force of friction has a nonzero limit.

Fretting corrosion wear was modeled using the deformation model of Winkler and the assigned elementary law of wear. The obtained theoretical results were compared with the available experimental data. It is demonstrated that the proposed model is adequate for the actual process of fretting corrosion.

The plane problem of the sliding contact of a punch with an elastic foundation when there is friction and wear is considered. Assuming the existence of a steady solution in a moving system of coordinates, relations are derived between the sliding velocity, the wear, the contact stresses and the displacements for an arbitrary dependence of the wear rate on the contact pressure. Taking into account the presence of a deformation component of the friction force, an equation is written for the balance of the mechanical energy for the punch - elastic base system considered. It is shown that the equality of the work of the external force in displacing the punch to the losses due to friction and the change in the shape of the foundation due to wear is satisfied when the work done by the contact stresses on the increments of the boundary displacements is equal to zero, and the frictional losses must be determined taking into account the non-uniformity of the distributions of the shear contact stresses and the sliding velocity in the contact area. Two special cases of the foundation in the form of a wide and narrow strip are considered, for which the total coefficient of friction is calculated, taking into account the deformation component of the friction force.

A number of formulations of the contact problem of the theory of elasticity when there is friction present in the case of unidirectional relative sliding of the interacting bodies (movable coupling of the sliding guide type) are considered. Particular attention is given to the behaviour with time of the contact shearing stress q 1 in a plane perpendicular to the sliding direction. It is established that this stress relaxes (decays) with time, which may serve as a basis for formulations of contact problems with unidirectional sliding of bodies, assuming that there is no stress q 1 in the contact area [1–4] .

Additional results on calculating the deformation force of friction for a rough indenter sliding on a viscoelastic foundation are presented. The results consider the influence of the roughness on the normal contact load. As in earlier studies, the deformation properties of a foundation are described by the Kelvin model and the roughness of an indenter is represented by the Cantor–Borodich fractal, which consists of a set of rectangular asperities.

A method for solving a certain system of singular integral equations with constant coefficients is proposed. It is based on a procedure for reducing singular equations to equations with continuous difference kernel; the solution of the latter is constructed by using the classical Fourier transform in the class of absolutely integrable functions. Explicit expressions for the solution of the singular integral equations under consideration are obtained.

The contact deformation of a thick elastic strip when there are shear boundary stresses is considered. The existing asymptotic relations, which describe such interaction, are represented in the form of a system of two singular integral equations of the deformation of an elastic half-plane with additive corrections for the finiteness of the width of the strip. A similar form of writing the equations to a large extent formalizes the transfer of the formulations and the methods of solving problems for a half-plane to similar thick-strip problems. The problem of the indentation of a punch into a strip with adhesion is considered as an example.

Asymptotic dependences of the deformation on the contact stresses are derived for a strip of variable width bound to an elastic half-plane. Similar relations were previously obtained in [1] for a strip of constant width.

We obtain sufficient conditions for the convergence of successive approximations to the solution of operator equations. We show how these conditions can be used in the case of nonlinear integral Hammerstein-type equations.

The approach previously described [11 for solving the contact problem with adhesion is extended to the case of a punch of arbitrary shape acted upon by a tangential load. The contact problem with adhesion for a symmetrical punch with a contact area that increases as a result of the loading was considered in [2-4] using an incremental approach. A solution of this problem was also given in [1] based on inversion, using the method described in [5], of the system of singular integral equations for the contact stresses, and an analysis of the additional conditions which ensure that this inversion is correct.

A new method of solving the problem of the adhesive penetration of a punch into an elastic half-plane is proposed, based on the well-known [1] procedure of inverting the equations for the contact stresses. The problem is considered in the refined formulation, which takes into account the tangential displacement of the boundary in the boundary condition for the normal displacement. A similar problem was solved previously in [2–4] using the incremental approach, which requires additional transformations of the initial equations.

The sensing of phase front of the vortex laser beams has been carried out with the help of a Hartmann-Shack sensor. The vortex beam is generated in the form of a Laguerre-Gaussian beam (LG0 1 mode) with the help of the special helicoidal phase plates manufactured by the kinoform technology. The measured shifts of focal spots on the hartmannogram are compared with the calculated shifts. From the measured wave front tilts the reconstruction of singular phase surface has been performed with using the novel reconstruction technique. The phase surface reconstruction is demonstrated in the case of distorted vortices as well. The correction of an optical vortex is undertaken in the close-loop adaptive system including the bimorph deformable piezoceramics-based mirror.