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Valentin L. Popov

Publications and source records attributed to Valentin L. Popov.

At least 19 recordsLinked to original sources
arXiv2020

Shape of a sliding capillary contact

We consider a classical problem of a capillary neck between a parabolic body and a plane with a small amount of liquid in between. In the state of thermodynamic equilibrium, the contact area between the bodies and the liquid layer has a circular shape. However, if the bodies are forced to slowly move in the tangential direction, the shape will change due to the hysteresis of the contact angle. We discuss the form of the contact area under two limiting assumptions about the friction law in the boundary line.

cond-mat.soft↗
arXiv2020

Dynamic Stiction Mode by Friction Vector Rotation

We numerically study a simple sliding system: a rigid mass pulled by a spring with a strong in-plane stiffness anisotropy and a small misalignment angle. Simulations show that the apparent stick phase appearing in this system is in reality a phase of very slow creep, followed by a rapid sliding, slip. Surprisingly, the absolute value of the friction force remains almost constant from the very beginning of the stick phase, merely rotating in the sliding plane. We call this specific mechanism of apparent stick due to rotation of the force vector "dynamic stiction".

cond-mat.soft↗
arXiv2020

Adhesive and non-adhesive contact of a rigid indenter and a thin elastic layer with surface tension

We consider an adhesive contact between a thin soft layer on a rigid substrate and a rigid cylindrical indenter ("line contact") with account of the surface tension of the layer. First, it is shown that the boundary condition for the surface outside the contact area is given by the constant contact angle - as in the case of fluids in contact with solid surfaces. In the approximation of thin layer and under usual assumptions of small indentation and small inclination angles of the surface, the problem is solved analytically.

cond-mat.soft↗
arXiv2018

Boundary Element Method for non-adhesive and adhesive contacts of a coated elastic half-space

We present a new formulation of the Boundary Element Method (BEM) for simulating the non-adhesive and adhesive contact between an indenter of arbitrary shape and an elastic half-space coated with an elastic layer of different material. We use the Fast Fourier Transform based formulation of BEM, while the fundamental solution is determined directly in the Fourier space. Numerical tests are validated by comparison with available asymptotic analytical solutions for axisymmetric flat and spherical indenter shapes.

cond-mat.soft↗
arXiv2018

Indentation of concave power law profiles with arbitrary exponents

We study analytically and numerically the process of indentation of cylindrical rigid indenter with concave face in form of a power-law function. In the well-known case of a parabolic concave indenter, the contact starts at sharp edges of the indenter and spreads inwards with increasing indentation depth. For all profiles with the exponent larger than 2, the contact area first spreads from the boarder inwards, but then a contact is established in the center of the indenter. Finally, the outer ring spreads inwards and the central contact area outwards until the complete contact is achieved. The critical indentation depth for the full contact is calculated ones proceeding from the full contact and looking for the condition of vanishing pressure and also proceeding from incomplete contact (in this case numerically, using Boundary Element Method). The results of both approaches coincide.

cond-mat.soft↗
arXiv2018

Adhesive contact between a rigid body of arbitrary shape and a thin elastic coating

Application of the principle of energy balance to a rigid indenter in contact with elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more complicated asymptotic analysis. This criterion allows calculating the adhesive strength of arbitrary contact of a flat-ended indenter, which occurs to be proportional to the area of the face of the indenter and does not depend on its shape. Similarly, the adhesive contact problem can be easily solved in the case of arbitrary three-dimensional shape.

cond-mat.soft↗
arXiv2018

Detachment of adhesive normal contact between a rigid circular flat punch and a viscoelastic half-space

We propose an approach to describe the propagation of a crack (or boundary of an adhesive contact) in a viscoelastic material which is only based on the consideration of the rheology of the material without the introduction of any additional dependency of the separation energy on the velocity of crack propagation. The suggested idea is illustrated with an example of kinetics of detachment of a flat-ended indenter from a viscoelastic medium. It is shown that under the given assumptions the crack propagation is accelerating until the critical configuration is reached and the contact detaches instantaneously. The suggested criterion can be basically applied to arbitrary shapes and arbitrary loading histories.

cond-mat.soft↗
arXiv2017

On the Rabinowicz like criterion of formation of wear particles in a system with a soft surface layer

In 1958, Ernest Rabinowicz suggested a simple criterion distinguishing the regimes of plastic smoothing and formation of wear particles in a contact of homogeneous sliding bodies. However, he did not consider any detailed mechanism of either plastic smoothing or debris formation. In a recent paper in Nature Communications, Molinari et al. have confirmed the criterion using explicit mesoparticle simulation. The work of Molinari's group provides a strong support to the general concept of Rabinowicz which is based on the consideration of competition of plastic deformation and fracture. It is interesting to apply this concept to more general configurations than those considered by Rabinowicz and Molinari's group. An important case is a system having a very soft surface layer. In the present paper, the analysis similar to that of Rabinowicz is applied to materials with soft layer. It is shown that in this case, too, both cases of plastic deformation and debris formation may occur. It would be interesting to verify this prediction by explicit meso-particle simulations similar to those of Molinari's group.

cond-mat.mtrl-sci↗
arXiv2017

Thermo - mechanical instabilities in friction contact

The phenomenon of corrugated surfaces is a known technical problem of tribological systems; considerable work has been published in the past on the aspect of rail corrugation of railway systems. Less known is a similar phenomenon observed within the cylinder-piston system of advanced automotive engines using aluminium cylinders. This paper investigates the condition leading to cylinder corrugation in the piston/cylinder system. Material investigations strongly indicate that heat in the contact is playing a major role. Using basic analytical relationships from contact mechanics, the condition required for the onset of such thermo-mechanical instabilities are investigated. Using the concept of a critical velocity it is shown that such instabilities can occur for a realistic set of parameters. A significant technical key factor is the friction coefficient.

cond-mat.mtrl-sci↗
arXiv2017

On the application of the Method of Dimensionality Reduction to two-dimensional contacts

The conventional formulation of the Method of Dimensionality Reduction (MDR) in contact mechanics is only applicable two "point contacts", that is to contacts of two unbounded three-dimensional bodies over final contact area. We analyze here if it is possible to find an at least approximate formulation of the MDR for "line contacts", that is contacts which contact area is unbounded in one direction. In this case the problem can be formulated as contact of two two-dimensional half-"spaces".

cond-mat.mtrl-sci↗
arXiv2017

Surface profiles with zero and finite adhesion force and adhesion instabilities

A simple but general analysis of stability of axis-symmetric adhesive contacts is provided. Adhesion is considered in the JKR-approximation. Depending on the shape of the contacting bodies, various scenarios are possible, including vanishing adhesive force, complete contact as well as transitions between these states.

cond-mat.soft↗
arXiv2016

Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials

Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single force acting on the surface of a half space with a power-law varying elastic modulus, the deformation produced by constant pressure acting on a rectangular element was calculated and the influence matrix was obtained for a rectangular grid. The inverse problem for the calculation of required stress in contact area from a known surface deformation was solved by use of conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used which drastically reduces the computation time. For the adhesive contact of graded material, the detachment criterion based on the method of Pohrt and Popov was proposed. A number of numerical test for the problem having exact analytical solution have been carried out confirming the correctness of underlying ideas and numerical implementation.

cond-mat.soft↗
arXiv2016

Reduction of friction by normal oscillations. I. Influence of contact stiffness

The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period, so that the sample starts to "jump". It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters - a dimensionless sliding velocity and dimensionless oscillation amplitude. This function in turn depends on the shape of the contacting bodies. In the present paper, analysis is carried out for two shapes: a flat cylindrical punch and a parabolic shape. Here we consider "stiff systems", where the contact stiffness is small compared with the stiffness of the system. The role of the system stiffness will be studied in more detail in a separate paper.

nlin.CD↗
arXiv2016

Reduction of friction by normal oscillations. II. In-plane system dynamics

The influence of out-of-plane oscillations on friction is a well-known phenomenon that has been studied extensively with various experimental methods, e.g. pin-on-disk tribometers. However, existing theoretical models have yet achieved only qualitative correspondence with experiment. Here we argue that this may be due to the system dynamics (mass and tangential stiffness) of the pin or other system components being neglected. This paper builds on the results of a previous study (Popov M. et al. Friction, 2016, submitted) by taking the stiffness and resulting dynamics of the system into account. The main governing parameters determining macroscopic friction, including a dimensionless oscillation amplitude, a dimensionless sliding velocity and the relation between three characteristic frequencies (that of externally excited oscillation and two natural oscillation frequencies associated with the contact stiffness and the system stiffness) are identified. In the limiting cases of a very soft system and a very stiff system, our results reproduce the results of previous studies. In between these two limiting cases there is also a resonant case, which is studied here for the first time. The resonant case is notable in that it lacks a critical sliding velocity, above which oscillations no longer reduce friction. Results obtained for the resonant case are qualitatively supported by experiments.

nlin.CD↗
arXiv2016

Influence of tangential displacement on the force of adhesion between a parabolic profile and plane surface

The force of adhesion of a rotationally symmetric indenter and an elastic half-space is analyzed analytically and numerically using an extension of the method of dimensionality reduction (MDR) for superimposed normal/tangential adhesive contacts. In particular, the dependency of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The developed method is applicable straightforwardly to adhesive contacts of any bodies of revolution.

cond-mat.soft↗
arXiv2016

Generalized master curve procedure for elastomer friction taking into account dependencies on velocity, temperature and normal force

In the sliding contact of elastomer on a rigid substrate, the coefficient of friction may depend on a large number of system and loading parameters, including normal force, sliding velocity, shape of contacting bodies, surface roughness and so on. It was argued earlier that the contact configuration is determined more immediately through the indentation depth than the normal force, and thus the indentation depth can be considered as one of "robust governing parameters" of friction. Both models of friction of simple shapes and fractal surfaces demonstrate that the coefficient of friction of elastomers should be generally a function of dimensionless combinations of sliding velocity, surface gradient, relaxation time and size of micro-contacts. The relaxation time does depend only on temperature and the surface slope and the size of micro contacts mostly on the indentation depth. Based on this general structure of the law of friction, we propose a generalized master curve procedure for elastomer friction where the significant governing parameter - indentation depth (or normal force) was taken into account. Unlike the generation of the classical master curve by horizontal shifting of dependence "friction - logarithm of velocity" for different temperatures, in the case of various indentation depth the shifting in both horizontal and vertical direction is required. We experimentally investigated coefficient of friction of elastomer on sliding velocity for different indentation depths and temperatures, and generated a master curve according to this hypothesis.

cond-mat.mtrl-sci↗
arXiv2015

The influence of system dynamics on the frictional resistance: insights from a discrete model

In order to examine the influence of system dynamics on sliding friction, we introduce the so-called micro-walking machine. This model consists of a rigid body with a number of elastic contact spots that is pulled by a constantly moving base. The system slides with dry friction on a rigid substrate. The kinematic coupling of the rotation and the translation of the rigid body results in varying normal and tangential forces at the contact spots. For certain parameter ranges this leads to self-excited oscillations in the vertical direction. A particular dynamic mode occurs which is characterized by a strong correlation between low or even zero normal forces and a fast forward motion. This effect is referred to as micro-walking. In addition to an experimental rig we use numerical integration and an extensive parameter study for the analysis. In theory, the reduction of the frictional resistance reaches up to 98%. These results are confirmed by the experiments where the maximal reduction was 73%. Our model shows that micro-vibrations play an important role for the dynamic influences on the frictional resistance of systems that exhibit apparently smooth sliding. The identification of the critical parameter range enables the systematic control of frictional resistance through the adjustment of attributes such as geometry and stiffness. In addition, it is possible to deduce guidelines for how tribological test rigs should be designed in order to get reliable results.

cond-mat.mtrl-sci↗