Papers by Sergey Aizikovich
Archive of Applied Mechanics, 2015
Torsion of a non-deformable circular punch attached to an elastic half-space with functionally gr... more Torsion of a non-deformable circular punch attached to an elastic half-space with functionally graded or multilayered coating is considered. The coating is represented by a set of alternating soft and hard (in terms of shear modulus values) layers. The boundaries of the layers can be sharp (piecewise-constant variation of the shear modulus) or smooth (continuously inhomogeneous or functionally graded coatings). An approximate analytical solution of high accuracy applicable for any value of coating thickness is constructed. The influence of number of layers and type of the boundaries between them on the kernel transform of the integral equation and on the contact stresses under the punch is investigated. It is shown that for certain parameter values of the problem substantial differences between the results for the continuous and piecewise-constant variation of the shear modulus with depth are obtained.
Key Engineering Materials, 2007
Recent advances in nanotechnology have revealed numerous new methods of manufacturing functionall... more Recent advances in nanotechnology have revealed numerous new methods of manufacturing functionally graded coatings and materials, but progress in this field is limited by the lack of knowledge about the mechanical behavior of such structures. Existing models of the mechanics of layered structures are not generally adequate for this purpose, since functionally graded structures can exhibit both qualitative and quantitative behavioral differences in comparison with homogeneous or layered structures, particularly if there is a significant gradient of elastic properties in the coating. In applications, interest is focused mainly on the deformation fields and stresses inside the inhomogeneous material caused by the contact tractions. Stresses at the interface between the functionally graded coating and the elastic half-space are of particular interest because of their influence on the propagation of cracks and other defects on this interface. Shear stresses at this interface associated with rapid variation in elastic properties with depth are particularly dangerous because of potential delaminations. In their work the authors: • develop a precise mathematical model and of the computational methods which makes it possible to achieve stable numerical results while analyzing the mechanical properties of functionally graded coatings; • study the variation effect in elastic properties on the maximum stresses in the surface layers of materials with functionally graded coatings caused by indentation.
An approximate analytical-numerical solution to the axisymmetric problem on thermo-mechanical ind... more An approximate analytical-numerical solution to the axisymmetric problem on thermo-mechanical indentation of a flat cylindrical punch into an arbitrarily-nonhomogeneous elastic halfspace is constructed by making use of the bilateral asymptotic method. The key point of this method lies in evaluation of the kernels in the obtained integral equations by making use of a numerical technique. Once the structure of the kernel is defined, it then is approximated by an analytical expression of special kind so that the solution of the integral equation can be achieved analytically. This fact allows for construction of the solution in an analytical form, which is convenient for analysis of the mechanical effects concerned with arbitrarily presumed nonhomogeneity of the material.
An investigation is presented of dual integral equations generated by various plane contact probl... more An investigation is presented of dual integral equations generated by various plane contact problems: a strip resting without friction on a rigid base (Problem 1), a strip clamped along the base (Problem 2), a wedge with a clamped face (Problem 3), and also be axisymmetric problems relating to the action of a ring-shaped stamp on a half-space (Problem 4), and the interaction of an elastic bandage with an elastic cylinder /1/ (Problem 5). The strip, wedge, half-space and cylinder may be uniform, laminar of continuously inhomogeneous. Analogous equations in terms of Laplace transforms are obtained in problems of coupled thermo-elasticity and consolidation theory of water-saturated media for the bodies listed here /2/.The method described in /3/ is generalized to construct solutions of the above problems. Well-posedness and solvability classes are established for the equations, proving that the approximate method proposed here is asymptotic in both directions with respect to a characte...
International Journal of Solids and Structures, 2015
Mechanics of Composite Materials, 2011
An approximate analytical method allowing one to efficiently solve, to a preassigned accuracy, co... more An approximate analytical method allowing one to efficiently solve, to a preassigned accuracy, contact problems for materials with properties arbitrarily varying in depth is developed. Its possibilities are illustrated with the example of torsion of an elastic half-space, having a coating inhomogeneous across its thickness, by a circular stamp. All the results obtained are rigorously substantiated. For the approximate solutions constructed, their error is analyzed. The asymptotic properties of the solutions are investigated. The cases of a nonmonotonic change in the elastic properties are considered. In particular, the analytical solutions are examined in the case where the variation gradient of the elastic properties changes its sign many times. The results derived allow one to solve the inverse problems of elasticity theory of inhomogeneous media (e.g., the problem on controlling the variation in the elastic properties of a covering across its thickness).
Zeitschrift für Metallkunde, 2005
Ultrathin polymeric films devoted for nanoimprint lithography were tested. Atomic force microscop... more Ultrathin polymeric films devoted for nanoimprint lithography were tested. Atomic force microscopy was used to study the surface topography, and the adhesive and nanomechanical/tribological behaviour. The wetting properties of the films were also evaluated, using a special test rig for the contact angle measurements.
Doklady Physics, 2009
ABSTRACT A method to find analytical solution for the problem of disk cracking in functionally gr... more ABSTRACT A method to find analytical solution for the problem of disk cracking in functionally gradient space was reported. The method was based on the assumption that shear modulus of the medium remained constant and the Poisson ratio varied according to an arbitrary law when leaving the crack plane. The method used the axisymmetric static problem for a normal-separation disk crack in an elastic inhomogeneous isotropic space. It was found that the crack was located in the plane and its center coincided with the coordinate origin. It was also observed that the strains, stresses, and displacements of crack were independent of angular coordinate. The method also found a relationship between normal stresses and the normal displacements of the half-space surface. The method determined the relative values of stress-intensity coefficients for various heterogeneity depending on the reduced crack size.
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013
An approach for constructing semi-analytical solutions in contact problems of the theory of elast... more An approach for constructing semi-analytical solutions in contact problems of the theory of elasticity for inhomogeneous layers is developed. The approach is efficient for the layer of arbitrary thickness which is either continuously inhomogeneous (functionally graded) or piecewise homogeneous (i.e. presented as a set of homogeneous layers with different elastic properties). The foundation is also assumed to be elastic, but much stiffer than the layer. The loads considered address the case of axisymmetric contact problems under torsion and indentation of a rigid circular punch with the flat base. The technique based on integral transforms is used to reduce the problems to the integral equations. Special approximations for the kernel transforms are used to obtain analytical solutions of the integral equations. The main results include computations of the profiles of contact stresses under the punch and the dependences of displacements with depth for different types of variation of elastic properties in the layer. The results are also compared with those obtained by other methods.
Frattura ed Integrità Strutturale, 2018
Ultrasonic vibrothermography is an effective and non-destructive method, which can be used for a ... more Ultrasonic vibrothermography is an effective and non-destructive method, which can be used for a quick detection of coating defects on large surfaces. Mechanical excitation of a layered structure induces inelastic deformation and, as a consequence, energy dissipation in the defective area and local heating. In this work, a three-dimensional numerical simulation of this process is applied to the bi-metallic layered structure with an edge crack. Two models of energy dissipation are considered (hysteretic damping model and visco-elastic Maxwell's model) for simulation of energy dissipation in a crack tip area under ultrasonic loading. The models allow us to study the effects of the loading frequency, loading direction and location of the coating defects on the heat dissipation and propose optimal regimes for the ultrasonic vibrothermography of bi-metallic layered structures.
An axisymmetric static problem for a penny-shaped crack in heterogeneous isotropic elastic space ... more An axisymmetric static problem for a penny-shaped crack in heterogeneous isotropic elastic space is considered. It is assumed axisymmetric distributions of the Young modulus, Poisson's ratio and residual stresses coaxial with the crack axis. The elastic moduli vary in orthogonal direction to the crack plane in accordance with specific laws. The analysis is performed for the case of co-sinusoidal distributions of the residual stresses, for which we compute the mode I stress intensity factors for the crack during its quasistatic growth. Introduction The development of numerical methods for analysing crack propagation in Functionally Graded Materials (FGM) is an important problem of material sciences. In this study a 3D problem of elastostatics addressing the quasistatic growth of a penny-shaped crack in a heterogeneous isotropic FGM medium subjected to axisymmetric external and residual loads is considered. The method utilises the previously developed analytical approach reported ...
Nanomaterials, 2020
The study focuses on in vitro tracing of some fundamental changes that emerge in teeth at the ini... more The study focuses on in vitro tracing of some fundamental changes that emerge in teeth at the initial stage of caries development using multiple approaches. The research was conducted on a mostly sound maxillary molar tooth but with a clearly visible natural proximal white spot lesion (WSL). Values of mineral density, reduced Young’s modulus, indentation hardness and creep as well as the molecular composition and surface microstructure of the WSL and bordering dentine area were studied. The results obtained were compared to those of sound enamel and dentine on the same tooth. A decrease of mechanical properties and mineral density both for the WSL and bordering dentine was detected in comparison to the sound counterparts, as well as increase of creep for the enamel WSL. Differences in molecular composition and surface microstructure (including the indenter impressions) were found and described. WSL induces a serious change in the state of not only the visually affected enamel but al...
Problems of Strength and Plasticity, 2015
Problems of strenght and plasticity, 2019
The paper addresses to the plane contact problem on an electrode on the surface of a functionally... more The paper addresses to the plane contact problem on an electrode on the surface of a functionally graded piezoelectric coating glued with no friction with a homogeneous piezoelectric half-plane. The coating and the substrate are assumed to be transversely isotropic, the axis of isotropy coincides with the axis of polarization and normal to the surface of the coating. Arbitrary independent variation of the electroelastic properties of the coating in depth is considered. Plane electrode is placed on the surface of the coating and potential difference is applied which leads to an el ectroelastic deformation of the coating and substrate. Using the integral transformation technique, the problem is reduced to the solution of the dual integral equation. This equation is solved by the bilateral asymptotic method, based on an idea of using Pade approximation of the kernel transform of the integral equation. An approximated dual integral equation is solved in a closed analytical form. Approxi...
Symmetry, 2019
Elastoplastic analysis of a composite cylinder, consisting of an isotropic elastic inclusion surr... more Elastoplastic analysis of a composite cylinder, consisting of an isotropic elastic inclusion surrounded by orthotropic matrix, is conducted via numerical parametric studies for examining its residual stress under thermal cycles. The matrix is assumed to be elastically and plastically orthotropic, and all of its material properties are temperature-dependent (TD). The Hill’s anisotropic plasticity material model is adopted. The interface between the inclusion and matrix is perfectly bonded, and the outer boundary of the cylinder is fully constrained. A quasi-static, uniform temperature field is applied to the cylinder, which is analyzed under the plane-strain assumption. The mechanical responses of the composite cylinder are strongly affected by the material symmetry and temperature-dependent material properties. When the temperature-independent material properties are assumed, larger internal stresses at the loading phase are predicted. Furthermore, considering only yield stress bein...
Вестник Донского государственного технического университета, 2015
The ion-plasma sprayed titanium nitride (TiN) coating on the prepared 40Cr steel substrate is inv... more The ion-plasma sprayed titanium nitride (TiN) coating on the prepared 40Cr steel substrate is investigated. A part of the coating surface was covered by the copper foil mask to measure its thickness afterwards. The properties and characteristics of the sample surface microtopography before and after coating deposition are studied by the atomic-force microscopy (AFM). The technique for the high-precision determination of the coating thickness using the results of the AFM scanning of the transition area between the substrate and the coating on the sample surface is described and applied. The calculated uncertainty of the measured value of thickness is significantly less than in other methods. Mechanical properties of the coating are measured by the instrumental indentation method; the significance of an accurate determination of the correct thickness for measuring the coating characteristics by the indentation technique is shown.
The problem about torsion by a circular indenter with flat base of transversely isotropic elastic... more The problem about torsion by a circular indenter with flat base of transversely isotropic elastic half-space with an inhomogeneous coating is studied. Mathematical statement of a problem is formulated. The problem is reduced to dual integral equations by using integral transformations technique. The scheme of numerical construction of kernel's transform of the integral equation is provided. Approximations of kernel's transform are constructed by expressions of a special kind. Analytical solutions of a problem are constructed for these approximations. It is proved that the constructed solutions are asymptotically exact both at large and small values of characteristic dimensionless geometrical parameter of the problem. The distribution of displacements and contact stresses on depth in cases of continuous variation of elastic properties in coating and homogeneous coating are analyzed.
In this work we consider the axially symmetric quasi-static problem of thermoelasticity for funct... more In this work we consider the axially symmetric quasi-static problem of thermoelasticity for functionally graded half-space, with elasticity modulus, Poisson ratio, heat conduction and linear expansion coefficients varying continuously in the near-surface layer. It is supposed that the area in the circle with known radius is being heated by the heat source with time-constant temperature. Outside the circle the surface is perfectly insulated. Analytic methods are used to solve the problem, particularly, the Hankel`s integral transform. At first solution reduces to solution of two-point boundary problem for system of ODEs with varying coefficients of sixth order. For stability of numerical solution of system, modulating functions method is used. Solution of mixed boundary problem then reduces to solution of dual integral equation. Properties of kernel transform allows us to apply well-established bilateral asymptotic method. Using this method, approximated expressions for heat flow and...
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Papers by Sergey Aizikovich