Roman Kulchytsky-Zhyhailo

Stress Distribution in Rotating Solids with Frictional Heat Excited Over Contact Region

The present contribution is devoted to discussion of axially symmetric contact problems for two smooth solids, pressed against each other in relative rotation, generating heat due to the friction between them. We discuss and compared solutions for two extreme cases, namely when the unloaded surfaces of solids are thermally insulated, and when the heat exchange is so large that it is justified to assume that the temperature of the outside region of contact can be assumed zero. We prove that the distribution of contact pressure and the radius of contact region are the same in both the cases of thermal conditions. The thermal stresses, however, differ considerably. We analyze the distribution of the second invariant of the stress deviator, and we discuss the possibility of appearance of tensile stresses.

A NONIDEAL CONTACT PROBLEM OF THERMOELASTICITY FOR TWO SOLIDS WITH A HEAT SOURCE

A generalized Hertz problem of thermoelastic solids in pressure, contacting over convex surfaces, has been discussed. At a certain moment of time a concentrated source of heat starts acting. Therefore the heat flux flowing through the region of contact is nonstationary. The problem considered is axially symmetric. The purpose is twofold: first the problem of thermoelasticity with time variation of temperature is taken into account; second the “paradox of a cooled sphere” has been investigated under time-dependent conditions. There is a possibility that the character of the boundary conditions can change in time. To obtain the solution we have applied the Laplace and Hankel integral transforms. The main point is to discuss the cases when the boundary conditions are such that the problem can be considered in terms of classical thermoelasticity and when the Barber-type boundary conditions have to be used. The solution has been obtained by means of a devised numerical algorithm such that the procedure is simplified. The results have been presented in diagram form suitable for discussion.

Semi-analytical solution of three-dimensional thermoelastic problem for half-space with gradient coating

Abstract The article deals with a homogeneous isotropic thermoelastic half-space with an inhomogeneous gradient coating under thermal loadings over an elliptically shaped area. The shear modulus, the thermal expansion, and thermal conductivity coefficients depend exponentially on the depth from the boundary surface, and the Poisson ratio is constant in the coating layer. The considered three-dimensional problem is solved by using the double-Fourier transform method. The distributions of displacements, temperature, and stresses are presented in the integral forms and analyzed numerically.

STRESSES IN COATING WITH GRADIENT INTERLAYER CAUSED BY CONTACT LOADING

Abstract The three-dimensional problem of elasticity concerning inhomogeneous half-space under normal and tangential loading applied in circular region was considered. The half-space is composed of the homogeneous body and double-layer coating which includes a homogeneous top coat and a gradient interlayer. The solution method is based on the two-dimensional integral Fourier transform. The influence of mechanical properties of coatings component and coefficient of friction on the first principal stress distribution was considered.

Stress Distribution in a Composite Coating by Local Loading of the Free Surface

Abstract A three-dimensional problem of the theory of elasticity for halfspace with multilayered coating with periodical structure is considered. The fundamental layer consists of two layers with different thicknesses and different mechanical properties. The coating is described by the homogenized model with microlocal parameters. The solution is derived by using integral Fourier transform. Calculations were conducted with the assumption of elliptical distribution of normal and tangential tractions applied to the surface of the layered system in a cir-cular area. Analysis of the stresses was restricted to the first principal stress distribution.

Axisymmetric Heat Conduction Problem for a Half-Space Covered with a Laminated Coating of Periodic Structure

The paper deals with a stationary heat conduction problem for a microperiodic, two-layered coating on a homogeneous half-space. The distribution of temperature and heat fluxes are obtained within the frame of the homogenized model with microlocal parameters [1,2, and within the framework of the classical heat conduction problem for a periodically layered structure. The influence of number of layers in the coating on the heat flux and temperature is analyzed.