Simulation of temperature field in a partially delaminated thermal barrier coating

Досліджено температуру термобар’єрного покриття, спричинену різницею температур основи та довкілля за теплообміну з довкіллям на лицевій поверхні покриття та недосконалого теплового контакту на інтерфейсі покриття-основа, що характеризується локальним підвищенням термоопору на ділянці міжфазного розшарування. Запропоновано спосіб зведення крайової задачі теплопровідності для покриття до системи інтегральних рівнянь Фредгольма другого роду відносно функцій, що є лінійними комбінаціями інтегральних характеристик температури покриття (середньої температури і температурного моменту). Побудовано числову схему розв’язування інтегральних рівнянь з використанням методу квадратурних формул. Наведено результати числового аналізу розподілу інтегральних характеристик температури в покритті – середньої температури та температурного моменту.The problem of determining temperature in a thin partially delaminated thermal barrier coating is considered taking into account the convective heat exchange with the surrounding environment at the front and end surfaces of the coating and the imperfect thermal contact with the base, which is modeled by thermal resistance. In view of deterioration of heat exchange between the base and the coating in the separation region, thermal resistance in this region is assumed to be greater than thermal resistance in the regions of full adhesion. The heat-transfer coefficient at the front surface of the coating is coordinate-dependent. With the use of the propositions of heat conduction in thin elements of constructions, a model for describing temperature field in a partially delaminated coating, caused by the difference between the temperatures of the base and the surrounding environment, is proposed. Utilizing the method of variation of constants, an approach for reducing the heat conduction boundary value problem for the coating to a system of Fredholm integral equations of the second kind for the functions that are linear combinations of the integral characteristics of the coating temperature (the mean temperature and the temperature moment) and the temperature of the surrounding environment and the base is developed. A numerical scheme for solving the system of integral equations is constructed using the quadrature method. In particular, Simpson's quadrature formulae are utilized to evaluate the integrals, and the system of Fredholm integral equations of the second kind is reduced to a system of linear algebraic equations. The results of numerical analysis of temperature distribution at the front surface of the coating and at the interface between the coating and the base are given for the case of thermal insulation of the end surfaces and the case of convective heat exchange with the surrounding environment at them. The distributions of the mean temperature and the temperature moment are examined for various values of thermal resistance in the separation region. It is revealed that an increase in thermal resistance leads to a significant temperature perturbation at the front surface as well as at the interface between the coating and the base. However, the value of the temperature moment in the separation zone is slightly decreasing in comparison with the case when the delamination does not occur at the interface between the coating and the base

Frictional contact of two solids with a periodically grooved surface in the presence of an ideal gas in interface gaps

The frictional contact between two solids, one of which having a periodically grooved surface, under the action of normal and shear load is investigated. The interface between the contacting solids consists of a periodic array of gas-filled gaps and a periodic array of contact regions, where stick-slip contact occurs. The corresponding plane contact problem is reduced to a set of two singular integral equations. A solution to the contact problem is obtained for a certain shape of the grooves. The analysis of dependences of contact parameters of the solids on the applied load and gas pressure is carried out

Rozwój stref plastycznych wokół międzyfazowej zamkniętej szczeliny, spowodowany strumieniem cieplnym

A bimaterial consisting of two conjugated half-planes possessing different thermophysical characteristics, with an interface crack closed due to external pressure is considered. The growth of interface plastic zones near the crack tips, caused by a heat flow and thermal resistance of crack faces, is investigated. The complex potentials of the problem that define main characteristics of the bimaterial thermal stress state are expressed in terms of interface jump discontinuities of temperature and tangential displacements, which simulate the crack and plastic zones. A system of singular integro-differential equations in these functions is obtained. The length of plastic zones is derived from the condition for interface shear stress boundedness in the tips of these zones. The closed form expresions for the displacement jumps of the bimaterial components and the plastic zones length are obtained for a certain thermal resistance.Praca poświęcona jest analizie utworzenia cienkich stref plastycznych wokół końców szczeliny umieszczonej na międzyfazowej granicy bimateriału złożonego z termicznie różnych półpłaszczyzn. Bada się rozwój odkształceń plastycznych spowodowany strumieniem cieplnym i oporem termicznym jej brzegów wokół końców zamkniętej zewnętrznym ciśnieniem szczeliny. Potencjały zespolone, które wyznaczają stan termosprężysty bimateriału, przedstawione są przez międzyfazowe nieciągłości temperatury i przemieszczeń stycznych, którymi modelowana jest szczelina i strefy plastyczne. Dla ich wyznaczania otrzymany jest układ równań singularnych całkowo-różniczkowych. Długość stref plastycznych oblicza się z warunku ograniczaności naprężeń stycznych międzyfazowych na końcach tych stref. Dla konkretnego oporu termicznego szczegółowo przeanalizowano nieciągłość przemieszczeń brzegów szczeliny i długość raf plastycznych

Thermoelastic behavior of a bimaterial with interface crack filled with an incompressible fluid

Thermo-stressed state of the bimaterial with the interfacial crack filled with an incompressible fluid is investigated. The bimaterial with zero Dundurs parameter is considered. The thermo-elastic problem is reduced to nonlinear systems of singular integro-differential equations for a temperature jump between the cracks faces and an opening crack. The pressure of the fluid is determined from the equation of the incompressible fluid. Using the method of successive approximations a numerical solution of the problem is constructed. The opening crack and temperature jump are determined by the finite sum for Chebyshev polynomials of the second kind. The coefficients for Chebyshev polynomials are determined from the system of linear algebraic equations. Having made numerical calculations, the dependences of the pressure of the fluid and the opening crack from the mechanical loads and density and direction of the heat flow have been constructed. The influence of fluid pressure on the stress intensity factor mode I are analyzed.Key words: bimaterial, interfacial crack, incompressible fluid, fluid pressure.Pages of the article in the issue: 206-209Language of the article: Ukrainia

Frictional contact of two solids with a periodically grooved surface in the presence of an ideal gas in interface gaps

The frictional contact between two solids, one of which having a periodically grooved surface, under the action of normal and shear load is investigated. The interface between the contacting solids consists of a periodic array of gas-filled gaps and a periodic array of contact regions, where stick-slip contact occurs. The corresponding plane contact problem is reduced to a set of two singular integral equations. A solution to the contact problem is obtained for a certain shape of the grooves. The analysis of dependences of contact parameters of the solids on the applied load and gas pressure is carried out