The equilibrium of the "heat-protective coating-substrate" system with an interface crack under the influence of a heat load localized at the upper boundary of the coating is considered. The coating-substrate system is modeled as a non-uniform band. The crack is modeled as a mathematical section, the banks of which are heat-insulated and stress-free; this leads to temperature and displacements jumps. The task is to find temperature jumps and displacements (opening functions) on the banks of the crack. Knowing the opening functions, you can calculate the stress-strain state at any point in the band. At the first stage, the problem of stationary thermal conductivity with a crack is solved. The solution is based on a combination of the Fourier transform and the targeting method. A hypersingular integral equation is obtained with respect to the temperature jump function on the separation. At the second stage, the problem of unbound thermoelasticity is solved. A system of hypersingular integral equations with respect to disclosure functions is obtained. The solution of integral equations is based on the collocation method, taking into account the behavior of transfer functions. The case of continuous change of material characteristics across the boundary of the "coating-substrate" section is considered. It was found that the value of the temperature jump is proportional to the amplitude of the heat flow; the temperature jump increases as the coating thickness decreases. In the case of a load that is located symmetrically relative to the center of separation, the temperature jump function and the opening function also have symmetry.

Рассмотрено равновесие системы "теплозащитное покрытие-подложка" с интерфейсной трещиной под действием тепловой нагрузки, локализованной на верхней границе покрытия. Задача состоит в нахождении скачков температуры и перемещений (функций раскрытия) на берегах трещины. На первом этапе решается задача стационарной теплопроводности с трещиной. Решение основано на сочетании преобразования Фурье и метода пристрелки. Получено гиперсингулярное интегральное уравнение относительно функции скачка температуры на отслоении. На втором этапе решается задача несвязанной термоупругости. Получена система гиперсингулярных интегральных уравнений относительно функций раскрытия. Решение интегральных уравнений базируется на методе коллокаций. Построены функции раскрытия в случае функционально-градиентного покрытия.