CALCULATION OF THERMAL STRESSES IN A SUBSTRATE−COATING SYSTEM
A. N. Astapov
Federal State-Funded Educational Institution of Higher Education "Moscow Aviation Institute (National Research University)", Moscow, Russia
D. V. Nushtaev
TESIS Limited Liability Company, Moscow, Russia
Lev N. Rabinskiy
Moscow Aviation Institute (National Research University),
4 Volokolamskoe Highway, Moscow, 125993, Russia
This publication is devoted to the creation and development of mathematical models and methods for estimating the level and regions of localization of thermal stresses arising in the substrate–coating system. The study of the strain–stress state (SSS) is carried out by successively increasing the
mathematical model used in order to increase the degree of conformity between the results obtained and the physics of the process under consideration.
The SSS, free from external forces and fastenings, was analytically investigated for a two-layer substrate–coating system under smooth thermal loading. A simply connected thermoelasticity problem was considered in the formulation of a plane-stress state. The SSS estimate was carried
out in the zero-moment approximation (without including the bending) under the assumption of a constant temperature over the wall thickness. The temperature dependences of thermal stresses in the wall layers were constructed. It was revealed that the current level of stress in the layers
depends, first of all, on the difference between the true coefficients of the temperature linear expansion
of the substrate and coating materials, as well as on the values of their elasticity moduli, Poisson's
coefficients, and thicknesses.
The numerical solution built on the basis of the finite element method (FEM) of the boundary-value problem of classical thermoelasticity, corresponding to the model underlying the analytical solution, led to identical results. The shortcomings and limitations introduced into the solution by the considered assumptions have been revealed.
A refined solution of the problem of determining the SSS in the substrate–coating system was proposed for thermal loading on the basis of the FEM, taking into account the arising flexural deformations. The solution was obtained for a semi-infinite plate in the formulation for generalized
plane deformation. of the account for bending led to a significant change in the level and nature of the distribution of thermal stresses along the wall thickness. It is shown that calculating SSS without explicitly taking into account the geometric shape of the substrate, even in the simplest case of a semi-infinite plate, leads to unacceptable errors. The basic requirements for finite-element models applied to the study of SSS in the substrate–coating system have been developed.
The SSS correction was carried out in the substrate–coating system on the basis of FEM by including the possibility of formation of irreversible plastic deformations in the coating layer at various temperatures. The associated flow law with the Mises yield criterion was used for the description of the elastic-plastic behavior of the coating material. It was shown that the appearance of inelastic deformations in the coating significantly affects the level of thermal stresses in the entire system.
The evaluation of the level and nature of the stress distribution makes it possible to scientifically approach the development of the coating architecture (the choice of the chemical and phase composition of the layers, their number and thickness), and to significantly reduce the number of experimental studies and tests, as well as the time and costs for their implementation.