Thermal stresses in a coating layer. I. General theoretical scheme

Abstract

The evolution of thermal stresses generated by a thermal perturbation of cylindrical symmetry in a flat infinite isotropic thermoelastic layer of constant (before perturbation) thickness on a half-space rigid substrate is theoretically investigated. The problem is considered in the framework of uncoupled linear thermoelasticity, in the quasi-stationary displacement field approximation. Thermal insulation of the layer is considered in two versions: (a) both its surfaces are adiabatically insulated, and (b) the free surface is adiabatically insulated, whereas the contact surface is kept at constant temperature. The free surface of the layer is assumed to be stress free, and the contact surface is kept on a rigid substrate. The proper equations are solved using suitable Hankel and Fourier transformations. Part I of the paper presents a general theoretical scheme of the problem in a general case (without specification of the perturbation), and it is illustrated by a simple, detailed example (time evolution of stresses at the contact surface of the layer, generated by a surface point instantaneous heat pulse in case a). The analysis of stresses in more realistic cases, modeling realistic situations will be presented in Part II.