Estimates of Temperature Stresses in Models of Dynamic Thermoelasticity
The study focuses on the mathematical models of the heat shock theory in terms of dynamic thermoelasticity and describes the constitutive relations for boundary value problems based on hyperbolic equations (the idea of local nonequilibrium of the heat transfer process), which underlie the investigated models. Boundary conditions of the first, second, and third kinds are presented in a generalized form for the corresponding types of thermal action on the boundary of a solid surface. Relying on operational solutions of the corresponding dynamic problems, the paper introduces a new approach to the study of the thermal reaction of a solid during intense heating or cooling of its surface. Furthermore, practically important engineering design relations are proposed for the upper estimate of thermal stress through stress jumps at the front of a thermoelastic wave. The latter makes it possible to quickly and qualitatively estimate the degree of danger of short-term dynamic stresses. Meanwhile, there is absolutely no need in a complex software package for numerical experiments based on exact analytical solutions to the problem of identifying the kinetics of changes in temperature stresses and establishing maximum and minimum points for comparing stresses with ultimate strength material on the reference data of the parameters included in the obtained estimates