ESTIMATION OF COUPLING IN A HEAT CONDUCTION EQUATION WITHIN THE DYNAMIC THEORY OF THERMAL ELASTICITY FOR A CLASS OF BRITTLE MATERIALS

Abstract

A heat conduction equation within the framework of the coupled dynamic theory of thermoelasticity is considered. Coupling in the heat conduction equation is estimated for a space with a constant initial temperature. This space contains a flat semi-infinite crack propagating at a constant velocity, and a constant temperature lower than an initial one (thermal shock) is instantly established on the edges of this space. The movement of the crack and the thermal shock on its shores determine dynamic effects that should be taken into account to estimate coupling in the heat conduction equation. It is demonstrated that, under real conditions of a thermal shock on massive bodies with cracks, one may ignore dynamic effects and coupling for materials that satisfy certain conditions imposed on their thermomechanical constants. This significantly simplifies the process of solving thermoelasticity problems for such bodies.