Thermo-stressed state of a body with a gas-filled crack

Abstract

The two-dimensional thermo-stressed state of a body containing a crack filled with an ideal gas
and subjected to a compressive load and a uniform steady heat flow is considered. The gas exerts
pressure on the faces of the crack, which is determined from the Mendeleev-Clapeyron equation,
and its effect on heat transfer between the crack faces is accounted for by thermal resistance,
which is proportional to a crack opening and inversely proportional to the gas thermal conductivity.
The corresponding thermoelastic problem is reduced to a system of nonlinear singular
integro-differential equations, and its approximate analytical solution is constructed. The effect of
the mass and the thermal conductivity of the gas inside the crack and the applied load on the stress
intensity factors are analyzed.