Steady-state thermal stresses in an elastic solid containing an insulated penny-shaped crack

Abstract

A solution is given for the steady-state thermal stress and displacement field in an infinite elastic solid containing an insulated penny-shaped crack. The problem is reduced to a mixed-boundary-value problem for the half-space, making use of Green's isothermal solution for the thick elastic plate in complex harmonic potentials and a particular thermoelastic solution due to Williams. In the axisymmetric case, the complex potential reduces to the real harmonic function used by Shail in his solution for the external crack. To illustrate the use of the method in both axisymmetric and non-axisymmetric problems, complete solutionsare given for (1) a uniform heat flow and (2) a linearly varying heat flow disturbed by an insulated penny-shaped crack.