Thermal stresses near tips of an insulated line crack in a semi-infinite medium under uniform heat flow

Abstract

On the basis of the two-dimensional theory of thermoelasticity, the thermal stress field near the tips of a thermally insulated line crack in a semi-infinite medium under steady-state uniform heat flow is discussed. The crack is replaced by continuous distributions of sources of temperature discontinuity and edge dislocations. Then we obtain a set of simultaneous singular integral equations for density functions. The solution is given in the form of the product of the series of Tchebycheff polynomials of the first kind and their weight function. By means of this method, the thermal stress singularities at the crack tips are estimated exactly and the stress intensity factors can be readily evaluated. The effects of the distance from the crack tip to the bounding plane surface of the semi-infinite medium and the angle of inclination of the line crack on the stress intensity factors are shown graphically.