Thermal stress singularities at tips of a crack in a semi-infinite medium under uniform heat flow

Abstract

In the framework of plane thermoelastic problems is discussed the thermal stress field near the tips of an arbitrarily inclined crack in an isotropic semi-infinite medium with the thermally insulated edge surface under uniform heat flow. The crack is replaced by continuous distributions of quasi-Volterra dislocations corresponding to line heat sources and edge dislocations, and we obtain a set of simultaneous singular integral equations for dislocation density functions, whose solution is given in the forms of series in terms of Tchebycheff polynomials of the first kind. 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. Numerical results are given for the particular case where the surface of the inclined crack is maintained at constant temperature and the heat supplied across the surface of the crack vanishes as a whole. The effects of the distance from the crack tip to the edge surface of the semi-infinite medium and the angle of inclination of the crack on the stress intensity factors and the initial direction of crack extension are shown graphically.