Heating of a half space containing an inclusion and a crack

Two-dimensional stationary problems of heat conduction and thermoelasticity for an elastic half space containing an elastic cylindrical macroinclusion and a thermally insulated crack are investigated. The problems are reduced to systems of two singular integral equations on closed (the boundary of the inclusion) and nonclosed (crack) contours. The numerical solutions of these systems are obtained by the method of mechanical quadratures for an inclusion in the form of an elliptic cylinder and a rectilinear crack in a half space heated by a friction heat flow uniformly distributed over a part of the surface of the half pace. For the problem posed for two cases of matrix-inclusion compositions (steel-aluminium and aluminium-steel), the numerical solutions are presented in the form of the plots of the stress intensity factors as functions of the dimensions of the inclusion and the distance between the inclusion and the crack.Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 4, pp. 34–40, July–August, 2004.