For movable circular regions of heating and cooling with respect to a weld in a plate, a method is proposed for determining their optimum location such that residual stresses decrease most effectively. We use a solution of the problem of thermoelasticity for an infinite plate on its heating by a heat flux described by a Ganssian distribution. On the basis of the Tresca-Saint-Venant yield condition, nomograms which make it possible to determine the distances of the centers of regions of heating to the center line of the weld are constructed.In the modern technology of thermal treatment, tempering is a method most extensively used for the reduction of residual stresses in metallic structures [1]. However, it is not suitable for large objects. Furthermore, at high temperatures, welded structures with closed welds, quenched structures, and inhomogeneous (as to thermophysical and mechanical properties) structures cannot be tempered. In these cases, local thermal treatment is used. The most promising is local thermal treatment with movable sources of heat parallel to welds. The effectiveness of this treatment depends substantially on the location of the sources of heat relative to the weld. The nomograms presented below enable one to determine the optimum distances of movable circular regions of heating and cooling to the weld.Consider a large welded plate with circular regions of heating and cooling which move with a constant rate v. Let us designate the distances of the centers of the regions of heating and cooling to the center line of the weld by a and b (Fig. 1). Assume that the temperature field and stresses at infinity tend to zero since the plate is large, its thermophysical and mechanical properties do not depend on temperature, the heating regime is steady in the Oxy coordinate system, which moves together with the regions of heating and cooling, and that the center line of the weld coincides with the Ox axis (Fig. 1). 0 It is known that longitudinal residual stresses t~xx after welding of thin-walled structures are tensile, as a rule 0 in the weld zone. In this case, it follows from the Tresca-Saint-Venant Oxx and transverse temperature stresses t~yy plastic elongation deformations, which reduce both plastic shortening deformations caused by welding and, respectively, residual stresses, will arise in those zones of the weld for which the sum of the values G ~ = Oxx~ _ ~yy0 and t t attains the yield limit.Od = (~X.X-(Iyy Let us determine the parameter o x in the case of heating with gas burners whose specific thermal flux along the radius of the region of heating is described approximately by a Gaussian distribution [3]:where q0 is the largest thermal flux in the center of the region of heating, k, is the heating concentration factor, and r is the distance from the center. For this purpose, we use the solution (which was published previously [4]) of a nonstationary problem of thermoelasticity for an infinite plate under its two-side heating by law (1). Let the plate be heated with two regions of heating wh...
