Relief of Residual Stresses by Heating Patterns

A method is presented for calculating the relief of residual stresses in a rectangular welded plate by local heating. The thermal stresses developed by the local heating patterns are illustrated by graphs. Plastic strain, hence plastic strain gradients, develop when the thermal stress combined with the residual stress exceeds the elastic limit of the material. To calculate the stress field caused by the plastic strains, an analogy between plastic strain gradients and body forces is applied. The Reuss-Mises incremental polyaxial inelastic stress-strain relationship is used. The stress field equation satisfying the conditions of equilibrium, compatibility, and the Reuss-Mises relation of the material are expressed in a system of simultaneous equations in finite difference form, and are solved by a digital computer. The effectiveness of local heating in the relief of residual stress is shown. The method does not require iteration and may be extended to plates of other shapes.