Equations are given for the determination of transient and residual stresses in plates subject to transient temperature distributions, based on the assumption of a viscoelastic, perfectly plastic material obeying a von Mises temperature-dependent yield condition. A numerical procedure for integrating the equations is developed and applied to the case of a symmetrically cooled plate. It is found that, for steel, viscoelasticity has little effect on the residual stress distribution, but the temperature dependence of yield stress is important. The types of residual stress distribution after cooling are similar to those for an elastic-plastic material with constant yield stress, and for this case the residual stress is given approximately by formulas developed earlier for a slowly varying heat input.

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