Rheological modelling of residual stresses and deformations of plates during non-uniform cooling

The time–space distribution of eigen-stresses and residual deformations of a plane plate which reaches its final solid state through a given transition process of non-uniform cooling is described here by means of a simple visco-elastic rheological model.The aging processes of the elastic and viscous properties are supposed to be temperature dependant in order to directly control the influence of the thermal history on the final stress and deformation conditions of the solid.The model is able to reproduce qualitatively well the development of eigen-stresses in the spatially symmetrical cooling processes of tempering or toughening, as well as the formation of eigen-stresses and permanent bending in the spatially asymmetrical cooling processes of heat curving.