Stress formation in solidifying bodies. Solidification in a round continuous casting mold

Abstract

In solidifying bodies, there is no stress-free reference state for the displacements as in normal bodies with fixed dimensions, which are stress free, in all their volume elements, in the isothermal state prior to cooling or prior to heating. This difficulty has been solved in the present work by using displacement rates, rather than displacements, and all the other relevant quantities also in time differentiated form. The equations obtained for the time differentiated quantities are integrated with respect to time to obtain the quantities themselves. Different assumptions on the material behavior have been used, viz. viscoplastic-elastic or purely elastic behavior. The concept was applied to bodies with cylindrical symmetry and, for the sake of simplicity and clarity, to the state of plane strain. The computational examples refer to the solidification of steel with 0.6 pct carbon in a round continuous casting mold. The calculated stress distributions show compressive circumferential stress at the surface of the strand and tensile stress in the interior of the solid shell. Shrinkage profiles depend mainly on the temperature profile and on the thermal strain data used, and can be approximated by the free shrinkage of the strand surface.