On the Calculation of Deformations and Stresses During Axially Symmetric Solidification

In this paper finite element modeling of the deformation and stress development in solidifying bodies is presented. Emphasis is given to axially symmetric problems and especially to the accurate implementation of thermal and mechanical phenomena occurring at the freezing front. More specifically, the interface velocity and location are treated as primary variables of the heat transfer analysis, and the isostatic stress condition at the front is utilized as an initial condition in the stress analysis. A hypoelastic-viscoplastic constitutive model and a rate form of the principle of virtual work are involved to model the stresses and deformation. The mechanical and thermal properties are allowed to vary with temperature and strain rate in a realistic manner. Several examples of calculated residual stresses are shown for pure aluminum under axially symmetric geometries and realistic boundary conditions. The effects on the evolving deformations and stresses of the melt pressure, geometry, and cooling conditions are examined and reported.