The Level Set Method for Solid-Solid Phase Transformations

Abstract

In thermal processing of alloys, homogenization of the as-cast microstructureby annealing at such a high temperature that unwanted precipitatesare fully dissolved, is required to obtain a microstructure suitedto undergo heavy plastic deformation. This process is governed byFickian diffusion and can be modelled as a Stefan problem. In binaryalloys, the interface concentration is the solid solubility predictedfrom thermodynamics. In multicomponent alloys, the interface concentrationsshould satisfy a hyperbolic equation and, therefore, have to be foundas part of the solution. Geometrical reductions are normally takenin the numerical solution of vector-valued Stefan problems. The aimof this work is to extend a level set method1 implemented for scalarStefan problems, to higher dimensional vector-valued Stefan problems.This extension is obtained by adding a nonlinear coupling of theinterface concentrations into the level set formulation. Computationalresults will be given for one-, two- and three-dimensional problems.