A ternary phase bi‐scale FE‐model for diffusion‐driven dendritic alloy solidification processes

It is of high interest to describe alloy solidification processes with numerical simulations. In order to predict the material behavior as precisely as possible, a ternary phase, bi‐scale numerical model will be presented. This paper is based on a coupled thermo‐mechanical, two‐phase, two‐scale finite element model developed by Moj et al. [2], where the theory of porous media (TPM) [1] has been used. Finite plasticity extended by secondary power‐law creep is utilized to describe the solid phase and linear visco‐elasticity with Darcy's law of permeability for the liquid phase, respectively. Here, the microscopic, temperature‐driven phase transition approach is replaced by the diffusion‐driven 0D model according to Wang and Beckermann [3]. The decisive material properties during solidification are captured by phenomenological formulations for dendritic growth and solute diffusion processes. A columnar as well as an equiaxial solidification example will be shown to demonstrate the principal performance of the presented model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)