This paper addresses a continuum-mechanical, bi-phasic, two-scale numerical model for casting and processing of metallic alloys. The solid and liquid physical states, which represents the solid and molten alloy, are formulated in the framework of the theory of porous media (TPM) including thermal coupling, finite plasticity superimposed by a secondary power creep law and visco-elasticity associated by Darcy's permeability for the solid and the liquid phase, respectively. In view of phase transition during solidification, a two-scale approach considering the phase-field on the micro-scale is proposed, where a double-well potential with two local minima for completely solid and liquid physical states is utilized. The finite element method based on the standard Gallerkin element formulation and the finite difference method was employed for the macro-scale and the micro-scale, respectively. Finally, the performance of the discussed model is demonstrated by the recalculation and validation of a solidification experiment.

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This articel focuses on a bi-scale numerical description for solidification process simulation. The macro-scale implies two phases which are the solid and liquid metallic alloy physical states described using the theory of porous media (TPM) enhanced by strong thermal coupling and finite elastic-plastic-creep temperature dependent material behaviour. Furthermore, a linear viscous melt as well as a laminar melt flow are adopted. The thermal driven physics of solidification is covered by a microscopic phase-field model. Therefore, a Ginzburg-Landau type free energy function is employed. After discussing the main model details, a real Bridgman oven numerical pre-model will demonstrate the principal performance.

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)

A numerical simulation of a solidification experiment is presented. The experimental setup consists of an empty screwed up mould, which is filled up with molten steel and cools down due to atmospheric conditions. During the cooling process, the temperature at the centre as well as the shrinkage at the narrow side, respectively, have been recorded. The simulation has been run via the software ANSYS modified by specific provided programmer interfaces, the User Programmable Features (UPFs). All required temperature dependent material parameters have been provided by ThyssenKrupp Steel Europe. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)