and Simulation 2
A multi-component, bi-scale continuum mechanical model for the simulation of thermal and diffusive driven metallic alloy solidification processes
Tim Ricken, TU Dortmund, Dortmund, GermanyLukas Moj, TU Dortmund University, Dortmund, GermanyCarla Henning, TU Dortmund University, Dortmund, GermanyIngo Steinbach, University of Bochum (ICAMS), Bochum, Germany
In order to predict the material coupled micro-macro behaviour of metallic alloy solidification as precisely as possible, a ternary-phasic, bi-scale continuum mechanical model for thermal and diffusive driven metallic alloy solidification will be presented.
The solid and liquid physical states are formulated in the framework of enhanced theory of porous media (TPM) , by transition rate terms and thermal coupling , respectively. Furthermore, finite plasticity superimposed by secondary creep law has been considered as well as a linear viscoelastic material law and Darcy’s permeability for the liquid phase material description, cf. .
The phase transition is formulated by a two-scale approach with two competitive approaches: a bi-phasic 1-D phase-field model based on Kobayashi  and a 0-D ternary-concentration model based on Wang/Beckermann . In the former, a double-well potential is utilized consisting of two local minima at completely solid and liquid physical states whereas the latter contains three different concentrations at the microscale considering columnar to equiaxed transition (CET) as well as the influence of solute diffusion. The strong coupling between volume fractions and concentrations of the alloying element considers the ejection of atoms from the crystal lattice and the associated change in solidification temperature range.
The finite element method (FEM) on the macroscale and the finite difference method on the microscale are employed to solve the macroscopic and the microscopic boundary value problem. Based on significant examples, the model as well as its advantages and disadvantages will be presented.
 R. De Boer. Theory of Porous Media. Springer, New York, 2000.
 Bluhm, J.: Modelling of thermoelastic porous solid with different. In: Ehlers, W. and Bluhm J. (Hrsg.): Porous Media: Theory, experiments and numerical applications, Springer, New York, 2002.
 L. Moj, T. Ricken and I. Steinbach: A continuum mechanical, bi-phasic, two-scale model for thermal driven phase transition during solidification, PAMM 15, 2015.
 Kobayashi, R.: Modeling and numerical simulation of dendritic crystal growth. Physica D: Nonlinear Phenomena, 410-423, 1993.
 C. Y. Wang and C. Beckermann: A unified solute diffusion model for columnar and equiaxed dendritic alloy solidification, Materials Science and Engineering A 171, 1993, Pages 199-211.