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.
%0 Journal Article
%1 Moj.2017
%A Moj, Lukas
%A Foppe, Manuel
%A Deike, Rüdiger
%A Ricken, Tim
%D 2017
%J GAMM--Mitteilungen
%K FEM Multi-scale Solidification Theory_of_porous_media phase-field
%N 2
%P 125--137
%R 10.1002/gamm.201720004
%T Micro-macro modelling of steel solidification: A continuum mechanical, bi-phasic, two-scale model including thermal driven phase transition
%V 40
%X 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.
@article{Moj.2017,
abstract = {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.},
added-at = {2019-11-06T16:19:50.000+0100},
author = {Moj, Lukas and Foppe, Manuel and Deike, R{\"u}diger and Ricken, Tim},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/215e5f5d5070bc1bef15af5a9548f8de1/timricken},
doi = {\url{10.1002/gamm.201720004}},
file = {7a4151c7-99f4-41de-ab7b-4878e66d9e91:C\:\\Users\\ac130180\\AppData\\Local\\Swiss Academic Software\\Citavi 6\\ProjectCache\\bkyd3fzxdr3rziq0dosvpq10u8ycyepwckx0sx\\Citavi Attachments\\7a4151c7-99f4-41de-ab7b-4878e66d9e91.pdf:pdf},
interhash = {63eebb01c9c455eeb50c9f032274245b},
intrahash = {15e5f5d5070bc1bef15af5a9548f8de1},
issn = {1522-2608},
journal = {{GAMM--Mitteilungen}},
keywords = {FEM Multi-scale Solidification Theory_of_porous_media phase-field},
number = 2,
pages = {125--137},
timestamp = {2019-11-06T15:19:50.000+0100},
title = {{Micro-macro modelling of steel solidification: A continuum mechanical, bi-phasic, two-scale model including thermal driven phase transition}},
volume = 40,
year = 2017
}
