Micro‐macro modelling of steel solidification: A continuum mechanical, bi‐phasic, two‐scale model including thermal driven phase transition. Issue 2 (14th December 2017)

• Record Type: Journal Article
• Authors: Moj, Lukas; Foppe, Manuel; Deike, Rüdiger; Ricken, Tim
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 40:Issue 2(2017)
• Page Start: 125
• Page End: 137
• Publication Date: 2017-12-14
• Subjects: Theory of porous media -- phase‐field -- multi‐scale -- solidification -- FEM; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201720004
• Languages: English
• ISSNs: 0936-7195

Abstract

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.