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Abstract

Numerical simulations of hot working processes have gained significant importance for the steel making industries in order to improve manufacturing. Such processes involve high thermo-mechanical loading due to high cooling and forming rates. Going one step back, the molten steel solidification can be part of the processing chain, where the solidification properties influence the resulting material quality, strongly.

Hence, a continuum-mechanical, bi-phasic, two-scale model is developed to predict thermal driven phase transition during solidification processes. The solid and liquid physical states are formulated in the framework of enhanced theory of porous media (TPM) [1], by transition rate terms and thermal coupling [2], respectively. Furthermore, finite plasticity superimposed by a secondary power-creep law has been considered to describe realistic material behaviour. A linear visco-elastic material law and Darcy’s permeability were chosen for the liquid phase material description. The phase transition is formulated by a two-scale approach considering the phase-field model on the micro-scale [3]. Here, a double-well potential, consisting of two local minima at completely solid and liquid physical states, is utilized. The finite element method and the finite difference method are employed to solve the macroscopic and the microscopic boundary value problem. A fundamental scaletransition assumption is the macro-homogeneity condition, also denoted as Hill-Mandel condition [4], which asserts the equality of virtual work between both scales.

Representative numerical examples, as well as the model performance will be shown.