Since several decades the continuous casting (CC) process became one of the dominant technologies for the metal production. The quality optimization and the production rate growth are the primary targets. Nowadays the numerical modelling is a valuable tool to assist in these aims. Moreover, it efficiently competes with the physical experiment and the industrial trials. One of the key issues with the high casting speeds especially for the thin slab products are the strong turbulent flow of the fresh melt being feed from the submerged entry nozzle (SEN) and the non-uniformity of the solidifying shell thickness. Thereby the electromagnetic braking (EMBr) is typically applied to damp the hot jets and to evenly redistribute the superheat. In the previous work it was shown by the authors that the presence of the highly conductive solid shell plays crucial role for the melt flow under the applied magnetic field. Excluding this interaction does not allow predicting the EMBr effects on the melt flow correctly during the solidification. Recently a viscoplastic deformation model was implemented to model a withdrawal of the solidified shell in a funnel type CC mold for a full 3D engineering geometry. An extended model was used to predict the macro-segregation during twin-roll casting of an Al-alloy using 2D assumption due to the large width / thickness ratio of the casted sheet. In the current study an effort is done to combine the viscoplastic deformation model of the solidified shell and the magnetohydrodynamics effects of the EMBr. The flow field alternation as well as the thickness of the solidified shell during CC are presented and analyzed with and without the magnetic field been applied.

In this study, a first attempt is made to bridge capillary-driven fragmentation and grain transport using a mixed columnar-equiaxed solidification model. Grain transport is an intrinsic feature of the employed solidification model which has been extensively investigated over the years. Regarding the capillary-driven fragmentation event, a new correlation between the number of fragments and interfacial area density of the columnar structure was recently established by Cool and Voorhees (2017) based on experimental research under isothermal conditions. Here, we propose to modify Cool and Voorhees’ equation to extend its range of applicability to the solidification-dominant stage without destroying the agreement with the reported measurements in the coarsening-dominant stage. With this improvement in the mixed columnar-equiaxed solidification model, capillary effects can be isolated from the motion of the phases during fragmentation events, which facilitates understanding of the results. Under pure diffusive solidification conditions (no flow or crystal sedimentation), the simulation results were validated against phase-field simulations. In more realistic scenarios where liquid flow and fragment sedimentation are both considered, the simulations indicate very reasonable results for the detection of columnar-to-equiaxed transition, which suggests that the newly proposed model can be an important tool for industrial casting applications. Moreover, flow direction and intensity were shown to affect the potential for local fragmentation. Graphic Abstract

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As it is known from literature, the metals tend to follow a viscoplastic law at high temperatures. Thereby, based on the authors’ previous developments to simulate the behavior of the equiaxed crystals packed bed, a viscoplastic stress model is applied to the thin slab casting process. The model is reduced to the single phase mixture formulation for faster and robust simulations. In this idea, the solidifying shell represents a ‘creeping solid’ and the Norton-Hoff type stress model is formulated with the model parameters obtained experimentally. A coupling procedure is established to converge the non-linear terms. The influence of the stress model parameters is investigated. Next the model is applied for the simulation of the thin slab casting to improve a previously developed technique: a viscoplastic rheology is applied to calculate the motion of the solidifying melt instead of imposing the velocities of the mush. The simulation results show that the most deformations happen at the funnel part of the mold, causing highest strain rates and the significant drop of the viscoplastic ‘apparent viscosity’ according to the Norton-Hoff law. The solid shell velocities are mostly uniform at the straight parts of the strand but a slight acceleration of the shell is observed along the funnel surface. Strong compression / expansion zones are detected at the funnel part, which could lead to defects formation. The solid shell thickness was successfully predicted as well and compared to the previous work by the authors.

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