Spatial Thermo-Mechanical Model of Mushy Steel Deformation Based on the Finite Element Method

The paper reports the results of work leading to the construction of a spatial thermo-mechanical model based on the finite element method allowing the computer simulation of physical phenomena accompanying the steel sample testing at temperatures that are characteristic for the soft-reduction process. The proposed numerical model is based upon a rigid-plastic solution for the prediction of stress and strain fields, and the Fourier-Kirchhoff equation for the prediction of temperature fields. The mushy zone that forms within the sample volume is characterized by a variable density during solidification with simultaneous deformation. In this case, the incompressibility condition applied in the classic rigid-plastic solution becomes inadequate. Therefore, in the presented solution, a modified operator equation in the optimized power functional was applied, which takes into account local density changes at the mechanical model level (the incompressibility condition was replaced with the condition of mass conservation). The study was supplemented with examples of numerical and experimental simulation results, indicating that the proposed model conditions, assumptions, and numerical models are correct.