Dynamical and Empirical Simulation Methods of Secondary Dendrite Arm Coarsening: A Comparative Approach

This chapter evaluate a comparative approach of Dynamical and Empirical Simulation Methods of Secondary Dendrite Arm Coarsening. The secondary dendritic arm spacing (SDAS) has a significant influence on the mechanical and physical characteristics of an alloy that has been dendritically solidified completely (wrought alloys) or partially (cast alloys). A practical yet straightforward approach for calculating the SDAS during and after solidification as a function of cooling rate is required for both the solidification simulation and casting practice. Based on many solidification experiments, a simple equation to calculate the SDAS (empirical method) is known to use the local solidification time, which can be obtained from the measured cooling curves (equiaxed solidification), or can be calculated from the temperature gradient and front velocity (directional solidification). In the present work, first, we show the effect of the curvature of the solid/liquid interface on the equilibrium concentrations and then the different processes of SDA coarsening. In our earlier paper, we demonstrated that using the empirical method, the final SDAS can be calculated with acceptable correctness in the case of four unidirectional solidification experiments of Al-7wt%Si alloy. The current study demonstrates that the known cooling curve was utilized in the numerical integration of Kirkwood's equations, allowing for the calculation of the SDAS both during and after solidification in good agreement with the experimental findings. We claimed that the approaches' accuracy is comparable to the two calculation methods. The equilibrium concentration in the liquid phase on the solid phase’s surface depends on the curvature of the solid phase. Consequently, diffusion in the liquid phase from high to low solute regions will result in the coarsening of the SDA. Still, the results of the solidification simulation (the microsegregation) will be more correct using the dynamical method. It is also shown that with the dynamical method, the SDAS can be calculated from any type of cooling curve, and using the dynamical method, it is proved that some different SDASs could belong to the same local solidification time.