CA Modeling of Microsegregation and Growth of Equiaxed Dendrites in the Binary Al-Mg Alloy

Abstract

A two-dimensional model based on the Cellular Automaton (CA) technique for simulating free dendritic growth in the binary Al + 5 wt.% alloy was presented. In the model, the local increment of the solid fraction was calculated using a methodology that takes into account changes in the concentration of the liquid and solid phase component in the interface cells during the solidification transition. The procedure of discarding the alloy component to the cells in the immediate vicinity was used to describe the initial, unstable dendrite growth phase under transient diffusion conditions. Numerical simulations of solidification were performed for a single dendrite using cooling rates of 5, 25 and 45 K/s and for many crystals assuming the boundary condition of the third kind (Newton). The formation and growth of primary and secondary branches as well as the development of component microsegregation in the liquid and solid phase during solidification of the investigated alloy were analysed. It was found that with an increase in the cooling rate, the dendrite morphology changes, its cross-section and the distance between the secondary arms decrease, while the degree of component microsegregation and temperature recalescence in the initial stage of solidification increase. In order to determine the potential of the numerical model, the simulation results were compared with the predictions of the Lipton–Glicksman–Kurz (LGK) analytical model and the experimental solidification tests. It was demonstrated that the variability of the dendrite tip diameter and the growth rate determined in the Cellular Automaton (CA) model are similar to the values obtained in the LGK model. As part of the solidification tests carried out using the Derivative Differential Thermal Analysis (DDTA) method, a good fit of the CA model was established in terms of the shape of the solidification curves as well as the location of the characteristic phase transition temperatures and transformation time. Comparative tests of the real structure of the Al + 5 wt.% Mg alloy with the simulated structure were also carried out, and the compliance of the Secondary Dendrite Arm Spacing (SDAS) parameter and magnesium concentration profiles on the cross-section of the secondary dendrites arms was assessed.