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 K/s, 25 K/s 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.
Highlights
Dendritic growth is one of the fundamental problems present in metallurgical research.The understanding and mathematical description of physical phenomena occurring during dendrite growth play a fundamental role in predicting the structure and properties of metals and alloys
The calculations were performed on a cellular automaton with elementary cells with dimension of 160 × 160, which corresponds to a flat area of 320 × 320 μm2
In order to determine the potential of the numerical model, the results of the Cellular Automaton (CA)
Summary
Dendritic growth is one of the fundamental problems present in metallurgical research. Beltran-Sanchez and Stefanescu [15] developed a model based on the concept of dendrite growth under steady-state conditions In this approach, the movement of the interface is controlled by the diffusion rate of the component rejected before the solidification front. Zhu and Stefanescu [18] developed a model in which the velocity of the liquidsolid interface depends on the difference between the instantaneous local equilibrium concentration and the instantaneous local actual concentration of the component in the liquid phase at the solidification front In the model, this difference was determined on the basis of the local temperature and interface curvature, and the solution of the diffusion equation. One of the problems in developing numerical CA solidification models is the correct calculation of the instantaneous composition of the liquid and solid phases in the interface cells. Analysis (DDTA) experiment and analyses of the chemical composition of EDS
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