Abstract
Grain structure and macrosegregation are two main factors determining mechanical properties of components and are strongly coupled during alloy solidification. A two-dimensional (2D) cellular automaton (CA)–finite element (FE) model is developed to achieve a direct macroscopic modeling of grain structure and macrosegregation during the solidification of binary alloys. With the conservation equations of mass, momentum, energy, and solute solved by a macroscopic FE model and the grain structure described by a microscopic CA model, a two-way coupling between the CA and FE models is applied. Furthermore, the effect of the fluid flow on the dendrite tip growth velocity is considered by modified dendrite tip growth kinetics. The CAFE model is applied to a quasi-2D benchmark solidification experiment of a Sn–3.0wt.%Pb alloy, and the grain structure and macrosegregation are predicted simultaneously. It is demonstrated that the model has a capacity to describe the undercooling ahead of the growth front. The growth directions of columnar grains, grain sizes, and columnar-to-equiaxed transition (CET) position are obviously modified by the fluid flow, and obvious segregated channels almost aligned with the orientations of the columnar grains are found. Qualitatively good agreement is obtained between the predicted segregation profiles and experimental measurements.
Highlights
Solidification is a process to fabricate raw materials or even products, playing an important role in the manufacturing industry
The cellular automaton–finite element (CAFE) model is applied to a quasi-2D benchmark solidification experiment of a Sn–3.0wt.%Pb alloy, and the grain structure and macrosegregation are predicted simultaneously
In order to clarify the effect of the fluid flow on the dendrite tip growth kinetics, the grain structure and fluid flow obtained by the present CAFE model are compared with those given by a degenerated CAFE simulation, in which the effect of the fluid flow on the dendrite tip growth kinetics is disabled
Summary
Solidification is a process to fabricate raw materials or even products, playing an important role in the manufacturing industry. Indirect macroscopic modeling is currently the most popular approach to industrial-scale castings [9,10,11,12,13,14] It solves one or several sets of conservation equations averaged over a representative elementary volume for the heat and mass transfer with thermodynamic considerations of the solidification [15], but the microstructure is not directly simulated. Various solidification experiments [20,21,22] were performed based on the tin–lead (Sn–Pb) alloys due to their strong segregation tendency and operability in the laboratory, giving better experimental benchmarks for numerical validation This contribution is devoted to achieving a direct macroscopic modeling with a 2D cellular automaton–finite element (CAFE) model, which is an extension of a newly developed FE model by the authors [23] for the prediction of macrosegregation during the solidification of binary alloys. The interaction between the fluid flow and the grain structure, as well as the effect of the orientations of columnar grains on the macrosegregation, are investigated in detail
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