Abstract
Using the micro-macroscopic computer simulation model of binary alloy solidification, based on a single domain control-volume calculations, and involving the tracking of columnar dendrite tips envelope for distinguishing different grain structures within the two-phase liquid-solid region, the paper reports the outcomes of the detailed analysis addressing the question of the influence of enhanced KGT crystal growth models on the predicted macro-segregation pattern in the Al-4wt.%Cu alloy cast. In particular, the analysis concerns the impact of a proper selection of the stability constant for the KGT model (based on a crystal-melt surface energy anisotropy strength and linear scaling law of the marginal stability theory) on the predicted dendrite tip under-cooling, volumetric solid fraction and actual solute concentration along the front of columnar dendrite tips. Differences in the resulting evolution of both: the under-cooled melt region within the mushy zone and the solute concentration fields calculated for the considered various kinetics of a grain growth are also reported and discussed.
Highlights
Complex fluid flow, heat and mass transfer processes, accompanying solidification of metal alloys at the scale of individual crystals and in a whole cast, are responsible for the developing micro and macroscopic grain structures, and for mechanical and thermo-physical properties of a final manufactured product
The dendrite tip kinetics is inherent part of computer simulations based on the above-mentioned front tracking approach, on the cellular automaton coupled with the finite element method [11], in the recently developed five-phase model [12] for deducing the growth of mesoscopic envelope linking active dendrite branches, and in others
Considering the above, the paper presents some new results of the extended analysis involving the influence of a chosen KGT dendrite tip kinetics on the predicted development of columnar and equiaxed grain regions within the mushy zone, macroscopic fields of temperature and species concentration, and on the numerically obtained macro-segregation patterns, for the Al-4wt%Cu alloy solidification driven by both molecular diffusion and thermo-solutal convection
Summary
Heat and mass transfer processes, accompanying solidification of metal alloys at the scale of individual crystals and in a whole cast, are responsible for the developing micro and macroscopic grain structures, and for mechanical and thermo-physical properties of a final manufactured product. Rebow and Browne [13] extended the most popular constrained (columnar) dendritic growth model of Kurz-Giovanola-Trivedi (KGT) [14] for aluminium alloys by new estimations of the dendrite tip stability parameter, based on measured values of their crystalmelt surface energy anisotropy strength and a simple linear scaling law of the microscopic solvability theory (MST) The influence of such an augmented 2D and 3D KGT models on the columnar mush – undercooled liquid interface position, on the solutal undercooling and the average temperature gradient at this interface, on the relative tendency to form an equiaxed zone and on the columnar to equiaxed transition (CET) phenomenon was, recently, analysed by Seredynski et al [15] for two selected examples of Al-4wt%Cu alloys solidification driven only by conduction. The issue of the role of thermal and solutal buoyancy forces in the process development, when compared to a pure diffusion case, is addressed For these purposes, the original authors’ micro-macroscopic computer simulation model is used, which is based on single domain control-volume calculations involving the tracking of columnar dendrite tips envelope (for distinguishing different grain structures within the mushy zone)
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