Magnesium alloys have been extensively used for structural and functional applications due to their low densities. In order to improve the mechanical properties, grain refinement of the microstructures of magnesium alloys has been studied for many years. However, an effective and efficient grain refiner or refinement technique hasn’t been achieved yet, especially for those with aluminium contained. In this study, solution for this problem has been discovered through further understanding of the solidification process, including the potency and the efficiency of nucleation particles, the role of solute, and the role of casting conditions. First of all, the study suggested that MgO particles can act as nuclei in magnesium alloys by measuring and analyzing the differences in cooling curves with various amount of endogenous MgO particles. The differences indicated that the number density of MgO particles has a huge influence on the microstructure. This idea has been fatherly proved by the inoculation of MgO particles in magnesium alloys because the microstructures have been significantly refined after the inoculation. A new kind of refiner (AZ91D-5wt%MgO) has been developed based on such understandings. Secondly, the study discovered that the role of solute has much smaller effect on the grain size than it was suggested in traditional understandings. The inverse-proportional relationship between the grain size and the solute is highly suspected and the major role of solute is to cause columnar- equiaxed transition. The role of casting conditions has also been studied in order to provide experimental evidence for the existence of melt quenching effect in magnesium alloys. It is shown that various casting conditions, such as pouring temperatures and mould temperatures, have large influence on the critical heat balance temperature after rapid pouring. In this study, a theoretical model based on the analysis of cooling curves is presented for grain size prediction. An analytical model of the advance of equiaxed solidification front is developed based on the understanding of the role of casting conditions. Eventually, all these understandings have been applied to magnesium direct-chill (DC) casting. The refined microstructure of DC cast ingots can further assist in understanding the mechanism of advanced shearing achieved by MCAST unit. The comparison of the ingots with and without melt shearing indicated that the advance shearing device can disperse MgO film into individual particles.

Um modelo matemático multifásico para a solidificação equiaxial de ligas binárias capaz de prever o efeito de taxa de resfriamento e da concentração de soluto no tamanho médio final de grãos foi proposto no presente trabalho. O modelo matemático foi desenvolvido através do conceito de envelope envolvendo os grãos, utilizando as equações de conservação de energia, massa e espécies químicas. O modelo de nucleação utilizado possibilita que novos núcleos possam surgir durante todo o período de resfriamento. As equações diferenciais foram obtidas através de uma média volumétrica das equações de conservação em um volume elementar representativo contendo três \"pseudofases\": sólido, líquido interdendrítico e líquido extradendrítico. O efeito de algumas variáveis de processamento sobre o tamanho médio final de grão foi analisado. Os resultados do modelo proposto foram comparados com resultados de alguns modelos disponíveis na literatura. / A multiphase mathematical model for the equiaxed solidification of binary alloys was proposed in the present work to predict the effects of the cooling rate and the average solute concentration on the final average grain size. The mathematical model was based on the concept of the grain envelope and on the conservation of energy, mass and chemical species. A nucleation model was adopted to consider the nucleation of new grains during the whole solidification time. The differential equations were derived from the volume average of conservation equations within a representative elementary volume that consisted of three pseudophases: solid, interdendritic liquid, and extradendritic liquid. The effect of some processing variables on the final average grain size was studied. The results from the proposed model were compared with those available in the literature from other models.

Um modelo matemático multifásico para a solidificação equiaxial de ligas binárias capaz de prever o efeito de taxa de resfriamento e da concentração de soluto no tamanho médio final de grãos foi proposto no presente trabalho. O modelo matemático foi desenvolvido através do conceito de envelope envolvendo os grãos, utilizando as equações de conservação de energia, massa e espécies químicas. O modelo de nucleação utilizado possibilita que novos núcleos possam surgir durante todo o período de resfriamento. As equações diferenciais foram obtidas através de uma média volumétrica das equações de conservação em um volume elementar representativo contendo três \"pseudofases\": sólido, líquido interdendrítico e líquido extradendrítico. O efeito de algumas variáveis de processamento sobre o tamanho médio final de grão foi analisado. Os resultados do modelo proposto foram comparados com resultados de alguns modelos disponíveis na literatura. / A multiphase mathematical model for the equiaxed solidification of binary alloys was proposed in the present work to predict the effects of the cooling rate and the average solute concentration on the final average grain size. The mathematical model was based on the concept of the grain envelope and on the conservation of energy, mass and chemical species. A nucleation model was adopted to consider the nucleation of new grains during the whole solidification time. The differential equations were derived from the volume average of conservation equations within a representative elementary volume that consisted of three pseudophases: solid, interdendritic liquid, and extradendritic liquid. The effect of some processing variables on the final average grain size was studied. The results from the proposed model were compared with those available in the literature from other models.

<p><a>Direct chill (DC) casting is the main production method for wrought aluminum alloys. In this semi-continuous process, significant heat is extracted through a narrow, solidified shell by impinging water jets. A combination of rapid cooling and inoculation of the liquid metal with heterogenous nucleation sites (grain refiner) produces the proper conditions for equiaxed solidification. As equiaxed grains nucleate and grow in the slurry, they are transported by natural convection until their eventual coalescence into a rigid mush. The preferential accumulation of these solute-depleted grains in localized regions of the casting can lead to long range composition differences known as macrosegregation. Because macrosegregation cannot be mitigated by subsequent processing, it is critical to understand and prevent its development during casting. </a></p> <p>Numerical models are often used to gain insight into the interplay of the different transport phenomena that cause macrosegregation. The formation of mobile equiaxed grains creates a multiphase system with many moving interfaces, causing several modeling challenges. In principle, a model could be formulated in terms of local instantaneous variables describing the evolution of these interfaces, however the associated computational cost prohibits its extension to the length scale of industrial castings. For this reason, macroscopic transport equations are mathematically formulated using volume averaging methods. Two different volume-averaged model formulations can be distinguished in the solidification literature. The first approach is the multiphase formulation, which solves separate sets of governing equations for each phase that are coupled using microscale interfacial balances. While this approach retains closure models to describe the behavior of the sub-grid interfaces, these interfacial models introduce significant uncertainty that is propagated through the model. The second approach is the mixture formulation, which solves a single set of governing equations for the mixture and utilizes more pragmatic closure relationships. While this approach significantly reduces the complexity and computational cost of the model, previous formulations have oversimplified the microscale transport. Recognizing the advantages and disadvantages of both formulations, a mixture model is rigorously derived, retaining appropriate relationships for the grain structure and microsegregation behavior in equiaxed solidification </p> <p>Implementation of this model into a 3-D finite volume method (FVM) code using a co-located grid is discussed along with appropriate treatment of the discontinuous body forces and phase mass fluxes across the interface between the slurry and rigid mush. More specifically, body forces in the momentum equation are treated at the face-centers of a control volume to prevent erroneous velocity oscillations near this interface, and a diffuse phase flux method is proposed to reduce the sensitivity of composition predictions to the numerical grid. The proposed methods are verified across a wide range of conditions present in equiaxed solidification. </p> <p>This model is then used to investigate the role of grain motion on macrosegregation development in equiaxed solidification, specifically in horizontal and vertical DC casting. In horizontal DC casting, the casting axis is perpendicular to gravity and there is a tendency for grains to accumulate along the bottom of the ingot. Feeding liquid metal through a constrained inlet near the bottom suspends grains in the slurry, both reducing the overall macrosegregation and improving the macrosegregation symmetry in the ingot. In vertical DC casting, the casting axis is parallel to gravity and there is a tendency for grains to accumulate in the center of the ingot. It is determined by a combination of simulations in the current work and previous experimental results that a strong localized jet at the centerline can suspend grains in the slurry and reduce negative centerline segregation. The change in segregation is attributed to a combination of reducing the accumulation of solute-depleted grains near the centerline and thinning the rigid mush where solidification shrinkage pulls enriched liquid away from the centerline. The strong localized jet also causes significant refinement and homogenization of the grain structure, which improves the mechanical properties of the ingot. These studies indicate that it is beneficial for DC casting practices to move towards agitated or stirred melts, and away from conventional practices which promote thermal stratification and localized accumulation of equiaxed grains.</p>

Melt convection and solid phase movement play an important role in solidification processes, which significantly influence the formation of grain structures and solute segregations. In general, the melt convection and grain movement are a result of buoyancy forces. The densities within melt are different due to the variation of temperature and concentration, leading to thermally and solutally driven melt convection. Similarly, the density differences between the grains and the bulk melt cause the grain movement, leading to solid sedimentation or grain floating, as the case may be. Free, unattached solid grains are produced by partial remelting and fragmentation of dendrites, by mechanical disturbances such as stirring or vibration and by heterogeneous nucleation of grains in solidification of grain-refined alloys. In this way, movement of solid crystals during solidification can be ascertained in the following two cases. In the first case, during columnar solidification of non-grain-refined alloys, solid movement is possible in the form of dendrite fragments detached from the columnar stalks by the process of remelting and fragmentation. Movement of grains during columnar solidification gives rise to altogether different microstructure from columnar to equiaxed. In the second case, during equiaxed solidification of grain-refined alloys, the movement of solid crystals is possible in the form of equiaxed dendrite crystals nucleated due to presence of grain refiners. The rate and manner by which the free solids settle (or float) will influence macrosegregation in metal castings. Control of the solidification process is possible through an understanding of the solid movement and its effect on macrosegregation and microstructure. With this viewpoint, the overall objective of the present thesis is to study, experimentally and numerically, the phenomenon of solid phase movement during solidification. Through this study, deeper insights of the role of solid phase movement in solidification are developed which can be used for possible control of quality in castings. Both columnar and equiaxed solidification are considered. Models for transport phenomena associated with columnar solidification with solid phase movement are rarely found in the literature, because of inherent difficulty associated with consideration of microscopic features such as remelting and fragmentation. To tackle this problem, solidification modules for remelting and fragmentation are developed first, followed by integration of these molecules in a macroscopic solidification model. A Rayleigh number based fragmentation criterion is developed for detachment of dendrite fragments from the developing mushy zone, which determines the conditions favorable for fragmentation of dendrites. The criterion developed is a function of net concentration difference, liquid fraction, permeability, growth rate of mushy layer, and thermophysical properties of the material. The effect of various solidification parameters on fragmentation is highlighted. The integrated continuum model developed is applied to stimulate the solidification of aqua-ammonia system in a side-cooled rectangular cavity. The numerical results are in good qualitative agreement with those of experiments reported in literature. A gentle ramp of the mushy zone due to settling of solid crystals, as also noticed in experimental literature, is observed towards the bottom of the cavity. The influence of various modeling parameters on solid phase movement and resulting macrosegregation is investigated through a parametric study. Movement of grains during columnar solidification gives rise to altogether different microstructure and sometimes may initiate a morphological transition of the microstructure from columnar to equiaxed if the number and size of equiaxed grains ahead of the columnar front become sufficient to arrest the columnar growth. The generalised model developed, considering solid phase movement during columnar solidification is used to predict columnar-to-equiaxed transition (CET) based on a prescribed cooling rate criterion. It is found that presence of convection significantly affects the solidification behaviour. Moreover, the movement of dendrite fragments and their accumulation at the columnar front further trigger the occurrence of CET. Cooling configuration, too significantly affects the nature of CET. In unidirectional solidification cases, the locations of CET are found to be in a plane parallel to the chill face. However, for the case of the non-unidirectional solidification (as in side-cooled cavity), the locations of CET need not be in a plane parallel to the chill face. In contrast to fixed columnar solidification, equiaxed solidification is poorly understood; in particular, the phenomena associated with solid crystal movement. Movement of unattached solid crystals, formed due to heterogeneous nucleation on grain-refiners, is induced by the convective currents as well as by buoyancy effects, causing the solid to sediment or to float, depending on density of solid compared to that of the bulk melt. While moving in the bulk melt these crystals can also remelt or grow. A series of casting experiments with AI-based alloys are performed to investigate the role and influence of movement of solid crystals on macrosegregation and microstructure evolution during equiaxed solidification. Controlled experiments are designed for studying, separately, settling and floatation of equiaxed crystals for different cooling conditions and configurations. Further, these experiments are carried out in convective and non-convective cases to understand the effect of convection on solid phase movement. Temperature measurements are performed at various locations in the mould during the experiments. After the cavity is solidified, microstructural and chemical analyses of the experimental samples are carried out, several notable features are observed in temperature histories, macrosegregation pattern, and microstructures due to settling/flotation phenomenon of solid crystals. It is found that the flow behavior of solid grains has a profound influence on the progress of solidification (in terms of grain size distribution and fraction eutectic) and macrosegregation distribution. In some cases, the induced flow due to solid phase movement can cause a flow reversal. The observations and quantitative data obtained from experiments, with the help of detailed solidification conditions provided, can be used for future validations of models for equiaxed solidification. Subsequently, numerical studies are carried out, using a modified version of the macroscopic model developed for columnar solidification with motion of solid crystals, to predict the transport phenomena during equiaxed solidification. The model is applied to simulate the solidification processes corresponding to each of the experimental cases performed in this study. For a better understanding of the phenomenon of movement of solid crystals, the following two special cases of solidification are also presented: 1) without movement of solid crystals and 2) movement of solid crystals without any relative velocity between solid and liquid phases. The numerical predictions showing nature of flow field and progress of solidification are substantiated by the experimental data for the thermal analysis, qualitative microstructural Images and quantitative microstructural analysis. It is concluded, with the help of various experiments and simulations, that movement of solid crystals influences the casting quality appreciably, in terms of macrosegregation and microstructures. It is expected that the improved understanding of the role and influence of solid phase movement during solidification processes (both columnar and equiaxed) obtained through this thesis will be useful for possible control of quality of as-cast products.