Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys

A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.     

Macrosegregation during dendritic arrayed growth of hypoeutectic pb- sn alloys: Influence of primary arm spacing and mushy zone length

Thermosolutal convection in the dendritic mushy zone occurs during directional solidification of hypoeutectic lead tin alloys in a positive thermal gradient, with the melt on the top and the solid below. This results in macrosegregation along the length of the solidified samples. The extent of macrosegregation increases with increasing primary dendrite spacings for constant mushy zone length. For constant primary spacings, the macrosegregation increases with decreasing mushy zone length. Presence of convection reduces the primary dendrite spacings. However, convection in the interdendritic melt has significantly more influence on the spacings as compared with that in the overlying melt, which is caused by the solutal buildup at the dendrite tips. Formerly Graduate Student, Chemical Engineering Department, Cleveland State University     

Modeling of the formation of under-riser macrosegregation during solidification of binary alloys

The formation of macrosegregation in a rectangular ingot with reduced cross section from the riser to the casting, chilled from the bottom, has been studied numerically. In addition to positive inverse segregation occurring near the chilled surface, very severe negative segregation around the under-riser region and moderate positive segregation near the top corners of the casting were found. Although large circulating vortexes are created by natural convection in the under-riser region during the early stage of solidification, the fluid flow in the mushy zone is dominated by solidification shrinkage. As a result, the final solute distribution in the casting is determined by the flow of solute-rich liquid in the mushy zone owing to the combined effects of solidification shrinkage and change of cross section from casting to riser. Detailed explanations regarding the effect of different flow phenomena on the formation of the segregations are provided. The effects of riser size and cooling condition at the bottom of the ingot on the formation of macrosegregation also were studied. The predicted negative and positive macrosegregations in the casting compared very well with the available experimental data.     

Mathematical modeling of macrosegregation of iron carbon binary alloy: Role of double diffusive convection

During alloy solidification, macrosegregation results from long range transport of solute under the influence of convective flow and leads to nonuniform quality of a solidified material. The present study is an attempt to understand the role of double diffusive convection resulting from the solutal rejection in the evolution of macrosegregation in an iron carbon system. The solifification process of an alloy is governed by conservation of heat, mass, momentum, and species and is accompanied by the evolution of latent heat and the rejection or incorporation of solute at the solid liquid interface. Using a continuum formulation, the goverming equations were solved using the finite volume method. The numerical model was validated by simulating experiments on an ammonium chloride water system reported in the literature. The model was further used to study the role of double diffusive convection in the evolution of macrosegregation during solidification of Fe 1 wt pct C alloy in a rectangular cavity. Simulation of this transient process was carried out until complete solidification, and the results, depicting the influence of flow field on thermal and solutal field andvice versa, are shown at various stages of solidification. Under the given set of parameters, it was found that the thermal buoyancy affects the macrosegregation field globally, whereas the solutal buoyancy has a localized effect.     

Investigation of Macrosegregation Formation in Aluminium DC Casting for Different Alloy Systems

Direct chill (DC) casting of aluminum involves alloys employing different solute elements. In this article, a qualitative analysis and comparison of macrosegregation formation is presented for three different alloy systems: Al-Mg, Al-Zn and Al-Cu. For this purpose, a multiphase, multiscale solidification model based on a volume-averaging method accounting for shrinkage-induced flow, thermal-solutal convection and grain motion is used and applied to an industrial-scale DC-cast ingot. The primary difference between these alloys is the thermal-solutal convection with Al-Mg having a competing thermal and solutal convection, whereas the other two systems have a cooperating thermal and solutal convection. In the study, the combined effect of the macrosegregation mechanisms is analyzed for each alloy to assess the role of the alloy system on the final macrosegregation.

     

Modeling freckle formation in three dimensions during solidification of multicomponent alloys

The formation of macrosegregation defects known as “freckles” was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-W alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.     

Computer Simulation of Solidification Transport Behaviours in Blade‐Like Castings under Transverse Static Magnetic Fields up to 25T

Numerical simulation of solidification transport phenomena/processes in a TiAl alloy blade‐like casting, under transverse magnetic fields of different strengths, was carried out. The simulation was based on a continuum solidification model and the computer codes developed by the authors. The simulation results show that, although the liquid flow in the bulk liquid region can be suppressed efficiently, the feeding flow in the mushy zone caused by the volume contraction, due to solidification shrinkage and thermal/solutal expansion, cannot be suppressed even under an ultra‐strong magnetic field up to 25T. This indicates that the forces driven by volume contraction are much stronger than those caused by the gravity. The natural convection can delay the directional solidification process, while the applied static magnetic field accelerates it to some extent, by weakening the natural convection. The magnetic field changes the coupled heat and species mass transfer to a diffusion type mechanism. The natural convection may be the cause for horizontal segregation. An ultra‐strong magnetic field is not necessary to achieve sufficient suppression of natural convection.     

Elimination of Hot Tears in Steel Castings by Means of Solidification Pattern Optimization

A methodology of how to exploit the Niyama criterion for the elimination of various defects such as centerline porosity, macrosegregation, and hot tearing in steel castings is presented. The tendency of forming centerline porosity is governed by the temperature distribution close to the end of the solidification interval, specifically by thermal gradients and cooling rates. The physics behind macrosegregation and hot tears indicate that these two defects also are dependent heavily on thermal gradients and pressure drop in the mushy zone. The objective of this work is to show that by optimizing the solidification pattern, i.e., establishing directional and progressive solidification with the help of the Niyama criterion, macrosegregation and hot tearing issues can be both minimized or eliminated entirely. An original casting layout was simulated using a transient three-dimensional (3-D) thermal fluid model incorporated in a commercial simulation software package to determine potential flaws and inadequacies. Based on the initial casting process assessment, multiobjective optimization of the solidification pattern of the considered steel part followed. That is, the multiobjective optimization problem of choosing the proper riser and chill designs has been investigated using genetic algorithms while simultaneously considering their impact on centerline porosity, the macrosegregation pattern, and primarily on hot tear formation.     

Mathematical simulation on coupled flow, heat, and solute transport in slab continuous casting process

A three-dimensional comprehensively coupled model has been developed to describe the transport phenomena, including fluid flow, heat transfer, solidification, and solute redistribution in the continuous casting process. The continuous casting process is considered as a solidification process in a multicomponent solid-liquid phase system. The porous media theory is used to model the blockage of fluid flow by columnar dendrites in the mushy zone. The relation between flow pattern and the shape of the solid shell is demonstrated. Double diffusive convection caused by thermal and concentration gradients is considered. The change in the liquidus temperature with liquid concentration is also considered. The formation mechanism of macrosegregation is investigated. Calculated solid shell thickness and temperature distribution in liquid core are compared with the measured quantities for validating the model.     

Undercooling-Induced macrosegregation in directional solidification

The accepted primary mechanism for causing macrosegregation in directional solidification (DS) is thermal and solutal convection in the liquid. This article demonstrates the effects of under-cooling and nucleation on macrosegregation and shows that undercooling, in some cases, can be the cause of end-to-end macrosegregation. Alloy ingots of Pb-Sn were directionally solidified upward and downward, with and without undercooling. A thermal gradient of about 5.1 K/cm and a cooling rate of 7.7 K/h were used. Crucibles of borosilicate glass, stainless steel with Cu bottoms, and fused silica were used. High undercoolings were achieved in the glass crucibles, and very low undercoolings were achieved in the steel/Cu crucible. During under-cooling, large, coarse Pb dendrites were found to be present. Large amounts of macrosegregation developed in the undercooled eutectic and hypoeutectic alloys. This segre-gation was found to be due to the nucleation and growth of primary Pb-rich dendrites, continued coarsening of Pb dendrites during undercooling of the interdendritic liquid, Sn enrichment of the liquid, and dendritic fragmentation and settling during and after recalescence. Eutectic ingots that solidified with no undercooling had no macrosegregation, because both Pb and Sn phases were effectively nucleated at the start of solidification, thus initiating the growth of solid of eutectic composition. It is thus shown that undercooling and single-phase nucleation can cause significant macrosegregation by increasing the amount of solute rejected into the liquid and by the movement of unattached dendrites and dendrite fragments, and that macrosegregation in excess of what would be expected due to diffusion transport is not necessarily caused by convection in the liquid.     

Influence of Forced/Natural Convection on Segregation During the Directional Solidification of Al-Based Binary Alloys

We analyzed the columnar solidification of a binary alloy under the influence of an electromagnetic forced convection of various types and investigated the influence of a rotating magnetic field on segregation during directional solidification of Al-Si alloy as well as the influence of a travelling magnetic field on segregation during solidification of Al-Ni alloy through directional solidification experiments and numerical modeling of macrosegregation. The numerical model is capable of predicting fluid flow, heat transfer, solute concentration field, and columnar solidification and takes into account the existence of a mushy zone. Fluid flows are created by both natural convection as well as electromagnetic body forces. Both the experiments and the numerical modeling, which were achieved in axisymmetric geometry, show that the forced-flow configuration changes the segregation pattern. The change is a result of the coupling between the liquid flow and the top of the mushy zone via the pressure distribution along the solidification front. In a forced flow, the pressure difference along the front drives a mush flow that transports the solute within the mushy region. The channel forms at the junction of two meridional vortices in the liquid zone where the fluid leaves the front. The latter phenomenon is observed for both the rotating magnetic field (RMF) and traveling magnetic field (TMF) cases. The liquid enrichment in the segregated channel is strong enough that the local solute concentration may reach the eutectic composition.     

Interdendritic Strain and Macrosegregation-Coupled Phenomena for Interdendritic Crack Formation in Direct-Chill Cast Sheet Ingots

In a study of the early stages of dendritic solidification in the direct-chill cast sheet ingots, the coupled effect of interdendritic strain and macrosegregation on the interdendritic cracks formation in dendritic equiaxed structure has been investigated by the metallographic study of ingot samples and by performing a set of mathematical analyses for AA-6061 and AA-1050 aluminum alloys. The metallographic investigation contains microstructure examinations and macrosegregation measurements of collected samples from plant trials. The mathematical analysis consists of a two-dimensional (2-D) fluid flow, heat flow, interdendritic strain, and macrosegregation-coupled model. Also, a simple approach to measure interdendritic crack has been developed based on the accumulative interdendritic strain criterion, local dendritic phases, and the crystal distortion correlation factor resulting from steep positive local segregation. The model predications have clarified the effect of high positive macrosegregation on the surface and subsurface interdendritic crack formation. It has been revealed that interdendritic strain starts to generate just below the liquidus temperature, resulting from shrinkage of liquid→solid phase transformation and contraction of dendritic solid in the incoherent mushy region. In this region, the coupled effect of the shrinkage/contraction mechanism increases the interdendritic distances between equiaxed crystals and the interdendritic crack begins to nucleate. Subsequently, in the coherent mushy region, the different interdendritic strain sources start to affect significantly the distances between equiaxed crystals in a diverse way, and therefore, the final morphology of interdendritic crack begins to form. The mechanism of interdendritic crack formation during dendritic equiaxed structure solidification and the possible solutions to this problem are discussed.     

Studies on transport phenomena during directional solidification of a noneutectic binary solution cooled from the top

In this article, we investigate the effects of laminar natural convection on directional solidification of binary fluids with noneutectic compositions when cooled and solidified from the top. The study is performed using aqueous ammonium chloride solution as the model fluid. In the first case, the initial concentration of ammonium chloride is less than the eutectic composition, leading to an aiding of the double-diffusive convection. In this case, solidification leads to the formation of a diffused matrix of dendritic crystals (mushy region) separating the pure solid and liquid regions. The mushy interface is characterized by a waviness, which is caused by a Rayleigh-Benard type of cellular motion in the liquid region. The cellular motions, which are caused by thermal and solutal buoyancy, cease once the thickness of the liquid layer falls below a critical value. The second case leads to a unique situation, in which crystals nucleated at the top wall of the cavity detach and descend through the lighter bulk fluid and, finally, settle at the floor of the cavity. In both the aforementioned cases, the features of convective transport are visualized using a sheet of laser light scattered through neutrally buoyant glass particles seeded in the solution. Numerical simulations are also performed for the first case, and the agreement with experimental results is found to be good.     

Four-Phase Dendritic Model for the Prediction of Macrosegregation,Shrinkage Cavity,and Porosity in a 55-Ton Ingot

A four-phase dendritic model was developed to predict the macrosegregation, shrinkage cavity, and porosity during solidification. In this four-phase dendritic model, some important factors, including dendritic structure for equiaxed crystals, melt convection, crystals sedimentation, nucleation, growth, and shrinkage of solidified phases, were taken into consideration. Furthermore, in this four-phase dendritic model, a modified shrinkage criterion was established to predict shrinkage porosity (microporosity) of a 55-ton industrial Fe-3.3 wt pct C ingot. The predicted macrosegregation pattern and shrinkage cavity shape are in a good agreement with experimental results. The shrinkage cavity has a significant effect on the formation of positive segregation in hot top region, which generally forms during the last stage of ingot casting. The dendritic equiaxed grains also play an important role on the formation of A-segregation. A three-dimensional laminar structure of A-segregation in industrial ingot was, for the first time, predicted by using a 3D case simulation.     

A thermodynamic prediction for microporosity formation in aluminum-rich Al-Cu alloys

A computer model is used to predict the formation and the amount of microporosity in directionally solidified Al-4.5 wt pct Cu alloy. The model considers the interplay between so-called “solidification shrinkage” and “gas porosity” that are often thought to be two contributing and different causes of interdendritic porosity. There is an accounting of the alloy element, Cu, and of dissolved hydrogen in the solid- and liquid-phase during solidification. Consistent with thermodynamics, therefore, a prediction of forming the gas-phase in the interdendritic liquid is made. The local pressure within the interdendritic liquid is calculated by macrosegregation theory that considers the convection of the interdendritic liquid, which is driven by density variations within the mushy zone. Process variables that have been investigated include the effects of thermal gradients and solidification rate, and the effect of the concentration of hydrogen on the formation and the amount of interdendritic porosity. These calculations show that for an initial hydrogen content less than approximately 0.03 ppm, no interdendritic porosity results. For initial hydrogen contents in the range of 0.03 to 1 ppm, there is interdendritic porosity. The amount is sensitive to the thermal gradient and solidification rate; an increase in either or both of these variables decreases the amount of interdendritic porosity.     

Numerical Simulation of Macrosegregation During Vertical Solidification

A continuum formulation based mathematical model has been employed to analyze the evolution of thermosolutal convection, isotherms, liquid fraction profiles and macrosegregation profiles during vertical solidification of lead-rich binary lead?Ctin alloys. The initial conditions, boundary conditions and microstructural parameters of this model have been taken from controlled experiments performed on lead?Ctin system. Numerical simulations were carried out for three chosen experiments on Pb-35?wt?pct. Sn alloy with different cooling rates. The convection was very weak in case of vertical solidification. It was also observed that the nature of the flow field did not show significant effect on thermal field. However, there was substantial effect of nature of flow on macrosegregation. It was found that the choice of permeability model, especially near the liquidus, played a significant role in the evolution of macrosegregation during vertical solidification. Through the use of appropriate permeability model, the predicted profile of average macrosegregation in ingots along the vertical (i.e., axial) direction showed reasonable agreement with experimental data over a wide range of cooling rates.     

小方坯齿轮钢连铸过程中的宏观偏析模拟

基于国内某厂齿轮钢小方坯连铸生产过程,利用ProCAST软件建立移动切片模型,能够高效模拟连铸过程中的宏观偏析,模型分别模拟研究了不同过热度、二冷水量和拉坯速度等对宏观偏析的影响。模拟结果与碳偏析检测结果吻合良好,验证了移动切片模型模拟连铸坯宏观偏析的准确性。由于溶质浮力的影响,内弧侧的宏观偏析强于外弧侧。随着过热度的增加,铸坯中心碳偏析度从1.06增加至1.15。过热度控制在25 ℃范围内,可以保证铸坯的宏观碳偏析度控制在1.10范围内。随着连铸二冷水量的增加,铸坯中心偏析改善程度较小,铸坯中心碳偏析度从1.16降低至1.13。随着拉坯速度的增加,铸坯中心偏析呈现加重的趋势,铸坯中心碳偏析度由1.14增加至1.21,拉坯速度控制在1.4 m·min–1范围内,可保证铸坯中心碳偏析度低于1.15。      

Experimental Investigation of Macrosegregation During Vertical Solidification of Lead–Tin Alloys

Thermosolutal convection during solidification of alloys is one of the major causes of macrosegregation. An experimental investigation was carried out on lead–tin alloys to study the evolution of macrosegregation during vertical solidification in laboratory. The emphasis was on accurate measurements of temperatures during solidification as well as segregation measurements and microstructural examination of solidified samples. The nominal compositions of ingots were Pb–35% Sn, Pb–19 wt% Sn and Sn–15 wt% Pb. Experiments were carried out at two superheats and different cooling rates. With decreasing cooling rate, increase in axial macrosegregation was observed in lead rich alloys. No macrosegregation was observed in tin rich alloys. Convection of interdendritic liquid was found to be responsible for macrosegregation. Also, from experimental data, heat flux to cooling water, local solidification times in the melt as well as dendritic arm spacings were determined.     

Three‐dimensional Simulation of Thermosolutal Convection and Macrosegregation in Steel Ingots

Thermosolutal convection and macrosegregation formation during the solidification of steel ingots are numerically simulated in three dimensions. The simulation is based on a fully coupled model for mass, momentum, energy, and species conservation equations. The interdendritic flow in the mushy zone is governed by Darcy's law, and the permeability term is discretized using an interpolated liquid fraction method. The numerical results for a benchmark test of macrosegregation in a Pb‐Sn alloy are compared with experimental data taken from the literature. The present model is applied to simulate the solidification of industrial steel ingots. Preliminary predictions are obtained, including the positive segregation in the hot top, and the conically shaped negative segregation zone at the bottom of the ingot. The predicted variation of the segregation ratio in carbon along the vertical centreline of an ingot is compared with measurements, and generally good agreement is observed. Future attention should be paid to the precision of prediction by considering complex solidification issues, such as the sedimentation of free equiaxed grains and the formation of shrinkage cavity.