grain structure and segregation in esa map team in physical

alloys and/or on model transparent systems,physical modelling at microstructure andmesoscopic scales (for example, largecolumnar front or equiaxed crystals) andnumerical simulation at all scales, up to themacroscopic scales of casting withintegrated numerical models.

1. IntroductionUnderstanding the structure formation insolidification processes is needed to predictthe links between grain structure andsegregation. Fig. 1 presents measurements ina steel cylindrical casting that show the links;they are clearly closely interrelated.Predicting the links requires studies thattackle a wide range of physical andengineering problems at several lengthscales. While the heat and solute flows areconsidered at the scale of the casting topredict temperature evolution and finalmacrosegregation patterns, the scale of thesolid-liquid interface is usually pertinent forthe study of microstructure and itsassociated microsegregation. However,considerations at intermediate length scalesare needed for the understanding of theformation of mesosegregation andmacrostructure features, such as theformation of channel segregates and thetransition between columnar and equiaxedgrain structures. Strong links between allthese scales exist, and numerical models areappropriate tools to investigate theinterplays between the physical mechanismsinvolved.

To build such a global model is still anongoing goal. Microstructure simulation isapplied for typically less than a cubicmillimetre, while the pertinent length scale

The main objective of this MAP project is theinvestigation of the formation of thetransition from columnar to equiaxedmacrostructure that takes place in casting.Indeed, grain structures observed in mostcasting processes of metallic alloys are theresult of a competition between the growthof several arrays of dendrites that developunder constrained and unconstrainedconditions, leading to the columnar toequiaxed transition. A dramatic effect ofbuoyancy-driven flow on the transport ofequiaxed crystals on Earth is acknowledged.This leads to difficulties in conducting preciseinvestigations of the origin of the formationof the equiaxed crystals and their interactionwith the development of the columnar grainstructure. Consequently, critical benchmarkdata to test fundamental theories of grainstructure formation are required, whichbenefit from microgravity investigations.These objectives are of direct interest to theproject’s industrial partners.

Accordingly, the project has gatheredEuropean groups with complementary skillsto carry out experiments and to model theprocesses, in particular with a view to usingthe reduced-gravity environment of theInternational Space Station to obtainbenchmark data. The ultimate objective is tocontribute significantly to the improvementof integrated modelling of grain structure inindustrially important castings. The approachis devised to deepen the quantitativeunderstanding of the basic physicalprinciples that, from the microscopic to themacroscopic scales, govern microstructureformation in solidification processing underdiffusive conditions, and with fluid flow in themelt. Pertinent questions are attacked bywell-defined model experiments on technical

of the process could reach a cubic metre(Rapaz, 1989). No direct simulation from themicro- to the macro-scale is foreseen using asingle modelling approach initiallydeveloped for the scale of themicrostructure (Voller & Porte-Agel, 2002).Thus, shortcuts need to be defined by usingelementary bricks developed for themodelling of intermediate length scalephenomena. For instance, one can integratea growth kinetics model that relates theundercooling to the velocity of a solid-liquidinterface, in a macroscopic model that tracksthe position of the growth front of a mushyzone. Thus, the diffusion problem ahead ofthe solid-liquid interface at the scale of themicrostructure is not simulated with adetailed description of the microstructurewhile the position of the growth front withrespect to the scale of the casting is takeninto account. With such approximation, thetemperature gradient in the region ofundercooled liquid formed ahead of thegrowing front can be assessed.

The latter example is a good illustrationof the main objective defined in this MAPproject. It consists of improving integratedmodelling of grain structure in industrialcastings. Several criteria have been definedfor the prediction of the columnar-to-equiaxed transition (CET) in casting. Theyrely on various mechanisms such as themechanical blockage of the columnar frontat a threshold value of the volume fractionof equiaxed grains (Hunt, 1984), thebreakdown of the columnar front and itsfragmentation when the temperaturegradient in the liquid vanishes (Gandin,2000) or the vanishing of the columnar frontundercooling due to solutal interactionbetween columnar and equiaxed structures

(Martorano et al., 2003). All these criteriadepend on the temperature gradient aheadof a columnar growth front, which controlsthe extent of the undercooled zone in whichnuclei are able to develop.

However, clear validation of criteria bycareful experimental investigation of the CETis not available. This is mostly becauseconvection of liquid and transport ofequiaxed grains play a key role on the grainstructures observed on the ground. TheCETSOL approach is devised to deepen thequantitative understanding of the basicphysical principles that, from themicroscopic to the macroscopic scales,govern structure formation in solidificationprocessing under diffusive conditions andwith fluid flow in the melt. Its strategy isbased on a joint attack of pending questionsby:

Well-defined model experiments on technicalalloys Collection of benchmark data fromsystematic series of— critical experiments under pure diffusive

conditions in microgravity;— critical experiments under convective

Grain Structure and Segregation in

Microgravity Castings

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Report of the ESA MAP Team in Physical Sciences

Columnar-to-Equiaxed Transition inSolidification Processing (CETSOL)

(MAP-99-117)

Fig. 1. A cross-section of a steel cylindrical casting with (left) thegrain structure map and (right) the segregation map(Fe-0.22wt%C-0.62wt%Cr-1.14wt%Ni-0.25wt%Mnalloy)(courtesy of Arcelor; Mazet, 1995).

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(b, c). The structure should be compared withthat produced without vibration and shownin Fig, 2a. For gvib = 1 g0 (f = 14 Hz,a = 1.25x10–3 m), the morphology of thedendritic microstructure becomes morehomogeneous. In particular, the eutecticborder found in Fig. 2a is suppressed inFig. 2b. The origin of the eutectic border wasexplained by Burden et al. (1973) andpredicted by Nguyen-Thi et al. (2005) usingthe numerical model developed by Lan & Tu(2000): melt made denser by rejected solutemoves towards any depressed region of thefront, which creates a zone of higherconcentration and thus further retardssolidification. Detailed analysis of thepredicted convection cells explains thedistribution of the temperature andcomposition fields which, combined with acriterion for microstructure selection basedon maximum growth temperature, results inprimary eutectic growth from the melt at theperiphery of the cylindrical samples in theabsence of vibration.

For gvib = 2.5 g0 (f = 50 Hz, a = 0.25x10–3 m),Fig. 2c shows that the microstructure isstrongly disturbed by convection.Morphologies are fragmented and a largenumber of clusters of globular cells ordendrites are distributed in a cross-section.Longitudinal sections confirmed that thestructure was strongly disturbed and apattern somewhat like equiaxed growth wasobtained for higher level of vibration.Presently, it is difficult to determine whethersecondary arms were detached or not fromprimary stalks during the growth process,which is a key question for the CET duringdirectional solidification.

2.2 Influence of Forced Convection onMicrostructure during DirectionalSolidification using a TravellingElectromagnetic Field

A gradient furnace with the possibility ofapplying a travelling magnetic field wasdesigned for the solidification of Al-basedalloys (Zaidat et al., 2005). The travellingmagnetic field drives a forced flow in theliquid above the solidifying interface, mainlywith a radial convection cell. The liquid flowsupward at the centre of the cylinder anddownward along its periphery. Experimentswere made with an Al-3.5wt%Ni alloy. Thealloy was refined with 0.5wt% of theconventional Al-5wt%Ti-1wt%B refiner.Structures were observed at the bottom partof the ingot in longitudinal sections madealong the ingot axis. Characterisations of thesuccessive transients and of the stationarymicrostructures were performed byexploiting the complementary informationobtained through conventional opticalmicroscopy after polishing steps (to evidencemicrostructures, eutectic) and anodicoxidation (to separate grains by differentcolours).

The effect of the travelling magnetic fieldis shown In Fig. 3 by comparison with aconventional Bridgman solidification.Whereas the dendritic grain structure

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investigation of the effect of moving solidparticles in the melt on meso- andmacrosegregation by means of a ensembleaveraging two-phase model is also beingundertaken (EPM).

2. Model Experiments2.1 Influence of Forced Convection on

Microstructure during DirectionalSolidification using Vibrations

Directional solidification experiments werecarried out in a Bridgman-type furnace(Nguyen-Thi et al., 2005). The effect of theforced convection by means of mechanicalaxial vibrations on the solidificationstructures was investigated in Al-Ni alloys.The parameters of the forced convection arethe amplitude, a, and the frequency, f, of thevibrations conducted parallel to thelongitudinal axis of the cylindrical samples.These parameters are translated into avibrational acceleration, gvib = a(2πf )2, andcompared to the terrestrial acceleration, g0.

Effects of the vibration are shown in Fig 2

conditions, with fluid flow in the meltdue to– natural buoyancy-driven convection,– convection induced by axial and

rotating vibrations (L2MP),– convection controlled by applying a

travelling magnetic field (EPM) and arotating magnetic field (ACCESS) withflow respectively perpendicular andparallel to the solidification front.

Modelling and simulations from micro- tomacrostructures

The phase-field technique (ACCESS) isapplied thanks to developments compatiblewith typical CET configurations. It permitsquantification of the interactions betweenthe heat and solute flows during the CET atthe scale of the dendritic microstructure. Inturn, this is useful for a sound comparisonwith the predictions of the global modelsbased on Cellular Automaton (CEMEF) andFront Tracking methods (UCD). An

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Fig. 3. Longitudinal cross-sections of an Al-3.5wt%Ni alloysolidified in a Bridgman furnace (a) without and (b, c) with atravelling electromagnetic field. (a, b) Anodic oxidation revealingthe grain structure and (c) metallographic etching showing thezones where the dendritic and eutectic microstructures aredominant. Velocity: 10–5 m/s, thermal gradient: 1900K/m,electromagnetic field intensity: 0.07 T. Sample diameter:8x10–3 m, length: 0.15 m. The metallographic etching was slightlyoff the axis of the cylinder, so that the microstructures in (b) and(c) are not identical.

Fig. 2. Metallographic transverse (bottom) and longitudinal (top) cross sections of Al-3.5wt%Ni cylindrical samples processed in a Bridgmanfurnace (a) without vibration, (b) and (c) with axial vibration. Velocity: 7.2x10–6 m/s, thermal gradient: 300K/m, frequency, amplitude andacceleration of vibrations: (b) f = 14 Hz, a = 1.25x10–3 m, gvib = 1 g0 and (c) f = 50 Hz, a = 0.25x10–3 m, gvib = 2.5 g0. Sample diameter:8x10–3 m, length: 0.1 m.


2.3 The Power-Down Technique duringDirectional Solidification

A power-down technique was developed in aBridgman-type furnace in order to reachtransient conditions under naturalconvection that lead to the CET (Sturz &Zimmermann, 2005). The procedure consistsof reducing the furnace heater temperaturewhile the sample is at rest throughout theexperiment. As a result, the temperaturegradient in the sample is decreased and thegrowth rate is increased simultaneously.Solidification starts with columnar dendriticmicrostructures from equilibrium and theCET occurs due to the continuous transientchange of the solidification rate and thetemperature field. Experiments with andwithout grain refiners were carried out asshown in Fig. 4. While the transition is sharpin the non-refined alloy, the transition in therefined Al-7wt%Si alloy is more progressive.

In a first experiment, the position of theCET was determined. Thermocouples werethen positioned in a second experiment inthe vicinity of the CET. Determination of thegrowth-front speed was also achieved usingultrasonic diagnostic. As a result of thesemeasurements, the speed of the growth frontand the temperature gradient could bedetermined at the position of the CET. Valueswere estimated to be 3x10–4 m/s to9x10–4 m/s for the speed and 400K/m to600K/m for the temperature gradient. Thesevalues are still only semi-quantitativemeasurements of the conditions at which theCET occurs. Difficulties of the measurementsare due to the nature of the growth front,which is delimited by a mushy zone. It wasfound that the speed value is in the range ofprevious results (Gandin, 2000b). This valuecorresponds to a dendrite growth

undercooling also in agreement with theliterature (Martorano et al., 2003).

3. Modelling and Simulations of the GrainStructures

3.1 Front-Tracking by the Control VolumeFinite Difference (FTCVFD) Model

A novel front-tracking algorithm wasdeveloped that treats the formation of thesolid phase from the liquid at a mesoscopicscale. It aims to track the development of thelimit between the mushy zone and the liquidrather than the solid-liquid interface(McFadden et al., 2005; Browne & Hunt, 2004).The same methodology was used formodelling the columnar grains and theequiaxed grains. The main objective of thiswork is to develop a model sufficientlyadvanced to be compared with experimentalresults of the CET. Initial findings from themodel have shown that large undercoolingmay exist ahead of the advancing columnarfront, thus giving the opportunity for equiaxedgrains to nucleate within the bulk liquid (Fig. 5).The vertical axis represents the distribution ofthe bulk liquid undercooling at a given time ina representative quadrant of a 2-D squarecasting. The X and Y axes correspond to thegeometrical representation of the quadrant.The propensity for the nucleation of equiaxedgrains can be quantified using an index(McFadden et al., 2005) proportional to thesurface integral of the undercooled zone. Thehigher the index, the greater the chance for the occurrence of a CET.

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restriction is obviously absent in the case ofcolumnar structure. Hypotheses forexplaining the effect of the travellingmagnetic field on the formation of anequiaxed structure are the decrease of theundercooling of the solidification front dueto forced convection that would reduce orsuppress the possibility for nucleation(Ananth & Gill, 1991), and/or the wash awayby forced convection of newly formedgrains towards hotter regions where theycould melt. It should be emphasised thatthe travelling magnetic field could also beused to study grain refinement in a non-refined alloy, similarly to the above withvibration. This type of experiment will alsobe carried out.

The metallographic etching of alongitudinal section of the cylindrical ingotthat was solidified with a travellingmagnetic field also reveals a central channelmade of a fully eutectic microstructure(Fig. 3c). This demonstrates well that thegrain structure and segregation are linked,and need to be studied concomitantly. Withthe alloy considered, as in the case withforced convection using axial vibration,zones of large segregation are easily madevisible because they consist of a fullydeveloped large eutectic zone growing as aprimary phase from the melt. This is anadvantage compared with industrial Al-based alloys (e.g., Al-7wt%Si or Al-4wt%Cualloys), in which only interdendriticeutectics usually develop as secondaryphases because segregation remainslimited.

revealed by anodic oxidation is fullyequiaxed in Fig. 3a, a longitudinal columnarstructure develops when applying atravelling magnetic field as shown in Fig. 3b.A similar difference is observed at the scaleof the microstructure: while a globularstructure is observed without magnetic field(not resolved in Fig. 3a), a dendritic structureis revealed in Fig. 3b and 3c. In fact, thepossibility for the development of a dendriticstructure is limited when no travellingmagnetic field is applied because of the highdensity of the equiaxed grain structure.Indeed, the solute layer developing aroundthe grains is of the order of the spacingbetween the grains. This geometrical

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Fig. 4. Longitudinal cross-sections of electrolytically etchedcylindrical samples of (a) non-refined and (b) refined Al-7wt%Siingots. Samples were produced using a power-down technique toincrease the solidification rate while decreasing the thermalgradient in the melt above the vertically developing mushy zone.Sample diameter 8x10–3 m, length 0.2 m. The left and right outersketches show, from bottom to top, the non-molten material, theregion of columnar growth and the region of equiaxed growth. Thevertical black bars indicate the size and position of the magnifiedregion with respect to the size of the sketches that represent thecasting.

Fig. 5. Snapshot of the spatial distribution of the undercooling ofthe bulk liquid in a quadrant of a square casting predicted usingthe Front Tracking Control Volume Finite Difference model. Coolingtakes place from the planes defined by coordinates x = 0 m andy = 0 m. While the solid and mushy zone is already well developed,a superheated zone remains at the centre of the casting defined bycoordinate x = y = 0.09 m.


computed according to the model proposedby Wang et al. (1995), and it is added as asource term in the formulation of the FEMmethod. In order to calculate the velocity ofthe grains that are free to move in the liquid,the model proposed by Ahuja et al. (1992)has been reprogrammed. The trajectory ofeach grain is computed with a dedicated CAalgorithm. The supersaturation entering thedendrite growth kinetics is computed using acorrelation that accounts for the effect of therelative flow velocity with respect to the solidvelocity as well as the orientation betweenthe dendrite growth direction and the fluidflow direction (Gandin et al., 2003). Finally, itis worth noting that the CAFE modelpresents similar objectives as the Eulerianmodel proposed by Wang & Beckermann(1996). The main difference is due to theLagrangian description used to track eachgrain with the CA method. Only the liquidvelocity is calculated with the FEM method.Such a simplification requires the transportof average quantities owing to the

movement of the solid phase to beaccounted for. This is achieved by thedevelopment of a new coupling schemebetween the CA and FEM method.

The experimental configuration proposedby Hebditch (1973) and Hebditch & Hunt(1974) is considered for the application of theCAFE model. It consists of a parallelepipediccavity 100 mm long, 60 mm high and 13 mmthick. All faces are carefully insulated exceptfor one of the smallest. As an example, Pb-48wt%Sn binary alloy is cooled and solidifiedby imposing a circulation of water in acopper chill that is maintained in contactwith this face. As a consequence of thisconfiguration, a 2-D Cartesian approximationof the transport phenomena can be made ifone neglects the interactions of the fluid flowwith the two largest faces of the mould(Desbiolles et al., 2003). The FEM mesh isrefined in both the horizontal and verticaldirections as shown in Fig. 6M. The location ofthe measurements of the composition in thefinal as-cast ingot are also shown in Fig. 6M. A

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applying the lever-rule approximation at themicroscopic scale of the dendrite armspacing and using the phase diagram data.In a macroscopic calculation, the presence ofthe mushy zone is a direct function of theaverage enthalpy and the local liquidustemperature. As soon as the enthalpy fallsbelow the enthalpy that corresponds to thelocal liquidus temperature, the solid starts toform and the volume fraction of solidconsequently increases. The final solid isformed at the eutectic temperature.

In order to account for the effect of thegrowth undercooling of the microstructure,as well as for the transport of equiaxedgrains that can freely develop in the liquid, aCellular Automaton (CA) method is coupledwith the macroscopic FEM method(Guillemot et al., 2004). The output of the CAmodel is the grain structure. Such a couplingbetween the micro- and macroscopicmethods enables non-equilibriumsolidification paths to be taken into account.The volume fraction of solid is not only afunction of the average composition andenthalpy, but also a function of the presenceof the mushy zone. The presence of themushy zone itself becomes a function of thelocation of the grains. The latter depends onboth the undercooling of the growingdendritic grain structure and itssedimentation and transport due to the fluidflow. The coupling with the movement of thefree equiaxed grains requires modification ofthe drag force entering the Navier-Stokesequation. This force depends on the relativevelocity of the liquid with respect to thesolid (i.e., velocity of the equiaxed grains), aswell as on the volume fraction of theequiaxed grains in the macroscopicelementary representative volume. It is

The equiaxed index was calculated forthree alloy compositions: Al-1%wtCu,Al-2%wtCu and Al-4%wtCu. In addition, eachalloy was simulated solidifying with threeheat transfer coefficients imposed at themould walls. In each case, the equiaxed indexstarts at zero and increases gradually at thebeginning. As the casting cools, theundercooled region expands and a rapidincrease in the equiaxed index results.However, as the solid fraction of the castingincreases further (and the liquid fractiondecreases), the equiaxed index peaks andsubsequently decreases to zero where theentire casting consists of solid and columnarmush. It is observed that, for any given alloy,the lowest heat transfer coefficient has thehighest peak value for equiaxed index. Thissuggests that a lower heat transfercoefficient at the mould walls encouragesthe equiaxed zone. Also, alloys with highersolute concentration have higher peak valuesfor equiaxed index and therefore a highertendency for an equiaxed zone to develop.These results agree qualitatively withexperimental results.

3.2 Cellular Automaton: the Finite Element(CAFE) Model

The finite element method (FEM) developedby Ahmad et al. (1998) is used to solve theaverage conservation equations for the totalmass, energy, mass of solute and momentum.As outputs of an FEM simulation, one canpredict the time evolution of the averageenthalpy, average velocity (the solid is fixed),and average solute composition. The averageenthalpy and solute composition areconverted into evolutions of temperature,solute composition of the liquid and volumefraction of solid. This is carried out by

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Fig. 6. Predictions from the Cellular Automaton Finite Element model showing the final (a) grain structure, (b) segregation map of Sn with itscomposition scale and (c) composition profiles for a Pb-48wt%Sn alloy. Equiaxed grains nucleated in the undercooled melt are free to moveowing to sedimentation and buoyancy-driven flows. The FEM mesh is drawn (M) together with horizontal lines indicating the location of theprofiles drawn in (c). The symbols in (M) indicate the location of the measurements (Hebditch & Hunt, 1974).


diameter rods were extracted from the as-cast structure), it is not possible to use theseexperimental results directly in order tovalidate the predictions of the CAFE model.Similarly, no detailed measurement of theaverage composition has yet beenconducted with the purpose of characteri-sing a segregation map with a definitionsmaller than the grain size. It is thus difficultto validate the present predictions ofmesosegregation. Furthermore, themeasurements are often carried out withsamples of several cubic millimetres. Suchmeasurements do not permit validation ofthe simulations, unless the predictedsegregation maps are also drawn byaveraging the average composition over thesame volume as used for the measurements.This procedure, however, has not been usedhere since it strongly rubs out the effect ofthe grain structure.

4. Conclusions and Future StudiesNew experimental devices have beendeveloped within the MAP project to obtainseveral means of forcing convection in themelt, employing axial vibrations and atravelling magnetic field. Additional devicesnot illustrated in this report employ arotating magnetic field and alternatedcrucible rotation; they are underdevelopment. These facilities are combinedwith Bridgman-type furnaces.

Experiments with forced convection,either due to vibration or travellingelectromagnetic field, clearly reveal the effectof convection on the development of themicro- and macrostructures. It is shown that,on Earth, forced convection is a means ofinfluencing the morphology of the dendriticgrain structure, going from columnar to

equiaxed and vice versa. So far, the effect offorced convection can only be superimposedon the effect of natural convection. It is thusnot possible to show the independent effectsclearly of natural and forced convections. Forthese reasons, experiments with forcedconvection are scheduled for theInternational Space Station. Similarly, sincenatural convection is known to influence theCET strongly, experiments will be carried outwith a low-gravity environment and noforced convection. This will provideconditions for the pure diffusion regime. Thepower-down technique will be the first tobenefit from microgravity, using aprogrammed sounding rocket facility. Theresults will be used as benchmark data thatcan be compared with physical mechanismsproposed to explain the CET.

In parallel, the global models are beingfurther developed for the prediction of grainstructure and segregation in casting.Additional modelling activities are based onthe phase-field method for the simulation ofthe interaction between the solute layers ofcolumnar and equiaxed grain structures, andthe ensemble averaging two-phase methodfor the prediction of macrosegreation andthe CET (Ciobanas et al., 2005). While theexperiments in microgravity and on Earth willprovide benchmark results, comparison withthe predicted grain structure, the position ofthe CET and the associatedmacrosegregation will be conducted.

AcknowledgmentsCETSOL is an ESA MAP project. The partnersalso express their gratitude to CNES, DLR,Enterprise Ireland (EI) and the nationalinstitutions supporting the project. Supportfrom Calcom S.A. (Lausanne, CH), Honeywell

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the literature (Beckermann, 2002; Lesoult etal., 1999), especially for larger ingot sizes. Thelimited size of the present Pb-48wt%Sn ingotdoes not favour such an effect. It should alsobe said that the grain structure model onlyconsiders the formation of equiaxeddendritic grains: no globulitic grain with ahigh inner-volume fraction of solid is takeninto account. Such limitation could bedetrimental for the application of thepresent model to the prediction ofsegregation induced by grain movement.The morphology of the equiaxed grainstructure not only plays a role onsegregation, but it is also expected to modifythe fluid flow considerably. Despite the factthat the latter effect is accounted for in thepresent model, the consequence on theoverall fluid flow remains limited andmacrosegregation is still mainly explained bythe same thermosolutal considerations thatlead to the segregation map computed witha purely macroscopic FEM calculation.

The effect of the grain structure onmesosegregation is less investigated in theliterature. The fact that instability of thegrowth front leads to further instability ofthe segregation map is well established forthe formation of channels that could giverise to freckle formation. But the propositionthat accumulation of transported equiaxedgrains on the growth front could lead to theformation of channels and eventuallyfreckles is new. Only in situ diagnostic bydirect visualisation of the formation of thegrain structure could validate this prediction.

Since the grain structure is difficult toextract from Hebditch & Hunt (1974) andHebditch (1973), and since themeasurements were carried on a very coarsegrid and for a relatively large volume (4 mm-

detailed table of the values of the parametersis given in Guillemot et al. (2004).

The results of the simulations are shownin Fig. 6. Maps of grain structures andmacrosegregation, as well as compositionprofiles are shown. Time evolution of thedevelopment of the grain structure showsthat equiaxed grains accumulate in thebottom region of the ingot bysedimentation. The general trends of thesegregation map are the same as thatpredicted by a purely FEM calculation(Ahmad et al., 1998). However, variationsknown as mesosegregations are alsopredicted at a smaller length scale. Thesevariations are due to the development ofequiaxed grains in preferred zones, leading toan instability of the segregation field thatfurther develops with the propagation of themushy zone. It is interesting to observe theformation of channels in the top-left side ofFig. 6b. The mechanism that has led to theformation of this channel is an instability ofthe growth front. Equiaxed grains havemoved and accumulated at a position closeto the actual root of the channels, formingarms of fixed equiaxed grains. These armsserved as a barrier to the fluid flow that thendeveloped preferentially on its sides. As aconsequence, a channel with enriched solutedeveloped between the arms, similar to themechanism leading to the formation of afreckle. The average composition profilesdrawn in Fig. 6c also show similar trends.

The calculations show that, in theconfiguration of the experiments performedby Hebditch & Hunt (1974), themacrosegregation is not directly influencedby the structural features. The effect of thetransport of equiaxed grains on themacrosegregation is well demonstrated in

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on Model Systems. Metall. Trans. 5, 1557-1564.

Hunt, J.D. (1984). Steady State Columnar andEquiaxed Growth of Dendrites andEutectic. Mater. Sci. Engng. 65, 75-83.

Lan, C.W. & Tu, C.Y. (2000). MorphologicalInstability due to Double DiffusiveConvection in Directional Solidification:the Pit Formation. J. Cryst Growth 220, 619-630.

Lesoult, G., Albert, V., Combeau, H., Daloz, D.,Joly, A., Stomp, C., Grün, G.U. & Jarry, P.(1999). Equiaxed Growth and RelatedSegregations in Cast Metallic Alloys. InConference IUMRS-ICAM’99, Beijing, China.

Martorano, M.A., Beckermann, C.,Gandin, Ch.-A. (2003). A Solutal InteractionMechanism for the Columnar-to-EquiaxedTransition in Alloy Solidification.Metallurgical & Materials Transactions 34A,1657-1674.

Mazet, Th. (1995). Etude des Structures deSolidification et des Ségrégations dans desLingots d’Acier. Ph.D. Thesis, InstitutNational Polytechnique de Lorraine,France.

McFadden, S., Browne, D.J. & Banaszek, J.(2005). Prediction of EquiaxedSolidification ahead of a Columnar Front:Indirect and Direct Methods. InSolidification and Gravity ’04 (Eds, Roosz, A.,Rettenmayr, M., Su, C.-H. & Gácsi, Z.),Materials Science Forum, Trans TechPublications Ltd, Switzerland.

Nguyen-Thi, H., Zhou, B.H., Reinhart, G.,Billia, B., Liu, Q.S., Lan, C.W., Lyubimova, T. &Roux, B. (2005). Influence of ForcedConvection on Columnar Microstructureduring Directional Solidification of Al-NiAlloys. In Solidification and Gravity ’04 (Eds,Roosz, A., Rettenmayr, M., Su, C.-H. & Gácsi,

Z.), Materials Science Forum, Trans TechPublications Ltd, Switzerland.

Rappaz, M. (1989). Modelling ofMicrostructure Formation in SolidificationProcesses. Internat. Mats. Rev. 34, 93-123.

Sturz, L. & Zimmermann, G. (2005). Columnarto Equiaxed Transition in Binary Al alloyswith and without Grain Refiners. InSolidification and Gravity ’04 (Eds, Roosz, A.,Rettenmayr, M., Su, C.-H. & Gácsi, Z.),Materials Science Forum, Trans TechPublications Ltd, Switzerland.

Voller, V. R. & Porte-Agel, F. (2002). Moore’s Lawand Numerical Modeling. J. Comput. Phys.179, 698-703.

Lang, C.Y., Ahuja, A., Beckermann, C. & de GrohIII, H.C. (1995). Multiparticle Interfacial Dragin Equiaxed Solidification. Metall. Mater.Trans. 26B, 111-119.

Wang, C.Y. & Beckerman, C. (1996). EquiaxedDendritic Solidification with Convection:Part I: Multiscale/Multiphase Modeling.Metall. Mater. Trans. 27A, 2754-2764.

Zaïdat, K., Ouled-Khachroum, T., Mangelinck-Noël, N., Reinhart, G., Dupouy, M.-D. &Moreau, R. (2005). Effect of TravellingMagnetic Field on the DirectionalSolidification of Refined Al-3.5wt%NiAlloys. In Solidification and Gravity ’04 (Eds,Roosz, A., Rettenmayr, M., Su, C.-H. & Gácsi,Z.), Materials Science Forum, Trans TechPublications Ltd, Switzerland.

109

physical sciences

Model for Columnar/EquiaxedSolidification of a Binary Alloy. InSolidification and Gravity ’04 (Eds. Roosz, A.,Rettenmayr, M., Su, C.-H. & Gácsi, Z.),Materials Science Forum, Trans TechPublications Ltd, Switzerland.

Desbiolles, J.-L., Thévoz, Ph. & Rappaz, M.(2003). Micro-/MacrosegreagtionModeling in Casting: A Fully Coupled 3DModel. In Modeling of Casting, Welding andAdvanced Solidification Processes X (Eds.Stefanescu, D. M., Warren, J, Jolly, M. &Krane, M), The Minerals, Metals andMaterials Society, Warrendale, USA, 245-252.

Gandin, Ch.-A. (2000a). From Constrained toUnconstrained Growth during DirectionalSolidification. Acta Materialia 48, 2483-2501.

Gandin, Ch.-A. (2000b). Experimental Study ofthe Transition from Constrained toUnconstrained Growth during DirectionalSolidification. ISIJ Internat. 40, 971-979.

Gandin, Ch.-A., Guillemot, G., Appolaire, B. &Niane, N.T. (2003). Boundary LayerCorrelation for Dendrite Tip Growth withFluid Flow. Mater. Sci. Engng. A342, 44-50.

Guillemot, G., Gandin, Ch.-A. & Combeau, H.(2004). Modeling of Macrosegregation andSolidification Grain Structures with aCoupled Cellular Automaton - FiniteElement Method. In Solidification Processesand Microstructures: A Symposium in Honorof Prof. W. Kurz (Eds. Rappaz, M.,Beckermann, C. & Trivedi, R.), The Minerals,Metals and Materials Society, Warrendale,USA, 157-163.

Hebditch, D.J. (1973). Segregation in Castings.Ph.D. Thesis, Oxford University, UK.

Hebditch, D.J. & Hunt, J.D. (1974).Observations of Ingot Macrosegregation

International Technologies Ltd. (Waterford,IRL), Hydro Aluminium Deutschland GmbH(Bonn, D), Industeel-Arcelor (Le Creusot, F),Irsid-Arcelor (Maizières-lès-Metz, F), PechineyCRV (Grenoble, F) and Snecma Moteurs(Moissy-Cramayel, F) is also acknowledged.

ReferencesAhmad, N., Combeau, H., Desbiolles, J.-L.,

Jalanti, T., Lesoult, G., Rappaz, J., Rappaz, M.& Stomp, C. (1998). Numerical Simulationof Macrosegregation: a Comparisonbetween Finite Volume Method and FiniteElement Method Predictions and aConfrontation with Experiments. Metall.Mater. Trans. 29A, 617-630.

Ahuja, A., Beckermann, C., Zakhem, R.,Weidman, P.D. & de Groh III, H.C. (1992).Drag Coefficient of an Equiaxed DendriteSettling in an Infinite Medium. InMicro/Macro Scale Phenomena inSolidification, ASME. HTD-218, AMD-139,85-91.

Ananth, R. & Gill, W.N. (1991). Self-ConsistentTheory of Dendritic Growth withConvection. J. Crystal Growth 108, 173-89.

Beckermann, C. (2002). Modelling ofMacrosegregation: Applications andFuture Needs. Int. Mater. Rev. 47, 243-261.

Browne, D.J. & Hunt, J.D. (2004). A Fixed GridFront-Tracking Model of the Growth of aColumnar Front and an Equiaxed Grainduring Solidification of an Alloy. NumericalHeat Transfer 45B, 395-419.

Burden, M.H., Hebditch, D.J. & Hunt, J.D.(1973). Macroscopic Stability of a Planar,Cellular or Dendritic Interface duringDirectional Freezing. J. Cryst. Growth 20,121-124.

Ciobanas, A., Baltaretu, F. & Fautrelle, Y. (2005).Ensemble Averaged Two-Phase Eulerian

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MAP Team Members

Academic Partners

Charles-André Gandin

Centre de Mise en Forme des Matériaux

(CEMEF) - UMR 7635, Ecole Nationale

Supérieure des Mines de Paris (ENSMP) -

BP 207, F-06904 Sophia Antipolis Cedex,

France.

Tel: +33 (0)4 93 95 74 27

Fax: +33 (0)4 92 38 97 52

Email: [email protected]

Bernard Billia

Laboratoire Matériaux et Microélectronique

de Provence (L2MP) - UMR CNRS 6137,

Université d’Aix-Marseille III - Faculté des

Sciences de Saint Jérôme, F-13397

Marseille Cedex 20, France.

Tel: +33 4 91 28 81 14

Fax: +33 4 91 28 87 75


Gerhard Zimmermann

ACCESS e.V., Intzestraße 5, D-52072 Aachen,

Germany.

Tel: +49 241 80 98 000

Fax: +49 241 38578

Email:

[email protected]

David Browne

University College Dublin (UCD), Department

of Mechanical Engineering, Belfield,

Dublin 4, Ireland.

Tel: +353 1 716 1901

Fax: +353 1 283 0534


Yves Fautrelle

Elaboration par Procédés Magnétiques (EPM) -

UPR CNRS 9033, Institut National

Polytechnique de Grenoble (INPG), Ecole

Nationale Supérieure d’Hydraulique et de

Mécanique de Grenoble (ENSHMG), F-38402

Saint Martin d’Heres cedex, France.

Tel: +33 4 76 82 52 02

Fax: +33 4 76 82 52 49


Industrial Partners

CALCOM ESI S.A.

PSE-Ecublens, CH-1015 Lausanne, Switzerland.

Honeywell International Technologies Ltd.

Unit 411, Western Industrial Estate, Cork Road,

Waterford, Ireland.

Hydro Aluminium Deutschland GmbH

CC Casting, Alloys and Recycling - R&D Bonn,

Georg-von-Boeselager Str.21, Postbox

2468, D-53117 Bonn, Germany.

Industeel-Arcelor

Centre de recherche des Matériaux du

Creusot, 56 rue Clémenceau, BP56, F-71202

Le Creusot, France.

IRSID-Arcelor

BP 30320, F-57283 Maizieres-les-Metz, France.

ALCAN

Centre de Recherche de Voreppe, BP 27,

F-38341 Voreppe cedex, France.

SNECMA Moteurs

Site de Villaroche, F-77550 Moissy Cramayel,

France.

“The columnar-to-equiaxed transition is oneof the main structural features observed incasting. It is believed to be a very importantissue with respect to the prediction ofmacrosegregation that develops at the scaleof the cast products. Its understanding is thusof primary importance for us. Further workshould be addressed in order to identify allphysical mechanisms that lead to thecolumnar-to-equiaxed transition. Indeed, theknowledge of such mechanisms is requiredfor further developments of computationaltools that aim to predict both structural andsegregation features of as-cast products.”

Jean-Marc Steiler, Technical Director, ArcelorResearch Centre

“We see a high relevance of this study for ourproduction in the cast houses of foundries. Wewant to state that we support the integrationof such research activities into global modelswhich are actually widely used by ourindustry. It is a must for a later usage byindustry that the overall influence of 3-Dmacroscopic effects like convection isincorporated into the evolution ofmicrostructure in every location of the castpart.”

Gerd-Ulrich Grün, Research and Development,Hydro Aluminium Deutschland GmbH


grain structure and segregation in esa map team in physical

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