1、Fractionation and Mold Filling of Semisolid SlurriesI:Isothermal ConditionO.J.Ilegbusi,K.A.Quach,and M.D.Mat(Submitted 29 December 1997;in revised form 15 September 1998)The fractionation and mold filling of semisolid slurries were numerically investigated for a range of moldgeometry,inflow velocity
2、,nozzle diameter,and fraction solid.The slurry was assumed to be a shear-thin-ning,non-Newtonian fluid.Fractionation was determined from the trajectories of isothermal particlesinjected into the slurry.The results indicate fractionation is reduced with a tapered mold,high-inflow ve-locity,large nozz
3、le diameter relative to mold,and low fraction solid.1.IntroductionSemisolid slurry processing is widely employed for produc-ing dispersion-strengthened,metal-matrix composites of nearnet shapes.The properties of the composite products arestrongly dependent on the slurry rheology and mold-fillingchar
4、acteristics.Slurry rheology is quite complex,being sheardependent and thixotropic.The mold filling of slurry is furthercomplicated by the occurrence of phase segregation or frac-tionation,depending on the operating conditions.This paperexamines this problem during mold filling of slurries at high-fr
5、action solid.The experimental works of Suery(Ref 1),Suery andFlemings(Ref 2),and Flemings(Ref 3),on semisolid,tin-leadalloys have demonstrated the effect of shear stress on mechani-cal behavior and phase segregation in the solidified composite.The numerical model of Ohnaka(Ref 4),on solidification o
6、fsemisolid slurries has been used for the design of castings ofcomplex shapes for industrial production.Relatively few studies,however,have addressed the prob-lem of fractionation of semisolid slurries.Secordel and Valette(Ref 5)provided some experimental data on semisolid steels,showing a direct co
7、rrelation between inflow velocity and liquidrejection during extrusion.This study was,however,limited tosteady state behavior.Kennedy and Clyne(Ref 6)performed aquasi-one-dimensional analysis of particle migration duringsolidification processing of metal-matrix composites.The dy-namics of isolated p
8、articles was considered,and there was noevidence the results could be applicable to highly loaded slur-ries of practical interest.This paper addresses phase segregation during mold fillingof semisolid slurries under assumed isothermal condition.Fractionation was determined from the trajectories of i
9、so-lated particles introduced with the slurry at the inlet.Theparticles were allowed to exchange momentum with theslurry.A range of operating parameters was investigated,in-cluding inflow rate,fraction solid,nozzle diameter,and moldgeometry.2.FormulationFigure 1 illustrates the systems considered,a
10、cylindrical anda tapered mold.The mold diameter at the inlet is 2.54 cm,andthe nozzle diameter ranges are from 1.27 to 2.03 cm.A semi-solid slurry of Sn-15%Pb alloy was injected from the bottom ofeach mold.The objective was to use an appropriate constitutivemodel of slurry rheology to represent the
11、mold filling processas well as possible phase segregation(or fractionation).Amathematical representation of this process under isothermalcondition required solution of the equations governing the con-servation of mass and momentum as well as representation ofthe slurry rheology,particle dynamics,and
12、 free surface.The slurry was assumed to behave as a non-Newtonian in-compressible fluid with a power-law dependence of the viscos-ity on the shear rate(Ref 7,8).This simple power-law modelhas been demonstrated to adequately reproduce the essentialshear-thinning characteristics of semisolid slurries(
13、Ref 7,8).The governing equations can thus be expressed as the fol-lowing:Keywordscasting,fractionation,mathematical analysis,non-Newtonian fluid,slurryO.J.Ilegbusi,K.A.Quach,and M.D.Mat,Department of Mechani-cal,Industrial,and Manufacturing Engineering,Northeastern Univer-sity,Boston,MA 02115.Fig.1
14、Schematic sketch of mold filling operation(a)cylindri-cal mold and(b)tapered moldJMEPEG(1999)8:31-34ASM InternationalJournal of Materials Engineering and PerformanceVolume 8(1)February 199931For mass conservation:u_=0(Eq 1)For momentum conservation:t(u_)+(uu_)=p+(Eq 2)where p is the static pressure,
15、u_ is the velocity vector,and isthe shear stress tensor related to slurry viscosity,thus:=uixj+ujxi(Eq 3)To determine,the slurry was assumed to be a non-Newto-nian fluid with a power-law rheology,thus(Ref 9):=m12(:)1/2n1(Eq 4)where is the rate of deformation tensor,(:)is the dyadicproduct of,and m a
16、nd n are empirical coefficients defined as(Ref 9,10):m=exp(9.783fs+1.435)(Eq 5)n=0.1055+0.41fs fs 0.30n=0.308+1.78fs fs 0.30(Eq 6)Although the relations in Eq 5 and 6 were originally derivedfrom the data on a semisolid tin-lead alloy(Ref 9,10),Ilegbusiand Szekely(Ref 7,8)have demonstrated their validity forother alloy systems.3.Determination of FractionationA quasi-multiphase approach was used to quantify frac-tionation.Specifically,a known number of particles was in-jected into the mold with th
