1998_watanabe control of composition gradient in a metal

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ELSEVIERPII: S1359-835X(97)00121-8

Composites Part A 29A (1998) 595-6018 1998 Elsevier Science LimitedPrinted in Great Britain. All rights reserved

1359-835U98/$19.00

Control of composition gradient in a metal-ceramic functionally graded materialmanufactured by the centrifugal method

Yoshimi Watanabea,*, Noboru Yamanakab and Yasuyoshi FukuiCaDepattment of Functional Machinery and Mechanics, Shinsho University,3-15-l Tokida, Ueda 386-8567, JapanbDepartment of Mechanical Engineering, Miyakonojo National College of Technology,473- 1 Yoshino-cho, Miyakonojo 885-8567, JapanDepartment of Mechanical Engineering, Kagoshima University, l-21-40 Korimoto,Kagoshima 830-0065, Japan(Received 17 December 7336; revised 7 October 7337; accepted 4 November 19971

The motion of ceramic particles in a molten metal of a viscous liquid under a centrifugal force is numericallymodeled to study the formation process of composition gradients. The simulated results are in good agreementwith those of experiments that used a plaster-corundum model functionally graded material (FGM). It is foundthat greater gradients are obtained in cases of thinner thickness, greater applied centrifugal forces and smallermesh size particles. In addition, the processing of mixed mesh size particles is examined. We conclude that the useof a mixture o f particle sizes is particularly useful to control the composition of metal-ceramic FGM smanufactured by the centrifugal m ethod. 0 1998 Elsevier Science Limited. A ll rights reserved.(Keywor ds: E. casting; C. computat ional modelling; centr ifugal method: functionally gr aded material ; viscous liquid)

INTRODUCTIONFunctionally graded materials (FGM s) a re a new class ofmaterials in which the composition and/or the microstruc-ture varied in one specific direction-3. FGM s are ofpractical interest because of the wide gradation of physicaland/or chemical properties that are possible. A number ofFGM manufacturing methods have been proposed, includ-ing the centrifugal method previously proposed by theauthors4-O. In this method, a thick-walled tube or ring isproduced from a mixture of a molten metal and solidceramics particles. Th e composition gradient is formedmainly from the difference in the centrifugal force producedby the difference in density between the molten metal andparticles.

Although the centrifugal method has the advantage ofpossible application to mass production, accurately control-ling and understanding the distribution of particle s rem ainsa difficulty. In this study, an attempt was made to establish aprocedure for controlling the composition gradientprecisely. Various processing parameters, such as cruciblefurnace temperature, mold heating furnace temperature andvelocity of mold rotation will significantly influence thecomposition gradient in the FGM . However, the determina-* Author to whom correspondence should be addressed.

tion of temperature distribution and the solidification timeduring the centrifugal method by experimental techniquesare very difficult, as the mold ro tates at a very high speedduring solidification. Moreo ver, estimation of the solidifica-tion time and temperature distribution during solidificationthrough heat- and mass-transfer analysis under realisticconditions during the centrifugal method is a complexproblem .

Therefore, for simplicity, we will disregard the tempera-ture distribution, and will regard the molten metal as aviscous liquid that obeys Stokess law. Then, we will beconcerned with the motion of ceramic particles in a viscousliquid under a centrifugal force. The formation process o fthe graded distributions of particles under a centrifugal forceduring FGM manufacturing can be simulated, taking sizeeffects such as particle size or ring size into consideration.

With the above in mind, th e graded distributions of solidspherical particles were analyzed theoretically and visua-lized with the aid of computer graphics. The process of thegraded composition formation under a centrifugal force canbe simulated considering the movement of each sphericalparticle that is suspended in the viscous liquid. M ixturesconsisting of plaster and corundum particles were chosen asexperimental models and rings having various gradedcompositions were manufactured by the centrifugalmethod. The results of the experiment were compared

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Gradient control in metal-ceramic graded material: Y. Watanabe et al.

with the simulations, and the validity of the method forcontrolling the composition gradient was discussed.

ANALYTICAL AND EXPERIMENTAL PROCED URE

Materials and experimentThe model material used for a metal-ceramic FGM w as a

mixture of plaster and corundum particles. The mixtureswere cast into thick-walled rings using a steel mold of ahorizontal centrifugal caster. Extensive d escriptions of thecentrifugal method and the model FGM have been presentedelsewhere4*8-0.

Plaster was used as an alternative to molten metal and theselected particle sizes were #60 mesh (from 235 to 265 pm)and #320 m esh (from 46 to 54 pm). The average volumefraction of corundum was kept to 1 5 ~01% in this study. Forexperimental convenience it was assumed that the viscosityof plaster before solidification was constant in the case of aconstant solidification period a nd 12 min w as selected forthe solidification period of the mixtures. However, theviscosity of the plaster depended on the volume of mixedwater. Thus, the relation between the solidification period ofmixtures and the volume of mixed water was measured bymean s of the Vicat apparatu s prior to the experiment. Theusage of the constant solidification period of mixtures as aparameter of viscosity could guarantee a constant viscosityof plaster throughout the experiments.The manufactured rings had an outer diameter of 90 mm ,a length of 30 mm and thicknesses of 10, 15 and 20 mm .Three levels of centrifugal force were applied, and arecharacterized by G num bers of 2.1, 12.4, and 80.0. Here, theG number is the ratio of the centrifugal force to gravity andis given by the following equation:

G = 2DoN2 (1)where Do is the diameter of the cast ring (m) and N is thevelocity of mold rotation (s-l). As a result, FGM ringshaving different graded compositions were obtained fromthe combination of particle size, thickness an d G num ber.Each ring was sectioned and the distribution of the corun-dum particles was measured along the thickness direction ona radial plane of the ring by a photographic method . Thethickness direction was divided into ten regions of equalwidth and the number of particles in each region wascounted. Since the average volume fraction of particleswas known to be 15 vol%, the variation of volume fractionwas calculated from the ratio of the particle numbers foreach region to the sum.Fundamental equations

During m anufacture of thick-walled tubes or rings ofmetal-ceramic FGM s, the system of ceramic particles inmolten metal behaves as a suspension of hard particles in aviscous liquid. Two significant forces act on each particle:the radial centrifugal force, and a viscous drag force in the

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opposite direction. The balance between these two forcescan be expressed as2m,$=lp,-_p,l$r 3 Gg-3ngD,$ (2)

where dxldt, d2xfdt2, m, p, g, D, and 7 are velocity, accel-eration, mass, density, gravitational acceleration, particlediameter and the viscosity of the molten metal, respectively.The subscript indices c and m denote ceramic and metal,respectively. The first term of eqn (2) represents the buoyantforce and the second results from the viscous drag. Themoving direction of the particles due to the centrifugalforce is determined by the relative values of densities: ifpc > pm, particles m ove tow ard the outer periphery of thering, an d vice versa. T he terms ,oc, pm, 7 and D, in eqn (2)ar e assumed to be time independent, and eqn (2) can besolved under the initial condition of dxldt = 0 at t = 0.The solution is

$= c-$~[l -exp( - &)I (3)In the case of Al-Sic FGM , the terminal velocity state isreached at a very early period of the centrifugal casting.Therefore the term of exp( - 9@8Dzp,) in eqn (3) becomesmuch smaller than one and then vanishes. Thus, eqn (3) canbe approximated by

dx bc ,dGgD:-_=dt 1817 (4)

It is obvious from eqn (4) that the velocity of the particles isproportional to the difference in density between particleand molten metal, to G number and to the square of theparticle diam eter, and it is inversely prop ortional to theviscosity of the molten metal.Computer simulation

It is known that the viscosity of the melt increasesaccording to the increase in number of particles in thesuspension. Various equations have been proposed topredict the variation of the viscosity in the case of arelatively large volume fraction of particles13. Mo st useful isthe Brinkmann equation14, which gives the viscosity 1 as

77 017= V( >.5 (5)l-- Vmaxwhere q. is the viscosity of the molten metal withoutparticles, V is the particle volume fraction and V, , is themaximum packing fraction. The V,,,, varies depending onthe packing cond ition and the theoretical value is in therange of 0.52 for the simple cubic packing to 0.74 for theclose packing of spherical particles. When we manufacturedthe Al-Sic FGM , the maxim um volum e fraction of SICparticle is determined to be around 43 ~01% ~. This m eansthat a packing of the simple cubic may be optimum and V, ,= 0.52 is chosen as the maximum packing fraction of theplaster-corundum system by taking account of the result ofthe Al-SIC system.


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The viscosity of plaster v. is kept constant in the presentstudy and eqn (4) can be rewritten using eqn (5):

(6 )where

andf(V)= II/ 2.5( >-- Vm a x

For ease of computer calculation, a concept of relative time,At = C dr. is introduced as an interval of calculation and eqn(6) is arranged as

where AX is the distance moved in unit time At for eachparticle. It is possible to evaluate the actual time dt if thevalue of the relative time is determined. The value of At = 7X lo6 m- s- is used here because the calculated distribu-tion pattern is unchanged even in the case of shorter At. Itcorresponds to dt = 0.5 s in the case of Al-Sic FGM man-ufactured under G = 10 0 where the material constants are p C= 3.15 Mg m-3, p m = 2.37 Mg rne3, and q. = 2.9 mPas. Itis also possible to evaluate the viscosity of plaster q. fromthe comparisons between experiment and analysis if theanalytical method is proper.

A final consideration for the simulation is the fact that theparticle diameters have a distribution range even at a fixedmesh size. This means the D, values are variable and AXgiven by eqn (7) will depend on the distribution shape range.We address this in our simulation by dividing thedistribution range into three groups of a minimum, averageand maximum particle sizes. A quarter is the minimum of235 pm particles, another quarter is the maximum of

265 brn particles and the rest is the average of 250 pmparticles in the case of #60 mesh particle. The particles ofeach group are initially arranged on equally divided latticepoints considering the volume fraction of particles, becausethe results were very similar to those obtained using a moredifficult Monte Carlo method.

Needless to say, the centrifugal force changes as theposition on the ring changes. Howev er, in this study, sincethe movement in unit time of At was calculated for eachparticle, the computer calculation becomes troublesomewhile using the above condition. Therefore, for ease ofcomputer calculation, the variation in centrifugal force wasnot taken into account in the simulation.

In addition, since the products by the centrifugal methodare rings or tubes, it is necessary to use a cylindricalcoordinate space when calculating the volume fraction ofthe reinforcing particles. Fortunately, the error due to thesubstitution of a 1-D Cartesian space for a cylindricalcoordinate space has the tendency to cancel th e error due toassuming a constant centrifugal force. Therefore, we willassume the 1-D Cartesian space.

RESULTS AND DISCUSSIONPart ic le d i s t r ibut io ns in exper iment

Model FGM rings are manufactured by the centrifugalmethod using mixtures of plaster and corundum. Typicalradial planes of sectioned rings having 15 mm thickness ofapplied G = 2.1, 1 2.4 and 80.0 are shown in Figures 1 and 2for #60 and #320 mesh particles, respectively. The standardexperimental conditions are 15 ~01% of corundum and12 min solidification period. The left and right edges of thepictures in Figures I and 2 correspond to the inner and theouter peripheries of the rings, respectively. It is found thatrings manufactured by larger G value clearly show thedarker contrast owing to the segregation of the corundum,which is black.

Figure 1 Micrographs of sectioned ring radial planes of 15 mm thickness containing #60 mesh corundum. The applied G number of (a). (b) and (c) are 2. I.12.4 and 80.0. respectively

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Gradient control in metal-ceramic graded material: Y Watanab e et al .

Figure 2 Micrographs of sectioned ring radial planes of 15 mm thickness containing #320 mesh corundum. The applied G number of (a), (b) and (c) are 2.1,12.4 and 80.0, respectively

0.0 0.2 0.4 0.6 0.8 1.0Normalized Thickness

Figure 3 The variations of corundum volume fraction measured fromFigure I containing #60 mesh corundum. The applied G number of (a), (b)and (c) are 2.1, 12.4 and 80.0, respectively

Figures 3 and 4 show the histograms of corundumvolume fraction measured from Figures 1 and 2, respec-tively. The ring thickness is normalized, where 0.0 and 1.0correspond to the inner and outer peripheries, respectively.It is found that the gradient of particle volume fractionincreases with increase of the G number. Moreo ver, smallergradients are obtained in the case of smaller particles ascompared in Figures 3 and 4. For the evaluation of thethickness effect on graded composition, 10 and 20 mmthickness rings using #60 particles are manufactured underthe same condition of Figure 3(b); applied G = 12.4. Thehistograms of corundum distributions are shown in Figure5(a) and (b ) for 10 and 20 mm thickness, respectively. Fromthe comparisons among Figure 3(b), Figure 5(a) and 5(b), itis found that thinner ring gives the greater gradation.

2 30 (c) G= 8 0 . 0


Figure 4 The variations of corundum volume fraction measured fromFi,spre 2 containing #320 mesh corundum. The applied G number of (a), (b)and (c) are 2.1, 12.4 and 80.0, respectively

Particle distributions in simulationInitially, calcula tion is perfo rme d under the condition of

15 ~01% of #60 m esh particles for 15 mm thickness ringwhere particles are positioned on equally divided latticepoints. T ypical results of the migration distance of eachparticle for the relative times 5At, 20A.t and 40At are shownin Figure 6. The left and right ends of the figures correspondto the inner and outer peripheries of the ring, respectively.The particles move left to right toward s the outer peripherywith the relative time spent.

Figure 7 shows the histograms of volume fraction in eachregion of Figure 6 for the quantitative comparisons. Asshown in Figure 7, the gradient of particle volume fractionincreases with the relative time. It should be noted here thatthe G number is inversely proportional to the actual timefrom eqn (4) and the solidification period is taken as

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constant. This means longer relative time is obtained in thecase of greater applied G value and vice versa. Thus, th eresults of computer simulation, relating to the G number, donot contradict the experimental results.

Next, we pay attention to the effect of particle sizes on theformation of graded composition. The particle distributionfor #120 (from 106 pm to 125 pm) and #320 m esh particlesare shown in Figure 8. The mean volume fraction ofparticles, the ring thickness, and the relative time are15vol%, 15 mm, and 40At. respectively, which are the sameconditions as in Figure 7(c). Thus, comparisons are madeusing the results of Figure 7(c) of #60 mesh particle, Figure8(a) of #120 mesh particle and Figure 8(b) of #320 mesh

4030

% 20._ 10OE?i 0

3 302 20

100

(b) Ring Thickness; 20mm 1


Figure 5 The effect of ring thickness on the variations of corundumvolume fraction measured using #60 mesh corundum and applied G = 12.4for the comparison with Figure 3(b). The ring thickness of (a) and (b) are 10and 20 mm, respectively

I-0.2

Figure 6 Simulation of particle movement under the condition of15 ~01% of ##60 mesh particles in the case of a 15 mm thickness ring.The relative times of (a), (b) and (c) are 5Ar, 20Ar and 40At. respectively.whereAt= X lOm-s-l

particle. The migration distance is greater in the case oflarger particles and the graded distribution decreases as theparticle size decreases, which shows good agreement withthe experiment.

Finally, simulation is done to confirm the effect of thering thickness on the graded distribution. The conditions ofmesh size. the mean volume fraction and the relative timeare #60. 15 ~01% and 40At. respectively, which are alsosame conditions as in Figure 7(c). The results of ringthickness 10 and 20 mm are shown in Figure 9. Therefore,comparisons are made using the results of Figure 9(Lz) of10 mm thickness, Figure 7(c) of 1.5 mm thickness andFigure 9(b) of 20 mm thickness. In this series. the gradationof particle distribution decreases as the ring thickness

30 -20 -10 -0 -

3089 20tia 103e 0u 40E79 30

20

100

(b) 20 At

0.0 0.2 0.4 0.6 0.8 1.1)Normalized Thickness

Figure 7 The variations of corundum volume fractton measured fromFigure 6 applying 15 ~01% of #60 mesh particles and 15 mm thickness. Therelative times of (a). (b) and tc) are SAr. 20At and 4OAr. respectively, whereAr = 7 X IO6 mm SC


Figure 8 The effect of nominal particle size on the variations of volumefraction simulated under the condition of 15 ~01%. 15mm thickness and40Ar for the comparison with Figure 7(c). The particle sizes of (a) and (b)are #I20 and #320 mesh particles, respectively


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Gradient control in metal-ceramic graded m aterial: Y. Watana be et al.

increases, which also agrees with experiment. In this way,the agreement between the results obtained by computersimulation and those obtained by experiment is excellent.

Some further explanation is required for the differencebetween experimental and simulation results near the outersurface of the ring. Although the simulation results alwaysshow a higher rate of accumulation near the outer surface ofthe ring than at other positions, the experimental results donot always show the same high accumulation. Thisdifference may come from the so-called wall effect inrheology, but an alternative possibility comes from theshape of particles. Although the shape of particles isassumed to be spherical in this study, the Sic particles in theAl-Sic FGM and the corundum particles in the plaster-corundum FGM are more granularly shaped than spherical.A number of studies have shown that any deviation in shapefrom spherical means an increase in viscosity for the samevolume fraction15. The assumption of spherical particlesalso leads to a higher rate of accumulation near the outersurface of the ring.

It must be emphasized here that despite the difference atthe very outer position of the ring, the results discussed hereare otherwise in good agreement with the experiments. Ourassumption of constant temperature distribution and cen-trifugal force did not adversely affect predictions of gradeddistribution of particles. Therefore, it is concluded that thepresent simulation is a useful tool to obtain the informationabout the graded composition of FGMs p roduced by thecentrifugal method.

Control of composition gradientThe composition gradient formed by the centrifugal

method can be affected by the difference in density betweenparticles and a molten metal, the applied G number, theparticle size, the viscosity of the melt, the mean volumefraction of particles, the thickness of the manufactured ringand the solidification time. It is obvious that both densityand viscosity are the materials constants and both thevolume fraction and thickness are the constants of theproducts. Moreove r, applied G number and solidificationtime show a mutual relation and the effect has already beenmentioned. One of the easily changeable and hopefulparameters for the control of the graded com position is theparticle size judging from eqn (6) and the simulated results.Therefore, the composition gradient m ay be controlledprecisely by using particles of different mesh sizesimultaneously. This idea was examined by both experi-mental and computer simulation of model materialscontaining both #60 and #320 mesh particles*.

*The effect of mix of different particle sizes on suspension viscosity hasbeen studied by Farris16. When the particle size ratio is 5:l (in this study,larger particle size (#60) and smaller particle size (#320) are 250 pm and50 pm, respectively), the suspension viscosity is strongly affected by thefriction of smaller particles at a total particles volume of more than 50%.However, the effect is small at a total particle volume of less than 30%.Since this is true in all but one of our cases, we can safely estimate theviscosity in binary particle size systems by eqn (5), which applies for singleparticle size systems.

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The resultant distributions of particles are shown inFigure 10, where Figure 10(a) is the experiment of G =12.4 and Figure 10(b) is the simulation of 40At. The volumefractions of #60 and #320 mesh p articles are 11.25 and 3.75vol%, respectively, and the ring thickness is 15 mm. InFigure 10, both distribution profiles ar e almost the same andsmoother compared with those in Figure 3(b), Figure 4(b),Figure 7(c) and Figure 8(b). As mentioned previously, themigration distance per unit time of #320 mesh particles(smaller particles) is shorter than that of #60 mesh particles(larger particles). The particle-free region in Figure 10 isconsequently shorter in comparison with that in Figure 3(b)or Figure 7(c). This means that the gradation in compositioncan be controlled not only by changing the G number or themean volume fraction of particles but also by applyingparticles of different mesh size simultaneously.

QJ 40 Cb) Ri i Thickness;0mmE3p 30


Figure 9 The effect of ring thickness on the variations of volume fractionsimulated under the condition of 15 ~01% of #60 mesh particles and 40Atfor the comparison with Figure 7(c). The ring thickness of (a) and(b) are 10and 20 mm, respectively


Figure 10 The effect of mix of different mesh particles on the variationsof volume fraction under the condition of 11.25 ~01% of #60 mesh particlesand 3.75 ~01% of #320 mesh particles and 15 mm thickness. (a) Experimentof the applied G = 12.4. (b) The simulation of 40At


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SUMMARYIn the present study, the movement of solid particles inviscous liquid was examined to establish a method ofcontrolling composition in functionally graded materials(FGM s) manufactured by the centrifugal method. Thegraded distributions of spherical ceramic p articles wer eanalyzed by a computer simulation. The graded distributionin FGMs manufactured by the centrifugal method will besignificantly influenced by many processing parameters.which include the difference in density between particlesand molten metal, the applied G number, the particle size,the viscosity of the molten metal, the mean volume fractionof particles, the ring thickness and the solidification time.The results of computer simulation did not contradict theexperiment using the mixture of plaster and corundum.Moreo ver, it is shown that the composition gradation can becontrolled more precisely using the mixed particles ofdifferent m esh size simultaneously. The computer simula-tion is useful to predict the graded composition of theproducts m anufactured by the centrifugal method.

ACKNOWLEDGEMENTSThe authors would like to express their thanks to Prof. K.Kume of Kagoshima University for his helpful guidance andadvice in using a Vicat apparatus. Part of the experimental

work described in this study was performed by Mr Y.Takeda, g raduate school student of Kagoshima University.

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Koizumi. M. and Urabe, K., Term-fo-Hagane, 1989, 75. 887.Rabin, B.H. and Shiota. I.. Functionally gradient materials. MRSBull., 1995, 20(l), 14.Hirai, T.. Functional gradient materials. In Materials Science andTechnology, Vol. 17B. Wiley-VCH. Weinheim, 1996.Fukui. Y., JSME Int. J. Series III. 1991, 34. 144.Fukui, Y.. Oya-Seimiya, Y. and Nakanishi, K., Trans. Jpn Sot,.Mech. Eng.. 1991, A57, 1790.Fukui. Y.. Yamanaka, N., Watanabe. Y. and Oya-Seimiya, Y.. J.Jprt Inst. Light Metals, 1994, 44, 622.Fukui, Y., Takashima. K. and Ponton. C.B.. J. Marer. Sci.. 1994,29.2281.Watanabe. Y. and Fukui. Y.. J. Jpn Inst. Light Metals. 1996.46, 395.Fukui. Y. and Watanabe, Y., Metall. Mater Trans. A, 1996. 27A.4145.Watanabe. Y.. Yamanaka, N. and Fukui. Y.. Z. Metalkd.. 1997.88.717.Kang, C.G. and Rohatgi, P.K.. Metal/. Mater. Trans. B. 1996. 27B.277.The Society of Gypsum and Lime, Japan teds.), Handbook ofGypsum and Lime. Gihodo Shuppan. Tokyo. 1972. p. 638.Frisch, H.L. and Simha, R., The viscosity of colloidal suspensionsand macromolecular solutions. In Rheology, Theory andApplications, Vol. 1. ed. F.R. Eirich. Polytechnic Institute of Brook-lyn. New York. 1956, p. 525.Brinkman, H.C., J. Chem. Phys.. 1952,20. 571.Barnes, H.A., Hutton, J.F. and Walters. K.. Rheology Series, 3: AnIntroduction to Rheology. Elsevier. Amsterdam, 1989, p. 123.Fatris. R.J.. Trans. Sot. Rheol., 1968, 12, 281.

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1998_watanabe control of composition gradient in a metal

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