Additional force field in cooling process of cellular Al alloy

Vol. 45 No.6SCIENCE IN CHINA (Series B)December 2002Additional force field in cooling process of cellular Al alloyZHENG Mingjun (郑明军)", HE Deping (何德坪)* &DAIGe(戴戈)Department of Materials Science and Engineering, Southeast University, Nanjing 210096, ChinaCorrespondence should be addressed to He Deping (email: dphe@seu.edu.cn)Received April 8, 2002Abstract The foaming process of Al alloy is similar to that of Al, but there is a solid-liquid statezone in the solidification process of cellular Al alloy which does not exist in the case of AI. In theunidirectional solidification of cellular Al alloy, the proportion of the solid phase gradually reducesfrom the solid front to the liquid front. This will introduce a force and result in a serious quick shrink-age. By the mathematic and physical mode, the solidification of the cellular Al alloy is studied. Thedata measured by experiment are close to the result calculated by the mode. This kind of shrinkagecan be solved by suitable cooling method in appropriate growth stage. The compressive strength ofthe cellular AI alloy made by this way is 40% higher than that of cellular Al.Keywords : cellular AI aly, unidirectional solidification, two phase zone, additional force fieldAl foam is a kind of low density functional material with a large amount of pore distributingin the Al. Al foam can be sorted into two kinds according to their pore structure. One is porous Alwhich has open pores. The other is cellular Al which has closed poresl1.Cellular Al has many special properties such as low density, high specific strength, energyabsorption property, damping capacity and sound, heat, electromagnetism insulation. Therefore, inthe 21st century, it has become one of the hotspots in material research!- 61.Since 19517, cellular Al has been studied as a pivot. Japan[8] and Chinal4- 6] have produced itsuccessfully. Products with well-proportioned pore and high porosity P = 85%- -91%) can beprepared. In recent years, some great progresses mainly on structure and properties have beenmade through the cooperation of Cambridge University, Harvard University and M.IT. However,the strength of cellular Al is relatively low and therefore its application is restricted. In order tomeet the requirement of higher specific strength for high tech area, cellular Al alloy becomes anew pivot of research. Refs. [9, 10] studied the preparation and properties of cellular Al-Si alloy(P<84%) and cellular A-Mg alloy (P<82% ) respectively. But in both cases the densities arenot low enough. So far, there is no successful report on cellular Al alloy with low density, well-proportioned pore, high specific strength and high preparing efficiency.Based on analyzing the difference between preparing cellular Al and cellular Al alloy, thephysical and mathematic model are established to stud中国煤化Ivo phase zones.By this model, the right solidification method has beenYCNMHGarAlalloywith* These authors contributed equally to this work.No.6ADDITIONAL FORCE FIELD IN COOLING PROCESS599high porosity (P = 86%- -91%). The cellular Al alloy samples produced in this way have well-proportioned pores, higher specific strength (than cellular AI), and have no big centralized poresand visible shrinkage.Experimental1.1FacilitiesThe experiment facilities must fit for the melting of Al alloy and the foaming technic such asdispersing viscosity- increasing agent uniformly, dispersing blowing agent uniformly, solidificationcontrolling, measuring the moving of the interface in foaming process and analyzing the porestructure by scanner and computer with special softwarel+- 61.Different from preparing cellular Al, the raw materials and the facilities adopted are as fol-lows: (i ) The raw material is ZL111 (8.0%- -10.0% Si, 1.3%一 1.8% Cu, 0.4%一 0.6% Mg,0.1%一0.35% Mn, 0.1%一0.35% Ti). For comparison, some pure Al was prepared also. (ii ) Theinner dimensions of the crucible is 100 mmX 100 mmX 200 mm. (1i) High precision l1X 10-3N■m) viscosity measuring apparatus for controlling the preparing process was used. (iv) Solidifi-cation controlling facility was ameliorated to use for either uni- or multi-directional solidification.(V ) AIll the samples were cut accurately and the pore structure was studied by scanner and com-puter to ascertain the influence of solidification model.Fifty experiments have been taken for ensuring the stability of the result in the solidification.1.2Research method and experimental phenomena1.2.1 Research method. Experiment is usually taken on studying materials for its complexity.Ref. [11] adopted simulative method that combined physical phenomena with experiment. Ref.[12] adopted deductive method that deduced physical phenomena from mathematics. Ref. [4]adopted the inductive method which derived mathematical expression from physical phenomena.The latter one is used in this paper. This method is very important in studying materials. The diffi-culty lies in finding out the essence from the phenomena and establishing a model to gain the re-sult in accardance with the experimental data.1.2.2 Experiment phenomena.The foam solidification is very important in preparing cellu-lar Al alloy. If the solidification controlling was not well, there would be many disfigurements inthe samples. The unidirectional solidification was applied in preparing cellular Al with a samplesize of 100 mmX 100 mmX 200 mm. Since the liquid in the zone that has not solidified can flowto the zone that is solidifying, the disfigurement caused by shrinkage could not take place. How-ever, when cellular Al alloy foam is solidified in the s:中国煤化工m would shrinklayer by layer after 30 s from a special heightX(X is n:YHC N M H Grpendicular axis .with a precision of 0.1 mm). The shrinking process completes in 5 s. The gross shrinkage is morethan 30% and the form of the cell changes from polyhedral to flat (fig. 1()). At the same time, the600SCIENCE IN CHINA (Series B)Vol.45cells in the zone lower than X keep their normal polyhedron form. The X would change when thecooling speed is changed. This phenomenon does not emerge in the cooling process of cellular Al(fig. 1(). Apparently, in order to prepare cellular Al alloy successfully, the driving force of thiskind of shrinkage must be found out.1 cmI cmFig. 1. Samples of cellular Al alloy and cellular Al during unidirectional solidification. (a) Shrinkage of cellularAl alloy, (b) cllular Al.2 Results and analysisThe foaming process of both cellular Al and cellular Al alloy includes two stages, growthstage and solidification stage. Cellular Al and0.88F0.86+cellular Al alloy have similar growth stage but0.84+0.82-their solidific ation stage are different.0.800.78 |2.1 Similarity in the growth stage of cellular AlA 0.76and cellular Al alloy melt0.74120.72The growth curve (ig. 2) of cellular Al al-0.700.68 tloy resembles the curve of cellular A1l4 in the0.66 t100 200300400 500 600growth stage. The growth curve has 3 stages:t/s中国煤化工ge (2), and cellcollap:MHCNMHGFig. 2. Foam growth curve of cellular Al alloy and cellularAl melt.In stage 1, the bubble nuclei form and growNo.6ADDTTIONAL FORCE FIELD IN COOLING PROCESS601up in the Al alloy (or Al melt) when the blowing agent is introduced in. Cell shape changes fromball to polyhedron. The growth speed is high and the time of this stage lasts for less than 180 s.The major influential factors in this stage include the melt viscosity, the quantity of blowing agent,the temperature of the melt and the stirring timel 31. These factors influence the physical transferproperties and the heat dynamical properties of the foam, and all the factors can influence eachother. So there have no balance in the foam, and all the cells move and growth ceaselessly.The stage 2 is located about 180- -450 s after the blowing agent is introduced in. The poros-ity (P) would not change and the cell' s figure has neartly changed to polyhedron (the connectionsection of the cells is Gibbs plateau channel and not planar). There is a balance system in the foam,so the cell and the porosity keep stable. This stage is the most suitable chance for cooling. In thispaper, the cooling time is in the start of stage 2. If the foam is not cooled in this stage, stage 3 willstart.In stage 3, the cells start collapsing and incorporating. So if cooling process starts in thisstage, the cellular Al alloy with well- proportioned structure could not be gained.2.2 Difference in solidification process and driving force model of shrinkageTo analyze the driving force of the obvious shrinkage in the solidification process of Al alloyfoam, several assumptions are made: ( i ) Before solidification, the temperature in the melt keepsstable and uniform; ( ii ) the bubbles are uniformly distributed in the melt; (1i) cooling starts fromthe stable stage 2; (iv) the sum of bubbles keeps unchanged from the stage 2 to the end of thesolid ification.Once solidification process starts, the shrinkbehavior of Al alloy foam will differ from that of Alfoam and lead to a shrinkage shown in fig. 1(a). It is .reasonable to assume that in solidification processof Al alloy foam there exists a driving force F (fig. 3)which changes the system mechanical balance anddoes not exist in case of Al foam. This differenceshould be attributed to the different physical proper-Fties of Al and Al alloy. Pure Al melt has a specialfreezing point but Al alloy freezes in a temperaturerange (the liquidus temperature and the solidus tem-perature of ZL111 are 598 and 538C respectively).εAt a cooling time τ, there is a temperature gradientin the foam. Therefore, in Al alloy foam there will中国煤化工be a freezing zone B at height ε (fig. 3) where liquidMHCNMHGAIalyfoamdurngundurectonal coolng, A, sold; B, solid + liquid; C,state and solid state exist together. The amount of liquid.602SCIENCE IN CHINA (Series B)Vol.45solid state decreases when height x increases. Zone B will move upwards as solidification processgoes on. Although there is also a temperature gradient in Al foam, zone B cannot be found. h-stead there is only a liquid-solid interface in Al foam.Since the distance between the solid atoms is smaller than that between the liquid atoms, theforce between the solid atoms is bigger. Therefore, the surface tension of the solid is bigger thanthat of liquid. The solid surface tension of metal is given in ref. [14]:4/3“σ=一56400.10-3J/m2，(1)2(Twhere ρ is the density of metal (g/cm?), and Zatomic number. The result of solid Al is 3.47J/m?. As a comparison, the surface tension ofliquid Al is 0.86 J/m215, only a quarter of theformer. Thus, there will be a surface tensionSolidLiquid+sdtidLiquidgradientdσ(fig. 4), which is determined bydxthe surface tension of liquid, the surface tensionof solid and the shape of liquidus and solidusS+ Asline in the phase diagram. The bigger the differ-ence between liquid surface tension and solidFig. 4. Cooling direction and surface tension along coolingsurface tension and the smaller the distance be-direction.tween liquid surface and solid surface are, the bigger the surface tension gradient will be. Thus,the mechanical balance in pure Al foam melt during unidirectional solidification will no longerexist in Al alloy foam melt.Taking a single cell in zone B into account, since the cell wall would transform from liquid toliquid-solid state, there will be a corresponding increase of surface tension△σ which is the valuerelating to the proportion of solid phase. Accordingly, the additional pressure exerted on cell wallwill alter fromAp=20l(2)to Ap,=201+A0),where r is curvature of cell wall, 0p and 4p2 correspond to additionalpressure of liquid cell and liquid-solid cell respectively. 4p2 can be as large as 4 times of△p,for cells near the lower boundary of zone B. Apparently, the original inner pressure of cells inzone B could not sustain this additional pressure, which中国煤化工clls.Take a layer of cells in zone B for ilustration. AYCNMHGnienceallofthe:cells in the figure are assumed to be balls). Force Ap2 points towards the inner of the cells. F isNo.6ADDTTIONAL FORCE FIELD IN COOLING PROCESS03the adhesion force between melt and crucible wall.Under the effect of force Op,， the cells wouldshrink. However, on condition that force F is larger△P:han Ap2, it will restrain the layer from horizontalshrinkage and thus only vertical shrinkage can takeAP:. AP:place. As long as the response time is sufficient and→fthe shrinking speed is high enough, this layer ofcells would turn to be flat as shown in fig. 1(b).Before the response time, the zone which has beensolidified could approximately keep the originalFig. 5. Force on the cellsof zone B.figure because the shrinking speed is very small.The moving speed of the solid face correlates with the cooling intensity. So the location of initialshrinkage (X) correlates with the cooling intensity. Accordingly, the larger the cooling intensity is,the farther from cooling face the initial location of flat cell will be. On the bottom layer of zone Bthe additional pressure under different cooling intensities can be regarded as the same (nearly 4times of that of liquid state). Based on mechanics principle, the acceleration of shrinking shouldbe the same. Therefore, the time for obvious shrinkage (obvious shrinkage is defined as shrinking3% of the original height) would be the same. That is to say, the response time has no relation withcooling intensity. Our experiment measurement shows that under different cooling intensities inAl alloy melt, the obvious shrinkage always takes place after the unidirectional cooling starts andlasts for 30 s. Once obvious shrinking starts, the shrinking speed will get quicker and quicker.By means of heat conduction analysis[16] o1solidification process while taking the influence ofthe foam into accountl!7), the location of the solidface when obvious shrinkage starts (30 s after cool-ing) can be calculated. In other words , the distancebetween the cooling face (bottom) and the initiallayer of obvious shrinkage, i.e. X, can be worked out(fig. 6). On condition that the calculated value ofsolid face location after 30 s cooling meets the loca-tion of initial obvious shrinkage tested in experi-ment, the correctness of this model will be verified.Fig. 6. Distance between the cooling face and startingshrinkage layer.2.3Heat conduction analysisTo simplifty the analysis, the following assumption中国煤化工( i ) The physical properties of the solid part and:YHC N M H Grelation with thetemperature, but may be different from each other.(ii ) The temperature varies along the x-direction only.604SCIENCE IN CHINA (Series B)Vol.45(ii) Conduction is the only heat-transfer mechanism within the system.(iV) The change of the thermal conductivity due to the variation of porosity can be ignoredbecause the change of the porosity in the stable stage is very small.(V ) Melting heat is the only source of intermnal heat.(vi) The solid fraction within the freezing zone has a linear relationship with the distance. Ithas a value of zero at the liquid front andfu at the solid front, where fsu is the solid fraction corre-sponding to the eutectic composition of the system to be analyzed.Assumption (vi) can be represented as follows:f,=f(1-x),(3)where x=X7E is thickness of the solidified part (m), and△ε is thickness of the freezingzone (m).As the solid continuously forms within the freezing zone, the latent heat of fusion is releasedaccordingly. This heat of fusion can be treated as internal heat generation within the freezing zoneB, expressed asIf、Q=ρL°At(4)where ρ is density of cellular Al alloy (kg/m ), and L is latent heat of fusion (J/kg).Combining eqs. (3) and (4) gets .o= ρLfsw de + xdA(5)dtFourier' s conduction equation can be written for both the solidified part and the freezingzone, and solved simultaneously with proper boundary and initial conditions. The completemathematical formulation for this problem is expressed asd2T 1 dT;(6)0x- Q| At2TQ_18T(7)8x2入2Q2 dtThe boundary conditions are ( i ) T(x=0)=-(T,-T)， (ii ) T(x=ε)=0， (ii)T(T2(x=ε)=0，(iv) T2(x=ε +0&)=0，(V )上2(x=ε +△8)=0， and (vi)(x=8)=)x~(x=8)+ρL(-fs)步leThe initial conditions ar i)中国煤化工d (i) e(=THCNMHG_0)= 0, wherea 1 is thermal diffusivity of solid (m2 ' s), u一.，c Is uie spectfic heat of cellu-Pclar Al alloy (J/Kg ' K), a 2 is thermal diffusivity of liquid (m?s-), T is temperature in solidifiedNo.6ADDTTIONAL FORCE FIELD IN COOLING PROCESS605part (K), T2 is temperature in freezing zone B (K), T。is solidus temperature (K), T is liquidustemperature (K), T。is temperature at cooling surface (K), ε is thickness of the solidified part (m),△ε is thickness of freezing zone B(m), λ 1 is thermal conductivity of solid (W. (mK)-), andλ2 isthermal conductivity of liquid (W. (m K)-+).2.4 Comparison of calculation results and test resultsBecause the thermal conductivity of cellular Al alloy is determined by the porosity and theporosity of the liquid and solid foam is nearly the same, the thermal conductivity[18] of the cellularAl with a porosity of 87.4% (the average porosity in this test) is adopted in this paper. The loca-tion of solid front where the obvious shrinkage starts can be calculated by computerl17] under adefinite cooling intensity. The heat physical parameters of crucible and cellular Al alloy are shownin table 1. The results calculated and tested are show n in table 2. Three cooling intensities are usedhere. The comparison shows that the calculation results are close to the test results. Since the wallof the crucible would conduct some heat, the error is introduced.Tablel Physical parameters of crucible and cellular Al alloyCrucibleAl alloy foamp/kg*m7.86X 103.51X 10(P= 87%)λ/W●(m.K)+46.890.1297131LJ●kg'3.96X 10'T/K811clJ-(kg- K)15.78X 1020.126869Table 2 Calculated and tested resultsX/mmCooling intension /W (m2 K)-Icalculat ed resulttest ed result207519.821.0272922.524.2303130.433.53 Discussion3.1 Solution of shrinkage problem in Al alloy foamBased on the analysis of the shrinkage problem in Al alloy foam in unidirectional solidific a-tion, a solution can be found. Since the solidification character of Al alloy is different from that ofpure Al, unidirectional solidification is improper for Al alloy foam. Instead, bulk cooling ought tobe considered. Although the surface tension gradient still exists while cooling from all direction,the solidified outer part of the sample provides a sustainable force against the additional pressure.Therefore, the shrinkage problem in Al alloy foam can berlund中国煤化工3.2 Sample and property of cellular Al alloy preparedTYHCNMHGThe samples prepared by the new method are shown in fig. 7. These samples have high po-rosity (86%- -91%), well- proportioned pore and no shrinkage. The collapse stresses of cellular Al606SCIENCE IN CHINA (Series B)Vol.45and cellular Al alloy are compared in fig. 8. The collapse stress of cellular Al alloy is 40% higherthan that of cellular Al.Fig. 7. Cellular Al aly sample. (a) 100 mmX 100 mm, (b) 0260 mm.2r4 Conclusions1+0(i ) The growth stage of melt foam of Al9|alloy is similar to that of cellular Al alloy.2,8上(ii) In cellular Al alloy, there is an extraforce gradient in the liquid-solid zone， which6-results in the shrinkage at a special height in口unidirectional cooling process.(ii) The solidification regularity in the liq-0.08 0.10 0.12 0.14 0.16 0.18pip,uid-solid zone has been studied by the mathe-matic-physical method. The result calculated isFig. 8. Copressive yield stress of cllular AI and cllular close to those tested.Al aloy. 1, Cellular Al; 2, cellular Al aloy.(iv) The shrinkage problem can be elimi-nated by the new cooling method. The cellular Al alloy with high porositv. well Droportioned poreand high specific strength has been prepared by this中中国煤化工、s of cellular Alalloy is higher than that of cellular Al by 40%.YHCNMHGAcknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos.50231010, 50081002 and 19982001).No.6ADDITIONAL FORCE FIELD IN COOLING PROCESS607References1. Ashby, M. F, Evans, A G, Fleck, N. A. et al, Metal Foams: A Design Guide, Boston: B-H Press, 2000, 1- 5.2. Banhart, J, Ashby, M. F, Fleck, N. A., Cellular metals and metal foaming technology, in International Conference onCellular Metals and Metal Foaming Technology, 2001 (eds. Banhart, J.. Ashby, M F. Fleck, N. A.), Bremen: Verlag MTT,2001,5- 55.3. Gibson, L. J, Ashby, M. F, Cellular Solids- Structure and Properties, 2ad ed, Cambridge: Cambridge UniversityPress, 1999, 1- -10.4. 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