An Investigation of Solidification Conditions and Melt Treatment on Microporosity Formation

Transcription

1 An Invetigation of olidification Condition and Melt Treatment on Microporoity Formation Paper# 6, ENG 18 eivan Davami a, Mehrdad haygan b a-ilamic Azad Univerity, Naeen Branch, Ifahan, Iran keivandavami@yahoo.com b-ilamic Azad Univerity, Najafabad Branch, Ifahan, Iran m.haygan@yahoo.com Mohammad azem Beharati Givi, Mahmod Mouavi Mahhadi Univerity of Tehran, Tehran, Iran bgivi@ut.ac.ir, mmoavi@ut.ac Abtract Cat aluminum-ilicon (Al-i) alloy are ued in automotive and indutrial weight-enitive application becaue of the alloy low denity and excellent catability. The preence of trapped ga and/or hrinkage pore in certain location within the cating ha been hown to influence mechanical propertie uch a tenile trength and fatigue life. Thee micromechanical defect could be found anywhere in the cating depending on the proceing condition. A large amount of poroity located in the center of the cating may have no effect on the mechanical propertie or fatigue performance. A maller, iolated pore near a urface may have ignificant impact on mechanical propertie. Hence, it i important to develop a comprehenive model to predict the ize, location and ditribution of microporoity in cating. In thi work, we model the effect of variou cating proce parameter on microporoity formation for equiaxed aluminum A356 alloy cating. The proce parameter include the cooling rate, grain refiner, and eutectic modifier melt addition. The comparion between the experimental reult and the imulation demontrate agreement and preent variou approache that have been implemented uccefully. 1. Introduction The baic principle behind cating procee are traightforward. Molten metal of ufficiently low vicoity flow into cavitie of complex hape and olidifie upon cooling. However, behind thi imple principle lie many complicated reaction and phae tranformation. If proper care i not taken, metal cating i prone to defect uch a mirun, macrohrinkage (macroporoity), microporoity, egregation, hot tear, and reidual tre. The deign objective of contemporary foundry engineer i to chooe an optimized geometry and proce parameter that eliminate or minimize defect evolution while enuring the deired microtructure.

2 1.1 Effect of Eutectic Modifier and Grain Refiner on Microporoity Formation Eutectic Modifier Aluminium alloy with ilicon (i) a the major alloying addition are ued widely by the indutry. However, the preence of the brittle, acicular ilicon phae in the microtructure ha hown negative effect on the mechanical propertie of cating. It i becaue the brittle nature of the large ilicon plate and the harp edge of the coare acicular ilicon phae promote crack initiation and propagation. The eutectic can be refined by an alloying proce known a modification. For aluminium-ilicon alloy, thi uually involve the addition of trontium (r) or odium (Na) into the melt. trontium modification i known to alter the amount, characteritic, and ditribution of poroity in Al-i cating. Although many theorie have been propoed to account for thee effect, mot can be conidered inadequate becaue of their failure to reolve contradiction and dicrepancie in the literature. A major concern with the refinement of the Al-i eutectic phae in Al-i alloy by r modification i the increaed tendency of microporoity formation [1]. In their tudy, C. M. Dinni et al. found that no apparent difference in the amount, ditribution, and morphology of poroity were oberved between r-free and r-containing alloy with no or very mall eutectic volume fraction. However, r modification ignificantly changed the amount, ditribution, and morphology of poroity in alloy with a ignificant volume fraction of eutectic. The addition of r reduced poroity in the hot-pot region of cating, and the pore became well dipered and rounded. Thi reult can be explained by conidering the combined effect of the cating deign and the difference in the pattern of eutectic olidification between unmodified and r-modified alloy []. Figure 1 and Figure how the microtructure of unmodified and modified A356 alloy, repectively. J. acaze et al. found that trontium doe not affect the primary olidification of Al dendrite but modifie the kinetic of the Al-i eutectic [3]. Although the ue of modifier in Al-i alloy promote an improvement in mechanical propertie, tudie are till needed to clarify the influence of modifier on the corroion reitance. It i well known that tructural parameter uch a grain ize and interdendritic pacing trongly affect corroion reitance of a-cat alloy [4 6]. A. Garcia et al. invetigated the effect of a eutectic modifier on the microtructure and urface corroion behavior of Al-i hypoeutectic alloy. In the tudy, modified and unmodified ample of an Al 9 wt % i alloy were olidified under imilar olidification condition, and after metallographic procedure, the corroion reitance wa analyzed by both the electrochemical impedance pectrocopy technique and the Tafel extrapolation method carried out in a.5 M NaCl tet olution at 5 C. It wa found that the Al 9 wt % i alloy cating in the modified condition tend to have it corroion reitance decreae when compared to the unmodified alloy. The tudy howed that hypoeutectic aluminum-ilicon alloy could have ignificant improvement in mechanical propertie by inducing tructural modification in the normally occurring eutectic. The eutectic modification may affect not only the mechanical propertie but alo the corroion reitance of uch alloy [7].

3 avaş ha found that among cating parameter uch a mold filling, liquid filtering, olidification time, and the diolved hydrogen level of the liquid alloy and liquid treatment of molten alloy with the addition of r, the local olidification time and the diolved hydrogen level of the melt were ignificant for microporoity formation [8]. Ruvalcaba found that treaming of olute-enriched liquid at the tip of high-order branche promote growth by local undercooling. Further, olute advection and local olute rejection due to the local growth caue olute pile-up at the root of the branche. Thi olute pile-up alter the local compoitional balance at the olid liquid interface at the root, cauing the root to remelt, which in turn reult in further branch detachment [9]. Boeira et al. [1] compared the experimental egregation profile and poroity evolution along the cating with theoretical prediction furnihed by the numerical model, by conidering a tranient metal/mold heat tranfer coefficient profile experimentally and determined that the numerical model depended on an experimentally determined heat tranfer coefficient profile. A great agreement between the imulated profile and the experimental invere copper profile wa hown. The imulation of poroity formation for an aniotropic channel ha conformed better with the experimental catter, with the experimental volumetric fraction of the pore profile preenting an acending trend from the chill to the top of the ingot [1]. H. Combeau invetigated the olidification of plate of different thicknee in a and mold. He calculated a maximum abolute preure drop of 7, Pa in the 7.5-mm-thick cating wherea thi maximum wa only 3 Pa in the 3-mm-thick cating. Conidering the condition of microporoity formation, thee reult howed the preure drop were far too low to account for the formation of micropore that were oberved experimentally. Hydrogen egregation had to be conidered and integrated in a model to give a good prediction of micropore appearance [11]. E. Obaldia calculated the amount of hydrogen uperaturation baed on the tranport of diolved hydrogen and ievert law. An innovative apect of hi work wa the extenion of the model to make quantitative prediction of the volume fraction of poroity. Although the hydrogen uperaturation etimated the amount of poroity, thee prediction were uually overetimated becaue the barrier of pore nucleation wa not conidered [1]. J. i invetigated electric current pule (ECP) with parallel electrode on the olidification tructure of pure aluminum. The experimental reult indicated that the olidification tructure cannot be refined when the ECP i applied before the molten metal tart nucleating. However, ignificant refinement of the olidification tructure could be achieved by applying ECP during the nucleation tage [13] Grain Refiner Undertanding the crytallization proce during olidification i an eential tep to tailor the mechanical propertie of olidified material. The phyical procee that govern crytallization are grain nucleation and the ubequent grain growth. In the indutrial production proce of aluminium alloy, the addition of titanium diboride (TiB ) particle along with olute titanium i widely ued to enhance the nucleation rate and control the grain growth during olidification. Thi procedure i generally referred a grain refinement. Although the mechanim reponible for grain refinement have been extenively tudied in

4 the lat few decade, a comprehenive undertanding i till lacking due to experimental difficultie in monitoring grain nucleation and growth in itu. The quetion of particular interet i how TiB particle, along with olute titanium reult in grain refinement, could be added, while no grain refinement i oberved if one of the two i miing. M. Zhang et al. have tudied grain refinement in aluminum alloy uing the edge-to-edge matching model. The reearcher found excellent atomic matching between Al 3 Ti nucleating ubtrate, known to be effective nucleation ite for primary Al, and the Al matrix in cloepacked direction and cloe-packed plane containing thee direction. The crytallographic feature of the grain refiner and the Al matrix are conitent with the edge-to-edge matching model. For three other typical grain refiner for Al alloy, TiC (titanium carbide) (when a=.438 nm), TiB, and AlB, the matching occur only between the cloe-packed direction in both phae and between the econd cloe-packed plane of the Al matrix and the econd cloe-packed plane of the refiner. According to the model, it i predicted that Al 3 Ti i a more powerful nucleating ubtrate for the Al alloy than TiC, TiB, and AlB. Thi agree with previou experimental reult [14].. Modeling of olidification Condition and Melt Treatment in Microporoity Formation.1 Cooling Rate The cooling rate play an important role in determining the microtructure of cating. A higher cooling rate reduce the olidification time and grain ize of the cating. Hence, grain denity increae with the cooling rate. According to experimental obervation, the average pore ize decreae a the cooling rate increae. There are a number of explanation for thi phenomenon. For a higher cooling rate, the dendrite arm pacing (DA) decreae a do intergranular region. Pore growth i thu limited. Another explanation i that with decreaed olidification time, there i le time for hydrogen to diffue from the olidifying dendrite to the liquid. Hence, the ga pore growth rate i inhibited.. Modifier Eutectic modifier are uually added to molten aluminium-ilicon alloy to refine the eutectic phae particle hape and improve the mechanical propertie of the final cat product. For aluminium-ilicon alloy, thi uually involve the addition of r or Na. In general, it i oberved that modified cating contain more poroity than unmodified cating. ome poible reaon have been propoed and tudied. In general, thee reaon can be categorized a increaing incluion content in the melt: - decreaing hydrogen olubility in olid metal - changing the olid/liquid interface morphology - reducing the urface tenion of the liquid metal - increaing the volumetric hrinkage

5 .3 Grain Refiner The effect of grain refiner on poroity are till under tudy. In general, it ha been oberved that the addition of grain refiner increae the number of grain nucleation ite, thu reducing grain ize. It ha been hown that grain refinement reduce both the volume fraction of poroity and the pore ize in A356 [15]. 3. Model Formulation In thi ection, the grain tructure evolution model will be preented. The model of ga pore evolution i then decribed. Finally, the technique for coupling thee two model i illutrated in detail. 3.1 Grain tructure Evolution Modeling Grain nucleation and growth are two phenomena that influence microtructure evolution during the olidification of a cating. In thi reearch, we will model heterogeneou nucleation and growth, a reaonable aumption for commercial cating Grain Nucleation To model heterogeneou nucleation in olidifying cating, two method have been propoed: an intantaneou model and a continuou model. The intantaneou model aume all nuclei are formed at a given undercooling temperature. The continuou model aume nucleation will occur continuouly between the equilibrium temperature (i.e., a the liquid undercool) and the maximum undercooling temperature. Due to implicity in program implementation, an intantaneou nucleation model i employed in the preent tudy. Uing thi method, the grain denity at a given location can be determined by correlation with the cooling rate, R: N = k + k R + k 1 3R where k 1, k, and 3, (1) k are parameter that need to be determined by empirical analyi of the cooling rate and grain ize in a real cating. Proceing condition, uch a the addition of grain refiner, eutectic modifier, and incluion content, are known to influence the relationhip between the grain denity and the cooling rate Dendrite Growth and Orientation There i a preferred crytallographic orientation for each grain. In our model, each equiaxed grain nucleated in the bulk of the cating i given a principal growth direction, a random poitive integer with uniform ditribution between 1 and 48. Each integer correpond to a defined crytallographic orientation in two dimenion. The dendrite growth kinetic can be calculated with the aid of the urz-giovanola-trivedi (GT) model [6, 7]. The relationhip between the dendrite tip velocity and the

6 undercooling temperature for the Al-7%u alloy calculated by a GT model i hown in Figure 3. In our model, a two-dimenional (-D) grid i generated from a given location in the cating where the microtructure and poroity prediction are of interet. The ite of the grid cale directly from the computational element ued in macrocopic imulation. The element ize of the grid in general i much finer than that of the control volume or element ize ued in a macrocopic heat tranfer calculation. The three-dimenional (3-D) heat tranfer calculation reult, uch a temperature and olid fraction, for each control volume i then mapped to a - D grid. The iothermal condition in every element i aumed, o the temperature profile of an element are applied uniformly to it cell. It i aumed that the microtructure evolution doe not influence the local thermal parameter. While uch an aumption may not reflect the phyical reality, it i a neceary aumption to apply a -D model to a 3-D proce. 3. Ga Pore Evolution Modeling The condition for a ga pore to grow in the olidifying melt i that the ga preure, P g, ha to be equal to or greater than the critical preure, P C : Pg P c () The critical preure i defined a PC = Pa + ρ gh + P + P σ, (3) where P a, ρ gh and P are the ambient preure, metallotatic preure, and hrinkage preure and urface tenion per unit area Pσ between ga and liquid, repectively. Pa and ρ gh are uually contant. Pg and P can be calculated a hown below. Auming that the pore i circular and that the urface tenion per unit area between ga and liquid i iotropic, P σ i given by the well-known equation: σ P G σ =, (4) r where σ i the urface tenion between ga and liquid, and r i the radiu of the pore [9]. G Figure 1: Typical microtructure of unmodified A356 alloy

7 Figure : Typical microtructure of r modified A356 alloy Figure 3: Dendrite tip velocity a a function of undercooling for A356 calculated by the GT model 3..1 Computation of Ga Preure In mot mathematical model for aluminium alloy, it i aumed that the hydrogen concentration in liquid and olid at the olidification temperature are in equilibrium. To verify thi aumption, the hydrogen diffuivity wa calculated, and the dendrite arm pacing of the pecimen wa oberved. The diffuivity of hydrogen, D (cm/ec), in olid aluminium i given a [19]: 1195 D =.11exp( ), (5) RT J 8 cm where R i the ideal ga contant ( ). From equation 5, at T = 83, D = 1 1. mol The diffuion ditance, lambda, i defined a: λ = Dτ, (6) where τ i the diffuion time. Given the diffuion time, the diffuion ditance can be calculated from equation 5 and 6. For a permanent mold gravity cating, the olidification time i about 5 1 econd. Therefore, the diffuion ditance i about 5 µ m. The ize of the dendrite arm for the A356 cating pecimen ued in thi tudy (to be dicued) i hown in Figure 4. It can be een that the ize for half the dendrite arm i approximately 1 µ m. ince the diffuion ditance and ize of dendrite arm are of the ame

8 order, the hydrogen atom can be aumed to have enough time to diffue from olid to liquid in the permanent mold Al alloy cating ued in thi tudy. Figure 4: ize of dendrite arm for A356 cating pecimen The complete equilibrium condition lead to: [ H ] [ H = ], (7) where [ H ] and [ H ] are the hydrogen concentration in the liquid and olid metal, repectively, and and are contant decribed below. Before the formation of the ga pore, the hydrogen ma balance equation i given a: ( 1 f ) H + f H H, (8) [ ] [ ] [ ] = where f i the olid fraction and [ ] H i the initial hydrogen content in the melt. In addition, the ma concentration of hydrogen diolved in olid and liquid metal i governed by ievert law: 1/ [ H ] 1/ = Pg and[ H ] = Pg, (9) which yield equation 7 for equilibrium condition. Combining equation 8 and 9, the ga preure before ga pore formation can be calculated a: 1 [ H ] P g = ( )( (1) ( ) ( 1) f The ga preure increae a olidification proceed. From equation 1, the maximum preure can be computed a: [ H ] P g,max = (11) Following claical nucleation theory, no ga pore will form if the maximum ga preure, P, i le than the critical preure, P c. Combining equation 3 and 11 allow u to g,max

9 approximate the critical initial hydrogen content, [ H ] C, above which a ga pore can form in the melt. From equation 3, P c.75 atm. If we aume P a =1 atm, then h =. m, N/m [], r = 1 µ m, and the negative hrinkage preure i neglected. Thu, [ H ] = P C, (1) that i, [ H ] = C PC. (13) In thi cae, when ml =.6, 1/ 1g atm H C.1ml / 1 σ G =.79 then [ ] = g. It hould be noted that the critical initial hydrogen content depend on many factor uch a alloy compoition, olidification condition, etc. Therefore, the above approximation provide an indication of the relationhip between the initial hydrogen content in the melt and the critical preure. When the initial hydrogen content i greater than the critical hydrogen content, ga preure will form at the critical olid fraction during olidification. From equation 8 and 9, the critical olid fraction can be found a: [ H ] f c = Pc (14) ( 1) Note that f c decreae a [ H ] increae and P c decreae. When the initial hydrogen content i high, the melt will reach the domain where ga pore will form at an earlier tage of olidification. Alo, the addition of eutectic modifier in the melt reduce the urface tenion of the liquid aluminium alloy, which reult in the reduction of P c (equation 3 and 4). Hence, the critical olid fraction i reduced, and ga pore can nucleate earlier and grow over a longer period of time. When the ga pore formation condition i atified a defined in equation, ome hydrogen will be trapped in the ga pore. The hydrogen ma balance equation in thi cae i given a fυ Pg [ H ] ρ = [ H ] ρ f + [ H ] ρ (1 f fυ ) + α, (15) T where [ H ] i the initial hydrogen content in the melt; [ H ] and [ H ] are the hydrogen content in the olid and liquid; ρ and ρ are the denitie for liquid and olid metal; f and fυ are the volume fraction of olid and poroity; α i a ga converion factor; Pg i ga preure; and T i the temperature. The lat term in the equation repreent the amount of hydrogen trapped in the ga pore. By ubtituting equation 9 into equation 15, the ga preure after the ga pore ha formed can be computed.

10 3.. Computation of hrinkage Preure The hrinkage preure aociated with liquid metal flow in the muhy zone repreent the contribution of olidification hrinkage in microporoity formation. To determine the hrinkage preure, the ma conervation equation mut be olved: ρ δf δf v ( 1) + div( f u) =, (16) ρ δt δt where ρ and ρ are denitie of olid and liquid metal; f, f v, and f are fraction of olid, poroity, and liquid; t i time; and u i the interdendritic flow velocity vector. The firt term in equation 16 repreent the volume hrinkage aociated with olidification. Thi hrinkage i compenated for by the growth of ga poroity or by liquid metal feeding. The interdendritic flow velocity, u, can be calculated by Darcy law []: u = ( P + ρ gt), (17) µ f where i the permeability of the medium, µ i the vicoity, f i the volume fraction of the liquid, P i the hrinkage preure, ρ i the denity of the liquid, g i the acceleration due to gravity, and t i the unit vector along the direction of gravity. The permeability i defined a: 3 f d =, (18) 18(1 f ) where d i the econdary dendrite arm pacing. The preure can be calculated by olving equation 16 through 18 imultaneouly Pore Formation Pore formation i a complex phenomenon. For the exiting mathematical model, the initial nucleu ize i uually aumed to be a fraction of the econdary dendrite arm pacing [] or a very mall number (1 µ m). In our model, the pore nucleu radiu i aumed to be equal to half the ize of the cell (5~1 µ m). Equation how that the ga pore can form only when it preure i ufficiently large to overcome the total local external preure. After every term contributing to equation and 3 i obtained by olving the baic equation, the program then check and decide whether the pore formation condition i met, i.e., the ga preure i greater or equal to the um of the local liquid metal preure and urface tenion. If the condition i atified, a ga pore i formed and i table. The program then randomly elect a liquid cell and aign it to become a ga pore Pore Growth A olidification continue, more hydrogen atom are rejected from the growing olid into the liquid. If the preure of the diolved hydrogen i ufficient, the pore can grow.

11 During each time tep, the preure term are calculated for every element in the location of interet. The calculation i reported until there are no liquid cell remaining in the element, i.e., until olidification i complete. 3.3 Coupling of Grain tructure and Pore Evolution Model In the micro-model, the time tep ued in the calculation hould be determined firt. From the GT model, the dendrite tip velocity V(mm/) i known given an undercooling temperature, (Figure 3). With a pre-defined cell ize d ( µ m), the time tep t() can be calculated: d t = (19) V After the time tep ha been determined, the microtructure prediction model tart with random election of nucleation ite. The election are made in every element in the twodimenional grid when the element reache the pecified undercooling temperature. The number of nuclei that will form every element i calculated: N p = x, () n where x i a random number that i uniformly ditributed between and 1, N i the number of liquid cell available in the element and n i the grain denity of the element. A nucleu will form if p 1.. For every element, N i decreaed by one after each iteration. On the other hand, the grain denity of the element, n, i decreaed by one only when the nucleu i formed (i.e., p 1. ). A flow chart for thi random cell election proce i hown in Figure 5. Figure 5: Flow chart for grain nucleu election In ubequent time tep, equiaxed grain growth i imulated. ince it i aumed that all the nuclei are formed at the ame undercooling temperature, the dendrite tip growth velocity will be the ame for all nuclei (Figure 3).With the number of nuclei in every element determined,

12 one could find the dendrite growth velocity that correpond to the change in the olid fraction calculated by the macro-model. After the growth velocity i determined, one need to chooe the time tep ued in the micro-model calculation. In the micro-model, a olid cell grow with the quare of the von Neumann nearet-neighbor configuration; however, it hould be noted that the dendrite tip correction cheme i not incorporated in our model. From experimental obervation, it i known that hydrogen ga pore form in a pherical hape in the melt [8]. The difference in pore hape depend on whether the pore are able to grow without obtruction or whether they are obtructed to a greater or leer extent by other dendrite growing in the melt [8, 9]. In the imulation, when the ga pore growth condition i atified, growth occur incrementally in tep determined by cell ize. Figure 6 i a chematic for the cellular automation ued to imulate ga pore growth in the model. A mentioned before, the radiu of the initial ga pore i aumed to be one-half the cell ize; thi mean that the ga pore will occupy one cell in the element, a hown in Figure 6(a). During the next time tep in the micro-model, if a ga pore ha already formed, the program will check the poibility for growth. By auming that the ga pore grow in increment of half the cell ize, the ga pore will have a radiu equal to one cell ize. Thi mean that the ga pore will occupy four cell in the element, a hown in Figure 6(b). A growth proceed, the ga pore then ha a radiu equal to one and a half of the cell ize. Thu, the ga pore will occupy nine cell in the element, a hown in Figure 6(c) and o on. In thi way, ga pore can grow radially (for two dimenion) a oberved in the experiment [8]. If ga pore cannot grow radially (i.e., near the end of olidification proce when mot of the molten metal ha olidified), it i aumed that ga pore will expand to the remaining liquid cell that urround the pore, if any. With thi aumption, the expanion of ga pore within a growing dendrite network can be imulated. During the olidification proce, hrinkage pore will form becaue ome of the liquid cell will be engulfed by olid, thereby choking the flow of the feeding liquid. In the model, the formation of iolated hrinkage pore i checked after every iteration (Figure 7). With the algorithm decribed above, a ga pore will be able to grow circularly if it i formed at an early tage of olidification. During thi time, the cating i motly molten metal. It i not difficult for the ga pore to find the liquid pool that i needed for the pore to grow radially. A olidification progree, the growth of the ga pore will be influenced by the advancing dendrite network. In the model, when a ga pore cannot grow radially, it will expand between the dendrite.

13 (a) (b) (c) Figure 6: chematic for the cellular automation ued to imulate ga pore growth 3.4 hrinkage-induced Microporoity Figure 7: Flow chart of the propoed model Cat metal part are ometime unuable becaue they have large internal ga pocket, or poroity, that develop when the metal hrink during olidification. Mot large-cale poroity can be eliminated by a careful deign of the cating mold to keep extra liquid metal in pecial region for feeding the hrinkage. When metal can flow to compenate for hrinkage, poroity uually doe not occur. Another type of poroity i referred to a microporoity becaue it uually appear a a ditribution of mall bubble whoe total volume fraction i typically about 1 percent or le. Having a mean of predicting the location and magnitude of microporoity i therefore of coniderable interet. FOW-3D microporoity model ha been developed for thi purpoe. The paive nature of the microporoity model mean that it may be ued in conjunction with macroporoity model and with either a pure heat conduction imulation or with full hydrodynamic imulation that include filling and olidification procee.

14 When a chill plate i inerted between the metal and the and (on the top, bottom, and end urface), a patially uniform metal temperature i no longer poible, and the olidification change dramatically. There i zero microporoity near the chill plate where the cooling rate i larget, and the local temperature gradient in the metal i large. In thi region, the metal reache complete olidification before the adjacent metal reache a critical olid fraction (and conequently i able to feed the hrinkage). Figure 8 how the computed microporoity along a centerline in the wedge together with the meaured microporoity. Although the computed value are conitently lower, the general agreement i quite good. Both the meaured and computed value are zero near the chill end, and both exhibit maximum value at the thick end of the wedge. Thee limit are what would be expected. The computed value plotted in Figure 8 are thoe along the wedge centerline and have not been area-averaged. Figure 8: Microporoity meaured (olid line) and computed (dahed line) in wedge 4. Concluion A two-dimenional model to predict pore ize, morphology, and location ha been developed for an A356 aluminium alloy olidifying under equiaxed grain tructure condition. To improve upon the conventional determinitic approach, the model link hydrogen ga evolution and microporoity formation mechanim with a probabilitic grain tructure evolution model with reaonable confidence. Thi information can then be ued to evaluate the tatic and dynamic mechanical performance of cating during the earliet tage of product definition. The following concluion are drawn from thi tudy:

15 1. For a permanent mold, Al alloy cating, the diffuion ditance and ize of the dendrite arm are of the ame order. Hence, the approximation of complete equilibrium for hydrogen diolved in olid and liquid can be aumed.. A olidification proceed, no ga pore form until the hydrogen ga preure reache a critical value. 3. There exit a critical initial hydrogen content below which the ga pore cannot form the melt. The critical initial hydrogen content depend on many factor uch a alloy compoition, olidification condition, etc. 4. When the initial hydrogen content i greater than the critical hydrogen content, ga pore will form at a critical olid fraction during olidification. The critical olid fraction decreae a the initial hydrogen content in the melt decreae and critical preure decreae. 5. From experimental obervation, the addition of grain refiner,.7 wt % TiB decreae the grain ize, pore area fraction, and pore ize of the cating. In addition, it i oberved that pore are more uniformly ditributed. 6. In addition to grain refinement, the cooling rate ha a trong influence on the grain ize. 7. The model ha been teted againt three experimental data et. Two tet involved a rectangular plate, and one involved a wedge. The model produce conitent approximation for all cae. It give good qualitative ditribution and reaonable quantitative reult. 8. In ome way, the preent microporoity model i imilar to a temperature and temperature-gradient functional criteria method for etimating hrinkage induced microporoity. Reference [1]. M. Miremaeili, J. Campbell,. G. habetari, and. M. A. Boutorabi, Precipitation of r-rich Intermetallic Particle and Their Influence on Pore Formation in r-modified A356 Alloy, Metallurgical and Material Tranaction A, Vol. 36, no. 9, ept. 5, pp. xx xx. [] C. M. Dinni, A.. Dahle, J. A. Taylor, and M. O. Otte, The Influence of trontium on Poroity Formation in Al-i Alloy, Journal of Metallurgical and Material Tranaction A, Vol. 35, no. 11, Nov. 4. [3] E. Martínez, D. M. Cinero, G.. Valtierra, and J. acaze, Effect of trontium and Cooling Rate upon Eutectic Temperature of A319 Aluminum Alloy, cripta Materialia, Vol. 5, no. 6, 5, pp [4] W. R. Oorio, C. M. A. Freire, A. Garcia, Journal of Alloy and Compound, Vol. 397,, 5, p. 179.

16 [5] W. R. Oorio, J. E. pinelli, N. Cheung, A. Garcia, Material cience and Engineering, Vol. 4A, no. 179, 6. [6] W. R. Oorio, C. M. A. Freire, and A. Garcia, Journal of Material cience, Vol. 4, 5, p [7] W. R. Oório, N. Cheung, J. E. pinelli, P. R. Goulart, and A. Garcia, The Effect of a Eutectic Modifier on Microtructure and urface Corroion Behavior of Al-i Hypoeutectic Alloy, Journal of olid tate Electrochemitry, March 7, pp [8] O. avaş and R. ayikci, Application of Taguchi Method to Invetigate ome Factor Affecting Microporoity Formation in A36 Aluminium Alloy Cating, Material & Deign, Vol. 8, 7, pp [9] D. Ruvalcaba, R. H. Mathieen, D. G. Ekin,. Arnberg, and. atgerman, In itu Obervation of Dendritic Fragmentation due to ocal olute-enrichment during Directional olidification of an Aluminum Alloy, Acta Materialia, Vol. 55 7, pp [1] A. P. Boeira, I.. Ferreira, and A. Garcia, Modeling of Macroegregation and Microporoity Formation during Tranient Directional olidification of Aluminum Alloy, Material cience and Engineering A, Vol. 435/436 6, pp [11] H. Combeau, D. Carpentier, J. acaze, and G. eoult, Modelling of Microporoity Formation in Aluminium Alloy Cating, Material cience and Engineering, Vol. 173, pp [1] E. Obaldia and. D. Felicelli, Quantitative Prediction of Microporoity in Aluminum Alloy, Journal of Material Proceing Technology, Vol. 191, 7, pp [13] J. i, J. Ma, Y. Gao, and Q. Zhai, Reearch on olidification tructure Refinement of Pure Aluminum by Electric Current Pule with Parallel Electrode, Material cience and Engineering, In Pre, 8. [14] M. Zhang, P. elly, M. Eaton, and J. Taylor, Crytallographic tudy of Grain Refinement in Aluminum Alloy Uing the Edge-to-edge Matching Model, Acta Materialia, Vol. 53, no. 5, 5, pp [15] A. nuutinen,. Nogita,. D. McDonald, and A.. Dahle, Poroity Formation in Aluminium Alloy A356 Modified with Ba, Ca, Y and Yb, Journal of ight Metal,1, pp [16] W. urz, B. Giovanola, and R. Trivedi, Theory of Microtructural Development During Rapid olidification, Acta Metallurgica, Vol. 34,1986, pp [17] J.. pittle and. G. R. Brown, Computer imulation of the Effect of Alloy Variable on the Grain tructure of Cating, Acta Metallurgica, Vol. 37, 1989, pp [18] M. E. Fine, Introduction to Phae Tranformation in Condened ytem, Macmillan Co., 1964, p. 7. [19] E. A. Brande and G. B. Brook (editor), mithell Metal Reference Book 7th ed., Butterworth-Heinmann, 199, pp [] J. D. Zhu and I. Ohnaka, Computer imulation of Interdendritic Poroity in Aluminum Alloy Ingot and Cating, Modeling of Cating, Welding and olidification Procee, 1991, pp