Modeling Liquid Phase Sintering of Hard metal powder compacts

Transcription

1 ing Liquid Phae Sintering of Hard metal powder compact Shama Shamaundar *, Maheha Siddegowda*, Pavanachand Chigurupati**, Rengarajan Raghavan***, Rameh Rao. S. *** * ProSIM AFTC # 326, 8th Main, III Stage, IV Block, Baavehwarnagar, Bangalore , INDIA info@pro-im.com ** Scientific Forming Technologie Corporation 5038 Reed Road, Columbu, Ohio, USA pchigurupati@deform.com ***Widia India Limited 8/9th mile, Tumkur Road. Bangalore , INDIA rr@widiaindia.com ABASTRACT The yield function and the contitutive equation developed for hardmetal powder are incorporated into a non-linear FEM imulation engine. Denification due to particle rearrangement, melting of additive particle, contact flattening, pore ize ditribution & liquid preure are modeled by chooing appropriate governing equation. Uing the denity gradient reulting from the compaction proce, the differential hrinkage at different region in the compact are predicted. The experimental meaurement and model predicted reult are compared. Detail of model development, FE analyi and validation are dicued with reference to different compact hape and grade of powder. It i demontrated that FEM imulation can be employed a a tool in the deign proce, to minimize/eliminate undeirable hrinkage related ditortion in liquid phae intering of hardmetal compact. 1: INTRODUCTION Liquid phae intering i defined a The thermal treatment of powder compact at a temperature below the melting point of the main contituent, for the purpoe of increaing it trength by bonding together of the particle. In cae of powder mixture the intering temperature may be above the melting point of the low melting contituent and below the melting point of the bae material e.g. tungten carbide/cobalt, iron/copper, copper/tin, o that the intering take place in the preence of liquid phae which i formed by the melting of low melting material, hence the term Liquid Phae Sintering. The liquid phae accelerate the intering proce. Main advantage of liquid phae intering are low intering temperature, fat denification, homogenization, and high final denitie. Mechanical and phyical propertie of liquid phae intered part are uperior to olid-tate intered part [1]. However hrinkage aociated with the denification during intering proce poe major challenge for the deigner. In cae of liquid phae intering of hardmetal compact the amount of linear hrinkage will be a

2 high a 17-22%. Indutrial deigner are concerned with the effect of ditortion ariing due to differential hrinkage in the component during intering. Shrinkage during intering i a function of local relative denity in the green compact. Variation of denity in the green compact arie a a reult of friction between powder and die/tool wall, geometry, differential punch/die movement, material flow characteritic and o on. Sintering behavior i tudied by variou reearcher [1-8,10,11], have modeled baic phenomenology of intering through mathematical modeling. However at the indutry level the deigner till go through traditional trial and error method during proce deign cycle. The preent work i aimed toward developing liquid phae intering model, which can be implemented in a FEM code and ued in the indutry a a deign tool. In the preent paper, development of model for liquid phae intering of hard metal, implementing thee model in a Finite Element code DEFORM TM 2D, and validation of the model with plant data [15] are dicued. 2: LIQUID PHASE SINTERING MODEL The driving force for denification during intering i the reduction in interfacial energy between particle. An appreciable volume fraction of liquid in the compact during intering, an appreciable degree of olubility of olid in the liquid and complete wetting of olid particle by liquid are the deirable condition for complete denification during liquid phae intering. Denification during liquid phae intering i a reult of everal mechanim. Thee mechanim get activated at different time/temperature during intering [3 ]. for liquid phae intering wa developed in Svoboda et al. [1] and a model for liquid phae intering applied to Si 3 N 4 and WC-Co wa developed by P.E. McHugh and H.Riedel [2]. The Liquid phae intering model choen for implementation comprie the following apect of liquid phae intering Primary rearrangement of the olid particle when the liquid phae i formed Grain hape accoodation by contact flattening Filling of large pore and grain coarening in the final tage of intering The rearrangement dominate in the initial tage after liquid formation, hape accoodation in the econd, and filling of large pore and grain coarening in the final tage of intering [2]. i formulated in term of tate variable: Solid volume fraction-d (relative denity of olid) which i the ratio of volume fraction of olid phae to the entire volume of the component, flattening train (δ), grain radiu (R), and liquid volume fraction (g). The liquid fraction (g) i aumed to be a function of the temperature only, which in turn i a function of time. Equation for olid denity i r m f D = D + D + D (1) where dot denote the derivative with repect to time and the upercript indicate the contribution by rearrangement (r), melting of additive particle (m), and contact flattening (f). In the following ection the evolution equation for tate variable are derived. 2.1: Particle rearrangement During intering liquid phae i formed in the compact at area, which contitute low melting particle. Capillary force pull thi liquid into particle neck and mall pore. The reulting liquid flow may lead to reidual pore at initial ite, which will be filled in the later tage of intering [8,9]. The penetration of liquid lead to welling of compact reulting from increaed particle ditance due to the additional liquid

3 introduced into the contact area. However the particle movement lead to rearrangement thu reulting in denification. The capillary force exerted on the olid particle by liquid and applied mechanical preure lead to the rearrangement of olid particle. Rearrangement require the liding of particle againt one another with a liquid film between particle. Hence the denification rate of the olid particle by rearrangement hould be depend on the vicoity of the liquid - η, liquid film thickne - δ b, and the area of the particle contact - c 2 in the following way. D r bdδ b R = ( σ σ )( D D ) ηc m 2 1 S = 0 if D1 DS where R i the radiu of the olid particle, D 1 correpond to the denity of the random dene phere packing, D 1 =0.63, σ i the intering tre, σ m i the mean tre acting on the material, which i equal to the negative of the applied mechanical preure, c i contact radiu, b i a dimenionle factor related to vicoity (η), taken a unity in computation. The liquid film thickne δ b i adopted form literature [3] to be in the order of 1.5nm. 2.2: Melting of additive particle During intering heating up to intering temperature, the low melting point particle will melt and liquid phae i formed. The iediate effect of melting i to reduce the olid denity according to if D 1 > D gd D m = 1 g (3) where g i the liquid volume fraction and the dot denote the derivative with repect to time. The diappearance of additive particle and partial olution of the bae material in the melt open the poibility for rearrangement of the olid particle, o that the total denity increae. 2.3: Contact flattening The denification rate of olid particle due to contact flattening i given by 3 f δd D = (4) 1 ( δ ) Where δ i the flattening train and δ i the flattening train rate. δ grow by olution/precipitation of the olid in to the liquid film and diffuion of the diolved olid atom out of the contact area in to the liquid collar to be depoited by on the particle urface outide the contact area [12-14]. Thi phenomenon i explained in detail by Riedel [2]. S (2) 4: IMPLEMENTATION OF MODEL AS CONSTITUTIVE EQUATION FOR NON LINEAR FEM CODE The contant and co-efficient, ued in thee mathematical model are dependent on the phyical, chemical propertie of contituent in powder mixture. Correponding to the powder characteritic uch

4 a olubility, liquid wetting, preure, proce condition uch a temperature and time, thee contant and co-efficient have different value. Variou material and proce parameter will have to be determined a applicable to thee material ytem and procee. Often, the individual variable cannot be determined at the operating condition. Thee are determined by invere olution. The data are derived from experimental reult and running the model for thee experiment in an iterative manner. By matching the experimental and model (theoretical / numerical) reult, the correponding material variable/contant are determined. Once the required et of variable, contant and co-efficient are determined in thi manner, they can be ued confidently in the model. In the preent work thee mathematical equation [1,2,3,4,5], which model the liquid phae intering, are implemented a a ubroutine for non-linear FEM code DEFORM TM [16]. During intering there are two major phenomena taking place. Heat tranfer within the component and denification reulting in hrinkage or deformation of original hape. The FEM oftware in which intering imulation ha to be carried out hould have the capability to handle coupled analyi of tranient heat tranfer and deformation (hrinkage). The intering model ubroutine i linked with the main olving engine of DEFORM TM, o that intering equation are olved for each nodal point to determine the intering proce variable at each tep of temperature change againt time. Figure-1 how the flow chart for intering proce. Figure 1. Flow chart for powder compaction and intering proce modeling Input data i entered in to the model through DEFORM TM pre-proceor. The FEM imulation engine doe the calculation and in the DEFORM TM pot-proceor the output reult are viewed both graphically and numerically. Denity ditribution in the green compact and compact geometry, which i the output of the powder compaction model, will go a an input in to the intering model. Since hrinkage in liquid phae intering i mainly dependent on denity ditribution in the green compact, to predict hrinkage and ditortion accurately, it i important to determine the initial denity ditribution accurately. In the preent work we have ued DEFORM TM a a FEM code to imulate the powder compaction. The denity

5 ditribution predicted by DEFORM TM modeling intering behavior. i imported in to the intering model and ued a a input for 5: EXPERIMENTAL DETAILS Validation of liquid phae intering model wa carried out for 15 experiment, which include three different component hape and three different grade of powder. To implify the validation and finetuning of the model, initial et of experiment were carried out with axi-yetry component. 5.1: Component 1 Firt et of experiment were carried out chooing a cylindrical component. The powder filled cavity i a cylinder of 14 diameter with a imple compaction procedure in which the preing troke i by downward movement of top punch with tationary die. Compacting to different height will reult in different average green denity and different denity gradient in the compact. Powder denity at the end of die filling wa meaured to be for grade-1, for grade-2 and for grade-3 powder. Figure 2a how the denity ditribution after compaction (green denity) and Figure 2b how the component geometry after compaction (meh with thin line) and after intering (meh with thick line) for the height green compact of grade-1 powder. Figure 2b how only right half of the centrally cut ection of the cylinder with central axi at the left hand ide. With different compact height and powder material 12 different ample were obtained. The variation in denity ditribution after compaction ha reulted in a taper in the vertical direction a hown in figure 2a. Hence diameter i meaured at the top and bottom end of the component, where top end correpond to top punch ide and bottom correpond to ejector ide. prediction alo capture the taper in the component. (a) (b) Figure 2. (a). Denity ditribution after compaction (b). The meh before and after intering * Detail of compaction procedure and FEM modeling of compaction are given in an adjoining paper by the author Figure 3a how the comparion between experimentally meaured dimenion and model prediction for bottom diameter for grade-1 powder. The x-axi repreent the average denity and y-axi repreent the bottom diameter. Experiment were conducted for 5 ample with different height reulting in nominal denity or average denity of 0.46, 0.48, 0.51, 0.54 and Similarly experimentally meaured top diameter and height of the component are compared with model prediction in figure 3b and 3c.

6 Bottom Diameter () Figure 3 (a) Top Diameter () Figure 3 (b) Height () Figure 3 (c) Figure 3. Comparion of experimental reult with model prediction for grade-1 powder material (a). bottom diameter (b). top diameter (c). height Experiment were conducted for the cylindrical component with grade-2 powder material, which ha coniderable difference from grade-1 with repect to compoition, grain ize and powder denity (Appendix, Table-3). For thi grade of material three ample were compacted for different height and intered. Average denitie of thee ample are 0.52, 0.53 and Comparion of model prediction with experimental reult for grade-2 how imilar trend a that of grade-1 powder material. The validation reult are hown in figure 4a,b and c.

7 Bottom Diameter () Figure 4 (a) Top Diameter () Figure 4 (b) Height () Figure 4 (c) Figure 4. Comparion of experimental reult with model prediction for grade-2 powder material (a). bottom diameter ( b). top diameter (c ).height Similarly for the ame cylindrical component experiment were conducted with grade-3 powder. The average denity of the ample wa 0.46, 0.50, 0.54 and The hrinkage reult of grade-3 powder have imilar trend with that of grade-1 and grade-2. Figure-5a, b and c how the comparion of model prediction with experimentally meaured dimenion.

8 Bottom Diameter () Top Diameter () Figure 5 (a) Figure 5 (b) Height () Figure 5 (c) Figure 5. Comparion of experimental reult with model prediction for grade-3 powder material (a). bottom diameter ( b). top diameter (c ).height 5.2: Component 2 The econd component choen i a tapered cylinder (figure 6a). Top diameter, bottom diameter and height are the three dimenion (figure 6b) conidered for validation. Denity gradient after compaction are

9 hown in fig 7a. The component geometry before intering and after intering i hown in Figure 7b. The reult of validation for grade-1 and grade-2 powder are given in table 1. Compaction procedure for thi component i by combined movement of top punch and die. Hence modeling of compaction involve relative movement of die and punch. In thi component depending on the grade, which correpond to different initial powder denity, the initial fill volume i different uch that the final intered dimenion are nearly ame. Thi difference in tarting volume i conidered in the compaction modeling. (a) (b) Figure 6. (a). Component geometry after compaction (b). Green compact dimenion (a) (b) Figure 7. (a). Denity ditribution after compaction (b). Geometry before and after intering Table-1. Comparion of Sintering experimental reult and model prediction for grade-1 powder Powder Grade Bottom Diameter Top Diameter Height Grade Grade : 3: Component 3 The third component i a cylinder with a central through hole a hown in the figure 7. Denity gradient at the end of compaction are given in figure 8a. Figure 8b how prediction of hrinkage after intering over green compact geometry. Quantitative comparion are given in table-2. Similar to the taper found in

10 the firt ample, in thi cae too hrinkage reult in taper along the axial direction on the outer urface hence outer diameter i meaured on the top ide and bottom ide. Top outer diameter, bottom outer diameter, inner diameter and height are the four dimenion conidered for validation. In thi component alo the compaction i through combined movement of top punch and die. Figure 7. Component geometry after compaction with green compact dimenion (a) (b) Figure 8. (a). Denity ditribution after compaction (b). Geometry before and after intering Table-2. Comparion of experimental reult and model prediction for grade-1 powder Powder grade ID OD - Bottom OD - Top Height Grade-1 Exp. Exp. Exp. Exp : DISCUSSION Comparing the intering model reult with the experimental reult, it can be inferred that the intering model i fairly accurate in modeling the intering. The model i ucceful in predicting the final height of

11 the intered component with good accuracy and alo the taper along the length of the cylinder in the firt cae. The reult for all the three grade of the powder and alo for all the ize of the component conidered for imulation are cloe to the experimentally meaured dimenion. The comparion of model prediction with experimental reult for the third component i really encouraging a thi particular component ha a through hole with compound die/punch movement during compaction. In thi particular component both inner diameter and outer diameter are hrinking along with height which i captured by the model. Thu it can be concluded that the model i uccefully emulating the liquid phae intering proce. From the validation reult it i oberved that the intering model i conitently predicting higher dimenion for both top diameter and height for all the ample. Thi deviation i probably becaue of the un-accounted wax, which i ued a lubricant that flow out of the compact during dewaxing proce before the beginning of the intering proce. Thi wax i of the order of 2-3% of weight. The preent model doe not account for dewaxing and correponding reduction in relative denity. Further fine-tuning of the model and alo a method to incorporate denity lo due to wax removal can further improve the accuracy of model prediction. 7: FUTURE SCOPE OF WORK So far, the inert geometrie that can be modeled uing 2D axi-yetric modeling have been conidered for validation. The model ha to be extended to 3D geometrie. Only hrinkage i conidered for validation of the model. Though hrinkage i the primary concern for engineer at the indutry, other proce variable like intering tre, grain ize etc alo have ignificant influence on the oundne of the component produced, hence validation ha to be carried for thee variable and qualitative and quantitative ignificance of thee variable have to be determined. The final goal of thi tudy i to build a uer friendly liquid phae intering model, which can be deployed at the indutry a a product deign tool in PM indutry. APENDIX Powder Grade Table 3. Powder grade compoition and Grain ize of the contituent % Compoition by weight WC Co Cubic Carbide Grain ize Micron % Compoition by weight Grain ize Micron % Compoition by weight Grain ize Micron Grade Grade Grade REFERENCES 1. G.Petzow and W.A.kayer Baic mechanim of liquid phae intering. Sintered Metal-ceramic compoite, 1984

12 2. J.Svoboda, H.Riedel and Rgeabel, A model for liquid phae intering, Acta metal. Vol.44, 1996, pp P.E. McHugh and H.Riedel, A liquid phae intering model: Application to Si 3 N 4 and WC-Co Acta metal. v45, 1997, pp S.J.L.Kang, A.Kayer, G.Petzow, and D.N.Yoon Elimination of iolated pore during liquid phae intering of Mo-Ni, Powder met., v27[2], 1984, pp D.N.Yoon, W.J. Huppmann Grain growth and denification during liquid phae intering of W-Ni, Acta Metall., v27, 1979, pp W.D.KingeryJ, Denification during intering in the preence of liquid phae. Applied Phyic, v30[3], 1959, pp S.J.L.Kang, K.H.Kim, and D.N.Yoon J. Am. Ceram. Denification and hrinkage during liquid phae intering, Soc, v69[2], 1986, pp H.H.Park, S.J.Cho, and D.N.Yoon, Pore filling proce in Liquid phae intering, Metall. Tran.A, v15a, 1984, pp S.M.Lee and S.J.L.Kang, Theoretical analyi of liquid phae intering: pore filling theory, Acta Metall., v46, 1998, pp J.Svoboda, H.Riedel, H.Zipe, Equilibrium pore urface, intering tree and contitutive equation for the Intermediate and late tage of intering-i., Acta Metall., v42, 1994, pp J.Svoboda, H.Riedel, H.Zipe, Equilibrium pore urface, intering tree and contitutive equation for the Intermediate and late tage of intering - II, Acta Metall., v42, 1994, pp J. Svoboda, H. Riedel, A Theoretical tudy of grain growth in porou olid during intering Acta Metall., v41, 1993, pp S.Haglund and J.Agren, W content in Co binder during intering of WC-Co Acta Metall., v46, 1998, pp O.H.Kown and G.L.Meing, Theoretical analyi of olution-precipitation controlled denification during liquid phae intering Acta Metall., v39, 1991, pp Widia India Limited data and component, tool geometry drawing. 16. Uer ubroutine manual upplied with DEFORM TM oftware