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Investigations in the compaction and sintering of large ceramic parts
Investigations in the compaction and sintering of large ceramic parts
Investigations in the compaction and sintering of large ceramic parts
Investigations in the compaction and sintering of large ceramic parts
Investigations in the compaction and sintering of large ceramic parts
Investigations in the compaction and sintering of large ceramic parts
Investigations in the compaction and sintering of large ceramic parts
Investigations in the compaction and sintering of large ceramic parts
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Investigations in the compaction and sintering of large ceramic parts

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  • 1. Journal of Materials Processing Technology 190 (2007) 243–250 Investigations in the compaction and sintering of large ceramic parts Peng Chen ∗ , Gap-Yong Kim, Jun Ni Department of Mechanical Engineering, University of Michigan, 1210 HH Dow Bldg., 2350 Hayward St, Ann Arbor, MI 48109, USA Received 11 September 2006; received in revised form 12 February 2007; accepted 22 February 2007Abstract In this study, a large ceramic part was successfully compacted and sintered using uniaxial die compaction technique. The effects of die design,compaction pressure, lubrication, sintering procedure and part orientation in the oven on the P/M part quality were investigated and the preferredprocess conditions were discussed and concluded. The main quality issues encountered were cracking and distortion. A finite element model forthe powder compaction process was also developed and validated. Based on the model, the relationship between the cracking location and thedensity distribution predicted from finite element analysis (FEA) was discussed.© 2007 Elsevier B.V. All rights reserved.Keywords: Uniaxial die compaction; Sintering; Lubrication; Die design1. Introduction tions of the parts. This density distribution mainly originates from particle–particle and die wall–particle friction, which cause Ceramics have become increasingly important in modern quality issues such as cracking and warpage during the sinter-industry due to their good mechanical and physical properties ing. Especially, when a large part size is considered, the poor[1]. Ceramic parts are generally produced by combination of control over the density uniformity of the green part becomescompaction and sintering. However, cracks and distortions have significant and results in part failures. In general, the dimen-been recognized as the most significant concerns, and often limit sions of the sintered compacts are in the range of 10–100 mmthe application of uniaxial die compaction technology to produce [4].large-scale ceramic parts. Cracks in powder metallurgy (P/M) The modeling methodology for powder compaction can becomponents primarily originate from the compaction prior to classified into three categories based on the length scale [5]:the sintering. Although the cracks may not become evident until (1) continuum models; (2) multi-particle models (discrete ele-the sintering has occurred, the root cause is most likely the poor ment models and particle dynamics models) [6–8]; and (3)interparticle bonding obtained prior to the sintering [1–4]. Usu- atomistic/molecular dynamics models [5,9]. Continuum mod-ally, micro-cracks that are invisible during the compaction are els assume that a response of a powder packing is continuouscarried over and enlarged during the sintering. Another common and similar to that of a solid material. Hence, they are attrac-challenge in sintering is the dimensional control of the sintered tive in practical applications and have been employed in thisproducts. Warpage could occur as a result of green density gra- study. There are two types of continuum models. The first isdient, friction drag (caused by the support material), gravity, and the micromechanical model [10,11], which provides a way totemperature gradient [4]. derive macroscopic model parameters from information on a Uniaxial die compaction is the simplest form of consolida- smaller particle-level length scale. The micro-to-macro tran-tion process that has been extensively used to densify powder sition is performed usually by homogenization techniques.materials. One disadvantage of this technique, however, is the The other is the empirical (phenomenological) model [12–14],variation of the pressed density that can occur at different loca- which is formulated using several ‘material’ functions that describe the response of a specific porous material to the stress. ∗ Corresponding author. Tel.: +1 734 615 7445 The objective of the study is to investigate the effects of pro- E-mail address: pengchen@umich.edu (P. Chen). cess parameters to obtain a crack-free ring shaped part, which0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2007.02.039
  • 2. 244 P. Chen et al. / Journal of Materials Processing Technology 190 (2007) 243–250 Fig. 1. (a) Instron 1136; (b) zirconia disk compaction die set; (c) section view of the tooling.has a final dimension of 90 mm after uniaxial compaction and relatively slow speed. Finally, the base plate was replaced by an ejection ring,sintering with minimum distortion. and the green part was pushed out. The die wall was lubricated with mineral oil, which was recommended by the powder vendor. Based on the shrinkage ratios from the preliminary experiments, the dimen-2. Experimental and simulation procedure sions of the die for the ring component was determined as shown in Fig. 2. A previous attempt with a one-piece die design similar to the disk shaped part2.1. Experimental setup and procedures as shown in Fig. 1 but with a diameter of 114 mm resulted in green parts with cracks due to excessive friction during ejection process, which caused a large Two types of experimental setup have been designed and fabricated for this density gradient in the green compact. Therefore, a split die design was adoptedstudy. To acquire a final part dimension of 90 mm, green part dimensions need to reduce the friction during ejection as shown in Fig. 2. The Container wasto be larger than 110 mm, which is rather large for a part made by uniaxial designed, so it may be split into two halves to facilitate the ejection process. Thecompaction. Since the final target part dimensions were larger than those of two symmetric pieces were assembled by eight screws and two aligning pins.a typical ceramic powder compaction and sintering, a preliminary experiment The core rod was designed to produce a ring shaped part, which was assembledwas performed to compact a cylindrical part with a diameter of 46.4 mm to by two screws and an aligning pin. All the tooling components were made frominvestigate appropriate range of process parameters. Based on the results from A2 tool steel, which were heat treated to the hardness of HRC 55 and werethis preliminary experiment, a die for the larger ring shaped part was designed precision ground.and fabricated. The detailed experimental setup for the compaction and sintering The experiment cycle requires assembly and disassembly of the die com-of both sizes are described below. ponents. First, the Dividable Container is assembled. Next, core rod and base A commercial zirconia powder (YSZ, Inframat Advanced Materials, LLC) plate are placed in the container, and then 380 g of zirconia powder is pouredstabilized by 3 mol% Y2 O3 was used for all the experiments conducted in this into the container. The Punch is placed on top of the powder, which is guided bystudy. The particles have a mean particle size of 0.5 m. the core rod and the container during the compaction. A constant punch speed is The setup for the preliminary experiment is shown in Fig. 1, which includes retained by Instron 1136 material testing system. After holding the punch at thea punch, a base plate, and a die. The components were made by precision milling final position until the load is stabilized, it is released at a relatively lower speed.and turning process from A2 tool steel. 50 g of zirconia powder was poured into After the compaction, the Dividable Container is disassembled, and the basethe assembled die/punch set. The setup was then placed in the Instron 1136 plate is detached from the core rod to eject the compact. Finally, the ejected partmaterial testing system for compaction, which had a single acting upper punch. is sintered in an oven. Three sintering procedures (Fig. 3) were used in this study.The compaction process was achieved by a constant punch speed. The punch Procedure II has a higher sintering temperature than Procedure I. Procedure IIIwas held at the final position until the force stabilized and was released at a has a very slow heating speed than those of Procedure I and II. Fig. 2. (a) Zirconia ring compaction die set; (b) section view of the tooling.
  • 3. P. Chen et al. / Journal of Materials Processing Technology 190 (2007) 243–250 245 Table 1 Material properties of zirconia powder [14] Full density Initial density Particle size β α 6.08 (g/cm3 ) 1.885 (g/cm3 ) 0.53 m (Nominal) 54.3◦ 0.03 E ν d R 206 GPa 0.31 1.53 MPa 0.835 Fig. 3. Illustration of the sintering procedures.2.2. Material modeling for compaction simulation In order to simulate the zirconia powder compaction process, a finite elementanalysis (FEA) model was developed utilizing the material property data from Fig. 5. Densification behavior of the zirconia powder [14].previous study in literature [14]. It is necessary to recognize the major physicalphenomena that occur during the compaction of ceramic particles. The com-paction process can be divided into three main distinctive stages. In the early deformation. If the stress state is such that Eq. (1) is satisfied, the material failsstages of compaction, particles are rearranged (we will refer to this as stage 0 in shearing. At high hydrostatic pressures, the yield surface is described by acompaction). As compaction force is further exerted onto the powders, the rel- cap surface, Fc :ative density (RD, which is defined as the ratio of the density of the compact tothe full density of the material) increases, and compaction is accommodated by R×q 2elastic deformation of the particles (stage 1 compaction). At higher pressure, the Fc (q, p) = (p − pa )2 +compact structure will breakdown with a small amount of particle rearrangement 1 + α − α/cos(β)(stage 2 compaction). −R × (d + pa × tan(β) = 0 (2) In this study, we employed the modified Drucker–Prager/Cap (DPC) model,which has been widely used in powder metallurgy and ceramic industry (Fig. 4). R is a material parameter that controls the shape of the cap. pa is anIt is a phenomenological model that has been adapted from soil mechanics. The evolution parameter that represents the volumetric inelastic strain driven hard-model is attractive in compaction modeling because it contains features that ening/softening, which is related to hydrostatic compression yield stress (pb ).are in accordance with the physical response of particulate compacts [12,15]. The parameters pa and R may be obtained from compaction experiments. TheThe DPC model at low hydrostatic pressure is a shear failure model, similar to parameter α does not have a physical meaning, but ensures a smooth transitionthose used in granular flow, which reflects the dependence of the strength on between the cap and the shear failure regions for numerical robustness. Typi-the confining pressure. This enables the model to predict the strength in tension cally, a small value (α = 0.01–0.05) is used to avoid the situation of α = 0, whichto be smaller than the strength in compression, a concept which is common for will form a sharp corner at the intersection of Fc and FS . This may lead torocks, brittle materials, and pressed powder compacts. In its simplest form, it numerical problems [16]. The geometric representation of the complete yieldis represented by a straight line in the p–q plane, which is also known as the locus is represented in the p–q plane as a limiting curve F(q, p, RD) = 0 in Fig. 4.Mohr–oulomb shear failure line, FS : This form is consistent with the DPC model implemented in the finite element package ABAQUS, which was used for this study.FS (q, p) = q − d − p × tan(β) = 0 (1) The FEA results were compared with the medium size compaction exper- iments (Ø = 46.4 mm). The material properties used for the simulation arewhere d and β are cohesion and internal friction angle, respectively. If the stress summarized in Table 1. These values were adopted from the experimental workstate is such that the corresponding Mises equivalent stress (q) and hydrostatic of Kim et al. [14] (3 mol% Y2 O3 stabilized zirconia powder, HSY-3.0, Daiichi-pressure (p) result in a value of F(q, p) < 0, then the stress causes only elastic Kigenso Kagaku Kogyo Co. Ltd., Japan). Fig. 5 shows the densification behavior of this powder. Considering the geometric symmetry of the process, only an axisymmet- ric section of the compact was simulated using the commercial FEA software, ABAQUS v6.5. The tooling was represented by rigid elements, whereas the material mesh for the powder consisted of an array of 4-node bilinear axisym- metric quadrilateral elements with reduced integration (CAX4R). 3. Results and discussions 3.1. Compaction of ceramic disk (Ø = 46.4 mm) 3.1.1. Compaction results and discussion As summarized in Table 2, different process parameter levels Fig. 4. The Drucker–Prager/Cap (DPC) model [5]. were investigated. The green part quality was evaluated in terms
  • 4. 246 P. Chen et al. / Journal of Materials Processing Technology 190 (2007) 243–250Table 2Experimental conditions for the compaction (Ø 46.4 mm disk)Case Pressure (MPa) Pressing speed (mm/s) Releasing speed (mm/s) Ejection speed (mm/s) Green Part 1 92.30 0.085 0.004 0.008 Horizontal crack 2 134.5 0.042 0.021 Manual Horizontal crack 3 118.7 0.042 0.008 Manual Horizontal crack 4 65.93 0.042 0.008 2.117 Crack free 5 (3 repeats) 65.93 0.042 0.008 4.233 Crack free 6 (3 repeats) 52.74 0.042 0.008 4.223 Crack freeof the occurrence of cracks. It was found that the most important tion as shown in Fig. 7. In general, the simulation results agreeprocess parameter was the compaction pressure. The effects of well with the experiment. The underestimation of the load atpressing, releasing and ejection speed on cracking were rela- the initial loading stage is most likely due to the inaccuracy oftively small. As long as the compaction pressure was less than the material modeling at low densities. As explained in [17], theor around 65.9 MPa, cracks did not occur. Typically, a crack material parameters for DPC model at low densities are usu-is initiated by the existence of a sharp density gradient. When ally not obtainable from the material testing experiment: thethe compaction force is reduced, the density gradient of the lower the density, the more measurement noise in the experi-green part also decreases correspondingly. Therefore, a smaller ment. In addition, the powders used in the experiment (Inframatcompression pressure helps to avoid cracks [2]. Fig. 6 shows a Advanced Materials, LLC) and simulation (Daiichi-Kigensosuccessful and an unsuccessful case from the compaction: one Kagaku Kogyo Co. Ltd.) were from different sources, which mayhas a horizontal crack (case #2), and the other is free of crack have contributed to the different loading characteristic, although(case #5). the powders were the same grade. The green part height from the simulation (11.866 mm) agreed well with that of the actual3.1.2. FEA results and discussion part (11.557 mm), and the final density of the green part from The loading curve obtained from the experiment case #5 from the simulation (2.554 g/cm3 , at the top surface) also matched theTable 2 was compared with the loading curve from the simula- actual part density (2.575 g/cm3 ). Furthermore, the model was utilized to study the relationship between the density distribution and the crack formation. Thus, a crack-free case (case #5) and a case with cracks (case #2) were simulated. Fig. 8 shows the relative density distribution of the simulated parts after ejection. Following observations have been made from Fig. 8. 1. The highest density in a crack-free case (case #5) occurred at the upper corner of the compact, which agreed with the common practice in the sense that the upper corner of the part experiences the highest compaction pressure [14]. On Fig. 6. Compacted part: (a) Case #2; (b) Case #5. Fig. 7. Loading curve comparison (Case #5).
  • 5. P. Chen et al. / Journal of Materials Processing Technology 190 (2007) 243–250 247 Fig. 8. Density distribution after ejection: (a) Case #5; (b) Case #2. the other hand, the highest density for the case #2 (which Fig. 9. Density distribution after ejection (ring compaction with a pressure of had cracks in the experiment) occurred below the upper 40.49 MPa). surface.2. Case #2 has a sharper density gradient near the upper corner The simulation results indicated the migration of the loca- region, and the corresponding relative density curves exhibit tion of the highest density region of a compact from the top a sharp distribution. This indicates a sudden change of density surface to below the surface as the pressure was increased. As in a localized area, while the relative density curves of case the pressure increased, cracks developed under the top surface #5 are smoother and corresponds to a more uniform density as shown in the actual part (Fig. 6a case #2). The location of the distribution. crack corresponds to the highest density area in Fig. 8b. WhenTable 3Zirconia ring compaction experiment conditionsCase Pressure (MPa) Green part before ejection Lubrication of the base plate surface Separation between the compact and lower portion of core rod and the base plateRing 1 40.49 Crack free Mineral oil A blade was used for the separation, which resulted in a bad compact surface conditionRing 2 40.49 Crack free Mineral oilRing 3 40.49 Crack free WaxRing 4 40.49 Crack free Aluminum foil Easy separation, but the foil was embedded into the compact, elimination of the foil resulted in a very bad compact surface condition and cracks, Fig. 9 a)Ring 5 40.49 Crack free Coolube 5500 metalworking fluid Failed, cracksRing 6 28.92 Crack free Water based graphite particle Successful lubricant (Lubrodal F705 ALX)Ring 7 57.84 Crack free Oil based graphite particle lubricant Successful, Fig. 9 b) (Lubrodal Hykogeen Conc HI)Ring 8 40.49 Crack free Oil based graphite particle lubricant Successful (Lubrodal Hykogeen Conc HI)Ring 9 52.05 Crack free Oil based graphite particle lubricant Successful (Lubrodal Hykogeen Conc HI)Ring 10 58.3 Crack free Oil based graphite particle lubricant Successful (Lubrodal Hykogeen Conc HI)Ring 11 63.62 Crack free Oil based Graphite Particle lubricant Successful (Lubrodal Hykogeen Conc HI)Ring 12 72.88 Crack free Oil based graphite particle lubricant Successful (Lubrodal Hykogeen Conc HI)
  • 6. 248 P. Chen et al. / Journal of Materials Processing Technology 190 (2007) 243–250the high-density region is located on the top surface, a densitygradient is created from top to bottom as indicated in Fig. 8,case #5. In contrast, as the pressure increased, the high-densityregion shifted under the top surface, and the density gradient wascreated such that it caused tensile internal stress at the locationas indicated in Fig. 8, case #2. It is speculated that the cracksinitiate from these highly dense regions to relieve the internalstress built up from the density gradient.3.2. Compaction and sintering of a large scale ceramicring (Ø = 114 mm)3.2.1. Compaction simulation results and analysis The simulation tool was used to detect potential cracks thatcan form in the ring shaped part prior to designing of an exper-imental setup. The resulting density distribution of the ejectedpart at a compaction pressure of 40.49 MPa is shown in Fig. 9.The relative density distribution was smooth, and no potentialcrack locations could be identified. This was proved later by theexperiment having the same condition (Case Ring 1 in Table 3).Higher densities were found at the top surface where the movingpunch contacted the powder. The density distribution at the ringinner perimeter is very close to that at the ring outer perimeter.The design change from the disk shape to the ring shape alsoreduced the required load due to the decreased contact area.3.2.2. Compaction experiment results and discussion Pressing speed and releasing speed of the punch also affectthe crack formation of the compacted parts. A too high punchspeed will result in a higher density at the contacting surface sus-ceptible to cracks. Also, a too high releasing speed will discharge Fig. 10. Green parts: (a) unsuccessful case (Ring 4); (b) successful casethe internal pressure too quickly and lead to cracks. Thus, based (Ring 7).on the process parameters used in Section 3.1, and a few trial-and-errors from both simulations and experiments with the new 3.2.3. Sintering experiment results and analysiscompaction die set, the pressing speed and releasing speed was Two biggest challenges encountered during the sintering areselected to be 0.042 and 0.002 mm/s, respectively. As shown in cracks and distortions. Cracks are mostly due to the non-uniformTable 3, the pressure for experiments was selected in the range density distribution induced from the compaction process andof values used in the simulation. The parts showed no cracks the temperature gradient [4]. The distortions that are commonlyafter the compaction; however, a strong bond was formed at observed in cylindrical parts are of a conical shape, which hasthe interface of the powder compact-base plate and the powdercompact-lower portion of the core rod. Hence, the green partswere frequently damaged during the separation process. In order to successfully detach the powder compact from thedie, various lubrication and separation methods were evaluatedas summarized in Table 3. Mineral oil, which was suggestedby the vendor, only seemed to be effective for smaller parts asseen in previous experiments. As the part size became largerand interface area increased for the ring shape part, all thecompacts failed during ejection (Ring 1 and Ring 2). The wax(Ring 3), aluminum foil (Ring 4), and metal working lubricant(Ring 5) also failed to maintain the part intactness while ejectingas shown in Fig. 10a. However, as demonstrated in cases Ring 6through Ring 12, the graphite particle based lubrication greatlyimproved the separation performance as shown in Fig. 10b. Forthe unsuccessful attempts, a mechanical press was used to ejectthe part, whereas the compact could be taken out by hands whengraphite lubrication was used. Fig. 11. Schematic view of the part orientations in the oven.
  • 7. P. Chen et al. / Journal of Materials Processing Technology 190 (2007) 243–250 249Table 4Sintering experiment conditions and resultsCase Compaction pressure (MPa) Sintering procedure Orientation of the part in the oven CracksRing 1 40.49 Procedure I Bottom up YesRing 6 28.92 Procedure II Sideways YesRing 7 57.84 Procedure III Bottom down NoRing 9 52.05 Procedure III Bottom down NoRing 10 58.30 Procedure III Bottom down NoRing 11 63.62 Procedure III Bottom down NoRing 12 72.88 Procedure III Bottom down NoTable 5Shrinkage and the dimensional differences between top and bottom after sinteringCase Shrinkage in diameter Height after sintering (mm) Diameter difference (mm) Conical taper Top BottomRing 1 0.271 0.282 31.43 1.32 7.22E–02Ring 6 0.292 0.283 32.36 1.04 4.20E–02Ring 7 0.258 0.263 27.78 0.5 1.80E–02Ring 9 0.267 0.278 31.84 0.9 2.83E–02Ring 10 0.256 0.266 30.18 0.83 2.75E–02Ring 11 0.254 0.259 29.93 0.62 2.07E–02Ring 12 0.249 0.254 29.86 0.41 1.37E–02been quantified by the amount of change in diameter over a unit (Ring 6 was orientated sideways in the oven so that the conicallength (conical taper) in this work. shape was purely due to shrinkage anisotropy). The other is the Three sintering procedures (Fig. 3) and various part orienta- friction drag introduced by the support substrate, which restrictstions (Fig. 11) in the oven were evaluated, and the results are the shrinkage of the bottom compared with the unrestricted topsummarized in Table 4. It was observed that the sintering curve portion (Fig. 12c).had a significant effect on the crack formation. The parts sin- Table 5 shows detailed information regarding the shrinkagetered using sintering Procedure III (Ring 7–Ring 12) are free of and the dimensional differences between top and bottom aftercracks while other parts which used sintering Procedure I and II sintering. Case Ring 1 in Fig. 12a demonstrates the combinedhad cracks (Ring 1 and Ring 6). A slower sintering procedure effect of friction drag and shrinkage anisotropy. Since the bottomhelped to prevent cracks by minimizing the temperature gradient of the green compact was placed facing upwards, the distortion[4]. from the density gradient and friction drag will multiply. Mea- According to the classic sintering theory [4], there are two sured conical taper in this configuration is the largest, and thecontributors to the conical shape. The first is the non-uniform result is confirmed by the observation. Therefore, to reduce thedensity distribution of the green part (shrinkage anisotropy). distortion by offsetting the distortion caused by the density gra-Since the bottom of the green part has a lower density com- dient and the friction drag, the bottom of the green part waspared with the top (Fig. 9), the bottom shrinks more than the placed facing down on the substrate. As confirmed by the con-top does and results in a conical shape as shown in Fig. 12b ical taper measurement (Ring 7–Ring 12), the measured taper significantly decreased. In addition, the effect of compaction force on the distortion can be observed from Ring 9 through Ring 12. A higher compaction force produced a denser green part, which resulted in less shrinkage during the sintering pro- cess, and therefore helps to reduce conical shape. 4. Conclusions In this study, a large-scale ceramic part (Ø114 mm) was suc- cessfully compacted and sintered using uniaxial die compaction technique. The effects of die design, compaction pressure, lubri- cation, sintering procedure, and part orientation in the oven on the P/M part quality were investigated, and the preferred process conditions were discussed. Furthermore, a FEA tool was utilized to predict the location of a crack for a disk shaped part. On theFig. 12. Illustration of the effect of shrinkage anisotropy and friction drag: (a) basis of the quantitative and qualitative analysis made herein,Ring 12; (b) Ring 6; (c) Ring 1. the following conclusions could be drawn: (1) A compaction
  • 8. 250 P. Chen et al. / Journal of Materials Processing Technology 190 (2007) 243–250pressure range of 30–75 MPa is preferred for the compaction [3] D.C. Zenger, H. Cai, Common causes of cracks in P/M compacts, Int. J.of zirconia powder using uniaxial die compaction. The less the Powder Metall. 34 (1998) 33–52.compaction force, the less tendency for cracking, but more ten- [4] R.M. German, Sintering Theory and Practice, first ed., Wiley, New York, 1996.dency for warpage after sintering. (2) In the case of disk-shape [5] A. Zavaliangos, Constitutive models for the simulation of P/M processes,ceramic compact (FEA simulation), crack occurred around the Int. J. Powder Metall. 38 (2002) 27–39.region where final density was the highest. The density distribu- [6] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granulartion curve showed an abrupt density distribution in the cracking assemblies, G´ otechnique 29 (1979) 47–65. earea. (3) The oil based graphite particle lubricant showed the [7] J. Lian, S. Shima, Powder assembly simulation by particle dynamics method, Int. J. Numer. Methods Eng. 37 (1994) 763–775.best performance in the uniaxial compaction of zirconia pow- [8] D.T. Gethin, R.S. Ransing, R.W. Lewis, M. Dutko, A.J.L. Crook, Numeri-der. The friction between the powder and the tooling surface was cal comparison of a deformable discrete element model and an equivalentreduced. Moreover, the tendency of zirconia powder sticking to continuum analysis for the compaction of ductile porous material, Comp.the tooling surface was eliminated to ensure a smooth separation Struct. 79 (2001) 1287–1294.process. (4) A two-piece split die design reduced the possibil- [9] F.X. Sanchez-Castillo, J. Anwar, Molecular dynamics simulations of gran- ular compaction: the single granule case, J. Chem. Phys. 118 (2003)ity of cracking during ejection. (5) The conical shape distortion 4636–4648.after sintering from the shrinkage anisotropy could be offset by [10] A.L. Gurson, Continuum theory of ductile rupture by void nucleation andthe friction drag of the support substrate. (6) A slow multi-step growth: Part I Yield criteria and flow rules for porous ductile media, J. Eng.sintering process (Procedure III) is preferred to prevent crack- Mater. T. ASME 99 (1977) 2–15.ing. (7) A higher compaction pressure resulted in less distortion [11] E. Arzt, The influence of an increasing particle coordination on the densi- fication of spherical powders, Acta Metall. 30 (1982) 1883–1890.due to less shrinkage during sintering. [12] D.C. Drucker, R.E. Gibson, D.J. Henkel, Soil mechanics and work hard- ening theories of plasticity, Trans. ASCE. 122 (1957) 338–346.Acknowledgement [13] K.H. Roscoe, J.B. Burland, On the generalized stress–strain behaviour of ‘wet’ clay, ENG PLAST (1968) 535–609. We greatly acknowledge the help from Jie Feng on con- [14] K.T. Kim, S.W. Choi, H. Park, Densification behavior of ceramic pow- der under cold compaction, J. Eng. Mater. T. ASME 122 (2000) 238–ducting the experiments and financial support from Powerix 244.Technologies. [15] PM Modnet Computer Modelling Group, Comparison of computer models representing powder compaction process, Powder Metall. 42 (1999) 301-References 311. [16] D. Hibbit, B. Karlsson, P. Sorensen, ABAQUS theory manual, version 5.4, Pawtucket, Rhode Island, 1994.[1] F. Klocke, Modern approaches for the production of ceramic components, [17] J.C. Cunningham, I.C. Sinka, A. Zavaliangos, Analysis of tablet com- J. Euro. Ceram. Soc. 17 (1997) 457–465. paction. I. Characterization of mechanical behavior of powder and[2] R.M. German, Powder Metallurgy Science, second ed., Metal Powder powder/tooling friction, J. Pharm. Sci. 93 (2004) 2022–2039. Industries Federation, Princeton, 1994.

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