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Effect of the particle size and the debinding process on the density of alumina ceramics fabricated by 3D printing based on stereolithography Haidong Wu a,1 , Yanling Cheng a,1 , Wei Liu a,n , Rongxuan He a , Maopeng Zhou a , Shanghua Wu a,n , Xuan Song b , Yong Chen b a School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, Guangdong, 510006 China b Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, USA article info Article history: Received 23 July 2016 Received in revised form 3 August 2016 Accepted 4 August 2016 Available online 5 August 2016 Keywords: Stereolithography Al 2 O 3 Debinding abstract In this study, Al 2 O 3 ceramics were printed by stereolithography from particles with different particle size distributions, which are the micro-sized Al 2 O 3 , nano-sized Al 2 O 3 , and a mixture of both. The inuence of the particle size and the debinding method on the density and morphology of the sintered bodies were investigated. The density of the samples containing both micro-sized and nano-sized alumina particles is highest among the three samples. Furthermore, the samples subjected to the vacuum debinding showed a higher density compared with the samples subjected to the traditional thermal debinding. The results suggest that the combination of a powder with a bimodal particle size distribution and the vacuum debinding process offers an effective way to print 3D ceramics with a good performance through ste- reolithography. & 2016 Elsevier Ltd and Techna Group S.r.l. All rights reserved. 1. Introduction 3D printing is a layer-by-layer fabrication technique allowing to directly produce three-dimensional objects from a digital model. Stereolithography (SLA) is a 3D printing technique based on curing a photo-reactive resin with a UV laser or another similar power source, and is known for its high accuracy and excellent surface nishing [16]. Ceramic parts with complex 3D shapes can be manufactured using this method by mixing the ceramic powder and the UV-curable resin together analogously to the colloidal processing of ceramic powders. However, the mechanical and functional properties of the thus fabricated ceramics are not ideal due to the limited solids content of the ceramic powders [7,8]. As known, in colloidal processing, a low solid content usually results in a low density of the produced ceramics. Therefore, the sinter- ability and formability of ceramics prepared by SLA are inversely correlated. When fabricating ceramic parts by SLA, the curing depth C d is a crucial parameter which determines the accuracy of the form- ability. It is given by: ϕ = Cd d Q E EC 2 3 ln λ = Δ Q n n d 0 2 2 where d is the mean particle size of the ceramic powder, ϕ is the volume fraction of the ceramic powder in the suspension, λ is the wavelength of the irradiation, n o is the refractive index of the re- sin, Δn is the difference in refractive index between the ceramic powder and the monomer solution, E is the exposure to provide polymerization of the monomer, and Ec is the critical exposure to provide polymerization of the monomer [911]. Compared with polymer-based SLA, additional factors related to the use of cera- mics obviously affect the line width and the curing depth. More- over, the traditional SLA equipment relies on the dispersions having viscosities lower than 5 Pa s (30 1/s ) [12]. Thus, the particle size and the volume fraction of the ceramics must be adjusted to meet the requirements of both of the formability and sinterability. Meanwhile, a ne particle size and a high volume fraction are necessary to obtain ceramics with a high density. Previous theoretical and experimental studies have demon- strated that an appropriate size distribution of the particles in the suspension promotes a dense packing of the particles in the cast body and, hence, increases the apparent density of the green body. In particular, Subbanna et al. [13], and Tari et al. [14] have shown that, in colloidal processing, it is possible to obtain high-density bodies using a bimodal particle size distribution in which ne and coarse powders are combined at an appropriate ratio. For instance, Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ceramint Ceramics International http://dx.doi.org/10.1016/j.ceramint.2016.08.024 0272-8842/& 2016 Elsevier Ltd and Techna Group S.r.l. All rights reserved. n Corresponding authors. E-mail addresses: [email protected] (W. Liu), [email protected] (S. Wu). 1 Both authors contributed equally to this work. Ceramics International 42 (2016) 1729017294

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Page 1: Effect of the particle size and the debinding process on ...yongchen/Papers/2016/...Ceramics International 42 (2016) 17290–17294. Zhou et al. [15] obtained a high concentrated aqueous

Ceramics International 42 (2016) 17290–17294

Contents lists available at ScienceDirect

Ceramics International

http://d0272-88

n CorrE-m1 Bo

journal homepage: www.elsevier.com/locate/ceramint

Effect of the particle size and the debinding process on the density ofalumina ceramics fabricated by 3D printing based on stereolithography

Haidong Wu a,1, Yanling Cheng a,1, Wei Liu a,n, Rongxuan He a, Maopeng Zhou a,Shanghua Wu a,n, Xuan Song b, Yong Chen b

a School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, Guangdong, 510006 Chinab Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, USA

a r t i c l e i n f o

Article history:Received 23 July 2016Received in revised form3 August 2016Accepted 4 August 2016Available online 5 August 2016

Keywords:StereolithographyAl2O3

Debinding

x.doi.org/10.1016/j.ceramint.2016.08.02442/& 2016 Elsevier Ltd and Techna Group S.r

esponding authors.ail addresses: [email protected] (W. Liu), swth authors contributed equally to this work.

a b s t r a c t

In this study, Al2O3 ceramics were printed by stereolithography from particles with different particle sizedistributions, which are the micro-sized Al2O3, nano-sized Al2O3, and a mixture of both. The influence ofthe particle size and the debinding method on the density and morphology of the sintered bodies wereinvestigated. The density of the samples containing both micro-sized and nano-sized alumina particles ishighest among the three samples. Furthermore, the samples subjected to the vacuum debinding showeda higher density compared with the samples subjected to the traditional thermal debinding. The resultssuggest that the combination of a powder with a bimodal particle size distribution and the vacuumdebinding process offers an effective way to print 3D ceramics with a good performance through ste-reolithography.

& 2016 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

1. Introduction

3D printing is a layer-by-layer fabrication technique allowing todirectly produce three-dimensional objects from a digital model.Stereolithography (SLA) is a 3D printing technique based on curinga photo-reactive resin with a UV laser or another similar powersource, and is known for its high accuracy and excellent surfacefinishing [1–6]. Ceramic parts with complex 3D shapes can bemanufactured using this method by mixing the ceramic powderand the UV-curable resin together analogously to the colloidalprocessing of ceramic powders. However, the mechanical andfunctional properties of the thus fabricated ceramics are not idealdue to the limited solids content of the ceramic powders [7,8]. Asknown, in colloidal processing, a low solid content usually resultsin a low density of the produced ceramics. Therefore, the sinter-ability and formability of ceramics prepared by SLA are inverselycorrelated.

When fabricating ceramic parts by SLA, the curing depth Cd is acrucial parameter which determines the accuracy of the form-ability. It is given by:

ϕ=

⎛⎝⎜

⎞⎠⎟Cd

dQ

EEC

23

ln

.l. All rights reserved.

[email protected] (S. Wu).

λ= Δ⎜ ⎟⎛

⎝⎞⎠

⎛⎝⎜

⎞⎠⎟Q

nn

d0

2 2

where d is the mean particle size of the ceramic powder, ϕ is thevolume fraction of the ceramic powder in the suspension, λ is thewavelength of the irradiation, no is the refractive index of the re-sin, Δn is the difference in refractive index between the ceramicpowder and the monomer solution, E is the exposure to providepolymerization of the monomer, and Ec is the critical exposure toprovide polymerization of the monomer [9–11]. Compared withpolymer-based SLA, additional factors related to the use of cera-mics obviously affect the line width and the curing depth. More-over, the traditional SLA equipment relies on the dispersionshaving viscosities lower than 5 Pa s (301/s) [12]. Thus, the particlesize and the volume fraction of the ceramics must be adjusted tomeet the requirements of both of the formability and sinterability.Meanwhile, a fine particle size and a high volume fraction arenecessary to obtain ceramics with a high density.

Previous theoretical and experimental studies have demon-strated that an appropriate size distribution of the particles in thesuspension promotes a dense packing of the particles in the castbody and, hence, increases the apparent density of the green body.In particular, Subbanna et al. [13], and Tari et al. [14] have shownthat, in colloidal processing, it is possible to obtain high-densitybodies using a bimodal particle size distribution in which fine andcoarse powders are combined at an appropriate ratio. For instance,

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Table 1Starting materials used for the fabrication of the three different types of samples.

Samples Starting material

Sample 1 Micro-sized Al2O3 powderSample 2 Mixture of micro-sized powder and nano-sized Al2O3 nanoparticlesSample 3 Nano-sized Al2O3 powder

H. Wu et al. / Ceramics International 42 (2016) 17290–17294 17291

Zhou et al. [15] obtained a high concentrated aqueous ceramicsuspensions by using a ceramic powder with a wide particle-sizedistribution. Fattahi et al. [16] reported that, compared with fibers,the reinforcing effect of Al2O3 platelets is due to two-dimensionalstiffening. Olhero et al. [17] reported that the presence of coarseparticles in the suspensions resulted in a shear-thinning behavior,whereas the compaction efficiency increased with the width of theparticle size distribution [18]. Thus it is believed that controllingthe particle size distribution, especially by adding coarser parti-cles, may be an effective way to meet the requirements of thesuspensions and the SLA process.

Furthermore, selecting an optimal sintering path guarantees ahigh density of the green body. So far, most studies focused on theformability during the SLA process, rarely considering the post-treatment process. However, the debinding is an important step ofeach slurry-based forming method. The residual carbides resultingfrom undecomposed organics are detrimental to the performanceof the prepared ceramic bodies. Compared with the widely usedthermal debinding process, a vacuum debinding process combinesthe debinding and the sintering cycle into a single processing stepand allows to minimizes damage caused by the handling of thefragile debound parts [19].

In this study, Al2O3 ceramic parts were printed by stereo-lithography from particles with different particle size distribu-tions, which are micro-sized Al2O3, nano-sized Al2O3, and a mix-ture of both. The influence of the particle size and the debindingmethod on the density and morphology of the sintered bodieswere investigated. The density of the samples containing bothmicro-sized alumina and nanoparticles was the highest among thethree samples. Furthermore, the samples subjected to the vacuumdebinding showed a higher density compared with the samplessubjected to the traditional thermal debinding. The results suggestthat the combination of a powder with a bimodal particle sizedistribution and the vacuum debinding process offers an effectiveway to print 3D ceramics with a good performance throughstereolithography.

1

2

3

2. Material and methods

2.1. Powder mixture preparation

A micro-sized Al2O3 powder and nano-sized Al2O3 powderwith a particle size of 9 mm and 50 nm, respectively, were used asthe starting materials in this study. Three types of samples wereprinted by digital micromirror-assisted SLA from micro-sizedAl2O3 powder, nano-sized Al2O3 powder, and a mixture of both ata 1:1 wt ratio. The starting materials used for the fabrication ofeach type of samples are listed in Table 1. The Al2O3 solids contentfor each sample was 65 wt%. The mixture was then diluted inethanol with ultrasound. After that, the mixture was ball-milled ina planetary ball mill for 6 h using zirconia balls. The suspensionwas then dried in an oven at 60 °C for 12 h. Finally, the driedpowder was sieved through a 100 mesh screen.

2.2. Preparation of the ceramic suspension

The premixed solution used to prepare the ceramic suspensionconsisted of four components: acrylamide (23.75 wt%), N, N′ me-thylenebisacrylamide (1.25 wt%), glycerine (10 wt%), and deio-nized water (65 wt%). The as-prepared powder was added to thepremixed solution, and polyvinyl pyrrolidone (PVP) K-15 was usedas the dispersant to form the ceramic suspension. The ceramicsuspension was then ball-milled for 12 h using zirconia balls. Thesuspension was then de-gased for 30 min using a vacuum mixer. Inorder to produce a UV-curable ceramic suspension, 2-hydroxy-2-

methyl-1-phenyl-1-acetone was added to the ceramic suspensionas initiator under ultrasound. In this study, the mass fraction of thephotoinitiator was selected to 1 wt% of the premixed solution.

2.3. Fabrication of the ceramic parts through stereolithography

The 3D model was created using the UG software, and then theMagics software was employed to generate the supporting struc-ture and to slice the parts. The final data was then imported intothe stereolithography machine. The alumina green body was ob-tained by stereolithography using the ceramic suspension men-tioned above. A schematic illustration of the stereolithographyprocess is shown in our previous literature [6,20,21].

Each individual pattern layer was cured by the ultraviolet laserselective scanning on the ceramic suspension. After the first layerwas cured, the supporting platform was moved down, and theceramic suspension was recoated on the cured surface with ablade. Then, the second layer was cured analogously. These stepswere repeated until the whole green body of the alumina part waseventually obtained.

2.4. Post processing of the alumina green body

) DryingAfter the green body was obtained, the residual water in thesample had to be removed by drying. A novel drying approachbased on using PEG 400 as the liquid desiccant was adopted inthis study [6]. For the PEG-based extraction process, the samplewas immersed in PEG 400, which was expected to result in auniform extraction rate in all directions.

) DebindingThe vacuum debinding was carried out in a tube furnace underlow vacuum conditions. For comparison, a thermal debindingprocess was also performed. The profiles of the vacuum andthermal debinding are confirmed in the Result and dicussionsection.

) Sintering

Regarding the densification sintering, Sample 1 and 2 weresintered at 1750 °C and Sample 3 with only the nanoparticles weresintered at 1600 °C for 4 h in a furnace (Thermconcept, HTK 16/18,Germany).

2.5. Sample characterization

The microstructure was characterized by scanning electronmicroscopy (JEOL JSM 6500F, JEOL, Japan). The thermal decom-position behavior was assessed by thermogravimetric analysis(TGA) and differential scanning calorimetry (DSC; Netzsch In-struments, Germany) under air flow using a heating rate of 20 K/min. The apparent densities were determined employing Archi-medes' displacement method.

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H. Wu et al. / Ceramics International 42 (2016) 17290–1729417292

3. Results and discussion

3.1. Morphology of the Al2O3 green bodies

A micro-sized alumina powder with a large particle size wasadded to the ceramic slurry to reduce its viscosity, which is ben-eficial for the forming process. The morphology of the as-printedceramic green bodies is compared in Fig. 1. Any inhomogeneity inthe green bodies may result in an accumulation of stress duringsintering. As shown in Fig. 1(a) and 1(c), both the micro-sized andthe nano-sized Al2O3 particles are homogeneously distributedthroughout the polymer matrix. In Fig. 1(b), the Al2O3 nano-particles are revealed to be embedded between the micro-sizedAl2O3 particles.

3.2. TGA-DSC analysis

For slurry-based forming methods, the thermal decompositionbehavior of the green part can be a guidance to establish a suitabledebinding schedule for the ceramics. Fig. 2 shows the TGA-DSCcurve for the Al2O3 green body. The same curve was obtained forall three types of samples.

Theoretically, the organics decompose between 500 and700 °C.The DSC curve depicted in Fig. 2 features three exothermicpeaks at 390.5, 439.5 and 524.0 °C, with the peak observed ataround 439 °C being the most prominent. The correspondingweight loss is illustrated in the DTG curve, and the total weightloss was up to 48.2%. The highest loss in weight of 23.89% occurredat 431.6 °C. Afterwards, the weight loss curve became more stableand no change was recorded at temperatures above 600 °C. Thisindicates that the decomposition is complete before the tem-perature reaches 600 °C. In order to completely remove the or-ganic components, the debinding process should reflect everydetail of the observed decomposition behavior. Delamination, theformation of micro-cracks and the occurrence of unevenly dis-tributed holes are common defects for such layer-by-layer printingprocesses. Therefore, the heating rate and the dwelling time mustbe carefully adjusted to avoid the formation of defects during thedebinding process.

3.3. Debinding and sintering of the Al2O3 parts

The vacuum debinding process was designed considering theTGA results. The heating rate was kept as low as 1 °C/min. Thetemperature was kept constant for a certain period of time whenthe temperature had reached a value corresponding to one of theexothermic peaks, and the dwelling time was the same for each of

Fig. 1. SEM micrographs revealing the microstructure of the green bodies fabricated fromtype 3.

those temperatures. A thermal debinding process with a muchmore precise temperature adjustment was also conducted forcomparison. The temperature curves used for the debinding pro-cess are shown in Fig. 3.

The cross-sectional morphology of the samples subjected to thevacuum debinding and the thermal debinding process are com-pared in Fig. 4 and Fig. 5, respectively. The obtained relativedensities are compared in Fig. 6. For both debinding methods,there was no obvious delamination, and no cracks formed. Fig. 4(a) reveals a loose morphology with micro-sized Al2O3 particlespiling up irregularly. According to Fig. 6, the relative density of thissample was only 65.7%. Thus it could be seen that densification isdifficult for micro-sized particles because the sintering kinetics islow due to the small surface energy. In comparison, Sample 3 withthe nano-sized Al2O3 particles showed a much larger surface en-ergy than Sample 1 , which made the densification less difficult.After sintering at 1600 °C (1750 °C for sample 1 and 2), the relativedensity increased to 89.2% (Fig. 6), much higher than the density ofSample 1. It is shown in Fig. 4(c) that nano-sized Al2O3 grainsdistributed homogeneously in the sintered body, but there are stillsome obvious pores in the corresponding microstructure. Fig. 4(b) shows a typical bimodal particle distribution with a mixture ofmicro-sized and nano-sized Al2O3 particles. As shown in Fig. 4(b),the spherical alumina nanoparticles take up the gaps between themicro-sized grains. Hence, the relative density of this sample wasthe highest among the three samples (91.2%). This phenomenoncould be explained by the effect of particle size combination. It hasbeen proven that usually optimization of the grain composition isan effective way for raising the volumn fraction of the ceramicsuspension and beneficial for reducing the viscosity of the ceramicsuspension, thus probably the density of the sintered body madefrom the combination powder would be higher than the monolicpowder [22–24]. Regarding the 3 samples subjected to the thermaldebinding, the microstructure of Sample 1 shows the same featurewith the sample subjected to the vacuum debinding, and also therelative density is 65.2% almost same with the relative density ofSample 1 via vacuum debinding. There are more pores existed inthe sintered body via thermal debinding for Sample 2 and 3 com-pared with Sample 2 and 3 via vacuum debinding. The respectiverelative density of Sample 2 and 3 via thermal debinding is 83.2%and 82.2% compared with 91.2% and 89.2% via vacuum debinding.

The results of this study show that the density of the samplescontaining both micro-sized alumina and nano-sized particles isthe higher than the monolic micro-sized powder and the nano-sized powder. Moreover, replacing some of the nanoparticles withlow-cost micro-sizd Al2O3 may be a feasible low-cost approach foran SLA-based fabrication of Al2O3 ceramics. Meanwhile, the

the three types of powder samples: (a) sample type 1, (b) sample type 2, (c) sample

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Fig. 2. Thermal decomposition behavior of the green bodies. (The DTG curve is the derivative of the TGA curve.).

Fig. 3. Temperature curves used for the debinding of the Al2O3 ceramics preparedthrough SLA.

Fig. 4. SEM micrographs revealing the morphology of the samples subjected to the va

H. Wu et al. / Ceramics International 42 (2016) 17290–17294 17293

vacuum debinding resulted in a much higher relative densitycompared with thermal debinding.

4. Conclusions

In this study, Al2O3 ceramics were printed by stereolithographyfrom particles with different particle size distributions, which arethe micro-sized Al2O3, nano-sized Al2O3, and a mixture of both.The influence of the particle size and the debinding method on thedensity and morphology of the sintered bodies were investigated.The density of the samples containing both micro-sized and nano-sized alumina particles is highest among the three samples. Fur-thermore, the samples subjected to the vacuum debinding showeda higher density compared with the samples subjected to thetraditional thermal debinding. The results suggest that the com-bination of a powder with a bimodal particle size distribution andthe vacuum debinding process offers an effective way to print 3Dceramics with a good performance through stereolithography.

cuum debinding process: (a) sample type 1, (b) sample type 2, (c) sample type 3.

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Fig. 5. SEM micrographs revealing the morphology of the samples subjected to the thermal debinding process: (a) sample type 1, (b) sample type 2, (c) sample type 3.

Fig. 6. Comparison of the relative densities of the different samples after the va-cuum and thermal debinding.

H. Wu et al. / Ceramics International 42 (2016) 17290–1729417294

Acknowledgements

This work was financially supported by the Science and Tech-nology Project of Guangdong Province (Grant no. 2016B090915002),and the Research Fund for the Introduction of the Leading Talents ofGuangdong Province (Grant no. 40012001).

References

[1] A. Zocca, P. Colombo, C.M. Gomes, J. Günster, D.J. Green, Additive manu-facturing of ceramics: issues, potentialities, and opportunities, J. Am. Ceram.Soc. 98 (2015) 1983–2001.

[2] M. Schwentenwein, J. Homa, Additive manufacturing of dense alumina cera-mics, Int. J. Appl. Ceram. Technol. 12 (2015) 1–7.

[3] Za.E. Zanchetta, M. Cattaldo, G. Franchin, M. Schwentenwein, J. Homa,G. Brusatin, P. Colombo, Stereolithography of SiOC ceramic microcomponents,Adv. Mater. 28 (2015).

[4] D.I. Woodward, C.P. Purssell, D.R. Billson, D.A. Hutchins, S.J. Leigh, Additively-manufactured piezoelectric devices, Phys. Status Solidi A 212 (2015)2107–2113.

[5] X. Song, Y. Chen, T.W. Lee, S. Wu, L. Cheng, Ceramic fabrication using mask-

image-projection-based stereolithography integrated with tape-casting, J.Manuf. Process. 20 (2015) 456–464.

[6] M. Zhou, W. Liu, H. Wu, X. Song, Y. Chen, L. Cheng, F. He, S. Chen, S. Wu,Preparation of a defect-free alumina cutting tool via additive manufacturingbased on stereolithography – Optimization of the drying and debinding pro-cesses, Ceram. Int. 42 (2016) 11598–11602.

[7] J.W. Choi, R.B. Wicker, S.H. Cho, C.S. Ha, S.H. Lee, Cure depth control forcomplex 3D microstructure fabrication in dynamic mask projection micro-stereolithography, Rapid Prototyp. J. 15 (2009) 59–70.

[8] T. Wohlers, T. Caffrey, I. Wohlerss, Additive Manufacturing and 3D PrintingState of the Industry, Wohlers Associates, Inc, Fort Collins, 2011.

[9] P. Gentry, John W. Halloran, Absorption effects in photopolymerized ceramicsuspensions, J. Eur. Ceram. Soc. 33 (2013) 1989–1994.

[10] P. Gentry, John W. Halloran, Depth and width of cured lines in photo-polymerizable ceramic suspensions, J. Eur. Ceram. Soc. 33 (2013) 1981–1988.

[11] W. Zhou, D. Li, Z. Chen, The influence of ingredients of silica suspensions andlaser exposure on UV curing behavior of aqueous ceramic suspensions instereolithography, Int J. Adv. Manuf. Tech. 52 (2011) 575–582.

[12] Kahn Chia Wu., (Ph.D. thesis), CH.3. University of Michigan, 2005.[13] M. Subbanna, P.C. Kapur, Pradip, Role of powder size, packing, solid loading

and dispersion in colloidal processing of ceramics, Ceram. Int. 28 (2002)401–405.

[14] G. Tari, J.M.F. Ferreira, A.T. Fonseca, O. Lyckfeldt, Influence of particle sizedistribution on colloidal processing of alumina, J. Eur. Ceram. Soc. 18 (1998)249–253.

[15] W. Zhou, D. Li, H. Wang, A novel aqueous ceramic suspension for ceramicstereolithography, Rapid Prototyping 16 (2010) 29–35.

[16] A.M. Fattahi, M. Mondali, Theoretical Study Of Stress Transfer In Platelet Re-inforced Composites, J. Theor. Appl. Mech.-Pol. 52 (2014) 3–14.

[17] S.M. Olhero, J.M.F. Ferreira, Influence of particle size distribution on rheologyand particle packing of silica-based suspensions, Powder Technol. 139 (2004)69–75.

[18] P.F. Luckham, M.A. Ukeje, Effect of particle size distribution on the rheology ofdispersed systems, J. Colloid Interface Sci. 220 (1999) 347–356.

[19] K.S. Hwang, H.K. Lin, S.C. Lee, Thermal, solvent, and vacuum debinding me-chanisms of PIM compacts, Mater. Manuf. Process. 12.4 (1997) 593–608.

[20] Y. Pan, C. Zhou, Y. Chen, A Fast Mask Projection Stereolithography Process forFabricating Digital Models in Minutes, J Manuf Sci E-T ASME, 134, 2012, pp. 76–87.

[21] X. Song, Y. Chen, Joint design for 3-D printing non-assembly mechanisms, in:Proceedings of ASME International Design Engineering Technical Conferencesand Computers and Information in Engineering Conference, 2012, pp. 619–631.

[22] C.H. Ju, Y.M. Wang, J.D. Ye, X.H. Li, Effect of particle size distribution ofn therheological behavior of dense alumnia suspensions, Journal of the ChineseCeramic Society, 34, 2006, pp. 985–991.

[23] Y. Ding, R.F. Chen, Y. Huang, J.L. Sun, Preparation of alumina slurries with lowviscous and high solid loading by different particle size mixing method, J.Chin. Ceram. Soc. 36 (2008) 58–62.

[24] A.A. Zaman, C.S. Dutcher, Viscosity of electrostatically stabilized dispersions ofmonodispersed, bimodal, and trimodal silica particles, J. Am. Ceram. Soc. 89(2006) 422–430.