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Fractions design of irregular particles in suspensions for the fabrication of multiscale ceramic components by gelcasting
Accepted Manuscript Title: Fractions Design of Irregular Particles in Suspensions for the Fabrication of Multiscale Ceramic Components by Gelcasting Authors: Zhongliang Lu, Kai Miao, Weijun Zhu, Yi Chen, Yuanlin Xia, Dichen Li PII: DOI: Reference:
S0955-2219(17)30525-3 http://dx.doi.org/doi:10.1016/j.jeurceramsoc.2017.08.002 JECS 11397
To appear in:
Journal of the European Ceramic Society
Received date: Revised date: Accepted date:
28-4-2017 1-8-2017 2-8-2017
Please cite this article as: Lu Zhongliang, Miao Kai, Zhu Weijun, Chen Yi, Xia Yuanlin, Li Dichen.Fractions Design of Irregular Particles in Suspensions for the Fabrication of Multiscale Ceramic Components by Gelcasting.Journal of The European Ceramic Society http://dx.doi.org/10.1016/j.jeurceramsoc.2017.08.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Fractions Design of Irregular Particles in Suspensions for the Fabrication of Multiscale Ceramic Components by Gelcasting Zhongliang Lua,c,,1, Kai Miaoa,b,c,1 , Weijun Zhua,c, Yi Chena, Yuanlin Xiaa, Dichen Lia,c a
State Key Laboratory for Manufacturing Systems Engineering and School of
Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China b
State Key Laboratory for Strength and Vibration of Mechanical Structures and School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China
c
Collaborative Innovation Center of High-End Manufacturing Equipment, Xi’an, 710049, China
Abstract A new approach for the preparation of suspensions with a high solid loading and low viscosity by using irregular particles was proposed. These suspensions were prepared for the fabrication of multiscale ceramic components by gelcasting. Based on the Funk-Dinger function and fractal theory, the closest packing theory was applied to optimize the volume fractions of different particles. The maximum solid loading of slurries prepared for gelcasting was 62 vol%, and the viscosity at a shear rate of 100 s-1 was only 0.29 Pa·s. By as-prepared suspensions, a decimeter-scale ceramic part with submillimeter features was fabricated successfully by gelcasting, which verify the feasibility of the proposed method. Keywords: Gelcasting; Irregular particles; Solid loadings; Rheological properties
Corresponding author. Tel.: +86 29 82665126; Fax: +86 29 82660114; E-mail: [email protected] two authors contributed equally to this work
1 The
1. Introduction Gelcasting, a ceramic forming process, was developed to overcome the limitations of other shape forming techniques such as injection molding and slip casting with lower fabrication costs, shorter forming time [1-3]. However, ceramic components with internal and external structures cannot be easily fabricated by this technique due to the restriction of mold opening process. Based on the stereolithography (SL) technology, the integral fabrication technique (IFT) was developed, allowing the fabrication of such components by gelcasting [4,5]. This method was initially proposed to fabricate the ceramic molds of hollow turbine blades. The ceramic mold is a decimeter-scale structure with cores inside, which are slender structures with submillimeter features. Suspension for this mold filling by gelcasting has to satisfy two requirements, good fluidity and a high solid loading. Suspension with good fluidity can ensure that the slurry can be poured successfully into the mold and all tiny structures inside can be duplicated; while a high solid loading can result in both higher density and less deformation, which can restrain defect formation in both green and sintered parts [6-8]. The viscosity of a suspension increases exponentially as the fraction of particles increases. Therefore, it is difficult to realize the preparation of suspension with features of a high solid loading and low viscosity. Based on the stabilizing mechanisms, many efforts have been made for the preparation of suspensions with a high solid loading and low viscosity. The change of the pH value can result in enlarging zeta potential and enhancing electrostatic repulsion, finally achieving a low viscosity [9]. The use of dispersant can also decrease viscosity by changing particle surface profiles or surface charge properties [10,11]. However, the adjustment of pH or dispersant may not work with increasing solid loadings [12]. It is widely recognized that broadening the particle size distribution (PSD) can increase the maximum fraction of a monodisperse system. Thus, polydispersity can
give a lower viscosity at the same volume fraction or permit a higher volume loading at the equivalent monodisperse viscosity. By introducing smaller particles, which could potentially fit in between the larger particles, it is possible to achieve a much higher volume fraction [13-16]. The viscosity of suspensions comprised of bimodal mixtures of ceramic powders have been investigated [17,18]. A size ratio about 8 and a proportion about 30-70 between average coarse and fine particle sizes showed the lowest viscosity with a high solid loading. By statistical design or experiments, fractions of three different particles were defined in a trimodal system. Although the suspension had a lower viscosity than the bimodal system, the optimization processes were sophisticated and time consuming [19]. Meanwhile, almost all of the previous attempts were applied for spherical particles only, optimizations for irregulars barely been proposed. This is largely been due to the perceivable difficulty in quantitative descriptions of sizes and shapes of irregular particles. However, particles with irregular geometries are in fact the type of particles which constitute the majority of ceramic powders [20]. What’s more, in the mass production by gelcasting, the use of irregulars to achieve suspensions can significantly reduce the production cost. In this paper, the fractal theory was applied to describe the geometrical morphology of irregular particles at first. Then, based on the Funk-Dinger (F-D) function, we put forward a simple method to optimize the volume fractions of such particles in suspensions, as the F-D function is widely used in the concrete, coal and food engineering to provide suspensions with required fluidity. Solid loadings of the alumina slurry were maximized and their rheological properties were measured. The microstructures and the mechanical properties were also investigated. Finally, centimeter-scale ceramic structures with submillimeter features were accurately fabricated by the prepared suspensions. 2. Material and Methods 2.1. Raw Materials
Four Al2O3 powders were obtained from a commercial vendor (Shangdong Zibo Aluminum Co., Ltd., Zibo, China). The powders had average sizes of 125, 40, 5 and 2 μm. In the gelcasting process, acrylamide (C2H3CONH2, AM, Kemiou Chemical Reagent Co., Ltd., Tianjin, China ) and N,N’-methylenebisacrylamide ((C2H3CONH)2CH2, MBAM, Kemiou Chemical Reagent Co., Ltd., Tianjin, China) were used as the monomer and crossing linking agent, respectively. Sodium polyacrylate (PAAS, Sinopharm Chemical Reagent Co, Ltd, China) was used as the dispersant. Ammonium persulphate ((NH4)2S2O8, APS, Sinopharm Chemical Reagent Co, Ltd, China) and N,N,N’,N’-tetramethylethylenediamine ((CH3)2NCH2CH2N(CH3)2, TMEDA, Sinopharm Chemical Reagent Co, Ltd, China) were used as the initiator and catalyst, respectively. Deionized water was used as solvent in the whole process. 2.2. Preparation of Aqueous Suspensions The premix solution was prepared by dissolving 15 wt% AM and MBAM in a ratio of 24:1. 1 wt% PAAS with respect to the Al2O3 powders was added as the dispersant. Aqueous suspensions with different solid loadings were prepared by mixing ceramic powders and the premixed solution under constant stirring. After ball-milling for 60 min and degassing for 5 min, the suspensions were obtained. In this process, the ballmilling time was restricted at 60 min to avoid significant changes in particle sizes. 2.3. IFT processing In this processing, an SL prototype for ceramic part was fabricated by SPS 600B (Xi’an Jiaotong University, China) using photosensitive resin (SPR 8981, Zhengbang Ltd., Zhuhai, China) firstly. Then, in the gelcasting, the suspension was poured into the SL prototype, then in situ polymerized to form green body under the effect of initiator and catalyst. After freeze-drying for 72 h, the green ceramic body was transferred into a furnace for pre-sintering. The green ceramic part was pyrolyzed at 600 °C for 30 min at a low heating rate of 0.5 °C/min in air, allowing the removal of
the SL prototype. The pyrolyzed part was further heated to 1350 °C for 3 h at a heating rate of 4 °C/min for the sintering of the matrix, followed by furnace cooling. After several post treatments, the ceramic part was finally obtained. 2.4. Testing Particle size analysis was conducted using a laser diffraction particle size analyzer (LS230, Beckman Coulter). The rheological properties of suspensions comprised of different powders were investigated by a controlled stress rheometer (AR 2000, TA instruments, New Castle, USA) with a concentric cylinder geometry. Prior to the measurements, pre-shearing was performed at a shear rate of 100 s-1 for 1 min and a pause for 1 min in order to transmit the same rheological history to all the suspensions being tested. The viscosities were measured at shear rates varying from 0.1-200 s-1. The room temperature strengths of ceramic samples after sintering were tested by a three-point bending test machine (HSST-6003QP, Sinosteel Luoyang Institute of Refractories, Luoyang, China) with a span distance of 30 mm at a cross-head speed of 8 mm/min using samples of a nominal size of 4 mm × 10 mm × 60 mm. Each data point represents the average value of five to ten individual tests. Microstructures were examined by scanning electron microscope (SEM) (SU-8010, Hitachi Ltd., Tokyo, Japan). The ceramic parts after sintering were inspected by X-ray scan (Y.Cheetah, YXLON Ltd., Hamburg, Germany). 3. Theory A reliable solution for the reproduction of natural continuously graded grains is represented by the F-D distribution function. This function is generally acknowledged in the concrete or coal engineering for the preparation of slurries with a closest packing density. The cumulative finer fraction reads as follows. U t Di
n Din Dmin n n Dmax Dmin
(1)
Where Di is the particle size of the considered fraction, Dmin is the minimum particle size and Dmax is the maximum particle size in the mixture system. The exponent n is the distribution modulus. The mix design of particle fractions could be understood as the realization of minimum deviation between Ut Di (the cumulative fraction based on F-D function) and Ud Di (the cumulative fraction after particle gradation). Therefore, the least square method in MatlabTM was used, and this optimization could be written as: 2
n
E U t Di U d Di min
(2)
i 1
The distribution modulus n allows controlling the amount of fine particles for a generated mix in a certain range. While a higher value of n lead to coarser blends, a lower n will produce mixes with fine blends [21]. For a certain kind of particles with similar morphology, the distribution modulus is a specific value when the maximum packing efficiency can be achieved. So the most important step in this optimization was the determination of n. According to fractal theory, assumed that in a mixture system, dmax is the maximum particle size, dmin is the minimum particle size and di is the particle size between dmax and dmin. ε (1＞ε＞0) and b are the particle size ratio and number ratio of adjacent fine and coarse particles, respectively. The relationship between ε and b is given by:
b P
(3)
Where P is the fractal dimension of particles, α is the correlation coefficient. Particle systems which are accord with this function can be defined as the fractal size distribution system. In this system, the gradation number is defined as k. For a particle with a size of dm, it can be written as:
dm dmax m The particle numbers of dm is:
( k m 0)
(4)
nm n0bm
(5)
Where nm is the particle numbers of dmax. The collection degree of particle numbers is defined as:
n(d m ) n(d m1 ) n(d m ) n0b m (b 1) n( d m ) d m d m1 d m d max ( 1)
(6)
Combining Eqs. (3) and (4), the following expression can be written as: P bm (1/ )m P dm P dmax
(7)
Substituting Eq. (7) into Eq. (6) gives: P n(dm ) n0 dm( P +1）dmax (b 1) / ( 1)
(8)
When the particle system becomes continuous distributed, the gradation number, k, would approach to infinity, ε and b would approach to 1, and n(dm) would be equal to n(d). Substituting Eq. (3) into Eq. (8) and calculating the limit gives: P n(d ) lim n0 d m ( P +1）d max (b 1) / ( 1) 1
P lim n0 d m ( P +1）d max ( P 1) / ( 1) 1
(9)
P ( P 1) n0 Pd max d
Then the cumulative volume of particles finer than d can be written as: d
Cvd
V ( d )
3
N (d )dd
d min d
Cvd
3
P ( P 1) N 0 Pd max d dd
d min
P 3 P CvN 0 d max (d 3 P d min ) P / (3 P)
Where Cv is the volume coefficient of particles. And the cumulative volume fraction of particles finer than d can be written as:
(10)
U (d ) V ( d ) / V ( d max ) 3 P 3 P 3 P (d 3 P d min ) / (d max d min )
(11)
The Eq. (11) was deduced based on the fractal distribution model of continuous size particles. Compared the Eq. (11) with the F-D function, the distribution modulus can be written as:
n 3 P
(12)
The optimum value for the densest packing of spherical particles is expected for n=0.37, while the P is 2, so the correlation coefficient, α=1.315 [22,23]. The fractal dimension of irregular particles can be determined by the area-volume method, which can be written as:
log[ S ( ) / ] V ( )1/3 log(a0 ) log[ ] P
(13)
β is the measurement scale, which changes with particle morphology. S(β) and V(β) are the surface area and volume of particles under the measurement scale of β, respectively, and a0 is a constant. Fig.1 shows the morphologies of the four alumina powders used in this study. Since these powders were prepared by the same process, the fractal features were statistically self-similar. Thus, β is a constant value in this study. Assuming the value of β is 1, the Eq. 13 can be rewritten as: log[V ] log[ S ]
3 log(a03 ) P
(14)
Fig. 1. Particle morphologies of the alumina powders: (a) D50=125 μm, (b) D50=40 μm, (c) D50=5 μm and (d) D50=2 μm. And the fractal dimension P can be determined by the slope of the liner plots of log[V] versus log[S].
Fig. 2. Particle size distributions of alumina powders. Fig. 2 shows the PSDs of four alumina powders. According to the particle sizes and specific surface areas of powders, the surface areas and volume were calculated. The results are shown in Table 1. After plotting the liner line of log[V] versus log[S],shown in Fig. 3, the fractal dimension P was calculated by the slope of this line, and the distribution modulus, n=3-α×P=3-1.315×2.038=0.3196. Table 1 Surface areas and volumes of four alumina powders. Surface Area/m2
Volume/m3
2 μm
1.631E-11
9.63E-18
5 μm
1.176E-10
1.057E-16
40 μm
3.387E-9
3.305E-14
125 μm
5.335E-8
1.035E-12
Fig. 3. Log(V) vs. Log(S). 4. Results and discussions 4.1. Verification of the Distribution Modulus Based on the fractal theory, the distribution modulus for these irregular particles was obtained. In order to verify this distribution modulus, rheological properties of suspensions comprised of different volume fractions of four powders were investigated. The volume fractions of different powders were determined by the distribution modulus which varies from 0.25 to 0.4, and were calculated in MatlabTM according to the Eq. (2). Table 2 shows the volume fractions of four powders at different n values. It can been seen that with the increase of n values, volume fractions of fine particles gradually decrease while the volume fraction of coarse particles increase, consistent with the F-D function. Table 2 Volume fractions of four alumina powders at different n values. n
0.25
0.3
0.3196
0.35
0.4
V2μm
31%
24%
22%
18%
13%
V5μm
10%
13%
13%
15%
16%
V40μm
28%
28%
29%
28%
28%
V125μm
31%
35%
36%
39%
43%
Suspensions with a solid loading of 58 vol% were prepared according to Table 2, and the rheological properties of suspensions were tested. The viscosity was measured
at shear rates varying from 0.1-200 s-1. The rheological curve of slurries with different n values are shown in Fig. 4. It is observed that suspensions have the lowest viscosities when the distribution modulus, n, is equal to 0.3196. The viscosity is only about 0.1 Pa·s at a shear rate of 100 s-1.When the distribution modulus increases from 0.25 to 0.3196, the viscosities at all shear rates decrease. As the distribution modulus continues to increase from 0.3196 to 0.4, the viscosities turns to increase. This trend in viscosities are consistent with the theoretical analysis based on the fractal distribution model, which predicts the suspension have the lowest viscosity when n is equal to 0.3196. We also prepared a slurry with a solid loading of 58 vol% based on the Farris theory [24]. Since the Farris theory only took the monosphere particles into account, without considering the shape of particles, the viscosity was higher than the one we prepared here. Therefore, the distribution modulus for these four particles can be set as 0.3196. Fig. 5 shows the relationships among PSDs curves of four powders, the fitting curve when n=0.3196 and the theoretical curve of F-D function, where the fitting curve is consistent with the theoretical one.
Fig. 4. Rheological curves of slurries with different n values varying from 0.25 to 0.4. The inset picture shows the rheological curves of slurries prepared by the Farris theory and n=0.3196.
Fig. 5. The PSDs curves of four powders, the fitting curve when n=0.3196 and the theoretical curve of F-D function. 4.2. Rheological Characteristics of Suspensions The rheological curve reflects the dispersion state of powders in a suspension. Usually, for non-dispersed slurries present a shearing-thinning behavior, which is associated with viscosities that decrease with increasing shear rates. On the contrary, well-dispersed stable slurries have a shear-thickening behavior. Compared to the rheological curves of ceramic slurries in other literatures, which usually showed a shear-thinning behavior at a lower shear rate, while a shear-thickening behavior at a higher shear rate, the rheological curves in this study were different [25,26]. It can be seen from the curves that all suspensions appear a shear thickening behavior at first, then shear thinning. We use 𝛾𝑚̇ to denote the shear rate at which the maximum viscosity is reached. The 𝛾𝑚̇ varies with n values, and it appears to increase toward a higher shear rate as the viscosity decrease. This phenomenon may be related to the settling of suspensions [27]. The settling velocity of particles can be calculated by the Stokes function [28]:
2( p s) g r 2 Vp 9 Where p is the density of powders, s is the density of suspension, r is the particle radius and is the dynamic viscosity of suspension. According to Eq. 15,
(15)
the settling velocity increases quadratically with an increase in particle size, and increases with a decrease in viscosity. Therefore, large particles are more likely to settle and form clusters of aggregates in a low viscosity slurry. When the measurement begins, with the increase of shear rates, the collision between particles is intensified, and the clusters of large particles are disaggregated. So the disordering of particles is improved and the free water among them is reduced. As a result, the slurries shows a shear thickening behavior, because of the increase of internal frictions between particles. After the clusters are totally disaggregated, the slurries show a shear thinning behavior by further increasing the shear rates. In this study, the slurry had the lowest viscosity when n was equal to 0.3196, thus the settlement was the severest among all these slurries, so as the cluster of aggregates. Thus a higher shear rate was required to eliminate this aggregates, and 𝛾𝑚̇ appeared at a higher shear rate than others. 4.3. Preparation of Ceramic Slurries with a High Solid Loading and Low Viscosity In order to prepare a ceramic slurry with a high solid loading and low viscosity, the effects of particle gradation on viscosity were investigated. One bimodal system and two trimodal systems were designed. The volume fractions of powders were determined by the above-mentioned method, and the viscosities were compared with the tetramodal one at a same solid loading of 58 vol%. Table 3 shows the volume fractions of different powders in these slurries. Table 3 Volume fractions of different particles in bimodal and trimodal systems. Bimodal
Trimodal-1
Trimodal-2
V2μm
/
34%
/
V5μm
50%
11%
41%
V40μm
50%
55%
22%
V125μm
/
/
37%
Fig. 6 shows the rheological curve of different slurries. Particle gradation has a substantial effect on the fluidity of slurries, as viscosities of slurries decrease when
the gradation number increases. In the bimodal system, the viscosity is over 1 Pa·s at a shear rate of 100 s-1, meanwhile viscosities decrease significantly when the slurry is changed from a bimodal system to a trimodal system. However, the reduction in viscosities is less obvious when the gradation number further increase to four. The reduction in viscosities caused by particle gradation can be attributed to the high packing density of particles. Since the midsized particles are packed into the pores formed by the coarse particles and the smaller ones are packed into the pores formed by the midsize and coarse particles, more free water between particles is released into the flow, thus the slurry have low viscosities [16]. It is interesting to compare two trimodal slurries, as they own a similar gradation number. The slurry consists of 125 μm, 40 μm and 2 μm powders has a better fluidity than the one consists of 40 μm, 5 μm and 2 μm powders. The introduction of 125 μm powders further broadens the PSDs, thus increasing the particle packing density and reducing relative viscosities [29].
Fig. 6. Rheological curves of slurries of different particle gradations. The room temperature strength of samples after sintering at 1350 °C is shown in Fig. 7. The bending strengths of the bimodal, trimodal-1, trimodal-2 and tetramodal samples were 9.27±1.19 MPa, 9.56±1.66 MPa, 17.31±0.73 MPa and 14.61±1.28 MPa. The bimodal system owns the lowest strength due to the low particle packing density. Although, according to the rheological test, the trimodal system consisting of 125 μm, 40 μm and 2 μm and the tetramodal system have relatively a high
particle packing density, the strength is not the highest. The presence of coarse particles leads to this phenomenon. The fracture morphologies of samples are shown in Fig. 8. As the number of particle gradation increases from two to four, particle packing becomes more and more dense. Although fine particles are stacked into the pores formed by coarse particles, the particle packing density in Fig. 8(a) is obviously less than other three, since pores between fine particles can also be founded easily. Microstructure of trimodal-1 system is shown in Fig. 8(b), where visible pores can barely be founded. Nevertheless, large gaps along coarse particles can be founded in Fig. 8(c) and (d), the size can reach to 5-6 μm, which destroy the integrity of matrix. That explains why the samples containing the 125 μm powders have low strengths, although they have high packing densities.
Fig. 7. Room temperature strengths of samples with different particle gradations.
Fig. 8. Fracture morphologies of samples (a) Bimodal system, (b) Trimodal-1 system, (c) Trimodal-2 system and (d) Tetramodal system. Although the samples of tetramodal system have a relatively low strength, the insufficiency in strength can be compensated by increasing the solid loadings. Fig. 9 shows the rheological curve of tetramodal slurries with different solid loadings varying from 58 vol% to 64 vol%. The viscosities increase with the increase in solid loadings. The insert picture in Fig. 9 shows the viscosities as a function of solid loadings at a shear rate of 100 s-1. The viscosities increase exponentially with the solid loadings, and exceeds 1 Pa·s when the solid loading reaches to 64 vol%. It is widely recognized that the slurry would not be suitable for gelcasting, when the viscosity is over 1 Pa·s at a shear rate of 100 s-1 [12,30]. Thus, in this study, the maximum solid loading of slurries we prepared was 62 vol%, and at this time the viscosity at a shear rate of 100 s-1 is 0.29 Pa·s. Besides, an obvious shift of 𝛾𝑚̇ to the region of low shear rates with the increasing in solid loadings can also be founded, which further confirmed that this rheological properties are caused by sedimentation. The room temperature strengths were also tested. Fig. 10 shows the strengths of samples as a function of solid loadings. The strengths of each batch were 14.61±1.28 MPa, 16.63±1.83 MPa, 18.72±1.94 MPa and 14.90±1.83 MPa. The strengths increase with the solid loadings, and reach the maximum at a solid loading of 62 vol%. After the solid loadings continue increase to 64 vol%, the strengths decrease. As the viscosities increase with the solid loadings, more air would be trapped into the suspensions during casting and eventually forming pores in the samples, which causes the reduction in strength.
Fig. 9. Rheological curve of slurries with different solid loadings varying from 58 vol% to 64 vol%. The inset picture shows the relationship between the solid loadings and the viscosities at a shear rates of 100 s-1.
Fig. 10. Room temperature strengths of samples with different solid loadings. 3.4. Case Study
Fig. 11. Diagram of the negative pressure gelcasting system. In order to demonstrate the effectiveness of this method in the preparation of suspension with a high solid loading and low viscosity, a ceramic mold was fabricated by the IFT processing. There is a plate-like ceramic core arrayed with dozens of circular holes at the trailing edge of this mold. The thickness of this core is 0.5 mm and the clearance between holes is about 0.7 mm. Fabrication of such tiny structure is a serious challenge for gelcasting. Not only a low viscosity is required for the filling of this structure, the slurry should also have a high solid loading to ensure sufficient mechanical properties. A tetramodal slurry at a solid loading of 62 vol% were prepared before gelcasting. 4 wt% polydimethylsiloxane (CPF-M1001, mean size: 40 μm, Cobano Ltd., Zhongshan, China) was added to improve the mid-temperature strength [5]. The gelcasting process was conducted in a negative pressure chamber equipped with a vibration platform to suppress the sedimentation and improve the filling capacity of slurries, which is shown in Fig. 11. The vibration frequency was controlled at 60 Hz with an amplitude of 3 mm, and the chamber pressure was 0.02 atm.
Fig. 12. X-ray scan and SEM images of the ceramic molds after sintering. (a) Pictures of the mold and internal cores fabricated by the IFT process, (b) Ceramic cores filled by the bimodal slurry at a solid loading of 54 vol%, (c) Ceramic cores filled by the tetramodal slurry at a solid loading of 62 vol%, (d-e) Microstructures of the ceramic parts After freeze-drying and sintering, the ceramic part containing fine structures was obtained, which is shown in Fig.12(a). Before this optimization was conducted, a bimodal slurry consisting of 40 μm and 5 μm with a ratio of 64:36 was used in our experiments. In order to fill these tiny structures, the maximum solid loading was restricted at 54 vol%, there was still an insufficient filling phenomenon even in this case. Fig. 12(b) shows the X-ray scan result of such ceramic parts before optimization, in which the whole structures are not fabricated completely. The missing parts exist between holes and have similar shapes of bubbles, which indicates that air was trapped between the micro-channels during casting due to the high viscosity. When the tetramodal ceramic slurry was used, the ceramic part after sintering is shown in Fig. 12(c). Although the solid loading is increased to 62 vol%,
all the circular holes are duplicated successfully. Insufficient filling phenomenon is not found between the holes. Fig. 12(b-d) show the micro-morphologies between holes, the integrity of such tiny structures is maintained, meanwhile particles are packed together with each other closely. That means the high solid loading slurry prepared by the method herein can realize the filling of such microstructures by gelcasting. In this study, a method for the preparation of suspensions with a high solid loading and low viscosity by irregular particles was proposed. And this method is very convenient for the preparation of slurries for the fabrication of ceramic parts with tiny structures by gelcasting. However the choice of particle sizes was not optimized in this study, these four different alumina particles were only used as a proof of principle to describe the optimization process and the effects on viscosities and mechanical properties. Moreover, this effects would be pronounced if the particle sizes are further optimized. 5. Conclusions This paper aimed at presenting a simple route to prepare a suspension by irregular particles for the fabrication of multiscale ceramic components by gelcasting. The volume fractions of different particles were defined by closet packing theory based on the F-D function and fractal theory. A high solid loading slurry (62 vol%) with low viscosity (0.29 Pa·s ) was prepared. Finally, as a demonstration, a ceramic mold with tiny structures was fabricated successfully by the above-mentioned method. Acknowledgments The authors thank Ph.D student Xudong Liang of University of California, San Diego and Ph.D student Yuanye Bao of City University of Hong Kong for their critical revisions on the manuscript. This work was supported by the State Basic Research Key Projects (973) of China through Grant No. 2013CB035703 and the Fundamental Research Funds for the Central University.
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S0955-2219(17)30525-3 http://dx.doi.org/doi:10.1016/j.jeurceramsoc.2017.08.002 JECS 11397
To appear in:
Journal of the European Ceramic Society
Received date: Revised date: Accepted date:
28-4-2017 1-8-2017 2-8-2017
Please cite this article as: Lu Zhongliang, Miao Kai, Zhu Weijun, Chen Yi, Xia Yuanlin, Li Dichen.Fractions Design of Irregular Particles in Suspensions for the Fabrication of Multiscale Ceramic Components by Gelcasting.Journal of The European Ceramic Society http://dx.doi.org/10.1016/j.jeurceramsoc.2017.08.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Fractions Design of Irregular Particles in Suspensions for the Fabrication of Multiscale Ceramic Components by Gelcasting Zhongliang Lua,c,,1, Kai Miaoa,b,c,1 , Weijun Zhua,c, Yi Chena, Yuanlin Xiaa, Dichen Lia,c a
State Key Laboratory for Manufacturing Systems Engineering and School of
Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China b
State Key Laboratory for Strength and Vibration of Mechanical Structures and School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China
c
Collaborative Innovation Center of High-End Manufacturing Equipment, Xi’an, 710049, China
Abstract A new approach for the preparation of suspensions with a high solid loading and low viscosity by using irregular particles was proposed. These suspensions were prepared for the fabrication of multiscale ceramic components by gelcasting. Based on the Funk-Dinger function and fractal theory, the closest packing theory was applied to optimize the volume fractions of different particles. The maximum solid loading of slurries prepared for gelcasting was 62 vol%, and the viscosity at a shear rate of 100 s-1 was only 0.29 Pa·s. By as-prepared suspensions, a decimeter-scale ceramic part with submillimeter features was fabricated successfully by gelcasting, which verify the feasibility of the proposed method. Keywords: Gelcasting; Irregular particles; Solid loadings; Rheological properties
Corresponding author. Tel.: +86 29 82665126; Fax: +86 29 82660114; E-mail: [email protected] two authors contributed equally to this work
1 The
1. Introduction Gelcasting, a ceramic forming process, was developed to overcome the limitations of other shape forming techniques such as injection molding and slip casting with lower fabrication costs, shorter forming time [1-3]. However, ceramic components with internal and external structures cannot be easily fabricated by this technique due to the restriction of mold opening process. Based on the stereolithography (SL) technology, the integral fabrication technique (IFT) was developed, allowing the fabrication of such components by gelcasting [4,5]. This method was initially proposed to fabricate the ceramic molds of hollow turbine blades. The ceramic mold is a decimeter-scale structure with cores inside, which are slender structures with submillimeter features. Suspension for this mold filling by gelcasting has to satisfy two requirements, good fluidity and a high solid loading. Suspension with good fluidity can ensure that the slurry can be poured successfully into the mold and all tiny structures inside can be duplicated; while a high solid loading can result in both higher density and less deformation, which can restrain defect formation in both green and sintered parts [6-8]. The viscosity of a suspension increases exponentially as the fraction of particles increases. Therefore, it is difficult to realize the preparation of suspension with features of a high solid loading and low viscosity. Based on the stabilizing mechanisms, many efforts have been made for the preparation of suspensions with a high solid loading and low viscosity. The change of the pH value can result in enlarging zeta potential and enhancing electrostatic repulsion, finally achieving a low viscosity [9]. The use of dispersant can also decrease viscosity by changing particle surface profiles or surface charge properties [10,11]. However, the adjustment of pH or dispersant may not work with increasing solid loadings [12]. It is widely recognized that broadening the particle size distribution (PSD) can increase the maximum fraction of a monodisperse system. Thus, polydispersity can
give a lower viscosity at the same volume fraction or permit a higher volume loading at the equivalent monodisperse viscosity. By introducing smaller particles, which could potentially fit in between the larger particles, it is possible to achieve a much higher volume fraction [13-16]. The viscosity of suspensions comprised of bimodal mixtures of ceramic powders have been investigated [17,18]. A size ratio about 8 and a proportion about 30-70 between average coarse and fine particle sizes showed the lowest viscosity with a high solid loading. By statistical design or experiments, fractions of three different particles were defined in a trimodal system. Although the suspension had a lower viscosity than the bimodal system, the optimization processes were sophisticated and time consuming [19]. Meanwhile, almost all of the previous attempts were applied for spherical particles only, optimizations for irregulars barely been proposed. This is largely been due to the perceivable difficulty in quantitative descriptions of sizes and shapes of irregular particles. However, particles with irregular geometries are in fact the type of particles which constitute the majority of ceramic powders [20]. What’s more, in the mass production by gelcasting, the use of irregulars to achieve suspensions can significantly reduce the production cost. In this paper, the fractal theory was applied to describe the geometrical morphology of irregular particles at first. Then, based on the Funk-Dinger (F-D) function, we put forward a simple method to optimize the volume fractions of such particles in suspensions, as the F-D function is widely used in the concrete, coal and food engineering to provide suspensions with required fluidity. Solid loadings of the alumina slurry were maximized and their rheological properties were measured. The microstructures and the mechanical properties were also investigated. Finally, centimeter-scale ceramic structures with submillimeter features were accurately fabricated by the prepared suspensions. 2. Material and Methods 2.1. Raw Materials
Four Al2O3 powders were obtained from a commercial vendor (Shangdong Zibo Aluminum Co., Ltd., Zibo, China). The powders had average sizes of 125, 40, 5 and 2 μm. In the gelcasting process, acrylamide (C2H3CONH2, AM, Kemiou Chemical Reagent Co., Ltd., Tianjin, China ) and N,N’-methylenebisacrylamide ((C2H3CONH)2CH2, MBAM, Kemiou Chemical Reagent Co., Ltd., Tianjin, China) were used as the monomer and crossing linking agent, respectively. Sodium polyacrylate (PAAS, Sinopharm Chemical Reagent Co, Ltd, China) was used as the dispersant. Ammonium persulphate ((NH4)2S2O8, APS, Sinopharm Chemical Reagent Co, Ltd, China) and N,N,N’,N’-tetramethylethylenediamine ((CH3)2NCH2CH2N(CH3)2, TMEDA, Sinopharm Chemical Reagent Co, Ltd, China) were used as the initiator and catalyst, respectively. Deionized water was used as solvent in the whole process. 2.2. Preparation of Aqueous Suspensions The premix solution was prepared by dissolving 15 wt% AM and MBAM in a ratio of 24:1. 1 wt% PAAS with respect to the Al2O3 powders was added as the dispersant. Aqueous suspensions with different solid loadings were prepared by mixing ceramic powders and the premixed solution under constant stirring. After ball-milling for 60 min and degassing for 5 min, the suspensions were obtained. In this process, the ballmilling time was restricted at 60 min to avoid significant changes in particle sizes. 2.3. IFT processing In this processing, an SL prototype for ceramic part was fabricated by SPS 600B (Xi’an Jiaotong University, China) using photosensitive resin (SPR 8981, Zhengbang Ltd., Zhuhai, China) firstly. Then, in the gelcasting, the suspension was poured into the SL prototype, then in situ polymerized to form green body under the effect of initiator and catalyst. After freeze-drying for 72 h, the green ceramic body was transferred into a furnace for pre-sintering. The green ceramic part was pyrolyzed at 600 °C for 30 min at a low heating rate of 0.5 °C/min in air, allowing the removal of
the SL prototype. The pyrolyzed part was further heated to 1350 °C for 3 h at a heating rate of 4 °C/min for the sintering of the matrix, followed by furnace cooling. After several post treatments, the ceramic part was finally obtained. 2.4. Testing Particle size analysis was conducted using a laser diffraction particle size analyzer (LS230, Beckman Coulter). The rheological properties of suspensions comprised of different powders were investigated by a controlled stress rheometer (AR 2000, TA instruments, New Castle, USA) with a concentric cylinder geometry. Prior to the measurements, pre-shearing was performed at a shear rate of 100 s-1 for 1 min and a pause for 1 min in order to transmit the same rheological history to all the suspensions being tested. The viscosities were measured at shear rates varying from 0.1-200 s-1. The room temperature strengths of ceramic samples after sintering were tested by a three-point bending test machine (HSST-6003QP, Sinosteel Luoyang Institute of Refractories, Luoyang, China) with a span distance of 30 mm at a cross-head speed of 8 mm/min using samples of a nominal size of 4 mm × 10 mm × 60 mm. Each data point represents the average value of five to ten individual tests. Microstructures were examined by scanning electron microscope (SEM) (SU-8010, Hitachi Ltd., Tokyo, Japan). The ceramic parts after sintering were inspected by X-ray scan (Y.Cheetah, YXLON Ltd., Hamburg, Germany). 3. Theory A reliable solution for the reproduction of natural continuously graded grains is represented by the F-D distribution function. This function is generally acknowledged in the concrete or coal engineering for the preparation of slurries with a closest packing density. The cumulative finer fraction reads as follows. U t Di
n Din Dmin n n Dmax Dmin
(1)
Where Di is the particle size of the considered fraction, Dmin is the minimum particle size and Dmax is the maximum particle size in the mixture system. The exponent n is the distribution modulus. The mix design of particle fractions could be understood as the realization of minimum deviation between Ut Di (the cumulative fraction based on F-D function) and Ud Di (the cumulative fraction after particle gradation). Therefore, the least square method in MatlabTM was used, and this optimization could be written as: 2
n
E U t Di U d Di min
(2)
i 1
The distribution modulus n allows controlling the amount of fine particles for a generated mix in a certain range. While a higher value of n lead to coarser blends, a lower n will produce mixes with fine blends [21]. For a certain kind of particles with similar morphology, the distribution modulus is a specific value when the maximum packing efficiency can be achieved. So the most important step in this optimization was the determination of n. According to fractal theory, assumed that in a mixture system, dmax is the maximum particle size, dmin is the minimum particle size and di is the particle size between dmax and dmin. ε (1＞ε＞0) and b are the particle size ratio and number ratio of adjacent fine and coarse particles, respectively. The relationship between ε and b is given by:
b P
(3)
Where P is the fractal dimension of particles, α is the correlation coefficient. Particle systems which are accord with this function can be defined as the fractal size distribution system. In this system, the gradation number is defined as k. For a particle with a size of dm, it can be written as:
dm dmax m The particle numbers of dm is:
( k m 0)
(4)
nm n0bm
(5)
Where nm is the particle numbers of dmax. The collection degree of particle numbers is defined as:
n(d m ) n(d m1 ) n(d m ) n0b m (b 1) n( d m ) d m d m1 d m d max ( 1)
(6)
Combining Eqs. (3) and (4), the following expression can be written as: P bm (1/ )m P dm P dmax
(7)
Substituting Eq. (7) into Eq. (6) gives: P n(dm ) n0 dm( P +1）dmax (b 1) / ( 1)
(8)
When the particle system becomes continuous distributed, the gradation number, k, would approach to infinity, ε and b would approach to 1, and n(dm) would be equal to n(d). Substituting Eq. (3) into Eq. (8) and calculating the limit gives: P n(d ) lim n0 d m ( P +1）d max (b 1) / ( 1) 1
P lim n0 d m ( P +1）d max ( P 1) / ( 1) 1
(9)
P ( P 1) n0 Pd max d
Then the cumulative volume of particles finer than d can be written as: d
Cvd
V ( d )
3
N (d )dd
d min d
Cvd
3
P ( P 1) N 0 Pd max d dd
d min
P 3 P CvN 0 d max (d 3 P d min ) P / (3 P)
Where Cv is the volume coefficient of particles. And the cumulative volume fraction of particles finer than d can be written as:
(10)
U (d ) V ( d ) / V ( d max ) 3 P 3 P 3 P (d 3 P d min ) / (d max d min )
(11)
The Eq. (11) was deduced based on the fractal distribution model of continuous size particles. Compared the Eq. (11) with the F-D function, the distribution modulus can be written as:
n 3 P
(12)
The optimum value for the densest packing of spherical particles is expected for n=0.37, while the P is 2, so the correlation coefficient, α=1.315 [22,23]. The fractal dimension of irregular particles can be determined by the area-volume method, which can be written as:
log[ S ( ) / ] V ( )1/3 log(a0 ) log[ ] P
(13)
β is the measurement scale, which changes with particle morphology. S(β) and V(β) are the surface area and volume of particles under the measurement scale of β, respectively, and a0 is a constant. Fig.1 shows the morphologies of the four alumina powders used in this study. Since these powders were prepared by the same process, the fractal features were statistically self-similar. Thus, β is a constant value in this study. Assuming the value of β is 1, the Eq. 13 can be rewritten as: log[V ] log[ S ]
3 log(a03 ) P
(14)
Fig. 1. Particle morphologies of the alumina powders: (a) D50=125 μm, (b) D50=40 μm, (c) D50=5 μm and (d) D50=2 μm. And the fractal dimension P can be determined by the slope of the liner plots of log[V] versus log[S].
Fig. 2. Particle size distributions of alumina powders. Fig. 2 shows the PSDs of four alumina powders. According to the particle sizes and specific surface areas of powders, the surface areas and volume were calculated. The results are shown in Table 1. After plotting the liner line of log[V] versus log[S],shown in Fig. 3, the fractal dimension P was calculated by the slope of this line, and the distribution modulus, n=3-α×P=3-1.315×2.038=0.3196. Table 1 Surface areas and volumes of four alumina powders. Surface Area/m2
Volume/m3
2 μm
1.631E-11
9.63E-18
5 μm
1.176E-10
1.057E-16
40 μm
3.387E-9
3.305E-14
125 μm
5.335E-8
1.035E-12
Fig. 3. Log(V) vs. Log(S). 4. Results and discussions 4.1. Verification of the Distribution Modulus Based on the fractal theory, the distribution modulus for these irregular particles was obtained. In order to verify this distribution modulus, rheological properties of suspensions comprised of different volume fractions of four powders were investigated. The volume fractions of different powders were determined by the distribution modulus which varies from 0.25 to 0.4, and were calculated in MatlabTM according to the Eq. (2). Table 2 shows the volume fractions of four powders at different n values. It can been seen that with the increase of n values, volume fractions of fine particles gradually decrease while the volume fraction of coarse particles increase, consistent with the F-D function. Table 2 Volume fractions of four alumina powders at different n values. n
0.25
0.3
0.3196
0.35
0.4
V2μm
31%
24%
22%
18%
13%
V5μm
10%
13%
13%
15%
16%
V40μm
28%
28%
29%
28%
28%
V125μm
31%
35%
36%
39%
43%
Suspensions with a solid loading of 58 vol% were prepared according to Table 2, and the rheological properties of suspensions were tested. The viscosity was measured
at shear rates varying from 0.1-200 s-1. The rheological curve of slurries with different n values are shown in Fig. 4. It is observed that suspensions have the lowest viscosities when the distribution modulus, n, is equal to 0.3196. The viscosity is only about 0.1 Pa·s at a shear rate of 100 s-1.When the distribution modulus increases from 0.25 to 0.3196, the viscosities at all shear rates decrease. As the distribution modulus continues to increase from 0.3196 to 0.4, the viscosities turns to increase. This trend in viscosities are consistent with the theoretical analysis based on the fractal distribution model, which predicts the suspension have the lowest viscosity when n is equal to 0.3196. We also prepared a slurry with a solid loading of 58 vol% based on the Farris theory [24]. Since the Farris theory only took the monosphere particles into account, without considering the shape of particles, the viscosity was higher than the one we prepared here. Therefore, the distribution modulus for these four particles can be set as 0.3196. Fig. 5 shows the relationships among PSDs curves of four powders, the fitting curve when n=0.3196 and the theoretical curve of F-D function, where the fitting curve is consistent with the theoretical one.
Fig. 4. Rheological curves of slurries with different n values varying from 0.25 to 0.4. The inset picture shows the rheological curves of slurries prepared by the Farris theory and n=0.3196.
Fig. 5. The PSDs curves of four powders, the fitting curve when n=0.3196 and the theoretical curve of F-D function. 4.2. Rheological Characteristics of Suspensions The rheological curve reflects the dispersion state of powders in a suspension. Usually, for non-dispersed slurries present a shearing-thinning behavior, which is associated with viscosities that decrease with increasing shear rates. On the contrary, well-dispersed stable slurries have a shear-thickening behavior. Compared to the rheological curves of ceramic slurries in other literatures, which usually showed a shear-thinning behavior at a lower shear rate, while a shear-thickening behavior at a higher shear rate, the rheological curves in this study were different [25,26]. It can be seen from the curves that all suspensions appear a shear thickening behavior at first, then shear thinning. We use 𝛾𝑚̇ to denote the shear rate at which the maximum viscosity is reached. The 𝛾𝑚̇ varies with n values, and it appears to increase toward a higher shear rate as the viscosity decrease. This phenomenon may be related to the settling of suspensions [27]. The settling velocity of particles can be calculated by the Stokes function [28]:
2( p s) g r 2 Vp 9 Where p is the density of powders, s is the density of suspension, r is the particle radius and is the dynamic viscosity of suspension. According to Eq. 15,
(15)
the settling velocity increases quadratically with an increase in particle size, and increases with a decrease in viscosity. Therefore, large particles are more likely to settle and form clusters of aggregates in a low viscosity slurry. When the measurement begins, with the increase of shear rates, the collision between particles is intensified, and the clusters of large particles are disaggregated. So the disordering of particles is improved and the free water among them is reduced. As a result, the slurries shows a shear thickening behavior, because of the increase of internal frictions between particles. After the clusters are totally disaggregated, the slurries show a shear thinning behavior by further increasing the shear rates. In this study, the slurry had the lowest viscosity when n was equal to 0.3196, thus the settlement was the severest among all these slurries, so as the cluster of aggregates. Thus a higher shear rate was required to eliminate this aggregates, and 𝛾𝑚̇ appeared at a higher shear rate than others. 4.3. Preparation of Ceramic Slurries with a High Solid Loading and Low Viscosity In order to prepare a ceramic slurry with a high solid loading and low viscosity, the effects of particle gradation on viscosity were investigated. One bimodal system and two trimodal systems were designed. The volume fractions of powders were determined by the above-mentioned method, and the viscosities were compared with the tetramodal one at a same solid loading of 58 vol%. Table 3 shows the volume fractions of different powders in these slurries. Table 3 Volume fractions of different particles in bimodal and trimodal systems. Bimodal
Trimodal-1
Trimodal-2
V2μm
/
34%
/
V5μm
50%
11%
41%
V40μm
50%
55%
22%
V125μm
/
/
37%
Fig. 6 shows the rheological curve of different slurries. Particle gradation has a substantial effect on the fluidity of slurries, as viscosities of slurries decrease when
the gradation number increases. In the bimodal system, the viscosity is over 1 Pa·s at a shear rate of 100 s-1, meanwhile viscosities decrease significantly when the slurry is changed from a bimodal system to a trimodal system. However, the reduction in viscosities is less obvious when the gradation number further increase to four. The reduction in viscosities caused by particle gradation can be attributed to the high packing density of particles. Since the midsized particles are packed into the pores formed by the coarse particles and the smaller ones are packed into the pores formed by the midsize and coarse particles, more free water between particles is released into the flow, thus the slurry have low viscosities [16]. It is interesting to compare two trimodal slurries, as they own a similar gradation number. The slurry consists of 125 μm, 40 μm and 2 μm powders has a better fluidity than the one consists of 40 μm, 5 μm and 2 μm powders. The introduction of 125 μm powders further broadens the PSDs, thus increasing the particle packing density and reducing relative viscosities [29].
Fig. 6. Rheological curves of slurries of different particle gradations. The room temperature strength of samples after sintering at 1350 °C is shown in Fig. 7. The bending strengths of the bimodal, trimodal-1, trimodal-2 and tetramodal samples were 9.27±1.19 MPa, 9.56±1.66 MPa, 17.31±0.73 MPa and 14.61±1.28 MPa. The bimodal system owns the lowest strength due to the low particle packing density. Although, according to the rheological test, the trimodal system consisting of 125 μm, 40 μm and 2 μm and the tetramodal system have relatively a high
particle packing density, the strength is not the highest. The presence of coarse particles leads to this phenomenon. The fracture morphologies of samples are shown in Fig. 8. As the number of particle gradation increases from two to four, particle packing becomes more and more dense. Although fine particles are stacked into the pores formed by coarse particles, the particle packing density in Fig. 8(a) is obviously less than other three, since pores between fine particles can also be founded easily. Microstructure of trimodal-1 system is shown in Fig. 8(b), where visible pores can barely be founded. Nevertheless, large gaps along coarse particles can be founded in Fig. 8(c) and (d), the size can reach to 5-6 μm, which destroy the integrity of matrix. That explains why the samples containing the 125 μm powders have low strengths, although they have high packing densities.
Fig. 7. Room temperature strengths of samples with different particle gradations.
Fig. 8. Fracture morphologies of samples (a) Bimodal system, (b) Trimodal-1 system, (c) Trimodal-2 system and (d) Tetramodal system. Although the samples of tetramodal system have a relatively low strength, the insufficiency in strength can be compensated by increasing the solid loadings. Fig. 9 shows the rheological curve of tetramodal slurries with different solid loadings varying from 58 vol% to 64 vol%. The viscosities increase with the increase in solid loadings. The insert picture in Fig. 9 shows the viscosities as a function of solid loadings at a shear rate of 100 s-1. The viscosities increase exponentially with the solid loadings, and exceeds 1 Pa·s when the solid loading reaches to 64 vol%. It is widely recognized that the slurry would not be suitable for gelcasting, when the viscosity is over 1 Pa·s at a shear rate of 100 s-1 [12,30]. Thus, in this study, the maximum solid loading of slurries we prepared was 62 vol%, and at this time the viscosity at a shear rate of 100 s-1 is 0.29 Pa·s. Besides, an obvious shift of 𝛾𝑚̇ to the region of low shear rates with the increasing in solid loadings can also be founded, which further confirmed that this rheological properties are caused by sedimentation. The room temperature strengths were also tested. Fig. 10 shows the strengths of samples as a function of solid loadings. The strengths of each batch were 14.61±1.28 MPa, 16.63±1.83 MPa, 18.72±1.94 MPa and 14.90±1.83 MPa. The strengths increase with the solid loadings, and reach the maximum at a solid loading of 62 vol%. After the solid loadings continue increase to 64 vol%, the strengths decrease. As the viscosities increase with the solid loadings, more air would be trapped into the suspensions during casting and eventually forming pores in the samples, which causes the reduction in strength.
Fig. 9. Rheological curve of slurries with different solid loadings varying from 58 vol% to 64 vol%. The inset picture shows the relationship between the solid loadings and the viscosities at a shear rates of 100 s-1.
Fig. 10. Room temperature strengths of samples with different solid loadings. 3.4. Case Study
Fig. 11. Diagram of the negative pressure gelcasting system. In order to demonstrate the effectiveness of this method in the preparation of suspension with a high solid loading and low viscosity, a ceramic mold was fabricated by the IFT processing. There is a plate-like ceramic core arrayed with dozens of circular holes at the trailing edge of this mold. The thickness of this core is 0.5 mm and the clearance between holes is about 0.7 mm. Fabrication of such tiny structure is a serious challenge for gelcasting. Not only a low viscosity is required for the filling of this structure, the slurry should also have a high solid loading to ensure sufficient mechanical properties. A tetramodal slurry at a solid loading of 62 vol% were prepared before gelcasting. 4 wt% polydimethylsiloxane (CPF-M1001, mean size: 40 μm, Cobano Ltd., Zhongshan, China) was added to improve the mid-temperature strength [5]. The gelcasting process was conducted in a negative pressure chamber equipped with a vibration platform to suppress the sedimentation and improve the filling capacity of slurries, which is shown in Fig. 11. The vibration frequency was controlled at 60 Hz with an amplitude of 3 mm, and the chamber pressure was 0.02 atm.
Fig. 12. X-ray scan and SEM images of the ceramic molds after sintering. (a) Pictures of the mold and internal cores fabricated by the IFT process, (b) Ceramic cores filled by the bimodal slurry at a solid loading of 54 vol%, (c) Ceramic cores filled by the tetramodal slurry at a solid loading of 62 vol%, (d-e) Microstructures of the ceramic parts After freeze-drying and sintering, the ceramic part containing fine structures was obtained, which is shown in Fig.12(a). Before this optimization was conducted, a bimodal slurry consisting of 40 μm and 5 μm with a ratio of 64:36 was used in our experiments. In order to fill these tiny structures, the maximum solid loading was restricted at 54 vol%, there was still an insufficient filling phenomenon even in this case. Fig. 12(b) shows the X-ray scan result of such ceramic parts before optimization, in which the whole structures are not fabricated completely. The missing parts exist between holes and have similar shapes of bubbles, which indicates that air was trapped between the micro-channels during casting due to the high viscosity. When the tetramodal ceramic slurry was used, the ceramic part after sintering is shown in Fig. 12(c). Although the solid loading is increased to 62 vol%,
all the circular holes are duplicated successfully. Insufficient filling phenomenon is not found between the holes. Fig. 12(b-d) show the micro-morphologies between holes, the integrity of such tiny structures is maintained, meanwhile particles are packed together with each other closely. That means the high solid loading slurry prepared by the method herein can realize the filling of such microstructures by gelcasting. In this study, a method for the preparation of suspensions with a high solid loading and low viscosity by irregular particles was proposed. And this method is very convenient for the preparation of slurries for the fabrication of ceramic parts with tiny structures by gelcasting. However the choice of particle sizes was not optimized in this study, these four different alumina particles were only used as a proof of principle to describe the optimization process and the effects on viscosities and mechanical properties. Moreover, this effects would be pronounced if the particle sizes are further optimized. 5. Conclusions This paper aimed at presenting a simple route to prepare a suspension by irregular particles for the fabrication of multiscale ceramic components by gelcasting. The volume fractions of different particles were defined by closet packing theory based on the F-D function and fractal theory. A high solid loading slurry (62 vol%) with low viscosity (0.29 Pa·s ) was prepared. Finally, as a demonstration, a ceramic mold with tiny structures was fabricated successfully by the above-mentioned method. Acknowledgments The authors thank Ph.D student Xudong Liang of University of California, San Diego and Ph.D student Yuanye Bao of City University of Hong Kong for their critical revisions on the manuscript. This work was supported by the State Basic Research Key Projects (973) of China through Grant No. 2013CB035703 and the Fundamental Research Funds for the Central University.
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