Powder mixing effect on the compaction capabilities of ceramic powders

Powder Technology 195 (2009) 227–234

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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c

Powder mixing effect on the compaction capabilities of ceramic powders Li Sun, Basak Oguz, Patrick Kwon ⁎ Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, United States

a r t i c l e

i n f o

Article history: Received 6 February 2009 Received in revised form 2 June 2009 Accepted 12 June 2009 Available online 21 June 2009 Keywords: Powder Agglomerate Mixing Compaction Relative density

a b s t r a c t By mixing any two of four alumina powders, a variety of powder mixtures were produced. The relationships among relative density, stress and strain were compared for those powder mixtures in order to investigate the powder mixing effect on the compaction capability. The compaction capability was quantified by the initial relative densities. Due to the difference in the average particle size ratio between two powders as well as the compaction capability difference of the powders, the initial relative density as a function of powder proportion can be described by either a linear or parabolic curve. The essential initial powder characteristics that exhibit each curve were identified. Also, the boundaries for each initial relative density versus powder proportion curve were proposed. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Powder Metallurgy (P/M) is the most common fabrication method for most ceramic and some metal engineering components. The three main steps of P/M to convert powders into useful objects are powder processing, forming operations, and sintering [1]. The powder processing may involve milling, which is the mechanical agitation used to break particles or agglomerates into smaller particles and mixing, which is the process of thorough incorporating of two or more powders [2]. Many methods are being used in forming operations of powders, such as injection molding, slurry techniques and compaction [1]. Conventional uniaxial powder compaction, which is performed with the pressure applied along one axis using hard tooling of die and punches, is the most widely used method to compact powders. Fig. 1 shows the detailed process for such a tool set during compaction. Samples after compaction are called “greens”. In pharmacology, green samples can be used immediately as pharmaceutical tablets. In the case of ceramics or metals, green samples are the precursor for attaining a dense body by sintering. Sintering describes neck formation and growth among the particles and eventual consolidation of the particles. It can occur at temperatures below the melting point by solid-state atomic transport phenomenon. However, some instances involve the presence of a liquid phase [1,3]. The three steps of P/M are closely related to each other. Each step influences the subsequent step(s). The initial powder characteristics, such as average particle size [4–7], particle shape [8], particle size distribution [5–7,9,10] and specific surface area [5] achieved during

powder milling and mixing, influence the compaction and sintering capability. The pressure [6,11] and the die wall friction [12] of the compaction step can affect the shape of green body due to different density distribution [12,13]. Several studies have already been preformed investigating the powder mixing effect on the compaction/packing of particles [4,8,14]. By adding single-sized fine sand/metal balls into single-sized coarse sand/ metal balls, Westman et al. [4] and McGeary [14] determined that the mixtures have reduced porosity, thus showing better compaction capabilities. For ceramic powders, however, this conclusion may not always be accurate since ceramic powders are quite different. Firstly, the particle size of a ceramic powder is usually much smaller than that of the sand or metal balls. The average particle size of a ceramic powder usually is on the order of submicron/micron, while the size of the sand or metal balls is on the order of millimeter to centimeter [4,8,14]. Secondly, by chemical/physical treatment, some ceramic powders can have much better compaction capability than other ceramic powders even if their material compounds are nearly identical. Thirdly and most importantly, most ceramic powders have a continuous distribution of particles [15]. Finally, due to the small particle size and large surface energy, agglomerations prevail in ceramic powders. Compared to the sand or metal balls, these unique characteristics may result in a unique relationship between the compaction capability and powder mixing for ceramic powders. Therefore, the main focus of the current study is to study the compaction of ceramic powders in relation to the powder characteristic and other mixing details.

2. Materials and experimental procedure ⁎ Corresponding author. Tel.: +1 5173550173; fax: +1 5173539842. E-mail address: [email protected] (P. Kwon). 0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.06.004

In the series of experiments, four high-pure and undoped alumina (Al2 O 3 ) powders with submicron/micron particle sizes were

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Fig. 1. The progression of motions for uniaxial die compaction.

investigated. The four powders were TMDAR (Taimei Chemical CO., LTD., Japan), CR-15, CR-6, and GE-1 (Baikowski Ind. Corp., U.S.A.). The detailed characteristics for the powders are summarized in Table 1. In the selection of the four powders, the study considered CR-15, CR-6, and GE-1, which are all from the same manufacturer, feature near identical chemical components. However, due to the difference in particle size distributions and mean particle sizes, the compaction capabilities of these three powders are quite different. TMDAR, on the other hand, was chosen because it is specially treated, both chemically and physically. Its particle size distribution has a very narrow nonlognormal range and it yields a sintered product with very low porosity. These two characteristics yield the well-known high compaction/sintering capability of TMDAR powder. The particle size distribution for each powder was measured in a water solution by the Malvern Mastersizer Micro (Malvern Instruments, England). The results, presented in Fig. 2, are almost identical to the manufacturer's reports. The size distributions of CR-15, CR-6 and GE-1 are nearly lognormal. The micrographs of the four raw powders were taken and shown in Figs. 3 and 4. The microstructure was observed via Scanning Electron Microscopy (JEOL 6400 V, Japan). The lower magnification micrographs (Fig. 3) show TMDAR contains much fewer agglomerates than the other three powders. The agglomerates of GE-1 are in flake shape while those of CR-15 and CR-6 are in near-spherical shape. Higher magnification micrographs from Fig. 4 show the single particles of each powder. The average size of each powder measured from the micrographs with the software called AnalySIS is consistent with Fig. 2. All possible two-powder combinations with the four powders were mixed in various mass ratios, and in total six powder mixture systems were produced. The mixture systems include TMDAR + CR15, TMDAR + CR-6, TMDAR + GE-1, CR-15 + CR-6, CR-15 + GE-1, and CR-6 + GE-1. In addition to four unmixed powders, each system contains nine powder mixtures, in which the proportions of one powder in the mixtures range from 10% to 90% in 10% intervals. In total, fifty-four powder mixtures were studied. The powders were mixed with Speed Mixer DAC 150 (FlackTek, Inc., USA) for 3 min (1 min for each cycle and totally 3 cycles) at the angular velocity of

1700 rad/s. Six grams of each powder mixture was measured by Adventurer AR 2140 (Ohaus Corp. USA) with a 0.0001 g resolution; and then poured into a single-action die made of 1144 Stress Proof steel. The inner diameter of the die, Din, is 22.19 mm. Before pouring the powders into the die, the die wall was lubricated with graphite powder (Panef Corp., USA). The top surface of the powder was flattened and then the top punch was inserted into the die until it touched the powder. The compaction load was applied on the top punch by MTS Insight 300 (MTS Systems Corp., USA). The speed was 10 mm/min and the stress resolution is 0.013 MPa. During the compaction, only the top punch moved. The compressive forces applied on the top (Ft) and bottom punches (Fb) as well as the displacement of the top punch (Zt) were recorded continuously as a function of time by the load sensors. At first, the pre-load of 0.5 MPa was applied to set an initial state. The preload is necessary to measure the compact characteristics accurately before starting the main compacting process. After pre-loading, the initial height of each sample, hi, was measured. This was done by measuring the total height of the two punches and the pre-loaded compact inside the die, then subtracting the height of the two punches. The measurement was achieved by a Marathon electronic digital caliper with a 0.02 mm resolution and a 150 mm measurement range. Considering the diameter of each compact to be the same as the inner diameter of the die, Din, the initial relative density, Ri, can be calculated by the following equation: Ri =

ρi m = Vi m = = 3:975 ρf ρf 2 4 πDin hi

where m, V, and ρ represent mass, volume, and density, respectively, and the subscripts i and f represent initial and theoretically fully value. The theoretical fully-density of alumina was taken as 3.975 g/cm3. After obtaining the initial relative density, the die set with preloaded compact was put back into the load frame, and then the load of 80 MPa was applied to compact samples. The final green samples produced a diameter of 22.19 mm and their heights ranged from

Table 1 Characteristics of the powders used in this study. Material

Powder name

Smallest particle size (μm)

Largest particle size (μm)

Mean particle size (μm)

Mean pore size (μm)

Alumina

TMDAR CR-15 CR-6 GE-1

0.1 0.17 0.23 3.5

0.33 1.15 1.72 23.9

0.17 0.41 0.60 9.76

0.09 0.18 0.27 0.24

Material

Alumina

Powder name

Chemical analysis (ppm) Na

K

Fe

Ca

Si

Mg

Bulk density (g/m2)

TMDAR CR-15 CR-6 GE-1

4 12 13 12

2 15 22 15

5 3 2 5

3 2 3 2

3 21 14 42

1 b1 b1 b1

0.9 0.45 0.6 0.45

ð1Þ

Fig. 2. Particle size distributions of the powders used in this study.

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Fig. 3. SEM micrographs at lower magnification of the raw powders a) TMDAR, b) CR-15, c) CR-6, and d) GE-1 (Acceleration voltage: 15 kV, Working distance: 15 mm).

Fig. 4. SEM micrographs at higher magnification of the raw powders a) TMDAR, b) CR-15, c) CR-6, and d) GE-1 (Acceleration voltage: 15 kV, Working distance: 15 mm).

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From the calculated ht, similar to calculating the initial relative density, the relative density at time t, defined as Rt, can be found as, Rt =

ρt m = Vt m = = : 3:975 2 ρf ρf 4 πDin ht

ð3Þ

In Eq. (3), the sample diameter was assumed to be matching the inner diameter of the die, Din. The corresponding stress, σt, at time t can be obtained by the punch diameter, Din, and the recorded load, Ft. σt =

Fig. 5. The relative density-stress curves by the compaction for a) CR-15 + TMDAR and b) CR-6 + GE-1.

7.05 mm to 9.1 mm. Thus, the height/diameter ratios of compacts were between 0.3 and 0.4. By keeping a low height/diameter ratio, the transmit force applied on the bottom punch and the applied force on the top punch were almost identical in the compaction. The discrepancy between the two recorded forces was less than 0.2%. The masses of the green samples were measured again after compaction. There was always an expected mass change due to the attachment of powders to the die wall and the punches as well as the powder loss during the transport. However, this change was very small, less than 0.4%, and was neglected. Several green samples were coated with nail polish and then their volumes were measured in water by Archimedes' principle. Those values were then compared to the corresponding volumes calculated by the final sample heights, hf, and diameter, Din. The discrepancies between the two groups of values were minimal, less than 1.1%. Therefore, only the calculated volumes are reported in this investigation.

Ft = St

Ft 2 1 πD in 4

ð4Þ

where St is the cross-sectional area of the top punch. The relative density-stress curves for each powder mixture group were then drawn. Fig. 5a and b shows the representative curves for the TMDAR + CR-15 and CR-6 + GE-1 powder mixture groups, respectively. For clarity, only six curves were included in each figure. Under a constant compaction load or stress, the difference of the relative densities represents the change in the compaction capability in different mixtures. A higher relative density represents improved compaction capability. Even though the absolute relative density values continuously increase with the compaction load, the relationship between the relative density and powder proportions remains similar for each powder mixture group as observed in Fig. 5. Therefore, one can conclude that the starting powder combination determines the compaction capability of each powder mixture. In addition, the initial relative density dictated by the starting powder combination can be used to quantify and compare the compaction capability of each powder mixture. The relationships between the initial relative density and the powder proportion are shown in Fig. 6 for all six powder mixture groups. For each curve, the left end is the 100% of the fine powder and the right end is the 100% of the coarse powder. The “fine” or “coarse” − powder is defined by the average particle size D of the powder. From Table 1, we know     D GE−1 N D CR−6 N D CR−15 N D TMDAR

ð5Þ

Fig. 6 shows two kinds of relationships between the initial relative density and the proportion of the coarse powder. 1) Linear relationship: TMDAR + CR-15 and CR-15 + CR-6 powder mixture groups show this characteristic. The maximum relative density corresponds to 100% of one of the powders.

3. Results and discussion 3.1. Relative density-stress relationship for various powder mixtures By the recorded top punch displacement, Zt, and the initial compact height, hi, or final compact height, hf, the sample height, ht, at time t can be calculate, 

ht = hi − Zt ht = hf + Zt

ðaÞ : ðbÞ

ð2Þ

The ht calculated by Eq. (2) (a) and (b) for any compact was the same. Therefore, two separate measurements, hi and hf, for each compact were for self-consistency.

Fig. 6. The initial relative density — coarse powder proportion for all six powder mixture groups after 0.5 MPa pre-load compaction.

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2) Nearly parabolic relationship: The maximum relative density of some powder groups with this relationship occurs with certain powder mixtures, such as TMDAR + CR-6, CR-15 + GE-1, and CR-6 + GE-1. This is similar to the conclusion of Westman [4] and McGeary [14]. However, the proportions of coarse powder in the powder mixture that attained the maximum relative density are between 40% and 60%. These values differ from the reported 30% by Westman [4] and McGeary [14] for sand and metal balls. Another powder system, TMDAR+ GE-1, has the maximum relative density at 100% TMDAR. 3.2. Relative density-strain relationship for various powder mixtures In the study of ceramic powders' compaction, Aydin et al. [16,17] defined axial true strain ε̄t as the following,   h  ε t = ln t : hi

j

j

strain curves. The relationship exactly fits into the following equation for each powder mixture, Rt = κe

 εt

ð7Þ

where κ has the same unit as density, g/cm3. Eq. (7) shows that a powder mixture with a higher density/compaction capability has a larger κ value. Table 2 displays the κ value for the TMDAR + CR-15 powder mixture group. The values in Table 2 are the same as the corresponding initial relative density values in Fig. 6. This indicates the physical meaning of κ in Eq. (7) is the “initial relative density”. From the relative density and strain definitions in Eqs. (3) and (6) as well as Eq. (1), the conclusion can be verified as below. Ri =

ð6Þ

Fig. 7(a) and (b) shows the representative relative density-strain curves for the TMDAR + CR-15 and CR-6 + GE-1 powder mixture groups, respectively. Comparing Figs. 7 and 5, the powder mixture with better compaction capability/density in Fig. 5 is also with a higher relative density under any strain values in Fig. 7. The Mircocal Origin and Wolfram Mathematica software were employed to calculate the trend functions of the relative density-

231

Rt =

m 3:975 2 πDin hi 4 m 3:975 2 πDin ht 4

g

⇒

1 2 πDin ht Rt h = 4 = t 1 2 Ri hi πD h 4 in i

  h  ε t = ln t hi

j

j

g

⇒Rt = Ri e

 εt

ð8Þ

Therefore, the method to compare compaction capability of various powder mixtures from their relative density-strain curves only needs to consider the initial relative density value. In other words, from either the relative density-stress or the relative densitystrain curves, one can use Fig. 6 to find the difference in the compaction capabilities of powder mixtures. It is important to emphasize that the initial relative density is dependent on the pre-load. For example, when the pre-load reduced to 0.3 MPa, the initial relative density for pure TMDAR was changed to 30.46%. If the stress/strain goes to zero, the initial density goes to the bulk density listed in Table 1. However, even the absolute value of the initial density varies, the relationship between the relative density and strain remains equivalent to Eq. (7) and the order of compaction capability/relative density remains unchanged. 3.3. Prediction of initial relative density versus coarse powder proportion curve shape from the characteristics of powders

Fig. 7. The relative density-strain curves by the compaction for a) CR-15 + TMDAR and b) CR-6 + GE-1.

Since the four powders used are the same material with nearly identical elements, the linear and parabolic types of curves in Fig. 6 may be a result from the difference in the particle size distributions and mean particle sizes. Numerous studies [4,6,14] mentioned that if fine particles can fill into the interstices among coarse particles, then the powder mixture should produce a better compaction capability. In this condition, the total volume does not necessary change with the addition of fine powder(s). This will be stated as a “non-disturbance” condition. For a bimodal discrete sphere size system, the particle size of coarse powder is at least 2.4 times of that of fine powder [16] to make a “non-disturbance” powder mixture. More strictly, the − − condition, D c/D f N 6.5, is required for the non-disturbance mixing − [16,18], where D represents the average particle size and the subscript, c or f, represent coarse or fine powder, respectively. For a continuous size distribution system, the limitation average particle size ratio value is approximately 3.6 [19,20]. If the average particle size ratio is less than 3.6, the fine powder cannot fill into the interstices of the coarse powders. The mixing of the two powders only results in stacking them together mechanically. Therefore, the relative density-powder proportion curve would be linear. Among the powder mixture systems we employed, TMDAR + CR-15 and CR-15 + CR-6 show this trend. The corresponding linear curves in Fig. 6 verify this assumption. However, the agglomerates in some powders (Fig. 2) may influence the pore/particle size and result

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Table 2 The coefficient k in Eq. (7) for each TMDAR + CR-15 powder mixture. CR-15

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

κ (g/cm3)

1.4228

1.3843

1.344

1.29

1.2401

1.1887

1.1296

1.0688

1.0131

0.9622

0.908

in partial filling of fine particles into coarse particles. The agglomerates may be the reason why some parts in those two curves are not perfectly linear. If the average particle size ratio is larger than 3.6, would the mixtures always have better compaction capability than each powder since the fine powder can fill into the interstice of the coarse powders? Based − − on Table 1 and Fig. 6, that will not be true. For example, the Dc/Df of TMDAR+ GE-1 powder mixture group equals 57.4. However, its highest density happens with pure TMDAR. This is due to the large difference in the compaction capabilities of the two powders. The initial relative density difference between TMDAR and GE-1 is as large as 12.1%. This shows that even the TMDAR does fill into the interstices of GE-1; the increase in the compaction capability due to the interstitial filling is negligible compared to the excellent compaction capability of TMDAR. Therefore, the excellent compaction capability of TMDAR dominates the compaction of the mixture, resulting in the highest density with pure TMDAR. For the remaining three mixture groups with parabolic curves shown in Fig. 6, the difference in the initial relative density between two powders ranges from 0.87 to 5.9%. In the three curves, the difference in the relative densities are small enough to be compensated by filling fine powder into the coarse powder, thus producing mixture (s) that have better compaction capability than the two powders. The Maximum Compaction Capability (MCC) occurs at 40-60% proportion of coarse powder, close to the powder with better compaction capability. When the difference in compaction capability between the powders increases, the proportion of powders at MCC shifts closer to the powder with better compaction capability. Once the compaction capability difference between the powders exceeds a threshold, the peak converts to the powder with better compaction capability, as shown in TMDAR + CR-15, CR-15 + CR-6, and TMDAR + GE-1 powder mixture groups. In these three powder mixture groups, the difference in the initial relative density between two powders ranges from 7.1 to 12.9%. Therefore, we considered the threshold should be around 7.1% relative density difference.

boundary for an initial relative density - powder proportion curve. Can the upper boundary also be found? In Westman and Hugill's study [4], the reciprocal of relative density of the compact was used to quantify the compaction capability of various sand mixtures. By assuming the fine powder is infinitesimal, one lower boundary was proposed for the curve, as the CO line in Fig. 8. By assuming a larger ball immersed in the infinitesimal balls/ water, the other lower boundary FN was obtained. The study concluded that the reciprocal of relative density–powder proportion curve should lie in the triangle CFK. Corresponding to Westman and Hugill's idea, the O and N points in Fig. 8 should convert to the maximum initial relative density of the powders in the initial density versus powder proportion curves. To obtain these maximum initial density values, each powder was put into the die set and then the die set was put on a plane sieves vibrator (Thomas Scientific, USA). The frequency of the vibration was set to 60 Hz and the amplitude was set to 4 mm. During the vibration, the particles rearranged to an optimal arrangement. The die set was then moved to the MTS machine and the powders were compacted to the 0.5 MPa pre-load. Fig. 9 shows the dependence of the initial relative

3.4. Discussion about the limiting boundaries of initial relative density– powder proportion curves The discussion above allows us to conclude that the straight line passing through both powders' initial relative densities sets the lower

Fig. 9. The dependence of the initial density on the vibration time for each powder.

Fig. 8. The dependence of the reciprocal of relative density on the proportion of coarse powder and its triangle boundary by Westman et al. [4].

Fig. 10. Triangle boundary for the initial relative density-powder proportion curve of CR-15 + GE-1 powder group.

L. Sun et al. / Powder Technology 195 (2009) 227–234

densities of the four powders in relation to the vibration time. Clearly, as a result of the particle rearrangement caused by the vibration, the initial relative density increases for each powder. The density increases with vibration duration, and converges to a final value. Each final value is considered to be the maximum initial relative density value for the corresponding powder. The lines, FMC and CMf, in Fig. 10, are obtained by connecting the relative density of the fine powder to the maximum relative density of the coarse powder and the relative density of the coarse powder to the maximum relative density of the fine powder, respectively. These two lines will build the upper boundaries for the initial relative densitycoarse powder proportion curve of CR-15 + GE-1 powder mixture group. And the triangle FCK creates the enclosed boundary. Fig. 11 shows the triangle boundaries for TMDAR + CR-6 and CR-6 + GE-1 powder mixture groups. Clearly, as CR-15 + GE-1, each initial relative density versus coarse powder proportion curve in Fig. 11 also lies within the corresponding triangle. 3.5. Discussion about the maximum packing/compaction relative density Brouwers [18] proposed an analytical expression to calculate the void fraction/packing density of continuous particle distribution powders of the lognormal type. The equation is φ = φ1

2   dmax −ð1−φ1 Þβ = ð1 + α Þ dmin

ð9Þ

where ϕ is the void fraction of the powder with continuous particle size distribution, dmax and dmin represent the maximum and minimum particle sizes, respectively. ϕ1 is the void fraction of assumed uniformly sized particles with the average particle size, α is the distribution modulus, and β is the scaled gradient of the void fraction. Commonly, both ϕ1 and β can be set as constant, and in Brouwers' study ϕ1 = 0.5 and β = 0.35 for fairly angular quartz. The distribution modulus α is typically between 0 and 0.37 and when α equals 0, the maximum packing fraction is obtained. Following the Brouwers' parameter setting of ϕ1 and β, the range of maximum relative packing densities of each powder was calculated, as presented in Table 3. To attain the maximum compaction density from the experiments, 3 g of each powder was vibrated for 150 min and then compacted to 220 MPa. After 180 MPa compaction, the relative densities were convergent to maximum values. Those experimental maximum relative densities are also listed in Table 3. For CR-15, CR-6, and GE-1 powder, the experimental values are less than the calculated values.

233

Table 3 The maximum relative packing density calculated by Brouwers' equation and from the experiments.

Calculated results Experimental results

α=0 α = 0.37 150 min vibration

TMDAR

CR-15

CR-6

GE-1

59.4% 58.4% 59.8%

64.2% 62.7% 52.5%

64.9% 63.3% 53.3%

64.3% 62.8 52.7%

Two reasons contribute to the lower experimental results, 1) the ϕ1 and β may not be exact for our powders, and 2) the agglomerates presented in the powders and the non-perfect spherical-shaped powder particles [15]. However, the order of the relative density/ compaction capability among these three powders is the same in both the calculation of Brouwers' equation and the experiments. From this point, the Brouwers' equation has an excellent potential for predicting the compaction capability of various powders. Contrary to CR-15, CR-6, and GE-1 powders, the experimental result for TMDAR is larger than the calculated result. As mentioned before, Brouwers' equation is suitable for the powder systems with lognormal particle distribution. However, the particle size distribution of TMDAR is not lognormal. Thus, the Brouwers' equation is not suitable to calculate its compaction capability. The non-lognormal size distribution powder systems have increased maximum packing fractions than lognormal distributed powders [15]. Thus, the compaction capability of TMDAR is improved compared to the other three powders. Therefore, when using Brouwers' equation to evaluate the compaction capability of powders, the particle size distribution of each powder should be lognormal.

4. Conclusions Several groups of powder mixtures were produced by mixing four alumina powders. After investigating their compact density versus stress and strain relationships, the initial relative density was determined to be appropriate for quantifying the compaction capability of each powder mixture. The powder mixing process changes the compaction capability of the powder mixtures. The shape of the initial relative density versus proportion of coarse powder curve depends on the ratio of average particle size, and the difference in the initial density of two powders. If the average particle size ratio is less than 3.6, or the average particle size ratio is larger than 3.6 but the initial relative density different is higher than 7.1%, the curve is linear. If the average particle size ratio is larger than 3.6 and the initial relative density difference is smaller than 7.1%, the curve is parabolic. The triangle enclosed by the line intersecting the relative density of the fine powder and the maximum relative density of the coarse powder, the line intersecting the relative density of the coarse powder and the maximum relative density of the fine powder as well as the line connecting the relative density of the fine and coarse powder form the boundary of the initial relative density-proportion of coarse powder curve. The experimental results also show Brouwers' equation has excellent potential for comparing the compaction capability of different powders with lognormal particle size distribution.

Acknowledgement

Fig. 11. Triangle boundaries for the initial relative density-coarse powder proportion curves of TMDAR + CR-6, CR-6 + GE-1 powder groups.

The authors would like to acknowledge Dr. Les Lee at AFOSR for supporting this work under the Contract Number F49620-02-1-0025. We also would like to thank Jacob Kloss and Sam Baldauf for their help in part processing. The authors also would like to express their gratitude towards Mr. Michael Rich and Mr. Brian Rook at Composite Materials and Structures Center of Michigan State University for the helpful discussion.

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