Science of Sintering, 41 (2009) 125-133
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doi: 10.2298/SOS0902125B
UDK 622.785:546.281'261
Design of Experiment Approach for Sintering Study of
Nanocrystalline SiC Fabricated Using Plasma Pressure
Compaction
M. G. Bothara1, P. Vijay2, S. V. Atre1, S.-J. Park3*), R. M. German4,
T. S. Sudarshan5 , R. Radhakrishnan5
1
ONAMI, Oregon State University, 106 Covell Hall, Corvallis, OR 97330
Indian Institute of Technology, Kanpur, India
3
CAVS, Mississippi State University, Starkville, MS 39762
4
San Diego State University, San Diego, CA
5
Materials Modification Inc., Fairfax, VA 22031
2
Abstract:
Plasma pressure compaction (P2C) is a novel sintering technique that enables the
consolidation of silicon carbide with a nanoscale microstructure at a relatively low
temperature. To achieve a high final density with optimized mechanical properties, the effects
of various sintering factors pertaining to the temperature–time profile and pressure were
characterized. This paper reports a design of experiment approach used to optimize the
processing for a 100 nm SiC powder focused on four sintering factors: temperature, time,
pressure, and heating rate. Response variables included the density and mechanical
properties. A L9 orthogonal array approach that includes the signal-to-noise (S/N) ratio and
analysis of variance (ANOVA) was employed to optimize the processing factors. All of the
sintering factors have significant effect on the density and mechanical properties. A final
density of 98.1% was achieved with a temperature of 1600 °C, hold time of 30 min, pressure
of 50 MPa, and heating rate of 100 °C/min. The hardness reached 18.4 GPa with a fracture
toughness of 4.6 MPa√m, and these are comparable to reports from prior studies using
higher consolidation temperatures.
Keywords: Nanocrystalline silicon carbide (SiC), Plasma Pressure Compaction (P2C),
Design of Experiment
1. Introduction
Silicon carbide (SiC) is used for applications in severe high temperature and high
stress conditions. It was accidentally synthesized by E.G. Acheson in 1891 [1]. Since then,
SiC has been applied because of its high hardness and strength, high thermal and electrical
conductivities, low coefficient of thermal expansion, and outstanding resistance to oxidation
and corrosion. The resulting applications range from abrasive to heating elements [2].
The usefulness of SiC is limited by its low degree of sinterability. The characteristics
of raw SiC powder have significant effects on the sintering response. To obtain a high
_____________________________
*)
Corresponding author: [email protected]
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densification rate at low sintering temperature, modern sintering technology requires small
particles to enable sintering [3]. Powders with small finer particle sizes have a benefit in a
lower sintering temperature and shorter sintering time. Further, sintering additive contents are
reduced with smaller particle sizes. This results in enhancement of properties such as
increased fracture toughness and higher strength at room temperature as well as high
temperature, tailorable electrical resistivity, enhanced wear resistance, and increased ductility
and greater superplasticity at high temperatures [4]. Enhanced properties are desired not only
for existing products such as armor, engine components, tool bits, and furnace heaters, but
also for several potential applications like power electronic packaging and advanced
microsystems in nuclear power generation [5].
In conventional processes, long sintering time is required to achieve full densification
with concomitant detriments due to grain growth. Novel processing techniques are required to
achieve full density while minimizing grain growth. Plasma pressure compaction (P2C) [6]
involves resistive heating of the powder compact by passing electric current through it. This
resistive heating is rapid (10 to 1000 °C/s), which when combined with pressure (~20 MPa)
results in full densification and minimal grain growth.
Sintering depends on the powder characteristics, as well as the additives and process
parameters such as sintering temperature, time, pressure, and heating rate, including the
potential for liquid phase sintering. This complexity further increases with the P2C technique
since it brings in new attributes from the electrical discharge specifics.
This study identifies the optimal processing conditions for sintering of nanocrystalline
SiC using the P2C system. Since there is little prior experience, mathematical models based on
statistical regression techniques are used to construct the processing conditions. Accordingly,
a P2C set of experiments are conducted using the Taguchi method to guide the experimental
design. This method is a simple, efficient, and generates a systematic approach optimization.
The effects of four sintering factors – namely, temperature, time, pressure, and heating rate –
are given with respect to density, hardness, and fracture toughness. The signal-to-noise (S/N)
ratio and the analysis of variance (ANOVA) techniques are used to calculate the contributions
of each of the processing parameters to the output characteristics.
2. Design of Experiment
The traditional approach to experimental work is to vary one factor at a time, holding
all other factors fixed. This method does not produce satisfactory results in a wide range of
experimental settings as the number of runs required for full factorial design increases
geometrically with the number of experimental variables. Fractional factorial design is
efficient and significantly reduces the number of runs and the time required to do the study.
We selected Taguchi’s method as design of experiment (DOE) approach. Taguchi’s method,
derived from the fractional factorial methods, is a robust statistical technique of proven
reliability [7]. It is economical as fewer experiments than the one-variable-at-a-time technique
are needed and the results can be associated with a statistical level of confidence. Hence, this
method is more flexible and more versatile than the classical DOE technique [8]. The Taguchi
method consists of a series of steps which when sequentially followed leads to an improved
understanding of the product or process. These steps include the selection of the appropriate
orthogonal array with given control factors, conducting the experiments, collecting the data,
and analyzing the experimental results. The orthogonal array is selected based on such factors
as the degree of influence, the interactions, desired resolution, and available resources.
Four parameters are considered here, temperature, time, pressure, and heating rate,
while the interactions between the factors were negligible with the L9 orthogonal array. Each
factor was designed with three levels that were selected based on a series of pretests. The
factors along with their levels are listed in Tab. I.
M.G. Bothara et al./Science of Sintering, 41 (2009) 125-133
127
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Tab. I Design of control factors for Taguchi Analysis
Factor
Level 1
Sintering Temperature (°C)
1600
Holding Time (min)
0
Sintering Pressure (MPa)
10
Heating Rate (°C/min)
20
Level 2
1700
30
30
60
Level 3
1800
60
50
100
The L9 orthogonal array was used to arrange the experimental trials, as shown in Tab. II. This
configuration required the minimum number of runs for experimental exploration [7].
Tab. II L9 orthogonal array for Taguchi Analysis
Factor A
Factor B
Exp
Sintering Temperature
Holding time
ID
(°C)
(min)
1
1600
0
2
1600
30
3
1600
60
4
1700
0
5
1700
30
6
1700
60
7
1800
0
8
1800
30
9
1800
60
Factor C
Pressure
(MPa)
10
50
30
30
50
10
30
10
50
Factor D
Heating Rate
(°C/min)
20
100
60
60
20
100
100
60
20
3. Experiment Procedure
After the identification of the orthogonal array, the experiments were conducted
according to Tab. II The output characteristics were measured, including density, hardness,
and fracture toughness. Details for these experimental methods are given below.
3.1 Material Preparation
A small α-SiC powder (Fujimi Co., Grade GC 30000, Japan) with average particle
size 70 to 90 nm was used for the experiments. The tap density and the pycnometer density
for this powder are 0.85 g/cm3 and 3.2 g/cm3, respectively. Sintering aids included AlN
(Nanostructured Ceramics) and Y2O3 (Nanostructured Ceramics) with particle sizes of 10-20
nm and 32-36 nm, respectively. The α-SiC with 5 wt.% AlN and 5 wt.% Y2O3 powders was
mixed for 24 h using a rotary mill. ZrO2 pellets were used as the milling media.
The milled powder was poured into a graphite die with an inner diameter of 25 mm.
A thin graphite foil separated the powder compact from the inner surface of the graphite die.
The graphite die containing the powder mixture was cold compacted using a uniaxial pressure
of 50 MPa to give a green density of around 35 %.
3.2 Plasma Pressure Compaction
The powder mixture was cold pressed in the graphite dies and sintered in the P2C
system. All the samples were first heated to 900°C for 5 min to ensure uniform temperature.
The temperature was measured by focusing an infrared thermometer on the graphite die
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through a sapphire window. During the isothermal hold at 900°C for 5 min, the pressure on
the graphite die was applied at 10 MPa, after which it was set at the specified level, 10, 30, or
50 MPa, for the remainder of the thermal cycle. The samples were heated from 900°C to the
desired sintering temperature with the predetermined heating rate and held there for a
predetermined sintering time. All the runs were conducted in flowing N2 atmosphere. After
this the power was removed, resulting in a cooling rate near 45°C/min. Nine runs were
conducted as listed in Tab. II.
3.3 Characterization
Density: The density was measured using the Archimedes method and calculated as a
percentage of the theoretical value of 3.26 g/cm3.
Microstructure: The samples were prepared for microstructural and mechanical
characterization by standard metallographic methods. They were diamond ground to ~50 μm
surface finish and then polished to 1 μm finish using a diamond paste. Subsequent etching in
CF4 – 10 % O2 plasma for 20 min selectively etched the grain boundaries for observation. The
grain morphology was observed using scanning electron microscopy (SEM). The line
intercept method was used to measure the mean intercept length from the SEM images as per
ASTM E112. A multiplication factor of 1.56 was used to calculate the mean threedimensional grain size [9]. Three images were analyzed for each sample and the average
values are presented here.
Hardness: Vickers hardness was measured per ASTM E384 using a Leco
microhardness tester. A load of 500 g was used to make the indentations. A NIST traceable
calibration steel block and a stage micrometer were used to calibrate the microhardness tester
prior to the hardness measurements.
Fracture Toughness: Fracture toughness was measured by the indentation method
[10] with a load of 1000 g. The hardness and toughness values reported here were averaged
over ten measurements.
4. Results
Density, hardness, toughness, and mean grain size were measured for the nine
fabricated using P2C under the conditions determined by the orthogonal array in Tab. II.
These values and their standard deviations are listed in Tab. III and the variations with the
processing factors are discussed below.
Tab.III The output characteristics based on the L9 orthogonal array.
Output Characteristics
Exp
Std
HV
Std
KIC
ID Density Grain Size
(%)
(μm)
Dev
(GPa)
Dev
(MPa√m)
1
62.5
–
–
2.1
0.2
1.9
2
98.1
0.73
0.02
18.4
0.4
4.6
3
99.8
0.72
0.03
21.1
1.3
4.6
4
100.0
0.70
0.01
21.5
0.9
5.3
5
99.8
0.64
0.04
23.1
0.6
5.4
6
98.4
0.70
0.05
19.6
0.3
4.8
7
99.1
0.72
0.02
18.2
0.2
4.8
8
99.7
0.81
0.02
18.1
1.0
4.8
9
99.0
0.85
0.04
19.3
0.6
4.4
Std
Dev
0.1
0.4
0.4
0.6
0.1
0.3
0.3
0.4
0.5
M.G. Bothara et al./Science of Sintering, 41 (2009) 125-133
129
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4.1 Density
Most of the SiC samples sintered in this study were > 98% dense. The sample
sintered at 1600°C with no hold time was only 62% dense. Traditional sintering techniques,
such as pressureless sintering, hot pressing ,or hot isostatic pressing, have been used to obtain
fully dense samples of SiC [11-12]. Various combinations of sintering aids such as B, C, Al,
Al2O3, AlN, Y2O3, and rare earth oxides have been used in the prior work [11-20], resulting in
a sintering temperature generally quoted between 1750 and 2100°C.
This study consolidated nanocrystalline SiC to full density near 1600°C with a hold
time of 30 min. This is attributed to the novel P2C sintering technique. It is speculated that
interparticle sparking breaks down surface oxide film [6], exposing active surfaces with a
greater propensity for densification. The spark induced fast heating suppresses low
temperature microstructure coarsening, thereby resulting in little grain growth. For
temperatures over 1600°C, more than 98% density was achieved in 30 min while at 1700°C, a
fully dense sample resulted for no hold time, which meant that the power was turned off as
soon as the sample reached 1700°C. This caused the cycle time of the sintering run to be very
short as compared to the traditional sintering techniques [11-20].
4.2 Microstructure
The mean grain size results are given in Tab. III, varying from 640 to 850 nm. The
microstructure of the SiC samples consisted of equiaxed SiC grains with a solidified remenant
of the liquid phase between the grains.
1600 °C, 30 min
50 MPa, 100 °C/min
1600 °C, 60 min
30 MPa, 60 °C/min
1µm
1µm
(a) Exp ID 2
(b) Exp ID 3
1700 °C, 0 min
30 MPa, 60 °C/min
1µm
(c) Exp ID 4
1800 °C, 0 min
30 MPa, 100 °C/min
1µm
1700 °C, 30 min
50 MPa, 20 °C/min
1700 °C, 60 min
10 MPa, 100 °C/min
1µm
(d) Exp ID 5
1800 °C, 30 min
10 MPa, 60 °C/min
1µm
(e) Exp ID 6
1800 °C, 60 min
50 MPa, 20 °C/min
1µm
(f) Exp ID 7
(g) Exp ID 8
(h) Exp ID 9
Fig. 1 SEM images for the SiC samples prepared based on the L9 orthogonal array.
1µm
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The liquid phase was uniformly distributed in the microstructure. Fig. 1 shows the
micrographs from the eight samples reached 98% density. Sample 1 reached only 62%
density and was not suitable for microstructure analysis.
4.3 Mechanical Properties
Tab. III shows the hardness ranged from 18 to 23 GPa when the density exceeded
98%, while the toughness ranged from 4.4 to 5.4 MPa√m. These are comparable to literature
values for SiC [11-20]. Thus, dense SiC samples with excellent properties were realized at
150°C below the typical sintering temperature reported in literature. Both, the hardness and
the toughness, did not show a large variation within the range of processing parameters
investigated here.
4.4 Analysis of Variation
The analysis of variance (ANOVA) from the results included the calculation of the
signal-to-noise (S/N) ratio and the contribution.
S/N Ratio
The S/N ratio is the statistical quantity representing the power of a response signal
divided by the power of the variation (noise) in the signal. The S/N ratio is derived from the
loss function and assumes different forms depending on the optimization objective. Since
maximization of the properties was the goal of this study, the equation depicting the “largerthe-better” was used for the analysis here. Thus, S/N ratios for the larger-the-better were
calculated from the following equation [133]
⎡1 ⎛ 1
S
1
1
= − 10 log 10 ⎢ ⎜⎜ 2 + 2 + 2
N
y 2 y3
⎢⎣ 3 ⎝ y1
⎞⎤
⎟⎥
⎟
⎠ ⎥⎦
(1)
where the denominator is the number of runs with the same level of a particular factor and yi
is the measured property for these runs. Tab. IV gives the S/N ratios for the four factors at
different levels for each of the outputs, i.e. the relative density, the hardness and the fracture
toughness.
Tab. IV The S/N ratios for the four factors for each of the output characteristics
Output
Factor
Level 1
Level 2
Level 3
A
38.14
39.95
39.94
B
38.16
39.93
39.92
Relative Density
C
38.14
39.93
39.97
D
38.16
39.87
39.99
A
11.28
26.55
25.35
B
11.28
25.81
26.00
Hardness
C
11.27
25.81
26.06
D
11.29
25.44
26.04
A
9.07
14.23
13.36
B
9.26
13.80
13.24
Fracture Toughness
C
9.16
13.80
13.76
D
9.17
13.50
13.76
M.G. Bothara et al./Science of Sintering, 41 (2009) 125-133
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Temp Time
Rate
Pr
Temp Time
Pr
Rate
14
40
S/N Hardness
S/N Relative Density
It indicates the S/N ratio at each level of the control factor and how it was changed when
settings of each control factor were changed from Level 1 to Level 2 to Level 3.
Note that the factor levels that minimize the sensitivity to noise in the measured
quantity are shown shaded.
The factor levels with the largest S/N ratios were the optimum levels as they
minimized the sensitivity over the range of noises. These are shown shaded in Tab. IV. Fig. 2
gives a graphical representation of the S/N ratios.
39
12
10
38
1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3 1 2 3
Factor Levels
Factor Levels
(a) relative density
(b) hardness
S/N Toughness
Temp Time
Pr
Rate
25
20
15
10
1 2 3 1 2 3 1 2 3 1 2 3
Factor Levels
(c) fracture toughness
Fig. 2 S/N ratios of all the four factors for each of the measured properties, (a) relative
density, (b) hardness and (c) fracture toughness, of the nanocrystalline SiC parts.
Optimal testing conditions for these control factors can be determined from these
response graphs. The graphs show the change of the S/N ratio when the setting of the control
factor was changed over levels. The best density value was at the higher S/N values in the
response graphs. Thus, the optimum combination of factors for relative density was
combination of A2, B2, C3, and D3 corresponding to 1700°C, 30 min, 50 MPa, and
100°C/min. Similarly, over the range examined here, the optimum combination for the
hardness was combination of A2, B3, C3, and D3 (1700°C, 60 min, 50 MPa, and 100°C/min),
and for the fracture toughness it was combination of A2, B2, C2, and D3 (1700°C, 30 min, 30
MPa, and 100°C/min).
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Contribution
Contribution (%)
The ANOVA also provide the effects of each of the four processing factors on the
output characteristics with rank, which is called the contribution. This is the statistical
treatment most commonly applied to the results of the experiment to determine the percent
contribution of each factor. Study of the ANOVA table for a given analysis helps to determine
which of the factors need control and which do not. All factors affect the measured properties
significantly. Figure 3 gives the plot for percentage contribution of each factor to the relative
density, the hardness and the fracture toughness.
Density
Hardness
Tougness
30
20
10
0
Temp Time
Pr
Rate
Fig. 3 Percentage contribution of each of the factors to the measured properties is plotted.
All the factors show significant contribution towards all the properties. The four
factors temperature, time, pressure, and heating rate contribute almost equally (~25%) to the
variation in the density and the hardness. For the fracture toughness, the contribution of the
sintering temperature was marginally greater than the contribution of the other three factors.
5. Conclusion
Nanocrystalline SiC consolidated using plasma pressure compaction (P2C) reaches
98.1% density with a sintering temperature of 1600°C, hold time of 30 min, pressure of 50
MPa, and heating rate of 100°C/min. The resulting 18.4 GPa hardness and 4.6 MPa√m
fracture toughness were comparable to prior reports for SiC sintered at much higher
temperature. The dense microstructures consisted of equiaxed SiC grains interspaced by the
remnants of the liquid phase formed by the sintering aids, AlN and Y2O3. The grain size was
on the order of 750 nm for most of the samples.
Using this experiment design approach, four processing variables, temperature, time,
pressure, and heating rate, were optimized to maximize the final density, hardness, and
fracture toughness. A L9 orthogonal array was used to arrange the processing factors around
three levels each. Signal-to-noise (S/N) ratios were calculated and used to determine the
optimum conditions for each output characteristic. Analysis of variance (ANOVA) showed
that all four sintering parameters were significant with respect to density, hardness, and
fracture toughness. The contribution of all the four factors to the variation in the measured
properties was equal, at about 25%. Hence, it was concluded that all the four factors needed to
be controlled while processing nanocrystalline SiC using P2C. Future studies need to expand
the orthogonal array used here needs to sense interactions between the various experimental
variables.
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References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
W. D. G. Boecker, Ceramics Forum International, 74 (5) (1997) 244.
C. K. Narula, Ceramic Precursor Technology and Its Application, Mc-Graw-Hill,
New York, 1995.
T. A. Ring, Fundamentals of Ceramic Powder Processing and Synthesis, Academic
Press, San Deigo, 1996.
I-W. Chen, L. A. Xue, J. Am. Ceram. Soc., 73 (1990) 2585.
T. Hinoki, A. Kohyama, Annales de Chemie: Science des Materiaux, 30 (2005) 659.
T.S. Srivatsan, B.G. Ravi, M. Petraroli, T.S. Sudarshan, International Journal of
Refractory Metals and Hard Materials, 20 (2002) 181.
P. J. Ross, Taguchi Techniques for Quality Engineering, Mc-Graw-Hill, New York,
1989.
D. C. Montgomery, Design and Analysis of Experiments, 3rd Edition, Wiley, New
York, 1991.
M. I. Mendelson, J. Am. Ceram. Soc., 52 (1969) 443.
K. Niihara, R. Morena, D. P. Hasselman, J. Mater. Sci., 1 (1982) 13.
H. Riedel, B. Blug, Multiscale Deformation and Fracture in Materials and
Structures, Kluwer Academic Publishers, Netherlands, (2000) 49.
C. Greskovich, J. H. Rosolowski, J. Am. Ceram. Soc., 59 (1976) 336.
V.A. Izhevskyi, A. H. A. Bressiani, J. C. Bressiani, J. Am. Ceram. Soc., 88 (2005)
1115.
G. E. Hilmas, T. Y. Tien, J. Mater. Sci., 34 (1999) 5605.
M. A. Mulla, V. D. Kristic, J. Mater. Sci., 29 (1994) 934.
J. J. Cao, W. J. MoberlyChan, L. C. De Jonghe, C. J. Gilbert, R. O. Ritchie, J. Am.
Ceram. Soc.,
(1996) 461.
H. Tanaka, Y. Zhou, J. Mater. Res., 14 (1999) 518.
Y. Zhou, H. Tanaka, S. Otani, Y. Bando, J. Am. Ceram. Soc., 82 (1999) 1959.
D. H. Kim, C. H. Kim, J. Am. Ceram. Soc., 73 (1990) 1431.
Y. W. Kim, M. Mitomo, T. Nishimura, J. Am. Ceram. Soc., 85 (2002) 1007.
L. Lu, B. W. Chua, M. O. Lai, R. M. Johar, Mater. Sci. Forum, 360-362 (2001) 615.
Садржај: Компресија плазма притиском (P2C) је нова техника синтеровања која
омогућава згушњавање силикон карбида са нано микроструктуром на релативно
ниској температури. Карактерисани су утицаји различитих фактора синтеровања у
односу на профил температура-време и притисак у циљу добијања велике финалне
густине са оптималним механичким својствима. У овом раду описан је
експериментални приступ који је коришћен за оптимизацију обраде SiC праха величине
100 нм и био фокусиран на четири фактора синтеровања: температура, време,
притисак и брзина загревања. Променљиве су укључивале густину синтеровања и
механичка својства. Примењен је приступ L9 управне матрице укључујући
сигнал/сметње (S/N) однос и анализу варијансе (ANOVA) на оптимизацију фактора
обраде. Сви фактори синтеровања су имали значајан утицај на густину и механичка
својства. Финална густина од 98.1% је добијена на температури од 1600оС, време
држања од 30 мин, притисак од 50 МРа и брзину загревања од 100оС-мин. Тврдоћа је
достизала 18.4 GPa са отпорношћу на лом од 4.6 MPa√m и ово је упоредљиво
резултатима других истраживања на вишим температурама консолидације.
Кључне речи: Нанокристални сликон карбид, компресија плазма притиском,
пројектовање експеримента