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A low-temperature high-strain-rate formable nanocrystalline superplastic ceramic
Scripta Materialia 56 (2007) 1103–1106 www.elsevier.com/locate/scriptamat
A low-temperature high-strain-rate formable nanocrystalline superplastic ceramic Dustin M. Hulbert, Dongtao Jiang, Joshua D. Kuntz, Yasuhiro Kodera and Amiya K. Mukherjee* Department of Chemical Engineering and Materials Science, University of California, One Shields Avenue, Davis, CA 95616, USA Received 23 January 2007; revised 2 February 2007; accepted 2 February 2007 Available online 11 April 2007
A fully dense nanocrystalline ceramic consisting of ZrO2, Al2O3 and MgAl2O4 was deformed at 1150 C at a strain rate on the order of 102 s1. Spark plasma sintering was used in this study as a means of consolidation as well as for subsequent superplastic deformation. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ceramics; Nanocomposite; Superplasticity; Low-temperature deformation; Spark plasma sintering
Nanostructured materials is an exciting area of materials research because bulk materials with grain sizes less than 100 nm exhibit novel mechanical and physical properties as compared with their microcrystalline counterparts. Nanostructured ceramic materials, in particular, are attractive because of their intrinsic strength at high temperatures, their chemical inertness (as compared with metals) and their resistance to erosion and abrasion. What they lack, however, is fracture toughness and machinability to a desired shape. The fracture toughness issue is being addressed and some exciting advances have been made in recent years [1,2]. The machinability issue is difficult to solve because, given the nature of atomic bonding and large interatomic forces, structural ceramics are quite brittle during machining operations. Often such operations give rise to surface cracks that act as sites for flaws and their propagation, ultimately leading to failure under loadcarrying service conditions. This manuscript points to another avenue, namely using superplasticity as a mechanism for arriving at a desired shape, but by using a distinctly different forming environment (within a pulsing electric field) that enables the operation to be conducted at vastly lower forming temperature and at a significantly higher strain rate [3–5].
* Corresponding author. Fax: +1 7530083; e-mail: akmukherjee@ ucdavis.edu
Superplasticity in ceramics has been studied since the first observation of fine-grain superplasticity in yttriastabilized tetragonal zirconia (YSTZ) by Wakai et al. in 1986 [6]. Since then a number of fine-grained ceramics have also demonstrated superplasticity [7,8]. However, the strain rates for optimal superplastic ductility in these investigations were rather low, i.e. on the order of 105 s1. High-strain-rate superplasticity (HSRS) is usually referred to as the demonstration of ductility at a strain rate of 102 s1 or higher [9]. Historically, HSRS was exhibited in metallic systems as early as 1988 [10]. HSRS in ceramic systems was not observed until 2000, when Kim et al. reported HSRS in a ceramic composite consisting of 30 vol.% a-Al2O3, 40 vol.% YSTZ and 30 vol.% MgAl2O4 (AZM), and with an impressive strain rate of 1 s1 [11]. If superplasticity is, indeed, at work in the aforementioned material system, then one would expect grain-boundary sliding (GBS) to be the rate-limiting process during deformation [12]. Because GBS involves the relative motion of individual grains, cavities will form at grain boundary (GB) ledges and triple points unless the stresses that nucleate and grow these cavities are accommodated. Without an accommodation mechanism, a large, uniform macroscopic strain cannot be realized in the material. By reducing the grain size, the stress concentration due to GBS is reduced. Also, the GB length over which atomic transport has to take place in order to accommodate the stress concentration due to GBS is reduced. Under these circumstances, the optimal strain rate for superplasticity
1359-6462/$ - see front matter 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2007.02.003
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D. M. Hulbert et al. / Scripta Materialia 56 (2007) 1103–1106
may be increased and optimal temperature may be reduced since the shorter length scales will allow for easier and more complete diffusional accommodation [13]. In the present work, the investigators strive to lower the HSRS deformation temperature to levels that would be commercially attractive, while still retaining the economic viability of HSRS. This was achieved by using spark plasma sintering (SPS) equipment to further enhance the kinetics of superplastic deformation process by taking advantage of the enhanced atomic transport rates garnered by the pulsing electric field found in the SPS chamber [14–16]. The starting materials were commercially available nano-sized powders: c-Al2O3 (Nanotechnologies, Austin, TX), with 15–20 nm particle size; MgO (Nanopowder Enterprises Inc., Piscataway, New Jersey), with 40 nm particle size; and tetragonal ZrO2 stabilized with 3 mol.% Y2O3 (Tosoh, Tokyo, Japan), with 24 nm particle size. The c-Al2O3 was subjected to high-energy ball milling (HEBM) for 24 h (using a SPEX 8000 mixer mill, in a WC vial with an 11 mm diameter WC ball) before 1 wt.% polyvinyl alcohol (PVA) was added as a dry milling agent to prevent severe agglomeration. Milling was followed by a 350 C heat treatment in air to burn off the PVA. The HEBM c-Al2O3 was then ball mixed with the ZrO2 and MgO using zirconia media (50–50 solid loading) in ethanol for 24 h. The mixed powder was dried, crushed using an alumina mortar and pestle and sieved (150 lm) before being pressed into a 19 mm diameter graphite die and sintered using a Dr. Sinter1050 SPS system (Sumitomo Coal Mining Company, Ltd.) under vacuum. After applying a pressure of 63 MPa, samples were heated from room temperature to 600 C in 5 min and then ramped to 1150 C in 2 min, this temperature being held for 3 min before turning off the power. Temperature was monitored by focusing an optical pyrometer on a hole that was drilled nearly through the die adjacent to the specimen. The same parameters above were used for SPS forming experiments except pressure was kept at less than 18 MPa until the maximum temperature was reached. Upon reaching 1150 C, the pressure was raised to 105 MPa over a time span of approximately 30 s. The dimensions of the radially symmetric punch used to form the AZM are as follows: the tooth-to-tooth distance measured from center to center is 4 mm, the depth of each tooth is 1 mm from trough to tip and the angle of incline of the teeth is 45. Densities were measured using the Archimedes’ method. Microstructural observation was carried out using a field emission high-resolution scanning electron microscopy (SEM). Grain sizes were estimated from SEM analysis and energy-dispersive spectroscopy was used to identify individual grains. Phase identification was done using X-ray diffraction (XRD) with Cu Ka radiation using a stepping scan with 0.01 per step. The as-sintered microstructure and XRD pattern are shown in Figures 1 and 2, respectively. The final density was 99.8% of the theoretical density of the composite (4.696 g cm3). From the SEM image of the as-sintered specimen (Fig. 1) the grain size was approximated to be 100 nm with an equiaxed grain morphology.
Figure 1. Scanning electron fractograph of the AZM composite microstructure after SPS at 1150 C for 3 min. The grains are equiaxed and approximately 100 nm in size.
Figure 2. XRD pattern of the as-sintered AZM compact. The MgO and Al2O3 reacted to form the intended MgAl2O4 phase. In addition, the c-Al2O3 transformed to a-Al2O3.
The XRD pattern (Fig. 2) shows that the MgO and Al2O3 reacted as planned, and formed the intended MgAl2O4 phase without leaving an excess of unreacted magnesia. What is further apparent from Figure 2 is that the c-Al2O3 transformed to a-Al2O3. Lastly, one notes the relatively broad peaks in Figure 2, which are due to the nanoscale grain size of the constituent phases. So far all of the superplastic deformation in the AZM system has been conducted inside a standard resistive heating type furnace. An intriguing question would be: ‘‘What would happen if the deformation of the AZM composite were to take place inside the SPS equipment?’’ Perhaps a better question would be: ‘‘Why not use the SPS equipment as a forming tool as well?’’ One immediate and obvious benefit of using the SPS equipment to perform superplastic deformation is the rapid process cycling time. Because the heating and cooling rates are so rapid, the specimen is at elevated temperature for only a short while, typically less than 5 min. This means that grain growth can be minimized while avoiding other microstructural instability issues associated with long exposures at high temperatures. Additionally, the pulsing DC electric field and spark plasma effect may have a beneficial role in enhancing superplasticity, resulting in surface activation of individual grains, field-assisted diffusion at grain surfaces and enhanced ion diffusion through an electron wind [14– 17]. Because nanoscale materials have so many diffusive pathways along grain boundaries and because the grain surface to volume ratio of such systems is so large, it seems reasonable that a synergism exists between SPS
D. M. Hulbert et al. / Scripta Materialia 56 (2007) 1103–1106
1105
Figure 3. The image on the left shows the dense AZM ceramic as sintered. The image in the middle shows the part formed at a record-setting low temperature of 1150 C and at very respectable strain rate of 2 · 102 s1. The image on the far right shows a sectioned quadrant of the formed specimen to better show the extent of deformation. The fine markers in all images are in millimeters, the numbers in centimeters.
forming operations and diffusive transport along grain boundaries in materials with ultrafine grains. Figure 3 provides evidence of such a synergism. The AZM specimen shown below was formed at 1150 C and at a strain rate of approximately 1.4 · 102 s1. In this case the normal forming strain rates were approximated in the SPS apparatus by dividing the original thickness of the specimen by the slope of the displacement vs. time plot shown in Figure 4. Strain rates were modeled and cross-checked in the SPS by using the somewhat more realistic relationships set forth in Eqs. (1) and (2). pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2 a2 þ x2 þ aÞ 3a ð1Þ e¼ 3a where e is the total true strain and a and x are shown in Figure 5. By taking the derivative of x with respect to time, the strain rate can be calculated as follows: e_ ¼
2_x qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3a 1 þ ax
ð2Þ
Here e_ is the true strain rate and x_ is the displacement rate given by the slope of Figure 4. The true strain rate is at a maximum value when x = a, resulting in a calculated strain rate of 2.7 · 102 s1. This value is well within the same order of magnitude as the value obtained when dividing the deformation rate by the original thickness of the specimen. The time from when the 99.8% dense AZM blank was placed into the SPS chamber to the time when the complex shape was held in hand was about 30 min. This represents, to our knowledge, the first time a dense ceramic blank has been formed into a complex shape at commercially attractive temperatures and strain rates.
Displacement and Displacement Rate vs. Time 3 Displacement (mm) 0.5
2.5
Displacement Rate
2 0
1.5 1
-0.5
0.5
0.05 mm/sec
-1
Displacement (mm)
Displacement Rate (mm/min)
1
0 -1.5 450
475
500
525
550
-0.5 575
Time (s)
Figure 4. The SPS data used to calculate the strain rate of superplastic deformation. The slope of the displacement curve during deformation is linear, with a slope of 0.05 mm s1.
Figure 5. A schematic showing the type of deformation as well as the location of the variables used to model the deformation in Eqs. (1) and (2).
This process should not be confused with sinter-forging, which has been around for some time and boasts some attractive features [5,17]. Sinter-forging refers to the consolidation and forming of a semi-porous compact into a finished shape and to full density. This type of concurrent consolidation and forming process is carried out in a resistively heated furnace at an optimum strain rate. However, Figures 3 and 4 do not illustrate the effects of a sinter-forging operation, as the material was already fully dense before superplastic deformation was carried out. This figure demonstrates the remarkable beneficial effect of a pulsing electrical field in the superplastic forming of fully dense ceramics. The constitutive relationship for superplastic deformation usually takes the form of [18,19] p D0 Gb b r n RTQ e ð3Þ e_ ¼ A kT d G where e_ is the strain rate, G is the elastic shear modulus, b is Burger’s vector, k is Boltzmann’s constant, T is the absolute temperature, d is the grain size, p is the grain-size dependence coefficient, n is the stress exponent, Q is the activation energy, D0 is the frequency term in the diffusion coefficient and R is the gas constant. GBS is generally the predominant mode of deformation during the superplastic flow. Plastic deformation by GBS is generally characterized by n = 2 and an apparent activation energy that is typically equal to that for grainboundary diffusion [19]. From Eq. (3) it is clear that, at a constant temperature and stress, a high-strain rate is more easily realized in specimens with smaller grains. Hence, the retention of fine grain size during the processing of ceramic nanocomposites will favor higher strain rates. As discussed
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earlier, a reduced grain size will also allow for a reduction of the deformation temperature because the reduced length scales will allow for more complete diffusional mass transport along the grain boundaries to accommodate the stress concentration due to the GBS observed in superplasticity. The large strains observed in the SPS-superplastic deformation of AZM in the pulsed electric field environment, the low stresses encountered in deforming the materials (105 MPa) and the equiaxed grain shape (a presumed result of threedimensional GBS during deformation) lend credence to the above suggestion. In addition, it should be pointed out that when GBSdominated superplasticity is operative as a rate-controlling deformation mechanism, the strain-rate sensitivity parameter extracted from tests conducted in compression by Zhou et al. correctly predicted the manifestation of the superplastic deformation mechanism [4]. In this investigation, due to specimen size limitations, the tests were conducted in a compressive load train. Combined with the die geometry (Fig. 5), this loading process resulted in a combination of shear and compressive stress states, somewhat akin to biaxial stretching. Another interesting point to consider is what happens when one uses the activation energy and stress exponent of the AZM system, as established by deforming this material in a standard resistively heated furnace while it is being deformed with servo-hydraulic equipment, and then inputs the data into Eq. (3) assuming a temperature of 1150 C [20]. The predicted strain rate is on the order of 106 s1, which is 4 orders of magnitude slower than what was actually measured in the SPS. This seems to suggest that there is, indeed, some significant enhancement of the kinetics of deformation garnered by the pulsing electric field found inside the SPS chamber. To the authors’ knowledge, for the first time a fully dense ceramic material has been superplastically formed at a commercially attractive temperature of 1150 C and at an economically viable strain rate of 102 s1. This was achieved by using the SPS equipment both as a tool for consolidation of ceramic powders and also for the subsequent superplastic forming of fully dense nanoceramic composites to desired shape. This remarkable feat was made possible by taking advantage of the enhanced diffusional transport in the SPS chamber environment. The authors would like to thank Umberto AnselmiTamburini for experimental assistance and helpful discussion. They would also like to thank Guo-Dong Zhan,
Alla Sergueeva, Katie Thomson and Nathan Mara for helpful discussion. This work is funded by the United States Office of Naval Research under Grant No. N00014-03-1-0148. [1] R.W. Siegel, S.K. Chang, B.J. Ash, J. Stone, P.M. Ajayan, R.W. Doremus, L.S. Schadler, Scripta Mater. 44 (2001) 2061–2064. [2] G.D. Zhan, J.D. Kuntz, J. Wan, A.K. Mukherjee, Nature Mater. 2 (2003) 38–42. [3] Z. Shen, H. Peng, M. Nygren, Adv. Mater. 15 (2003) 1006–1009. [4] X. Zhou et al., Mater. Sci. Eng., A 394 (2005) 353–359. [5] G.D. Zhan, J.E. Garay, A.K. Mukherjee, Nano Lett. 5 (2005) 2593–2597. [6] F. Wakai, S. Sakaguchi, Y. Matsuno, Adv. Ceram. Mater. 1 (1986) 259–263. [7] Y. Yoshizawa, T. Sakuma, Acta Metall. Mater. 40 (1992) 2943–2959. [8] F. Wakai, H. Kato, Adv. Ceram. Mater. 3 (1988) 71–76. [9] K. Higashi, M. Mabuchi, in: A.H. Chokshi (Ed.), Superplasticity in Advanced Materials, Trans Tech Publications, Zurich, 1997, p. 267. [10] T.R. Bieler, A.K. Mukherjee, in: S.I. Anderson et al. (Eds.), Mechanical and Physical Behavior of Metallic and Ceramic Composites, Riso National Laboratory, Roskilde, 1998, p. 297. [11] B.N. Kim, K. Hiraga, K. Morita, Y. Sakka, Nature 413 (2000) 288–291. [12] J. Pilling, N. Ridley, Superplasticity, The Institute of Metals, London, 1989. [13] K. Morita, K. Hiraga, Y. Sakka, J. Am. Ceram. Soc. 85 (2002) 1900. [14] Mamoru Omori, Mater. Sci. Eng., A 287 (2000) 183–188. [15] Y. Oishi, K. Ando, Y. Sakka, in: M.F. Yan, A.H. Heuer (Eds.), Advanced Ceramics, Additives and Interfaces in Electronic Ceramics, vol. 7, American Ceramic Society, Columbus, OH, 1993, p. 208. [16] P. Shewmon, in: Diffusion in Solids, second ed., The Minerals, Metals & Materials Society, Warrendale, PA, 1999, p. 223. [17] P.C. Panda, J.W. Wang, R. Raj, J. Amer. Ceram. Soc. 69 (2002) 1900. [18] A.K. Mukherjee, Treatise on Materials and Technology, in: R.J. Aresenault (Ed.), Plastic Deformation Materials, vol. 6, Academic Press, New York, 1975, p. 163. [19] A.K. Mukherjee, in: H. Mughrabi (Ed.), Plastic Deformation and Fracture of Materials, Materials Science and Technology, vol. 6, VCH Verlagsgesellschaft mbH, Weinheim, 1993, p. 407. [20] B.A. Kear, A.K. Mukherjee, Far-from-equilibrium processing of nanostructured ceramics, in: J.R. Groza, (Ed.), CRC Handbook, in press.
A low-temperature high-strain-rate formable nanocrystalline superplastic ceramic Dustin M. Hulbert, Dongtao Jiang, Joshua D. Kuntz, Yasuhiro Kodera and Amiya K. Mukherjee* Department of Chemical Engineering and Materials Science, University of California, One Shields Avenue, Davis, CA 95616, USA Received 23 January 2007; revised 2 February 2007; accepted 2 February 2007 Available online 11 April 2007
A fully dense nanocrystalline ceramic consisting of ZrO2, Al2O3 and MgAl2O4 was deformed at 1150 C at a strain rate on the order of 102 s1. Spark plasma sintering was used in this study as a means of consolidation as well as for subsequent superplastic deformation. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ceramics; Nanocomposite; Superplasticity; Low-temperature deformation; Spark plasma sintering
Nanostructured materials is an exciting area of materials research because bulk materials with grain sizes less than 100 nm exhibit novel mechanical and physical properties as compared with their microcrystalline counterparts. Nanostructured ceramic materials, in particular, are attractive because of their intrinsic strength at high temperatures, their chemical inertness (as compared with metals) and their resistance to erosion and abrasion. What they lack, however, is fracture toughness and machinability to a desired shape. The fracture toughness issue is being addressed and some exciting advances have been made in recent years [1,2]. The machinability issue is difficult to solve because, given the nature of atomic bonding and large interatomic forces, structural ceramics are quite brittle during machining operations. Often such operations give rise to surface cracks that act as sites for flaws and their propagation, ultimately leading to failure under loadcarrying service conditions. This manuscript points to another avenue, namely using superplasticity as a mechanism for arriving at a desired shape, but by using a distinctly different forming environment (within a pulsing electric field) that enables the operation to be conducted at vastly lower forming temperature and at a significantly higher strain rate [3–5].
* Corresponding author. Fax: +1 7530083; e-mail: akmukherjee@ ucdavis.edu
Superplasticity in ceramics has been studied since the first observation of fine-grain superplasticity in yttriastabilized tetragonal zirconia (YSTZ) by Wakai et al. in 1986 [6]. Since then a number of fine-grained ceramics have also demonstrated superplasticity [7,8]. However, the strain rates for optimal superplastic ductility in these investigations were rather low, i.e. on the order of 105 s1. High-strain-rate superplasticity (HSRS) is usually referred to as the demonstration of ductility at a strain rate of 102 s1 or higher [9]. Historically, HSRS was exhibited in metallic systems as early as 1988 [10]. HSRS in ceramic systems was not observed until 2000, when Kim et al. reported HSRS in a ceramic composite consisting of 30 vol.% a-Al2O3, 40 vol.% YSTZ and 30 vol.% MgAl2O4 (AZM), and with an impressive strain rate of 1 s1 [11]. If superplasticity is, indeed, at work in the aforementioned material system, then one would expect grain-boundary sliding (GBS) to be the rate-limiting process during deformation [12]. Because GBS involves the relative motion of individual grains, cavities will form at grain boundary (GB) ledges and triple points unless the stresses that nucleate and grow these cavities are accommodated. Without an accommodation mechanism, a large, uniform macroscopic strain cannot be realized in the material. By reducing the grain size, the stress concentration due to GBS is reduced. Also, the GB length over which atomic transport has to take place in order to accommodate the stress concentration due to GBS is reduced. Under these circumstances, the optimal strain rate for superplasticity
1359-6462/$ - see front matter 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2007.02.003
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D. M. Hulbert et al. / Scripta Materialia 56 (2007) 1103–1106
may be increased and optimal temperature may be reduced since the shorter length scales will allow for easier and more complete diffusional accommodation [13]. In the present work, the investigators strive to lower the HSRS deformation temperature to levels that would be commercially attractive, while still retaining the economic viability of HSRS. This was achieved by using spark plasma sintering (SPS) equipment to further enhance the kinetics of superplastic deformation process by taking advantage of the enhanced atomic transport rates garnered by the pulsing electric field found in the SPS chamber [14–16]. The starting materials were commercially available nano-sized powders: c-Al2O3 (Nanotechnologies, Austin, TX), with 15–20 nm particle size; MgO (Nanopowder Enterprises Inc., Piscataway, New Jersey), with 40 nm particle size; and tetragonal ZrO2 stabilized with 3 mol.% Y2O3 (Tosoh, Tokyo, Japan), with 24 nm particle size. The c-Al2O3 was subjected to high-energy ball milling (HEBM) for 24 h (using a SPEX 8000 mixer mill, in a WC vial with an 11 mm diameter WC ball) before 1 wt.% polyvinyl alcohol (PVA) was added as a dry milling agent to prevent severe agglomeration. Milling was followed by a 350 C heat treatment in air to burn off the PVA. The HEBM c-Al2O3 was then ball mixed with the ZrO2 and MgO using zirconia media (50–50 solid loading) in ethanol for 24 h. The mixed powder was dried, crushed using an alumina mortar and pestle and sieved (150 lm) before being pressed into a 19 mm diameter graphite die and sintered using a Dr. Sinter1050 SPS system (Sumitomo Coal Mining Company, Ltd.) under vacuum. After applying a pressure of 63 MPa, samples were heated from room temperature to 600 C in 5 min and then ramped to 1150 C in 2 min, this temperature being held for 3 min before turning off the power. Temperature was monitored by focusing an optical pyrometer on a hole that was drilled nearly through the die adjacent to the specimen. The same parameters above were used for SPS forming experiments except pressure was kept at less than 18 MPa until the maximum temperature was reached. Upon reaching 1150 C, the pressure was raised to 105 MPa over a time span of approximately 30 s. The dimensions of the radially symmetric punch used to form the AZM are as follows: the tooth-to-tooth distance measured from center to center is 4 mm, the depth of each tooth is 1 mm from trough to tip and the angle of incline of the teeth is 45. Densities were measured using the Archimedes’ method. Microstructural observation was carried out using a field emission high-resolution scanning electron microscopy (SEM). Grain sizes were estimated from SEM analysis and energy-dispersive spectroscopy was used to identify individual grains. Phase identification was done using X-ray diffraction (XRD) with Cu Ka radiation using a stepping scan with 0.01 per step. The as-sintered microstructure and XRD pattern are shown in Figures 1 and 2, respectively. The final density was 99.8% of the theoretical density of the composite (4.696 g cm3). From the SEM image of the as-sintered specimen (Fig. 1) the grain size was approximated to be 100 nm with an equiaxed grain morphology.
Figure 1. Scanning electron fractograph of the AZM composite microstructure after SPS at 1150 C for 3 min. The grains are equiaxed and approximately 100 nm in size.
Figure 2. XRD pattern of the as-sintered AZM compact. The MgO and Al2O3 reacted to form the intended MgAl2O4 phase. In addition, the c-Al2O3 transformed to a-Al2O3.
The XRD pattern (Fig. 2) shows that the MgO and Al2O3 reacted as planned, and formed the intended MgAl2O4 phase without leaving an excess of unreacted magnesia. What is further apparent from Figure 2 is that the c-Al2O3 transformed to a-Al2O3. Lastly, one notes the relatively broad peaks in Figure 2, which are due to the nanoscale grain size of the constituent phases. So far all of the superplastic deformation in the AZM system has been conducted inside a standard resistive heating type furnace. An intriguing question would be: ‘‘What would happen if the deformation of the AZM composite were to take place inside the SPS equipment?’’ Perhaps a better question would be: ‘‘Why not use the SPS equipment as a forming tool as well?’’ One immediate and obvious benefit of using the SPS equipment to perform superplastic deformation is the rapid process cycling time. Because the heating and cooling rates are so rapid, the specimen is at elevated temperature for only a short while, typically less than 5 min. This means that grain growth can be minimized while avoiding other microstructural instability issues associated with long exposures at high temperatures. Additionally, the pulsing DC electric field and spark plasma effect may have a beneficial role in enhancing superplasticity, resulting in surface activation of individual grains, field-assisted diffusion at grain surfaces and enhanced ion diffusion through an electron wind [14– 17]. Because nanoscale materials have so many diffusive pathways along grain boundaries and because the grain surface to volume ratio of such systems is so large, it seems reasonable that a synergism exists between SPS
D. M. Hulbert et al. / Scripta Materialia 56 (2007) 1103–1106
1105
Figure 3. The image on the left shows the dense AZM ceramic as sintered. The image in the middle shows the part formed at a record-setting low temperature of 1150 C and at very respectable strain rate of 2 · 102 s1. The image on the far right shows a sectioned quadrant of the formed specimen to better show the extent of deformation. The fine markers in all images are in millimeters, the numbers in centimeters.
forming operations and diffusive transport along grain boundaries in materials with ultrafine grains. Figure 3 provides evidence of such a synergism. The AZM specimen shown below was formed at 1150 C and at a strain rate of approximately 1.4 · 102 s1. In this case the normal forming strain rates were approximated in the SPS apparatus by dividing the original thickness of the specimen by the slope of the displacement vs. time plot shown in Figure 4. Strain rates were modeled and cross-checked in the SPS by using the somewhat more realistic relationships set forth in Eqs. (1) and (2). pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2 a2 þ x2 þ aÞ 3a ð1Þ e¼ 3a where e is the total true strain and a and x are shown in Figure 5. By taking the derivative of x with respect to time, the strain rate can be calculated as follows: e_ ¼
2_x qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3a 1 þ ax
ð2Þ
Here e_ is the true strain rate and x_ is the displacement rate given by the slope of Figure 4. The true strain rate is at a maximum value when x = a, resulting in a calculated strain rate of 2.7 · 102 s1. This value is well within the same order of magnitude as the value obtained when dividing the deformation rate by the original thickness of the specimen. The time from when the 99.8% dense AZM blank was placed into the SPS chamber to the time when the complex shape was held in hand was about 30 min. This represents, to our knowledge, the first time a dense ceramic blank has been formed into a complex shape at commercially attractive temperatures and strain rates.
Displacement and Displacement Rate vs. Time 3 Displacement (mm) 0.5
2.5
Displacement Rate
2 0
1.5 1
-0.5
0.5
0.05 mm/sec
-1
Displacement (mm)
Displacement Rate (mm/min)
1
0 -1.5 450
475
500
525
550
-0.5 575
Time (s)
Figure 4. The SPS data used to calculate the strain rate of superplastic deformation. The slope of the displacement curve during deformation is linear, with a slope of 0.05 mm s1.
Figure 5. A schematic showing the type of deformation as well as the location of the variables used to model the deformation in Eqs. (1) and (2).
This process should not be confused with sinter-forging, which has been around for some time and boasts some attractive features [5,17]. Sinter-forging refers to the consolidation and forming of a semi-porous compact into a finished shape and to full density. This type of concurrent consolidation and forming process is carried out in a resistively heated furnace at an optimum strain rate. However, Figures 3 and 4 do not illustrate the effects of a sinter-forging operation, as the material was already fully dense before superplastic deformation was carried out. This figure demonstrates the remarkable beneficial effect of a pulsing electrical field in the superplastic forming of fully dense ceramics. The constitutive relationship for superplastic deformation usually takes the form of [18,19] p D0 Gb b r n RTQ e ð3Þ e_ ¼ A kT d G where e_ is the strain rate, G is the elastic shear modulus, b is Burger’s vector, k is Boltzmann’s constant, T is the absolute temperature, d is the grain size, p is the grain-size dependence coefficient, n is the stress exponent, Q is the activation energy, D0 is the frequency term in the diffusion coefficient and R is the gas constant. GBS is generally the predominant mode of deformation during the superplastic flow. Plastic deformation by GBS is generally characterized by n = 2 and an apparent activation energy that is typically equal to that for grainboundary diffusion [19]. From Eq. (3) it is clear that, at a constant temperature and stress, a high-strain rate is more easily realized in specimens with smaller grains. Hence, the retention of fine grain size during the processing of ceramic nanocomposites will favor higher strain rates. As discussed
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earlier, a reduced grain size will also allow for a reduction of the deformation temperature because the reduced length scales will allow for more complete diffusional mass transport along the grain boundaries to accommodate the stress concentration due to the GBS observed in superplasticity. The large strains observed in the SPS-superplastic deformation of AZM in the pulsed electric field environment, the low stresses encountered in deforming the materials (105 MPa) and the equiaxed grain shape (a presumed result of threedimensional GBS during deformation) lend credence to the above suggestion. In addition, it should be pointed out that when GBSdominated superplasticity is operative as a rate-controlling deformation mechanism, the strain-rate sensitivity parameter extracted from tests conducted in compression by Zhou et al. correctly predicted the manifestation of the superplastic deformation mechanism [4]. In this investigation, due to specimen size limitations, the tests were conducted in a compressive load train. Combined with the die geometry (Fig. 5), this loading process resulted in a combination of shear and compressive stress states, somewhat akin to biaxial stretching. Another interesting point to consider is what happens when one uses the activation energy and stress exponent of the AZM system, as established by deforming this material in a standard resistively heated furnace while it is being deformed with servo-hydraulic equipment, and then inputs the data into Eq. (3) assuming a temperature of 1150 C [20]. The predicted strain rate is on the order of 106 s1, which is 4 orders of magnitude slower than what was actually measured in the SPS. This seems to suggest that there is, indeed, some significant enhancement of the kinetics of deformation garnered by the pulsing electric field found inside the SPS chamber. To the authors’ knowledge, for the first time a fully dense ceramic material has been superplastically formed at a commercially attractive temperature of 1150 C and at an economically viable strain rate of 102 s1. This was achieved by using the SPS equipment both as a tool for consolidation of ceramic powders and also for the subsequent superplastic forming of fully dense nanoceramic composites to desired shape. This remarkable feat was made possible by taking advantage of the enhanced diffusional transport in the SPS chamber environment. The authors would like to thank Umberto AnselmiTamburini for experimental assistance and helpful discussion. They would also like to thank Guo-Dong Zhan,
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