Metallurgical and Materials Transactions A

, Volume 44, Issue 4, pp 1908–1916

Spark Plasma Sintering of Nanostructured Aluminum: Influence of Tooling Material on Microstructure

Authors

  • Dongming Liu
    • Department of Materials Science and EngineeringShandong University
    • Department of Chemical Engineering and Materials ScienceUniversity of California Davis
  • Yuhong Xiong
    • Department of Chemical Engineering and Materials ScienceUniversity of California Davis
  • Ying Li
    • Department of Chemical Engineering and Materials ScienceUniversity of California Davis
  • Troy D. Topping
    • Department of Chemical Engineering and Materials ScienceUniversity of California Davis
  • Yizhang Zhou
    • Department of Chemical Engineering and Materials ScienceUniversity of California Davis
  • Chris Haines
    • Powder Metallurgy & Particulate TechnologyUS Army, TACOM-ARDEC
  • Joseph Paras
    • Powder Metallurgy & Particulate TechnologyUS Army, TACOM-ARDEC
  • Darold Martin
    • Powder Metallurgy & Particulate TechnologyUS Army, TACOM-ARDEC
  • Deepak Kapoor
    • Powder Metallurgy & Particulate TechnologyUS Army, TACOM-ARDEC
  • Julie M. Schoenung
    • Department of Chemical Engineering and Materials ScienceUniversity of California Davis
    • Department of Chemical Engineering and Materials ScienceUniversity of California Davis
Article

DOI: 10.1007/s11661-012-1533-6

Cite this article as:
Liu, D., Xiong, Y., Li, Y. et al. Metall and Mat Trans A (2013) 44: 1908. doi:10.1007/s11661-012-1533-6
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Abstract

The influence of tooling material, i.e., graphite and WC-Co, on the microstructure of a spark plasma sintering (SPS) consolidated, nanostructured aluminum alloy is studied in this paper. The results show that tooling selection influences microstructure evolution, independent of process parameters. The influence of tooling on microstructure is rationalized on the basis of the following factors: heating rate, electrical current density, localized heating, and imposed pressure. A theoretic framework, based on the physical properties of graphite and WC-Co, is formulated to explain the observed behavior.

1 Introduction

Spark plasma sintering (SPS) is a recently developed powder consolidation technology that is capable of being applied to metals, alloys, ceramics, and composites.[13] In SPS, a pulsed high-amperage, direct current is used concurrently with a superimposed uniaxial pressure to consolidate powders. In comparison with well-established consolidation methods such as hot pressing, where the samples are heated externally, the thermal energy during SPS is generated in situ, i.e., by the mold elements, as well as by the powder being sintered in case of conductive powder. This technique possesses the advantage of sintering samples under conditions of high heating rate [up to 1000 K/minutes (1000 °C/minutes)] and high pressures (up to 1000 MPa), which also depend on the mold material and sintering temperature used. Consequently, materials can be consolidated at relatively low temperatures and under shorter time intervals, thereby minimizing changes to the starting microstructures, relative to conditions generally present during conventional consolidation methods.[1,3,4]

There is a wide body of literature showing that SPS process conditions significantly influence the microstructure of the consolidated material and thereby mechanical response.[57] Not surprisingly, numerous investigators have sought to optimize process parameters via studies aimed at understanding densification mechanisms. In related work, Zadra et al. found that temperature and pressure work together to enhance the neck growth between the powder particles and the application of the sintering pressure at high temperature is beneficial to the improvement of mechanical property of the consolidated aluminum samples in comparison with that at room temperature.[8] Santanach et al. investigated the influence of SPS consolidation parameters on α-Al2O3 powder (0.14 μm) and proposed that sintering can be divided into two stages: densification without grain growth at lower temperatures and grain coarsening with further densification at higher temperatures.[9] The results of Munir et al. showed that an electrical current can accelerate the solid state reaction between Mo and Si, but the growth rate of the product phases, which are MoSi2 and Mo5Si3, are independent of the current direction and the pulse patterns.[10] Kubota et al. reported on the SPS consolidation behavior of nanostructured pure aluminum powder using an applied pressure of 49 MPa at 873 K (600 °C) for 1 h. Interestingly, following SPS consolidation, the nanostructured material consisted of a mixture of nanostructured grains approximately 300 nm with interdispersed coarse grains 2 to 5 μm in size.[11] In a study that combined numerical analysis with experiments, Grasso et al. reported that the application of a low sintering pressure (i.e., 5 to 20 MPa) led to a high temperature with an accompanying high thermal gradient that was thought to be responsible for the observed non-uniform microstructure when using a constant electrical current to consolidate WC powder by SPS.[12] In contrast, a low temperature and hence low thermal gradient led to the formation of a uniform microstructure in experiments involving a high sintering pressure (i.e., 60 to 80 MPa) for the same current conditions corresponding to low sintering pressures.[12] In recent work, Liu et al. reported on the influence of processing conditions, e.g., the pressure loading mode, starting microstructure (i.e., atomized vs cryomilled powders), sintering pressure, sintering temperature, and powder particle size on the consolidation response and associated mechanical properties of compacts consolidated from nanostructured Al 5083 powder.[13] In another study, Xiong et al. developed a numerical framework using COMSOL Multiphysics modeling and simulation software to provide insight into the mechanisms responsible for densification of the nanostructured Al powder.[14]

An inspection of the above-described experimental and numerical studies, however, shows that in almost all cases, the SPS experiments were conducted using mold-plunger tooling assemblies fabricated out of graphite; graphite is an attractive material given its stability, high-temperature resistance, and machinability characteristics.[15] Graphite tooling assemblies, however, are limited by their compressive strength, which is on the order of 200 MPa at room temperature.[16] Hence, in the case of SPS experiments that require high pressures (e.g., >200 MPa), tungsten carbide (WC) is the preferred material for SPS tooling. WC/Co has a high compressive strength at room and elevated temperatures, and hence may be readily used as SPS tooling for applications that require high pressure and high temperature. For instance, the compressive strength of WC-6 wt pct Co is 5.4 GPa[17] at room temperature. Additionally, the WC-10 wt pct Co shows a compressive strength as high as 2.0 GPa and 1.0 GPa at temperatures of 973 K and 1273 K (700 °C and 1000 °C), respectively.[18] Interestingly, information on the influence of SPS tooling material on the resultant microstructure of consolidated materials is essentially non-existent. Accordingly, the present work was motivated by the following questions. First, what is the influence of tooling materials (e.g., graphite and WC/Co) on the microstructure of nanostructured Al during SPS? Second, can the thermal fields resulting from the different tooling materials be correlated to any observed microstructure changes in the case of nanostructured Al? The selection of nanostructured Al for the present study was motivated by recent interest in consolidation of bulk nanostructured metals from powders.[1922]

2 Experimental

The nanostructured powder used in the present study was prepared as follows. First, inert gas atomized Al 5083 (Al-4.5Mg-0.57Mn-0.25Fe in wt pct) powder was milled in a slurry of liquid nitrogen (LN) for 8 h in a modified Svegvari attritor using stainless steel balls. The ball-to-powder ratio was 32:1 and 0.2 pct stearic acid (CH3(CH2)16COOH) was added prior to milling to prevent agglomeration during milling. At the completion of the milling experiments, the powder/LN slurry was collected in a stainless container and then transferred to a nitrogen glove box to minimize atmospheric contamination. Detailed information on cryomilling can be found in the literature.[23,24] In the present study, the size of the cryomilled powder particles used for the SPS experiments was in the range of 10 to 25 μm, as established by sieving. Moreover, sieving was performed under a controlled atmosphere (i.e., inside a glove box) to minimize atmospheric contamination.

A Dr. Sinter SPS-825S system was used to consolidate the cryomilled powder into bulk samples under a vacuum of <10 Pa. For each experiment, 3.0 g of powder was loaded into the tooling assembly with an inner diameter of 20 mm, as illustrated schematically in Figure 1(a). Dimensional tolerances were held within ±0.127 mm (±0.005 in) for the die and +0.0000 mm/−0.0127 mm (+0.0000 in/−0.0005 in) for the plungers. Surface roughness was specified at 6.3 μm roughness average (Ra), associated with a roughness number of 9. The tooling assembly and powder were heated to 623 K (350 °C) in 2 minutes followed by slow heating to 673 K (400 °C) in 1 minute and a 3-minute hold at 673 K (400 °C) (Figure 2). The power was then turned off and the sample was cooled to room temperature in the SPS chamber to minimize oxidation. A preload of about 9 MPa was applied before sintering to insure good electrical conduction between the plunger and the sample, the sample and the mold, and the plunger and the mold. Then, the target pressure of 100 MPa was uniformly loaded in the temperature range of 623 K to 673 K (350 °C to 400 °C) during heating and unloaded at a temperature of 473 K (200 °C) during cooling. A pulse pattern (on:off ratio of 12:2) was applied during SPS. The temperature was measured by a K-type thermocouple, which was inserted to a depth corresponding to one-third the thickness of the tooling wall. To investigate the influence of tooling materials on the microstructure of the SPS-consolidated Al alloy, two mold-plunger tooling assemblies, one manufactured using Isocarb I-85 graphite (Electrodes Inc. CT) and a second one using WC-5wt pct Co (United Die Company, NJ), but with identical configurations, were employed to sinter the cryomilled powder. The densities of the consolidated materials were determined on the basis of the Achimedes’ method according to ASTM B311-08. In this paper, relative density is presented as a percentage relative to the published theoretic value of 2.66 g/cm3.[25]
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Fig. 1

Schematic diagram of the mold/sample/plunger assembly and the assumed three layers for the calculation of heating rate ratio (HRR): (a) mold/sample/plunger assembly, (b) a cutaway view of the assembly, and (c) a schematic diagram of the three layers

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Fig. 2

Schematic diagram of the temperature and pressure schedule during SPS

Samples for transmission electron microscopy (TEM) were prepared by sectioning material parallel to the cross section of the consolidated material (perpendicular to the pressure direction). The TEM coupons were ground, dimpled to a thickness of about 10 μm, and thinned further to electron transparency using a Gatan PIPS 691 ion-milling system at a voltage of 4 V. The microstructure observation was carried out using a Philips CM12 TEM at a voltage of 100 kV (Figure 3(a)) and a JEOL JEM 2500 SE TEM operating at a voltage of 200 kV (Figures 5(a) and (c)). In order to measure the grain size of the cryomilled powder and the SPS-consolidated samples, a series (30 to 50 images) of higher magnification TEM images providing clear views of grain boundaries (GBs) were randomly selected. Typically, we found that the edge region near the ion-milled orifice provided a clear view of GBs. In the case of equiaxed grains, the diameter was reported as the grain size, whereas for grains with an irregular morphology, the length and width values were averaged and reported. The dimension of the grains was measured using the image analysis software analySIS FIVE (Olympus Imaging America Inc, PA).
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Fig. 3

Microstructure (a) and grain size distribution (b) of cryomilled Al 5083 powder

3 Results

The microstructure of the cryomilled Al 5083 powder particles consists of two types of grains, i.e., equiaxed grains (> 90 vol. pct) and elongated grains (<10 vol pct), please refer to.[14] In Reference 14 and the present study, an elongated grain is defined as a grain with an aspect ratio that exceeds 2. Because the content of the elongated grains is relatively small, they are not included in the grain size distribution histogram. Figures 3(a) and (b) show the microstructure and grain size distribution in the cryomilled Al 5083 powder, respectively. From Figure 3(b), it can be seen that most of the grains fall in the nanoscale regime (i.e., 10 to 100 nm), whereas some with a diameter of 100 to 130 nm are occasionally observed.

Table I summarizes the processing conditions and the density measurement results of the SPS-consolidated samples. Sample 5083-G, which was sintered using a graphite mold-plunger tooling assembly (GMPTA), has a density of 2.637 g/cm3 (99.1 pct of theoretic density), showing that nearly complete densification is achieved. Similarly, its counterpart, Sample 5083-WC, which was consolidated using a WC-Co mold-plunger tooling assembly (WCMPTA), also shows a relative density of 99.1 pct.
Table I

Processing Conditions and Density of the SPS-Consolidated Samples

Designation

Tooling Material

Processing Conditions

Density (g/cm3)

Ample 5083-G

graphite

673 K (400 °C) × 3 min @ 100 MPa

2.637

Sample 5083-WC

WC-5wt pct Co

2.636

The temperature of the tooling as a function of time is shown in Figure 4; the precise location is discussed in the Experimental Section. The results show that the thermal profiles for the graphite and WC-Co were almost identical during the heating and holding stages. During the cooling stage, however, the temperature of the graphite tooling decreased faster than that of WC-Co.
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Fig. 4

The temperature of the tooling as a function of time and tooling material

Both consolidated materials exhibit a bimodal microstructure composed of fine grains with a size range of 10 to 200 nm and coarse grains (200 to 1000 nm), as shown in Figures 5(a) and (c). However, there were apparent differences in the microstructures of the Al 5083 sintered using graphite and WC-Co tooling even though the starting powder was identical. For example, differences in the grain size distribution were quantified as grain number fraction versus grain size and the results are shown in Figures 5(b) and (d). To that effect, sample 5083-G shows a much coarser microstructure and wider grain size distribution relative to sample 5083-WC. The percentage of the fine grains (10 to 200 nm) in the former is approximately 71 pct, whereas the coarse grains (>200 nm) account for 29 pct, based on the observation of 547 grains from a series of TEM micrographs. The average grain diameter in Sample 5083-G is 179 nm with a standard deviation of 145.4 nm. With an average grain size of 102 nm and a standard deviation of 82.3 nm, sample 5083-WC exhibited a much finer microstructure and narrower grain size distribution. The proportion of fine grains is > 92 pct, as determined by counting 551 grains in numerous TEM images.
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Fig. 5

Microstructure and grain size distribution: (a) and (b) for sample 5083-G, and (c) and (d) for sample 5083-WC

4 Discussion

Four factors are proposed to contribute to the observed differences in microstructure of the materials studied herein, i.e., the heating rate of the sample, the current density passing through the sample, the localized heating, and the localized pressure at the contacts between the particles. These are discussed in detail below.

4.1 Comparison of the Heating Rate of the Samples

The tooling materials affect the heating of the sample during SPS. This behavior can be rationalized if one considers the physical properties of the two materials of the tooling assembly. To render the problem tractable, the sample/mold/plunger assembly is assumed to consist of three layers separated by two imaginary planes parallel to the sample’s top and bottom surfaces, respectively, as schematically shown in Figure 1(c). Layer I contains the upper plunger and the upper part of the mold, the sample and the middle part of the mold are included in layer II, and layer III is composed of the bottom plunger and the lower part of the mold. The sample and the mold in layer II make a parallel circuit, and the electrical current flowing through the mold Id and the sample Is can be calculated by
$$ I_{\text{s}} = \frac{{R_{\text{d}} }}{{R_{\text{s}} + R_{\text{d}} }}I\quad I_{\text{d}} = \frac{{R_{\text{s}} }}{{R_{\text{s}} + R_{\text{d}} }}I $$
(1)
where I is the total electrical current and Rs and Rd are the resistance of the sample and mold, respectively. The thermal energy transfer between the mold and the chamber can be safely neglected as the sintering occurred in vacuum (<10 Pa) and a sintering temperature was 673 K (400 °C). Under the assumption that there is no heat transfer between layers II/I, layers II/III and sample/mold interfaces, the heating rates of the sample and the mold in layer II can be estimated by
$$ \dot{T}_{\text{s}} = \frac{{I_{\text{s}}^{2} R_{\text{s}} }}{{C_{\text{s}} m{}_{\text{s}}}} = \frac{{(\frac{{R_{\text{d}} }}{{R_{\text{s}} + R_{\text{d}} }}I)^{2} R_{\text{s}} }}{{C_{\text{s}} A{}_{\text{s}}H_{\text{s}} \rho_{\text{msn}} }} $$
(2)
$$ \dot{T}_{\text{d}} = \frac{{(\frac{{R_{\text{s}} }}{{R_{\text{s}} + R_{\text{d}} }}I)^{2} R_{\text{d}} }}{{C_{\text{d}} A{}_{\text{d}}H_{\text{d}} \rho_{\text{md}} }} $$
(3)
where \( \dot{T} \), C, A, H, ρm are the heating rate, specific heat, cross-section area, height, and density, respectively, with the subscripts s, d, and n designating the sample, mold, and nominal, respectively. It then follows that
$$ \frac{{R_{\text{d}} }}{{R_{\text{s}} }} = \frac{{\rho_{\text{ed}} \frac{{H_{\text{d}} }}{{A_{\text{d}} }}}}{{\rho_{\text{esn}} \frac{{H_{\text{s}} }}{{A_{\text{s}} }}}} $$
(4)
where ρesn, ρed are the sample’s nominal electrical resistivity and the mold’s electrical resistivity, respectively. Additionally, the ρesn can be estimated by[26]
$$ \rho_{\text{esn}} = \frac{{\rho_{\text{es}} }}{{(1 - \frac{\Uptheta }{{\Uptheta_{\text{M}} }})^{\text{m}} }} $$
(5)
where ρes is the electrical resistivity of the material being sintered and ΘM and Θ are the powder tap porosity and compact porosity, respectively. m = 1 + (1 − ΘM)0.8 is a constant.[26] The heating rate ratio (HRR) of the sample and the mold can then be calculated as
$$ \frac{{\dot{T}_{\text{s}} }}{{\dot{T}_{\text{d}} }} = \frac{{C_{\text{d}} \rho_{\text{md}} \rho_{\text{ed}} H_{\text{d}}^{2} }}{{C_{\text{s}} \rho_{\text{msn}} \rho_{\text{esn}} H_{\text{s}}^{2} }} $$
(6)
In the case illustrated in Figure 1(c), Hd = Hs, and thus the heating rate ratio in Eq. [6] can be simplified as
$$ \frac{{\dot{T}_{\text{s}} }}{{\dot{T}_{\text{d}} }} = \frac{{C_{\text{d}} \rho_{\text{md}} \rho_{\text{ed}} }}{{C_{\text{s}} \rho_{\text{msn}} \rho_{\text{esn}} }} $$
(7)

It should be noted that this value represents an upper bound of the heating rate ratio in the case of HRR > 1, for the following reasons. First, there is heat transfer between layers II/I, layers II/III and sample/mold interfaces. In fact, thermal diffusion between the interfaces accelerates the heating of the mold and decreases the heating rate of the sample. Second, the contact resistance at the sample/plunger interface will likely be higher than the ideal contact conditions assumed in the present model, causing a reduction in the flow of electrical current and heating rate of the sample. Despite these simplifications, the proposed model provides a useful framework to analyze and compare the thermal characteristics of the mold and the sample during SPS.

To render the problem tractable, the following assumptions are made:
  1. (1)

    The density of the compact changes proportional to the displacement of the SPS ram head during SPS.

     
  2. (2)

    The electrical resistivity of Al 5083 at 673 K (400 °C) is threefold that at RT (in reference to aluminum[27]) and the electrical resistivity varies proportional to the temperature increment. The other parameters, i.e., the specific heat, density and electrical resistivity of graphite and WC-Co, specific heat, density of Al 5083, used in this paper are their room temperature values (see Appendix, Table AI).

     
  3. (3)

    The relative density of the compact was 64 pct prior to sintering and 99 pct after the pressure was loaded, considering that the relative density of the random packing powder was 64 pct[28] and the sample had a relative density of 99.1 pct after SPS consolidation.

     
On the basis of the temperature in Figure 4 and displacement z of the SPS ram head recorded by the computer unit during SPS, the HRR was estimated by Eq. [7] and the results are shown in Figure 6. It can be seen that the values of HRR decrease when the temperature changes from room temperature (RT) to 623 K (350 °C) (0 to 120 seconds) followed by an increase from 623 K to 673 K (350 °C to 400 °C) (120 to 180 seconds). The decrease in HRR results from an increase in the electrical resistance of the sample during heating, whereas the increase can be attributed to the application of pressure, which causes a rapid densification (displacement vs time in Figure 6) and thus a decrease of the resistance of the compact. In addition, the HRR value for GMPTA is much higher as compared to that for WCMPTA. The results shown in Figure 4 demonstrate that both graphite and WC-Co experienced similar heating rates during SPS. Hence, it can be concluded that the heating rate experienced by the Al 5083 powder during SPS was higher in the case of GMPTA relative to that associated with WCMPTA.
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Fig. 6

The heating rate ratio (HRR) and the displacement of the ram head vs time during SPS. The HRR was calculated by Eq. [7]. z and temperature were measured by computer unit

4.2 Comparison of the Amperage Passing Through the Samples

The difference in the amperage passing through the samples during SPS contributes to the observed differences in microstructure. The proportion (Is/I) of electrical current shared by the sample as a function of time, which was estimated based on Eqs. [1], [4], and [5], is shown in Figure 7(a). Similar to HRR, Is/I also displays a decreasing trend from RT to 623 K (350 °C) (0 to 120 seconds) followed by an increase in the temperature range of 623 K to 673 K (350 °C to 400 °C) (120 to 180 seconds). This trend can be attributed to changes in electrical resistance of the compact during SPS, as discussed above in reference to changes in the HRR values. From Figure 7(a), it can also be seen that most of the electrical current flows through the sample when using GMPTA. However, in the case of using a WCMPTA, the electrical current passing the sample accounts for only a small fraction of the total current. Even though at 99 pct relative density, the ratio of Is/I is only about 19 pct. Based on the total electrical current I recorded by the computer unit during SPS, Is/I in Figure 7(a), the electrical current Is amperage passing through the sample was estimated and the results are shown in Figure 8. From Figure 8, it can be seen that the Is associated with the GMPTA is significantly higher than that associated with the WCMPTA. It is known that the imposition of an electrical current can enhance mass transport through electromigration,[29] point defect generation,[30] and enhanced defect mobility.[31] For instance, in related work, the presence of pulsed electrical current of 700 A was shown to significantly enhance neck growth when sintering copper spheres to a copper plate at 1173 K (900 °C).[32] Hence, it may be argued that a higher electrical current density, coupled with a higher localized temperature (as discussed in the next section), promoted grain growth during consolidation, and hence is responsible for the coarser microstructure observed in sample 5083-G (see Figures 5(a) and (b)).
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Fig. 7

The percentage (Is/I) of the electrical current passing the sample, the relative density as a function of time during SPS. (a) RT—673 K (400 °C) sintering and (b) RT consolidation

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Fig. 8

The total electrical current I, the electrical current Is flowing through the sample, and the displacement z of the ram head vs time during SPS

In order to investigate the effect of the temperature on the electrical current distribution between the sample and mold, the Is/I was calculated under the assumption that the consolidation occurs at room temperature and the change in sample density is the same as that associated with RT—673 K (400 °C) sintering, as illustrated in Figure 7(a). The results are shown in Figure 7(b). From Figures 7(a) and (b), it can be seen that the dependence of the electrical resistivity of Al alloy on temperature shows a marked influence on the electrical current distribution in the case of loose powder and a relatively small influence in the case of a dense compact when using GMPTA. For instance, at time = 116 seconds [temperature = 613 K (340 °C) for RT—673 K (400 °C) sintering and prior to the application of pressure], the Is/I for the RT—673 K (400 °C) sintering (Figure 7(a)) is 58 pct, whereas the sample accounts for 79 pct for RT consolidation (Figure 7(b)). When time = 200 seconds [the temperature is 673 K (400 °C) for RT—673 K (400 °C) sintering and after the application of the targeted pressure], the percentage of the electrical current shared by the sample is 93 pct for the RT—673 K (400 °C) sintering and 98 pct for room temperature consolidation. However, when using WCMPTA, the temperature rise results in a significant reduction of the value of Is/I (Figure 7(a)) relative to room temperature consolidation (Figure 7(b)). For instance, when time = 112 seconds [the temperature is 613 K (340 °C) for RT—673 K (400 °C) sintering and prior to the application of pressure], the Is/I is 2.1 pct for the RT—673 K (400 °C) sintering (Figure 7(a)) and 5.5 pct for RT consolidation (Figure 7(b)). At time = 200 seconds [the temperature is as high as 673 K (400 °C) for RT—673 K (400 °C) sintering and after the application of the pressure], the sample accounts for 19 pct of the total electrical current for RT—673 K (400 °C) sintering and 41 pct for RT consolidation.

4.3 Localized Heating

It is also proposed that localized heating contributes to the observed variations in microstructure. The presence of particle interfaces in loosely packed powders is likely to contribute to localized heating at the contact between two powder particles. The temperature change ΔT close to the contact (Figure 9(a)) of two powder particles can be estimated by[33]
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Fig. 9

The temperature change during a duration of the pulsed electrical current (2.7 ms × 12 = 32.4 ms) and localized pressure close to the particle contact. (a) a schematic diagram and (b) calculated results. The electrical current amperage used is the mean value of Is in the first 3 min shown in Fig. 8. The powder particle diameter is taken as 20 μm, the mold inner diameter = 20 mm

$$ \Updelta T = \frac{1}{{\pi^{2} }}\frac{{I_{\text{p}}^{2} \rho_{\text{es}} \Updelta t}}{{C_{\text{s}} \rho_{\text{ms}} [r_{\text{p}}^{2} - (r_{\text{p}} - x)^{2} ]^{2} }} $$
(8)
where x is the distance in the radial direction from the particle contact as shown in Figure 9(a), rp is the radius of the powder particle, Δt is a duration of the pulsed current (2.7 ms × 12 = 32.4 ms), Cs, ρms, and ρes are the specific heat, the mass density of the particle, and the electric resistivity, respectively, of the particle powder and the same to those in Eqs. [1] to [7], and Ip is the current passing through the powder particle, which can be calculated by[33]
$$ I_{\text{p}} = \frac{{4r_{\text{p}}^{2} }}{{\phi^{2} }}I_{\text{s}} $$
(9)
where ϕ is the diameter of the sample and Is is the current flowing through the sample. The ΔT calculated using the averaged value of Is of the first 3 minutes in Figure 8 is shown in Figure 9(b). It can be seen that the ΔT is higher in the case of using the GMPTA relative to that using the WCMPTA. The higher localized temperature can facilitate the grain growth and thus formation of a localized coarse microstructure. Not surprisingly, the proportion of coarse grains in sample 5083-G is higher than that in sample 5083-WC, as shown in Figures 5(a) through (d).

4.4 Localized Pressure

The localized pressure also influences microstructure. During SPS, the pressure Pc close to the contact of two powder particles can be estimated by (Appendix B)
$$ P_{\text{c}} = \frac{\sqrt 2 }{\pi }P_{\text{a}} \frac{{r_{\text{p}}^{2} }}{{r_{\text{p}}^{2} - (r_{\text{p}} - x)^{2} }} $$
(10)
where Pa is the applied pressure, rp is the radius of the particle, and x is the distance to the contact point. The localized pressure has a magnitude in the GPa range close to the particle contact point (Figure 9). Published results show that a high pressure can induce grain growth in nanostructured metals or alloys at high temperatures[34] and in some cases, even at room temperature.[3537] It is hence suggested that a high localized pressure, coupled with a high local temperature and electrical current density, is the factor that will enhance grain growth in regions close to the contact points. TEM observations provide support to this suggestion as shown in Figures 5(a) and (c).

5 Summary

Al 5083 nanostructured powders were consolidated via SPS using graphite and WC-Co tooling. The resultant differences in microstructure were discussed using a theoretic framework based on the physical properties of graphite and WC-Co and revealed two important findings. First, the powders experienced different heating rates and thus different thermal profiles under two circumstances, although the molds experienced almost identical thermal profiles during SPS. Second, differences in sample electrical current density, local temperature coupled with local pressure influenced microstructural evolution during SPS.

Acknowledgments

This paper is based upon work supported by the US Army TACOM-ARDEC under contract No. W05QKN-09-C-118 and the Office of Naval Research with grant No. N00014-07-1-0745. Part of D. Liu’s work is also supported by the Young Scientist Foundation of Shandong Province, China (No. BS2009CL043), and the innovation foundation of Shandong University (2012TS032).

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© The Minerals, Metals & Materials Society and ASM International 2012