Final stage free sintering and sinter forging behavior of a yttria-stabilized tetragonal zirconia

PII: S1359-6454(97)00105-5

Acta mater. Vol. 46, No. 2, pp. 719±729, 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Britain 1359-6454/98 $19.00 + 0.00

FINAL STAGE FREE SINTERING AND SINTER FORGING BEHAVIOR OF A YTTRIA-STABILIZED TETRAGONAL ZIRCONIA D. M. OWEN1 and A. H. CHOKSHI2{ Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, U.S.A. and 2Department of Metallurgy, Indian Institute of Science, Bangalore 560012, India

1

(Received 11 January 1997; accepted 4 March 1997) AbstractÐA comprehensive study was undertaken to characterize quantitatively the ®nal stage sintering behavior of a yttria-stabilized tetragonal zirconia (YTZ) under free sintering and sinter forging conditions and to evaluate the role of deformation which occurs concurrently during sinter forging. The results indicated that the activation energies for densi®cation were 585 245 and 620270 kJ molÿ1 during free sintering and sinter forging, respectively, which were similar to the value of 6502 70 kJ molÿ1 observed for deformation during sinter forging. Sinter forging experiments revealed that the densi®cation rate, rÇ, was proportional to s2, where s is the applied stress, whereas the deformation rate, Çe, was proportional to s3. Microstructural observations showed that grain growth kinetics were independent of the volume fraction of porosity. After extensive creep deformation during sinter forging, grains remained equiaxed with average linear intercept grain sizes of 0180 nm. A detailed analysis of possible mechanisms revealed that densi®cation in YTZ is controlled by the rate of grain boundary vacancy absorption. Furthermore, it was demonstrated that deformation mechanisms in porous and dense YTZ are identical.

1. INTRODUCTION

The availability of ceramic powders with crystallite sizes of less than 100 nm has generated considerable interest in the development and properties of dense materials with nanocrystalline grain sizes [1, 2]. One of the potential applications of these materials is in superplasticity, involving large strain to failure, in which the strain rate for superplastic deformation is inversely proportional to the grain size raised to an exponent greater than 02 [3]. The potential applications of these materials in bulk form have not yet been realized due to the rather limited success in sintering these powders to full density while retaining the initially ®ne crystallite sizes. In summarizing early data on sintering of several ceramics, Gupta [4] observed a sharp increase in the grain size as the relative density exceeded 090%. This value of relative density is associated with a transition from the intermediate to the ®nal stage of sintering which corresponds to a change from a continuous open pore network to the development of an isolated pore structure. Clearly, an understanding of the processes associated with ®nal stage sintering is essential for progress in the fabrication of bulk nanocrystalline ceramics. Finer grained ceramics can be produced by utilizing techniques which increase the densi®cation rate

relative to the grain growth rate by enhancing densi®cation and/or hindering grain growth. Stress or pressure assisted sintering techniques are employed commonly to enhance densi®cation rates and shorten processing times at high temperatures. The technique of sinter forging, referring to sintering under an applied uniaxial load with no lateral constraint, was ®rst utilized by Rahaman and coworkers [5, 6] and Venkatachari and Raj [7, 8] who recognized the need to understand the in¯uence of high temperature deformation processes on sintering behavior; the shape change of a specimen during such experiments arises from the concurrent processes of creep and densi®cation. The measurements of the axial strain and either the transverse strain or the density can be utilized to evaluate simultaneously the kinetics of creep deformation and densi®cation. The kinetics of densi®cation can be represented generally as
exp…ÿQS =RT†…s=3 ‡ sS †q rA …1† where rÇ is the densi®cation rate, QS is the apparent activation energy for sintering, R is the gas constant, T is the absolute temperature, s is the applied stress, sS is the inherent sintering stress and q is the stress exponent for densi®cation. Similarly, high temperature creep deformation may be expressed by an equation of the form: p
…s=G†n …2† eA…b=d† where Çe is the strain rate, b is the magnitude of the

{To whom all correspondence should be addressed. 719

720

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING

Burgers vector, d is the grain size, p is the inverse grain size exponent, and n is the stress exponent. As noted elsewhere, equations of this form can be used to analyze deformation by both di€usion creep and dislocation creep [9]. An equation of this form is utilized to evaluate the stress exponent for creep during sinter-forging, and to compare the creep behavior of porous and fully dense ceramics. Following the initial report by Wakai et al. [10] of an elongation of 170% in a superplastic 3 mol% yttria stabilized zirconia (3YTZ), there have been numerous studies on superplasticity in this material [11]. In the context of superplasticity and nanocrystalline materials, it is interesting to note that nanocrystalline zirconia powders were made ®rst by Mazdiyasni et al. [12] almost thirty years ago. Nanocrystalline 3YTZ powders with crystallite sizes of <50 nm are now readily available on a commercial scale. However, free sintering of these powders leads usually to grain sizes on the order of 00.3 mm in bulk specimens. In spite of the numerous studies on factors such as the in¯uence of agglomerates on processing, and transformation toughening in zirconia, a review of the literature reveals a sparseness in quantitative data on densi®cation in zirconia, especially on the ®nal stage of sintering. Slamovich and Lange [13] studied the ®nal stage sintering characteristics of 3YTZ containing model pore sizes and distributions created by the pyrolization of latex spheres; they concluded from microstructural observations that the rate of pore closure during ®nal stage sintering was dependent on the number of grain boundaries intersecting the pore surface. Wang and Raj [14] reported an activation energy of 615280 kJ molÿ1 for sintering of zirconia; however their data were obtained at lower relative densities in the range of 70±80%, corresponding to the intermediate stage of sintering. Recently, Chen and Mayo [15] have been successful in producing fully dense 3YTZ compacts with a grain size of 85 nm by low temperature free sintering. It is generally recognized that the rate of densi®cation can be enhanced signi®cantly by the application of a compressive load. Hot-pressing involves the application of a uniaxial compressive load to a porous solid placed within a cylindrical die, whereas sinter-forging involves the application of a compressive load on a porous solid without any lateral constraints. There is very limited information available on the sinter forging characteristics of YTZ. Panda et al. [16] conducted experiments on YTZ compacts under constant displacement rate conditions at a single temperature. Ciftcioglu and Mayo [17] and Akmoulin et al. [18, 19] reported results on the deformation behavior of porous YTZ under constant strain rate conditions; in these studies, analyses of experimental data did not consider the shape change arising from densi®cation. Preliminary ex-

periments on free sintering and constant load sinter-forging of 3YTZ revealed that it was possible to obtain ®ner grain sizes by sinter-forging [20]. Boutz et al. [21] also studied the low temperature sinterforging characteristics of a 2.6 mol% yttria stabilized zirconia. More recently, Skandan and coworkers [22] reported a grain size of 45 nm in fully dense 3YTZ sinter forged at relatively high pressures and low temperatures. A comparison of the above sinter-forging experiments reveals several discrepancies. First, while Panda et al. [16] and Ciftcioglu and Mayo [17] reported stress exponent values for creep, n, of 03, Akmoulin et al. [18, 19] obtained a stress exponent of 02 and Boutz et al. [21] reported a value of 02.6. A similar discrepancy has been noted in deformation studies on fully dense 3YTZ [11], and this may be related in part to the di€erences in impurity content of the powders. Second, while Panda et al. [16] attributed densi®cation to a plasticity controlled process, based on the observation that the volumetric strain (densi®cation) was related solely to plastic strain, Boutz et al. [21] noted that densi®cation was related both to plastic strain as well as the stress. Finally, in none of the above studies on sinter-forging were fundamental parameters such as the temperature or stress dependence of the densi®cation rate evaluated explicitly. The present study was undertaken with the speci®c objective of investigating quantitatively the role of concurrent deformation during ®nal stage sintering in an yttria stabilized tetragonal zirconia by characterizing the stress and temperature dependence of densi®cation and deformation during sinter forging. These results are compared to observations made on specimens which were sintered without an applied stress. 2. EXPERIMENTAL

High purity 3 mol% yttria stabilized tetragonal zirconia (3YTZ) powders obtained from the Nikkato Corporation, Japan, were utilized for the present experimental study. The following compositional analysis was provided by the manufacturer in wt%: Y2O3: 5.28 (=2.95 mol%), Al2O3: <0.005, SiO2: <0.002, Fe2O3: 0.004, Na2O: 0.020, ZrO2: Balance. The as-received powder was characterized using electrophoresis, BET and transmission electron microscopy. Slurries containing 20 vol.% solids were prepared in high purity water with a resistivity of 18.2 MO, assuming a theoretical density for 3YTZ of 6.08 g cmÿ3. The slurry was dispersed with additions of hydrochloric acid to adjust the pH to 2.0 2 0.2, vibrated ultrasonically, and ¯occed immediately using dilute sodium hydroxide to adjust the pH to 07. Cylindrical specimens 9.5 mm in diameter were formed by pressure ®ltration at 20 MPa, and were dried for a minimum of 12 h at

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING

90±958C. The relative green densities of the pellets, r0, were determined from measurements of the specimen dimensions and weight. The free sintering and sinter forging experiments described below were conducted in air in the temperature range of 1523 to 1723 K. The specimens were heated rapidly to 773 K in 10 min; the heating rate was then reduced to 10 K minÿ1 between 773 K and the desired sintering temperature. During free sintering experiments, the temperature was held at the isothermal sintering temperature until the apparent relative density exceeded 99%, or for a maximum of 25 h. Sinter forging experiments were interrupted after a predetermined time at which point the load was removed. The density of the sintered specimens was determined using Archimedes' principle with ethyl phthalate as the immersion ¯uid. Repeated density measurements indicated that the measured relative densities were accurate to within 00.2%. In addition, the creep strain accumulated during sinter forging, ec, was calculated using the measured axial strain, ez, and the change in relative density, with the equations given by Raj [23]:   1 r ec ˆ 3ez ‡ ln f …3† ri 3 where rf and ri are the ®nal and initial densities, respectively. The free sintering behavior was characterized by the measurement of radial shrinkage using alumina dilatometry. The variation of density with time for each experiment was calculated by assigning the ®nal specimen diameter and relative density to the last datum point collected at the sintering temperature and using the relation rrel=rf(Df/Drel)3, where rrel is the instantaneous relative density, rf is the ®nal relative density, Df is the ®nal specimen diameter, and Drel is the instantaneous specimen diameter. Additionally, some pellets were sintered for shorter times without concurrent shrinkage measurements to characterize the microstructural evolution. All the specimens fabricated for sinter forging were presintered simultaneously in air to increase the relative density to approximately 75%; the ends on the compacts were then ground parallel and the densities were determined from mass and dimensional measurements. Sinter forging experiments were conducted under constant compressive load conditions, without any transverse constraints, at temperatures in the range of 1573±1673 K. The loads were chosen to give nominal initial stresses of approximately 10, 16 and 26 MPa, de®ned as the load divided by the cross sectional area without accounting for specimen porosity. The specimens were positioned in the center of two SiC loading rams and the furnace was heated to the sinter forging temperature using the heating cycle described above. The load was applied as the furnace reached

721

the isothermal sinter forging temperature. Sinter forging times were chosen to give ®nal relative densities in the range of 090 to 100% for each temperature±load combination. Specimens were heated also to the three sinter forging temperatures without an isothermal hold or the application of load to determine the initial density and grain size for each of the three temperatures. Following free sintering or sinter forging selected specimens were examined by scanning electron microscopy to characterize the microstructure. Sinter forged specimens were ground ®rst to reveal a ¯at surface parallel to the loading axis. The specimens were mounted and polished metallographically to a 0.25 mm diamond ®nish. The polished sections were etched thermally at least 50 K below the sintering temperature for no more than 1 h, which resulted in no measurable change in the relative density. The specimens were coated with a thin layer of gold and examined using a Cambridge 360 scanning electron microscope. The grain sizes were measured directly from the scanning electron micrographs using an image analysis system. Sucient linear intercept measurements were made to reduce the error of the mean for 95% con®dence level to R5%. The grain sizes of the sinter forged specimens were measured in the directions parallel, L1, and perpendicular, L2, to the stress axis; the average grain size was de®ned as L = (L1L22)1/3. 3. RESULTS

The results from the powder characterization, free sintering, and sinter forging experiments on single phase 3YTZ are presented in the following sections. 3.1. Powder characterization The determination of the zeta potential as a function of pH for the as-received powder revealed that the isoelectric point (IEP), de®ned as the pH where x = 0, occurs at 07. The maximum value of x was 040 mV for pHs ranging from 2 to 4. The speci®c surface area determined using BET was 12.62 m2 gÿ1. Examination of several transmission electron micrographs of the powders in the dispersed state revealed the individual crystallites to be approximately equiaxed with a narrow size distribution. Aggregates consisting of a few crystallites also were observed. Direct measurements of several crystallites resulted in an average particle size of 4325 nm. 3.2. Free sintering behavior of 3YTZ The relative density of the ®lter pressed and dried green bodies, r0, was typically 39.5 20.5%. The di€erence between the ®nal specimen diameter measured with the radial dilatometer during the experiment and calipers following the experiment was

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING

less than 40 mm. It was observed also that the mass decreased slightly during sintering by 01%. Evaluation of the calculated variation of relative density with time resulted in several observations. First, the relative green density calculated by extrapolating the curves back to the beginning of the experiment was 38.7 20.2% as compared with the measured green densities of 39.5 20.2%. This slight discrepancy can be attributed to the observed loss in specimen mass during sintering noted above. Second, the constant heating rate portion of the curves were identical for the three specimens sintered isothermically at 1623, 1673 and 1723 K and shrinkage initiated by 1325 K for all three specimens. The uniformity of the sintering behavior during constant heating rate sintering indicates that specimen to specimen variation was negligible. 1.05

(a)

1.00 0.95 0.90

ρrel

0.85 0.80

3YTZ ρO = 40%

0.75 0.70

T (K)

ρi (%)

0.65

1623 1673 1723

60.4 64.6 77.1

0.60 0.55

0

25

50

100

75

t (s) x 103

(b)

3YTZ ρO = 40% T (K) ρi (%)

10 -4

r

60.4 64.6 77.1

10-4

·

10-5

Q R

10-6 5.70

5.80

5.90

6.00

6.10

6.20

104 T -1 (K-1) Fig. 2. Arrhenius plot of densi®cation rate vs reciprocal absolute temperature for relative densities between 86 and 96%. The apparent activation energy for sintering of 3YTZ varies substantially with relative density.

Finally, it should be noted that the relative densities corresponding to the onset of isothermal sintering, ri, were signi®cantly di€erent: the values of ri were 60.4, 64.6 and 77.1% for sintering temperatures of 1623, 1673, and 1723 K, respectively. Figure 1(a) shows the variation in relative density with isothermal sintering time for specimens sintered at 1623, 1673 and 1723 K. Inspection of the data reveals clearly that relative densities of >99% are obtained by free sintering for 07 and 14 h at 1723 and 1673 K, which is consistent with data reported earlier for 3YTZ. The densi®cation rate is plotted against the relative density in Fig. 1(b): the densi®cation rate decreased continuously with increasing relative density. The data shown in Fig. 1 were used to determine the activation energy for sintering at constant values of relative density. Figure 2 is a plot of the densi®cation rate vs reciprocal absolute temperature at relative densities between 86 and 96%. The activation energies calculated in this manner varied greatly from 830 to 480 kJ molÿ1, decreasing with increasing relative density, with errors as high as 175 kJ molÿ1. 3.3. Sinter forging behavior of 3YTZ

(s-1) ·

1623 1673 1723

3YTZ Q (kJ mol-1) 86 830 + – 175 88 795 + – 155 90 770 + – 110 92 720 + – 30 94 624 96 480

ρrel (%)

ρ (s-1)

722

10

-5

10 -6 84

88

92

rrel (%)

96

100

Fig. 1. (a) Variation in the relative density with time for free sintering of 3YTZ at temperatures of 1623, 1673 and 1723 K; (b) Variation of densi®cation rate with relative density for 3YTZ free sintered at temperatures of 1623, 1673 and 1723 K.

The sinter forged specimens exhibited little or no barrelling and were crack free. The specimen diameters changed very little during sinter forging. The transverse strains, de®ned as et=ln(Df/Di), where Df and Di are the ®nal and initial specimen diameters, respectively, were less than 22.5% with the exception of the highest stress at 1623 K. At the highest stress the transverse strains ranged from 5 to 10%. Figure 3 shows the variation with time in the relative density (left axis) and creep strain (right axis) for specimens tested at 1623 K and a stress of 10 MPa. It is apparent from Fig. 3 that the densi®cation and deformation rates, indicated by the

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING 24

110 10

ρrel (%)

εc (%)

90 8

3YTZ T = 1623 K σ = 10 MPa

4 0

85

R 75

0

8000

10

70 16000

3YTZ T = 1623 K ρrel (%) q 90 92 94 96

2.0 2.1 2.2 2.3

± ± ± ±

0.2 0.1 0.2 0.4

1 q

10-5 10

σ (MPa)

-6

5.90

6.00

6.10

6.20

6.30

6.40

6.50

10 4 T -1 (K-1)

slopes of the respective curves, decrease continually with increasing time or density. The variation of the densi®cation rates and deformation rates with relative density were determined from the slope of the best ®t curve to the date of the type shown in Fig. 3 for each combination of stress and temperature. The in¯uence of stress on densi®cation rate is illustrated in Fig. 4, which is a logarithmic plot of densi®cation rate vs stress for various relative densities at T = 1623 K. The data clearly fall on parallel straight lines so that rÇAsq, with values of q equal to 2.0, 2.1, 2.2 and 2.3 for relative densities of 90, 92, 94, and 96%, respectively. Similarly, from a logarithmic plot of creep rate vs stress, the creep stress exponents, n, were calculated to be 3.1, 3.1, and 3.4 for relative densities of 90, 93 and 97%, respectively.

ρ· (s-1)

20 10 10 10

Q

80

Fig. 3. Variation with time in relative density (right) and creep strain (left) for 3YTZ specimens sinter forged at 1623 K and 10 MPa.

5

± ± ± ±

10-5

t (s)

10-4

-4

600 580 610 690

ρ· (s-1)

10

95 12

10-3

90 92 94 96

100

16

-4

3YTZ σ = 10 MPa ρrel (%) Q (kJ mol -1)

-3

105

20

723

50

Fig. 4. In¯uence of applied stress on densi®cation rate during sinter forging of 3YTZ for relative densities between 90 and 96%. The stress exponent for densi®cation, q, was 02 each value of rrel.

Fig. 5. Determination of the activation energy for densi®cation during sinter forging of 3YTZ. The apparent activation energies for densi®cation determined at four values of rrel were between 580 and 690 kJ molÿ1, with an average value of 620 270 kJ molÿ1.

The activation energies for densi®cation and creep were determined from Arrhenius plots of densi®cation rate or creep rate vs reciprocal absolute temperature. Figure 5 illustrates the in¯uence of temperature on densi®cation rate for four di€erent values of rrel. The activation energies for densi®cation, Qs were 600, 580, 610, and 690 kJ molÿ1 for relative densities of 90, 92, 94, and 96%, respectively, resulting in an average value of 620270 kJ molÿ1. The temperature dependence of creep deformation at di€erent relative densities, determined in a similar manner, yielded values of the activation energy for creep deformation, Qc, of 720, 640 and 580 kJ molÿ1 for relative densities of 90, 93 and 97%, respectively, with an average value of 6502 70 kJ molÿ1. The in¯uence of porosity on creep rate for di€erent stresses was determined by evaluating the variation of the creep rate with apparent porosity, fa, de®ned as 1 ÿ rrel, at a temperature of 1673 K for di€erent stresses. As reported below, the grain size did not increase signi®cantly during sinter forging at 1673 K, and therefore, the observed decrease in the deformation rate with time can be attributed solely to the change in fa. The creep rate was observed to increase exponentially with porosity: the variation of creep rate with porosity may be de®ned using a relation of the form ÇedAeÇ fexp(ÿafa) where Çed is the creep rate of the dense material, Çef is the creep rate of the material with porosity fa and a is an empirically determined constant. The values of a calculated for stresses of 10, 16 and 25 were 22, 18 and 18, respectively, with an average value of 19. 3.4. Microstructural characterization Several specimens were free sintered at 1673 K without concurrent measurement of radial shrink-

724

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING

Fig. 6. Scanning electron micrographs of 3YTZ sintered at 1673 K: (a) free sintering, rrel070%, L = 150 nm, (b) free sintering, rrel=96.5%, L = 210 nm and (c) sinter forged, 10 MPa, rrel=99.7%, L = 180 nm. Grains remained equiaxed during sinter forging after the accumulation of 25% creep strain.

age for various times to obtain a range of relative densities. The microstructural evolution during sinter forging was characterized using measurements of grain size prior to sinter forging and after the longest duration experiment for each combination of stress and temperature. The initial grain size was determined from specimens which were heated to each of the three di€erent sinter forging temperatures without the isothermal soak or the application of load. Figure 6 shows scanning electron micrographs of specimens densi®ed at 1673 K: (a) free sintered with rrel070%, (b) free sintered with rrel=96.5%, and (c) sinter forged at 10 MPa with

rrel=99.7%, with grain sizes of 0150, 210 and 180 nm, respectively. The microstructures contain a narrow distribution of equiaxed grains and it is clear from Fig, 6 that grain growth during sintering of 3YTZ is not very rapid. During sinter forging the values of the grain aspect ratio, L1/L2, were between 0.93 and 1.07 even though creep strains as high as 40% were accumulated. Figure 7 illustrates the variation of the average linear intercept grain size, L, with relative density for free sintering (open symbols) and sinter forging (®lled symbols). During free sintering, the average grain size appears to increase more rapidly as the relative density exceeds 90%. However, the average grain size increases only by a factor of 1.5 as the relative density increases from 70 to 99%. In ad-

240

220 B

9

3YTZ Free sintered Sinter forged

8 7

L (nm)

180 B B B

B

160 B

–3 – 3 L – L o (nm 3 ) x 10 6

B

200

3YTZ T = 1673 K

6 5 4 3 2

B B

140

1 0

120 60

65

70

75

80

85

ρrel (%)

90

95 100 105

Fig. 7. Variation of average grain size with relative density for free sintered (open symbols) and sinter forged (®lled symbols) 3YTZ. Average grain sizes in the sinter forged specimens were typically smaller: all the nearly dense specimens sinter forged at 1573 and 1623 K had a ®nal average grain size of 0180 nm.

0

10000

20000

30000

t – t o (s) Fig. 8. Evaluation of the grain growth kinetics during free sintering of 3YTZ at 1673 K. The data plotted as L3ÿL30 vs time fall on a single straight line as the relative density increases from 70 to 0100%, indicating that the grain growth behavior is independent of porosity.

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING

N

LNg ÿ L0 g ˆ Kg …t ÿ t0 †

…4†

where Ng is the grain growth exponent, Kg is a temperature dependent kinetic constant, and subscripts 0 refer to initial values. In a porous material both grain boundaries and pores must migrate for grain growth to occur and the pores to remain at the boundary. Therefore, the e€ective boundary mobility will be controlled by the slower of pore mobility or the inherent boundary mobility. Theoretical predictions of Ng are in the range of 2±4 for various processes [24], with a value of Ng=3 being reported for grain growth in dense 3YTZ [25]. The kinetics of grain growth during sintering were evaluated by plotting L3ÿL30 vs time for the data obtained on free sintered 3YTZ at 1673 K, as shown in Fig. 8. The initial grain size, L0, corresponds to an isothermal sintering time of t = 0. Inspection of Fig. 8 shows that the data fell on a single straight line; although the relative density increases from 70% to nearly 100%, there is no apparent change in the kinetics of grain growth. From the slope of the curve in Fig. 8, the kinetic constant Kg, was calculated to be 2.5  10ÿ25 m3 sÿ1.

4. DISCUSSION

The discussion that follows will ®rst address the observed dependences of the densi®cation and deformation rates on experimental parameters and the microstructural evolution, The second part will examine the possibility of various rate controlling mechanisms for densi®cation of 3YTZ. 4.1. Evaluation of parameters for densi®cation and deformation 4.1.1. E€ect of stress on densi®cation and deformation. The in¯uence of stress on densi®cation behavior was illustrated in Fig. 4, where the densi®cation rate was shown to be proportional to s2, independent of the relative density. This represents the ®rst report of the stress dependence of densi®cation during sinter forging of 3YTZ. Panda et al. [16] plotted the densi®cation rate vs stress on a linear scale and noted that the curves were non-linear, but they did not obtain explicitly the relationship between the densi®cation rate and the stress. Similarly, Boutz et al. [21] also concluded that the densi®cation±stress relationship was non-linear, but they did not characterize the relationship explicitly. The

implications of a densi®cation stress exponent value of q = 2 will be discussed in more detail below. The early studies on sinter forging of ceramics suggested that the inherent sintering stress could be estimated experimentally as function of relative density [8, 9]. The total driving potential for sintering is the sum of the inherent sintering stress, ss, and the hydrostatic component of the applied stress, s/3. Therefore, the densi®cation rate may be expressed as s q
rA …5† ‡ sS 3 The sintering stress may be estimated graphically as a function of relative density by plotting rÇ 1/q vs s/3 on a linear scale: sS is determined at the intersection of the extrapolated data with the stress axis at rÇ =0. The data from the present study (Fig. 4) were evaluated in this manner for four values of relative density: 90, 92, 94 and 96%. The analysis revealed that each line intersected the stress axis near zero, and the errors associated with extrapolating the best ®t straight line to rÇ =0 were on the order of any apparent di€erences in the individual values of sS. The near zero values of sS indicate that the inherent sintering stress in 3YTZ is small compared with the hydrostatic component of the applied stress. The creep stress exponent of n = 3 obtained in the present study on porous 3YTZ tested under sinter-forging conditions is comparable to the values observed in creep of fully dense 3YTZ [11], and has also been reported in other studies on sintering forging [16, 17]. The deformation behavior of porous and dense 3YTZ may be compared directly at a constant temperature by appropriately compensating the strain rates for di€erences in grain size and 10-1

10-2

· exp(–αφ ) (µm s-1) εL a

dition, it is clear that grain growth during sinter forging is minimal for the specimens sinter forged at 1573 and 1623 K: all the fully dense specimens have approximately equivalent grain sizes. The grain sizes at the highest temperature, 1673 K, are comparatively larger by 013% and 022% for the initial and ®nal conditions, respectively. Normal grain growth kinetics are expressed typically using an equation of the form

725

10-3 10-4

3YTZ T = 1673 K α = 19 φa (%) L (µm) 0 0.41 3 0.18 7 0.18 10 0.18

10-5

10-6 10-7 3

10

σ (MPa)

100

300

Fig. 9. Creep strain rate compensated by grain size and porosity vs stress for 3YTZ at 1673 K. Data obtained on fully dense 3YTZ [11, 26] and porous 3YTZ fall on the same curve indicating the operation of identical deformation mechanisms.

726

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING

3YTZ -1 Q = 585 ± 45 kJ mol ρrel (%)

10-4

. ρρn (s -1 )

86 88 90 92 94 96

10-5

Q R

5.70 5.80

5.90 6.00 6.10 6.20 10 4 T -1(K -1 )

6.30

Fig. 10. Densi®cation rate normalized by initial and instantaneous relative density vs 1/T. The data obtained at 1623 and 1673 K all coincide at single points: the activation energy determined in this manner was 5852 45 kJ molÿ1.

porosity. Figure 9 illustrates such a plot of compensated strain rate ÇeLpexp(a fa) vs s: the data on dense 3YTZ were taken from an earlier study by the present authors [11, 26, 27]. The exponential relationship between the apparent porosity and strain rate was given above, with the constant a = 19. The inverse grain size exponent for high temperature deformation of 3YTZ when n = 3 has been reported as p = 1 [11, 26, 27]. It is clear that there is excellent agreement between the data, thereby indicating the operation of similar deformation mechanisms in fully dense and porous materials. 4.1.2. In¯uence of temperature on densi®cation and deformation. The activation energy for sintering may be determined from isothermal or constant heating rate experiments. Wang and Raj [14, 28] have shown that the activation energies determined from constant heating rate and isothermal sintering were essentially identical and independent of relative density. The present data on free sintering of 3YTZ yielded a wide range of activation energies over a small range of relative density: the calculated apparent activation energies decreased from >800 kJ molÿ1 at a density of 86% to <500 kJ molÿ1 at 96%. The variation in activation energies may be a result of experimental errors, a change in activation energy with temperature, or the di€erences in initial densities at the isothermal sintering temperature. It is unlikely that experimental error or di€erences in individual specimens resulted in the observed variations in activation energies for sintering. As noted earlier, the specimens exhibited identical sintering characteristics during the con-

stant heating rate portion of the temperature cycle and the relative green densities calculated from the extrapolation of the curves to the start of the heating cycle compared favorably to the measured green densities. Very limited tracer di€usion data are available for the ZrO2ÿY2O3 system [29±31], primarily for cubic yttria stabilized zirconia with higher yttria content. In addition, all of the reported values of Q for the various species are signi®cantly lower than those observed in the present study. Therefore, the possibility of a genuine transition in the activation energy can not be evaluated critically. The initial relative density at the isothermal sintering temperature may also in¯uence the densi®cation characteristics. Macroscopically, the apparent porosity, fa, is indicative of the driving force for sintering and may be expressed in terms of the relative density, rrel, as fa=1 ÿ rrel. The relative decrease in the driving force for sintering with increasing relative density at a given temperature and initial relative density may be expressed as rÇA(1 ÿ rrel)/(1 ÿ ri). It is clear from this relation that the relative decrease in sintering rate at a ®xed value of rrel will be greater as the initial density increases. The e€ect of the initial relative density on the sintering rate can be incorporated by compensating the apparent densi®cation rate by the initial and instantaneous apparent porosities as rÇrn, where rn=(1 ÿ ri)/(1 ÿ rrel). Figure 10 shows a plot of rÇ rn vs Tÿ1 for the present results on 3YTZ using initial densities (ri) of 60.4, 64.6 and 77.1% for sintering temperatures of 1623, 1673 and 1723 K, respectively. The data for 1623 and 1673 K all coincide at a single point, although there is some scatter in the data for 1723 K. The activation energy calculated considering all the points was 585245 kJ molÿ1, which is lower than the values determined without accounting for the variation in initial density. In addition, the errors in activation energies are also reduced substantially. Figure 10 indicates that variations in initial density at the sintering temperature may signi®cantly in¯uence the evaluation of activation energies for sintering. The value of Qs=585245 kJ molÿ1 compares favorably to that reported by Wang and Raj [14] of 615270 kJ molÿ1 determined at lower relative densities of 70%. It should be noted that in the isothermal sintering experiments of Wang and Raj [14] the initial densities were very similar. In addition, the average activation energy for densi®cation determined from the sinter forging experiments was 620270 kJ molÿ1. The excellent agreement between these values indicates the di€using species and path controlling the rate of sintering is independent of relative density in the range of 070±100%, and whether sintering is conducted with or without a uniaxial stress.

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING

In the present study, the average creep activation energy observed during sinter forging was 650 270 kJ molÿ1. It is interesting to note that activation energies for elevated temperature deformation of 0600 kJ molÿ1 are reported often in studies on 3YTZ, as tabulated elsewhere [11]. 4.1.3. Microstructural evolution. The kinetics of grain growth have been evaluated in some detail above, and it was shown that the presence of pores does not alter the kinetics of grain growth in 3YTZ. Slamovich and Lange [13] observed that the pores were similar in size or larger than the grains and therefore would not in¯uence the e€ective mobility of the grain boundaries. There were two signi®cant observations regarding the microstructural evolution during sinter forging. First, the measurement of the linear intercept grain size in the directions parallel and perpendicular to the stress axis revealed that the grains remained essentially equiaxed after accumulation of creep stains approaching 40%, thereby suggesting that deformation in 3YTZ occurs by a grain boundary sliding/grain rearrangement process [3, 10, 11, 27]. Second, the ®nal grain sizes were equivalent in the nearly dense specimens sinter forged at 1623 K and various stresses; the linear intercept grain size was 0180 nm, even though the processing times were di€erent. The kinetic constant for grain growth, Kg, at di€erent stress at 1623 K can be estimated using equation (3), with Ng=3, and the relevant experimental data. The values of Kg were calculated as 1.5  10ÿ25, 6.3  10ÿ25, and ÿ25 3 ÿ1 15.8  10 m s , for stresses of 10, 16 and 25 MPa, respectively: an increase by a factor of 010 as the stress increases from to 10 to 25 MPa. Therefore, it is clear that stress enhances or dynamic grain growth occurs in porous 3YTZ. Panda et al. [16] also reported that the average grain size in dense specimens was 300 nm, regardless of the displacement rate and, hence, processing time. Extensive dynamic grain growth during tensile deformation of dense 3YTZ has also been reported by Nieh and Wadsworth [25] and Schissler et al. [32]. These results imply that the reduction in grain size during sinter-forging is related largely to the shorter testing time as compared with free sintering. 4.2. Evaluation of possible stress-assisted densi®cation mechanisms Pore closure during sinter forging may occur as a result of plastic deformation around the pore or the di€usional ¯ow of vacancies away from the pore. These two mechanisms operate independently of one another and, therefore, the faster process will control the rate. Di€usional pore shrinkage involves vacancy migration and vacancy absorption, the slower of which will control the rate of pore closure. Each of these three possible rate controlling

727

mechanisms (plastic deformation, vacancy migration and vacancy absorption) will be considered below and compared to the results obtained on 3YTZ. Models for plasticity controlled pore closure are of the form suggested by Hancock [33] or Beere and Speight [34]: @rp =@tArp e
…5† where rp is the pore radius. Since the strain rate, Çe, is proportional to sn, plasticity controlled pore closure implies a similar stress dependence for both deformation and densi®cation, i.e. n = q. During sinter forging of 3YTZ the value of n was 3, whereas the densi®cation stress exponent q was 2, independent of relative density. Therefore, the present results are not consistent with a plasticity controlled shrinkage mechanism. It should be noted that Panda et al. [16] attributed the observation of the non-linear variation of the densi®cation rate with stress and the approximate correlation between creep strain and volumetric or densi®cation strain to the occurrence of plasticity controlled densi®cation on 3YTZ. This suggestion is not supported by the results obtained in the present study or by the study of Boutz et al. [21]. Di€usional closure of spherical pores resulting from an applied compressive stress has been modelled in three dimensions recently by the authors [35, 36] assuming the migration and absorption of vacancies in grain boundaries, with pores coordinated by several tetrakaidecahedral grains. Irrespective of the speci®c details, all models of pore closure controlled by vacancy di€usion will lead to a densi®cation rate that is directly proportional to stress, such as in di€usional creep [37± 39], or models developed for cavity growth [34, 40, 41]. A linear dependence of the densi®cation rate on stress was not observed in the present experiments (q = 2) and, therefore, densi®cation may not be attributed to a vacancy migration controlled process. One speci®c model for densi®cation controlled by the rate of vacancy absorption leads to an expression for the pore closure rate @rp/@tAs2 [36]; this model is based on an earlier analysis by Burton [42] for interface reaction controlled di€usion creep. The stress dependence predicted for the vacancy absorption process is q = 2, which agrees with the value determined experimentally. Therefore, it is concluded that densi®cation rate in 3YTZ is controlled by the process of grain boundary vacancy absorption. Similar to migration controlled di€usional pore shrinkage, equations for vacancy absorption controlled pore shrinkage are analogous to models of interface reaction controlled di€usional creep [42, 43], which predict a non-linear stress dependence for creep deformation.

728

OWEN and CHOKSHI: FINAL STAGE FREE SINTERING 5. SUMMARY AND CONCLUSIONS

REFERENCES

1. The application of uniaxial sinter forging stresses signi®cantly enhanced the rate of densi®cation in a 3 mol% yttria stabilized tetragonal zirconia (3YTZ). It was shown the densi®cation rate was proportional to the square of the stress: this represents the ®rst report of the stress dependence of densi®cation in 3YTZ. A critical evaluation of the possible densi®cation mechanisms revealed that the present results are consistent with densi®cation controlled by an interface reaction process involving vacancy absorption. 2. Free sintering and sinter forging experiments indicated that the activation energies for densi®cation and deformation may be expressed by an average value of 0615 kJ molÿ1. It was demonstrated that a lack of proper consideration of variations in the initial densities at the sintering temperature can lead to erroneous determinations of the activation energy for sintering. 3. A creep stress exponent of n = 3 was determined and the creep rate was found to vary exponentially with the apparent porosity. It was illustrated that deformation rates in dense and porous materials compared favorably when the data are compensated for di€erences in grain size and porosity, thereby demonstrating that porous and dense 3YTZ deform by the same mechanism. 4. Microstructural observations revealed that the grain growth behavior was independent of the relative density in the range of 070 to 100% and, therefore, the presence of pores and pore morphology did not in¯uence the grain boundary mobility. During sinter forging it was observed that the grains remained ®ne and equiaxed after accumulation of large compressive strains, consistent with the occurrence of deformation by a grain boundary sliding mechanism. Final average linear intercept grain sizes of 0180 nm were obtained in fully dense specimens, after sinter-forging powders with an initial crystallite size of 043 nm. The grain growth rates were observed to increase with applied stress, indicating the occurrence of signi®cant deformation enhanced or dynamic grain growth. It is concluded that the ®ner grain sizes achieved by sinter-forging are related to the shorter testing times as compared with free sintering.

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AcknowledgementsÐThis work was supported by the National Science Foundation under Grant No, DMR9023699. One of us (DMO) also acknowledges a fellowship from the Army Research Oce under contract no. DAAL 03-86-G-0196. Additional support of this work by the Department of Science and Technology (India) and the U.S. Air Force Oce of Scienti®c Research is also acknowledged gratefully.

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