Acta Materialia 51 (2003) 3571–3583www.actamat-journals.com

High-temperature deformation of Al2O3/Y-TZP particulatecomposites

Jue Wanga, Eric M. Taleff a,b, Desiderio Kovara,b,∗

a Materials Science and Engineering Program, The University of Texas at Austin, Austin, TX 78712, USAb Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712, USA

Received 10 January 2003; received in revised form 20 March 2003; accepted 21 March 2003

Abstract

Al2O3/Y-TZP particulate composites with compositions of between 20 and 80 vol.% Y-TZP were produced bytapecasting, lamination, and sintering. The processing methods employed resulted in fine grain sizes with only smallvariations between the composites produced. The resulting particulate composites were tested in compression at atemperature of 1350°C over strain rates from 10�5 to 3.16 × 10�4 s�1. Microstructural changes during testing wereminor. Stress exponents were measured to the range from approximately two to three, which are consistent with pub-lished data on similar materials from tensile experiments. Models of composite creep behavior are compared to theexperimental data over the full range of compositions studied. A constrained isostrain model is found to provide betterpredictive capabilities than either an unconstrained model, an isostress model, or a rheological model. Furthermore,the constrained isostrain model provides the most reasonable predictions for creep rates of 100% Al2O3 and 100% Y-TZP materials. 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: High-temperature deformation; Compression test; Creep

1. Introduction

The difficulty of fabricating ceramic componentswith complex shapes has been a major obstacle tothe commercialization of structural ceramics.Because of high hardness and low ductility, mach-ining costs can represent up to 90% of the totalmanufacturing cost for a ceramic component[1].

∗ Corresponding author. Tel.:+1-512-471-6271; fax:+1-512-471-7681.

E-mail address: dkovar@mail.utexas.edu (D. Kovar).

1359-6454/03/$30.00 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.doi:10.1016/S1359-6454(03)00175-7

The discovery in 1986 of superplastic 3 mol%yttria-stabilized tetragonal zirconia (3Y-TZP)brought the promise of dramatically reducingmanufacturing cost by allowing ceramics to be for-med to near-net shape at elevated temperatures[2].Since that time, superplasticity has been reportedin a wide variety of ceramics and ceramic com-posites[2–8]. One prerequisite for achieving super-plasticity in ceramics is a fine grain size that isresistant to both static and dynamic grain growth.Particulate composites consisting of two well-mixed phases can exhibit high resistance to coars-ening[9] and, therefore, provide a path for achiev-

3572 J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

ing superplasticity [10]. The high-temperaturedeformation behavior of particulate compositesconsisting of Al2O3 and Y-TZP has been studiedextensively, largely because these two-phase com-posites are stable in air at high temperatures, donot form intermediate compounds, and can exhibitremarkably high tensile elongations of up to625% [11].

Previous studies of Al2O3/Y-TZP compositeshave shown that, when tested in tension, the stressexponent is about 2 over a large range of compo-sitions (0–80% Al2O3), strain rates (10�7–10�2 s�1)and temperatures (1250–1650 °C), suggesting thata common deformation mechanism may existunder these conditions [12–15]. Most of the studiesof Al2O3/Y-TZP particulate composites haveaimed at achieving superplasticity; thus, testingtemperatures in these studies have generally beenvery high (1450–1650 °C). At these temperatures,dynamic grain growth and other microstructuralchanges, such as alteration of grain shape and cavi-tation, have been observed [15,16]. As suggestedby Nieh et al. [17], differences in grain sizebetween composites with different compositions,as well as microstructural changes during testingat high temperatures, make the interpretation ofdeformation mechanisms quite challenging.

In the present investigation, the influence ofAl2O3 volume fraction on the deformation responseof Al2O3/Y-TZP particulate composites at elevatedtemperature is studied for composites ranging from20 to 80 vol.% Al2O3. Ultra-high-purity Al2O3 andhigh-purity Y-TZP were used to fabricate speci-mens in order to minimize impurity content. Pro-cessing routes and processing temperatures wereselected to minimize differences in grain size withcomposition. Specimens were tested in com-pression at a relatively low temperature of 1350 °Cand to relatively small strains (engineering strain of~10%) to minimize microstructural changes duringtesting. With these precautions, the high-tempera-ture deformation behaviors of five Al2O3/Y-TZPparticulate composites containing from 20 to 80vol.% Al2O3 were experimentally evaluated. Thedata obtained are compared to data available in theliterature and to existing theoretical models for par-ticulate composites.

2. Experimental procedure

2.1. Processing

High-purity, 3 mol% yttria-stabilized tetragonalzirconia powder (3Y-TZP, Tosoh, Tokyo, Japan)and high-purity alumina powder (AKP-50, 99.99%purity, Sumitomo Chemical Co. Ltd., Tokyo,Japan) were used as raw materials. A dispersant(PS3, ICI Americas Inc., Wilmington, DE) wasdissolved in methyl ethyl ketone (99.5+%, Mal-linckrodt Baker Inc., Paris, Kentucky), methyl iso-butyl ketone (99.8%, Sigma Chemical Co., St.Louis, MO) and cyclohexanone (99.0%, EMIndustries, Gibbstown, NJ) before adding the cer-amic powders to the liquids. After ball milling theslurries for 24 h, a plasticizer (butyl benzyl phthal-ate, Solutia Inc., St. Louis, MO) and a polymerbinder (Butvar B76, Monsanto Company, St.Louis, MO) were added before mixing again for24 h to homogenize the slurry. Slurries were pre-pared with solid contents of 20, 40, 50, 60, and 80vol.% Al2O3, with the balance Y-TZP. Compo-sitions in this study are designated by the volumefraction of Al2O3; for example, 20A contains 20vol.% Al2O3 and 80 vol.% Y-TZP.

Slurries of each composition were individuallytape-cast onto glass substrates using a doctor bladewith a gap height of 600 µm. The tapes were thor-oughly dried, cut into 23 × 47 mm rectangularsheets, and then stripped from the glass substrate.The rectangular sheets were then stacked within ametallic die and pressed at 120 °C under a pressureof 40 MPa for 15 min to bond the sheets. Follow-ing binder-burnout, the resulting billets were sin-tered in air at 1450 °C for 1 h. The heating rateand cooling rate employed were 5 and 15 °C/min,respectively. Individual specimens were cut fromthe billets and ground to final shape using a dia-mond wafering blade and a diamond grindingwheel.

2.2. Microstructure analysis

The density of each billet was measured usingthe Archimedes method, with water as the immer-sion medium. Specimens were prepared for analy-sis in a scanning electron microscope (SEM) by

3573J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

grinding and polishing with diamond discs, pastes,and suspensions with a final grit size of 1 µm.After polishing, the specimens were thermallyetched at 1370 °C for 20 min to reveal grain struc-ture. SEM images were taken in digital format andwere analyzed using image analysis software(Clemex Vision Version 2.2, Quebec, Canada).Mean grain sizes and grain size distributions, basedon the equivalent circular diameter of individualgrains, were determined. Equivalent circular diam-eter, D, is defined as D = (4A /π)1/2, where A isthe cross-sectional area of the grain. The averagegrain size, d, is 1.27 times the mean equivalent cir-cular diameter [18].

2.3. Mechanical testing

The sintered particulate composites were cut andground into rectangular bars with the dimensions6 × 4 × 4 mm, with the longest edge perpendicularto the laminated layer interfaces. Testing was per-formed at 1350 °C in air using a split tube furnacewith MoSi2 heating elements. Loading was appliedusing a computer-controlled servohydraulic testframe equipped with SiC compression fixtures andwater-cooled mounts. BN powder was used as alubricant between the test samples and the SiCcompression platens to minimize the effects of fric-tion and barreling.

Flow stress was measured during strain-rate-change (SRC) tests using nine steps in engineeringstrain rate, which is defined as the displacementrate divided by the length of the sample at thebeginning of each step. A prestrain of approxi-mately 2% was initially applied at a strain rate of1.00 × 10�4 s�1 in order to ensure mating betweenthe sample and compression platens and to stabil-ize the sample microstructure. Following the pre-strain step, seven steps with strain rates from1.00 × 10�5 s�1 up to 3.16 × 10�4 s�1 wereapplied. The strain rate of 1.00 × 10�4 s�1 wasrepeated in the final step of the series to test forflow stress repeatability. Engineering strain andstress were obtained from load–displacementcurves by assuming that the displacement of thecrosshead corresponded to the reduction in theheight of the specimen, after compensation forelastic deflection. True stress, true strain, and true

strain rate were derived from engineering stress,strain, and strain rate under the assumptions of uni-form deformation and volume conservation. Dueto the small strain for each step, the true strain ratewas within 2% of the engineering strain rate foreach step.

3. Results

3.1. Microstructure

Scanning electron micrographs of the Al2O3/Y-TZP particulate composites containing 20–80vol.% Al2O3 are shown in Fig. 1 both before andafter SRC testing. The grains with the light shadingare Y-TZP and the grains with the dark shadingare Al2O3. The Al2O3 and Y-TZP phases are gener-ally well-dispersed except at high volume fractionswhere some clustering of the phases is apparent.All of the materials exhibit high densities (�98%)and fine grain sizes. Narrow grain size distributionsare observed for both phases, as shown in Fig. 2.The mean grain size of Al2O3 ranges from 0.46to 0.35 µm and decreases slightly with increasingvolume fraction of Y-TZP. The mean grain size ofY-TZP varies from 0.22 to 0.32 µm, with thesmallest size occurring at the greatest Al2O3 con-tent. Average grain sizes and densities are given inTable 1. A comparison of the microstructuresbefore and after testing is shown in Fig. 1 and indi-cates that the grain shapes remain equiaxed andthat very little grain growth occurred during test-ing, as shown in Table 1. In addition, no measur-able change in density was detected after testing,indicating that appreciable cavitation did not occur.

3.2. Deformation behavior

Data from a representative SRC test of a 20Aspecimen are shown in Fig. 3. The total strain forthis test is e = 0.126. After a brief transient at everyrate change, a reasonably steady-state stress is ach-ieved. As is demonstrated in Fig. 3 by the repeatedsteps at a strain rate of 10�4 s�1, the flow stress ata given rate is nearly constant over the range ofstrains imposed in any single SRC test. Behaviorssimilar to those shown in Fig. 3 were observed in

3574 J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

Fig. 1. Scanning electron micrographs are shown of Al2O3/3Y-TZP particulate composite specimens (a) 20A, (b) 20A after testing,(c) 40A, (d) 40A after testing, (e) 50A, (f) 50A after testing, (g) 60A, (h) 60A after testing, (i) 80A, and (j) 80A after testing.

3575J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

Fig. 2. Grain size distributions are shown for (a) 20A, (b) 40A, (c) 50A, (d) 60A, and (e) 80A samples before testing.

3576 J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

Table 1Mean grain sizes and their standard deviations for Al2O3/Y-TZP particulate composites before and after deformation

Particulate Relative Before deformation After deformationcomposite density

(%)

dAl2O3(µm) dY-TZP (µm) dAl2O3

(µm) dY-TZP (µm)

20A 99.1 0.35 ± 0.14 0.32 ± 0.15 0.35 ± 0.15 0.32 ± 0.1240A 98.0 0.39 ± 0.17 0.29 ± 0.12 0.39 ± 0.16 0.31 ± 0.1150A 98.2 0.40 ± 0.16 0.29 ± 0.11 0.41 ± 0.18 0.32 ± 0.1260A 99.4 0.46 ± 0.22 0.30 ± 0.11 0.46 ± 0.20 0.30 ± 0.1180A 98.2 0.46 ± 0.18 0.22 ± 0.07 0.46 ± 0.24 0.24 ± 0.09

Fig. 3. A plot of true stress versus true strain is shown froma 20A specimen during a representative SRC test. The dashedline indicates the flow stress at a strain rate of 1.00 × 10�4

s�1.

SRC tests of all the composites tested, except for60A and 80A, where some strengthening occurredat the end of the test, likely because of slight graincoarsening. As discussed before, the results frommeasured grain size before and after deformationdo not definitively support grain growth. However,the occurrence of slight grain coarsening for 60Aand 80A during the deformation is still possibledue to the limitations in the accuracy of grain-sizemeasurement (see Table 1).

The relationships between true stress and strainrate are plotted on log–log scales in Fig. 4 for eachof the five compositions tested. At a given strainrate, the flow stress decreases as the volume frac-

Fig. 4. Strain rate dependencies on stress are shown forAl2O3/Y-TZP particulate composites.

tion of Y-TZP increases. The negative curvatureapparent in the data of Fig. 4 indicates a decreasein stress exponent with increasing stress for a givencomposition. Stress exponents vary from approxi-mately two to three, as indicated by the slopesidentified in Fig. 4. A value of n = 3 is observedat low Al2O3 content and low stresses. A value ofn = 2 is observed at stresses above approximately20–30 MPa. The strain rate associated with thetransition from n = 3 to 2 increases as the Al2O3

volume fraction decreases. At the highest stresses

3577J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

(s � 100 MPa) and highest Al2O3 volume frac-tions, the apparent stress exponent is reduced tovalues of less than two, which may be the resultof slight coarsening of the 60A and 80A micro-structures during SRC tests, leading to strengthen-ing in the latter SRC test steps.

4. Discussion

4.1. Comparison with existing models

In general, the strain rate, e, in the deformationof polycrystalline materials at elevated temperaturemay be expressed using the phenomenologicalequation for creep [19]:

e � A�sE�n�bd�p

exp��Qc

RT� (1)

where s is the stress, E is the dynamic, unrelaxedYoung’s modulus, T is the absolute temperature, bis the magnitude of Burgers vector, d is the grainsize, n is the stress exponent, p is the inverse grain-size exponent, Qc is the activation energy for creep,R is the gas constant, and A is a material constant.

French et al. proposed that the creep of particu-late composites can be analyzed using isostress orisostrain models [20]. The isostress model assumesthat the average stress in the composite, sc, is equalto that in each component of the composite, s1 ands2 for a two-component composite, i.e. sc = s1

= s2. The average strain rate in the composite, ec,is then given by

ec � V1e1 � V2e2 (2)

where V1 and e1 are the volume fraction and strainrate of component one and V2 and e2 are the vol-ume fraction and strain rate of component two. Theisostrain model, on the other hand, requires thatthe strain in each component of the compositeequal the average composite strain, i.e. ec = e1 =e2. Thus, the strain rates must also be equal, i.e.ec = e1 = e2. The average stress in the compositecan be represented for the isostrain case as

sc � V1s1 � V2s2 (3)

Assuming that each component obeys Eq. (1), the

isostrain model predicts the composite flow stressto be

sc � V1K1e1/n1c � V2K2e1/n2c (4)

where Ki = Ei(Ai)1/ni(di /bi)pi /niexp(Qci /niRT) foreach component i.

A rheological model has also been proposed byChen and Xue to predict the deformation responseof particulate composites when one phase is rigidand the other is deformable [10]. This model hasbeen previously applied to Al2O3/Y-TZP and otherparticulate composites [10,14]. Using the rheolog-ical model, the strain rate of the composite isgiven by

ec � (1�V2)(2+n1)/2asn1 (5)

where V2 is the volume fraction of rigid inclusions,n1 is the stress exponent of the deformable matrix,and a is a reference strain rate [21]. In theAl2O3/Y-TZP system Al2O3 has been assumed tobe rigid [15].

To determine the applicability of these modelsto the materials used in this study, experimentaldata were fit using a non-linear, least-squaresmethod to Eqs. (2), (4) and (5). For the isostrainmodel, the fitting parameters were n1, n2, K1 andK2, where the subscripts 1 and 2 represent Y-TZPand Al2O3, respectively. For the isostress model,the fitting parameters were e1 and e2 and, for therhelogical model, the fitting parameters were n1

and a. Since microstructural stability degradeswith less than 10–20 vol.% second phase [22,23],the compositions that were measured for this studywere limited to 20–80 vol.% Al2O3. Thus, thecurve fits were used both to assess the agreementbetween the data and models and to extrapolatefrom the data for comparison with the propertiesof Al2O3 (doped with Y3+) and Y-TZP. A summaryof the curve-fitting results at s = 50 MPa ispresented in Table 2.

Fig. 5 presents three plots of the logarithm ofstrain rate against volume fraction of Al2O3 at flowstresses of 20, 50, and 70 MPa, respectively. Fitsof an isostress model, a rheological model, an isos-train model, and a constrained isostrain model,which is discussed in the next section, match thedata well within the range of Al2O3 compositions(20–80 vol.%) for which data are available. Extra-

3578 J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

Table 2Results from non-linear curve fits at s = 50 MPa and T = 1350 °C

Model Governing equation Fit parameters

n1 n2 a e1 e2 K1 K2

(a) Constrained ec = s2c(V1K1 + V2K2)�2 1634 8422

isostrain(b) Isostrain sc = V1K1e1/n1c + V2K2e1/n2c 0.25 2.74 3.8 × 1015 2898(unconstrained)(c) Rhelogical ec = (1�V2)(2 + n1) /2asn1 0.087 0.0003(d) Isostress ec = (1�V2)e1 + V2e2 0.0003 �0.00008

1-Y-TZP; 2-Al2O3.

polations of the fitted equations beyond the compo-sitions are also examined. When the fitted equa-tions extrapolate to 100% Y-TZP, the creep ratespredicted by all the models seem to be physicallyrealistic, which will be discussed further in the nextsection. When the fitted equations extrapolate to100% Al2O3, the creep rate predicted by the rheol-ogical model is zero, and the creep rate extrapo-lated from the isostress model is negative. Bothzero and negative values of creep rate for 100%Al2O3 (doped with Y3+) are physically unrealistic.As suggested by Yoon and Chen, the assumptionthat Al2O3 is rigid is likely violated in this system[21]. In contrast, the isostrain model provides amore reasonable prediction of the creep rate of100% Al2O3 than do either the rheological modelor the isostress model. However, when the fittingparameters in the isostrain model are left uncon-strained, the results given by least-squares fits forthese parameters are not satisfying. For example,at s = 50 MPa, using the isostrain model, the bestfit value of the stress exponent for Y-TZP is n1

= 0.25, which is significantly less than the exper-imentally measured values of 2–3.

4.2. Constrained isostrain model

Good agreement is found between a constrainedisostrain model and the available data. To furtherexamine the applicability of the isostrain model,the effects of constraining the stress exponents torealistic values, consistent with those observedexperimentally, are investigated. Previous studies

indicate that n = 1–3 for 3Y-TZP [24–27] andvalues between 1 and 2 have been reported forfine-grained Al2O3 [27,28]. By assuming that thestress exponents in each phase are equal (i.e. n =n1 = n2), Eq. (4) can be simplified and written interms of the composite strain rate, ec:

ec � snc(V1K1 � V2K2)�n (6)

Eq. (6) was used to fit the experimental data atstresses of 20, 50, and 70 MPa using three integervalues for n, i.e. n = 1, n = 2 and n = 3 to determinean approximate value of n for the constrained isos-train model. Only integer values of n were selectedbecause integer values of n are predicted fromexisting theoretical models [17,25–27] and becauseour ability to distinguish to more than one signifi-cant digit is limited by the experimental data.Unlike the fits shown in Fig. 5, where each curveis independently fit at each stress, the constrainedisostrain model was required to fit data at all threestresses simultaneously using one set of fit para-meters, i.e. K1 and K2 at a given n. The resultingfits are shown in Fig. 6. These results suggest thatn = 2 is a better choice than either n = 1 or n =3, and it is also a physically realistic value (seeFig. 4).

Qualitative comparison with the other fittedequations indicates that the constrained isostrainmodel provides that most satisfying result. In Fig.5, the fits resulting from the constrained isostrainmodel (for n = n1 = n2 = 2) are shown as solidlines. The constrained isostrain model deviatesmost from the data points of the 60A and 80A.

3579J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

Fig. 5. Strain rate is plotted as a function of volume fractionof Al2O3 for Al2O3/Y-TZP particulate composites at stresses of(a) 20, (b) 50, and (c) 70 MPa.

Fig. 6. Fits of the constrained isostrain model to experimentaldata over a wide range of stresses are shown for (a) n = 1; (b)n = 2; (c) n = 1.

3580 J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

For these materials, the constrained isostrain modelpredicts a faster creep rate than was experimentallyobserved, which is the correct deviation when thecoarser grain sizes of the 60A and 80A materials,compared with the other particulate composites,are considered.

Predictions of normalized creep rate for pure Y-TZP are shown in Fig. 7 for the four models con-sidered. In Fig. 7, creep rate is normalized by theaverage grain size of pure Y-TZP (dY-TZP�0.30 µm), assuming a grain-size exponent of p =2. Jimenez-Melendo et al. [25] summarized allavailable data on the creep rate of Y-TZP at 1350°C in the same fashion, and the results of theirsummary are shown in Fig. 7 as a solid line rep-resenting the average of e·d2 values they presentedand dashed lines representing the approximatescatter in those data. The constrained isostrainmodel is closest to the average of the data availablefrom the literature, as is shown in Fig. 7. Further-more, the isostrain and the constrained isostrainmodels provide more reasonable predictions for thecreep rate of 100% Al2O3 than do the other models.

Fig. 7. Predictions of creep rate for pure Y-TZP are shownfor the four models considered and are compared to a fit of allavailable creep data from pure Y-TZP, as given by Jimenez-Melendo et al. (solid line), and the approximate scatter of thosedata (dashed lines) [25].

At s = 50 MPa, the creep rates predicted for 100%Al2O3 (doped with Y3+) by the isostrain model andthe constrained isostrain model are 1.5 × 10�5 and3.5 × 10�5 s�1, respectively. Unfortunately, Al2O3

cannot retain a fine grain size during creep defor-mation at 1350 °C, and thus no experimental dataare available for comparison. Indeed, the ability topredict physically realistic creep rates for compo-sitions that are difficult or impossible to fabricateor test is one of the major advantages of the con-strained isostrain model.

4.3. Comparison with previous studies

All of the data available from the literature forAl2O3/Y-TZP particulate composites similar tothose of the present investigation were compiledand are listed in Table 3. Although the Al2O3/Y-TZP particulate composites prepared for this studywere processed using techniques different fromthose of other investigations [12,14,15], the micro-structures produced are quite similar, with well-dispersed Al2O3 and Y-TZP phases. The grainsizes of the materials in the present study are finerthan those of previous investigations by factors of1.5 and 2 for the Y-TZP and Al2O3 phases, respect-ively [14], after compensation for the methods ofgrain-size measurement used in each investigation.

For Al2O3/Y-TZP composites tested in com-pression at temperatures of 1400–1550 °C, a pre-vious study has indicated that the stress exponentincreases monotonically with temperature from 1.2at 1400 °C to 1.9 at 1550 °C [12]. In contrast, sub-sequent studies on similar materials conducted intension [13] and compression [29] consistentlyindicated much higher stress exponents of between2 and 3 at temperatures from 1250 to 1650 °C,as shown in Table 3. In the current study, stressexponents are approximately 2 at high Al2O3 con-tent and high stresses and approximately 3 at lowAl2O3 content and low stresses (see Fig. 4). Thediscrepancy between the current results and a pre-vious study that reported stress exponents of lessthan 1.5 in compression may result from the rela-tively high values and narrow range of strain ratesat which those tests were conducted, as shown inTable 3. Data of the present investigation also sug-gest that a transition occurs to lower values of

3581J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

Table 3Creep behavior of Al2O3/Y-TZP particulate composites, as given in the literature

Material Grain size T (°C) e (s�1) Test a n(µm)

Reference Vol.% Y- Al2O3

Al2O3 TZP

Wakai et al. [12] 27.3 0.90 0.80 1400–1550 10�4–2 × 10�3 C 1.2–1.9Owen and Chokshi [29] 27.3 0.70 0.70 1292 10�8–10�3 C 2.8

T 2.8Nieh et al. [13] 27.3 0.50 0.50 1450–1650 8 × 10�5–5 × 10�3 T 2.0–3.0Wakai and Kato [15] 27.3 0.50 0.50 1250–1450 10�7–10�2 T 2.0–2.2Wakai et al. [14] 50.0 0.51 0.61 1250–1450 10�7–10�2 T 2.1–2.4Wakai et al. [14] 69.2 0.59 0.99 1250–1450 10�7–10�2 T 1.9–2.4Wakai et al. [14] 85.7 0.47 1.00 1250–1450 10�7–10�2 T 1.7–2.1

a C, compression; T, tension.

stress exponent as strain rate increases, which isconsistent with previous studies [28,30].

To examine the influence of volume fraction ofAl2O3 on deformation behavior, the constrainedisostrain model was used to analyze all currentlyavailable data. The data were normalized to a 50Acomposition by plotting ec[(V1K1 + V2K2) / (0.5K1

+ 0.5K2)2] versus stress on dual logarithmic scales,as is shown in Fig. 8(a). By plotting the data inthis manner, the data from 20A, 40A and 50A withsimilar grain sizes (dAl2O3

�0.38 µm, dY-TZP�0.30 µm) fall onto a single curve with a slope of2, which is labeled in Fig. 8(a) as “fi ne grains” .Wakai et al. have studied the Al2O3/Y-TZP com-posite system using samples with a slightly largergrain size than in the present study. They testedthese materials at 1350 °C in tension [14,15]. Theirdata from materials with 27.3 and 50 vol.% Al2O3

(labeled as 27.3AW and 50AW, both of whichhave similar grain sizes (dAl2O3

�0.55 µm,dY-TZP�0.50 µm), are also shown in Fig. 8(a).These data are fit with a line of slope 2, which isshown in Fig. 8(a) with the label “coarse grains” .The constrained isostrain model is used to success-fully collapse the data from particulate compositesof different compositions, but similar grain sizes,onto a single curve. The differences in grain sizesresult in a difference in flow stress. The 60A and80A materials have Al2O3 grain sizes which areintermediate between those of the materials with

data along the “fi ne grains” and “coarse grains”lines in Fig. 8(a). Data from 60A and 80Amaterials should, thus, lie between those of the“fi ne grains” and “coarse grains” lines, which isshown to indeed be the case in Fig. 8(b). Theobserved grain size dependence, compositiondependence, and similarities in stress exponentbetween the data obtained in compression for thecurrent study and previous data obtained in tensionsuggest that the same deformation mechanisms aredominant in compression and tension.

5. Conclusions

The deformation behaviors of Al2O3/Y-TZP par-ticulate composites have been systematically stud-ied under conditions for which changes in micro-structure during testing have been deliberatelyminimized. The results of these tests suggest thatstress exponents are approximately 2 at high Al2O3

contents and high stresses and approximately 3 atlow Al2O3 contents and low stresses. There is littledifference in deformation mechanism betweenAl2O3/Y-TZP particulate composites tested in thecurrent study in compression and those tested pre-viously in tension. Good qualitative agreementbetween the experimental data and a constrainedisostrain model, for which the stress exponents ofthe constituent Al2O3 and Y-TZP phases are con-

3582 J. Wang et al. / Acta Materialia 51 (2003) 3571–3583

Fig. 8. The logarithm of strain rate, normalized to a 50 vol.%Al2O3 composition by the constrained isostrain model, is plottedagainst the logarithm of flow stress for composites with (a) lessthan 50 vol.% Al2O3 and (b) greater than 50 vol.% Al2O3. Thefit lines have a slope of 2.

strained to physically realistic values, is observed.This model successfully predicts the difference inflow stress and strain rates with different compo-sitions, but similar grain size.

6. Acknowledgments

This work was supported by the TexasAdvanced Research Program under Grant #003658-0426-1999.

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