Acta Materialia 52 (2004) 5485–5491

www.actamat-journals.com

Superplastic deformation of Al2O3/Y-TZP particulate compositesand laminates

Jue Wang a, Eric M. Taleff a,b, Desiderio Kovar a,b,*

a Materials Science and Engineering Program, The University of Texas at Austin, 1 University Station C2200, Austin, TX 78712, USAb Department of Mechanical Engineering, The University of Texas at Austin, 1 University Station C2200, Austin, TX 78712, USA

Received 1 June 2004; received in revised form 4 August 2004; accepted 8 August 2004

Available online 15 September 2004

Abstract

Al2O3/Y-TZP particulate composites and particulate laminates with varying compositions and ratios of layer thickness were fab-

ricated by tapecasting, lamination, and sintering. Tensile strain-rate-change (SRC) tests were conducted on the particulate compos-

ites and particulate laminates at a temperature of 1350 �C and compared to previous results where tests were conducted in

compression. Stress exponents for particulate composites and laminates were measured to be approximately two in both tension

and compression. The observed similarity of SRC data suggests that a common deformation mechanism exists in tension and com-

pression. Elongation-to-failure tests were also conducted at 1350 �C at a constant true-strain rate of 10�4 s�1. It was found that the

elongation-to-failures of particulate laminates are lower than for particulate composites with similar overall compositions because of

interlayer constraint in the particulate laminates which induces cavitation in the harder layer. The increase in flow stress from

dynamic grain growth was used to determine that flow stress depends on grain size to approximately the 1.5 power. Elongations

for fine grained particulate composites produced by pressureless sintering were similar to those described in the literature for

hot-pressed particulate composites of similar composition, but with slightly coarser grain sizes.

� 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Superplasticity; High temperature deformation

1. Introduction

One of the major problems with using ceramics tomanufacture components with complex shapes is high

machining costs [1]. To reduce manufacturing costs,

superplastic ceramics with enhanced formability have

been extensively studied during the past two decades

[2–7]. Al2O3/Y-TZP particulate composites have been

found to exhibit excellent resistance to grain coarsening

[8] and to exhibit superplasticity at elevated tempera-

tures [6,7]. Recently, Al2O3/Y-TZP particulate lami-nates, where each layer is itself a particulate

1359-6454/$30.00 � 2004 Acta Materialia Inc. Published by Elsevier Ltd. A

doi:10.1016/j.actamat.2004.08.008

* Corresponding author. Tel.: +1 512 471 6271; fax: +1 512 471

7681.

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

composite, have also been studied because they offer

potentially superior mechanical properties at both low

and high temperature [9]. In previous studies of particu-late composites and particulate laminates, compression

testing has been used extensively [9,10] because it is use-

ful for measuring deformation behaviors to large strains,

but tensile testing is also needed to fully characterize the

formability of these materials.

In the present work, selected Al2O3/Y-TZP particulate

composites and laminates were tested in tension. Strain-

rate-change (SRC) tests were conducted at 1350 �C witha total engineering strain of less than 16%. In addition,

elongation-to-failure tests were also performed at

1350 �C with a constant true-strain rate of 10�4 s�1,

allowing superplastic behaviors of Al2O3/Y-TZP

particulate composites and laminates to be investigated.

ll rights reserved.

5486 J. Wang et al. / Acta Materialia 52 (2004) 5485–5491

2. Experimental procedure

High-purity, 3 mol% yttria-stabilized tetragonal zir-

conia powder and high-purity alumina powder were

used as raw materials. 20 vol% Al2O3/Y-TZP (20A),

60 vol% Al2O3/Y-TZP (60A) particulate composites,and their laminates (20A/60A) were fabricated by tape-

casting, lamination, and pressureless sintering. Tapes

with a length of 76 mm, a width of 38 mm, and a thick-

ness of 40 lm were laminated to form a billet. For the

laminates, the ratios of layer thickness were varied from

1:1 to 1:4. For 1:1, each layer was one-tape thick; for 1:2

and 1:4 the thinner layer was one-tape thick and the

thicker layers were two and four times as thick,respectively. The total thickness of each billet was

approximately 2 mm prior to sintering. Following bind-

er-burnout, the resulting billets were pressureless sin-

tered in air at 1450 �C for 1 h. The resulting laminates

are designated by the composition of the layers and

the ratios of layer thicknesses, e.g. 20A/60A (1:1) con-

sists of 20A and 60A layers, where the ratio of layer

thicknesses is 1:1. Details of the processing, sintering,and characterization procedures can be found in previ-

ous papers [9,10].

Pin-loaded, dog-bone tensile specimens were pre-

pared with a gage length of 27.25 mm, a gage width of

3.1 mm, and a thickness of 0.8 mm by diamond-machin-

ing. The tensile direction was oriented parallel to the

layer interfaces of laminates, i.e. the isostrain orienta-

tion [10,11]. Tensile SRC tests were performed undervacuum (�10�5 Pa) at 1350 �C over a range of true-

strain rates from 1 · 10�5 s�1 to 3.16 · 10�4 s�1 [10].

The total engineering strain was less than 16% during

the SRC testing procedure. For selected samples, elon-

gation-to-failure tests were conducted immediately

following the SRC tests at 1350 �C at a constant true-

strain rate of 10�4 s�1. The engineering strain and engi-

neering stress were obtained by assuming that thechange in displacement of the crosshead corresponded

to the increase in the gage length of the specimen. True

strain and true stress were derived from engineering

strain and stress. Following completion of the tests,

the changes in the gage-length of the specimens were

measured directly and reported as the maximum engi-

neering strain at failure. The densities of all materials

prior to testing and selected specimens after testing weremeasured using the Archimedes method, with water as

the immersion medium.

Fig. 1. Microstructures of 20A particulate composites in (a) the grip,

(b) the gage after SRC testing, and (c) the gage after SRC and

elongation-to-failure testing. The orientation of the applied stress is

horizontal.

3. Results

3.1. Microstructure

SEM micrographs of 20A particulate composites

after tensile SRC testing and elongation-to-failure test-

ing are shown in Fig. 1. Fig. 1(a) shows the microstruc-

ture in the grip section, while Fig. 1(b) and (c) show the

microstructures in the gage section. The grains with

lighter shading are Y-TZP and the grains with darker

J. Wang et al. / Acta Materialia 52 (2004) 5485–5491 5487

shading are Al2O3. Because the stress in the grip section

during testing was much lower than in the gage, and be-

cause the testing temperature was lower than the sinter-

ing temperature, the grip section experienced very little

deformation. It was therefore assumed that the micro-

structure in the grip section is representative of themicrostructure prior to testing. As shown in Fig. 1(a),

in the grip section both phases exhibit an equiaxed grain

shape and fine grain sizes. The average grain sizes for

each phase in the particulate composite 20A are�dAl2O3

¼ 0:34 lm and �dY�TZP ¼ 0:32 lm. In the gage sec-

tion, no measurable grain growth is observed and the

grain shapes remain equiaxed after SRC testing. In con-

trast, significant grain growth occurs and some elonga-tion of the grains is apparent after elongation-to-failure

testing. After elongation-to-failure testing, the average

grain sizes for eachphase in the 20Aparticulate composite

are �dAl2O3¼ 0:46 lm and �dY�TZP ¼ 0:43 lm.

SEM micrographs of 20A/60A (1:1) particulate lami-

nates after elongation-to-failure testing are shown in

Fig. 2. During testing, the layers remain bonded, but sig-

nificant grain growth occurs, especially in the harderlayer, 60A. For both particulate composites and lami-

nates, a 3–4% decrease in density was measured after

elongation-to-failure tests, whereas less than a 1% de-

crease in density was measured after SRC tests. This de-

crease in density is the result of an increase in porosity

from cavitation.

3.2. Deformation behavior

Fig. 3 presents data accumulated from SRC tests as a

plot of the true-strain rate against true stress, on dual

Fig. 2. Microstructures of 20A/60A (1:1) particulate laminates in the gage se

stress is horizontal.

logarithmic scales. Fig. 3(a) and (b) contain data,

respectively, from isostrain compression and isostrain

tension experiments; compression data are from [9].

The slope of data in Fig. 3 is equal to the stress expo-

nent, n, from the phenomenological equation for creep,

which can be written as [12,13]

_e ¼ ArE

� �n bd

� �p

exp � Qc

RT

� �; ð1Þ

where r is the stress, E is the dynamic, unrelaxed

Young�s modulus, T is the absolute temperature, b is

the magnitude of Burgers vector, d is the grain size, 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. For both

Al2O3/Y-TZP particulate composites and particulatelaminates, data from each test condition exhibit a stress

exponent which is slightly greater than two and which

increases slightly with decreasing strain rate. The data

for the particulate laminates lie between those of the

two particulate composites from which they are com-

posed. Moreover, the flow stresses produced by a given

material at a given strain rate under tension and com-

pression are very similar. This similarity in SRC data be-tween tension and compression is further discussed in

the section that follows.

Fig. 4 showsdata froma representative tensile SRC test

followed by an elongation-to-failure test for a 20A partic-

ulate composite. Since no observable changes in grain size

or grain shape are apparent after the SRC test, it is

assumed that performing the SRC test prior to the elonga-

tion-to-failure test does not significantly affect the totalelongation-to-failure. During the elongation-to-failure

ction after elongation-to-failure testing. The orientation of the applied

Fig. 3. Data from tensile SRC tests at 1350 �C are presented as the

logarithm of true-strain rate versus the logarithm of true stress, (a)

Isostrain compression [14]; (b) Isostrain tension.

Fig. 4. Representative tensile SRC test followed by an elongation-to-

failure test for 20A particulate composites. The true-strain rate for the

elongation-to-failure test portion of the test was 10�4 s�1.

5488 J. Wang et al. / Acta Materialia 52 (2004) 5485–5491

portion of the test, an increase in flow stress with strain is

observed, indicating that hardening from grain growth

occurs. The resulting elongation-to-failures for the 20A,

20A/60A (1:1), and 20A/60A (1:2), are 148%, 84%, and

59%, including both the strains from elongation-to-

failure testing and SRC testing. As expected, the elonga-tion-to-failure increases with the overall volume fraction

of Y-TZP in the composites.

4. Discussion

4.1. Comparison with compression data

It was previously shown that the constrained isostrain

model provides an accurate description of the high-tem-

perature behaviors of Al2O3/Y-TZP particulate lami-

nates [14]. Considering a laminate where the volume

fractions of layers 1 and 2 in the laminate are given by

V1 and V2, the constrained isostrain model predicts that

creep in the laminate is given by,

_e ¼ rV 1K1 þ V 2K2

� �n

; ð2Þ

where Ki ¼ EiðAiÞ1=niðdi=biÞpi=ni expðQci=niRT Þ and the

material constants are defined in Eq. (1) for each com-

ponent i. In this study, the composition of layer 1 is

20A and the composition of layer 2 is 60A. It is clear

from the Fig. 3 that n � 2 for both the 20A and 60A par-

ticulate composites. Thus, based on the Eq. (1), the

creep of both 20A and 60A satisfy the relation,

ri ¼ Ki � _e1=2i : ð3ÞTo determine the Ki values, Fig. 5 presents both the

tension and compression data for 20A and 60A by plot-

ting log10 _e versus log10r; compression data are from [14].

Fig. 5. Data for 20A and 60A from both tension and compression

SRC tests at 1350 �C are presented as the logarithm of true-strain rate

versus the logarithm of true stress. Compression data are from [14].

The solid lines are fits to the data where the slope was constrained to 2.

J. Wang et al. / Acta Materialia 52 (2004) 5485–5491 5489

Both the tension and compression data for each material

were then simultaneously fit by constraining the slope to

a value of 2, giving a value of K1 ¼ 3252 MPaffiffis

pfor

the 20A particulate composite. Similarly, the fit for the

60A particulate composite gives a value of K2 ¼6521 MPa

ffiffis

p.

To examine the influence of volume fraction of hard

layer 60A on deformation behavior of Al2O3/Y-TZP

particulate laminates, the data were normalized to a

20A/60A (1:1) composition by plotting _e½ðV 1K1þV 2K2Þ=ð0:5K1 þ 0:5K2Þ�2 versus stress on dual logarith-

mic scales, as shown in Fig. 6. By plotting the data in

this manner, all of the available data for particulate lam-

inates with varying thickness ratios and for both tensionand compression tests can be compared. From this plot,

it is clear that the data fall onto a single curve with a

slope of approximately 2. The observed similarity of

SRC data for tension and compression tests confirms

that a common deformation mechanism exists in tension

and compression for these materials.

4.2. Grain size dependence

For Al2O3/Y-TZP particulate composites and lami-

nates, significant grain growth occurs during elonga-

tion-to-failure tests. To evaluate the grain-size

dependence on flow stress, the experimental data were

analyzed using data from the 20A particulate composite

and the phenomenological equation for creep (Eq. (1)).

The stress exponents for Al2O3/Y-TZP particulate com-posites and laminates based on the SRC tests were ob-

served to be approximately two. Therefore, the flow

stress is proportional to the grain size raised to the p/2

power, i.e.

r / dp=2: ð4Þ

Fig. 6. The logarithm of strain rate, normalized to a 20A/60A (1:1)

composition by the constrained isostrain model, is plotted against the

logarithm of flow stress for 20A/60A particulate laminates. The fit line

is constrained to a slope of 2.

Table 1 summarizes the flow stresses and grain sizes

of 20A at the beginning and at the end of the elonga-

tion-to-failure test for which true strain rate was held

constant, corresponding to true strains of e = 0.14 and

0.92. Flow stresses were corrected by considering the ef-

fect of cavitation, i.e.

rcorrected ¼ r� A0

A0ð1� CvÞ; ð5Þ

where A0 is the area of the specimen and Cv is the cav-

itation volume fraction, which was determined from the

measured densities. Note that the cavitation volume

fraction is assumed to be equal to the cavitation area

fraction [15]. The inverse grain size exponent, p, was

then determined using the relation:

rcorrectedje¼0:14

rcorrectedje¼0:92

¼�dY�TZP

��e¼0:14

�dY�TZP

��e¼0:92

!p=2

: ð6Þ

Because Y-TZP was the major phase for the 20A par-

ticulate composite, only the grain sizes of Y-TZP were

considered. These calculations yield p = 3.1 and thus,

for n = 2, r � d1.55.

Previously, Nieh et al. studied the effect of grain size

on superplastic flow in 27.3 vol% Al2O3/Y-TZP. Theirresults indicated that the flow stress at a constant true

strain-rate and at a given strain was proportional to

the grain size raised to a power of 0.75, i.e. r � d0.75, giv-

ing p = 1.5 [7,16]. The 20A particulate composite in our

study shows a stronger grain-size dependence. The fol-

lowing three items are potential sources for differences

between the results of the present study and the Nieh

et al. study. First, a finer grain size was achieved inthe present study (�dAl2O3

¼ 0:34 lm and �dY�TZP ¼0:32 lm in the present study, compared to �dAl2O3

¼�dY�TZP ¼ 0:5 lm in the Nieh et al. study). Second, the

flow stress of Y-TZP has a stronger grain-size depend-

ence than has been reported for of Al2O3/Y-TZP partic-

ulate composites (r � d2 for Y-TZP versus r � d0.75 for

27.3 vol% Al2O3/Y-TZP) [17]; the 20A composition used

in the present study contained more Y-TZP than the27.3 vol% Al2O3/Y-TZP used in the Nieh et al. study.

Third, the test techniques were different between the

studies. In the present study, the influence of dynamic

grain growth was measured; in the Nieh et al. study,

the true strain was held constant and the flow stress

was measured in samples with different initial grain

sizes. In the method used by Nieh et al., both dynamic

able 1

avitation volume fractions, flow stresses, and grain sizes for 20A

articulate composite during elongation-to-failure testing

Cv (%) r (MPa) rcorrected (MPa) �dY�TZP (lm)

.14 0.9 30 30.3 0.34

.92 3.8 42 43.7 0.43

T

C

p

e

0

0

Fig. 7. Illustration of the effect of constraint on the stress state in the particulate laminates. The harder layers are represented by the lighter shading.

5490 J. Wang et al. / Acta Materialia 52 (2004) 5485–5491

grain growth and changes in the initial grain size may

influence the measured value of p. However, the effect

of dynamic grain growth could not be considered in

their analysis [7,16].

4.3. Superplastic deformation

Previous studies have shown that hot-pressed Al2O3/

Y-TZP particulate composites exhibit a large elonga-

tion-to-failure at 1450–1600 �C, especially for compos-

ites with high Y-TZP contents [3,7,18]. In the present

study, the samples were pressureless sintered, which re-

sulted in slightly more residual porosity than hot-

pressed materials used in previous studies. Additionally,elongation-to-failure testing was conducted for the pre-

sent study at a relatively low temperature of 1350 �Cto minimize changes in microstructure during testing.

Despite these differences, both of which should reduce

elongation-to-failure, the measured elongation-to-fail-

ures were similar to those obtained in previous studies.

For example, Wakai et al. demonstrated an elongation

of 146% at 1450 �C and an initial strain rate of2.78 · 10�4 for a hot-pressed particulate composite, con-

sisting of 27.3 vol% Al2O3 and the balance Y-TZP [18].

In the present study, a 20A particulate exhibited an

elongation of 148% at 1350 �C and a constant true-

strain rate of 10�4 s�1. The relatively large elongation-

to-failure in this material can be attributed to its fine ini-

tial grain size ð�dAl2O3¼ 0:34 lm and �dY�TZP ¼ 0:32 lmÞ

compared to that of Wakai et al. ð�dAl2O3¼ �dY�TZP

¼ 0:5 lmÞ [18] and the relatively large grain size expo-

nent of these materials. Previous studies show that the

tensile ductility of superplastic ceramics is limited by

cavitation [19,20]. The cavities develop as a direct conse-

quence of the applied stress, i.e. higher stress levels lead

to higher levels of internal cavitation [21]. Because flow

stress increases with grain size, a critical grain size exists

above which the cohesive strength of grain boundaries isexceeded, resulting in cavitation and eventual fracture.

Thus, elongation-to-failure of ceramics typically in-

creases with decreasing grain size. In the case of speci-

mens from the present study, the fine grain size

compensated for the lower initial density, yielding elon-

gations similar to those observed previously for higher

density but coarser grained Al2O3/Y-TZP particulate

composites.

The present study shows that the particulate laminate

20A/60A (1:2), which had an overall composition of 46.7

vol% Al2O3, had an elongation-to-failure of only 59% at1350 �C and a true strain-rate of 10�4 s�1. For Al2O3/Y-

TZP particulate composites with similar overall compo-

sition, Wakai et al. reported an elongation-to-failure of

approximately 100% at 1450 �C at an initial strain rate

of 2.78 · 10�4 s�1 for a 50 vol% Al2O3/Y-TZP particu-

late composite [18]. Lower test temperature and greater

residual porosity in the materials used in the current

study should not significantly reduce the elongation-to-failure of 20A/60A (1:2) laminate since these effects are

compensated by the finer grain size. Thus, these differ-

ences most likely result from the laminate architecture.

Previous studies have shown that in uniaxially aligned,

fiber reinforced composites [22,23] and in simple lami-

nates [9,14], interlayer constraint results in the develop-

ment of additional stresses which do not arise

in particulate composites. As shown schematically inFig. 7, for unconstrained layers pulled in tension within

the plane of the layers, differential strains arise in the

harder and softer layers. However, when the layers are

constrained by bonding their interfaces so that the

strains in the layers must be equal, additional in-plane

stresses arise. These stresses, which are tensile in the

harder layer and compressive in the softer layer, are

superimposed on the applied tensile stress. Thus, cavita-tion is enhanced in the harder layer compared to an

unconstrained material. This resulting enhancement of

cavitation in the hard layer reduces the elongation-to-

failure of laminates compared to particulate composites

with the same overall composition.

5. Conclusions

Al2O3/Y-TZP particulate composites and particulate

laminates were fabricated by tapecasting, lamination

and sintering. Tensile SRC tests were conducted at

1350 �C to a total strain of less than 16%. During tensile

J. Wang et al. / Acta Materialia 52 (2004) 5485–5491 5491

SRC testing, the grain shapes remaine equiaxed and no

changes in grain size were apparent. However, subse-

quent elongation-to-failure tests to large strains pro-

duced extensive grain growth and cavitation. There was

little difference in high-temperature deformation behav-

ior between Al2O3/Y-TZP particulate composites (orparticulate laminates) tested in tension and compression,

indicating that the deformation mechanisms are similar

in tension and compression. A comparison of the behav-

iors of particulate composites and particulate laminates

showed that, for the same overall composition, particu-

late laminate composites have intrinsically lower ductility

because of interlayer constraint. For particulate compos-

ites, the flow stress had a strong grain-size dependence,i.e. r � d1.55, and elongation-to-failures increased with

volume fraction of Y-TZP. By comparing the results

for particulate composites with those from previous stud-

ies, it was shown that the detrimental effect of porosity on

tensile ductility can be compensated for by decreasing

grain size. Thus, the ductility of low-cost sintered materi-

als can compare favorably to high density, hot-pressed

ceramics, provided that a fine grain size is achieved.

Acknowledgements

This work has been supported by the Texas Ad-

vanced Research Program under project #003658-

0426-1999 and NSF under grant DMR-9974476.

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