Residual Stresses in Alumina±Zirconia LaminatesDavid J. Green,* Peter Z. Cai and Gary L. Messing

Department ofMaterials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA

Abstract

Signi®cant residual stresses can arise in hybrid cera-mic laminates during the densi®cation and coolingprocessing cycles. The densi®cation stresses in alu-mina±zirconia laminates were calculated assuming thelayers to be linear viscous with data obtained by cyclicloading dilatometry. These stresses placed the zirconialayers in biaxial tension and even at 1MPa or less,they were su�cient to cause a type of linear cavitationdamage. The methodology was also applied to asym-metric laminates, successfully predicting theirobserved curling behaviour. Thermal expansion mis-match stresses arise during cooling, again placing thezirconia layers in residual biaxial tension and leadingto the formation of transverse (channelling) cracks.The stresses were calculated using both elastic andviscoelastic formulations and were con®rmed withindentation measurements. Additions of alumina to thezirconia layers were e�ective in reducing both sourcesof residual stress and allowed crack formation duringprocessing to be avoided. Residual stresses were alsoshown to improve mechanical performance. # 1999Elsevier Science Ltd. All rights reserved.

Keywords: residual stresses, laminates, thermalexpansion, Al2O3, ZrO2.

1 Introduction

Hybrid ceramic laminates, which are composed ofalternating layers of two or more di�erent ceramicmaterials, have emerged recently as a viable alter-native to ®bre-reinforced ceramic composites forstructural applications. Fabrication of laminatedstructures usually employs relatively low-cost con-ventional processing routes, such as tape casting,sequential slip casting, coating techniques, etc. Theprocessing and mechanical behaviour of laminateshas been recently reviewed by Chan.1 Varioustoughening mechanisms are available in theselaminates. Some workers have emphasized the useof a low fracture energy interface between the layers

to de¯ect cracks, similar to ®bre reinforced ceramiccomposites.2 In other cases, it appears the changesin elastic modulus, fracture toughness and residualstresses between the layers can play a role in thetoughness and strength behaviour.3±10 In trans-forming ceramics, the presence of the layers canin¯uence the transformation zone size11 and inceramic±metal laminates, crack bridging e�ects canbe important.12

A particular challenge in the processing of cera-mic laminates is to understand the nature of theresidual stresses, particularly if they are to be usedto enhance the mechanical properties. Invariably,the materials chosen for the layers will possess dif-ferent sintering and thermal expansion strains.Thus, one expects that residual stresses will ariseboth in heating, when the laminate is ®rst densi®ed(di�erential densi®cation), and in cooling as thelayers contract (thermal expansion mismatch). Thedi�erential densi®cation will place the layers ineither biaxial tension or compression, leading toinhibition or enhancement of the densi®cation. Thetensile stresses can be particularly troublesome asthey can give rise to `sintering' cracks.13 Duringcooling, the residual stresses can also lead to crackingand three primary crack morphologies have beenobserved: transverse, longitudinal and debondcracks. Transverse (channelling) cracks form as aresult of the in-plane tensile stresses whereas long-itudinal surface cracks form in the `compressed' layerbecause of the tensile stresses that arise at its freesurfaces.13±15 Transverse and `edge-e�ect' crackingcan be prevented if the thickness of the `tensile' layeris reduced below a critical value.14,15 Alternatively,the critical thickness can be increased by reducing theresidual stress or increasing the fracture toughnessof the layers.This paper reviews a series of recent papers that

studied the residual stresses that arise in alumina-zirconia laminates during processing and the rolethese stresses play in the mechanical perfor-mance.16±18 Residual stresses have been observedpreviously in Al2O3±ZrO2 trilayers and multi-layers.5±9 Yttergren et al.5 have shown that thepresence of compressive residual stresses on thesurface gives rise to higher values of strength andpost-indentation strength over the monolithic

Journal of the European Ceramic Society 19 (1999) 2511±2517

# 1999 Elsevier Science Ltd

Printed in Great Britain. All rights reserved

P I I : S 0 9 5 5 - 2 2 1 9 ( 9 9 ) 0 0 1 0 3 - X 0955-2219/99/$ - see front matter

2511

* To whom correspondence should be addressed.

counterparts. The overall approach in the workbeing reviewed here, was to measure the parametersthat control residual stress and then perform theo-retical calculations to determine their magnitude.The stress values were then veri®ed by independentmeans. The residual stresses were also linked to theobserved types of processing damage and to themechanical performance of the laminates.

2 Overview of Experimental Procedure

The starting powders for this work were an MgO-doped Al2O3 powder (Premalox, Alcoa) and aCeO2-stabilized ZrO2 powder (TZ-12Ce, Tosoh),both with particle sizes in the range of 0.2±0.3�m.The layers were produced by tape casting, punchedinto rectangles and formed into green bodies bythermal lamination to form symmetric and asym-metric laminates. The asymmetric laminates curlduring ®ring as a result of the di�erential shrink-age. Measurement of the curvature change wasemployed as an indirect con®rmation of the theo-retical approach used for calculating the di�erentialshrinkage stresses in the symmetric laminates. Inthe symmetric laminates, the Al2O3 and ZrO2 rec-tangles were stacked in an alternating sequence to atotal of 23 layers, with both of the surface layersbeing Al2O3. In the asymmetric laminates, threeAl2O3 layers were on one side and three ZrO2 lay-ers were on the other, forming a laminate resem-bling a bilayer. In addition to the laminates madeof alumina (A100) and zirconia (Z100) layers,symmetric and asymmetric laminates were fabri-cated in which the compositions of the Z100 layerswere modi®ed by adding 10, 20 and 30 wt% alu-mina. These are denoted as Z90, Z80 and Z70layers, respectively. Thus, a total of four ZrO2-containing layers were used to form four types oflaminates: A100-Z100, A100-Z90, A100-Z80, andA100-Z70. The addition of Al2O3 to the ZrO2 layerswas used to examine the e�ect of changing the sin-tering shrinkage and thermal expansion mismatchbetween the layers.After a binder burnout cycle, most laminates

were subjected to a single ®ring cycle. The lami-nates were heated at 5�Cmin, sintered at 1530�Cfor 90min and were cooled at 3�Cmin. The asym-metric laminates were sintered in a tube furnace forin-situ observation of the curling that occurs dur-ing sintering.16 The di�erence in densi®cation ratesbetween the layers led to curvature development atabout 1000�C and the curvature was measuredfrom photographs taken at 50�C intervals. Thecomplete details of the processing and micro-structural characterization are available else-where.16 Residual stress in the outer alumina layers

of the symmetric laminates was determined fromindentation crack length measurements.18

The strength and post-indentation strength of theas-processed symmetric laminates was determinedusing four-point bending. The details of the mechan-ical characterization are available elsewhere.18

3 Densi®cation Stresses

Figure 1 shows the linear shrinkage curves formonoliths of some of the layer compositions.16

There is a signi®cant mismatch in the sinteringstrains for the unconstrained layers of alumina(A100) and zirconia (Z100). The addition of 30wt% alumina (Z70) clearly decreased the mismatchin sintering strain and strain rate.Bordia and Scherer19 contend a simple linear

viscous constitutive relationship is su�cient tomodel the mechanical response of a sintering com-pact. This is consistent with models for di�usionalcreep which yield a linear correlation betweenstress and strain rate. This is also an attractivesuggestion as viscoelastic models can be cumber-some or even intractable and di�cult to modify forporosity changes. Viscous behaviour also impliesthat densi®cation stresses in symmetric laminateswill depend primarily on the mismatch in sinteringstrain rate. To determine the viscosity of the layers,cyclic loading dilatometry was used.20 In this tech-nique, a cyclic stress is applied to a compact as it isheated and densi®ed in a dilatometer. Figure 2shows an example of such data for alumina as itapproaches the maximum sintering temperature.The shaded bars represent the periods when thestress is applied. The stress application leads tochange in strain rate and elastic strains are notdetected, in line with the proposed viscous beha-viour. It is also interesting to note that the compacttends to `recover' slightly when the stress is

Fig. 1. Linear sintering shrinkage strains for A100, Z100 andZ70 specimens.

2512 D. J. Green et al.

removed with the strain rate being lower than thestress-free value. By measuring the strain rate forvarious stresses, viscosity can be determinedthroughout the densi®cation process. Figure 3shows the viscosity for the densifying alumina as afunction of temperature. A rapid decrease in visc-osity is observed for temperatures above �950�C.It is also useful to determine the viscosity±Young'smodulus ratio, i.e., the relaxation time for a Max-well viscoelastic model. The Young's modulus, E,was determined as a function of the relative den-sity, �, using21,22

Eÿ Eg

E0 ÿ Eg� �ÿ �g

1ÿ �g�1�

where Eg and E0 are the Young's moduli at theonset of densi®cation and at theoretical density,respectively, and rg is the relative density of thegreen body. The relaxation time data are shown inFig. 4 . For a heating rate of 5�Cmin, one wouldexpect relaxation times less than 10 s would besu�cient to allow the body to behave essentially ina viscous fashion. From Fig. 4, one notes there is afairly sharp transition from elastic to viscous

behaviour. In a symmetric laminate with alternat-ing layers (subscripts 1 and 2), the stress can becalculated for elastic layers using13

�1 � 1

1�mn

� �E1

1ÿ �1

� ��e �2�

where

m � h1h2

and n � E1

1ÿ �1

� �1ÿ �2E2

� ��3�

h is the layer thickness, E is Young's modulus, � isPoisson's ratio and �e is the (unconstrained) mis-match strain. Using the analogy between Hooke'sLaw (linear elasticity) and Newton's Law (linearviscosity), the stresses in viscous layers can also becalculated from eqns (2) and (3) with E becominguniaxial viscosity, � the Poisson's ratio for the viscousmaterial and �e the mismatch in strain rate. Anexample of the densi®cation stress calculation isshown in Fig. 5 for the zirconia layers, which aresubjected primarily to biaxial tensile stresses duringdensi®cation. The maximum stress occurs at�1300�C but the magnitudes are <1MPa. The dataprimarily re¯ect the mismatches in strain rate for the

Fig. 3. Calculated uniaxial viscosity as a function of tempera-ture for alumina.

Fig. 5. Layer sintering mismatch stresses in the ZrO2 layer forthe A100±Z100, A100±Z90, A100±Z80 and A100±Z70 symmetriclaminates calculated from the mismatch in sintering strain rate.

2. Linear shrinkage strain between 900 and 1500 �C for alu-mina (A100) using thermomechanical analyzer.

Fig. 4. Measured viscosity-to-elasticity ratio (relaxation time)

Residual stresses in alumina-zirconia laminates 2513

unconstrained layers.16 The addition of the zirconiato the alumina layers is found to reduce these stresses.A more complete viscoelastic treatment was also

performed for these laminates17 but this analysisonly changed the stresses at temperatures <500�C.Further re®nements were also made to determinehow the residual stresses change the in-plane den-si®cation behaviour 17 but this led to only modestincreases in stress. This small e�ect is a result oftwo competing e�ects in which, for example, theincrease in viscosity from the densi®cation in thecompressive layers is o�set to a large degree by thedecrease in the driving force for sintering caused bythe densi®cation. Figure 6 shows the ®nal results ofthe more complete viscoelastic calculations.17

Interestingly, it was predicted that residual stressesmay also occur at the maximum sintering tem-perature but the bodies will be more coherent inthis ®nal densi®cation stage.The densi®cation stresses calculated above are

low but are close enough to the sintering stress thatde-sintering or other damage mechanisms may bepossible.17 Microstructural observations afterlaminate processing identi®ed linear arrays of voidsin the zirconia layer and these voids appeared to benucleation sites for the transverse cracks thatformed for some of the laminates during cooling.16

These pores are similar to the creep cavitationdamage observed in ceramics. In a separate set ofexperiments,23 alumina tapes were formed intouniaxial tensile specimens. These specimens werethen subjected to stresses up to 2MPa, while beingsubjected to the standard ®ring cycle. Damage wasobserved with almost identical morphology to thatseen in the laminates, con®rming that damage canarise in laminates during densi®cation even at ten-sile stresses of �1MPa.To further test the densi®cation stress calcula-

tions, the theoretical approach was also used topredict the degree of curling and stresses that ariseduring the ®ring of asymmetric laminates. The

results of the predicted curvature calculations areshown inFig. 7 and are compared to the experimentalmeasurements. The agreement between the theoryand experiment is very good. For the asymmetriclaminates, bending leads to a more complex stressdistribution with tensile stresses occurring not inthe zirconia layers (near the interface) but also inthe outer alumina surface. Stresses up to �1.8MPawere calculated for the alumina surface and in somelaminates, cracking was observed at this location.16

4 Thermal Expansion Mismatch Stresses

The main di�culty in producing the alumina-zir-conia laminates was the occurrence of transverse(channelling) cracks in the zirconia layers. Chan-ging heating and cooling rates did lead to somedi�erences in crack spacing but only the A100-Z70system was found to be completely free of cracks16.It was initially assumed that these cracks werebeing formed primarily by the stresses that ariseduring cooling. Figure 8 shows the measured ther-mal expansion coe�cients, �, for monoliths of thevarious layer types as a function of temperature, T.As the thermal expansion of zirconia is less thanalumina, the zirconia layers will be placed in biax-

Fig. 6. Calculated viscoelastic stress in the ZrO2-containinglayers for the A100±Z100, A100±Z90, A100±Z80 and A100±

Z70 symmetric laminates.Fig. 7. Calculated and measured curvature for the A100-±Z100,A100-±Z90, A100-±Z80 and A100-±Z70 asymmetric laminates.

2514 D. J. Green et al.

ial tension. As expected, the alumina additions tothe zirconia layers decrease the thermal expansionmismatch.The elastic stresses in the layers that arise during

cooling from the thermal expansion mismatchstrain can be calculated from eqns. (2) and (3) byrecognizing

�e ��T

�2 ÿ �1� �dT �4�

It was assumed that these stresses start to ariseonce the temperature drops below 1200�C.13 Theresults of the calculations are shown in Fig. 9 andstresses as high as 420MPa were predicted. Theaddition of 30 wt% alumina dropped the stress to�240MPa. As indicated earlier, transverse crack-ing in these laminates can only occur if the layerthickness is above a critical value, tc, given by14

tc � 4K2IC

��2R�5�

where Kic is the fracture toughness of the layer andsr is the residual stress. The decrease in the resi-dual stress with the alumina addition increases thecritical thickness by a factor �3, making transversecracking less likely for a ®xed layer thickness. Thevalue of the fracture toughness of the zirconia layerwas determined to be 7.7MPa

����mp

.18 For the

A100±Z100 laminate, the critical thickness wascalculated to be 430�m. Since the actual layerthickness was �120�m, theoretically, the trans-verse cracking should not have occurred. One pos-sible explanation, consistent with the earlierdiscussion, is that the linear damage incurred dur-ing densi®cation e�ectively decreases the fracturetoughness. The stresses that arise during coolingwere also calculated from the viscoelastic data.17 Itwas determined that changes in the cooling rateabove 1200�C can in¯uence the magnitude of thesestresses and hence to some degree, can control thecracking behaviour.For the remainder of the paper, only the crack-

free Z70±A100 laminate is discussed, though somechanges were made in the laminate geometry. Thebase laminate system consisting of 120�m thickZ70 and A100 layers was denoted as 1A±1Z. In thesecond system, the thickness of both layers werereduced by a factor of 2 (0.5Z±0.5A). In the lastsystem, the zirconia layers were made twice asthick (1A±2Z). For the ®rst two systems, the resi-dual stress in the alumina layers was calculated tobe ÿ215 MPa and for the last system ÿ430 MPa.By comparing the ®rst two systems it was possibleto determine whether interaction with the zirconialayer in¯uenced the fracture toughness. The thirdsystem was chosen to show the e�ect of changingthe residual stress.In order to con®rm the theoretically calculated

residual stresses in the outer alumina layers,indentation crack lengths on the laminates werecompared to those on monolithic alumina. It wasassumed that the stress in the outer layers wasuniform and that the indentation crack sizes weresmaller than the layer thickness. For this situation,one can write18

�R � KIC1ÿ c0=cR� �3=2

�����cRp �6�

where c0 and cR are indentation crack length forthe stress-free and stressed surfaces, respectively,and is a geometric constant (�1.26). The resultsof this analysis are shown in Fig. 10 and goodagreement is found between the stresses calculatedfrom thermal expansion mismatch and change inindentation crack length. The main discrepanciesare found for the thin layers at the higher loads,presumably because the indentation cracks hadpenetrated past the outer layer.

5 E�ect of Residual Stress on Indentation Strength

If the outer layers are in residual compression, oneexpects an increase in indentation strength of the

Fig. 8. Coe�cients of thermal expansion (CTE) for A100,Z100, Z90, Z80 and Z70 measured by dilatometry.

Fig. 9. Calculated biaxial thermal stresses during cooling inthe ZrO2 layer for the A100±Z100, A100±Z90, A100±Z80 and

A100±Z70 symmetric laminates (elastic solution).

Residual stresses in alumina-zirconia laminates 2515

laminates compared to monolithic alumina whentested in ¯exure. This e�ect leads to an apparentincrease in fracture toughness provided cracksinitiate at the surface. Clearly, if this is the mainstrengthening mechanism for these laminates, itwould not be very useful at high temperaturesbecause the residual stresses will relax.The indentation strength of a laminate, �f, can be

calculated in a straightforward manner if it is againassumed that the stress in the outer layer is uni-form and that the indentation crack sizes aresmaller than the layer thickness. This approachgives 18

�f � �K 4=3IC

P1=3

!ÿ �R �7�

where � is an indentation parameter. The indenta-tion strength behaviour is shown in Fig. 11 and onecan see the compressive stresses not only increasethe indentation strength but also change the slopeof the strength±load behaviour in this log±log plot.It is important to realize the stress values here are

the actual values in the alumina layers. In the bendtest, the elastic modulus of alumina is about a fac-tor of two higher than zirconia. This leads to amodulation in the linear stress gradient normallyassociated with a ¯exure test. In particular, thestresses in the alumina were determined to be�20% higher for the base laminate than nominalvalues calculated assuming the beam is homo-geneous.18 Figure 12 compares the nominal inden-tation strength data with that predicted by Eqn. (7)for the 1A±1Z and 0.5A±0.5Z laminates. Theagreement is good even though there was evidencethat the cracks interacted with the underlying lay-ers, changing crack shape.18 In particular, thise�ect appeared to in¯uence the amount of stablecrack growth on the tensile surface.

6 Conclusions

Signi®cant residual stresses can arise in hybridceramic laminates during densi®cation and coolingprocessing cycles. It is critical to understand thesource of these stresses as this is not only one of thekeys to successful processing but these stresses canalso impact the mechanical performance. The dif-ferential densi®cation stresses can be calculatedassuming the layers are linear viscous and arisefrom the mismatch in sintering strain rates. Cyclicloading dilatometry is a useful technique to deter-mine the viscous properties of ceramics that arerequired in the stress calculations. This dilato-metric data showed a fairly sharp transitionbetween elastic and viscous behaviour for the sin-tering compacts. For the laminates consideredhere, the densi®cation stresses placed the zirconialayers in biaxial tension and even though the stresswere 1MPa or less, they were su�cient to cause atype of linear cavitation damage. This damage wasalso found to be preferred sites for the crackingthat occurs during cooling. Additions of alumina

10. Calculated residual stress in the A100 surface layer usingeqn. (6) for the 1A±1Z, 1A±2Z and 0.5AÐ0.5Z laminates. Thedata points on the right represent the calculated values from

the measured coe�cients of thermal expansion.

Fig. 12. Indentation strength of the 1A±1Z (open symbols)and 0.5A±0.5Z laminates (shaded). The line is drawn fromeqn. (7) with a modulus correction18. The regions near the

ordinate axis are the ¯exural strengths of the laminates.

Fig. 11. Schematic showing the e�ect of a compressive resi-dual surfaces stresses on indentation strength. The bars on the

left represent the (non-indented) strength.

2516 D. J. Green et al.

to the zirconia layers was e�ective in reducing thedensi®cation stresses. More exact viscoelastic cal-culations were performed but these re®nementsmade relatively small changes to the stress history.In order to con®rm the stress values, the experi-mental approach was also applied to asymmetriccomposites and was successful in predicting theobserved curling behaviour.Higher stresses arise during cooling, placing the

zirconia layers again in residual biaxial tension,leading to the formation of transverse (channelling)cracks. Additions of alumina to the zirconia layerswas successful in reducing these stresses. Viscoelasticcalculations showed these stresses could be reducedto some degree by reducing the cooling rate at tem-peratures >1200�C. The di�erential contractionstresses were also determined from indentation cracklength measurements and good agreement wasobtained with the theoretical calculations.For bend testing of alumina±zirconia laminates

at ambient temperatures, the thermal expansionmismatch stresses in the outer (alumina) layers ledto an increase in indentation strength and anapparent decrease in the load exponent. Thisbehaviour was shown to be consistent with theore-tical considerations. The residual stresses also ledto strengthening of the hybrid laminates.

References

1. Chan, H. M., Layered ceramics: processing and mechan-ical behaviour. In Annual Review of Materials Science,Vol. 27, ed. E. N. Kaufmann. Annual Reviews Inc., PaloAlto, CA. 1997.

2. Clegg, W. J., Kendall, K., Alford, N., Button, T. andBirchall, J. D., A simple way to make tough ceramics.Nature, 1990, 347, 455±457.

3. Watkins, T. R. and Green, D. J., Fracture behaviour ofCVD SiC-coated graphite: I. Experimental results. J. Am.Ceram. Soc., 1992, 76(12), 3066±3072.

4. Watkins, T. R. and and Green, D. J., Fracture behaviourof CVD SiC-coated graphite: II. Conditions for onset ofmultiple cracking. J. Am. Ceram. Soc., 1993, 77(3), 717±720.

5. Yttergren, R-M. F., Zeng, K. and Rowcli�e, D. J., Residualstress and crack propagation in laminated composites. InCeramic Transactions, Vol 46, ed. J. P. Singh and N. P.Bansal. American Ceramic Society, Westerville, OH, 1994,pp. 543±553.

6. Wang, H. and Hu, X., Surface properties of ceramic

laminates fabricated by die pressing. J. Am. Ceram. Soc.,1996, 79(2), 553±556.

7. Oechsner, M., Hillman, C. and Lange, F. F., Crackbifurcation in laminar ceramic composites. J. Am. Ceram.Soc., 1996, 79(7), 1834±1838.

8. Prakash, O., Sarkar, P. and Nicholson, P. S., Crackde¯ection in ceramic/ceramic laminates with strong inter-faces. J. Am. Ceram. Soc., 1995, 78(4), 1125±1127.

9. Lakshminarayanan, R., Shetty, D. K. and Cutler, R. A.,Toughening of layered ceramic composite with residualsurface compression. J. Am. Ceram. Soc., 1996, 79(1), 79±87.

10. Kragness, E. D., Amateau, M. F. and Messing, G. L.,Processing and characterization of laminated SiC whiskerreinforced Al2O3. J. Comp. Mater., 1991, 25(4), 433±452.

11. Marshall, D. B., Ratto, J. J. and Lange, F. F., Enhancedfracture toughness in layered microcomposites of Ce-ZrO2 and Al2O3. J. Am. Ceram. Soc., 1991, 74(12), 2979±2987.

12. Chen, Z. and Mecholsky, J. J., Toughening by metalliclamina in nickel/alumina composites. J. Am. Ceram. Soc.,1993, 76 (5), 1258±1264.

13. Hillman, C., Suo, Z. and Lange, F. F., Cracking of lami-nates subjected to biaxial tensile stresses. J. Am. Ceram.Soc., 1996, 79(8), 2127±2133.

14. Ho, S. and Suo, Z., Tunnelling cracks in constrained lay-ers. J. Appl. Mech., 1993, 60(4), 890±894.

15. Ho, S., Hillman, C., Lange, F. F. and Suo, Z., Surfacecracking in layers under biaxial residual compressivestress. J. Am. Ceram. Soc., 1995, 78(9), 2353±2359.

16. Cai, P. Z., Green, D. J. and Messing, G. L., Constraineddensi®cation of Al2O3/ZrO2 hybrid laminates: I. experi-mental observations. J. Am. Ceram. Soc., 1997, 80(8),1929±1939.

17. Cai, P. Z., Green, D. J. and Messing, G. L., Constraineddensi®cation of Al2O3/ZrO2 hybrid laminates: II. viscoe-lastic stress computation. J. Am. Ceram. Soc., 1997, 80(8),1940±1948.

18. Cai, P. Z., Green, D. J., and Messing, G. L., Mechanicalcharacterization of Al2O3/ZrO2 hybrid laminates, J. Eur.Ceram. Soc., 1998, 5, 2025±2034.

19. Bordia, R. K. and Scherer, G. W., On constrained sinter-ingÐI. Constitutive model for a sintering body; and II.Comparison of constitutive models. Acta Metall., 1988,36(9), 2393±2409.

20. Cai, P. Z., Messing, G. L. and Green, D. J., Determina-tion of the mechanical response of sintering compacts bycyclic loading dilatometry. J. Am. Ceram. Soc., 1997,80(2), 445±452.

21. Lam, D. C. C., Lange, F. F. and Evans, A. G., Mechan-ical properties of partially dense alumina produced frompowder compacts. J. Am. Ceram. Soc., 1994, 77(8), 2113±2117.

22. Nanjangud, S. C., Brezny, R. and Green, D. J., Strengthand Young's modulus behaviour of a partially sinteredporous alumina. J. Am. Ceram. Soc., 1995, 78(1), 266±268.

23. Sglavo, V. M., Cai, P. Z. and Green, D. J., Damage inAl2O3 sintering compacts under very low tensile stress. J.Mater. Sci. Letts., in press.

Residual stresses in alumina-zirconia laminates 2517