Acta Materialia 50 (2002) 4677–4686www.actamat-journals.com

Piezo-spectroscopy at low temperatures: residual stresses inAl2O3–ZrO2(Y2O3) eutectics measured from 77 to 350 K

V.M. Oreraa,∗, R. Cemboraina,b, R.I. Merinoa, J.I. Pen˜a a, A. Larreaa

a Instituto de Ciencia de Materiales de Aragon, C.S.I.C. - Universidad de Zaragoza, 50009-Zaragoza, Spainb Present address: CEIT, San Sebastian, Spain

Received 30 April 2002; received in revised form 31 July 2002; accepted 1 August 2002

Abstract

High-resolution, piezo-spectroscopic studies were performed in alumina/zirconia eutectic composites with differentY2O3 contents and microstructures at different temperatures using the ruby R-line luminescence. Measurements at 77K allowed the precise determination of the average stress and its distribution in the alumina phase. A normal distributionfunction was obtained in most of the cases. In some composites the highest stresses are relaxed by micro cracking,giving an asymmetrical distribution function. In the composites with stabilized zirconia the residual stresses originatefrom the differences in the thermal expansion coefficients of the component phases. A linear dependence of the thermos-tresses with temperature was obtained in the 77–350 K temperature range. The effective elastic modulus for thermos-tresses was 118± 2.7 GPa. Using the coefficients of thermal expansion of the component phases and making an extra-polation of the low temperature values the stress-free temperature of 1270± 35 K was determined. 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Residual stresses; Piezo-spectroscopy; Al2O3/ZrO2 composites; Directional solidification

1. Introduction

The determination of the residual stresses incomposites materials is of great importance inorder to understand their mechanical properties.For quantitative analysis of the residual stress fieldin a composite some few methods are available.X-ray diffraction methods, though accurate, lack ofgood lateral resolution and besides they are diffi-

∗ Corresponding author. Tel.:+34-976-761-333; fax:+34-976-761-229.

E-mail address: orera@posta.unizar.es (V.M. Orera).

1359-6454/02/$22.00 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.PII: S1359 -6454(02 )00322-1

cult to apply in heterogeneous samples. Instead,optical microscopy techniques based on the piezo-spectroscopic (PS) effects permit a lateral resol-ution of a few microns. The PS techniques are nondestructive and admit the simultaneous recordingof Raman and luminescence spectra in the specialmicrostructure features focused in the microscope.The PS measurements are based on the previousdetermination of the PS coefficients. These coef-ficients relate the spectroscopic observable, forexample the line position, with the stress. DifferentPS effects have been studied in several materialsfrom oxides or non-oxides inorganic compounds topolymers. A very complete review of the different

4678 V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

PS techniques and their applications can be seenin Ciacchi et al. [1].

In the PS measurements it is important to achi-eve the best spectral resolution. Decreasing themeasurement temperature improves the resolution.In the case of a homogeneous material the thermalbroadening due to the electron-phonon interactionalmost disappears at 77 K when only the intrinsicline-width is left.

In the present work we used the variation of theCr3+ emission in the alumina phase, in particularof the R2-line position, with the applied stress tostudy the residual stress state of someAlumina/Zirconia melt grown eutectic composites(AZE) [2]. Although this technique has been exten-sively used in the past to measure, for example,the room temperature residual stresses in polycrys-talline ceramics and composites [3,4] here, weinvestigate the possible advantages of the low tem-perature measurements in these studies. Further-more, the Al2O3–ZrO2 composites we studied arecandidates for high temperature applications wherea combination of strength, thermal stability andchemical inertness are needed. These micro-com-posite material systems can be fabricated via thesolidification of eutectic melts. They possess a highdensity of interfacial area and a small inter-phasedistance that prevent the formation of large defectsduring processing. Consequently, melt-growtheutectics of these conventionally brittle materialsare surprisingly tough at room temperature and upto near the eutectic point [5]. Laser processing isa suitable technique for producing large rods ofAl2O3–ZrO2 eutectic (AZE) composites. Recently,the production of large plates of this material bylaser zone melting has also been reported [6].

We have studied several AZE samples in differ-ent stress situations. In the samples without yttriathe residual stresses due to the tetragonal to mono-clinic zirconia phase transformation are dominantand the alumina is under tensile strength. For Y2O3

doping levels above 3 mol% the zirconia is stabil-ized in its tetragonal or cubic phase, the residualstresses are due to differences in the coefficients ofthermal expansion (CTE) and the alumina is undercompression [7]. Different residual stresses arealso obtained by changing the topology of themultiphase material. Depending on the growth con-

ditions two type of microstructures can beobtained. The columnar colony microstructure isfound in the fast-solidified materials. However, ahomogeneous, colony-free three-dimensional inter-penetrating network is obtained in the slowlygrown materials. Performing PS measurements atdifferent temperatures we obtained valuable newinformation about the tensile state in the differ-ent samples.

2. Experimental procedure

Starting materials were commercially availableAl2O3 (99.99%, Aldrich), ZrO2 (99+%, Alfa) andY2O3 (99.99%, Aldrich) powders. The powderswere milled in a vibrator mill (model MM2000,Retsch, Haan, Germany) with alumina compo-nents, fired in air at 1000 °C for one hour, hand-milled in an agate mortar and mixed into thedesired compositions. Precursor rods, 1–2 mm indiameter and 50–100 mm in length, were preparedfrom the powder mixture of the oxides by sinteringat 1500 °C. Directionally solidified eutectic fiberswere then produced from the precursor fibers bythe laser, floating zone-method, as described else-where [8]. The Y2O3 concentrations in the ZrO2

phase were measured by Energy Dispersive Spec-troscopy technique carried out in a TransmissionElectron Microscope [9]. The samples were cutand polished with diamond paste for opticalmeasurements.

Ruby luminescence was measured using thehigh-dispersion set-up of a triple 0.5 m mono-chromator with an optical multichanel detector.The spectral resolution was 0.15 cm�1. The shiftswere measured with respect to the R2 line of anAl2O3:Cr3+ (0.11 wt % Cr2O3) single crystal whichat 295 K appears at 14433 cm�1. For the growth ofthis ruby crystal we used the same Al2O3 startingpowder (99.99% Aldrich) than for the eutecticsamples. The setup allows us to measure sequen-tially three samples at each temperature, two eutec-tic samples and the ruby with the optical micro-scope. The spectra were corrected for instrumentalerrors using the 14,431 cm�1 line of a neon dis-charge lamp. A region of about 1 µm diameter and4 µm in depth can be analyzed using 100× objec-

4679V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

tive lens and 400 µm field aperture in the imagefocal plane but in order to obtain sample averageinformation most of the data we present wereobtained with a 10× objective and spatial resol-ution of about 100 µm. Measurements were perfor-med at different temperatures from 77 to 500 Kin an optical microscope adapted liquid nitrogencryostat (below 300 K) and a thermostat for T �300 K. To assure a good thermal contact sampleswere glued to the sample holder with silver paste.The thermal stability and accuracy was ±0.5 K.

3. Results and interpretation

3.1. Sample composition, structure andmicrostructure

Three alumina/zirconia eutectic compositionswere formulated. The alumina/monoclinic zirconia,m-AZE (63 mol% Al2O3 and 37 mol% ZrO2), thealumina/cubic zirconia, c-AZE where the zirconiaphase was doped with 12.2 mol% Y2O3 and thealumina/tetragonal zirconia, t-AZE with 5.12mol% Y2O3. The m-AZE composite was grown inorder to obtain two samples with different micro-structure. In fast growth conditions (100 mm/h) themicrostructure consists of colonies of the aluminamatrix containing a regular distribution of zirconiafibers (m-AZEo). Colonies are formed by facetedalumina grains growing along the [0001] sapphirec-axis, which contain a very fine and regular dis-persion of ZrO2 rods with well-defined orientationrelationships [10]. Slow growth (10 mm/h) pro-duces a homogeneous and colony free microstruc-ture, (m-AZEd, t-AZE and c-AZE), characterizedby an interpenetrating network of both phases.These microstructures can be observed in the SEMpictures given in Fig. 1 of reference [7]. Transversecross-sections of eutectics showing these micro-structures are also given here for clarity (see Fig.1). In the case of the interpenetrating microstruc-ture, the phase orientations clearly correspond toan interpenetrating bicrystal, however, the phasesdo not always grow along a simple and well-defined crystallographic direction [10].

The micrographs show a continuous matrix ofα-Al2O3 with zirconia inclusions. In the case of the

Fig. 1. Transverse cross-sections of ZrO2(Y2O3)–Al2O3 eutec-tics showing the ordered colony (a) and intepenetrating (b)microstructural sizes.

ordered m-AZEo sample rods of monoclinic zir-conia about 0.3 µm in diameter and �60 µm longare embedded in the Al2O3 matrix. Broadly speak-ing, the microstructure in the slowly grownsamples is formed by a homogeneous dispersionof zirconia inclusions with a length to width ratio

4680 V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

close to 3 and spacing around 2 µm in a continuousalumina matrix [9]. It is clear that with thesemicrostructures and given the spatial resolutionused in the spectroscopic experiments, of about100 µm, we are obtaining average information ofeach sample.

From the point of view of the thermo stresses,tetragonal zirconia is similar to the cubic zirconia.Consequently, here we will only discuss in detailthe results corresponding to composites of mono-clinic (0 mol% yttria) and cubic (12 mol% yttria).Besides the ordered m-AZEo we analyzed twosamples of 0 mol% yttria (m-AZEd) both withhomogeneous interpenetrating disordered micro-structure but with different tensile states. The firstone described by Pardo et al. [7] presents a non-relaxed stress state whereas in the second one, thecoarser microstructure favors microcrackingwhich, produces some relaxation of the tensilestresses [11].

3.2. Piezospectroscopy

Using the values of the piezospectroscopic ten-sors, �ij, of the R-line emission in ruby, as determ-ined by He and Clarke we can calculate theresidual stresses in the alumina phase from thepeak shift �n between the stressed and theunstressed ruby [12]. In particular, the shift of theR2 line (in cm-1) can be related with the hydrostaticstress component sh (in GPa) by the scalarrelationship:

�n2�2.54(s11 � s22 � s33) � 7.61sh (1)

Evidently, the stresses in the zirconia phase shZ

can be evaluated from the static equilibrium con-dition as:

fAshA � fZshZ � 0 (2)

where fA (=0.7) and fZ (=0.3) stand, respectively,for the volume fraction of alumina and zirconia.

In Fig. 2 we show the Cr3+ luminescence peaksmeasured at 77 K in unstressed ruby and in thealumina phase of three characteristic eutecticsamples. The spectra consist of the R1 and R2 lines,associated to the E(2E)→4A2 and 2A(2E)→4A2 tran-sitions of the Cr3+(d3) respectively. It is wellknown that their peak positions depend strongly on

Fig. 2. 77 K luminescence spectra of unstressed ruby(continuous line), monoclinic AZE with ordered microstructure(�), non-relaxed monoclinic AZE with disordered microstruc-ture (�), and cubic AZE (�).

the stress applied to the alumina phase, and on thetemperature. At 77 K the R luminescence lines ofunstressed ruby appear at approximately 14,420and 14,451 cm-1 blue shifted with respect to 14,403and 14,433 cm-1 at room temperature. Ruby is con-sidered the unstressed standard situation of this ionin alumina. In the composites, the R lines presentvariations on the peak positions, half-widths andshapes. They were essentially depolarized presum-ably due to the strong depolarizing effects associa-ted to the high refractive index contrast betweenphases and fine microstructure. Clearly, the R linesof the eutectic samples are much broader thanthose of the unstressed ruby. All the residualstresses fell within the compressive region (blueshift) in the sample with yttria, while most of thealumina regions in the m-AZE sample were undertensile stress with some minor regions under com-pression (Fig. 2).

As expected for homogeneously broadenedemissions, the ruby line half-width increases withtemperature [13]. Similar thermal broadening canbe observed in all the samples and at high tempera-tures (over 300 K) the line-widths of eutectics andunstressed ruby are very similar. In Fig. 3 we givethe experimental full width at half maximum(FWHM) of the R2 peak of ruby, ordered and dis-ordered m-AZE as a function of temperature. It canbe seen that at low temperatures the FWHM of

4681V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

Fig. 3. R2 line FWHM measured at different temperatures.Unstressed ruby (�), monoclinic AZE with ordered microstruc-ture (�), and non-relaxed monoclinic AZE with disorderedmicrostructure (�).

some eutectics can be one order of magnitudehigher than that of unstressed ruby. This differenceis caused by the presence of temperature inde-pendent inhomogeneous line broadening due pre-sumably to the presence of a stress distribution inthe eutectic composites [3,9]. At high temperaturesthe homogeneous broadening dominates and theinhomogeneous is partially masked. In the com-posites, the inhomogeneous broadening is pre-dominant over the homogeneous one for T �150 K.

3.3. Line-shape model

To obtain information about stress values, theirdistribution and evolution with temperature frompiezospectroscopic measurements, we must fit cor-rectly the experimental emission curves and sys-tematize a method that allowed knowing the half-widths and the peak positions accurately. Theunstressed ruby R lines are very narrow at 77 K,and each R line can be fitted by a superposition oftwo Lorentzians (L) 0.35 cm-1 apart and 0.65 cm-1

widths. According to Henderson and Imbush datathese doublets appear because of the splitting ofthe 4A2 Cr3+ ground state [13]. The L profiledescribes the homogeneous line broadening. How-ever, for our purpose, the shape of each R-line canbe well approached by only a single L curve,

y(n) � L(n�nc,wL), leaving as fitting parametersthe peak position, nc, and the full width at halfmaximum wL. The unstressed ruby lines experi-ence a shift towards low energies and homo-geneous thermal broadening at high temperatures.Their line-shape being also well fitted with two Lfunctions through all the temperature range up toRT. Further increase of temperature produces bothline broadening and peak overlapping. At T �300 K the accuracy in the peak position determi-nation deteriorates. Above 500 K the two R1 andR2 peaks are so broad that they completely overlapeach other and the determination of the individualfitting parameter set is not longer reliable.

As we have seen above, in the eutectic samples,the peaks are wider than in unstressed ruby at lowtemperatures because of the inhomogeneous broad-ening effect (stress distribution). A random straindistribution is described by a Gaussian (G) func-tion where the FWHM wG is 2.35 times the stan-dard deviation of the G distribution. The homo-geneous broadening cause an L line-shape. Whenboth mechanisms are operative the line shape isdescribed by a Voigt profile which is a convolutionof the G and L functions V(n) defined as:

y(n) � y0 � AwL2ln2p3/2w2

G��

��

e�t2

�wL

wG

�ln2�2

� �2(n�nc)wG

�ln2�t�2dt (3)

where, y0 is the offset and A the amplitude. Theleast-squares fit of the overlapping R1 and R2 lineswith Voigt functions is difficult mainly when someexperimental noise and/or non-linear backgroundare present. To avoid that problem it is customaryto make an analytical approach to the Voigt func-tion, for example a linear combination of L(n) andG(n) such as [14,15]:

y(n) � y0 � A�m2p

wL

4(n�nc)2 � w2L

� (1 (4)

�m)�4ln2

wG�pe�4ln2

w2G

(n�nc)2�where m is the profile shape factor or mixing ratio.Although the physical meaning of this pseudo-Voigtian function (psV) is not clear, it reproducesreally well most of the experimental curves. How-

4682 V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

ever, to obtain meaningful R2 parameters we haveto use eq. (3). We analyzed the experimental spec-tra using the following procedure. First we fittedthe two peaks with a double psV function (eq. (4)).This way we can obtain the individual R1 and R2

experimental components; each of them can be fit-ted with a Voigt function (eq. (3)). In the fit to theVoigt function we took as the lorentzian width wL

that of the unstressed ruby measured at the sametemperature. In Fig. 4 we illustrate the procedure.The luminescence spectrum of the non-relaxed m-AZE sample at 77 K was fitted by a psV function.A similar good fitting is also observed in all thet-AZE and c-AZE samples. Using the psV fittingparameters we generated the curve correspondingto the R1 line, which is subtracted from the experi-mental curve leaving the isolated R2 band. Finallythis band is fitted by the V-function and the peakposition and distribution widths are obtained as fit-ting parameters.

3.4. Stress distribution

In Table 1 we give the peak positions and theirshifts for four studied samples at 77K. The R2-lineshift we find in the melt growth c-AZE compositeof �3.5 cm�1 is larger than �1.6 cm�1 measuredby Ma et al. in sintered composites of similar com-

Fig. 4. Line-shape fitting procedure. Below: 77 K lumi-nescence spectrum of a disordered m-AZE sample (�). Con-tinuous line shows the two peak psV fitting curve. Above: R2

component (�). Continuous line is the R2 fitting with a Voigtcurve with a Lorentzian component of 1.3 cm�1 FWHM.

position [16]. In Table 1 we also give the hydro-static stresses calculated with eq. (1). The com-pressive hydrostatic stresses for Al2O3 in all thesamples with either tetragonal or cubic zirconia arefairly similar. On the contrary, there is a markeddifference in the tensile strength of samples withmonoclinic zirconia but different microstructure.The effect of the microstructure on the residualstresses of AZE composites at 300K was pre-viously discussed in [7,11].

At low temperatures (T � 150 K) wL � �wG, the stress broadening is larger than the homo-

geneous broadening. In the cubic, tetragonal andnon-relaxed monoclinic AZE samples, the line pro-files can be well fitted by a voigtian function,Gaussian convolution of narrow lorentzians. In thecase of the nearly isotropic R2 line and using eq.(1) the line-shift distribution can be directly tra-duced to a stress distribution.

�sh(GPa)�wG(R2) /7.6 (cm�1) (5)

The results for the FWHM distribution are givenin Table 1. It is interesting to notice that the stressdistribution is broader in the case of m-AZEsamples than in the t- and c-AZE samples.

However, in some cases the stress distributiondoes not corresponds to a gaussian function. Anexample is given by the relaxed m-AZE sample.In this case, and following the arguments givenabove, the stress distribution can be approximatelyobtained directly from the low temperature spec-troscopic measurements. In Fig. 5(a) we presentthe hydrostatic stress distribution, measured by thelow temperature intensity of the R2 line, of m-AZEsamples with disordered microstructure with andwithout stress relaxation. The non-relaxed samplepresents a normal distribution of stresses centeredat about 560 MPa and with a FWHM of about 950MPa. However, the line-shape of the stress-relaxedsample could not be well fitted with the symmetricvoigtian functions. It could be only fitted withasymmetrical functions indicating that in this sam-ple the distribution of stresses is not random. Fromthe line-shape in the low temperature spectra it canbe deduced that the stresses higher than a thresholdstress have been released, and that only the lowerones remain. Fig. 5(b) better illustrates this effectwhere we give the curve resulting from subtraction

4683V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

Table 1R-line parameters, hydrostatic average stress sh and FWHM stress distribution �sh of non-relaxed samples measured at 77 K

Parameter Ruby m-AZE-o m-AZE-d t-AZE c-AZE

R1 nc (cm�1) 14,20.62 ± 0.02 14,425.6 ± 0.1 14,424.7 ± 0.1 14,416.38 ± 0.05 14,416.75 ± 0.05R1 FWHM (cm�1) 1.5 ± 0.05 10.5 ± 0.1 7.5 ± 0.1 3.5 ± 0.05 4.3 ± 0.05R2 nc (cm�1) 14,451.05 ± 0.02 14,456.7 ± 0.1 14,455.1 ± 0.1 14,447.11 ± 0.05 14,447.49 ± 0.05R2 FWHM (cm�1) 1.3 ± 0.05 10.0 ± 0.1 7.2 ± 0.1 3.2 ± 0.05 3.9 ± 0.05sh (MPa) 750 ± 15 540 ± 15 �510 ± 10 �460 ± 10�sh (MPa) 1300 950 420 520

Fig. 5. (a) Stress distribution function obtained from the R2

emission line at 77 K in non-relaxed disordered m-AZE(continuous line) compared with a sample of the same compo-sition but with the stresses relaxed by microcracking (dottedline). (b) Difference between the non-relaxed and relaxed stressdistribution functions.

of the spectra of the relaxed from that of the non-relaxed sample. The area under the emission lineswas previously normalized. Stresses with a peakdistribution around 800 MPa are relaxed towards�100 MPa. We confirm that micro crackingphenomenon permits tensioning relaxation, in factcracks normal to the interface, as expected for ten-sile tangential stresses occurring when the CTE ofthe particle is smaller than that of the matrix havebeen observed in these ‘stress relaxed’ samples byelectron microscopy [9].

We also used the piezo-spectroscopic measure-ments to analyze the temperature dependence ofthe stresses. In Fig. 6 we show the values of sh inthe useful temperature interval of measurement(77–350 K) for both c and m-AZE samples. Weobserved two different behaviors. First, the hydro-static stresses are positive for m- and negative forthe c-composites. This corresponds to the fact thatalumina in the first sample is under tension and inthe second under compression. Also, in the c-sam-ple we appreciated a linear decrease of |sh| withtemperature. However there is not such an evidenttendency in the m-sample where the stress valueremains essentially constant within the error limits.

4. Discussion

Both the magnitude and the temperature depen-dence of the residual stresses in AZE compositesvary with the zirconia phase composition. Theexplanation of this difference is the following: Asthe melt cools, the constituent phases solidify andexperience different volume contractions, due to

4684 V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

Fig. 6. (a) Hydrostatic residual stresses versus temperature of:monoclinic (�), and cubic AZE (�). The lines represent thebest fitting linear curves. (b) Fitting curve to the cubic zirconiadata given by eq. (6) and extrapolation to s h � 0 to obtain T0

(see text).

their distinct thermal expansion coefficients (CTEmismatch). In the c- and t-AZE samples azc �aa, ( on average, from 0 to 1000 °C, aa �8.2 × 10�6, azt � 10.6 × 10�6 and azc �11 × 10�6 K�1) [17]. Consequently the zirconiaphase contracts more than the alumina phasewhich, is under compression stress. The residualthermal stress in the alumina phase is given by:

s(T) � K∗e(T) � K∗�T0

T

(aA � aZ)dT (6)

where K∗ is an effective elastic modulus relating

the thermal strain e with the thermo stresses andT0 represents the temperature below which thestresses can not be relaxed by plastic deformation.Clearly, when the measurement temperatureincreases the total stress diminish, as the intervalbetween T0 and the measurement temperature andhence, the expansion differences between the twophases decreases as it has been observed in Fig. 6.

In the case of monoclinic zirconia the residualstress is nearly temperature independent in themeasurement range. Here, the CTE mismatch issmall (azm � 7.5 × 10�6 K�1) [18] and the maincontribution to the residual stresses arises from themartensitic volume expansion. In the case of thecubic and tetragonal samples, fitting of the stressversus temperature data by eq. (6) gives us thethermoelastic modulus K∗. Further extrapolationto sh � 0, allow us to estimate the temperature T0

at which thermo elastic stresses develop. However,in order to fit eq. (6) to the data of Fig. 6 we haveto solve the following problems. Due to spectraloverlapping our data restring to 350 K and belowit and T0 is expected to be above 1000 K. Conse-quently, it is crucial to know accurate values of theCTE of the phases in all the temperature rangefrom T0 to T. It is also necessary to know the mech-anical properties of the composite in the measure-ment temperature range. The later is a minor dif-ficulty because the changes of the elastic constantsin the 77–350 K temperature range can be con-sidered to be negligible. For example, the bulkmodulus B depends on the molar volume as Vm

4/3

and the RT values can be used down to 0 K withan error of less than 1%.

With respect to the thermal expansion coef-ficients at RT and above it they are well describedby second order polynomials. According to Hill-man et al. [19] the CTE misfit is given by theexpression:

aA � aZ � �3.15 × 10�6 (7)

� (1.0 × 10�10)T�(5.5 × 10�13)T2

where T is given in K. The integral of eq. (6) is apolynomial of third degree in T. The T � T0 limitcontributes to the independent term. In Fig. 6(a)we show the result of the fitting of eq. (6) to thesh versus T data for the c-AZE sample, giving

4685V.M. Orera et al. / Acta Materialia 50 (2002) 4677–4686

K∗ � 118.6 ± 2.7 GPa. It can be seen that the fit-ting is linear in the measurement range as it corre-sponds to the leading role of the independent termin eq. (7). The extrapolation to T0 � 1270 ± 35 Kis shown in the Fig. 6(b). T0 being the experimentalonset temperature for stresses relaxation via plasticdeformation. Plastic deformation occurs in zirconiaat temperatures above 1200 °C, which are higherthan those for alumina [20]. Consequently, in thecomposite the stress relaxation is limited by thealumina. The onset temperature we find is 150 Klower than previously used by us to calculatethermo elastic stresses [7], and a little lower thanother values derived in the literature [4,21] for cer-amic samples but it agrees very well with theresults of Dorre and Hubner [22] who reportedtemperatures of 900 °C for basal slip and 1150 °Cfor prismatic and pyramidal slip in single-crystalalumina.

With respect to the magnitude of the thermo-elastic constant K∗, this is an effective elasticmodulus which depends on the elastic constantsand volume fractions of the component phases aswell as of the sample topology. One possible geo-metric analog to the interpenetrating microstructureof the c-AZE samples is a topology of isolated zir-conia spherical particles in an alumina matrix offinite dimension. Using the generalized self-con-sistent approach it has been shown that [17]

K∗ �3fZ

3 /4mA � fA /KZ � fZ /KA

(8)

K and m being the bulk and shear modulus respect-ively. Using the following elastic constants,KZ � 205.2 GPa, KA � 251 GPa and mA � 162GPa taken from [22] we find K∗ � 97.5 GPa ingood agreement with 118 GPa obtained fromexperiments.

It is interesting to point out here that in the com-putation of the residual stress we neglected thepossible contribution from the anisotropy of theAl2O3 phase itself. In our compounds the aluminaphase can be visualized rather as a continuouscrystal than as individual small, random orientedgrains. Besides, even in the ceramics of this com-position this contribution to the total average stressis very small [16].

5. Conclusions

We proved that low temperature and high-resol-ution measurements of the ruby R-line lumi-nescence allows us the precise determination of theaverage residual stresses and its distribution in sev-eral alumina–zirconia composites. In the com-posites with monoclinic zirconia the stresses aremainly due to the volume increase of the zirconiaphase caused by the martensitic transformation andalumina is under tension. In some samples stressrelaxation has been evidenced by the decrease inthe average stress value as well as by the asymmet-ric stress distribution function. In samples withtetragonal or cubic zirconia the origin of thestresses is thermo elastic and the alumina is undercompression. The temperature dependence of thethermo stresses permits the determination of theeffective elastic modulus and the free-stress tem-perature that governs the thermo elastic process.The later is in accordance with the onset tempera-ture for creep in alumina. The effective elasticmodulus also agrees with that predicted from asimple model of independent zirconia particles per-fectly bonded to the alumina matrix.

Acknowledgements

We gratefully acknowledge support from theSpanish Ministry of Science and Technology(CICYT MAT2000-1495 and MAT2000-1533-C03-02). R. Cemborain also thanks the C.S.I.C. fora grant.

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