M A T E R I A L S SCIENCE &

ENGINEERING

A E L S E V I E R Materials Science and Engineering A219 (1996) 148-155

Microstructural aspects of superplastic deformation of AlaO3/ZrO2 laminate composites

O. Flacher a,*, J.J. Blandin a, K.P. Plucknett b, C.H. Caceres b, D.S . Wilkinson b alnstitut National Polytechnique de Grenoble, G~nie Physique et M~canique des Mat&iaux, ESA CN~RS 5010, BP 46,

38402 Saint-Martin d'Hb'es Cedex, France bDepartment of Materials Science and Engineering, Mc Master University, Hamilton, Ontario LSS 4L7, Canada

Received 29 January 1996; revised 12 April 1996

Abstract

Mechanical properties in superplastic conditions of A12Os/ZrO 2 laminate composites were studied in compression. The as-received material consists of an appropriate stacking of 140 gm thick layers, containing 10 or 20 vol.% ZrO2 particles. It is shown that an increase in zirconia content limits alumina grain growth and decreases the creep resistance of the corresponding layers. Possible causes of these variations in creep behaviour are proposed in relation to grain refinement effect and a specific rheology of the zirconia inclusions. The relative contributions of plastic deformation and phase boundary sliding to the total deformation are also discussed, based on the compared variation with strain of two parameters related to the grain shape.

Keywords: Alumina grain growth; Alumina-zirconia composites; Intragranular deformation

1. Introduction

Superplastic deformation of ceramics requires to pro- duce fine grain structures after sintering. In the case of pure alumina, low-temperature sintering ( < 1300°C) is a way to obtain submicrometer microstructures. How- ever, superplastic deformation induces generally dy- namic grain growth which has a tremendous effect on the plastic stability of the material. To limit grain boundary mobility in alumina, two methods have been particularly investigated: solute drag and second phase pinning. From this viewpoint, superplastic deformation of both MgO-doped alumina [1,2] and alumina-zirco- nia composites [3-7] have been widely investigated.

Tape casting of laminate structure has been demon- strated to present advantages in comparison with classi- cal sintering of monolithic bodies [8,9]: the flaw size is limited by the thickness of each layer and a controlled architecture can be achieved through the cross section of the composite. It results from these advantages that the toughness of the laminate is generally higher than that of the corresponding monolithic material, when

* Corresponding author.

processed in a conventional way [8,9]. Moreover, due to differences in thermal expansions, an appropriate stack- ing of layers containing different zirconia amounts can develop residual internal stresses, which may lead to an additional increase in toughness of the composite [8,10].

The aim of this work is to present some results dealing with the microstructural changes which occur during superplastic deformation of a laminate structure of alumina-zirconia layers produced by tape-casting.

2. Experimental procedure

A12Os-ZrO 2 laminates were prepared from A120 3 (Alcan BACO RA t07 LS) and ZrO2-3mol%Y203 (Tosoh TZ-3YS) powders using the tape casting and lamination process. Tapes of A1203-10 vol.% ZrO2 (A layer) and of A1203-20 vol.% ZrO2 (B layer) were produced via a tape casting process outlined elsewhere [11,12]. The tapes were then stacked (according to the sequence AAA-BB-AAA), thermocompressed at 120°C to laminate the layers together, and finally sintered at 1580°C for 2 h. The thickness of each layer was approx- imately 140 ~tm after densification. Image analysis was performed from mechanically polished and thermally

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O. Ftaeher et aL/ Materials Science and Engineer#~g A219 (I996) 148-i55 149

etched samples, observed by scanning electron mi- croscopy (SEM). Before image analysis, grain (or phase) boundaries are duplicated from SEM micro- graphs on transparencies by hand-drawing. This proce- dure is expected to erase the second order fluctuations along the boundaries which could affect the calculation of some characteristic parameters, such as the perimeter of the grains. Afterwards, the drawing is scanned and the boundaries are thinned (which means that the thick- ness of the boundary is reduced to one pixel) and then smoothed. In these conditions, the perimeter P and the surface S of each grain are estimated.

Mean grain size was defined as the mean equivalent diameter of the grains (<d>) observed on SEM micro- graphs, according to the relation (d> = 1.38 (x / -~ . Two aspect ratios of the grains were calculated: F1-- p2/4~rS and F2 = LmaJLmin. For each data point, five micrographs were considered. Lmax and Lmin are defined as follows. In each direction of measurement, a mean linear intercept length/7, is estimated. From the various obtained /2 values, maximum (Lma~) and minimum (Lm~) lengths can then be deduced. It must be under- lined that F2 is not estimated for each grain. In particu- lar F2 does not correspond to the parameter (which is sometimes used as a shape parameter) defined as the mean value of the ratios (major axis/minor axis), each ratio being estimated for each grain. The specific mean- ings of F1 and F2 are discussed in the following para- graphs.

Mechanical testing was performed in compression in air at 1470°C and in the strain-rate range from 10-4 to 10 -3 s-1. The time needed to reach 1470°C was ap- proximately 1 h and an homogenisation period of 30 rain was systematically applied before testing. The lam- inates being thin, three of them were superposed to form a sample (total thickness ,.~ 3.4 ram), in order to have a correct compression state. Diffusion bonding took place between the laminates during the first steps of the compression tests and no sliding was observed between these laminates. Consequently, in such condi- tions, the materials can be described as a stacking of 24 layers. Both velocity-change and constant strain-rate tests were carried out. The compression axis was chosen perpendicular to the layers. True stress was calculated from the change of the specimen thickness by assuming constant specimen volume.

3. Results

3. I. Microstructure o f the as-received material

Fig. 1 shows the cross-section of the as-received material. The dark zones correspond to A1203+ I0 vol.% ZrO2. The two types of layers (A and B) are well defined with straight interfaces and no significant resid-

A

B

A

Fig. 1. Micrograph of the cross-section of the sintered material (the white zone corresponds to AI203 + 20 vol.% ZrO2 and the dark zones correspond to A1203 + 10 vol.% ZrO2).

ual porosity was detected from SEM observations at the interfaces between the two types of layers. It must be, however, mentioned that density gradients were reported through similar sintered tapes elaborated by the same technique [12]. It occurs when a thin imperme- able skin forms on the top surface of the tape during drying. This inhibits further drying and reduces the green density of all except the top 5 /~m of the tapes. However, green density gradients diminish as the zirco- nia content increases, because of the increased porosity of the tapes, enabling continued solvent evaporation. It was then thus observed that these intralayer density gradients disappear for layers with zirconia content higher than 5% [12].

From the SEM observations, it was no longer possi- ble to localize the former interfaces between layers having the same composition, namely A/A and B/B interfaces. The SEM micrograph shown in Fig. 2, dis- plays a typical microstructure of the as-received mate- rial. Mean grain sizes (<d>) were determined to be 1.2 and 1.1 gm, respectively for the poor and rich zirconia layers. This difference results in a higher size of alumina

Fig. 2. SEM micrograph of A1203 + 10 vol.% ZrO2 layer in as-re- ceived conditions.

i50 O. Flaeher et al. / Materials Science and Engineering A219 (1996) I48-155

B

A

Fig. 3. SEM micrograph of cross-section deformed material at e = - 0.4. Interface A12Q + 10 vol.% ZrO2 (A)/A1203 + 20 vol.% ZrQ (B)

grains in the poor zirconia layers ((LA12o3)= 1.3 and 1.2 y m , respectively for the 10 and 20% zirconia lay- ers). No abnormal grain growth is detected in the as-received structure in both layers. A homogeneous distribution of the ZrO2 grains is also observed in both layers. Most zirconia grains are faceted and located at alumina junctions, but some nearly spherical zirconia particles are also present within some alumina grains (arrows in Fig. 2). Whatever the layers, the zirconia grain size is approximately 0.6 gm, namely smaller than the alumina one. In both layers, a value of FI equal to 1.5 is measured. It indicates that the grains can proba- bly not be described as perfectly equiaxed, since regular hexagons correspond to a parameter F~ equal to 1.1. As soon as the microstructure is not assumed to be per- fectly equiaxed, it becomes relevant to get data in relation to orientation effects. Linear intercepts mea- sured along several directions in both the sheet plane and the cross-section plane were shown to be relatively independent on both the orientations of the observed sections and on the direction of interception (F 2 g 1). That means that no preferential oriented microstructure has developed during the elaboration process, and par- ticularly during the lamination step at 120°C.

3.2. Microstructure o f the material after superplastic deformation

By velocity-change tests, and despite a significant strain-hardening, a stress exponent n close to 2 was obtained in the strain rate range (2 x 10 -4 s - t ; 5 × t0 -4 S- 1) at a temperature equal to 1470°C. Mechani- cal testing were then performed at a constant strain-rate equal to 4 x 10-4 s - 1 at 1470°C, up to strains of - 0.4 and - 0.9.

Figs. 3 - 5 show some typical microstructures of the deformed material (e = - 0.4). F rom these micrographs several features can be underlined.

Fig. 4. SEM micrograph of cross-section deformed material at e = - 0.4. AlzO3 + 10 vol.% ZrOa layer.

(1) No interaction between layers is observed during deformation, as illustrated by the observation of an interface A/B shown in Fig. 3. In other words, the initial straight aspect of the interfaces between lay- ers is not affected by deformation.

(2) F rom measurements of the variation of the layer thickness after deformation, differences are ob- tained between the two types of layers. After a strain e = - 0 . 4 , a ratio between the strain reached in each type of layer 8B/eA g 1.5 is obtained. Since the stress axis is perpendicular to the interface planes, each layer is assumed to be identically stressed. I t means that the layers with 20 vol.% of zirconia particles admit a higher deformability than the other ones.

(3) F rom Figs. 4 and 5, it can be deduced that a preferential orientation of the microstructure is de- veloped in both layers leading to an elongated structure in a perpendicular direction to the stress

Fig. 5. SEM micrograph of cross-section deformed material at e = - 0.4. AI203 + 20 vol.% ZrO 2 layer.

O. Flacher et al. / Materials Science and Engineering A219 (I996) i48-155 151

Fig. 6. Evidence of a zirconia particles clustering in the planes perpendicular to the stress axis. e = -0 .4- A120 ~ + 20 vol.% ZrOa layer.

axis. This was further confirmed by the calculation of F2 after deformation, which was found to be close to 1.5 and 1.3, respectively for the 10 and 20% zirconia layers.

(4) Dynamic grain growth takes place during super- plastic deformation of the composite. This process seems to be enhanced in the case of the poor zirconia layers, since after deformation, mean grain sizes ((d)) were found to be 1.5 and 1.3 /~m, respectively for the 10 and the 20% ZrOa layers.

(5) A clustering of zirconia particles occurs during deformation, especially in the plane perpendicular to the stress axis, as illustrated on Fig. 6 (arrows). As expected, this process is more pronounced as zirconia content increases. In the A1203 + 10 vol.% ZrO2 layers, the frequency of ZrO2/ZrOa grain boundaries in reference to the population of inter- faces (namely AlzOJA1203, AlaO3/ZrO 2 and ZrO2/ Z r Q interfaces), after a strain of -0 .4 , is more than twice the initial one [13].

(6) Some intergranular cavities are induced by super- plastic deformation (arrows in Figs. 4 and 5) and additional micrographs seem to indicate that the A1203 + 10 vol.% ZrOa layers exhibit much stronger sensitivity to cavitation than zirconia-rich layers. Strain-induced cavitation during superplastic defor- mation of alumina has been widely reported [14,15], whereas fine grained zirconia generally do not cavi- tate during superplastic deformation in compres- sion [16,17].

4. Discussion

Significant zirconia additions in alumina is known to generally promote deformability of the resulting com- posite [4-7]. It has been essentially attributed to two causes: a higher deformability of the zirconia particles in reference to the one of the alumina matrix ('soft

inclusion' effect) and/or a refinement effect during sin- tering associated with a decrease in the grain growth which usually occurs during superplastic deformation ('grain size' effect).

A first explanation which is frequently pointed out to explain the softening effect which can result in the introduction of zirconia particles in an alumina matrix, deals with a higher deformability of the zirconia parti- cles in reference to that of the alumina matrix [4,7]. An increase of the softening process has even been associ- ated to a threshold amount of ZrO2 particles. This threshold was estimated to approximately 15 vol.% and corresponds to the percolation of zirconia particles through the alumina matrix [4]. It must be however underlined that this threshold was estimated according to the assumption that zirconia and alumina grains admit the same mean size [4]. This condition is not satisfied for the investigated material, for which the mean size of the zirconia particles is roughly one half of the mean size of the alumina grains. Since Bouvard and Lange [18] have demonstrated that the percolation threshold is a function of the grain size ratio between the two phases, the percolation threshold of the zirco- nia particles is likely to be different from 15 vol.%. Moreover, even if a percolation of the zirconia particles is assumed, since the alumina matrix also percolates, the deformation of the composite is expected to be controlled by the 'harder' phase, namely the alumina grains.

The deformability ratio can also be estimated accord- ing to the theological model proposed by Chen [19]. This model describes the composite as a non-newtonian fluid mixture containing uniformly dispersed soft spher- ical inclusions. In such a framework, the softening effect of the introduction of the soft particles depends on the stress exponent n exhibited by the matrix (~ = Ko -~) and it is then assumed that the value of n was not dependent on the inclusion content (p). This can be expressed according to:

i = (1 - p) -- 53n + 7/36 X K o "n (1)

The description of A1203-ZrO 2 creep by Chen's model has been already reported [20]. As already men- tioned, a value of n close to 2 was obtained for the investigated material. If this value is introduced in Chen's formulation, a ratio ~B/~A equal to 1.4 is ob- tained, which is in relatively good agreement with the experimental observations. Nevertheless, it must be noted that, from the SEM observations, no particularly large variation in the shape of zirconia particles is obtained, which tends to indicate that the plastic defor- mation of this phase is not so different from that of the alumina grains. In conclusion, the 'soft inclusion' effect associated with the introduction of ZrO2 particles in the alumina matrix, if its occurs, is not likely to be the unique cause of the observed softening.

152 O. Flacher et al. / Materials Science and Engineering A219 (1996) 148-155

The 'grain size' effect must then be considered. As expected, the mean grain size is smaller in the A1203 + 20 vol.% ZrO2 layers than in the A1203 + 10 vol.% ZrO2 layers. The mean grain size d is known to be a key parameter in superplastic behaviour, according to:

A / G \ ' / b \ P ~=

In this relation, i is the strain-rate, A a metallurgical parameter,/~ the shear modulus, n the stress exponent, b the Burgers vector, Def f the effective diffusion coeffi- cient, o- the flow stress and p the grain size exponent which depends on the main mechanism of accommoda- tion of phase boundary sliding (PBS). In the case of alumina, it has been demonstrated that p can vary from 1 (accommodation of PBS by interface reaction, gener- ally associated with a value of n close to 2) to 3 (accommodation of PBS by grain (or phase) boundary diffusion, generally associated with a value of n close to 1), depending on the mean grain size, the temperature and strain rate of deformation in the superplastic regime [1,14,21]. In the case of A1203-ZrOz composites, the dependence of the grain size exponent on the exper- imental conditions of deformation has not yet been clearly established. Since in the investigated materials, alumina is the major phase (its volume fraction is greater or equal to 80%), we can assumed that the results obtained by Fridez [14] concerning the super- plastic deformation of MgO-doped A1203 with a mean grain size of 1.6 gm, can be extended to AlaO3-ZrO 2 composites. According to previous results of Fridez, the experimental conditions of this study are expected to lie in the vicinity of the transition between the two control mechanisms. As a consequence, it appears hazardous to choose a value of p. If two values of p (1 and 3) are taken into account in this study, the mean strain-rates in the two layers can be estimated, under the assump- tion that the material deforms according to an isostress scheme, which leads to:

6A -- KA \~BB/ (3)

If differences in mean strain rates of the two layers are assumed to result only from a grain size effect, then KB----KA, which leads, after a strain equal to -0 .4 , to a ratio ~B/kA from 1.1 ( p = l ) to 1.3 (p=3). These results must be compared with the experimental ratio of 1.5. From this comparison, it can be concluded that if PBS is controlled by diffusion along grain (or phase) boundaries, the softening effect of the introduction of zirconia particles in the alumina matrix can be at- tributed in a large extent by a grain size effect. Never- theless, from the relatively high value of the experimental stress exponent (n ~ 2), a contribution of interface reaction to the accommodation of PBS cannot be excluded. Moreover, it must be reminded that the

determination ofp is particularly delicate in the case of alumina-rich composite, since significant grain growth is generally activated during deformation, which can also affect the morphology of the grains.

The grain growth kinetics of the deformed materials have been investigated in static and dynamic condi- tions. The results can be described according to:

d q - d~ = Kt (4)

The determination of q is not straightforward since values from 3 to 5 are in agreement with the experimen- tal data. Such values of q between 3 and 5 have been reported for grain growth in MgO-doped alumina [14,22,23]. Gruffel [23] obtained a value of 3 and he has showed that this value was not significantly affected by superplastic deformation. He reported for an alumina doped with 500 ppm MgO annealed at 1450°C, q = 3 and K = 3 . 4 + 0 . 4 10 -4 ~tm 3 s - t . In the case of the investigated material, as a result of the limited experi- mental data, it was not possible to estimate q. Indeed, values from 3 to 5 fitted in quite similar ways to the experimental data. For the sake of illustration, Fig. 7 shows the plots of the grain growth kinetics with q = 3 from the measured values of (d) and (do). The results for the A1203 + 20 vol.% ZrOa layer in static conditions were not plotted since no significant variation of the mean grain size was detected in the investigated time domain. As expected, the increase in zirconia content results in a refinement of the microstructure in the as-received conditions. It can be also noted that super- plastic deformation promotes grain growth significantly since the mean grain size of the A1203 + 10 voL% Z r Q layer remains relatively constant in static conditions. Table 1 summarizes the deduced values of K for the three investigated conditions depending on the value of q. Despite the limited data, some conclusions can be drawn from Table 1, which do not depend on the value of q in the range 3-5. Firstly, the value of K (for q = 3) obtained in static conditions for the A1203 + 10 vol.% ZrO2 layer is significantly lower than that obtained at 1450°C for MgO-doped AlzO3 by Gruffel [23]. This means that the zirconia particles are particularly effi- cient as inhibitors of alumina grain growth. Secondly, superplastic deformation strongly enhances grain growth in both layers. In the case of the A1203 + 10 vol.% ZrO 2 layer, a factor of approximately 15 is obtained for the investigated strain-rate (4 x 10- 4 s - 1). Similar values of the exponent q in both static and dynamic grain growth during superplastic deformation of ceramics has already been reported by Nieh and Wadsworth [24] in the case of yttria-stabilised tetrago- hal zirconia polycrystals (q = 3). Lastly, the increase from 10 vol.% to 20 vol.% of ZrOz particles in the AlaO3 matrix reduces by a factor close to 3 the value of K. These variations in grain growth kinetics between the two types of layers result in an increasing difficulty

O. Flacher et aL /Materials Science and Engineering A219 (I996) 148-155 153

2.5

2

1.5

V 1 I

xJ 0.5 V

A1203 + I 0 % vo[. ZrO2 (dynamic)

lzO3 + 20 % vol. ZrO2 (dynamic)

+ A1203 + 10 % vol. ZrO2 (static

0 5000 10000 15000 20000

time (s)

Fig. 7. Plots of experimental grain growth kinetics in both layers, for static and dynamic conditions.

to quantify the impact of the grain size on the differ- ence in the creep behaviour of the layers. Additional work is then required before any define conclusion about this impact.

If the macroscopic deformation results mainly from PBS, an intragranular deformation (ID) is likely to take place. Then, it can be worth-while to estimate qualita- tively the ID contribution and its possible variations with strain.

A way to get such data is to investigate the variation of the aspect ratio parameters with strain. From SEM observations, it can be deduced that a preferential orientation of the microstructure is developed in both layers during deformation. The variations with strain of F1 and F,_, for both alumina and zirconia grains, are illustrated in Fig. 8 for A1203 + 10 vol.% ZrO2 layers and in Fig. 9 for A1203 + 20 vol.% ZrOz layers. Since the deformability of each kind of layers depends on the zirconia amount, each curve is plotted in reference with the true strain undergone by the corresponding layer. Whatever the layer, both parameters increase with

Table I Values of K depending on the q value

q = 3 q = 4 q = 5 K K K i n g m 3s -1 in/xm 4 s - 1 i n g m s s - 1

A1203+ 10 voI.% ZrO z 3x10 -5 3 x t 0 -5 7 x t 0 -5 (static conditions)

AI,O3+ I0 voI.% ZrO 2 40x10 - s 60x10 -5 l l 0 x l 0 -5 (dynamic conditions)

KDYN/KsTAT (A1203+ 10 13 20 i6 vol.% ZrO,_)

A1203+20 vol.% ZrO 2 15x 10 .5 20x 10 - s 35x I0 - s (dynamic conditions)

I~A/K B 2.7 3 3.1 (dynamic conditions)

strain but not in the same way. F~ is nearly constant in the first steps of deformation and then sharply increases with strain. F2 increases uniformly during the whole deformation. Moreover, the increase of F2 during the first step is more pronounced for the A-layer than for the B-layer. When both phases are individualized, no variation of the aspect ratios was detected for zirconia. Consequently F~ and F2 express the aspect ratio changes of alumina grains.

The contribution of the deformation of the grains e~ to the total strain is frequently deduced from the rela- tion [4,25]:

2 L

where LI! and L± are the intercept lengths, respectively parallel and perpendicular to the loading axis. How- ever, such an identification between the value of eG and the extent of intragranular deformation (by diffusion or dislocation creep) does not take into account a possible reorganization of the initial distribution of grains in the microstructure, t f the grains are not initially equiaxed as it seems to be the case for the investigated material, the interpretation of eG dependence upon strain be- comes more delicate.

Some data can be deduced from the differences be- tween the significance of the two aspect ratio parame- ters (F1 and F2). F1 is representative of the average morphology of the grains, and, consequently, can be considered as an intrinsic parameter, whereas F2, which is also dependent on grain morphology, takes into account the spatial distribution of the grains in relation to an external system of reference. Consequently, differ- ences between their strain dependencies may contribute to separate intragranular deformation from grain rear- rangements, particularly in the case of a non-equiaxed initial population of grains.

154 O. Flacher et at. / Materials Science and Engineering A219 (i996) I48- t55

1.8

1.6

t.4

1.2 A1203 + 10 vol. % ZrQ

0 0.5 1 1.5

Strain Is]

Fig. 8. Aspect ratio parameters F1 and F2 versus strain for grains (A1203 and ZrO2) in the 10 vol.% ZrO2 layers.

A possible explanation to the difference between the dependence on strain of F~ and F2 can then be pro- posed in terms of two successive controlling deforma- tion processes. In the first steps of deformation, a rearrangement of the grains occurs preferentially, which is associated With a roughly constant value of F 1. The increase of F2 is thus the result of the alignment of the initially non-equiaxed alumina grains perpendicular to the stress axis. In such a framework, the initial value of F2 ( ~ 1) may be related, not to an equiaxed microstruc- ture, but to a random spatial distribution of quite elongated grains. When a majority of alumina grains are aligned perpendicular to the stress axis, grain boundary sliding becomes harder to activate and the contribution of the intragranular deformation to the macroscopic strain is more important, which leads to similar increases of F1 and F2, as shown in Figs. 8 and 9.

Moreover, attention has to be drawn to other strain- induced variations in the microstructure, like the distri- bution of the zirconia particles through the alumina matrix, which control the proportion of the types of interfaces (A12OJA12Q, A1203/ZrO= and ZrO2/ZrO2) through the composite layers. As already mentioned, a clustering of zirconia particles occurs during deforma- tion, leading to an increase of the frequency of ZrO2/ ZrO2 contacts. It confirms previous results obtained by Martinez et al. [26] on superptastically deformed mono- lithic A1203 + 20 vol.% ZrO2 composites. It was at- tributed to a decrease in interface energy during the neighbour switching process which is involved during the clustering process. Since grain boundary sliding is the major strain contributing mechanism of flow in superplastic deformation, a variation of the relative fraction of interfaces can also significantly affect the mechanical behaviour of the composite.

1.8

t.6

1.4

1.2

FI T

F2 . . . . . . . .

A1203 + 20 vol. % ZrO2

0 0.5 t 1.5

Strain ]~l

Fig. 9. Aspect ratio parameters F 1 and F a versus strain for grains (AI203 and ZrOz) in the 20 vol.% ZrO 2 layers.

O. Flacher et al. /Materials Science and Eng#~eering A219 (1996) 148-155 155

5. Conclusion

Superp tas t ic p roper t i e s o f an A1203/ZrO 2 l amina te compos i t e were obse rved at 1470°C, resul t ing in a stress exponen t close to 2. Z i r con ia par t ic les l imit efficiently gra in g rowth in bo th s ta t ic and d y n a m i c condi t ions . A decrease in creep resis tance is observed in the r ich z i rconia layers (20 vol.%). This decrease can be at- t r ibuted , at least par t ia l ly , to a gra in ref inement effect, in pa r t i cu la r i f phase b o u n d a r y sl iding (PBS) is as- sumed to be con t ro l l ed by gra in (or phase) b o u n d a r y diffusion. F r o m the c o m p a r i s o n be tween the va r i a t ion with s t ra in o f two aspect ra t io pa ramete r s , re la ted to the shape o f the grains, i n fo rma t ions are o b t a i n e d concern ing the respect ive con t r ibu t ions of p las t ic defor - m a t i o n and PBS to the to ta l de fo rma t ion . I t is f o u n d tha t these con t r ibu t ions are l ikely to d e p e n d on strain. In o ther words , the first steps o f d e f o r m a t i o n consis t essential ly in a spat ia l r e a r r angemen t o f the grains. W h e n s t ra in is increased, a progress ive con t r i bu t i on o f plas t ic d e f o r m a t i o n occurs.

Acknowledgements

The au thors t h a n k R6gion R h 6 n e - A l p e s for f inancial suppor t as a pa r t o f an O n t a r i o / R h 6 n e Alpes co l l abora - tion.

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