Refractories

VoL 36, Nos. 3 - 4, 1995

UDC 666.762.5.017.620.174

DEFORMATION AND FRACTURE OF ZIRCONIA CERAMICS STABILIZED BY CeO2. II. CRACK RESISTANCE G. A. Gogotsi, 1 V. I. Galenko, I V. P. Zavada, i and M. V. Swain 2 Translated from Ogneupory, No. 3, pp. 8 - 11, March, 1995. Original article submitted February 1, 1994. Investigations of crack resistance of four types ofzirconia-base ceramics stabilized by 9% CeO2 are described. In three types of ceramics cracks develop against the background of the formation of a wide zone of transformation transitions, whose size decreases with decrease in the grain size of the materials. In the ceramics with the finest grain composition (1.14 lain) such a zone is absent. The measured results are highly divergent as a function of the method used for estimating the length of the cracks, namely, visual examination and determining the compliance of the specimens. It is assumed that the divergence can be attributable to the presence of a zone of transformation transitions at the tip of a crack and along it.

measured under a microscope and the zone of transformation transitions was photographed. The length of the crack was also estimated by the compliance c of the specimen using the relation [2]

In [1] we presented the results of testing ceria-stabilized zirconia ceramics for strength and deformability. The present work is devoted to the investigation of the crack resistance of such ceramics. We tested specimens 4.8 x 2.8 x 25 mm in size with an initial notch of depth 2.4 m m and width 0.25 mm for crack resistance. The specimens were subjected to three-point bending with the distance between the supports being 20 ram. In order to make observations o f the initiation and development of cracks and the formation o f a zone of transformation transitions easier, one of the side faces o f the specimens was polished. We used the traditional technique of constructing Rcurves, although we were aware o f its deficiency due to inelastic deformation o f the ceramics. The technique was chosen because we were not convinced that the concept of J-integral was applicable to transformation-strengthened materials. The only energy parameter used was the specific energy of fracture. Just as in experiments on determining strength and deformability we recorded the dependence between the applied force P and the deflection 8 o f a specimen (the P - 5 diagram) and the acoustograms o f force-total AE count (the P - N diagrams). The specimens fractured in a few loading unloading cycles. After each cycle the length of the crack was

ct

c = co (1 + 4.5 ~YZa da) ,

(1)

0

where co is the compliance of the specimen without a notch; Y is the K-calibration [3]; cz is the relative (with respect to the specimen's height h) depth of the stress concentrator. The P - 5 diagrams for Ce-TZP-II ceramics are presented in Fig. 1, which also shows calculated (from the P - 5 diagrams) dependences between the crack length lcr and the stress intensity coefficient K ~ , which is found from the relation o f linear fracture mechanics

K~= Vail=:2,

(2)

where a is the nominal stress attained in the given load cycle. Despite the stepwise shape of the R-curves obtained, especially those for the visual data, we can say that the latter are quite different from the data determined from the compliance. Judging by the visual measurements, the values of Km tend to increase with the growth of a crack, while the results on compliance show a tendency to decrease. We can say that the Ce-TZP-II-Ce-TZP-IV materials virtually do not differ within the scattering range, whereas the Ce-TZP-I ceramics

1 Instilme for Strength Problems, Academy of Sciences of Ukraine, Kiev, Ukraine. 2 CSIRO, Australia.

78 0034-3102/95/3603-078512.50© 1995 Plenum PublishingCorporation

Deformation and Fracture of Zirconia Ceramics Stabilized by CeO2

79

/~, mm

P,N

KIR,

Crack growth

° ,':o'\

100

/

x - - Ce-TZP-I 0 - - Cc-TZP-H

MPa- ra~a10

/

X_

O O )

/~ mm 50

50

100

I

8, pm

Fig. 1. P - 8 diagram and R-curves for Ce-TZP-II ceramics: o) in visual estimation o f l¢~; O) in estimating lcr from compliance.

has substantially higher K~. However, b y the P - 8 diagTams all the materials differ in the developed force, which decreases from Ce-TZP-I to Ce-TZP-IV. On the other hand, the specific work of fracture y is the lowest in Ce-TZP-I (Table I). It is very important that the differences in the R-curves obtained by different methods follow directly from the greater length of cracks determined visually 1~ (Fig. 2). We can be sure that the differences are not caused by elementary measuring errors for the following reasons: I. Errors of optical measurements of crack length would more likely result in reduced values of l~ due to the smaller opening of the crack at the tip and the limited resolving power of the microscope. Therefore, although such an error is obviously present, it cannot be decisive for the distinction between l~ and l~. At the same time, we have no grounds to think that the error in measuring l~ is caused by nonlinearity of the material, because the slope of the diagram is determined for the linear-elastic behavior of the material. 2. Errors in the determination of the slope of the P - 8 diagram and hence the compliance and the length of the crack do not exceed 5%, whereas the deviations between the experimentally determined compliance c c and the compliance c" calculated from l~ amount to 200% or more (Fig. 3). 3. Substantial errors in relations (1) and (2) are unlikely, because the results of tests of glass specimens with a sharp crack and specimens of aluminum oxide with thin (0.l-mm-

TABLE 1. Work of Fracture in Ce-'fZP Ceramics Ceramics Ce-TZP-I Ce-TZP41 Ce-'I'ZP-III Ce-TZP-IV

% J. rn-2

/(7," MPa- rn-it2

308 454 494 452

10.4 12.6 13.1 12.6

* I(7 is a conventional fracture toughness calculated from 3, (an analog of the parmaeter KI,); K~ = ~'q"~, where E is the modulus of elasticity.

o

~

I

Fig. 2. Dependence between crack l e n d s from the specimen's compliance (l~).

mm

determined visually (l~) and

,j

Cv

/

/ 0

1

l~,mm

Fig. 3. Change in the ratio c~/c c o f ~ ¢ calculated and measured compliances of a specimen with increase in the crack length l~ ; the notation is as in Fig. 2.

wide) notches3 of different depths have shown a good relationship of l c and l v when KtR does not depend (in accordance with the classical concept) on the length of the stress concentrator (see, for example, [4]). In this connection, it is interesting, though hard to explain, the fact that the difference between c c and cv increases with increase in the crack length by a nearly linear law, i.e., cC/c v = A + k 3 l ~ . Importantly, this correlation is characterized by a rather high correlation coefficient r for A very close to 1 (Table 2); it seems that the correlation ofthe slope k3 in the sequence Ce-TPZ-I - Ce-TPZ-IV is also not accidental. Note that the differences between l~c and l~ and between cc and cv lead to indeterminacy in the evaluation of the J-integral, which must be even more complicated than the deterruination of the R-curves. This is so because the J - i n t e ~ l is calculated on the basis of the P - 8 curve directly and from the actual len~d~ of the crack. Therefore, in our case it is calculated by two approaches that are rather contradictory. 3 The exis~nce of a pronounced R-curve in this material prevents the use of a sharp crack for testing.

80

G.A. Gogotsi et ai. N) 103 )ulses

8

e,N

I

P-N

0

Fig. 4. Characteristic zones of t - m transitions in Ce=TZP-II ceramics at different loading stages: a) before the crack starts to move; b ) after motion of the crack, x 70.

In contrast to smooth specimens used for the determination of strength [1], Ce-TZP4 specimens tested for crack re= sistance did not exhibit a well defined zone of transformation transitions. At the same time, in the other types of ceramics [5] such zones were clearly seen (Fig. 4). Observations showed that this zone is formed as a result of discontinuous egress of arrow-like zones with different widths and lengths from the tip of the notch (thouo~hwe can state that their thickness grows in going from Ce-TZP-II to Ce-TZP-IV). The number o f such zones increases with the load, and the zones merge and form a continuous zone at the tip of the notch, which transforms into several separate arrow-like zones at some distance from the notch. The crack is initiated in the continuous zone and, as it grows, the continuous zone moves forward, always in advance of the crack tip. On the whole, just as in tests of smooth specimens, we may speak o f an "avalanche" nature o f the formation of the zone of t - m transitions. The change in the total area S of the zone of transformation transitions as a function of the crack length can be approximated by a linear correlation S=So + k41~, whose quantitative parameters are different for the Ce=TZF-II, Ce=TZP-III, Ce-TZP-IV materials but change regularly in this

T A B L E 2. Parametersof the CorrelationDependence cC/cV-lc~ Ceramics

ka, m m -1

A

r

0.522 0.552 0.834 0.946

1.02 1.05 0.98 0.95

0.99 0.94 0.99 0.99

Ce-TZP-I Ce-TZP-II Ce-TZP-IH Ce-TZP=IV

TABLE 3. Paramelers of the Correlation Dependence S - lc~

Ceramics Ce-TZP-II Ce-TZP-III Ce-TZP-IV

/,4,mm

So,ram:

r

W, mm

0.34 0.38 0.66

0.083 0.224 0.453

0.99 0.97 0.99

0.37 0.45 0.58

I0

P-8

20

8, ttrn

Fig.5. Enlarged deformation diagram P - 8 and acoustogram loading cycle.

P - N of a

sequence (Table 3). Because of the almost constant width of the zone around the crack, this linear dependence enables us to represent the process of development of the zone with the growth of the crack in the form o f an unchanging leading re= glen that moves in front o f the crack and a rectangular region along the crack. In this case the parameter So (see Table 3) will reflect the area of the leading region and k4 will be the width o f the rectangular region, which virtually corresponds to the values measured in the middle part of the zone of transformation transitions (the quantity W in Table 3). AE data are also of some interest. In the Ce-TZP-I ceramics AE, if present, was at the level of acoustic noise, whereas in the other three materials the total AE count was an order o f magnitude greater than the value obtained in tests of smooth specimens. However, just as in the tests of smooth specimens, AE was observed only in the formation of a pro= nounced zone of t - m transitions with no linear correlation between the area S of the zone and N. As we noted above, this may be attributable to the fact that AE is largely deter= mined by the number o f steps in the formation of regions (an analog of the number of strips in the case of smooth specimens) rather than by the size of the steps. In the se= quence Ce-TZP-II-Ce-TZP-IV the rate of growth of N with increase in the area S decreased, as the maximum attainable value of N in the experiment decreased. It is noteworthy that the AE data do not reflect the initiation of a crack. Along with the absence of AE in the Ce-TZP-I ceramics this indicates that the growth o f cracks in these materials is either accompanied by AE with much lower intensities than in the t - m transitions or there is no AE at all (presumably, due to the gradual development of cracks rather than their stepwise development as in conventional ceramics). In conclusion we should mention some interesting facts. The formation of the zone o f transformation transitions occurs not only in the process of loading a specimen but also in its unloading. This is indicated by the nonlinear nature of the unloading curve, which does not coincide with the curve of the next loading, and in unloading we observe AE (Fig. S).

Deformation and Fracture of Zirconia Ceramics Stabilized by CeO2

It is also interesting that an already emerged crack can be "blocked" (perhaps, due to the special features o f the formation o f the zone o f transformation transitions) and this generates a new crack from the notch. In our case (Fig. 6a) two cracks were blocked and only the third (central) one led to the fracture o f the specimen (note that the opposite face o f the specimen had only one crack). New cracks can emerge not only from the notch, but also in the vicinity of the main crack in the body o f the material (Fig. 6b), which may also be a manifestation of blocking.

81

Fig. 6. Formationof several maincracksfrom a notch (a) and from a crack (b): a) x 280; b) x 70.

CONCLUSIONS The initiation and formation o f the zone of phase transitions by mechanical stresses mostly occurs in an avalanche mode. The degree o f "avalancheness" in this process is determined by the grain composition of the material and the form o f the stress state in it. The main crack that leads to fracture of the specimens passes virtually in the middle o f the zone o f transformation transitions, which indicates weakening of the material in this zone.

The presence of such weakened zones and the nonuniformity o f their distribution over the specimen may necessitate additional substantiation or ref'mement of conventional approaches to calculating true stresses in ceramic specimens with phase Wansitions. Though it has been assumed that only microcracks can develop in the zone o f transformation transitions, the Ce-TZP ceramics exhibited for the first time the effect o f blocking a rather extended crack with subsequent initiation and growth of another main crack. This effect can hardly be described on the basis o f known concepts o f fracture mechanics. Since the data on crack resistance obtained by visual measurements and by estimating compliance diverge, it can-

not be excluded that a similar refinement or correction should be required when applying fracture mechanics to other transformation-strengthened materials.

REFERENCES 1. G. A. Gogotsi, V. I. Galenko, V. P. Zavada, and M. V. Swain, "Deformation and fracture of zirconia ceramics stabilized by CeO2. I. Strength and deformability," Ogneupory, No. 1, 8 - 12 (1995). 2. A.A. Dabizha and S. Yu. Pliner, "Strengthening of ceramic materials due to the phase transition of ZrO2," Ogneupory, No. I 1, 23 - 29 (1986). 3. P. E. Royes and I. W. Chert, "Transformation plasticity of CeO2stabilized tetragonal zirconia polycrystals: I. Stress assistance and autoeatalysis," J. Amer. Ceram. Soc., No. 71, 343-353 (1988). 4. G. A. Gogotsi, V. N. Zavada, and A. N. Fesenko, "Methods and some results of investigation of R-curves in ceramics,' Zavod Lab., No. 2, 3 7 - 43 (1992). 5. L. R. F. Rose and M. V. Swain, "Transformation zone shape in ceria-partially-stabilized zirconia," Acta Met., 36(4), 955- 962 (1988).