High-temperature fracture behavior of porous zirconia ceramics

Materials Science and Engineering, A 154 ( 1992) L 11 - L 14

L 11

Letter

High-temperature fracture behavior of porous zirconia ceramics s. M. Barinov High-Tech Ceramics Research Center, Academy of Sciences, Ozernaya 48, Moscow, 119361 (Russia) (Received December 19, 1991; in revised form February 19, 1992)

Abstract Fracture experiments were performed with notched and unnotched three-point bending specimens of porous zirconia ceramics at high temperature. It is shown that introduction of coarse filler particles into a porous matrix substantially increases the work-of-fracture of porous ceramics. The effect rises with the increase in the ratio of the filler and matrix particle sizes. The contribution of various factors determining the filler effects on the work-of-fracture value is estimated.

1. Introduction Porous ceramic materials are finding expanding application in engineering as filters, catalyst supports, etc. Porous ceramics sintered from the spherical particles of fully stabilized zirconia are one such material [1]. Intended for operation under conditions of thermocyclic loading, this ceramic material should possess a high thermal stress fracture resistance. Porous ceramics have low strength and, therefore, their behavior during thermocyclic loading is determined according to known criteria [2] by crack propagation resistance, the integral characteristic of the latter being the work-of-fracture (WOF) 7v. In crack propagation, processes such as microcracking, crack deflection, with its interaction with the interfaces in the material structure, and crack bridging can be realized in porous non-transforming ceramics. The effectiveness of the influence of these processes on the

WOF depends on the ceramic's structure. In particular, the creation of structural heterogeneities, e.g. by introducing coarse particles of filler into the relatively finegrained matrix, is a well-known method of enhancing resistance to fracture and reducing the susceptibility of the brittle material to catastrophic failure. This technique is used in the concretes [3] and ceramic composite materials [4, 5]. Such an approach is also effective for porous ceramics [6]. The present paper is aimed at investigating the influence of the size of the filler particles on resistance to fracture and assessing the contributions of the various factors affecting the work-of-fracture of the porous ceramics based on zirconia at its assumed service temperature.

2. Experimental details The specimens of porous materials have been produced from spherical powders of commercial zirconia containing 6 wt.% CaO as a stabilizing additive. According to the data of X-ray phase analysis, the phase composition of the powders corresponds to the cubic modification of ZrO 2 with a content of less than 5% monoclinic constituent. The specimens of the porous ceramics were obtained by dry pressing with the use of a binder in the form of an aqueous solution of aluminum chloride and by subsequent sintering in a gas-oxygen furnace at a temperature of 2200 °C for 4 h [a]. For testing, specimens were obtained using monofractional powders with the particle size from 40 to 50 /~m and, in addition, specimens from bifractional powders. The initial bifractional mixtures contained 40 vol.% of the powder with particle size from 40 to 50 /~m and 60 vol.% of the powder of coarse filler. Data on the granulometric composition and content of the open pores in the tested materials after sintering are given in Table 1.

TABLE 1. Characteristics of tested materials Series

Size of matrix particles (/~m)

Size of filler particles (/~m)

Volume ratio matrix/filler

Content of open pores (%)

M B1 B2

40-50 40-50 40-50

-200-250 315-400

100/0 40/60 40/60

32 25 21

Elsevier Sequoia

L 12

Letter

The specimens were tested at a temperature of 1400°C in a stiff testing Instron-type machine, equipped with a vacuum furnace with Ta-heaters. Tests were performed on specimens with the size 7 × 7 × 36 mm 3 and a thin side notch of 3.5 mm depth, as well as on specimens without a notch. The notch was machined with a thin diamond wheel saw. The measured notch tip curvature radius was approximately 50 ~m. The specimens were loaded with a cross-head speed of loading device equal to 8 × 10- 6 m s-~ in three-point bending mode with the distance between the supports amounting to 28 mm. Using the load-deflection diagrams of the notched specimens, two characteristic values of the deformation specific work were determined: (i) The value of 71 corresponding to the crack propagation initiation from the notch tip (WCI) calculated as half of the work of elastic deformation release rate Go: 7, = G c / 2 = K,02(1 -

v2)12E

(1)

where K,0 is the stress intensity factor value at the start of crack propagation from the notch tip; E is the elasticity modulus; and v is Poisson's ratio; (ii) The value of WOF }'v corresponding to the ratio of the total work of deformation of the notched specimen (until fracture) to the doubled area of the surface of the weakened section of the specimen: 7v = ( U - U0)/2n( W - a0)

(2)

where U is the total deformation work of the specimenmachine system; U0 is the work of deformation caused by the compliance of the loading device; W is the width of the specimen; B is the thickness of the specimen, and a 0 is the depth of the initial notch. Figure 1 shows a typical load-deflection curve

(desigr/ated OABC) for a notched specimen as a scheme. The values of Kl0 in eqn. ( 1 ) were calculated by the value of load corresponding to the point of deviation of the load-deflection diagrams from linearity (point A). The values of U in eqn. (2) were proportional to the area of the O A B C diagram, and the value of U0 was calculated through the area of the triangle OB'C' corresponding to the work of deformation of the loading device.

3. Results

The load-deflection diagrams of the notched specimens had a pronounced stage of non-linear deformation after reaching the limit of proportionality. It can be assumed that the deformation non-linearity of such a brittle material is caused by the subcritical crack extension from the notch tip. The non-linearity extent rises with the introduction of filler into the matrix, which results in the increase of the WOF and WCI values. Table 2 gives the values of ~/t and 7F for the tested materials. It is shown in Fig. 2 that, with the increase of the ratio of the filler particle radius R to the matrix particle radius r, not only is the value of WCI 71 or WOF 7F increased but also the difference between them. This fact is indicative of the enhancing of crack pinning TABLE 2. Values of 7j and Yvfor tested materials YF(J m-2)

Series

71(J m-2)

M

4.0

7.1

BI B2

7.1 9.3

19.0 35.2

30

/

. B ~ ./

B

¢'4

E --'-o2c ..._"

(.3

3= I

old

L,..

0

C"

~C DEFLECTION

Fig. 1. Load-deflection curve O A B C for notched bending specimen and corresponding deformation diagram OB'C' of loading device.

i

4

, R/r

Fig. 2. Effect of the filler particle size on the WOF(TF.) and WCI (7~) difference.

Letter

L 13

ture surface real area Sr to the area So = B ( W - a o ) of the specimen section through which the fracture passed. To make the estimation simple, let us assume that S 0 = Sin, where S m is the area of matrix fracture surface. It is possible to assess the true area of the fracture surface and, consequently, WOF, when the filler is introduced into the matrix. With the volume content of the filler equal to V, the area of the fracture surface increases because of the enveloping of coarse particles to the value

E 04

¢o L O

52

S r = S 0 - )Ln~R 2 + )~n2~R

4

R,/ r Fig. 3. Effect of the filler particle size on the WOFc/WOFm ratio. effectiveness with increase of the ratio R/r and, consequently, of the reduction of the tendency of the porous material to catastrophic failure. Figure 3 shows the dependence of the ratio of the composite materials WOFc to the matrix WOFm on the particle radii ratio R/r. As can be seen, the introduction of 60 vol.% of particles with a diameter of 315-400 /xm into the porous matrix leads to an approximately fivefold increase in the work-of-fracture of the ceramics.

4. Discussion

At least three effects causing increase in WOF when coarse particles of filler are introduced into a porous matrix, can be taken into consideration: (i) The increase of the fracture surface area as a result of enveloping the coarse particles with the main crack. (ii) The additional work done as a result of changing the crack surface deflection with respect to the direction of action of the maximal tension stresses and proceeding to the fracture according to the combination of the modes I, II and III of crack propagation. (iii) The additional work connected with the formation and development of some dissipative zone (process zone) at the crack tip. The ratio of the contributions to the increase of WOF caused by each of the indicated processes can be assessed from the known model representations.

4.1. Increase of fracture surface area When calculating WOF, the real relief of the fracture surface of the specimen is not taken into account. Therefore, the value of WOF which is determined experimentally is proportional to the ratio of the frac-

2

(3)

where n is the number of filler particles on the fracture surface and 2 is the statistical factor describing the distribution of segments of coarse particles on the fracture surface, i.e. the surface relief. The second component in the right-hand side of eqn. (3) takes into account the decrease of the fracture surface at the expense of "exclusion" of the area of the circles with the average statistical radius 2 l/2R, and the third component considers the increase of the indicated area at the expense of "addition" of the area of surfaces of the appropriate spherical segments. The modification of eqn. (3) gives the following relation: WOFc/WOFm

-~

Sr/S m =

1 + 2 V 2/~

(4)

since ~nR2/Sm = V 2/3. It follows from eqn. (4) that the effect of the increase of the surface area does not depend on the size of the introduced particles of the filler and is determined only by their volume content. The experimental value of 2 determined by scanning electron microscope fractography is close to 0.5. For the tested materials V= 0.6. The total effect of the WOF increase should amount to about 1.42, which is less than the experimental values (Fig. 3).

4.2. Crack deflection The influence of the crack deflection with respect to the direction of action of the maximum tension stresses was considered in [5, 7]. The effects of inclination and rotation of the crack surface were taken into account. It was assumed that the crack propagation resistance is determined by the values of the local stress intensity factors kj, k 2 and k3: ki= KIFi( qJ, O)

(5)

where Fi(cp, 0) is a function of the angles of inclination and rotation of the crack; and index i is equal to 1, 2, 3 in accordance with modes I, II and III of crack propagation. The estimations made in ref. 7 showed that the maximum value of WOF, when the spherical particles are introduced into matrix, amounts to WOFc/WOFm = 1 + 0.87 V

(6)

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Letter

Shown in Fig. 4 is the dependence of the ratios WCI/ w and WOF/w on the size of the filler particles. As can be seen, the size of the energy dissipation zone increases with the increase of the size of the particles. As follows from the data given in Fig. 4, the ratio WOF/w corresponds approximately to the filler particle size. Consequently, the linear dimension of the process zone is proportional to the filler particle size in the porous material.

6

C) .¢..-

E ~4 t,

© D¢.-

5 2

5. Conclusions

¢)

I

1

I

2

t

3

~

R/r

I

5

~

I

7

8

Fig. 4. Effect of the filler particle size on the WCI/w and WOF/w values. and does not depend on the size of the filler particles. With the volume content of the filler particles V= 0.6, the increase of W O F reaches 1.52, which is less than the experimental value (Fig. 3). 4.3. Formation o f process z o n e

According to the generally accepted formal analogy between the process zone in the brittle materials and plastic zone [4], the linear size of the process zone at the crack tip can be assessed as ra = a ( K , / o * ) ~

(7)

where a is a coefficient; o* is the stress within the process zone preventing the crack opening displacement. Two characteristic values of r d can be assessed quantitatively: at the start of the crack, rdO, which is proportional to K102and at the transition to the unstable crack propagation, rd¢, which is proportional to K~¢:. By its meaning the value o* in eqn. (7) is the fracture stress and, therefore, it can be determined experimentally by testing the unnotched specimens. It can be assumed that the value of o* is equal to or, at least, proportional to the value of the ultimate bending strength. In this case, eqn. (7) can be modified as follows:

rd0 =/3(ri/W)

(8a)

rdc =/3(7F/W)

(8b)

where/3 = a(1 - v2), w = o ' 2 / 2 E is the specific elastic energy stored in the unit of the material volume.

(1) The introduction of the coarse filler particles (60 vol.%) into the porous matrix substantially increases the work of crack initiation and, particularly, the work-of-fracture (up to five times). The effect rises with the increase of the ratio of the sizes of the filler and matrix particles. (2) The estimations show that the increase of workof-fracture, with the introduction of coarse particles, is not only the result of the increase in the fracture surface area and the effects of crack deflection. Evidently, some zone of dissipation of the work of external forces is formed at the main crack tip. The linear size of this zone is proportional to the size of the filler particles, as the state of the limiting equilibrium of the crack is reached.

Acknowledgment The author is grateful to Mr. S. Grevtzev for his help in specimens testing.

References 1 Yu. L. Krassulin, V. N. Timofeev, S. M. Barinov, A. N. Asonov, A. B. Ivanov and G. D. Shnyrev, Porous Structural Ceramics, Metallurgy Press, Moscow, 1980, pp. 35-52. 2 D.P.H. Hasselman, J. Am. Ceram. Soc., 52 (1969) 600-607. 3 Z. P. Ba~ant and M. T. Kazemi, J. Am. Ceram. Soc., 73 (1990) 1841-1853. 4 A.G.Evans, J. Am. Ceram. Soc., 73(1990) 187-201. 5 K.T. Faber and A. G. Evans, Commun. Am. Ceram. Soc., 66 (1983) 94-95. 6 Yu. L. Krassulin and S. M. Barinov, Powder Met. Intern., 14 (198.2) 36-38. 7 K. T. Faber, A. G. Evans and M. D. Drory, in R. C. Bradt, A. G. Evans, D. P. H. Hasselman and F. E Lange (eds.), Fracture Mechanics of Ceramics, Vol. 6, Plenum, New York, London, 1983, pp. 77-91.