Refractories, Vol. 34, No. 11, November, 1993

SCIENTIFIC RESEARCH THERMAL-SHOCK RESISTANCE OF HETEROGENEOUS

CERAMICS

AND R E F R A C T O R I E S

G.A. Gogotsi

UDC 666.76.017:536.496

The search for new materials suitable for making continuous steelcasting equipment, gas-turbine blades, rocket nozzles, and other high-temperature devices, in the second half of this century has aroused increased interest in ceramics and refractories which are being examined as prospective design materials. This has stimulated the development of research into their mechanical behavior, including thermal-shock resistance, since the typically low thermal conductivity of such materials usually causes high thermal stresses that are especially dangerous in nonstationary thermal loading conditions. Although successes have been reported in studies into thermal-shock resistance [1], there are still many unexplained problems, especially those connected with the processes and rules governing the breakdown resistance of such heterogeneous materials, which are being increasingly used in technology. Criteria of Thermal-Shock Resistance and Measures of Brittleness. By the start of this century specialists investigating thermal-shock resistance had already carried out not only experimental work in the form of technological trials of the suitability of certain articles for working in the above conditions, but were attempting analytical determinations (knowing the properties of the materials) of their potential working capacity under the action of heat. This involved the appropriate choice of combinations of properties (criteria of thermal-shock resistance [2, 3]) among which the most acceptable in practice proved to be the criterion RI proposed by Kingery [4]: crr~(l-#) R! _

o~b

I:'CZ

EO:

'

where % is the strength;/~ is the Poisson ratio; E is the elasticity modulus; a is the coefficient of linear thermal expansion. This criterion expresses the logical proposal (in accordance with the theory of thermoelasticity) to the effect [5] that the more deformable the material (%/E - deformation limit according to Hooke's law) then the lower will be ~, and the higher the thermal-shock resistance. Another complex RIv, mathematically formulated by Hasselman [3], has become well known: ix.'

ET

where "7 is the effective surface energy. If we use the Griffiths relationship % = Kx/yE/%2 (where K is a coefficient determined by the form of loading, the geometric form of the crack, etc.), the complex R Iv can be examined as a proposition to the effect [5] that the better resistance to destruction is exhibited by that material in which the critical length of the crack is greater. In the deduction of these and other similar criteria (e.g., Rst [3]) based on ideas in thermoelastic theory and the linear mechanics of breakdown, the authors actually started from assumptions on a linear relationship between the deformations and stresses, i.e., Hooke's law.

Institute of Strength Problems, Academy of Sciences, Ukraine. Translated from Ogneupory, No. 11, pp. 2-8, November, 1993.

0034-3102/93/1112-0539512.50

9

Plenum Publishing Corporation

539

d %

~lim

elim g

Fig. 1. Deformation diagram for an inelastic material: % - strength limit; elim limiting deformation; eed -- elastic deformation; TE - total specific energy; EE elastic specific energy.

/./I

(

//

/f

II [

,/

I l,~B2~ea

d, N/ram 700

d

200 750

.. \

3/?

Ij

7\I

o

20

1BO

0

tO

20

30

4",9 x,,mm

Fig. 2. Microdestruction in ceramic A-3: a) method of curring the specimen: P) force applied to specimen; 1-4) plates cut along axis x; Bz-B2o) parts of plate in compression zone; b) section of plate surface B 1; x 30; c) section of plate surface A2o, • 30; d) size of microcracks on each part of plate E/T-tOtal length of microcrack on the lateral surface of plate B1-B20; a - stresses acting at moment of specimen failure. 540

TABLE 1. Some Characteristics of Materials Under Investigation Material

Density, g/era 3

Open porosity, %

A 1 A-2 A-3 Y-1 Y-2 Y-3 u K Z T T-C

3.72 3.N3 3.46 4.90 . 3.45 4.84 4.(19 2.26 5.71 1.48 3.(;7

1,2 5,7 9,4 4,1 30 0.6 2.0 30 -

Brittleness measure

1 0,66 0,53 1 1 1 0,64 0,72 0,44

0

I

0

0,37

Dynamic elasticity modulus, kN/mm~

300 241 156 193 I44 43 107 64 216 347 1 I9

Deformation limit, %

0,026 0,024 0,027 0,039 0,038 0,038 0,042 0,096 0,460 0,060 0.120

However, in many cases refractories and ceramics are to a certain degree inelastic [6, 7], and so their actual mechanical behavior is not taken into account by the above-mentioned criteria, which does not help to validate the evaluation made of thermal-shock resistance. The development of ideas on the measure of brittleness X* [8] and proposals about classifying low-deformation materials according to the features of their mechanical behavior [9], dividing them into brittle (x = 1), obeying Hooke's law, and into relatively brittle (X < 1) materials, prone to nonelastic deformation, contributed to a certain clarification in the limits of criteria utilization [5]. Figure 1 shows that the more the material is inelastic (the lower is X) then the more its deformation limit '%m differs from the elastic deformation eed, as determined by Hooke's law. Taking this into account, k is possible to correct, for example, the criterion R I by replacing the value of the elastic deformation (ab/E) in it by the actual deformation Elim, determined in an experimental way. From the definition of the measure of brittleness (see Fig. 1) it follows that it too can be considered as a crkerion of thermoelasticity: for all equal conditions the more thermal-shock resistant will be that material with a lower measure of brittleness, since it will be more deformable, and it will accumulate less elastic energy, which upon the attainment of the limiting condition will provide the energy needs for the development of the crack. Materials and Method. The inelasticity of heterogeneous ceramics? and refractories at room temperature is usually connected with the development of microcracks formed during manufacture or during loading [10, 11]. As confirmation of this, investigations were carried out in which corundum ceramic made with zirconia was used [12]. Specimens in the form of rectangular rods measuring 10 x 15 x 120 mm, where broken under three-point bending, and then along the axis, using lowspeed diamond cutters, were cut into plates. Each plate was divided into 40 parts; A 1-A2o and B 1-B2o (Fig. 2a) on the surface of which we measured the microcracks using a scanning microscope (Fig. 2b, c). The data obtained (Fig. 2d) suggest that the length and number of cracks in the surface of the part, close to the loading zone and situated in the tensile zone, are several times greater than in the part cut from the stressed zone of the specimens. These data conftrm the fact of microdestruction in the structure of inelastic material, which is not recorded in elastic materials. Similar results are known for concrete [14]. In these investigations, besides the above-mentioned material, designated A-3 (see Table 1) we also used alumina ceramics made by dry pressing, A-1 (without additives), A-2 (with 15 % c~-Al203 platelets, length 0.3 mm and width 0.2 #m); from yttrium oxide Y- 1 and Y-2 (without additives), (with 15 % Y203.A1203); Y-4 (with 25 % Y203.A1203), cordierite K and

*The measure of elasticity equals the ratio of specific elastic energy (EE) accumulated in the specimen, at the moment of failure, to the total specific energy (TE) expended on its deformation at the same moment: X = EE/TE = r shown in Fig. 1).

c olIimode (key 0

?Homogeneous ceramic is usually linearly elastic, and on the whole the features of mechanical behavior of ceramic and refractory are identical, and so only the term "ceramic" is subsequently used. 541

~Z l N / r a m 2

&7'

z~D -

t

x

~

Y~ I

1

200

Y-3

I

" 4gO

50~7

800 ATz, ~

Fig. 3. Relationship between the bending strength a z of the chilled specimen and the drop in temperature AT z between the furnace and the cooling bath for ceramics based on yttria; this shows a section of the surface of Y-4 ceramic with ~ T z = 600~ (x15). d z N/mm2

ez, 10-2%

20

8

lO

8

0

I

t*

a,y[

a,e I

g

400

L

&Tz, *C

Fig. 4. Change in the characteristics of A-3 ceramic caused by chilling: a) relationship between residual strength a z and deformation limit ez and ATz; b) relationship between measure of brittleness X and relative stresses aa/ez, recorded at the moment of the development of a continuous acoustic emission signal and ATz; AT0 and ATcr variations in temperature causing microand macrodestruction of ceramics respectively. zirconia Z (stabilizer 9% MgO). We also studied hot-pressed ceramics made of titanium carbide T (no additives), and T-C (with 30% graphite fiber). The investigations of the thermal-shock resistance were carried out on specimens in the form of coaxial, hollow cylinders heated at a constant rate by increasing the temperature in the internal surface. Tests were done on equipment of the TS type [15]; we measured the temperature of the specimen, its diametral expansion, and the acoustic emission. The parameter

542

I

or, N/mm2

Measure of brittleness

0,~7 [ ~o

T

a,i5

a,eo

500' E,1z~z

700

" 3,. .

No_

r p ~ ~ ~

"~ 0,4,

4OO

~l~m 2170 O

0

70

20

Content of ~ -AIeOS,%

Fig. 5

JO

21717

400

AxTz, ~

Fig. 6

Fig. 5. Relationship between the variations in temperature ATp, deformation limits elim, the elastic constituent of the deformation limit eed and the measure of brittleness, and the content of o~-A1203 platelets in the aluminabased ceramics. Fig. 6. Relationship between the residual strength crz of ceramic Z and the variations in temperature ATz. of thermal-shock resistance was the variation in temperature ATp at the moment of specimen failure, equal to the difference in the temperature of its internal Tint and external Text surfaces. The resistance to thermal loading was also studied on specimens in the form of rectangular rods chilled in a cold bath to room temperature, after preheating in a resistance furnace [16]. Here the thermal-shock resistance was characterized by the variation in temperature ATz between the furnace and bath, which, for example, corresponds to the irregular fall in the residual strength of the specimens (in this case ATz = 2~Tcr) determined during subsequent tests under 4-point bending. During bending of the chilled specimens we also measured the deformation points, acoustic radiation, and elasticity; these measurements were also considered to be an indicator of thermal-shock resistance. Mechanical factors were determined using the method and apparatus developed by the present author for the specification of ceramics and refractories [17, 18]. The tests for strength, deformability, and elasticity were made with the fourpoint-bending test, using rods measuring 3.5 x 5 x 50 ram. The critical coefficient of stress intensity, the work of breakdown, and the R-curves were investigated through 3-point bending of notched rods measuring 5 x 3.5 x 25 rnm; the elasticity modulus was calculated according to measurements of the rate of ultrasonic dissemination along the axis of the specimen. Experimental Results. Chill testing of yttria ceramics showed that for Y-I, Y-2, and Y-3 ceramics there is a critical variation in temperature 2~Tcr between the furnace and the bath (Fig. 3), corresponding to an irregular fall in the residual strength; in ceramic Y-4 the relationship az-2XT z is smoothly declining, and it exhibits the lowest fall in the a z value. A distinctive feature of Y-4 ceramic (as for Y-3) is that the surface of the chilled specimen exhibits not only a network of microcracks, but a developing macrocrack. During the tests on hollow coaxial cylindrical specimens of Y-I, the destructive fall in temperature ATp was 140~ and for Y-4 180~ During the chill tests on A-1 we determined the critical temperature variation ATcr as 180~ and for A-2 ceramic (and other compositions with ~-A1203 platelets) the Crz-2~Tz diagram was descending. For A-3 ceramic we established that this diagram has an initial horizontal section, after which a smooth reduction sets in for the residual strength az (Fig. 4). Also revealed was a drop in the temperature 2~T0 at which an increase in the deformation limits of the material ez commences, together with a reduction in the stress cra, corresponding to the development of a continuous acoustic emission during bending of the thermally damaged specimen. During the testing of hollow coaxial cylindrical specimens of A-1 and A-2 ceramic, and also the same ceramics containing 5, 10, 20, and 30% c~-Al203 platelets, it was found that with small additions the magnitude of the fall in temperature zXTp is reduced (Fig. 5). For an addition of 20 % platelets (and this causes an increase in elim with a reduction in x) ATp begins to increase; we noted this effect previously for aluminoboronitride [19]. However, with a 5% addition we registered a fall in the rate of destruction of the specimen, and with 15 % addition this process became stable; the cracks grew gradually with an 543

Fig. 7. Deformation diagrams (left) and section of the surface fractures of ceramic based on yttria (right).

Kt~,.,.,N / r a m 312

.

f

1

y-y

-~ ~** x ' ~ x - ' ~ * - x'-'---'x

>'-Z

I

o

0,~"

,

'

z,'O

x

I

,75/,Icr,mm

Fig. 8. Curves for yttria-based ceramics; A/cr) length of destructive crack. increase in the variation in temperature in the specimen. With a high concentration of platelets the facial surfaces of the specimens developed numerous microcracks [20], and a macrocrack developed due to coalescence. It is typical that hollow coaxial cylindrical specimens of heterogeneous material, during rapid increases in temperature vT of the internal surface in the range 2-200~ are usually destroyed gradually, or in an irregular way. With increase in vT the rate of this process was increased, as was detected visually during measurements of the diametral expansion of the specimens or acoustic radiation [21]. In contrast to this, the specimens of homogeneous materials were destroyed only catastrophically. In the tests on ceramic Z the effect proved to be somewhat different. When vT = 2~ the specimens were destroyed suddenly for ATp = 620~ (temperature Text reached 600~ When vT = 200~ it was not possible to destroy the specimens by heating to Tim = 1300~ Tint was in this case significantly lower, and equalled only 260~ For this relatively brittle ceramic (X = 0.44), the relationship Crz-AT z (Fig. 6) exhibited an irregular fall in the residual strength a z, while we would expect [23] (see also Fig. 2) that it should be descending*. Analysis of Experimental Results. The analysis shows that heterogeneous ceramics may be elastic (X = 0) or inelastic (x < 1) as is seen from the Y203 ceramic, for example (Fig. 7). Compared with homogeneous materials, on the basis of which they have been created, heterogeneous materials may have higher (ceramics T and T - C ) or lower (A-1 and A-2) deformation limits~ Therefore, in each actual case we need to study the deformation diagrams, and evaluate the measure of brittleness of the materials, since these determine the main features of their mechanical behavior. Identical data for this particular ceramic were obtained previously by other authors [22]. 544

cr, N l m m 2 ,

cr, N t m m 2

50

/ 0

20

/

/ ..--

1/7

r !

I,,

2

~, 70~ ~ o

e

E, TS~ "

Fig. 9. Change in the relationship between stress ~r and deformation under bending e of specimens due to thermal damage in chilling: ) ceramic Y-1B; .... ) ceramic Y-4; notation on curves - ATz , ~ If the material is inelastic, then the lower its X values, the less elastic energy will be accumulated during loading (see Fig. 1); this energy is used up during damage by the crack development. The microdestruction of its structure, with which the inelasticity is connected, not only causes a blunting of the tip of the developing macrocrack, but it also absorbs the energy, which in another case might Supply the energy needs of this microcrack. Moreover, the energy consumption during microdestruction may be one order greater than during macrodestruction [24]. With a destruction in X (increased inelasticity) [23], there is an increase in the work of destruction "Vwof(it characterizes the resistance of the structure to crack development) compared with the effective surface energy 7nht, characterizing the material's resistance to crack initiation. For example, for ceramic A-3, 7nbt = 7.8 J.m -2 ( K i c = 1.2 N/mm3t2), and 3'wof = 84.9 J-m -2. The inelastic materials do not contain a barrier to breakdown (increase in the KIc values, determined on a notched specimen, compared with a sharp crack). For example, in ceramic Z in both cases KIc = 10 N/ram 3/2 [25]. For the homogeneous ceramic, the difference in Kic may be 2-4 times. We also note that for inelastic materials the R-curve effect is typical. Thus, for ceramic Z the maximum value of KIR equals 14 N/mm 3/2 [25], but for ceramic A-3 it is 6 N/ram 3/2. However, the R-curve effect can be noted for the elastic, but heterogeneous ceramic (Fig. 8). At the same time the porosity (ceramic Y-2) may only slightly influence the R-curve, which for homogeneous dense ceramics is usually fiat [12] (no increase in the KIR values with the growth of the crack). Comparing Fig. 3 with Fig. 8 one would think that the assessment of thermal-shock resistance that is becoming fashionable using the Rcurve, is far from universal. In the light of the above (see Fig. 3), we can postulate that the slope of the az - A T z curves for ceramics Y-2 and Y-3 (absent in Y-l) is connected with the change in the features of the resistance to crack dissemination in these materials. The fact that the structure in inelastic heterogeneous ceramics provides stable growth in the destructive thermal cracks due to microdestruction is supported by data in Fig. 9, which compares curves for the stress-deformation of specimens of material similar to Y-1 (Y-1B) and material Y-4, before and after their chill testing. In Y-4 material which has a descending a z - A T z curve (see Fig. 3) the effective thermal stresses, practically for all temperature variations, prove to be sufficient for the gradual development of microcracks, due to the reduction in the value of crT. The growth in the microcrack is connected with the drop in temperature ATo (see Fig. 4), for which we note a change in the structure, and consequently in the behavior of the ceramic during subsequent thermal loadings. Microdestruction also caused a reduction in the rate of breakdown of alumina coaxial specimens with increase in the number of c~-A1203 platelets (see Fig. 5). The jumplike nature of breakdown in this case is due to the fact that the crack, beginning to spread and then stopping, causes relaxation in tensile peripheral stresses in the specimen. And the next stage of its destruction commences only when, with rise in effective stresses, there builds up adequate elastic energy for further development of thermal cracking. This periodic process can be repeated up to complete destruction of the specimens. To explain the causes of the behavioral peculiarities of ceramic Z during thermal loading, let us examine the temperature changes in the properties (Fig. 10). During heating to 600~ (temperature of external surface of specimen where the dangerous tensile stresses operate, where v T = 2~ the ceramic became elastic (X = 1); and moreover, there were sharp falls in strength, crack resistance, and deformability. In contrast to this when vT = 200~ (temperature in danger zone for tensile stress was 260~ the characteristics of the ceramic proved to be much higher than in the first case, and it was 545

Klc, N/ram312 ,12

"

-

a,8

~

p

,o 30

6

o,1+- 20

3

IO 0_

0

--

I

I.

~00 800 12DO Temperature, ~

1500

Fig. 10. Temperature changes in the characteristics of ceramic Z. still relatively brittle. This is affected by the chilling tests (see Fig. 6). At the chilling temperature it was actually a brittle material, and therefore catastrophic destruction was noted. We observe that the pseudoplastic-brittle change, typical of relatively brittle ceramics, is also characteristic of Y-4 ceramic [23], but it occurs at about 1000~ and therefore does not affect the results shown in Fig. 3. These observations draw attention to the fact that in an analysis of the investigation into the thermal-shock resistance of relatively brittle (inelastic) materials, it is desirable to take account of the temperature relationship with the measure of brittleness, and the results of evaluating the thermal-shock resistance at any given temperature cannot be sufficient as a means of validating the assessment of the possible, actual working capacity of these materials.

CONCLUSIONS An all-round investigation was made of the behavior of heterogeneous ceramic materials (GKM) based on alumina, yttria, and zirconia, during thermal and mechanical loading; this demonstrated that the thermal-shock resistance is due to the combined effects of deformation features and the structure's resistance to breakdown. It is noted that the important factors in evaluating the thermal-shock resistance of inelastic GKM, characterized by a measure of brittleness of less than unity, are the inherent R-curve effects, the excess of the value of ~'wofover the value 7abt, the equality of the KIe determined on specimens with a notch and on those with a sharp crack, and the high sensitivity to the rate of thermal and mechanical loading. Using, as an example, alumina containing zirconia additive, we show that with increase in the stresses in the inelastic heterogeneous material, there is an increase in the length and number of microcracks controlling the features of its mechanical behavior. Using, as an example, zirconia ceramic stabilized with magnesia, we show that there may be a relationship between the thermal-shock resistance of inelastic heterogeneous materials and the temperature changes of their mechanical characteristics.

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2. 3. 4.

546

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21. 22. 23. 24. 25.

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547