SCIENTIFIC-TECHNICAL SECTION

STPs

AND CRACK P~SISTANCE OF CERAMICS.

REPORT NO.

1.

CORDIERITE UDC 6 6 6 . 7 6 + 0 ] + 6 2 0 . 1 7 4 + 6 2 ] . 4 8

G. A. Cogotsi, V. P. Zavada, and F. Ya. Kharitonov

The introduction of ceramics into machine construction makes it important to develop and improve methods for mechanical tests of such materials and for accurate determination of characteristics of their mechanical behavior in the service temperature range []]. Both an evaluation of serviceability and an understanding of mechanisms of fracture in ceramics require a thorough analysis of strength indices, the scatter of these indices, crack resistance characteristics, and parameters which describe subcritical crack growth. The present article reports results of a study of ceramics based on cordierite and reaction-sintered silicon nitride, which are widely used in different areas of high-temperature technology [2]. Strength and ductility tests were conducted on prismatic specimens with rounded lateral edges using a ground diamond instrument. Strength was determined in pure bending. The distance between the internal and external loading points was 20 and 40 mm, respectively. Relative changes in strength (such as with a temperature increase) were studied in transverse bending by a concentrated force (distance between supports 40 mm). This made the study quite a bit easier, since it permitted the use of a fairly simple cassette device which fed the specimen onto the loading support [3] and allowed the testing of nine specimens per furnace heating. A feature of the tests at room temperature was the use of a self-adjusting support, which reduced methodological errors in the study to a minimum [4]. The ultimate strength Ou.s was calculated from the maximum load, i.e., without allowance for the nonlinearity of the stress--strain curves of the specimens. This probably led to some overstatement of the strength values, particularly at high temperatures. Ductility was also studied in pure bending, the zone of which was 40 m m with a length of the cantilever part of the specimen equal to 20 mm. The strains were determined both by means of strain gages stuck to the specimens (at room temperature) and by deflectometer (at temperatures of 20-]400~ which measured specimen deflection in the zone of pure bending. The crack resistance characteristics were determined by the double torsion method [4, 6]. Thanks to this, the same specimen was used to determine the critical stress intensity factor (Kit) and the dependence of KI on crack velocity during subcritical growth (KI -- V curve) [4]. To do this, we prepared sheet specimens which were loaded at four points on one of the narrow faces -- Fig. l (the distance between the internal and external loading points was 5 and 20 mm, respectively). For directional propagation of the crack along the specimen axis, we made a slit of a depth which was roughly half the specimen thickness. The stress intensity factor was calculated from the formula [6]

[ Kx = P l

where P is men; h n i s

3(l-l-v)]1/2

(1)

bh.~h,, (I -- 1,26h/b)

the l o a d ; ~ i s t h e t o r s i o n arm; b and h a r e the w i d t h and t h i c k n e s s the specimen thickness under the slit; v is Poisson's ratio.

C r a c k v e l o c i t y V i n t h e s p e c i m e n s was d e t e r m i n e d accordance with the procedure described in [6].

of the speci-

by t h e method o f l o a d r e l a x a t i o n

in

In the high-temperature tests, t h e t e s t i n g e q u i p m e n t was a u g m e n t e d by s p e c i a l l y d e v e l oped e l e c t r i c a l resistance f u r n a c e s and c e r a m i c s u p p o r t s . To d e t e r m i n e t h e s t r e n g t h and ductility characteristics, we u s e d f u r n a c e s w i t h s i l i t e h e a t i n g e l e m e n t s and l o a d i n g s u p p o r t s made o f s i l i c o n n i t r i d e . The t e s t s i n v o l v i n g d e t e r m i n a t i o n o f c r a c k r e s i s t a n c e characteristics in double torsion were conducted with a furnace with a heater made of platinum-rhodium Institute of Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Problemy Prochnosti, No. ]2, pp. 7-]], December, ]984. Original article submitted November 2], ]983.

0039-23]6/84/]6]2-1651508.50

9 1985 Plenum Publishing Corporation

1651

A-A

~--A

o

II

b

IO

~5

6o

7

g~

T5 a

~0

75

L, m m

C

Fig. I. Transverse (a) and longitudinal (b) sections of the loading element of the unit for double torsion of the specimens, and the temperature distribution along the specimen axis (c): I) specimen; 2) lower support; 3) loading rod; 4) upper support; 5) loading roller; 6) uncoupling roller; 7) platinum-rhodium heater; 8) heater frame; 9) thermal insulation. wire and microlite supports. Heating in these furnaces was controlled with modernized VRT-3 regulators, which ensured an automatic increase in temperature to the prescribed level at a constant rate of 15 deg/min. The temperature was measured and recorded in the tests with a platinum-rhodium thermocouple connected to a KSP-4 potentiometer. One feature of the furnace with the platinum-rhodium heater is the location of the loading supports outside the uniform-heating zone (Fig. I). This significantly reduced the temperature of the supports and background relaxation of the load [6] due to support creep, thereby appreciably reducing the error of the crack velocity determination. However, this location of the supports created some nonuniformity in the temperature field of the specimen along its axis. To determine the zone in which specimen temperature could be considered uniform, we conducted additional tests. Here we used a model sheet of the same dimensions as the double torsion specimen and attached six control thermocouples along the sheet axis 15 mm from each other. The sheet was then placed on the supports in place of a specimen and the furnace was heated. The temperature distribution along the sheet axis at different furnace temperatures is shown in Fig. Ic. It can be seen that the temperature near the support is considerably lower than the temperature measured by the working thermocouple located in the middle zone of the furnace. Sheet temperature increased rapidly with increasing distance from the support and was practically stabilized at a distance of 25-30 mm from the support, here corresponding to the temperature measured by the working thermocouple. Thus, we studied crack resistance using specimens with a preinduced crack longer than 25 mm. As a result, the crack resistance parameters were determined in that part of the specimen the temperature of which corresponded to the temperature of the middle zone of the furnace. The present article reports on a study of cordierite ceramic K-2 [7]. Although this ceramic has proven very stable in thermal loading and is used fairly widely to make electricheater parts, there has not been sufficient study of its mechanical behavior. The test specimens were prepared from several semifinished products measuring 5 x 100 x 300 mm made by the method of semi-dry pressing of granulated powder (grain size 0.3-0.8 mm). The unit pressure was 50 MPa. Petrographic studies established that this ceramic contains about 50-55% cordierite (crystal size I-2 pm), mullite (grain size I-4 pm), and a substantial number of fragments of corundum grains (grain size I0-60 pm). Along with the main crystalline phases, we encountered aggregates of fireclay and grains of iron oxides and quartz. The crystals of the new formations were surrounded by thin cementing films of glass I-2 pm thick. Specimens cut from the semi finished products were ground to the dimensions 3.5 • 4.5 x 50, 4.5 x 5.0 x 90, and 4.5 x 25 x 75 mm and used to determine strength, ductility, and crack resistance, respectively.

1652

o, MPa P.N

50 t~

E

"5

2

1

80

8O

~O 40 20

2 I

~.0

80

Fig. Fig. 20~

f20

~, IJrn

2

L,O0

I

I

800

Fig. 3

2. Stress--strain curves of cordierite ceramic K-2: 2) T = 600~ 3) T = 800~ 4) T = 1000~

1)

T

=

Fig. 3. Dependence of the physicomechanical characteristics of cordierite ceramic K-2 on temperature: 1) ultimate strength; 2, 3) dynamic and static elastic moduli, respectively; 4) critical stress intensity factors.

These

Interest in detailed studies of cordierite stems from its nonlinear stress--strain curves are nonlinear even at room temperature, as was noted in [8].

curves.

Determination of the ductility of cordierite, characteristic stress--strain curves of which are shown in Fig. 2 for different temperatures, illustrates that this material is also relatively brittle at 20~ [5], with a brittleness measure X equal to 0.72. This result was obtained in the strain measurements made both with the deflectometer and with the strain gages. The mean value of the static elastic modulus, determined from the slope tangent of the stress--strain curves, was 67 GPa according to the deflectometer and 66.9 GPa according to the strain gages at stresses close to zero. The mean values of the dynamic elastic modulus, calculated from the rate of propagation of ultrasound in the material,* were also typically close (71.0 GPa). The closeness of the elastic moduli obtained by different methods is evidence of the satisfactory reliability of the methods. The nonlinearity of the stress--strain curves increases considerably with an increase in test temperature to 1000~ (Fig. 2), while the brittleness measure decreases to X = 0.35. One feature of these curves at intermediate temperatures is their negligible nonlinearity. Thus, at 600~ the brittleness measure of ,ordierite ceramic K-2 is practically equal to unity; i.e., the material becomes brittle. ,\L 800~ the material, as under environmental conditions, proves to be relatively brittle -- with a brittleness measure equal to 0.9. It should be noted that a similar increase in the brittleness measure with temperature was noted earlier for graphite [9]. In evaluating the possibility of practical use of a structural material, an important role is played by statistical characteristics of its strength [I]. In studying the latter, we tested specimens cut from semifinished product No. 2 (semifinished product No. ] was used to study ductility). These specimens were loaded in pure bending. Here, we determined the mean ultimate strength and the homogeneity factor, which corresponded to a two-parameter Weibull distribution (Table 1, semifinished product No. 2). Since there was some discrepancy between the mean values of ultimate strength of the specimens cut from semifinished products Nos. l and 2, we conducted additional tests of specimens from nine other semi finished products (SP's). As a result (Table l) we found substantial scatter of the values of mean ultimate strength determined in tests of specimens from different SP's. These results show that although the material of one SP may be relatively homogeneous (for example, SP No. 2, for which the homogeneity factor was 10.6), the material may be considerably less uniform at the boundaries of even one batch of products. This fact is sometimes overlooked, so incorrect conclusions are made regarding the actual characteristics of the materials of which a product is made. This consideration is not important in the present study, since our main goal here is to study the basic features of the mechanical behavior of cordierite ceramic K-2, not the features of its certification. Figure acteristics

3 shows results of study of the temperature dependences of the mechanical charof cordierite (SP No. 10). It can be seen that with an increase in temperature

*The measurements

were made by A. N. Negovskii. 1653

V, m . s e c -t

I

/ /

t0-~

104

1

1.5 1,8 /~I, MN 9 m-a/2

v. m.sec-I l

J

7

1O-~

&Sg~. MN" m-S/~

3.0

Fig. 4. KI--V c u r v e s ite ceramic K-2: 1)

2) T = 600~ T = 1000~ TABLE K-2

Results of Statistical

I.

No. of semifinished product

1

2 3 4

5 6 7 8

9 10 11 For all specimens

Numberof specimens

Densi ty, g/cma

of cordierT = 20~

3) T = 800~

Investigations

Mean ultimate strength, MPa

4)

of the Strength of Cordierite Ceramic

S )and ard deviation, MPa

5 47 10 10 10 i0 10 10 I0 I0 3

2,25 2,26 2,23 2,32 2,30 2,30 2,24 2,21 2,26 2,27 2,29

39,0 49,2 44,0 48,0 46,0 56,5 40,7 47,3 40,7 42,1 49,0

4,3 5,4 9,0 12,4 9,0 14,5 6,7 11,3 7,1 6,4

135

2,26

47,2

9,3

Coefficient Range of ultimate strength, of varia" MPa

iron,% I 1,0

I0,9 20,5 25,7 19,6

25,8 16,6 23,8 17,3 15, 1 -19,7

I' min

max

34 30,8 33,6 32,0 35,0 39, I 33,0 33,6 24,8

44 60,4 65,0 70,7 62,4 80,3 51,8 71,9 50,4

32,8

53,5

40,6

53,8

24,8

80,3

Homogeneity factor m

10,6

6,3

to 600~ the ultimate strength (curve I) first decreases slightly and then increases noticeably at a temperature of about I000~ Abrupt softening of the material then begins. A similar increase in strength at 1000~ was seen for other cordierite materials, but softening began at higher temperatures [8]. Study of the temperature dependence of crack resistance (curve 4) also revealed an increase in Klc with temperature. Meanwhile, this increase is insubstantial at temperatures up to 800=C. Then there is a sharp increase in the critical stress intensity factor at I000~ It should be noted that a similar temperature dependence of Klc was obtained using the method of bending a notched beam. However, the crack resistance recorded here was somewhat lower than in the double torsion test. The temperature dependence of the dynamic elastic modulus (curve 2) is typically similar to the temperature dependence of ultimate strength, while the static elastic moduli (curve 3) decrease with an increase in test temperature and at I000~ become almost half the values obtained at room temperature. There is a significant discrepancy between the measured static and dynamic elastic moduli at high temperatures. Additional investigations will be required to explain this fact. Together with determination of the critical stress intensity factors, we studied KI--V curves corresponding to different test temperatures (Fig. 4). As for most ceramics [4, 6], the dependence of crack velocity V on the stress intensity factor KI is described well by the power function

V

1654

=

A.K~,

(2)

where A and n are empirical parameters. are linear.

The relations obtained in logarithmic coordinates

An increase in Klc with test temperature leads to a shift in the high-temperature KI--V curves to the region of higher values of KI. With an increase in test temperature to 600~ the exponent n in Eq. (2) increases (56-155). It then decreases substantially and, at 1000~ n = 9. This is evidence of the low resistance of the ceramic to subcritical crack growth in this temperature range. Thus, the ceramic is susceptible to creep and should be characterized by low values of rupture strength. In analyzing the results obtained, let us turn to the agreement between the temperature dependences of the investigated physicomechanical characteristics. Thus, at 600~ a decrease in strength is accompanied by a decrease in ductility and an increase in the brittleness measure and the slope tangent n of the KI--V curve, while at ]000~ there is an increase in elasticity and crack resistance and a decrease in the slope tangent of the KI--V curve. Whereas features of the mechanical behavior of cordierite at ]000~ can be explained by the presence of plastic strain, increasing crack resistance and cumulative strain and thus increasing strength and reducing the static elastic modulus, the observed changes in the m~chanical characteristics at 600~ cannot apparently be explained without additional information on the mechanical behavior of this material and without fractographic studies. LITERATURE CITED ] .

2. 3. 4. 5. 6. 7. 8. 9.

G. A. Gogotsi, Strength of a Nitride Ceramic Used in Machine Construction [in Russian], Izd. Akad. Nauk Ukr. SSR, Inst. Probl. Prochn., Kiev (1982). H. R. Maier, H. J. Pohlmann, and A. Krauth, "Design criteria and structural testing of ceramic components," Proc. Br. Ceram. Soc., 26, 17-30 (1978). V. P. Zavada, N. N. Zudin, V. I. Nerodenko, et al., "Bending strength tests of powdered materials in exploratory investigations," Poroshk. Metall., No. 6, 85-95 (1983). G. A. Gogotsi, V. I. Galenko, and V. P. Zavada, "Method of testing in four-point bending," Prob~. Prochn., No. 2,,i05-ii0 (1981). G. A. Gogotsi, Inelasticity of Ceramics and Refractories [in Russian], Izd. Akad. Nauk Ukr. SSR, Inst. Probl. Prochn., Kiev (]982). B. J. Pletka, E. R. Fuller, and B. J. Koephe, "An evaluation of double torsion testing," in: Fract. Mech. Appl. to Brittle Mat., ASTM (1979), pp. ]9-37. V. L. Balkevich, Engineering Ceramics [in Russian], Stroizdat, Moscow (1968). E. Gugel, "Indialith (Cordierit) als Basis temperatur-wechselbestadiger feuerfester Baustoffe," Ber. Dtsch. Keram. Ges., 44, 547-553 (]967). G. S. Pisarenko and G. A. Gogotsi, "Evaluating the brittleness and strength of lowdeforming ceramics," Neorg. Mater., No. 12, 2109-2113 (1976).

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