Time-dependent mechanical behaviour of alumina ceramics

0013-7944@1 s3.00 + cl.00 Pergamon Press pk.

h%g&zee&gFM&U.?&chanics Vol. 40, No. 413,pi. 863-870,lPPl Printed in Great Britain.

TIME-DEPENDENT MECHANICAL BEHAVIOUR ALUMINA CERAMICS

OF

A. T. YOKOBORI, JR. wt

of Mechanical Engineering II, Tohoku University, Aoba, Aramaki, Sendai, 981 Japan T. ADACHI

Faculty of Science and Engine&ng,

Ishinomaki Senshu University, 1 Shinmito, Minks, rs~nomaki, 986 Japan T. YOKOBORI

School of science and Engineering, Teikyo University, Toyosatodai, Utsunomiya, 320 Japan Ah&act-The strength of ceramics has teen thought to be controlled by a stress corrosion mechanism, but experimental results which do not obey this mechanism have been reported mcently. In this paper, dynamic fatigue test, static fatigue test, stress relaxation test and measurement of internal friction were carried out for the smooth specimens of ahmGna ceramics. Furthermore, we simulated the dynamic fatigue characteristics by using a viscoelastic model. From these results, it was shown that ahm&a ceramics have viscoeiastic properties and their mechanical properties were also affected by this mechanism. In addition, we discuss the effects of added components and grain size on dynamic fatigue.

1. ~RODU~~N THEFRACTURE MECHANISM of ceramics has been assumed to be controlled by the stress corrosion induced by a moist air environment. In many cases, pre-cracked or notched specimens are used for the convenience of analysing the experimental results. The stress corrosion occurs easily, due to high stress con~ntration at the crack tip. Therefore crack pro~gation under moist air conditions has been observed in general. Under the condition of high frequency rate, the fatigue life of alumina ceramics with large pores becomes shorter and fracture occurs when the stress intensity factor of the pore increases and equals the fracture toughness[l, 21. Therefore, crack growth was assumed to occur from the defect. Furthermore, it was shown that fatigue life within the region of higher frequency rate was controlled by the ~clicd~endent mechanism and was controlled by the time-dependent mechanism within the region of lower frequency rate[3, 191. Usually, the time-dependent mechanism was related to the stress corrosion cracking, but the controlling factor of the time-dependent mechanism has not yet been clarified. Therefore, in this paper, we carried out dynamic fatigue test, stress relaxation test and meas~ment of internal friction to clarify its mechanism. Furthermore, theoretical analysis was also carried out based on the viscoelastic model. We also discussed the effect of added components and grain size of alumina ceramics on the characteristics of dynamic fatigue[rl]. 2. MATERIALS, EXPER~NT~

APPARATUS AND PROCZDURE

2.1. Materials

The ceramic materials investigated are two grades of polycrystalline alumina. The amount of added components and the average grain size for each material are shown in Table 1. One contains 96% pure alumina oxide and the other contains 92%. The 96% specimens were flat plates 60 mm in length, 10 mm in width and 1 mm thickness and 120 mm in length, 10 mm in width and 1 mm in thickness. The former were used for dynamic fatigue test, stress relaxation test and static fatigue test and the latter were used for measurement of internal friction. The 92% specimens were flat plates 70 mm in length, 4 mm in width and 1.5 mm in thickness. The surfaces were ground and polished. All specimens were smooth specimens. EFM UV~S-K

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A. T. YOKOBORI, JR. et al.

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Table 1. Added components and grain size Composition

AhO, SiO, CaO MgO

Average grain size @m)

92% 7%

Load Cell

96% 4%

!? 2.33

4.33

Fig. 1. The experimental apparatus for the dynamic fatigue test.

2.2. Dynamic fatigue test The experiments were carried out by a four-point bending method (Fig. 1). Crosshead speed was varied from 0.09 mm/mm to 25 mm/min. The stress rate dependence of bending strength was investigated. Major and minor spans were 30 mm and 10 mm, respectively. The experiments were carried out in air and water. 2.3. Stress relaxation test The stress relaxation test was carried fatigue test. The strain, which equals the stress was measured for about 5000 s. The relaxation curves were then characterized we calculated relaxation times[6,7].

out using the same experimental device as in the dynamic stress level of 240 MPa, was applied and the decrease in experiment was carried out in water and in air. The stress by the stress relaxation theory of the Maxwell model and

2.4. Measurement of internalfriction Internal friction[fHO] was obtained by using the resonance vibration method. The experimental apparatus is schematically shown in Fig. 2. The frequency of the oscillator was varied around the first natural frequency and the amplitude of vibration was measured to draw a resonance curve as in Fig. 3. The internal friction was calculated by

Driving transducer

Driving transducer

Frequency counter

Fig. 2. The experimental apparatus for measurrment of internal friction.

Frequency Fig. 3. Resonance curve.

Mechanical behaviour of ahmina ceramics

500

I ’ o 96% Alumina

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500

92% Alumina

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0 l

a

1ooL

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F p 200 d

in Air

100

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100 10’ lo2 Stress Rate , MPalsec

lo-

lo3

100 10’ 102 Stress Rate , MPaIsec

lo3

Fig. 5. The bending strength in water.

Fig. 4. The bending strength in air.

The internal friction is related to relaxation time by on

(2)

4x 1 + (o7)2 where o is angular frequency and z is relaxation time. 2.5. Static fatigue test

The static fatigue test was carried out by using a static fatigue testing machine. Specimens were loaded by four-point bending. Major and minor spans were 40mm and lOmm, respectively. Weight was directly loaded onto the specimen. If the specimen did not fail after 106s, then the test was stopped. 3. EXPERIMENTAL

RESULTS

3.1. Dynamic fatigue

The experimental results of the dynamic fatigue test in air are shown in Fig. 4. The bending strength of 96% alumina ceramics[5] is larger than that of 92% alumina. Both bending stren@hs increase with increasing stress rate. In water, the strength of 96% alumina is also larger than that of 92% alumina (Fig. 5). The strengths in water are smaller than those in air, as shown in Fig. 6. The stress rate dependence of bending strength in water is smaller than that in air. 3.2. Stress relaxation The result of the stress relaxation test is shown in Fig. 7. Even on alumina ceramics, stress relaxation obviously occurs. The stress in water relaxes rapidly compared to that in air. The stress 500

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Fig. 6. The effect of environment on bending strength.

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2

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Time ,

x102 set

Fig. 7. The effect of environment on stress relaxation.

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A. T. YOKOBORI, JR. ef al.

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Table 2. The stress relaxation time

Table 3. The intemal friction

Environment

Relaxation time

Environment

Internal friction

Air Water

5.0 3.8

Air Humid air

4.14 x 10-4 4.42 x lo-’

relaxation time was analysed based on the relaxation theory of the Maxwell model, The results are summarized in Table 2. The relaxation time in water is smaller than that in air. 3.3. Internal friction The internal frictions in 100% humid air and in air were calculated as shown in Table 3. The internal friction in 100% humid air is larger than that in air. We also calculated the relaxation time from these internal frictions. The relaxation time in 100% humid air becomes smaller (rhmd sir/rcr = 0.9368). 3.4. Static fatigue The results of the static fatigue test in air are shown in Fig. 8. The fatigue life increases with decreasing applied stress. The results in water were similar to those in air, but the fatigue life in water became shorter than that in air (Fig. 9). 4. DISCUSSION The strength of alumina ceramics increases with increasing stress rate in general. This property is mainly controlled by the time-dependent mechanism. We investigated this mechanism by using the quasi-static loading method[3]. In this method, the load is increased step by step and held for a certain time (10s) at each load level (see Fig. 10). The method is suitable for estimating time-dependent mechanisms, because the hold time promotes time-dependent mechanisms. The results are shown in Fig. 11. The strength decreases remarkably, as compared with that of the dynamic fatigue test as shown in Fig. 11. This time-dependent mechanism has usually been attributed to stress corrosion, but if the strength is controlled by the stress corrosion mechanism, the bending strength in water should be much affected by stress rate, as shown in Fig. 12, because corrosion is controlled by time-dependent rate process theory. However, our results obtained for smooth specimens are different. The strength decreased in water and the stress rate dependence became smaller. This result did not correspond to the characteristics of the stress corrosion mechanism. On the other hand, from our experimental results in this paper, stress relaxation obviously occurs on alumina ceramics. The stress in water relaxed remarkably. That is, the relaxation time in water became shorter than that in air. In addition, the relaxation time in 100% humid air I

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Time , set Fig. 8. The static fatigue life in air.

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Fig. 9. The Weibull distribution of static fatigue life.

calculated from the result of internal friction also became shorter. The tendency of the relaxation time is identical with that obtained by the internal friction test. Therefore, alumina ceramics are considered to have the characteristic of viscoelasticity. We then analysed the dynamic fatigue characteristics by using a viscoelastic model (Fig. 13)[11]. The results are shown in Fig. 14. If the coefficient of viscosity of this model becomes larger, the dashpot becomes di5cult to move, the model behaves elastically and the strength does not depend on the stress rate. On the other hand, if the coefficient of viscosity becomes smaller, the dashpot deforms very easily and the model also behaves elastically. In this case, the strength decreases and does not depend on the stress rate. If the viscosity takes an intermediate value, the strength increases with increasing stress rate. These are typical viscoelastic characteristics, which correspond well with those of the dynamic fatigue of alumina ceramics, as shown in Fig. 6. Furthermore, both the relaxation times obtained by the stress relaxation test and the measurement of internal friction become shorter in water. A shorter relaxation time means a smaller value of viscous coefficient in the viscoelastic model. That is, these analytical results are in good agreement with experimental results. Therefore, alumina ceramics are proved to have viscoelasticity and the dynamic fatigue characteristics of smooth specimens are shown to be controlled by the viscoelasticity. The stress rate dependence for cracked specimens is different from that for smooth specimens[l2] and the characteristic of dynamic fatigue is written as shown in Fig. 12. In this case, since the stress concentration was induced at the tip of the crack, stress corrosion is assumed to be promoted at the crack tip. Therefore, we must consider two mechanisms, that is, viscoelasticity and

Time

,t

Fig. 10. Quasi-static loading method.

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A. T. YOKOBORI, JR. et al,

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Quasi Static Loading

lo* loo 10’ Stress Rate , MPa I set Fig. 11. The experimental result of the quasi-static loading method.

stress corrosion mechanisms for estimation of the mechanical behaviour of alumina ceramics. Especially, in the case of smooth specimens, the strength is mainly controlled by the time-dependent mechanism of viscoelasticity. The viscoelasticity of alumina ceramics is considered to be caused by the glass phase in the grain boundary. It was shown that even at room temperature, mechanical properties are also affected by the viscoelasticity. That was assured by the experimental result of the in situ observation of the grain boundary during crack growth, which showed the occurrence of slipping grain at the boundary[l3]. Concerning the results of the static fatigue test in air and water, the time-dependent mechanism will be controlled, but detailed analysis of which mechanism is controlled, say stress corrosion or viscoelasticity, will be a future problem. For smooth specimens both mechanisms should be noted. The bending strength of 96% alumina ceramics is larger than that of 92% alumina. In other words, the strength increases if the purity becomes higher. The effect of grain size on the strength of ceramics has been investigated and is suggested to scatter by test methods[l4]. However, Yokobori et al. clarified the effect of grain size and notch tip radius on fracture strength for steel[l6,17] and it was related to the case of alumina ceramics[ 151, as shown in Figs 15 and 16. These characteristics are valid for both steel and alumina ceramics[l8], but concerning our

in air E2

5

in water 7

i

or

ir

Fig. 12. The dynamic fatigue characteristics caused by stress corrosion.

Fig. 13. The viscoelastic model.

Mechanical behavior of alumina ceramics

869

rplO0 Nsl mm3 80 - -10 Ns/mm3 h rpO.SNslmm3 “E E 2 40 - El=10 N/mm*,E2=20N/mm* - E3=5N/mm2,X=21mm oy 0 ““““’ 0 10 20 30 40 V (mm/s) Fig. 14. The analytical result by the viscoelastic model.

experimental results of 96% and 92% alumina ceramics, the values of grain size are different from each other; the ,difference of fracture strength for both alumina ceramics does not correspond to the effect of grain size, so the characteristic of the strength of the alumina ceramics is also assumed to be affected by the effect of purity. 5. CONCLUSIONS (1) The stress rate dependence of bending strength in water becomes smaller than that in air. The relaxation times in a water environment calculated from the stress relaxation test and the measurement of internal friction were shorter than that in air. The short relaxation time means a small value of viscous coefficient and small stress rate dependence of strength. These are assured by the theoretical analysis based on the viscoelastic model, so it was shown that alumina ceramics have viscoelastic properties and their strength is also controlled by viscoelasticity for the time-dependent mechanism, especially for smooth specimens. (2) The viscoelastic characteristic is due to the glass phase of the grain boundary. (3) The dynamic fatigue characteristics for cracked specimens are explained by the stress corrosion mechanism. However, if the crack length becomes short, the characteristic is thought to be controlled by viscoelasticity. Therefore, two mechanisms-stress corrosion and viscoelasticitymust be considered for estimation of the behaviour of alumina ceramics.

Carbon Steel

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Grain

Size

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Fig. 15. The effect of grain six. and notch tip radius on cC.

A. T. YOKORORL, JR. et al.

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Grain Size D ,mm Fig. 16. The effect of grain size and notch tip radius on %.

(4) The strength of alumina ceramics is estimated by grain size and notch tip radius or crack tip radius, but our experimental results of smooth specimens do not follow the above. Thus, changes of purity also affect the strength. Acknowledgement-We

gratefully acknowledge Asahi Glass Ltd. for preparing specimens.

REFERENCES [l] H. Ohara, A. T. Yokobori, Jr., M. Nakaguchi, Y. Aizawa and T. Ada&i, J. Jup. Sot. Strength Fracture Mater. 23, 1 (1985) [in Japanese]. [2] H. Ohara, A. T. Yokobori, Jr. and K. Nojiri, J. Cerum. Sot. Jap. 95, 1059 (1987) [in Japanese]. [3] A. T. Yokobori, Jr., T. Ada&i, T. Yokobori, H. Abe, J. Nakayama, H. Takahashi and H. Miyata, A&ances in Fracture Research (ICF’I), Vol. 4, p. 2927. Pergamon Press, New York (1989). [4] A. T. Yokobori, Jr., T. Ada&i, T. Yokobori, H. Abe, H. Fujita and J. Nakayama, J. Jup. Sot. Strength Fracture Mater. 24, 46 (1989) [in Japanese]. [5] H. Ohara, A. T. Yokobori, Jr., T. Ada&i and M. Chikuni, Proc. Jap. Sot. Strength Fracture Muter. 35 (1987) [in Japanese]. [6] L. E. Nielsen, h4echwtical Properties of Polymers (Translated by S. Onog). Kagakudojin (1965) [in Japanese]. [7] A. V. Tobolsky, Properties and Structure of Polymers (Translated by K. Murakami et at.). Tokyo Kagaku Dojin (1965) [in Japanese]. [S] S. Nagasaki (Ed.), Experiments of Metal Science. Agne (1964) [in Japanese]. [9] N. H&i, Elasticity and Non-elasticity. Kyoritsu Shuppan (1972) [in Japanese]. [lo] H. Suzuki (Ed.), Strength of Metal. Agne (1972) [in Japanese]. [II] A. T. Yokobori, Jr., T. Adachi, T. Yokobori and C. Y. Jian, to be published. [12] T. Yamada, H. Awaji and Jun-T-Kon, 88 MRS ht. Meet on Advanced Materiuls (1988). [13] G. Vekinis, M. F. Ashby and P. W. R. Beaumont, Acta Metall. (in press). [14] E. Dorm and H. Hubner, Alumina. Springer-Verlag, Berlin (1984). [IS] H. Ohara, A. T. Yokobori, Jr. and M. Kurosaki, J. Jap. Sot. Strength Fracture Muter. 29, 85 (1985) [in Japanese]. [16] T. Yokobori, Y. Sawaki and S. Nakanishi, Trans. Jap. Sot. Me& Engrs 45, 1183 (1979) [in Japanese]. [17] T. Yokobori, Fracture mechanics. Proc. Int. Symp. on Fracture Mech., p. 91. Univ. Press of Virginia (1978). [18] A. T. Yokobori, Jr., Science of Machine 40, 104 (1988) [in Japanese]. [19] A. T. Yokobori, Jr., T. Ada&i, T. Yokobori, H. Abe, H. Takahashi, J. Nakayama and H. Fujita, J. Ceram. Sot. Jap. % 957 (1990).