Variation of initiation time for stress corrosion cracking in Zircaloy-2 cladding tube

Reliability Engineering 9 (1984) 19-23

Variation of Initiation Time for Stress Corrosion Cracking in Zircaloy-2 Cladding Tube

S. S h i m a d a a n d M. N a g a i Nippon Nuclear Fuel Development Co., Ltd, 2163 Narita-cho, Oarai-machi, Higashi-ibaraki-gun, Ibaraki-ken, 311-13 Japan (Received: 12 October 1983)

ABSTRACT Variation of initiation time for iodine-induced stress corrosion cracking (SCC) was evaluated in Zircaloy-2 cladding tubes. The data obtained from internal gas pressurization SCC tests revealed that the cumulative distribution of the initiation time couM be described by a Weibull distribution. The behavior of the shape, scale, and location parameters against the hoop stresses applied to Zircaloy-2 cladding tubes was also investigated.

1.

INTRODUCTION

The crack growth rate of iodine-induced stress corrosion cracking (SCC) in Zirca!oy is expressible using fracture mechanics parameters, e.g. stress intensity factor K. 1 - 3 The authors have previously formalized the crack growth rate in Zircaloy-2 cladding tube as a function ofK. 4 However, the time to failure of Zircaloy-2 cladding tubes varied widely even under the same test conditions, and the data suggested that the variation of time to failure was probably caused by initiation time of SCC cracking. 4 Hence, in this paper, the variation of initiation time is studied statistically using data from SCC tests for Zircaloy-2 cladding tubes. 4 19 Reliability Engineering 0143-8174/84/$03-00© ElsevierApplied Science Publishers Ltd, England, 1984. Printed in Great Britain

S. Shimada. M. Nagai

20

2.

EXPERIMENTAL

The internal gas pressurization SCC test method was used for Zircaloy-2 tubing. The tube specimens were internally pressurized by argon which contained iodine vapor. Three test series V1, V2, and V3 were made in which the maximum hoop stresses of 294, 267, and 241 M Pa were applied at the inner surfaces, respectively. The pressure applied to a specimen was kept constant until the specimen failed due to SCC. Details of the test method and results have been explained elsewhere. 4 The initiation time data for each test series VI, V2, and V3 are plotted on Weibull paper and shown in Figs. 1-3, respectively.

3.

ANALYSES

Just as the time to failure of iodine-induced SCC in Zircaloy-2 tubing was approximated by a Weibull distribution, 5 so was the variation of

99

90

5O

1o

I

°°

I

05

i

i

i

i

i I

I t-u1

Fig. 1.

I

I

2

I

I

5

I

I

I

I

10

(h)

Distribution of the initiation time in VI series (maximum hoop stress: 294 MPa) on Weibull paper.

Stress corrosion cracking in Zircaloy-2 cladding

21

99

~

50

/

:/ 0

-U.

/

10 o

1

i

I 2

i

I

I 5

I

I

t - u2

Fig. 2.

i

I I I 10

I 20

(h)

Distribution of the initiation time in V2 series (maximum hoop stress: 267 MPa) on Weibull paper.

oj

99

90

50

10 5

1

i

i i

1

i

I

I

I

2

t-u3

Fig. 3.

I

5

I

I

I

I I

10

i

I

20

i

I

J

50

(h)

Distribution of the initiation time in V3 series (maximum hoop stress: 241 MPa) on Weibull paper.

22

S. Shimada, M. Nagai

initiation time. The cumulative distribution for time t distributed as the three-parameter Weibull is given by F(t)=l-exp

-

(1)

where m > 0, b > 0, and u > 0. The three parameters m, b, and u for each test series were determined using the method proposed by Sakai and Tanaka. 6 The results are shown in Fig. 4 against hoop stress. The values of ut, u 2, and u 3 in Figs. 1-3 corresponded to the values of u at 294, 267, and 241 M P a in Fig. 4. The lines in Figs. 1-3 were also calculated by substituting the values of m, b, and u at 294, 267, and 241 M P a in Fig. 4 into eqn. (1), respectively.

10 3

10 ~

10 2

10 2

101

101

JE v

,,~ z JO

E 100

10 °

10 ~

10'

q

-0-; m --I- ; b .-,i- ; u 10

I 250

20( HOOP

Fig. 4.

STRESS

I

IO 2

300 ( MPa )

Changes in the parameters, rn, b, and u, of the Weibull distribution against hoop stress.

Stress corrosion cracking in Zircaloy-2 cladding

4.

23

DISCUSSION

It has been demonstrated that the Weibull distribution might be suitable for evaluating the variation of initiation time from Figs. 1-3. Furthermore, a few interesting features can be pointed out from Fig. 4. Firstly, the shape parameter m, which determines the shape of the distribution, decreased with decreasing hoop stress. Secondly, the scale parameter b, which is an index of the characteristic life, was consistent with the general features related to the time to failure versus applied hoop stress obtained by the internal gas pressurization SCC tests for Zircaloy-2 cladding tube. 5 Lastly, the parameter u, which is called the location parameter or the minimum life, behaved differently from the characteristic life b. For example, the decrease in hoop stress from 294 to 267 MPa prolonged the latter markedly, while it hardly affected the minimum initiation time, which changed the most when the hoop stress was down to 241 MPa. Attention should also be paid to the fact that the Weibull distribution shown in Figs. 1-3 were for specimens with an inner surface area of 3.4cm 2 and, as already has been reported, 5'7 the tube size affects the distribution of the initiation time and, hence, the time to failure. 5.

CONCLUSIONS

The variation of initiation time for iodine-induced SCC in Zircaloy-2 cladding tube can be approximated by a Weibull distribution. The characteristics of the shape parameter, the scale parameter, and the location parameter were also investigated phenomenologically. REFERENCES 1. Kreyns, P. H., Spahr, G. L. and McCauley, J. E. J. Nucl. Mater., 61 (1976) p. 203. 2. Videm, K. and Lunde, L. ASTM (American Society for Testing and Materials) STP 681 (1979), p. 229. 3. Shann, S. and Olander, D. R. Nucl. Technol., 53 (1981), p. 407. 4. Shimada, S., Nishimura, S., Amano, K., Nagai, M. and Yagawa, G., submitted to Journal oJ the Atomic Energy Society oj Japan (in Japanese). 5. Shimada, S. and Nagai, M., Journal of the Society of Materials Science (Japan), 32(352)(1983), p. 26. 6. Sakai, T. and Tanaka, T., Ibid., 31(348) (1981), p.941. 7. Shimada, S. and Nagai, M., Ibid., 32(360) (1983), p. 1025.