PSI - Issue 22

Yaroslav Dubyk / Procedia Structural Integrity 22 (2019) 275–282

282

8

Yaroslav Dubyk / Structural Integrity Procedia 00 (2019) 000 – 000

Finally, results of our analysis are summarized in Table 4. It was noticed, that critical crack length distribution is well fitted by a normal distribution, but a leak rate is best fitted by a Weibull distribution.

Table 4. Mean and standard deviation for Critical Crack Length and Leak Rate

Crack orientation

Crack type

l, mm (Normal distribution)

Q, l/min (Weibull distribution)

Mean

SD

a

b

Circumferential

IGSCC

253

8.02

359.49 699.14 502.80 225.76 457.90 328.10

1.79 2.40 4.24 1.67 2.23 3.31

Corrosion fatigue

PWSCC IGSCC

Axial

176

10.89

Corrosion fatigue

PWSCC

4. Conclusions A probabilistic Leak-Before-Break analysis for WWER-1000 unit was performed based on the Failure Assessment Diagram (FAD), treating strength and crack morphology parameters as stochastic values. In order to perform probabilistic calculations, Critical temperature of brittleness and Yield (Ultimate) Stress were fitted by normal distribution, based on experimental data taken from the manufacture documentation found at the Ukrainian NPP. The statistical behavior of the leak rate and critical crack length for different defect orientation was examined treating crack morphology parameters as a normally distributed random variables. The failure probability was calculated using Monte-Carlo simulation, with and without the safety factor of 10. Calculations with safety factor proved to be very conservative, thus a reduction of conservatism is possible for LBB concept. Analysis of the resulting statistical data allowed to fit them with normal distribution for the critical crack length and Weibull distribution for the leak rate, parameters for these distributions for several types of crack were estimated. It was proven, then crack morphology parameters highly affects the leak rate, the leak rate distribution becomes more scattered. Among the mechanical characteristic, a Fracture toughness has more influence rather than Ultimate of Yield strength. For future work a Leak Rate model should be improved, as Henry-Fauske model has a drawback in two-phase physics, because the leak rate characteristics should be treated accurately for nuclear safety. Acknowledgements The author is grateful to his co-workers for the help and support in writing this article. References Orynyak, I., Ageiev, S., Radchenko, S. (2015a). Local and Global Reference Stress for Circumferential Irregular-Shaped Defects in Pipes. Journal of Pressure Vessel Technology 137(4), 041203, doi: 10.1115/1.4028680. Orynyak, I., Ageiev, S., Radchenko, S., Zarazovskii, M. (2015b). Local Limit Load Analytical Model for Thick-Walled Pipe With Axial Surface Defect. Journal of Pressure Vessel Technology 137(5), 051204, doi: 10.1115/1.4029523. Orynyak, I., Yakovleva, E., Dubik, Ya. (2012). The application of the combined method of weight functions for the determination of a through-wall crack opening area in a shell. Strength of Materials 44(6), 600-616. Park, J. H., Cho, Y. K., Kim, S. H., Lee, J. H. (2015). Estimation of leak rate through circumferential cracks in pipes in nuclear power plants. Nuclear Engineering and Technology 47(3), 332-339. PNAE G-7-002-86. 1989. Code for Strength Calculations of Components and Piping in Nuclear Power Plants . Energoatomizdat, Moscow. Rudland, D. L., Wilkowski, G., Scott, P. (2002). Effects of crack morphology parameters on leak-rate calculations in LBB evaluations. Journal of Pressure Vessel and piping 79, 99-102. Stefenini L., Blom F.J., 2018, Probabilistic leak before break. PVP2018-84056, ASME 2013 Pressure Vessels and Piping Conference, ASM E, Parague, Czech Republic. Timofeev, B. T., Blumin, A. A., Anikovsky, V. V., (2000). Fracture toughness of 10GN2MFA steel and its welds. International Journal of Pressure Vessels and Piping 77(4), 195-201. Zahoor, A. (1989). Ductile Fracture Handbook. Reports NP-6301-D, N14-1. Electric Power Research Institute, Palo Alto, CA.