PSI - Issue 22

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

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

concept was applied for Main Circulating Piping (MCP), Emergency Core Cooling System (ECCS) passive pipelines and Pressurizer piping. As we can see, only piping of the first circuit are selected, as they have large dimensions, and are of the main concern for the Reactor safety. A set of calculations were conducted for Normal Operating(NO) conditions, Safety Shutdown Earthquake (SSE) and several emergency situations like: shaft jamming of a reactor cooling pump and break of the piping’s connected to the considered ones (a set of LOCA events). Material properties were used as minimal guaranteed by the PNAE, and safety coefficient according to operation conditions were applied, also a safety coefficient of 2 for critical through wall crack together with safety coefficient of 10 for leak rate (LR) detection ( 38 l/min is a well-known LR criterion) were applied. To support these activities, a series of burst experiments for WWER piping (straight pipe, bend and nozzle) were conducted, see Orynyak et al. (2015a, 2015b). As a result, LBB concept was successfully applied for all Ukranian's WWERs. The main idea of current paper is to extend deterministic LBB analysis to probabilistic evaluation, and to investigate the correctness of Leak Rate safety coefficient value of “ 10 ” . To achieve these aims, we have used real material data for MCP steel, found in the piping documents on Zaporizhzhya NPP. Based on static and dynamic calculations, the most loaded places were selected, where the cracks were postulated. Crack opening area was calculated according to originally developed procedure (Orynyak et al., 2012), which accounts for membrane and linear stress components thought the wall thickness. Leak rate calculations are based on the modifed Henry – Fauske flow model (Park et al., 2015), accounting for stochastic crack morphology (Rundlan et al., 2002).

Nomenclature σ ul

Ultimate Strength, [MPa] Yield Strength, [MPa] Reference Stress, [MPa] Fracture Toughness, [ MPa√m ]

σ yl σ r

K IC

Stress Intensity Factor (SIF), [MPa√m] Young modulus, [GPa] Half-length of the crack, [m] Crack Opening Area (COA), [mm 2 ] Leak Rate (LR) through crack, [l/min]

K I

E

l

A l,m

Q

2. Background and mathematical formulation 2.1. Materials

The first step in analysis is defining the material properties and their probabilistic characteristics. For WWER units main circulation piping are made from 10GN2MFA ferrite steel. To obtain a realistic statistic distribution, we used real data from Zaporizhzhya NPP, from all six units, tested in time of piping production. This distribution for temperatures of 20 and 350 ° C for yield and ultimate strength are presented in Fig. 1, and the calculated distribution parameters are given in Table 1. We can see, that normal distribution well describes our strength characteristics. Mean values of stochastic data are about 30% bigger for 20°C and 8% bigger for 350ºC, then minimum guaranteed according to PNAE G-7-002-86 (1989). Using real manufactured data from WWER-1000 NPP, gives us a more realistic estimation of probability values.

Table 1. Minimum (according to PNAE), mean and standard deviation of the mechanical properties.

Material Property

20, ° C

350, ° C

PNAE

Mean

SD

PNAE

Mean

SD

Yield Stress, MPa Ultimate Stress, MPa Young Modulus, GPa

343 540 210

452.58 580.45

28.04 30.91

294 491 190

395.02 533.01

30.55 22.69

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