PSI - Issue 17

Salatiel Pérez Montejo et al. / Procedia Structural Integrity 17 (2019) 123–130 Salatiel Pérez Montejo et al/ Structural Integrity Procedia 00 (2019) 000 – 000

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4

This is a critical situation as it is considered as the maximum tolerable size of such crack. Table 1 reports the geometrical parameters of this case. Regarding the material of the vessel, it is a Low Alloy Steel SA-533 Grade B, Class I and the normal pressure of operation is 1000 psi. Table 1 Geometrical dimensions of the part through thickness crack Inches Internal radius of the vessel 100 Thickness of the vessel t 5 Crack length 2c 7.5 Crack depth a 1.25 The methodology proposed by the United States Nuclear Regulatory Commission (USNRC) in the section 5.3.2 of the NUREG-0800 was used. The start-up and shut down transients were considered in the determination of the allowable pressure and temperature of operation. Equation (1) was used for the determination of the fracture toughness (K IR ) curve. It is suitable for those reactors which started their operation before 1999. (0.014493[ 160]) 26.777 1.223 T RT IR K e − + = + (1) The stress intensity factor I K , due to the internal pressure and the thermal conditions, was evaluated with the following equation, proposed in Standard Review Plan for the Review of Safety Analysis Reports for Nuclear Power Plant: LWR Edition (USNRC, 1981). 2 ( ) ( ) I I I IR K K pressure K thermalgradient K = +  (2) The fracture toughness ( IR K ) should be greater than the stress intensity factor at all time during the start-up and shut down (heating and cooling). The SIF I K generated by the thermal gradient was evaluated with the equation proposed in A. Zahoor, Ductile Fracture Handbook volume 3. (A. Zahoor, 1990) * 1 I K a F   = (3) 1 is a geometrical factor and it has been validated experimentally, The thermal stress  at beltline was evaluated with equation 11 of NB-3653.2 of the Section III of the ASME code. 2(1 ) T E     = − (4) For the problem at hand, It K (thermal gradient) was calculated with equation 3 and 4. Its was 28.98 ksi inch . The I K (pressure) was calculated with the following equation. It was obtained from S.R.P. 5.3.2. Rev. 1 (USNRC,1981). IP m m K M  = (5) m M was evaluated with Fig. 1 of S.R.P. 5.3.2 Rev. 1. A value of 2.17 was estimated. The circumferential stress m  developed by an internal pressure of 1,000 psi, was evaluated with the following relationship: 3.2. Analytical calculation of the Stress Intensity Factor.

PR t

m  =

(6)

Ip K is 47.74 ksi inch .

Under these conditions,

In a next step, 124.46 IR K ksi inch = was obtained. T RT − was calculated with equation 1. For this purpose, the following relationship was used.