PSI - Issue 28

Casper Versteylen et al. / Procedia Structural Integrity 28 (2020) 1918–1929 Versteylen/ Structural Integrity Procedia 00 (2020) 000–000

1926

9

is compared to the temperature of the crack tip, the probability for cleavage fracture can be estimated using equation 1. The stress intensity factor can be plotted against the temperature. The stress intensity factor (SIF) is shown for all temperatures and all cracks for standard ASME crack sizes in Fig. 5. At low temperatures and high stress intensity factors the probability for cleavage crack is highest. During the transient the maximum SIF at lowest temperature seems to be reached and surpassed, which means the maximum is reached during the 1000 second transient. The size effect of the ASME postulated crack is studied by decreasing its size by 10% and increasing the size by 10%. The aspect ratio which is prescribed by ASME should be conservative. If the aspect ratio is increased from 0.33 to 0.67, keeping the crack depth constant and decreasing the crack length, � does indeed decrease. The highest J-integral value is not at the deepest point for this cracks.

200

180

160

140

crack 4 crack 5 crack 6 crack 7 crack 8 crack 9 P_0.05 P_0.95

120

1/2 ]

100

80

K j [MPa∙m

60

40

20

0

0 25 50 75 100 125 150 175 200 225 250 275 300

Temperature [ °C]

Fig. 5.

SIF as function of the temperature in the crack tip, for standard ASME size cracks.

Using the maximum SIFs obtained from the FEM calculation and the corresponding crack temperatures as input for the cumulative probability for of cleavage crack initiation, we obtain the probability of cleavage fracture for cracks of these sizes and locations during a pressurized thermal shock. The cumulative probability for cleavage fracture is calculated for the ASME postulated crack sizes at different locations. The stress intensity factor was calculated conservatively using the maximum J-integral occurring close to the crack tip at every time step. A combination of the lowest crack-tip temperature and the maximum SIF causes the highest probability of fracture. This largest cumulative probabilities are given in in absolute values.