Environmental Engineering Reference
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9.21
Formation of new cracks on Weibull curves with two and
three parameters: 1) fraction of cracks in tubes (physical); 2)
Weibull curve with two parameters; 3) Weibull curve with three
parameters.
The exact number of actual defects can be determined only from by
destructive experiments and it not possible to say which method is more
accurate. Given that the simulation using the effective PDD value is more
logical, it should be assumed the number of actual defects identified by
this method is closer to the real values.
Crack formation
Statistical analysis of ISI data allows to estimate the number of cracks formed
during the 1st cycle of operation. The Weibull distribution function is used
in this case. Figure 9.21 shows the cumulative proportion of cracks occurred
in each ISI and their Weibull functions with two or three parameters. The
combined proportion of the cracks is calculated in the actual field, i.e., the
number of actual cracks is calculated. Note that, as shown in Fig. 9.21, the
Weibull curve with three parameters agrees better with the experimental points
than the curve with two parameters. Thus, to estimate the number of cracks
it is necessary to use the Weibull function with three parameters.
The results of simulation
Figure 9.22 shows the results of the forecast of the number and size of the
cracks obtained by statistical modelling using the Monte Carlo method. The
ISI data for model F steam generators from the 8th ISI is used to predict
the number of cracks formed and the maximum size of cracks at the 9th
ISI. Simulation is repeated 1000 times and the results are statistically
analyzed. The results were obtained as probability distributions.
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