In the VIPER software, cracks are assumed to exist in BWR vessel welds due to two causes — original manufacturing defects and service-induced cracks which initiate in the stainless steel cladding. These cracks are assumed to grow as a function of operating time due to fatigue crack growth and SCC of the low alloy steel vessel material. Simultaneously, the vessel beltline region is assumed to embrittle due to irradiation. Monte Carlo simulations of these processes are employed in VIPER, which include fracture mechanics crack growth calculations due to fatigue and SCC, and a comparison of predicted crack sizes to the critical crack size due to normal operation as well as possible transient conditions. The governing transient condition was determined to be a LTOP event, since BWRs are not subject to PTS.

The effects of ISI are imposed at appropriate inspection intervals, assuming a POD curve for the inspections. Flaws that are detected during ISI are assumed to be repaired, and thus eliminated from the population, such that they can no longer grow to a leak or vessel failure.

The axial vessel beltline welds are divided into a series of segments, and each segment is analyzed separately to account for axial gradients of irradiation fluence in the welds, which peaks at the core centerline, and decays at elevations above and below that location. The failure frequencies from each segment are weighted by their respective weld volume, and summed to determine failure frequency for the entire vessel.

Modes of failure considered are:

1. Vessel fracture during normal operation (KI > KIc)

2. Vessel fracture during an assumed LTOP event. The LTOP event considered is pressurization to 1,150 psi (7.93 MPa) at 88°F (31°C), which is assumed to occur at a frequency of 1E-3.

3. Predicted crack growth to 80% of wall thickness before failure modes 1 or 2 occurs (LBB)

The results for a typical BWR are given in the following table:

Table I.2 Summary of BWR RPV Beltline PFM Results

These provide an estimate of the probability (per vessel year) of breaks of various sizes due to vessel beltline failures. To complete this table, it was assumed that a leak (LBB mode failure) corresponds to a crack of length = 60 inches (1525 mm) that breaks through and begins leaking as a through-wall crack of this length (since the wall thickness is approximately 6 inches (150 mm), and cracks in VIPER are assumed to have a ten to one aspect ratio). Dave Harris ran this case using the PRAISE code leakage rate prediction capability (See Appendix F for description), and computed a leak rate of 193 gpm (733 lpm) for an axial crack of this size in a BWR vessel. Thus, predicted LBB mode failures from the RPV beltline were treated as Category 1 breaks. Predicted vessel fractures, either during normal operation or due to LTOP events were treated as complete RPV ruptures, which were assumed to result in very large, Category 6 breaks. Intermediate break sizes were then determined by log-log interpolation between these two extremes. The sharp increase in large break probability between years 40 and 60 is attributable to the combined effect of two aging mechanisms — crack growth and RPV embrittlement.