Physico–statistical models based on the residual defectiveness of structural materials - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 172

c

max

∫

ϕc c= ( ) d 1,

c

d

where χ max is the maximum possible size of the defects in this product.
The probabilistic part of residual defectiveness is used to determine the
probability of the existence of defects that are larger than χ cr and defects
that are larger than [χ] d.ser .
The safety of the product is defined as the probability of existence of
defects that are larger than χ cr and the reliability of the product is defined
as the probability of finding defects that are larger than [χ] d.ser .
The reliability determined using the criterion of leakage of pressure
vessels and piping (for 'leak before break' state) described by the equation:

N leak = 1 - P def ( a * ≥ s , t ),
where a is the size of the defect in the direction of the wall thickness, s is
the wall thickness of the vessel or pressure pipeline.
The method is illustrated by the following examples.

Example 1
It is necessary to ensure the quality of two pipelines with the inside
diameter D = 800mm and the wall thickness s = 34mm made of a pearlitic
steel. The critical size of the defects in transverse welds are shown in Fig.
5.43 (curve 3). The defects permissible in service were identified by the
fracture mechanics equations and the safety factor (curve 2 in Fig. 5.43).
Norms of defects in manufacture are shown by curve 3.
The standard NDT method applied before operation (after installation)
identified 60 discontinuities.
All the detected discontinuities (defects) are presented as histograms
in Fig. 5.44.
The characteristic defect size is the width of the defect in the wall
thickness direction or, more accurately, the minor axis of the ellipse which
was used to schematize all known defects.
At the ratio a / c ≈ 0.5 the critical size of the defect corresponds to a
= 15 mm, [ a ] d.ser = 6mm. For the maximum size in manufacture [ a ] man =
1.15 mm (Fig. 5.43).
Despite the fact that the maximum size of the defect was identified
a max = 13mm, the horizontal axis shows the critical size of a cr = 15 mm.
The equation describing the number of detected defects N det depending
on the size a is:

￿ ￿ ￿ ￿ ￿

N det = Aa -n [1-exp [-α ( a - a 0 )].

According to the inspection results, the minimum size of the detected
defect was a = 0.6 mm.