Physico–statistical models based on the residual defectiveness of structural materials - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 119

to the size of structural elements).
The number of submicroscopic defects in the metal (also called lattice
defects - dislocations, vacancies, etc.) is very large. In a 1 cm 2 section
there are 10 8 -10 12 dislocations.
Microscopic defects are associated with the process of production of
ingots, pressure working, manufacturing of semi-finished products. They
are mainly micropores, non-metallic inclusions, mikrotears, etc.
The number of microscopic defects is much smaller than that of the
submicroscopic ones, but is still large. There can be several defects on
1 cm 2 .
Macroscopic discontinuities are usually characteristic of welded
joints. The probability of starting operation of a structure with a macroscopic
defect in the base metal is very small, possibly 3-5 orders of magnitude
smaller than the probability of occurrence of defects in welded joints (this
does not apply to cast components).
As an example, the characteristic defects in a critical component of the
nuclear reactor - steam generators (SG) - immediately after manufacture are
shown below. In Ref. 74 macrodefectiveness was evaluated as the number of
defects per 10 m of the weld γ L per 1 t of deposited metal γ d m . In studying
the manufacturing technology of SGs made of steel 22K quantitative data
for γ L and γ d m were obtained, depending on the type of welding and the size
of the welded structural element (Fig. 5.1).
Obviously, the number of defects according to the standards for the
manufacture of unit length or mass ranges from about 1 to 1000.
In general, it can be argued that the number of defects in the structure
decreases with increasing defect size (Fig. 5.2a). In this case, it can be
assumed that for a structure weighing several tons the curve tends to infinity
as the size of defects tends to zero.
The curve in Fig. 5.2a can be expressed as equations, the simplest of
which is:

￿ ￿ ￿ ￿ ￿

N = Aa -n , [5.1]

where a is the characteristic size of the defect, such as depth (in the direction
of the wall of the pressurevessel); A, n are the constants for the given
structure, steel grade and manufacturing technology.
The following exponential equation can also be used

N ( a ) = λ exp [-λ a ],

where λ is a constant.
A shortcoming of this equation is that it does not adequately describe
the number of small defects.
The curve in Fig. 5.2a can be restricted on the right-hand side. For
pressure vessels and piping this restriction is the wall thickness s (see Fig.
5.2b).