Physico–statistical approach taking defects into account and using binomial distribution - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 103

- determination of the intensity of the transition of the element of the
composite unit of equipment or piping to the limiting state;
- determination of the reliability of equipment or pipeline.
The relationships between the above procedures are shown in Figure 4.2.
To construct a probabilistic model of nucleation of new defects, four
problems should be solved: on the basis of operating experience and
experimental studies to identify factors that affect defect nucleation;
construct mathematical models of the influence of factors on defect
nucleation, define the probability of nucleation of a defect under the effect
of the identified factors; a mathematical model that combines nucleation
of all defects.
Analysis of operating experience and experimental studies has shown that
nucleation of defects is a complex multifactorial process. In many cases,
defect nucleation was of an individual character as it was associated with
individual violations of manufacturing and installation technology or with
individual violations of the water-chemical regime. The model of nucleation
of defects is constructed taking into account factors that can be determined
for several power units. These factors differ for pearlitic and austenitic steels.
Moreover, the following factors can be defined for pearlitic steels :
mechanical fatigue damage cumulation (low-cycle fatigue); vibration
exposure (high-cycle fatigue), hydrogen embrittlement.
For austenitic steels : mechanical fatigue damage cumulation (low-cycle
fatigue); vibration exposure (high-cycle fatigue), oxygen and chloride
cracking, formation of defects near copper deposits.
The mathematical model of nucleation of defects is based on the damage
as a characteristic of damage cumulation, leading to the formation of
defects. In this case, the criterion of defect nucleation is the condition

a d = 1 . [4.22]

Regulatory approaches are used to determine mechanical fatigue damage.
In this case, a mp is determined by the formula
1

￿ ￿ ￿ ￿ ￿

N

[4.23]

∑

a =

i

,

md .

[ ] N

i = 1

0 i

where [ N 0 i ] is the permissible number of cycles at the i i-th type of the
calculation regime of change of stress; N i is the number of cycles at the i -th
type of the calculation regime of stress changes.
The damage for every corrosive factor is determined by the formula

t

d t

∫

a = ,

[4.25]

cd .

t

corr

0

where τ corr is the time to defect nucleation under the effect of corrosion.
It is assumed that the combined effects of mechanical and corrosive
factors lead to damage which is determined by the non-linear summation