Environmental Engineering Reference
In-Depth Information
shown in Table 9.4 is used. The maximum size of the crack measured in
the 9th ISI is 6.8 mm.
Thus, the growth of cracks due to corrosion in steam generator tubes
was estimated using Monte Carlo methods and statistical approaches. The
input data for evaluating the statistical characteristics of crack growth
and initiation of cracks were the ISI data. The proposed analysis method
was used to predict crack propagation at the end of the life cycle. The
efficiency of the method was tested by comparing the predicted data with
the known data.
9.3 Application of a probabilistic method based on
two-parameter distribution
Ths section considered the construction of a probabilistic model of failure
in the analysis of efficiency of heat exchanger tubes
56
.
Since 1990 the Russian nuclear power plants have been using the eddy
current method for testing the quality of metal. Application of this type of
inspection is usually accompanied by the detection of a sufficiently large
number of defects. This led to the need to justify the performance of tubes
of steam generators and prepare recommendations for preventive plugging
of these tubes in the presence of defects. The eddy current method allows
to detect a large number of defects of different length and depth and also
the scatter of the values of the mechanical properties of materials of heat
exchanger tubes in the certificate data. This indicates the need to use it
analysing the performance.
Summary results of the probabilistic assessment of the permissible and
critical defect sizes according to various failure criteria
The probability of formation of through-wall defects and large-scale failure
is determined using the approach described in section 4.2, based on the
consideration of the three failure mechanisms: the onset of stress corrosion
cracking, establishment of the limiting plastic state (ductile fracture);
corrosion fatigue growth of defects.
If the failure probability of tubes depends on their locations, then the
failure probability for each group of tubes during time interval
t
for
i
heat
exchanger tubes inthe given set
n
is determined by the formula:
[
Pt
−
]
ni
i
i
i
[9.14]
P t C Pt
()
=
( ()) 1
()
,
−
n
n
where
P
(
t
) is the probability of failure of one of the tubes in time interval
t
which is regarded as the same for a group of tubes;
C
n
i
is the binomial
coefficient, defined as
!
n
i
n
C
=
.
[9.15]
ini
!(
−
)!
The cumulative probability of leakage or large-scale failure in
n
heat
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