Environmental Engineering Reference
In-Depth Information
(
k
= 1) and the experimental histogram obtained in the second inspection
of the cladding of the casing. Similar curves were also plotted for the third
(Fig. 5.39c) and fourth (Fig. 5.39d) inspections. In the calculations it was
taken into account that the observed defects were repaired and that the area
changed from inspection to inspection.
It is interesting to compare the calculated number of detected cracks
N
calc
exp
. For the second inspection these values
are respectively: 13.5 and 12, for the third inspection 33 and 34, and for
the fourth inspection 6, 8 and 5.
Thus, the proposed calculation method gives satisfactory agreement
between the calculated curves and the experimental histograms. Essentially,
the procedure for predicting the results of subsequent inspections is included
in the algorithm for evaluation of the residual defectiveness (see Fig. 5.37),
which is also well supported by experiments on the test sample.
tot
with the experimental data
N
tot
5.2.5 Credibility and probabilistic components of residual
defectiveness
It has already been mentioned that, in general, the number of defects in a
structure decreases with increasing size of defects. It is obvious that there
are size ranges where the number of defects is reliably equal to 1, more
than 1 or much greater than 1. It is also clear that there is a size range
where the defect may or may not be. The size range where the defect (or
discontinuity) is present in the structure reliably in the amount equal to or
greater than 1, can be called the reliable part of the residual defectiveness.
The size range where the defect (or discontinuity) may or may not be is
the probabilistic part of the residual defectiveness. The boundary between
these regions is formed by defects (discontinuities) with dimensions (
a
d
, c
d
).
The probabilistic part of residual defects, i.e. discontinuities with the
size (
a
, c) ≥ (
a
d
, c
d
) is of special interest in terms of strength, reliability
and residual life.
The following section is concerned with one of the methods for
determining the quantitative characteristics of the probabilistic part of
residual defectiveness and examples of their definitions for a number of
structural elements of the nuclear reactors. The function of the integrated
density of distribution of the probability of existence of discontinuities with
dimensions (
a, c
) is expressed by the equation:
( ,)
ac
max
∫∫
N a c dadc
(,)
in
′′
11
( ,)
ac
P ac a c
(,) ( , )
≥
=
,
[5.23]
ac
,
( ,)
ac
max
∫∫
N a c dadc
(,)
in
(
ac
)
DD
where
N
in
(
a
, c) is the function of defectiveness if inspection is not
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