Environmental Engineering Reference
In-Depth Information
corresponding mathematical expectations and variances.
Therefore, the mathematical expectation and variance of the range of
the stress intensity coefficients over time Δτ
l
are
i
i
i
M K
[
D
(
Dt
] = [K ( )] - [ ( )];
M
t
MK
−
t
[4.36]
l
l
l l
l
l
1
i
i
i
DK DK DK
−
[
D t
(
)] = [ ( )]
t−Dt
[
( )].
[4.37]
It should be noted that the growth of fatigue defects is possible if the range of
the stress intensity factors is not lower than
l
l
l
l
l
l
1
i
K
t
, depending
on the environment in which the structure works. This should be taken into
account in the determination of the mathematical expectation and variance
of the amplitude of stress intensity factors by rejecting the values below the
threshold, followed by normalisation of the distribution obtained. In addition,
the values of the stress intensity factor are different for different points of
the front of the calculated cracks (defects), for example, points corresponding
to the maximum depth and the maximum length of the defects. Therefore,
the corresponding mathematical expectation and variance of stress intensity
factors [4.36], [4.37] for these points, which determine the direction of the
growth of fatigue defects in the depth and length, will be different.
Correction of the distributions of depth and length of defects due to their
corrosion-fatigue growth during time interval Δτ
l
, provided that no new
defects form during this time, is reduced to increase of the mathematical
expectation
i
t
or
K
()
()
min
max
i
i
i
Ma
[ ( )] =
t
M a
( )] + [
t
M a
D Dt
(
)
[4.38]
l
i
l
−
l
l
and an increase in the variance
Da
[ ( )] =
i
t
D a
i
( )] + [
t
D a
D Dt
i
(
) .
[4.39]
The length distribution of defects is corrected by the same procedure
as the depth of defects.
Thus, the correction of the distributions of depth and length of defects
due to their corrosion-fatigue growth during time period Δτ
l
, provided no
new defects form during this time, is accompanied by:
- 'shift' of distributions to the right by the value of the mathematical
expectations of the depth or length of defects;
- 'stretching' in relation to the mathematical expectation of the axis of
depth or length of defects, respectively, {
D
[
a
i
(τ
l
)]/
D
and [
a
i
(τ
l
-1
)]}
0.5
and
{
D
[
l
i
(τ
l
)]/
D
and [
l
i
(τ
l
-1
)]}
0.5
times.
Inspection may detect defects which do not meet requirements on the
quality of metal. In the next stage these defects are repaired. Therefore, it
is necessary to adjust the distribution of sizes (width and depth) and the
number of defects in the metal structure
57
. The following main characteristics
of inspection of metal should be taken into account in correcting these
distributions:
l
i
l
−
l
l
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