Environmental Engineering Reference
In-Depth Information
consider two schemes of merger of the nucleated defects with the defects
existing in the structure:
- In the first scheme, defects formed in the cells located in the surface
or subsurface layers of metal structures merge with the existing defects.
This increases the length of defects in the structure;
- In the second scheme, the defects formed in the cells located in
the inner layers of metal of the structure merge with the existing defects
resulting in an increase of the depth of defects in the structure. For the first
scheme of merger of defects only the distribution of the length of the defects
is corrected and this is accompanied by the 'shift' of the distribution to the
right by the value of mathematical expectation of the length of the nucleated
defects and by 'stretching' in relation to the mathematical expectation on
the axis of the length of the defects {
D
i
[
l
i
(τ
1
)]/
D
i
[
l
i
(τ
l
-1
)]}
0.5
times.
In the second scheme only the depth of defects is corrected and this
is accompanied by a 'shift' of the distribution to the right by the value
of the mathematical expectation of the depth of nucleated defects and by
'stretching' in relation to the mathematical expectation on the axis of the
depth of defects in {
D
i
[
a
i
(τ
1
)]/
D
i
[
a
i
(τ
l
-1
)]}
0.5
times.
Fatigue growth of defects is possible if the range of the stress intensity
coefficients is not lower than
K
i
imin(τ
(τ
l
) or
K
i
max
(τ
l
), depending on the
environment in which the structure operates. This should be taken into
account in the mathematical expectation and dispersion of the range 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 differ 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, for these points defining
the direction of fatigue growth of the defect into depth and length will be
different and the corresponding mathematical expectations and variance of
the stress intensity factors will also differ.
In this case, adjustment of the distribution of the depth and length
of defects due to their corrosion-fatigue growth in the time interval Dt,
provided no new defects nucleate during this period, is accompanied by:
- 'shift' of distributions to the right by increasing the value of the
mathematical expectations of the depth or length of defects;
- 'stretching' in relation to the mathematical expectation on the axis of
the depth or length of defects, respectively, {
D
[
a
i
(τ
l
)] /
D
i
[
a
i
(τ
l-
l
)]}
0.5
and
{
D
[
l
i
(τ
l
)]/
D
i
[
l
i
(τ
l
-1
)]}
0.5
times.
The stress intensity factors
K
i
I
[σ
i
(τ
1
),
a
i
(τ
l-
1
),
l
i
(τ
l-
1
)],
K
i
I
[σ
i
(τ
l-
1
),
a
i
(τ
l-
1
),
l
i
(τ
l-
1
)] and, correspondingly, the range of stress intensity factors Δ
K
i
I
(Δτ
l
)
depend on the size (width and depth) of defects, which in the framework
of this approach are random variables and, therefore, they also are random
variables. The statistical distribution of the stress intensity factors can
be obtained numerically if the appropriate distributions of depths and
lengths of the defects are known. The distributions are characterised by the
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