Environmental Engineering Reference
In-Depth Information
If the defects formed in the neighboring cells, it is assumed that these
defects have merged into a single defect. The average size of nucleated
and merged defects over time Δτ
l
, taking into account Ref. 64, is defined
as follows:
i
Fk
=
(
Dt ×
)
Fa
;
= 0.54
FF la
;
=
5
,
[4.33]
0.5
0.5
i
sens
0.5
0.5
0.5
0.5
i
K
Dt
is a parameter corresponding to the average size of the
nucleated defect and depends on the partition of the element into the
cells, on the number of these cells and on the likelihood of nucleation
of a defect in the
i
i-th element. Assuming that the depth and length of
nucleated defects are described by, for example, a log-normal distribution,
the formulas [4.32]) and [4.33] are used to determine the mathematical
expectations
М
3
[
а
i
(Δτ
l
)]>
М
3
[
l
i
(Δτ
l
)] and dispersion
D
3
[
а
i
(Δτ
l
)],
D
3
[
l
i
(Δτ
l
)] of
these distributions.
When carrying out adjustment of distributions of depth, length and the
number of defects in a structure due to the nucleation of new defects over
time Δτ
l
, two cases should be considered:
- the nucleated defects are far away from the defects present in the
structure;
- new defects form in the immediate vicinity of the defects already
present in the structure. This result in merger of these defects.
For the first case, the depth distribution of defects is adjusted as follows
where
(
)
0.5
l
i
i
i
i
v
(
t ×
)
pa
(
t
)
+
v
(
Dt ×
)
pa
(
Dt
)
1
−
i
i
l
−
1
n
1
n
1
i
[4.34]
pa
( )=
t
,
i
1
i
v
()
t
1
where
are the the densities of distribution of the depths
of the defects existing in the
i
i-th element of a composite unit, respectively,
at time τ
1
, and
i
i
pa
( ),
t
p a
−
(
t
)
i
1
i
l
1
t D
is the density of distribution of the depth
of nucleated defects in the
i
i-th element of the structure for time period Δτ
l
;
v
i
(τ
l
) is the the mathematical expectation of the number of defects in the
i
-th
element of the structure at time τ
l
, after accounting for the defects nucleated
by the formula
(
);
n
pa
i
(
)
l
−
1
1
i
i
i
v
(
t =
)
v
(
) +
t
v
(
).
Dt
[4.35]
n
1
in li
−
n
1
The procedure for correction of the length distribution of defects is
identical with that used for correction of the depth distribution of defects.
The distribution of the number of defects is always corrected at the
nucleation of defects irrespective of any conditions and is reduced to
calculation of the mathematical expectation using formula [4.35].
For the second case, new defects nucleate in the immediate vicinity
of the defects present in the structure and this leads to their merger. We
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