Environmental Engineering Reference
In-Depth Information
of damage from each factor
62
. In this case, prior to non-linear summation
of damage from each factor, the factors are ranked in the order from high
to low, i.e. the first number
a
d
1
, is assigned the highest value of all the
failure rates. Accordingly, the damage from the joint action of all factors
is given by:
a
a
=
d
1
,
[4.25]
d
(1
−
a
)/ (1
−
a
)/ (1
−
a
)/...
d
2
d
3
d
4
where
a
d
1
,
a
d
2
,
a
d
3
,
a
d
4
is ranked damage by each factor.
Thus, formulas [4.22] and [4.25] determine the conditions under which
the defects nucleate as a result of the combined action of mechanical and
corrosive factors.
The ranked damage from the corrosive factors in formula [4.25] is
expressed on the basis of the time to nuleaction of defects in accordance
with [4.24]. The damage from mechanical factors is defined in accordance
with [4.23]. It is assumed that the characteristics included in the formula
for determining the failure rate from the effect of mechanical and corrosive
factors are random variables and are described by statistical distributions.
Based on the above, it is possible to determine the probability of nucleation
defects anywhere in the structure.This probability, in accordance with the
criterion of nucleation of defects [4.22] is defined as follows
P
n
=
P
(
a
d
≥ 1).
[4.26]
where
P
s
is the the probability of nucleation of a defect anywhere in the
structure.
Given the large number of characteristics with the corresponding
statistical distributions and the non-linear dependences which define the
damage, the probability of nucleation is estimated by statistical simulation
(Monte Carlo)
63,64
.
To solve the problem of determining the number of incipient defects in
relation to the operating time, the composite unit sample is divided into
elements on the grounds of features of the structure, taking into account
the values of the loading parameters: pressure and temperature, uniformity
(homogeneity) of the stress-strain state, the number of defects and material
properties. Elements are divided into cells assuming that each cell may
contain a nucleus for a future defect. Given that a defect may form in each
cell, the size of this cell should correspond to the size of the incipient
defect. In general, the metal of the structure is divided into cubic elements
and the area of one face of this element is equal to the area corresponding
to the sensitivity of inspection of metal
P
sens
. In this case, different cells
within one element are exposed to different effects of different factors
influencing defect nucleation. Therefore, to analyze the number of incipient
defects, the cells are placed in groups existing in similar conditions during
operation, for example, in layers over the wall thickness of the structure.
The probability of formation of a single defect in any cell of each group
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