Environmental Engineering Reference
In-Depth Information
where the index
j
meets the criterion of failure (
j
= 1 - corrosion cracking,
J
= 2 - ductile fracture).
The probability of failure
j
Pt
in the presence of a crack at time
t
for the case of continuous cracks is replaced by
P
T
jL
(
t
) and for the case of
large-scale destruction by
P
cr
jL
(
t
). These probabilities are defined as follows:
1
1
()
s
=
∫
a
P t
1
T1
()
PatF atda
( ,)
( ,) ;
[4.13]
cr
jL
1
1
jL
0
π
=
∫
2
R
P t
1
()
PltF lt dl
(, )
l
(, )
.
[4.14]
cr
cr jL
1
1
1
jL
0
The distribution of critical crack dimensions at the appropriate fracture
criterion is defined as follows:
a
K
P at F
( ,)
=
(
K t
,);
cr
1
SCC
[4.15]
11
L
11
L
1
SCC
a
R
[4.16]
The distributions of critical crack lengths calculated by the appropriate
failure criterion
P at F K t
( ,)
=
(
,).
cr
Po
2
12
L
12
L
po
2
F lt
are defined similarly to [4.15] and [4.16].
The probability of failure of heat exchanger pipes for each criterion
j
in the time interval
t
is determined by the summation of the probabilities
of failure of all sections of the pipe according to this criterion. The total
probability of failure of pipes according to two criteria for the failure time
t
is defined as:
l
(, )
cr
1j
P
(
t
) =
P
1
(
t
) + [1 -
P
1
(
t
)]
P
2
(
t
).
[4.17]
The size of leaks in a vessel or pressure pipeline for a given length and
orientation of the continuous crack is determined in two ways:
- realistic calculation and
- conservative calculation.
Realistic calculation
is reduced to determining the equivalent area of
opening of the crack edges on the basis of the size of the continuous crack.
Conservative calculation
is based on conservative assumptions that the
size of a hole is equal to the size of the local zone of concentration of
elastic energy in the vicinity of the crack.
When analysing the efficiency of heat exchange pipes of steam generators
it is assumed that the number of damaged heat exchanger pipes (problems
with the steam generator pipes of nuclear power plants are described in
section 9.1) can be described by the binomial distribution, provided the heat
exchanger tubes are in the same service conditions and the same medium
of the secondary circuit and that the failure of one pipe has no effect on
the failure of other pipes. If the fracture of pipes depends on their location,
then for each group of pipes the probability of failure in time period
t
for
i
heat exchange pipes from the considered number
n
P
n
i
(
t
) is determined
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