Environmental Engineering Reference
In-Depth Information
The characteristic size can be represented by the minor axis
a
of the
ellipse which schematizes the defect, and the ratio
a
/
c
is taken to be
constant for all
a
, starting from the conditions of maximum growth rate of
the defect in service; here
c
max
∫
N
=
ϕ
( , )
a c dc f a
=
( ),
in
0
for example, in the case of a uniform stress field
a
/
c
= 2 and the normal
law for the distribution
c
with the mean value
c
= 2
a
and the dispersion
D
=
a
/2 one obtains
c
1
−−
(
cc
)
max
∫
−
n
N
=
Aa
exp
dc
=
in
2
Dc
2
()
2
π
D
0
c
2
max
=
Aa
−
n
∫
exp
−−
(
c a
2 )
2
/ 0.5
a dc Aa
2
=
−
n
.
a
π
0
Residual defectiveness is the difference between
N
in
and
N
det.prod
. In this
case
N
det.prod
is determined from the analytical expression
N
in
P
dd
(χ), i.e.
residual defectiveness
N
res
can be expressed by the equation
N
res
=
N
in
(1 -
P
dd
).
The product safety
S
is defined as the probability of absence in
the product of defects larger than or equal to χ
cr
, where the residual
defectiveness
N
res.safe
in the range of defects that are important for safety,
are determined as the probability of absence in the product of defects whose
size is equal to or greater than the critical size χ
cr
in the service mode of
the product:
c
bef
− − c
∫
Reliability
R
is determined as the residual defectiveness
N
res.rel
in the
range of defects and is defined as the probability of absence of defects,
whose size exceeds the maximum size of the defects χ
d.ser
allowable is
service:
S
=1
N
S
=1
Nd
( )
;
res.safe
res
c
cr
c
bef
S
∫
R N
=1
−
=1-
Nd
( )
cc
;
res.rel
res
c
d.ser
Further, the residual defectiveness is divided into the reliable part in
which defects with sizes χ ≤ χ
d
are reliably detected, and the probabilistic
part in which defects with sizes χ > χ
d
may or may not be.
The boundary between the reliable and probabilistic parts of residual
defectiveness χ
d
is determine the condition:
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