Environmental Engineering Reference
In-Depth Information
a
f
1
∫
N
=
da
.
m
D
K
[4.3]
a
C
1
0
1
−
R
Substituting the previous expression into expression [4.3] and solving it
with respect to the finite size of the crack
a
f
, we can determine the increase
in the crack length Δ
a
N
under the influence of
N
load cycles.
Usually, by defect we mean a discontinuity larger than the permissible
size in service. For brevity, any crack-type discontinuity in metals will be
sometimes called a defect.
4.1.3 Growth of discontinuities in static loading in a
corrosive environment
The crack growth rate under static loading in a corrosive environment can
be described by an equation of the following type:
da
/
d
τ =
C
τ (∆
K
)
m
,
[4.4]
where
C
τ
and
m
τ
are the constants depending on material properties and the
environment;
a
is crack length, τ is time.
In Ref. 29, the crack growth rate is described by the following equation:
da
/
dt
=
f
(
a
)
z
,
[4.5]
where
a
is crack length,
t
is time,
f
(
a
) is the function of crack length
a
, and
z
is a
statistical random variable which takes into account a random error.
One of the simplest forms of equation [4.5] is as follows:
da
/
dt
=
Ca
λ
z
,
[4.6]
where
C
and λ are constants. Logarithmic transformation of both sides of
equation [4.6] leads to the following:
log(
da
/
dt
) = log
C
+ λlog
a
+ log
z
.
[4.7]
The constants
C
and λ can be obtained from the linear relationship
between the variables log
a
and log (
da/dt
).
Damage for each corrosive factor is determined from
56
t
d
t
∫
a
=
,
[4.8]
where the
a
cd
is the damage from the corrosive factors at time τ; τ is the time
to nucleation of defects in the corrosive environment.
cd
t
0
cor
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