Environmental Engineering Reference
In-Depth Information
where
da/dn
= crack growth rate (in/cyc)
k, l, m
= empirical exponents
R
OL
= overload ratio; ratio of peak stress between spectra to
S
maxmax
(b) A
threshold model
, which contains a minimum size of stress intensity below which there
is no crack growth (equivalent to the endurance limit,
S
e
, on an
S-N
curve):
da
/
dn
= 0
i f
K
max
£
K
TH
da
/
dn
µ (1 -
R
f
)
k
K
max
i f
K
max
>
K
TH
(12-16b)
where
K
TH
= threshold stress intensity (psi-in
0.5
)
and
(c) a combination of these two models.
When correlating model predictions with the results of laboratory fatigue crack propaga-
tion tests of pre-cracked specimens under spectrum loading, the retardation model was found
to underestimate the lives of lower-stress specimens while the threshold model underesti-
mated the lives of higher-stress specimens. Equations for a combined model that best cor-
rects these deficiencies are as follows, with empirical constants for
ASTM A-6
steel, both base
and weld metal:
da
/
dn
= 0
i f
K
max
£
K
TH
(12-17a)
da
/
dn
= 3
x
10
-
10
(1 -
R
f
)
2.4
(
K
max
/1, 000 )
3
(
S
max
/
S
maxmax
)
2
(1/
R
OL
)
(12-17b)
i f
K
TH
<
K
max
<
K
C
da
/
dn
= ¥
i f
K
max
=
K
C
(12-17c)
R
f
³ 0
R
OL
³ 1.0
(12-17d)
K
TH
= 5
.
00 + 52
.
0 exp [-11
.
0(1 -
R
f
)] psi - in
0
.
5
(12-17e)
000
psi
-
i n
0.5
K
C
= 125,
(12-17f)
where
K
C
=
fracture toughness
material property in tension (psi-in
0.5
)
Fracture occurs upon a single application of a stress intensity equal to the fracture tough-
ness, a material property that can be determined by standardized test procedures such as
ASTM E
-399 [ASTM 1993]. Figure 12-19 is a graph of Equations (12-17). The primary
line defines crack-propagation rates for constant-amplitude cycles with
R
f
= 0, at maximum
stress intensities between a threshold of 5,000 psi-in
0.5
and the fracture-toughness of 125,000
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