Environmental Engineering Reference
In-Depth Information
schematic drawing of typical material behavior. For most materials, a threshold,
G
th
, exists, below which no crack growth occurs. For
G
max
>
G
th
, crack grow
occurs, but the rate depends on
G
min
, where
G
min
is the minimum
cyclic applied energy release rate. For
G
max
increasing close to
G
Ic
(the fracture
energy), the crack growth rate increases rapidly. For intermediate values of
Δ
G
=
G
max
−
G
the
crack growth rate can be described in terms of the Paris-Erdogan relation [43]. For
Mode I cracking, the Paris-Erdogan relation can be written as [44]:
Δ
d
a
( 1 )
n
N
=Δ
AG
(
)
d
where
a
is the crack size,
N
is the number of cycles,
A
and
n
are the fi tting param-
eters. The crack growth rate, d
a
/d
N
can be understood as the crack extension per
load cycle and has the units mm/cycle.
As an example, results from cyclic crack growth experiments are shown in Fig. 14
[44]. The results are obtained from tests of DCB specimens loaded with wedge
forces under constant load amplitudes. For this specimen confi guration, the range
of the energy release rate increases with increasing crack length. Thus, a single test
gives data for the crack growth rate under various values of
G
. A curve-fi t, based
on the Paris-Erdogan relation (1), is shown as a solid line in the fi gure.
For materials experiencing large-scale bridging under cyclic crack growth, the
situation is more complicated. As the crack tip advances, a large-scale bridging
zone develops. The bridging stresses restrain the crack opening, leading to a
decreasing crack growth rate [45]. However, the cohesive laws that operate under
cyclic loading are likely to be different from those present under monotonic crack
opening. Thus, the cohesive laws should be characterized as a function of the num-
ber of cycles. Precisely how this should be done is not quite clear, although a few
ideas have been developed [45-47].
Δ
10
-3
Mode I
10
-4
10
-5
da/dN = 2.16
×
10
-11 1.49
×
(
Δ
)
10
-6
10
1
10
2
10
3
I
(J/m
2
Δ
Figure 14: The crack growth rate, d
a
/d
N
, is shown as a function of the energy release
rate range,
Δ
G
, for a unidirectional glass fi ber/epoxy composite [ 44 ].
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