Chemistry Reference
In-Depth Information
mensions
D
cr
and
d
f
, one of possible causes of which can be the influence of
d
f
on local plasticity level (see chapter five) and, hence, on crack boundaries
(fracture surface) roughness degree. In Fig. 8.3, two straight lines are drawn,
giving possible theoretical relation
D
cr
(
d
f
). The straight line 1 is drawn in as-
sumption, that the brittle fracture, to which the criterion n = 0.25 (or
d
f
= 2.5,
see the Eq. (1.9)) corresponds [11], is realized at
D
cr
= 1, that is carried out,
and ductile fracture - at n = 0.5, that is, for true rubbers. The straight line 2
as a matter of fact is similar to straight line 1, but it is drawn in assumption
of ductile fracture achievement (sample general yielding) at n = 0.475 [11].
However as the data of Fig. 8.3 show, the value
D
cr
= 2.0 (limiting value
D
cr
)
is reached at
d
f
≈ 2.72, that is, at the transition from quasibrittle (quasiduc-
tile) fracture to ductile one [11].
FIGURE 8.3
The relation between fractal dimensions of stable crack
D
cr
and polymer
structure
d
f
for PASF samples. The straight lines drawing mode explanations are given in the
text [8].
In Ref. [4], it has been shown that between stress intensity factors (resis-
tance to crack propagation) for fractal crack
K
I
(
D
cr
) and smooth one-dimen-
sional cut (i.e., idealized crack with smooth boundaries)
K
Io
the following
relationship exists with precision to a multiplicative constant of order one:
(
)
Kl
-
1
D
2
K D
(
)~
cr
,
(8.1)
I
cr
I0 cr
