Chemistry Reference
In-Depth Information
1
V
=
rB
d
,
(10.19)
f
pp
2
where
r
p
is local plastic deformation zone length, d
p
its critical opening, B
is sample thickness. In its turn, the value d
p
is determined according to the
Eq. (5.15).
Believing for the first approximation
D
= 3, the value
L
can be estimated
from the Eqs. (10.18), (10.19) and (5.15). The estimations showed, that
D
change within the limits of 2 ÷ 3 at
L
calculation gave the greatest error of
~0.3%, that was not reflected practically on the value
D
, calculated accord-
ing to the Eq. (10.17).
The material constant
C
is determined as follows [42]:
G
C
=
Ic
,
(10.20)
a
where
a
is sharp notch length.
The fracture surface fractal dimension at quasibrittle fracture
br
f
d
is de-
termined according to the Eq. (4.50) and at quasiductile fracture - according
to the Eq. (4.51). And at last the value
d
fr
for fractal Griffith crack
br
fr
d
can be
estimated according to the Eq. (5.17) at the condition
m
= 2.
In
Fig. 10.12
the dependences of fracture and fracture surface fractal
dimensions, calculated according to the Eqs. (1.9), (4.50), (4.51) and (5.17)
and the values D, calculated according to the Eq. (10.17) are adduced as a
notch length function for HDPE samples in Sharpy impact tests. The values
D
and
d
f
very good correspondence is quite obvious by both the dependence
on the course and absolute values. This means, that the fracture energy
U
value for HDPE is defined by polymer structural state, which is character-
ized by fractal dimension
d
f
. The coupling of
U
(or
A
p
) with the value
d
fr
at
fracture type (mechanism) correct choice is determined by the dimensions
d
f
and
d
fr
intercommunication, expressed through Poison's ratio value [41].
Fracture of a polymer samples with notch in impact tests conditions is
usually analyzed usually within the frameworks of linear fracture mechanics
[13, 22]. If samples are broken down by brittle mode and local plastic defor-
mation zone at notch tip is small, then for critical strain energy release rate
G
Ic
, which is material plasticity measure, receiving the following expression
is used (without a kinetic effects appreciation) [23]:
U
=
G
Ic
BD
∅,
(10.21)
