Chemistry Reference
In-Depth Information
see, the linear growth
l
st
at
r
p
increase is observed, that is, local plasticity
intensification increases sample stability to crack propagation. At
l
st
= 0 the
value
r
p
≈ 0.6 mm, in other words, at the values
r
p
< 0.6 mm the fracture will
be realized by instable crack. The plot of Fig. 13.9 allows to estimate the
value
l
st
according to the following empirical relationship [1]:
r
0, 4
1, 7
-
p
l
=
, mm.
(13.11)
st
In
Fig. 13.10
,
the comparison of experimental and calculated according
to the Eq. (13.11) stable crack critical length values is adduced, which shows
satisfactory correspondence of theory and experiment.
In Refs. [7, 17] it has been shown, that elasticity modulus
E
is the linear
function of strain e and at e = 0 extrapolates to the theoretical limit
E
o
(see
Fig. 3.2). In its turn, the theoretical (maximum) fracture stress s
th
of solid,
having no defects, is estimated as follows [18]:
s
th
= 0.1
E
o
.
(13.12)
For the considered polymer films two sources of s
th
decrease can be
distinguished: mechanical stress concentration at stable crack tip and an-
harmonicity local “splash” owing to material structure modification in pre-
fracture zone - ZD. The first factor can be taken into account by stress con-
centration coefficient
K
s
introduction (see the Eq. (5.10)) [7]:
1/ 2
12
al
+
K
=+
st
.
(13.13)
s
d
c
The another factor is taken into account by the ratio of Grüneisen param-
eters of nondeformed polymer g
L
and oriented material in ZD g
or
[1].
The Grüneisen parameter g
L
, characterizing intermolecular bonds anhar-
monicity level in polymer, is determined according to the following relation-
ship [19]:
1
+
n
.
(13.14)
g
≈
0, 74
L
12
-
n
