Chemistry Reference
In-Depth Information
As it is known [1, 2], the dilation concept of solid bodies fracture process
assumes negative fluctuation density formation - dilaton, length of which
is defined by phonons free run length L. In this case the overloading coef-
ficient κ on breaking bonds can be expressed as follows [3]:
D
κ
=
,
(7.1)
a
where
a
is the interatomic distance.
The values L of order of 100 Å were obtained for the oriented polymers
[3]. However, in Refs. [4, 5] it was demonstrated for nonoriented polymers,
subjecting to high-rate fracture, that the value L ≈
a
(i.e., κ ÷ 1) and such
dilaton, consisting of two neighboring atoms, was named “degenerated” one
[4]. It was also found [6], that in this case experimentally determined values
of athermic fracture stress turn out to be essentially (2 ÷ 3 times) smaller than
theoretically calculated ones. A small values κ (÷ 0.2 ÷ 1.0) is one more im-
portant feature of nonoriented polymers fracture in impact tests. This means,
that the stress on breaking bonds is essentially lower than nominal fracture
stress of bulk sample. And at last, it was found out [7], that the value κ re-
duces at testing temperature growth and the transition from brittle fracture to
ductile (plastic) one. These effects explanation was proposed in Refs. [4-7],
but development of fractal analysis ideas in respect to polymers lately and
particularly, Alexander and Orbach work [8] appearance, which introduced
the “fraction” notion, allows to offer the major treatment of polymer fracture
process [9, 10], including the dilaton concept [1-3] as a constituent part.
The values κ can be calculated by two modes. In the first from them
the value κ (κ
1
) is calculated according to the equation [5]:
C
E
g
=
a
,
(7.2)
s
a
where g
s
is structure-sensitive coefficient,
C
a
is atomic heat capacity, a is
thermal expansion linear coefficient,
E
is elasticity modulus.
The second method is consists of the equation application [11]:
s
T
€
3
11
4
T
‚
s
= --
0
tr
,
(7.3)
„
…
f
e
κ
T
eT
†
‡
2
tr
where s
f
is the fracture stress, sf
o
is theoretical strength, equal to 0.1E,
T
is
testing temperature,
T
tr
is transition temperature, which is equal to glass tran-
