Chemistry Reference
In-Depth Information
to restraints imposed by nondeformed polymer, surrounding the indentor.
However, a number of authors of Ref. [3, 7, 8] showed, that the constant
c
value could differ essentially from 3 and be varied within the wide enough
limits of ~1.5÷ 30.
The elasticity role in the indentation process was offered to account
for the purpose of analysis spreading on wider range of solids. Hill obtained
the following formula for solid body having elasticity modulus
E
and
Poisson's ratio n [7]:
é
ù
2
E
ê
ú
H
=+
1
ln
,
(12.2)
ê
ú
v
( )
3
31
-
ns
ê
ú
ë
û
Y
and the empirical Marsch equation has the form [7]:
æ
ö
÷
E
ç
÷
H
=+
0,07
0,6ln
s
ç
÷
ç
ø
(12.3)
v
ç
è
÷
Y
s
Y
The Eqs. (12.2) and (12.3) allow to give the ration
H
v
/s
Y
for epoxy poly-
mers at the condition of the known
E
and s
Y
and the value n can be calcu-
lated with the help of the Eq. (2.20) by mechanical tests results.
Let us consider now the physical nature of the ratio
H
v
/s
Y
deviation from
the constant
c
≈ 3 in the Eq. (12.1). The structure fractal dimension
d
f
can be
calculated according to the Eq. (1.9) at the natural condition
d
= 3.
The Eqs. (1.9), (2.20) and (12.3) combination allows to obtain fractal
variants of Hill and Marsch equations, accordingly [9]:
é
ù
H
2
2
d
ê
ú
v
=+
1
ln
f
(12.4)
ê
ú
( )( )
s
3
4
--
d
3
d
ê
ú
ë
û
Y
f
f
and
æ
ö
÷
3
d
ç
÷
H
=+
0,07
0,6ln
3
d
s
f
ç
÷
ç
v
÷
Y
ç
-
è
ø
f
.
(12.5)
