YIELDING PROCESS - Fractal Mechanics of Polymers - page 86

where n e is macromolecular binary hooking network density, values of which
for HDPE and PP are adduced in Ref. [99], F = 4.
The value r cl can be determined as follows [77]:

nS

, (4.64)

r =

st

cl

ph

pac

where n st is statistical segments number per one cluster ( n st = 12 for HDPE
and 15 - for PP [77]), h pac is packing coefficient, for the case of dense pack-
ing equal to 0.868 [100].

cr
s (1) and noncrystalline nc

FIGURE 4.25

s (2) regions
contributions in yield stress value s Y on strain rate in logarithmic coordinates for HDPE [93].

The dependences of crystalline

The shear modulus G , which, has been noted above, is independent on
e  , is accepted as B . Now the value

s can be determined according to the
Eq. (4.60), assuming, that n st changes proportionally to j cl ( Fig. 4.22 ) . In
Fig. 4.25, the dependences of

nc

s on strain rate e  are adduced for
HDPE (the similar picture was obtained for PP). As it follows from the data
of this figure, at the condition

cr
s and

nc

cr
s = const the value s grows at e  increase

nc

and at e  ≈ 150 s- 1

s , that is, a noncrystalline regions contribution in
s Y begins to prevail [93].

s >

cr

nc