IMPACT TOUGHNESS - Fractal Mechanics of Polymers - page 194

lips”). Proceeding from these considerations, definite correlation between h p
and h d . Should be expected the adduced i n Fig. 10.3 p lot h p (h d ) confirms this
supposition. As it was expected, h d increase results to h p growth. At h d ¢ 1the
value h p makes up approximately 1.8 mm. The brown model [12] assumes,
that brittle-ductile transition is realized at the condition:

B

, (10.4)

r =

p

2

where B is a sample width.
For HDPE samples the brittle-ductile transition is realized at n ≈ 0.35 or
h d ≈ 0.42 (the Eqs. (1.9) and (10.2)), corresponding to r p ≈ 0.85 mm (Fig.
10.3), that is much smaller than the value, assumed by the criterion (10.4)
(at B = 6 mm). The relation between r p and h d for HDPE can be written as
follows [3]:

r p ≈ 2h d , mm,

(10.5)

or, with the Eq. (10.2) appreciation:

r p ≈ 4.2( d f - 2.5), mm. (10.6)

It is known [13], that molecular mobility intensification results to en-
ergy dissipation increase and enhancement of polymer toughness at failure.
In chapter two, it has been shown that the molecular mobility level can be
characterized by the value of fractal dimension of chain part between mac-
romolecular entanglements nodes D ch (1< D ch < 2 [14]). Fractional part D ch
change (i.e., D ch - 1) from 0 up to 1 gives all possible spectrum of molecular
mobility of this chain part. In Fig. 10.4 , the relation between h d and ( D ch - 1)
is adduced, which has the expected character and is written analytically as
follows [3]:

h

d ≈ D ch - 1.

(10.7)