IMPACT TOUGHNESS - Fractal Mechanics of Polymers - page 213

polymers, which have devitrificated amorphous phase at testing temperature
(polyethylenes, polypropylene), should be attributed to the first group, to the
second one a rigid-chain polymers with high glass transition temperature
T g ¢ 425 K, typical representative of which is polycarbonate. Polycarbonate
(PC) was called earlier even a polymer with anomalously high toughness
[22]. However, it was clarified later, that polysulfone, polyarylates of indus-
trially produced DV (PAr) and other polymers number possess the similar
properties [56]. Such behavior of the two indicated groups of polymers can
be named superplasticity, that is, the ability to sustain large plastic strain
without fracture [6]. The authors of Ref. [57] considered the physical causes
of a polymers superplasticity within the frameworks of fractal analysis.
The dissipated impact energy fraction h d can be estimated according to
the Eq. (10.1) and the value d fr - according to the Eq. (4.50). As it is known
[58], the fracture surface fractal dimension d fr can be expressed alternatively
with the help of h d and polymer structure automodelity coefficient L with
the condition L i = C ∞ [7] appreciation as follows [57]:

( )

ln 1 - h

d

d =- 2 ,

(10.28)

fr

ln C

∞

and the condition of solid bodies ductile fracture has the following form [6]:

d fr > 2.70. (10.29)

From the Eq. (10.28) it follows, that large values d fr reaching, that is,
ductile fracture can be realized either by h d enhancement or by C ¢ reduc-
tion. For polymers the value h d is connected with molecular mobility level,
which can be characterized by fractal dimension of the chain part between
entanglements D ch [14]. In Fig. 10.16 the relation between ( D ch - 1) and h d
for the 10 studied in Ref. [57] polymers is adduced, from which follows their
approximate equality (deviation from the linear dependence for PAr, PSF
and PASF is due to the condition b fr < 1 in the Eq. (10.1) nonfulfillment [58].
The dependence h d ( D ch - 1) for the 10 different polymers, adduced in Fig.
10.16, is identical to the similar dependence for HDPE samples with various
length of notch, tested at different temperatures ( Fig. 10.4 ), that indicates
high community degree of the relation between h d and D ch .