LOCAL PLASTICITY - Fractal Mechanics of Polymers - page 108

Within the frameworks of plasticity fractal concept [35] it has been
shown that yielding process is realized not in the entire polymer sample
volume, but only in its part, the fraction of which makes up (1 − c). The
Poisson's ratio value for the deformed up to yielding state polymer gives
the Eq. (4.9). The value c characterizes polymer fraction, which does not
participate in yielding process, but subjects to elastic deformation. For semi-
crystalline polymers in the used testing temperatures range T - 293 ÷353 K
this fraction includes devitrificated amorphous phase and crystalline phase
part, subjected to partial mechanical melting (disordering). In other words,
the parameter c characterizes structural state of the deformed polymer. It is
clear, that the indicated above structure components, possessing very small
stiffness (their elasticity modulus makes up several megapackals), cannot
influence on plastic constraint and consequently it can be supposed, that the
value k cons will be the smaller the higher fraction of elastically deforming
component c for HDPE. The relation of the values k cons and c, adduced in
Fig. 5.8, confirms completely the made above suggestion.
The size of shear deformation local zone r p to a great extent defines im-
pact toughness A p of HDPE samples with a sharp notch [36]. The values k cons
enhancement at notch length a increase, as a matter of fact meaning local
yield stress

s growth, should result to value r p reduction, if to issue from
general postulates of Dugdale model (see the Eq. (5.3)) [4]. The dependence
r p ( k cons ), adduced in Fig. 5.9 , shows the expected r p reduction at k cons growth
and demonstrates correctness (at any rate, qualitatively) of Dugdale model
application for the description of local plasticity in HDPE.

loc

FIGURE 5.8 The relation of plastic constraint factor k cons and elastically deforming regions
fraction c at testing temperature 293 (1), 313 (2), 333 (30 and 353 K (4) for HDPE [32].