LOCAL PLASTICITY - Fractal Mechanics of Polymers - page 106

The greatest draw ratio l max of polymer can be estimated according to
the Eq. (5.8). In Fig. 5.6, the comparison of l max and l ZD is adduced, from
which it follows, that l max exceeds systematically l ZD (see als o Table 5.1 ) .
The reasons of this discrepancy are obvious - strictly speaking, the Eq. (5.8)
is valid for rubbers only ( D ch = 2.0) and does not take into consideration ste-
ric hindrances, induced D ch reduction in glassy state, that is, availability of
“frozen” local order (clusters). These hindrances can be taken into account
by a simple semiempirical mode: in glassy state corrected value l max (l fr ) is
equal to [28]:

D 2

ll =

ch

(5.11)

fr max

Since for rubbers D ch = 2.0, then for them the Eq. (5.11) gives trivial
identity. The comparison of calculated by the indicated mode values l fr and
l ZD , adduced in Fig. 5.6, shows their good correspondence.
Thus, the stated above results demonstrated the fractal analysis possibili-
ties at polymers local deformation description. In each from the described
cases fractal dimension of either element has simple and clear physical sig-
nificance that allows to obtain both empirical and analytic correlations be-
tween different structural levels in polymers and also describe their evolu-
tion in polymers deformation and failure processes.

FIGURE 5.6 The relation between draw ratios l ZD and l max (1), l ZD and l fr (2) for PASF

[28].

At local plasticity zones formation near defect, in particular, a notch,
polymer volume, which is in yielding state, is surrounded by elastically de-
formed material. This results to local yield stress-enhancement and the given