YIELDING PROCESS - Fractal Mechanics of Polymers - page 54

offered defect concept the Baily Hirsh relationship is also true for polymers.
This means that dislocation analogs are true for any linear defect, distorting
the material ideal structure and creating the elastic stresses field [20]. From
this point of view high defectness degree of polymers will be noted: r d ≈ 10 9
¢ 10 14 cm -2 for amorphous metals [21], and r d ≈ 10 14 cm -2 for polymers [28].
Hence, the stated above results indicate that in contrast with metals, for
polymers realization of the Frenkel mechanism during yielding is much
more probable rather than the defects motion ( Fig. 4.1 ) . This is due to the
above-discussed (even diametrically opposed) differences in the structure of
crystalline metals and polymers [1].
As it has been shown above using position spectroscopy methods [22],
the yielding in polymers is realized in densely packed regions of their struc-
ture. Theoretical analysis within the frameworks of the plasticity fractal con-
cept [35] demonstrates that the Poisson's ratio value in the yielding point, in Y ,
can be estimated as follows:

n

Y = nc + 0.5 (1 - c),

(4.9)

where n is Poisson's ratio value in elastic strains field, c is the relative frac-
tion of elastically deformed polymer.

FIGURE 4.4 The relation between calculated and shear stress at yielding t Y , corresponding
to the Eq. (4.8), for PAr (1), HDPE (2) and EP (3) [20].