YIELDING PROCESS - Fractal Mechanics of Polymers - page 52

applying much lower external stress than for the process including simulta-
neous breakage of all atomic bonds by the sliding plane [3].

FIGURE 4.3 The relationship between theoretical t o and experimental t Y shear stresses
at yielding for polytetrafluoroethylene (1), HDPE (2), polypropelene (3), polyamide-6 (4),
poly(vinil chloride) (5), polyhydroxiester (6), PC (7), polysulfone (8) and PAr (9) [20].

Payerls and Nabarro [3] were the first who calculated the shear stress
necessary for the dislocations motion, t dm . They used a sinusoidal approxi-
mation and deduced the expression for t dm as follows:

2
1

G

- 2 p ab (1 - n )

t = e

i i

, (4.5)

dm

- n

where n is the Poisson's ratio and parameters a i and b i are of the same mean-
ing as in Fig. 4.2 .
By substituting reasonable n value, for example, 0.35 [27], and assuming
a i = b i , the following value for t dm is obtained: t dm = 2 × 10 -4 G . Though for
metals this value is higher than the observed it Y , it is much closer to them
than the stress calculated using simple shear model (the Frenkel model , Fig.
4.1 ).
However, for polymers the situation is opposite: analogous calculation
indicates that their t dm does not exceed 0.2 MPa, which is by two orders of
magnitude, approximately, lower than the observed t Y values.