FRACTAL CRACKS - Fractal Mechanics of Polymers - page 167

FIGURE 8.5 The dependence of stable crack length l cr on its fractal dimension D cr for PASF

[8].

Let us consider in conclusion the physical significance of stable crack
fractal dimension D cr in PASF samples. As it has been shown in Ref. [12],
the stress concentration coefficient K S of triangular crack is given by the
Eq. (5.10). In Fig. 8.6 t he relation between parameters D cr and K s for PASF
sample (solvent - chloroform) is adduced, from which K s linear reduction
follows at D cr growth. Thus, the dimension D cr for stable crack has the simple
physical significance - it is the value, reciprocal to stress concentration level
at crack tip.
Hence, the stated above results have shown, that the stable crack in
PASF samples, obtained from different solvents, can be treated as stochastic
fractal, whose dimension D cr has clear physical significance - its value is
reciprocal to stress concentration degree at a crack tip. The value D cr is de-
termined unequivocally by polymer structure fractal dimension d f and in its
turn, influences on PASF samples fracture process parameters [8].
Since by their physical significance the dimensions of fracture surface
d surf and stable crack D cr are identical, then this circumstance allows to reveal
the dependence of d surf on polymer structure characteristics and its fracture
mechanism. The authors of Ref. [9] accepted structure fractal dimension d f
as its characteristic and Fig. 8.7 t he dependences d

br
fr

d

duc
fr

( d f ) and ( d f ), are