FRACTAL CRACKS - Fractal Mechanics of Polymers - page 166

FIGURE 8.4 The dependence of critical stress intensity factor K Ic on fractal parameter

( )

in logarithmic coordinates for PASF [8].

1 - D 2

l

cr

cr

( )

1 - D 2

l

corresponding to the Eq.
(8.1), in logarithmic coordinates is shown, which is approximated satisfacto-
rily by a straight line. As the Eq. (8.1) shows, the fractal resistance to crack
propagation K I ( D cr ) is approximately equal to K Io at the condition D cr = 1 or
(

In Fig. 8.4, the dependence of K Ic on

cr

cr

)

1 - D 2

l

cr

= 1. From the plot of Fig. 8.4 it follows, that absolute value K I ( D cr )
can be both greater and smaller than K Io , which can be assumed as material
constant. The relation between K I ( D cr ) and K Io is defined mainly by stable
crack advancement value through ZD ( l cr ). The value l cr itself is the function
of G ch , as it follows from the plot of Fig. 8.5 . The stable crack is not propa-
gated (i.e., samples fracture occurs by instable Griffith crack propagation) at
D cr = 1.0 or, as follows from the plot of Fig. 8.3 a t d f = 2.5 (n = 0.25). In other
words, from the point of view of fractal analysis the condition of transition
from stable to instable crack can be expressed as follows [8]:

cr

12

d ~ l

. (8.2)

cr cr