FRACTAL CRACKS - Fractal Mechanics of Polymers - page 169

Besides, in the same figure the points represent the values D cr for PASF,
calculated according to the Eq. (5.9) and the plots of Fig. 8.1 slope. As one
can see, the dimensions D cr and

fr d good correspondence is observed, from
which the conclusion can be made, that PASF film samples fracture by sta-
ble crack mechanism is related to ductile fracture mechanism. These results
demonstrate clearly, that the d fr value for polymer samples can be predicted,
proceeding from the two indicated above factors: polymer structure and its
fracture mechanism [13].
In Ref. [1], the stationary crack (notches) self-braking effect for some
film samples of blends polyarylate arylene sulfone oxide/polycarbonate
(PAASO/PC) was described. The indicated effect consists of monotonous
increase of fracture stress sf f at sharp notch length a growth. In Refs. [2, 3],
this effect was explained within the frameworks of mechanics of continua
by mechanism of notch blunting by local plastic deformation zone. Methods
of fractal analysis development in respect to fracture process [4, 5] allows
to apply them for the indicated effect explanation [14]. Let us note that the
found dependence s f ( a ) contradicts to the known Griffith equation. It has
been assumed, that this contradiction is due to crack boundaries fractality
(roughly speaking, roughness, see, Fig. 8.2 ) influence underestimation and
the fractal Griffith crack model [4] using will allow to explain the indicat-
ed discrepancy the more so, the mobile cracks self-braking possibility was
shown in Ref. [15] within the frameworks of fractal analysis.
In Fig. 8.8 , the optical microphotographs block is shown, illustrating a
stable crack and local plastic deformation zone development in sample of
blend PAASO/PC (PC content C PC = 20 mas. %), which is very similar to
analogous process for PASF samples (Fig. 5.2). As one can see, (the stable
crack is developed from a sharp notch ( a = 1 mm), has a triangular form and
a sharp tip. The most important feature of this crack is its self-similarity,
which is expressed in the constant ratio of its opening d cr to length l cr . As and
earlier, this circumstance allows to simulate stable crack by stochastic fractal
and determine its dimension D cr according to the Eq. (5.9). As the estima-
tions show, the stable crack fractal dimension D cr is monotonously increasing
C PC function and it changes within the limits of 1.38 ÷ 1.81 ( Fig. 8.9 ).

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