FRACTAL CRACKS - Fractal Mechanics of Polymers - page 163

The studies carried out earlier have shown that polymer film samples
strength to a considerable extent is defined by growth parameters of stable
crack in local deformation zone (ZD) at a notch tip [1-3]. As it has been
shown in Refs. [4, 5], the fractal concept can be used successfully for the
similar processes analysis. This concept is used particularly successfully for
the relationships between fracture processes on different levels and subject-
ing fracture material microstructure derivation [5]. This problem is of the
interest in one more respect. As it has been shown earlier, both amorphous
polymers structure [7] and Griffith crack [4] are fractals. Therefore, the pos-
sibility to establish these objects fractal characteristics intercommunication
appears. The authors of Refs. [8, 9] consider stable cracks in polyarylatesul-
fone (PASF) film samples treatment as fractals and obtain intercommunica-
tion of this polymer structure characteristics with samples with sharp notch
fracture parameters.
In Fig. 5.2, ZD and stable crack development succession at PASF sample
with sharp notch deformation (the sample was obtained from the solution in
chloroform) is shown. This figure demonstrates, that sample macroscopic
strain increase results to both ZD size raising and advancement of stable
crack, having the form of triangle with a sharp tip. Maslow [4] showed that
the Eq. (5.9) was valid for a fractal crack. This relationship allows to verify
correctness of a crack presentation as stochastic fractal with dimension D cr .
In Fig. 8.1 , the dependences 2lnd cr (ln l cr ) of cracks parameters, measured by
photographs, for PASF three samples (solvents − dichloroethane, chloro-
form and N, N-dimethylformamide) are shown in double logarithmic coor-
dinates. The indicated dependences are approximated well by straight lines,
passing through coordinates origin, and this means, that the Eq. (5.9) condi-
tions are fulfilled and a stable crack in PASF film samples can be considered
as stochastic self-similar fractal with dimension D cr , determined from the
plots, adduced in Fig. 8.1, slope.
The electron microscopy data confirm the made conclusion. I n Fig. 8.2 ,
the microphotograph of stable crack boundary in PASF sample (solvent -
chloroform) is adduced. As one can see, the fracture surface has microrough-
nesses at any rate of two levels (~1 mcm and ~20 nm) that allows to apply
fractal models for PASF samples fracture process [4, 5].