Stable crack fractal dimension

Let us consider in conclusion the physical significance of stable crack fractal dimension in PASF samples. As it has been shown in Ref [12], the stress concentration coefficient Kg of triangular crack is given by the Eq. (5.10). In Fig. 8.6 the relation between parameters and for PASF sample (solvent - chloroform) is adduced, fi om which linear reduction follows at growth. Thus, the dimension for stable crack has the simple physical significance - it is the value, reciprocal to stress concentration level at crack tip. 

Figure 11.6 shows the plots for the variation of versus r j for two amorphous polymers the plots correspond to relationship (11.28). In other words, a stable crack in polymer film samples is a stochastic fractal with the dimension 1.48. The linearity of plots shown in... 

It has been found that the basic elements of structure of initial and deformed polymers are homogeneous fractals that can be characterised by their fractal dimension. Examples of such elements are macromolecular coil, supermolecular organisation as seen in the cluster structure and a stable crack in film samples of polymers. These examples are given as examples of the possible variants of the term "multifractality with reference to polymers. 

In Figure 14.4 double logarithmic dependences 2 In 8 = /(In r) are presented for two amorphous polymers which have appeared to be linear and by virtue of it, correspond to Equation (14.7). Otherwise, the stable crack in film polymeric samples is a stochastic fractal with dimension 1.48. Linearity of the diagrams presented on Figure 14.4 reflects the self-similarity of a crack at different stages of its growth. Thus, at the macroscopic level polymers the fractal properties are also displayed. 

Long, Q. Y, Suqin, L., Lung,C. W. (1991). Studies ofthe Fractal Dimension of a Fracture Surface Formed by Slow Stable Crack Propagation. J. Phys. D Appl. Phys., 24(4), 602-607. 

In Fig. 8.3, the relation between fractal dimensions of structure and stable crack for PASF samples is adduced. As it was to be expected from the most general considerations, the intercommunication existed between di-... 

FIGURE 8.3 The relation between fractal dimensions of stable crack and polymer structure for PAST samples. The straight lines drawing mode explanations are given in the... 

The dependence of stable crack length / on its fractal dimension D for PASF... 

Hence, the stated above results have shown, that the stable crack in PASF samples, obtained from different solvents, can be treated as stochastic fi actal, whose dimension has clear physical significance - its value is reciprocal to stress concentration degree at a crack tip. The value is determined unequivocally by polymer structure fractal dimension and in its turn, influences on PASF samples fracture process parameters [8]. 

FIGURE 8.6 The dependence of stress concentration coefficient of stable crack on its fractal dimension D for PAST [8],... 

---