Griffith fractal crack

Preston, S., B.S. Griffiths, and I.M. Young. 1997. An investigation into sources of soil crack heterogeneity using fractal geometry. Eur. J. Soil Sci. 48 31-44. 

It is known [5], that at elastoplastic behavior a system crack-local deformation zone deviates from thermodynamical equilibrium and for its analysis a principles, correct for close to equilibrium systems, for example, Griffith theory, are inapplicable. Besides, prefailure zone structure is differed from elastically deformed material structure (Fig. 5.3) that complicates additionally process analysis. As it was noted above, for polymers this effect is displayed as the formation of local deformation zones near crack tip, containing microvoids and oriented material (crazes) or oriented material only (ZD) [20]. Therefore, for fracture analysis in such cases fracture fractal theory is applied, using fractal analysis and general principles of synergetics [28]. 

Mosolov, A. B. (1991). Fractal Griffith Crack Zhumal Tekhnicheskoii Fiziki, 67(7), 57-60. 

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 fiactal 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 subjecting 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 possibility 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 intercommunication of this polymer structure characteristics with samples with sharp notch fracture parameters. 

Let us note in conclusion, that the adduced above results have shown that the fractal Griffith crack model application can not only improve quantitative conformity of theoretical and experimental data, but also obtain qualitatively new picture of fracture processes. 

The fiacture surface fractal dimension at quasibrittle fracture is determined according to the Eq. (4.50) and at quasiductile fracture - according to the Eq. (4.51). And at lastthe value for fractal Griffith crack d can be estimated according to the Eq. (5.17) at the condition tn = 2. 

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