International Journal of Fracture 56: R33-R38, 1992. © 1992 Kluwer Academic Publishers. Printed in the Netherlands. R3 3 THE FRACTAL CHARACTERIZATION OF PROPAGATING CRACKS V.V. Silberschmidt Mining Institute, Ural Department of the Russian Academy of Sciences 78A K. Marx Str., 614007 Perm, Russia tel: 3422/640688 In this report we study the application of the fractal approach for characteri- zation of a crack propagating in a brittle stochastic media by an example of the rectangular region ABCD, which contains the symmetry plane (and an apex) of the V-shaped notch. We shall consider this region to be the cross-section of the rectangular beam loaded with a constant force S on its ends far from the cross-section under study. The direction of the force is perpendicular to the region ABCD. We shall divide this cross-section into the elements whose dimensions correspond to the requirements of the elementary volume (all macroscopic parameters could be considered to be constant within such an element). All the non-uniformity of the mechanical properties and a stochastic character of the damage accumulation will be taken into account by setting the distribution of these parameters along the elementary volumes in a random way. The character of such a distribution is defined by experimental data and must reflect in general both non-uniformity of the strength properties and the difference in the rates of the defects development at various points of the material. The present work uses a continuum approach to describe solids with microdefects [1-3]. The results of the statistical-thermodynamic analysis of a medium with microcracks and study of the characteristic reactions of solids to the evolution of the population of defects [4] allows the derivation of the macroscopic constitutive equations on the basis of the non-equilibrium thermodynamics taking into account the processes interaction of change of the stress-strain state and damage accumulation. The system of state equation consists of the physical equation (elasticity or plasticity law) and the kinetic equation which describes the evolution of the ensemble of defects. In a traditional case of the V-shaped notch the crack-microcrack interaction becomes the leading factor in crack propagation and in damage accumulation. So, besides the usual state equations one should account for the exact crack in terms of the stress intensity factors. The stress redistribution in this case could be described on the basis of known results, for example by formulas from [5]. For the case under study the system of the constitutive equations can be reduced to the load redistribution low for structural elements due to the crack Iizt Journ of Fracture 56 (1992)