The Minkowski dimension and critical effects in fractal evolution of defects

Creation of the programs for determination of the Minkowski dimension and other corresponding fractal characteristics are the main result of this paper. The programs were created also for the one-side fractal dimension. The stable numerical algorithm of multiplicative differentiate is given in this paper. One confirms that the critical effect occurs and it is corresponding to creation of the macroscopic crack through the breaking of the early formed microdefects. The singularity occurs at the moment at which the percolation is simultaneously observed. A character of the singularity is well visible - the jump for tens of orders occurs. The critical effect was observed in the computer simulations of the fatigue process. (C) 2000 Elsevier Science Ltd. All rights reserved.