International Journal of Fracture

, Volume 103, Issue 1, pp 71-94

First online:

The fractal growth of fatigue defects in materials

  • M. RybaczukAffiliated withInstitute of Materials Science and Applied Mechanics, Wrocław University of Technology
  • , P. StoppelAffiliated withInstitute of Materials Science and Applied Mechanics, Wrocław University of Technology

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Material defects growing during fatigue or damage process are described in terms of fractals. The assumed, uniform energy distribution over fractal defects corresponds to generalized energy density, treated as material characteristics. It has been shown that the way of evolution as well as the main features of an irreversible process are determined by characteristic (for a given material) fractal measures. The macroscopic range of length scales has been introduced via additional energy dependence upon macroscopic volume limiting defects evolution. Under certain constrains imposed upon defects growth, the effect similar to phase transition can be observed. The transition point coincides with the singularity of characteristic measures. In turn, the singularity comes from macroscopic limitations of defects growth. Theoretical results are compared with numerical simulations of the simplified stochastic fibre break process in composites. The simplified model has been generated in a way allowing to exclude heat outflow from the simulated system. This makes possible to examine defects growth over full range of scales beginning with the microscopic level. The calculated singularity appears at percolation point when observed correlated defects approach macroscopic size in accordance with the proposed theoretical model.

Key words:  Fatigue process, fractal defects theory, numerical simulations.