The percolation model, which describes the geometrical feature of two dimensional plane-like pattern formed by the stochastic process in the random medium, is considered to be a simple one for the formation and growth of crack-like defects in the materials. We have simulated the internal crack size distribution for a wide range probabilities of penetrating in the three dimensional materials using the Monte Carlo procedure based on this percolation model. In particular, we have made an attempt to apply the simulated results for concept of extremes of materials behaviors, the well-known Weibull distribution of fracture strength in brittle materials. The main results obtained are as follows;
(1) Under the condition of a constant probabilities of penetration, the percolation clusters which is defined as the crack, are distributed in size as the Parato type frequency density function;
f(a)=Ka
-(n+1) (in a range of large a)
where a is
a charateristic cluster diameter, and
K and
n are positive parameters.
(2) The statistical distribution of the simulated maximum size of claster (maximum crack size) in each specimen is expressed in terms of the second asymptotic function of largest value in the sense of the statistics of extremes.
(3) The application of the concept of fracture mechanics to the simulated crack size distribution characteristics provides the physical explanation for the experimental facts that the fracture strength of brittle materials follows a two-parameter Weibull distribution.
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