Percolation theoretical treatment of two-dimensional fragmentation in solids

Abstract

The fracture of solids is idealized as the formation of fragments by randomly distributed cracks on a network. A percolation problem in the post-critical regime is defined for the dual lattice of the network and a count of connected clusters is made to obtain the fragment distribution. For a two-dimensional material the fraction of fragments whose size exceeds a size s is compared with the Mott distribution function, namely an exponential decrease with s ^1/2. High crack densities are found to lead to a faster decrease than this. Most experimentally observed exploding cylinders show such behaviour. In the asymptotic region of large sizes, the results yield an exponential drop of the fragment numbers with size.