Fragmentation by Crack Branching

Abstract

Two-dimensional lattice models of crack branching give rise to fragmentation if disorder is introduced in the model. The resulting fragment-size distribution is analyzed within a simple analytical model and by numerical simulations. The analytical model gives, under rather general conditions, a power-law distribution over the entire size range. In the specific case studied, the exponent ranges from $-\infty$ to $-0.5\mathrm{}$, depending on the stopping probability of cracks. The analytical results are consistent with the numerical simulations.