Dimensional effects in dynamic fragmentation of brittle materials

It has been shown previously that dynamic fragmentation of brittle D-dimensional objects in a D-dimensional space gives rise to a power-law contribution to the fragment-size distribution with a universal scaling exponent 2−1∕D. We demonstrate that in fragmentation of two-dimensional brittle objects in three-dimensional space, an additional fragmentation mechanism appears, which causes scale-invariant secondary breaking of existing fragments. Due to this mechanism, the power law in the fragment-size distribution has now a scaling exponent of ∼1.17.