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 approximately 1.17 .