  We study the brittle fragmentation of spheres by using a three-dimensional
Discrete Element Model. Large scale computer simulations are performed with a
model that consists of agglomerates of many particles, interconnected by
beam-truss elements. We focus on the detailed development of the fragmentation
process and study several fragmentation mechanisms. The evolution of meridional
cracks is studied in detail. These cracks are found to initiate in the inside
of the specimen with quasi-periodic angular distribution. The fragments that
are formed when these cracks penetrate the specimen surface give a broad peak
in the fragment mass distribution for large fragments that can be fitted by a
two-parameter Weibull distribution. This mechanism can only be observed in 3D
models or experiments. The results prove to be independent of the degree of
disorder in the model. Our results significantly improve the understanding of
the fragmentation process for impact fracture since besides reproducing the
experimental observations of fragment shapes, impact energy dependence and mass
distribution, we also have full access to the failure conditions and evolution.
