same and depend solely on the normal component of the impact velocity. Studying the crack patterns, amount of damage, fragment masses, and velocities, we provide a quantitative foundation of the concept of damage, fragmentation, and shattering in ball impact, which was introduced recently on a more qualitative basis [@agglomerate]. We show the existence of a critical impact velocity $v_c$ which distinguishes two regimes of the impact process, [*i.e.*]{} below the critical velocity damage mainly occurs in a conical region around the impact site with a large residue, however, above $v_c$ an ensemble of oblique cracks develop and the disc breaks up into pieces. In agreement with experimental results, fragment masses are found to follow the Gates-Gaudin-Schuhmann distribution (power law) [@kelly] with an exponent independent of the velocity and angle of impact. The velocity distribution of fragments exhibit an interesting anomalous scaling behavior when changing the impact velocity and the size of the disc.

An important application of our results, besides the ones mentioned at the beginning, is to the optimization and control of tumbling mill performance. These questions are of utmost practical importance as they have a tremendous influence on power draft, wear of the balls and liners and breakage 