Mass-velocity correlation in impact induced fragmentation of heterogeneous solids

We study the impact fragmentation of disordered solids by means of a discrete element model focusing on the velocity and mass-velocity correlation of fragments. Simulations are performed with plate-like objects varying the plate thickness and the impact velocity in broad ranges. Depending on the impact velocity the breakup process has two different outcomes: at low velocities the sample gets only damaged, to achieve fragmentation, where no large residues survive, the impact velocity has to surpass a critical value. In the fragmented phase the velocity components of fragments are power law distributed with a stretched exponential cutoff, where the impact velocity and plate thickness mainly control the standard deviation of the distributions. Mass velocity correlation is only pointed out for thin plates, while it disappears for three-dimensional bulk samples. In the damage phase of thin plates the mass and velocity of fragments proved to be strongly correlated, however, in the fragmented phase correlation occurs in the vicinity of the critical velocity and it is limited to the large fragments only. The correlation function decays as a power law with different exponents for small and large fragments in good agreement with recent experimental findings. We show that the mass-velocity correlation originates from the spatial dependence of the mass and velocity of pieces inside the fragmenting body.