Critical behavior and energy dependence of mass distributions in impact fragmentation

We study fragmentation during high-velocity impact for the projectile–bumper system numerically. To this purpose we use two-dimensional particle-based simulation and describe the interparticle interaction by the pair Lennard–Jones (LJ) potential. The evolution of fragments after impact is considered. It is found that there are regions of fast and slow changes of mass distribution with characteristic time tc, when the fragmentation becomes critical. For t>tc fast relaxation of the distribution to a power-law steady state for the intermediate masses and a weak drift in the region of the small and large masses is observed. For the steady-state distributions the critical point appears at a nonzero impact velocity. It is found that the power-law exponent increases with energy imparted to the projectile–bumper system non-monotonically. For impact velocities about the sound speed of material it may be approximately considered as a constant. It is considered the mass-size relation estimating the typical size of fragments of the gyration radius at the steady-state stage of the fragmentation. For the middle and large masses the fragments can be regarded as fractal objects. The fractal dimension does not change much with the variation of the projectile–bumper system size and impact velocity, and its mean value is close to fractal dimension of percolation.