Critical Behavior and Energy Dependence of Mass Distribution in High-Velocity Impact Fragmentation

Experiments on the high-velocity impact fragmentation for the projectile-bumper system show: (i) the threshold nature of fragmentation [1]; (ii) the similarity of the debris cloud structure [2]. However the current experimental resources cannot give a more detailed picture of the critical and scaling effects of the fragments distribution in a cloud and investigate the fragments structure “in-situ”. These gaps may be filled up by computer simulation [3]. We study fragmentation during high-velocity impact for the projectile-bumper system numerically. To obtain a statistically considerable number of fragments as well as to avoid huge amount of calculations we use two-dimensional particle-based simulations and describe the interparticle interaction by the pair Lennard-Jones potential. Moreover, using the simple model under minimum number of initial assumptions we clarify the understanding of universal properties of the impact fragmentation. The two essential parameters of modeling are: (i) the impact velocity; (ii) the system’s size at condition that ratio of the bumper thickness to the projectile diameter is a constant. 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 control parameter is the impact velocity. The transition to the fragmentation also occurs here as the phase transition. The critical impact velocity is practically independent on the size of the projectile-bumper system. 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 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.