Transition from damage to fragmentation in collision of solids

loss in the flow. Collision of particles also occurs in the solar system in planetary rings. In this case the energy dissipation due to impact damage might also influence the large scale structure formation in the rings @26#. On a larger length scale in the solar system, the so-called collisional evolution of asteroids due to subsequent collisions, and the formation of rubble piles in the asteroid belt, are still challenging problems @6#. Among industrial applications the breakup of agglomerates in chemical processes can be mentioned. Due to experimental difficulties, the computer simulation of microscopic models is an indispensable tool in the study of these impact phenomena @12‐17#. In the present paper we want to elaborate upon the impact fracture and fragmentation of solids at low imparted energy using a two-dimensional dynamical model of breakable granular solids. Simulating collisions of two solid disks, we show that, depending on the imparted energy, the outcome of a collision process can be classified into two states: a damaged state and a fragmented state, with a sharp transition in between. Analyzing the energetics of the impact and the resulting fragment size distributions, we give numerical evidence that the transition point between the damaged and fragmented states behaves as a critical point. The transition proved to be the lower bound for the occurrence of power law size distributions. The possible mechanism of the transition between the two states is discussed. In spite of the specific features of the system studied here, most of our results can be considered generally valid for impact phenomena mentioned above. After giving a short summary of the main ingredients of our model in Sec. II, the numerical results concerning to the energetics of the collision process and to the size distribution of fragments will be presented in Secs. III and IV, respectively. In Sec. V, we discuss the possible mechanism of the transition and some general consequences of our work for other types of fragmentation phenomena.