Modeling and simulation of dynamic fragmentation in brittle materials

Fragmentation of brittle materials under high rates of loading is a commonly occurring phenomenon, but quantitative descriptions of the process have been elusive. Several models for dynamic fragmentation have been suggested in the past. In the present paper we consider two such models based on energy balance and compare their predictions of fragment size to the results of numerical simulations. This comparison shows that the energy-balance models lead to estimates of fragment size which are an order of magnitude larger than the calculated ones. These differences seem to be due to the fact that these energy-balance models deal with the onset of the fragmentation event; they do not include the time dependence of the process. In reality, fragmentation occurs over finite time during which energy continues to be supplied to the system, and cracks nucleate and propagate throughout the body. Therefore, we propose a model that includes the time history of the process and the number, distribution, and strength of flaws in the material. This model is studied by means of both simple analytical methods and computations. The results provide a consistent picture of fragmentation as a transient event.