Modeling and simulation of dynamic fragmentation in brittle materials

摘要

Fragmentation of brittle materials under high ratesof loading is a commonly occurring phenomenon, butquantitative descriptions of the process have been elusive.Several models for dynamic fragmentation have been suggestedin the past. In the present paper we consider two such modelsbased on energy balance and compare their predictions offragment size to the results of numerical simulations. Thiscomparison shows that the energy-balance models lead toestimates of fragment size which are an order of magnitude largerthan the calculated ones. These differences seem to be due to thefact that these energy-balance models deal with the onset of thefragmentation event; they do not include the time dependence ofthe process. In reality, fragmentation occurs over finite timeduring which energy continues to be supplied to the system, andcracks nucleate and propagate throughout the body. Therefore,we propose a model that includes the time history of the processand the number, distribution, and strength of flaws in the material.This model is studied by means of both simple analytical methodsand computations. The results provide a consistent picture offragmentation as a transient event.