Length scales and size distributions in dynamic fragmentation

The shatter of a cherished wine glass on impact with the kitchen tile, the spallation in the high-energy collision of atomic nuclei, the fragmentation of the Shoemaker-Levi comet on passage of the Roche limit of the Jovian gravitational field, collectively span vast length scales, yet are each examples of dynamic fragmentation with a number of commonalities. In the above examples, as well as many other dynamic fragmentation events, the consequence is the breakage of the body into some number of fragments that are distributed over size. At the heart of a satisfactory theory is the prediction of the number of fragments and the statistical distribution of these fragments over size. A theory based on energy principles is found to provide length scales that govern both the characteristic fragment size and the distribution spread. Fundamental failure and fracture properties of the material are central in determining the nature of the fragment size distribution. Fragment size distributions can range from relatively tight exponential functions to power-law relations spanning a number of decades in fragment size. The fragment distribution and the dynamic fracture processes leading to power-law distributions bear striking similarities to hydrodynamic turbulence. Onset of fracture asymptotes to a range of length scales in which destruction is self-similar and fractal, requiring that consequences, including the fragment size distributions, exhibit a power-law dependence on the length scale. The theory is described and supporting experimental evidence is provided.