Scaling Behavior of Fragment Shapes

We present an experimental and theoretical study of the shape of fragments generated by explosive and impact loading of closed shells. Based on high speed imaging, we have determined the fragmentation mechanism of shells. Experiments have shown that the fragments vary from completely isotropic to highly anisotropic elongated shapes, depending on the microscopic cracking mechanism of the shell. Anisotropic fragments proved to have a self-affine character described by a scaling exponent. The distribution of fragment shapes exhibits a power-law decay. The robustness of the scaling laws is illustrated by a stochastic hierarchical model of fragmentation. Our results provide a possible improvement of the representation of fragment shapes in models of space debris.