Dynamic Buckling and Fragmentation in Brittle Rods

We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength $\lambda$ for the buckling instability, and experimentally verify the resulting scaling law for a range of materials including teflon, dry pasta, glass, and steel. For brittle materials, buckling leads to the fragmentation of the rod. Measured fragment length distributions show two peaks near $\lambda/2$ and $\lambda/4$. The non-monotonic nature of the distributions reflect the influence of the deterministic buckling process on the more random fragmentation processes.