Scaling laws for two-metallic spheres in a head-on collision

Two-sphere collision (TSC) as a kind of fundamental impact phenomena is of both science and engineering significance. The classic theories based on Hertz contact mechanics work well for TSC at low speeds, but fail to describe high-speed behaviors with damages such cracks and debris. In this work, with TSC experiments and simulations, we measure two key parameters: the elastic restitution coefficient and momentum transfer factor with the relative collision speed up to 120 m/s in laboratory experiments and up to 1000 m/s in numerical simulations. We further perform the dimensional analysis to obtain the scaling laws for the restitution coefficient and momentum transfer factor. It reveals that the relative speed and the speed ratio of TSC respectively dominate the elastic restitution and momentum transfer. Compared to the previous models, the TSC scaling laws show a better prediction of both experimental and simulation data. This work increases the understanding of TSC mechanism at high speeds.