A study of the restitution coefficient in elastic-plastic impact

The aim of this work is to provide useful quantitative support for theories of the restitution coefficient for normal impacts involving plastic: deformation, especially in the region close to the threshold at which plastic deformation begins. The impacts were from spheres of 5 mm diameter of aluminium oxide (which deformed elastically), dropped on to thick plates of mild steel or aluminium alloy. Very accurate measurements of impact and rebound velocities were made for drop heights from 1.75m down to 0.6mm, covering a range of velocities down to the yield threshold. Most of these results are in the elastic-plastic velocity range over which the indentation pressure varies from its value at initial yield of about 1.1 sigma(gamma), to the value when full plasticity is established of about 2.8(sigma gamma). The variation in the restitution coefficient with velocity in this range closely fits the rebound model of Tabor, which allows the indentation pressure to vary through the Meyer index II. The fitted values of n take into account these elastic-plastic effects as well as work hardening, demonstrating that a power-law compliance relationship is a very good model for the increase in indentation pressure as plasticity develops. Full plasticity only becomes established at impact velocities which are of the order of 100 times the velocity at which initial yield takes place. Models which assume a constant indentation pressure (perfect plasticity) are not a good match for the data in the elastic-plastic regime.