Impact and rebound of an elastic–plastic ring on a rigid target

Abstract

This paper studies the impact and rebound behaviour of a thin-walled elastic–plastic circular ring after it impinges onto a rigid wall with initial velocity V0 by finite element method. Through the dimensional analysis and a systematic simulation with different ring geometries and material properties, three non-dimensional parameters are identified, which dominate the impact duration and rebound velocity of the ring; and they are: (1) the ratio of wall thickness to average radius, η=h/R; (2) the yield strain of the material, Y/E; and (3) the non-dimensional initial velocity of the ring, ν≡V0/VY, where VY≡Y/(Eρ)1/2 denotes the yield velocity of the material [3].When the initial velocity is low, the impact between the ring and rigid plate remains elastic, the compression duration could be analytically obtained, and it agrees well with the numerical results, while the restitution duration is about 3/4 of the compression duration. The corresponding coefficient of restitution (COR) is found to be independent from the material property, whereas it increases from 0.75 to 0.78 when the thickness ratio changes from 1/20 to 1/40. With the increasing of initial velocity, a four-hinge crushing mode and a subsequent five-hinge mode are identified, which are different from the crushing mode of a ring under static compression. The variations of compression and restitution durations, rebound velocity and COR are discussed in detail, while some of them are compared with those of the impact of a solid ball onto a rigid wall. The effects of the ring geometry and material properties on these variables are also presented. The rebound velocity is found to reach the maximal at about a half of material׳s yield velocity when the initial velocity of the ring is about twice of the yield velocity, resulting in COR being 0.25 for all the materials and geometries adopted in this paper.