Experimental and theoretical analyses of elastic-plastic repeated impacts by considering wave effects

Repeated impacts of a sphere against a slender beam have been analyzed theoretically and experimentally. The analyses were performed with regard to a repeated impact process of a sphere striking repeatedly at the midpoint of the beam. The impact results in a local plastically deformed region with depth that is an insignificantly small part of the elastic beam cross-section. The theoretical analysis has been done by combining ten different theoretical contact models with the theoretical method that considers approximately the wave effects induced by impacts. The issue under investigation is to compare the selected contact model and to study the wave effect on impact behavior. The numerical results of theoretical analysis have been compared with the experimental data, and show that there are large differences in the calculated results for impact behavior obtained from the various models. The theoretical and experimental results show that selecting the appropriate contact model is very important on predicting contact behavior. For the contact time, Hertz model and ML model match well with the experimental results. For the accumulated permanent indentation, MYC model matches well with the experimental results. For COR (coefficient of restitution), CYM, Stronge and KK models match the experimental data well as the initial impact velocity of the sphere v0 < 1.5 m/s, and Thornton and MYC models match the experimental data well as v0 > 1.5 m/s. For the rebound velocity, KE and KK models match well with the experiments. For an overall consideration of elastic-plastic contact deformation behavior, MYC model is more adequate to deal with the repeated impact problem of elastic-plastic beam. Large differences have been found between the theoretical analysis with and without considering the wave effects. Without considering the wave effects, the theoretical predictions in COR and in the rebound velocity of the sphere are unreasonable. It is clear that the wave effect induced by impact is very important for elastic-plastic impact problems of flexible structures.