Coefficient of Restitution in a Low-Velocity Normal Impact Using Elastoplastic Contact Stiffness

Abstract

Elastoplastic deformation during particle impact occurs widely in many engineering applications. The material properties characterizing both the elastic and plastic behavior play an important role in particle impact. A non-linear contact stiffness-based model representing the elastic and plastic deformation of the material is used to obtain the coefficient of restitution during the impact of a sphere on a deformable substrate. The model consists of the Maxwell combination of perfectly plastic component and a non-linear elastic component. The proposed model is used to estimate the plastic energy dissipation during the impact. An analytical solution is obtained for residual contact radius and coefficient of restitution expressed in terms of experimentally determinable parameters. Our approach yields a single dimensionless parameter referred to as the “indentation parameter,” Λ, and it is shown that the impact response and coefficient of restitution for various impact situations can be determined based on this indentation parameter. The proposed model accurately predicts the residual contact radius and coefficient of restitution, validated through experimental results of low-velocity impacts (1–4 m/s) over a flat sample of aluminum alloy (Al6061) impacted by steel and zirconia balls. The present model is further compared with other existing theoretical contact models for the elastoplastic impact and the extension of the present model for other dissipative systems is also discussed.