Development of plastic nonlinear waves in one-dimensional ductile granular chains under impact loading

Abstract

A modified split Hopkinson pressure bar (SHPB) was used to load one-dimensional granular chains of metallic spheres under impact loading rates. These homogeneous chains, comprised of brass spherical beads ranging from a single sphere to a chain of sixteen, are of interest because of their unique wave propagation characteristics. In the elastic range, for loads around 10s of N, nonlinear elastic solitary waves have been observed to form. In this work, loading magnitudes spanning from 9kN to 40kN – considerably higher than most previous works on these systems which have been conducted in the elastic regime – cause the granular chains to severely deform plastically. The aim of this study is to identify whether a nonlinear solitary-type wave will be generated under such high load levels, and if so, under what conditions (e.g., chain length, load level, etc.) it will do so. The propagating pulse was found to assume a distinctive shape after travelling through five beads, similar to the elastic case where solitary waves are realized with a traveling wavelength of five bead diameters. The wave speed of the plastic pulses observed here was seen to depend on maximum force, indicating that indeed it is a nonlinear wave in nature and is comparable to the elastic solitary wave. Locally, the plastic dissipation at every contact point through the chains was studied by measuring the residual plastic contact area. It was found that after the formation of the plastic nonlinear solitary wave had occurred there is also decreasing plastic deformation along the chain length except at the end beads in contact with the SHPB, which rebound into the SHPB bar causing larger plastic dissipation locally. To our knowledge this research is the first effort to investigate in detail the development and evolution of solitary-like waves in the plastic regime and will form the basis of future work in this area.