Numerical analysis of longitudinal elastic-plastic waves with radial effects

Abstract

The two-dimensional problem of longitudinal elastic-plastic waves in circular rods taking radial-inertia effects into account is solved based on the finite-element method and an explicit integration algorithm. The elastic-plastic constitutive equations are the yield criterion of von Mises with isotropic work hardening and the Prandtl-Reuss flow rule. Numerical results are shown for the region near the impact end of a semi-infinite rod for two sets of boundary conditions, namely prescribed longitudinal velocity and prescribed longitudinal stress at the bar end. The lateral motion of the struck end is assumed to be unrestrained (zero shear stress). The numerical results show response characteristics which deviate from the one-dimensional solution and which are in a good qualitative agreement with a number of experimental observations reported in the literature. These impact test results have been examined with respect to the predictions in order to separate radial- and strain-rate effects. Several specific calculations for the various test conditions have been performed to obtain quantitative agreement with experimental observations.