Edge impact of an elastic-plastic semi-infinite plate

The edge impact of an elastic-plastic semiinfinite plate subject to conditions of plane strain is investigated analytically and experimentally. The theoretical analysis is based on the strain-rate-independent theory of plastic-wave propagation. The plate is initially unstressed; the boundary condition for the edge of the plate corresponds to constant-velocity longitudinal impact except that the step in velocity has a finite rise time. Calculations are carried out according to both the approximate one-dimensional theory and the two-dimensional theory for an elastic-plastic isotropic work-hardening material. The rise time for both solutions is chosen so as to optimize the agreement between theoretical and experimental strain-time profiles. A numerical solution of the two-dimensional equations is obtained by using a difference method developed by Clifton;¹ the onedimensional approximation is solved by the well-known method of characteristics. The problem was approximated experimentally by the axial collision of 4-in.-diam annealed aluminum thick-walled cylinders with a diameter-to-wall-thickness ratio of ten. For impact velocities of 90, 130 and 160 ips (corresponding to maximum strains of 0.12, 0.22 and 0.36 percent, respectively), dispersive characteristics and maximum strain amplitudes of the strain wave are found to be in good agreement with the theoretical predictions of both solutions. However, the two-dimensional solution indicates that the stresses, strains and velocities in regions of high strain-rate are highly nonuniform across the plate thickness.