An Analysis of Longitudinal Elastic-Plastic Pulse Propagation

The one-dimensional, rate-independent theory of elastic-plastic wave propagation for smooth stress-strain curves concave toward the strain axis is applied to the problem of a long uniform bar loaded at one end by a pressure pulse of short duration. The essential features of the solution are obtained for the case of a semi-infinite bar and for the case of a finite bar whose other end is stress-free by using the method of characteristics in the t-x plane. The general shape of boundaries in the t-x plane which separate regions governed by the dynamic elastic equations from regions governed by the dynamic plastic equations is presented. The nature of the discontinuities that occur at these boundaries is also discussed. For the finite-bar case the analysis is given for materials which exhibit isotropic work hardening and for materials for which the stress-strain behavior in tension is independent of any previous compression. The main features of the solution are in agreement with the behavior observed for annealed, commercially pure aluminum bars subjected to explosive loading at one end. These experiments will be reported subsequently.