Propagation of Longitudinal Deformation Waves in a Prestressed Rod of Material Exhibiting a Strain-Rate Effect

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Abstract
We consider the longitudinal propagation of stresses above the yield stress in a material exhibiting a strain-rate effect. The system consists of a semi-infinite rod subjected to end impact. If the rod is prestressed above the yield point and if the impact stress is not too large, the equations of motion are linear. Integral representations of the solutions can be obtained by the method of Laplace transforms. It is shown in general that the strain-rate solutions approach asymptotically the solutions obtained by von Kármán and Taylor in a treatment which neglects the strain-rate effect. The propagation of the unloading wave is considered for the case in which the initial wave is a shock wave. The condition which defines the regions in the x—t plane, where the loading and unloading equations apply, is given. It is shown that an unloading shock wave will be absorbed except for the case of a material which does not work-harden. In this case the complete solution of the unloading problem is obtained.