Dynamic Flexural Buckling of Rods Within an Axial Plastic Compression Wave

Rods impacting a rigid target at velocities sufficient to produce several percent axial strain are found to buckle plastically with a fairly reproducible wavelength. This phenomenon is investigated for materials which exhibit strain-hardening, a property which is crucial to the theory. The buckling motion is treated as a perturbation of the motion associated with the axial compression. It is assumed that the axial strain rate dominates the extensional strain rate due to bending, so that no strain-rate reversal occurs until after the buckling is well developed. Elastic deformations are neglected, and the material is taken to follow a linear strain-hardening law. It is found that the predicted wavelength and buckling time are in reasonable agreement with experimental results.