The effect of radial inertia on brittle samples during the split Hopkinson pressure bar test

For a valid split Hopkinson pressure bar (SHPB) or Kolsky compression bar experiment, the sample should be in dynamic stress equilibrium over most of the test duration. In this study, we investigate the effect of radial inertia on elastic samples during a valid SHPB test. We present closed-form equations for the three additional stress components induced by radial inertia for incompressible and compressible, linear elastic samples. These equations should assist in the early experimental designs. As the experiments proceed and more is learned about the sample response, numerical analysis can be used to obtain a more refined account of the sample response and dynamic material strength.