Numerical prediction of the propagation of elastic waves in longitudinally impacted rods: Applications to Hopkinson testing

Abstract

Simple expressions, based on one-dimensional elastic wave theory, are established which permit prediction of normal force and particle velocity at cross-sections of a non-uniform linearly-elastic rod. The initial normal force and particle velocity at each cross-section of that rod must be known. In order to assess the validity of the assumptions, an experimental test on a cone-shaped rod is performed. Numerical results are provided for two different configurations: a rod shaped at one end in order to perform the Hopkinson three-point bend test and a rod heated at one end for a high temperature dynamic test. The given expressions are so easy to program that a common spreadsheet program is sufficient to implement and perform the calculation. They enable the influence of an impedance variation to be quantified a priori. In the case of the Hopkinson three-point bend test, the wave distortion is not very important if the rise time is long and the length of the shaped end is short. For a heated rod, the conventional Hopkinson treatment is not available when the temperature is too high. Some effects of an idealized quasi-static specimen for both Hopkinson three-point bend and non-uniform temperature are included.