NUMERICAL PREDICTION OF THE PROPAGATION OF ELASTIC-WAVES IN LONGITUDINALLY IMPACTED RODS - APPLICATIONS TO HOPKINSON TESTING

Simple expressions, based on one-dimensional elastic wave theory, are established which permit prediction of normal force and particle veloc ity at cross-sections of a non-uniform linearly-elastic rod. The initi al normal force and particle velocity at each cross-section of that ro d must be known. In order to assess the validity of the assumptions, a n experimental test on a cone-shaped rod is performed. Numerical resul ts 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 expre ssions are so easy to program that a common spreadsheet program is suf ficient to implement and perform the calculation. They enable the infl uence of an impedance variation to be quantified a priori. In the case of the Hopkinson three-point bend test, the wave distortion is not ve ry 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 n ot available when the temperature is too high. Some effects of an idea lized quasi-static specimen for both Hopkinson three-point bend and no n-uniform temperature are included.