On the errors associated with the use of large diameter SHPB, correction for radially non-uniform distribution of stress and particle velocity in SHPB testing

Abstract

The large diameter (up to 100 mm) Split Hopkinson Pressure Bar (SHPB) setup is used throughout the world to test large-cell heterogeneous materials, small structures, etc. This paper proposes a correction method to take into account the non-uniform distribution of stress and particle velocity (non-plane wave effect) in large diameter setups, following the theory of wave propagation in an infinite cylindrical elastic or viscoelastic rod. Such a non-plane wave effect depends on the pressure bar diameter and the high-frequency components contained in the signals. This correction procedure can be performed together with the wave dispersion correction, which is already incorporated for many large diameter bars used. For the various metallic and Nylon viscoelastic bars (up to 60 mm diameter) available in our laboratory, the relative difference between the average values of the particle velocity (and stress) in a cross-section and that calculated with a standard one-dimensional analysis is found to be inferior to 5%. However, this difference increases with a higher impact velocity, because signals containing more important high-frequency components are generated by higher impact velocities. In order to find an upper limit of the potential error for bars of various diameters, the theoretical pulse signal for a perfect impact between two infinite cylindrical rods is used, which gives the highest signal spectrum. With this theoretical pulse, such an upper limit of the potential error for different bar diameters (up to 200 mm) is found. It shows that the potential average error can reach up to 12% for a 100-mm-diameter bar currently used in the world.