On the propagation coefficient of longitudinal stress waves in viscoelastic bars

A key stage in both the use of polymer rods in Split Hopkinson Pressure Bar (SHPB) testing and in establishing the material properties of these rods is the experimental determination of the propagation coefficient. An analytical investigation of the experimental arrangements used to ascertain the propagation coefficient is reported. A wave model for longitudinal waves that incorporates both viscoelastic material properties and the effect of lateral motion of the rod is used to provide a closed form solution for the attenuation coefficient and phase velocity of a polymer rod. The load pulse at the end of a bar is approximated for the coaxial impact of two types of striker (steel bearing balls and short viscoelastic rods). The propagation coefficient is then calculated from simulated strain histories along the bar. These calculated propagation coefficients are compared to the closed form solution. This enables the errors associated with different experimental arrangements to be assessed virtually and thereby provides guidance for future experimental programmes. The effects of overlapping waves and signal noise are investigated also. The experimental techniques are validated by the analysis and the importance of lateral inertia on the choice of experimental set-up is highlighted.