Development of a Curved Hopkinson Bar for Long Wavelength Impact Events

Abstract

A study of the feasibility of using a curved Hopkinson bar for the measurement of impact load and energy transmission is presented. The length requirements of straight prismatic bars commonly used to measure long wavelength impact events are often prohibitive, and the use of curved bars can result in a significant increase in wavelength capabilities while reducing the overall size of the measurement apparatus. The ABAQUS/Explicit finite element analysis (FEA) program is used to model steel bars of circular cross section bent with various bend radii and at various bend angles ranging from 15 to 180 degrees. A uniform compressive pressure pulse of known amplitude and wavelength is applied to the FEA models and the wave propagation behavior predicted by ABAQUS/Explicit is then compared to the response predicted by the theory of wave propagation in curved bars and experiments performed using curved bars. The numerical results show good agreement with the theoretical and experimental results. Significant distortion of the incident wave as it travels around the bend results in a transmitted pulse that is not characteristic of the input pulse, particularly at larger bend angles and long wavelengths. The energy transmitted around the bend radius contains only a fraction of the initial impact energy due to large reflections that develop at the bend radius, and this loss increases significantly at larger bend angles and smaller bend radii. However, the transmitted energy can be used to predict the incident energy at a variety of bend angles and bend radii. A curved carbon steel Hopkinson bar is fabricated with a bend angle of 180 degrees and instrumented with strain gauges to monitor the wave propagation within the bar at several locations resulting from a compressive impact pulse. The experimental results agree well with the results predicted using explicit dynamic FEA. The results of this study indicate that a curved Hopkinson bar can be used to predict the impact energy applied to the incident end of the bar using the measurement of the energy transmitted around the bend in the bar. The overall length of the curved Hopkinson bar apparatus can be significantly less than a comparable straight bar apparatus.