One of the experimental techniques for characterising materials under the effect of high strain rates is the split Hopkinson pressure bar (SHPB) test. This week a brief introduction to the basics of this technique is covered.
If you have an engineering background, it is likely that you have come across one of the most famous testing methods for characterising materials: the tensile/compression test. In that case, a sample is usually subjected to a controlled displacement (usually in mm/min). The result is the force-displacement curve and from those results and the geometry of the sample, the determination of the stress-strain curve for the material is pretty straight forward. Despite the fact that this test can be performed for a different range of speeds, these velocities are normally quite low. In these terms, there are many cases where engineers are interested in the stress-strain curve for dynamic cases, since some materials can exhibit different behaviour depending on the strain rate (e.g. crushing of an automotive component). For that reason, in order to obtain the desired characteristic curve, other methods have to be used, such as the split Hopkinson pressure bar test.
One of the most interesting things about the SHPB test is that there is no official standard to follow. However, there are some common features with regards to the necessary equipment. In these terms, every Hopkinson bar test should have:
- Two cylindrical long bars. Their length has to be big enough in order to obtain one-dimensional wave propagation. They are called incident and transmitted bar, respectively.
- Fixtures to ensure that the bars are perfectly aligned and that they can freely move after an impact occurs.
- Gas gun. This device is the launches a striker bar which impacts the incident bar. Hence, a controlled compressive pulse is achieved.
- Two sets of strain gages. Each set should be placed in the middle of both the incident and transmitted bars.
- Equipment for data acquisition (e.g. amplifiers, oscilloscopes…).
In this test, the sample is placed in between the two long bars. Then the gas gun launches the striker, which impacts the incident bar. This generates a compressive wave that travels through that bar until it reaches the end of the bar. Hence, part of the signal is reflected as a tensile wave in the interface between the incident bar and the sample. In addition, the rest of the signal keeps travelling as a compressive wave through the transmitted bar. Typical results of the SHPB test are illustrated in Figure 2.
Apart from that, it is remarkable that the same material is used for all the bars (i.e. incident, transmitted and striker bars). Different materials can be used, depending on the material that you are trying to characterise. For instance, two of the most common materials used for the bars are maraging steel and magnesium.
Furthermore, preliminary calculations can be done in order to have an idea of the values which should be obtained. Besides, it is important to state that the results are recorded in volts, so in order to post-process them, some transformations have to be applied to the experimental data in order to get strain-time results. Then, more expressions can be applied to those strain signals so that the stress-strain curve can be determined. Those expressions are well known and they can be easily found in most of the publications about the SHPB test.
Since there is no standard, in order to design the test for specific conditions, some recommendations can be found in references  and . Those suggestions allow the engineer to define the length of the striker bar, specimen dimensions and the impact velocity for a certain strain rate.
Finally, I would like to highlight the fact that another phenomenon is always observed in the results of this tests: dispersion. A rough definition could be the oscillations that are observed in the signals. If you read about the topic you will probably find that this effect is usually mentioned but almost none of the authors correct it. There are two typical approaches to try to correct the dispersion in the SHPB test: the use of a pulse shaper and an analytical correction. The first one refers to a small cylindrical pad that can be placed at the beginning of the incident bar, so that the striker impacts that pad instead of the long bar. The second one is based on the method which was introduced by Follansbee and Frantz . Although those authors expressed that the dispersion effect could be corrected following three apparently simple steps (based on the Fourier Transform), in reality some issues arise when trying to apply their method. In particular, some of the parameters which are required for that correction are not clear enough. In fact, some authors mention this methodology in their publications but they do not apply it correctly: they just identify a value in the frequency domain that they consider to be high and then they apply a filter to remove data. Since that approach is just destroying data, as part of a research project, I managed to develop a numerical routine in order to apply a correction to the strain signals following the Follansbee and Frantz approach, using additional information from Bancroft’s research .
I hope you have found this information useful and if you have any questions about the physics or the post-processing of the results (including the dispersion correction), please feel free to contact me.
 Gray, G. T. (2000), “Classic Split-Hopkinson Pressure Bar Testing”, in Kuhn, H. and Medlin, D. (ed.) ASM Handbook Volume 8: Mechanical Testing and Evaluation, ASM International, Ohio, pp. 462-474.
 Ramesh, K. T. (2008), “High Strain Rate and Impact Experients”, in Sharpe, W. N. (ed.) Springer Handbook of Experimental Solid Mechanics, Springer Science+Business Media, Boston, pp. 929-959.
 Follansbee, P. S. and Frantz, C. (1983), “Wave propagation in the split Hopkinson pressure bar“, Journal of Engineering Materials and Technology, vol. 105, pp. 61-66.
 Bancroft, D. (1941), “The velocity of Longitudinal Waves in Cylindrical Bars”, Physical Review, vol. 59, pp. 588-593.