PSI - Issue 42

Sebastian Henschel et al. / Procedia Structural Integrity 42 (2022) 110–117

116

S. Henschel and L. Kru¨ger / Procedia Structural Integrity 00 (2019) 000–000

7

beginning and the end of the measurement were observed. This was explained by a small superposition of incident and reflected pulses at the site of measurement. Consequently, it is also possible to omit the test without specimen with respect to the calibration. The calibration factors can be directly derived from the actual test by following the procedure shown in Fig. 5 since the calibration is independent of the actual pulse shapes. The engineering strain in the specimen can be directly evaluated from the optical measurement of u 1 and u 2 : ε = ( u 1 , OE − u 2 , OE ) / h 0 . This is most advantageous at small strains. Although pulse shaping is a technique to analyze these small strains Chen et al. (2003), a combination of a long incident pulse and an additional pulse shaping can cause a superposition of incident and reflected pulses. However, this superposition does not a ff ect the exact measurement of u 1 , OE and u 2 , OE , see Fig. 6b. Hence, the stress / strain relationship can be accurately measured at small strains even for relatively long incident pulses. The proposed calibration method was compared with the conventional ‘bars apart’ calibration of the incident bar, see Tab. 1. It was observed, that the measured ε I , max was slightly higher than the calculated value. This was attributed to the further acceleration of the striker bar during the velocity measurement. The light barriers used in the test setup have a distance of 100 mm. Furthermore, there is a distance of 150 mm between the second light barrier and the point of impact. The striker will be further accelerated along these distances. Hence, the actual impact velocity is assumed to be higher than the measured velocity. Consequently, the measurement of the actual displacements and their use for the calibration of the bar instrumenta tion is advantageous over the the conventional ‘bars apart’ calibration. This is especially true if v S is not measured in the vicinity of the striker impact. The accuracy of the proposed method is determined by the accuracy of the optical displacement measurement. The calibration within the exten someter is given by the objective lens. Hence, the accuracy is determined by the correct angle (90 ◦ ) between the bar axis and the extensometer axis. The accuracy can be checked by inserting blocks of defined thickness, i.e. gauge blocks, between the incident and the transmitted bars. When applying Eqs. 10 and 11, it is observed that the knowledge of the wave speed c is actually not required. It is also possible to incorporate c into the calibration factors K 1 and K 2 . Hence, K 1 and K 2 would be much larger and would have the unit m / Vs. In contrast, the calibration method ’bars apart’ for both the incident and the transmitted bars depends on the exact knowledge of c . The proposed method was evaluated for compressive loading. In other types of split Hopkinson pressure bars, e.g. for tensile or fracture mechanics loading, the mechanisms of wave propagation and the concepts of calculating forces and displacements are the same. Consequently, as long as the displacements u 1 and u 2 can be measured optically, the calibration of the bar instrumentation is possible. In the present paper, a new method for the dynamic calibration of the instrumentation of a split Hopkinson pressure bar is proposed. The new method is purely based on displacement measurements at the interfaces between bars and specimen. To this end, the calculated displacements (from bar instrumentation) are compared to the optically mea sured displacement of these interfaces. Hence, the actual loading of the specimen is taken into account. It is shown by a combined experimental and theoretical approach that assumptions on pulse transmission can be avoided. Especially, assumptions on momentum conservation are not necessary. Dispersion correction is not necessary during dynamic calibration. Furthermore, modifications of the SHPB setup for calibration purposes are omitted. Consequently, unde sirable e ff ects of calibration changes, e.g. due to damage of the instrumentation, can be detected during tests with a specimen. The di ff erences and benefits of the new method are summarized in Tab. 2. Furthermore, independent of a superposition of incident and reflected pulses, the strain in the specimen can be evaluated from the very beginning of the loading by using the optical extensometer. Table 1. Comparison of calculated and mea sured maximum incident pulse strains, and relative di ff erences. The calculated strain was derived from Eq. 4. The measured strain was obtained after calibration with Eq. 10. ε I , max v 0 calc. meas. rel. di ff . m / s % % % 7.0 0.072 0.073 1.4 8.7 0.090 0.092 2.2 8.8 0.090 0.093 3.2 11.5 0.118 0.121 2.5 5. Conclusions