PSI - Issue 42

Sebastian Henschel et al. / Procedia Structural Integrity 42 (2022) 110–117 S. Henschel and L. Kru¨ger / Procedia Structural Integrity 00 (2019) 000–000

115

6

0.5 1.5 Measured displ. u OE / mm 1.0

0.5 1.5 Measured displ. u OE / mm 1.0

v 0 = 7.0 m/s PS: Cu ∅ 5x1.0

v 0 = 8.7 m/s PS: none

-1

-1

K 2 = 1.34 V

K 2 = 1.34 V

-1

-1

K 1 = 1.04 V

K 1 = 1.04 V

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0

c U SG dt / Vmm

(b)

(a)

c U SG dt / Vmm

Fig. 5. Calibration with Eqs. 10 and 11. (a) Test in Fig. 4a, (b) Test in Fig. 4b.

6

3

3

v 0 = 11.5 m/s PS: Cu ∅ 5x0.5

u 1,OE u 2,OE u 1,SG u 2,SG G42CrMo4+QT

4

2

TB

Displacement u OE / mm 0 1 2

IB

2

1

u 2,OE

u 1,OE

0

0

Bar signal U / V

-200 0 200 400 -2 G42CrMo4+QT

Displacement / mm

-1

0

100 200 300 400

(a)

(b)

Time / µs

Time / µs

Fig. 6. Measured and calculated signals (with specimen): (a) incident, reflected and transmitted pulses; measured displacements at positions 1 and 2. (b) Comparison of measured and calculated displacements after dynamic calibration.

the bars, this rectangular pulse was also measured in the transmitted bar. High-frequency oscillations were attributed to wave dispersion. As a consequence of the rectangular shape of the pulse, the displacements u 1 and u 2 had a constant slope. Di ff erences between u 1 and u 2 were attributed to elastic deformations between the black-and-white edges at the incident and transmitted bars. The incident and transmitted pulses in Fig. 4b are very smooth without any high-frequency oscillations. This is explained by the damping e ff ect of the pulse shaper acting analogously to a low-pass filter. Since the pulses are nearly shaped like a half sine, the displacements exhibit no constant slope. The measured displacements in Fig. 4 were compared with the displacements calculated from the bar signals. Hence, the calibration factors K 1 and K 2 of the incident and transmitted bars were obtained by applying Eqs. 10 and 11, respectively. The results are given in Fig. 5. It was observed, that the calibration was not a ff ected by the shape of the incident and transmitted pulses. In both cases, a linear relationship between calculated and measured displacements was found. Hence, the incident pulse used for calibration does not necessarily need to exhibit a plateau region. Furthermore, the instrumentation of the transmitted bar was calibrated within the same test. There is no need to separately perform the two calibrations ‘bars apart’ and ‘bars together’. The range of calibration was a ff ected by the maximum displacement achieved during the test. The maximum displacement in a test without a specimen does only depend on the striker length and velocity. The calibration obtained from the above-described results was checked in tests with a specimen. The incident, reflected and transmitted pulses as well as the measured displacements at the positions 1 and 2 are shown in Fig. 6a. As expected, the transmitted pulse is proportional to the stress-time-relationship of this dynamic compression test. Furthermore, a reflected pulse is generated since the specimen has a much lower impedance than the incident bar. In Fig. 6b, the calculated displacements are additionally plotted. It was observed, that displacements derived from the calibrated bar signals ( u SG ) match the optically measured displacements ( u OE ) very well. Only small deviations at the