PSI - Issue 75

Lewis Milne et al. / Procedia Structural Integrity 75 (2025) 419–425

422

4

L.Milne et al. / Structural Integrity Procedia 00 (2025) 000–000

900

c

800

a

700

b

600

strain rate [%/s] velocity [mm/s] displacement [mm] strain [%]

500

0.2m/s 2m/s 6m/s 18m/s

400

300

Stress (MPa)

200

100

0

-0.02 0.02 0.06 0.1 0.14 0.18 0.22 0.26 0.3 0.34 0.38

-100

Strain (Dimensionless)

900

y = 34.216x+ 611.29 R² = 2E-05

y = -273843x 4 + 197677x 3 - 51388x 2 + 5288.2x+ 487.25 R² = 0.9149

800

700

d

600

σ uts = 673.1 MPa

500

data yield

σ pl = 611.3 MPa

400

plas�c elas�c

300 Stress (MPa)

σ min = 491.1 MPa

Linear (yield) Poly. (plas�c) Linear (elas�c)

200

y = 712569x- 24.743 R² = 0.9722

100

0

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-100

Strain (Dimensionless)

Fig. 2. DIC analysis of a specimen and experimental data: a) location of probes and corresponding virtual extensometer of length 20mm; b) obtained experimental data at 0.2 m / s – plots from top to bottom – strain [%], displacement [mm], strain rate [% / s] and velocity [mm / s]; c) stress-strain curves for S355JR from high strain rate testing; d) curve smoothing approach demonstrated on an S355JR sample at 6 m / s.

measured relative to a facet point component defined at the grips of the specimen, where any deformation would be negligible. At each probe point, the Y-strain [%], Y-strain rate [% / s], Y-displacement [mm] and Y-velocity [mm / s] were evaluated, as shown in Fig. 2b. The specimen was fixed in the bottom end by the stationary grip and pull up by the moving grip. For the extensometer, the length, the % change in length, and the rate of change of length were evaluated. Some issues were encountered with the processing. For specimens tested at the highest strain rate, there was often either motion blur due to the frame rate being low, or a lack of contrast due to the frame rate being too high. Once the DIC strain measurements were obtained, they then had to be aligned with the stress measurements from the load cell. This was challenging, as the sampling rate for each was di ff erent and the exact time of impact could be di ffi cult to determine exactly at the lower test rates. When aligned at initial impact, the stress and strain values had to be on a common time scale to plot them against each other, as stress was recorded at 500 kHz and the DIC was measured at 9-20 kHz. As such, linear interpolation was necessary to estimate the strain values between measurement frames. Linear interpolation would again lead to inaccuracies, however, especially for the faster tests where there are fewer measurement points across the test duration. This resulted in some parameters such as elastic modulus being impossible to accurately determine from the test results. This leaves the strength as the main value that could be extracted, as it was less sensitive to accurate alignment of the data. Then the full stress-strain curve could be plotted with a representative set of the results for S355JR at each test rate shown in Fig. 2c. There is some oscillation observable in the stress-strain curve. These oscillations are caused by longitudinal vibrations and generated from the impact point of the test, thus the magnitude of the vibrations increases with the impact velocity. As such, it can be seen that the impact is negligible at 0.2 m / s, but it dominates the response at 18 m / s, making the extraction of any values challenging. Despite this, a clear increase in both the yield and tensile strength with strain rate can be observed in the results shown in Fig. 2c. To extract useful values from the stress-strain curves, curve smoothing was therefore necessary. To achieve this, the plots were split into 3 regions: (1) the elastic region with the elastic slope as and extracted parameter E ; (2) the yield plateau region with the yield strength σ pl ; (3) the strain hardening region ending with the necking described as UTS. A linear trendline was applied to the elastic and yield regions, and a 4th-order polynomial fit was applied to the plastic region. From this two yield strength values were extracted: σ min , where the plastic region trendline intercepts the elastic region trendline, and σ pl , corresponding to the stress at the plateau. The UTS was also determined as the highest value on the plastic region trendline. This process is shown in in Fig. 2d.