## 3 Results  
### Identification of Strain-Rate-Dependant Flow Curves  
Frequently, Equation (1) is used to calculate a nominal strain rate based on the nominal traverse velocity set in a high-speed tensile test. This is a simple approach in order to provide a good approximation of the mean strain rate during a significant part of the test, specifically for the plastic deformation of the specimen until the onset of localization. However, it is obvious that the velocity of the traverse during the test is subject to the control of the machine and, consequently, the actual strain rate can vary during the test due to inaccuracies in this control. In order to determine the actual strain rate, the displacement of the traverse was recorded and the time derivative was calculated in order to obtain the traverse velocity, which was in turn referred to the measurement length according to Equation (1). Figure 6 presents the actual course of the strain rates as a function of the elongation for all test speeds considered in this study. It can be seen that the strain rate at the start of the test is significantly below the nominal value. Furthermore, there is a transient phenomenon at the start, which can probably be attributed to the measurement technique. As the test progresses, the strain rate in the specimen approaches the respective target value and remains at a relatively constant level. Finally, at the end of the test, the curve rises again and reaches values that are significantly higher than the nominal strain rate. This is probably due to the localization of the strain and the initiation of fracture. Based on this typical course or the curves, an average value of the strain rate for the entire test was identified and is indicated in Figure 7 as the actual value. The deviation of the nominal and the actual strain rate values varies from 10% to 20% in the range of strain rates considered here. It is important to consider this deviation when attributing the flow curves measured during the high-speed tensile test to a specific strain rate. Figure 8 exemplarily shows the yield curves obtained from the three experiments performed at an actual strain rate of 0.08/s (i.e., a nominal strain rate of 0.1/s) as well as the mean values from these measurements. Based on this, a flow curve approximation according to Swift/Hockett-Sherby was calculated (see Equation (3)) and extrapolated up to a degree of deformation of 1.0. \[\sigma_{F}=(1-K_{1})[K_{2}(K_{3}+\varphi)^{K_{4}}]+K_{1}[K_{5}-(K_{5}-K_{6})e^ {-K_{7}\varphi^{K_{6}}}] \tag{3}\]  
Figure 7: Nominal and actual values of the strain rate obtained during the tests for nominal strain rate 0.1/s (**a**), 5/s (**b**), 50/s (**c**), and 200/s (**d**). In Equation (3), \(\sigma_{F}\) is the yield stress and \(\varphi\) is the degree of deformation. An Excel solver was used to adjust the function to the measured flow curve and to calculate the parameters \(K_{1}\) to \(K_{8}\). Figure 8 also provides the calculated parameters and the approximated yield curve at an actual strain rate of 0.08/s. There is a very good agreement between the calculated and measured values. Here, the curve obtained for an actual strain rate of 0.08/s was taken as the basis for the approximation, which was subsequently approximated according to Equation (4), using conditional coefficients, C\({}_{1}\) and C\({}_{2}\), as well as experimental data for the strain rates studied. The logarithmic dependence on the strain rate and the values of these coefficients for the tested actual strain rates of 4, 60, and 180/s are shown in Figure 9.  
\[\sigma=f(\varphi)=\sigma_{f}\cdot C_{1}+\frac{\sigma_{f,0}}{C_{2}} \tag{4}\]  
Figure 8: The yield curve of the material DC06 for an actual strain rate of 0.08/s. Figure 9: Logarithmic dependency of coefficients C\({}_{1}\) and C\({}_{2}\) on the strain rate.