## 4 Discussion  
The main question addressed in this study is whether DEFORM-3D simulation based on constitutive parameters derived experimentally from low strain rate uniaxial compression testing can be used to generate accurate flow stress data for high strain rate test conditions. In this study, we show that DEFORM-3D uniaxial compression simulation can be used to determine the flow stress that is comparable with what is obtainable experimentally, even at very high strain rates that are difficult to test in the laboratory. The findings from this work are situated within the context of the challenges associated with conducting high strain rate uniaxial compression testing in the laboratory. There is currently no single piece of equipment that can be used to carry out compression testing over a wide range of strain rates that represent industrial hot working processes. Table 4 shows typical strain rates for different metalworking processes, which are between 0.0001/s for sheet forming and 1,000,000/s for high-speed machining. The screw-driven and servo-hydraulic systems have a limit of 5 to 200/s [12; 13], which is far below the upper limit of 1000/s used in forging and rolling operations. The alternative, the SHPB, cannot be used at strain rates below 100/s [12; 13]. Most hot-working laboratories are equipped with either screw-driven or servo-hydraulic systems, while few laboratories have an SHPB machine. Consequently, most studies on hot compression testing used a maximum strain rate of 10/s. In studies where a strain rate above 10/s was used, the results were not easily reproducible, and a great deal of time and resources went into conducting these experiments. Depending on the machine used, numerous parametric adjustments must be made based on trial and error to achieve the desired strain rates. This makes it difficult to have a general overview of the response of both commercial-grade and emerging metallic alloys over a wide range of imposed strain rates that cut across different industrial working processes. In this study, we showed that established constitutive parameters from lower strain rate (0.1 to 10/s) uniaxial compression testing of three types of titanium alloys (one commercial-grade, Ti-6 Al-4V, and two experimental grades, Ti-4.5 Al-1V-3 Fe and Ti-6 Al-1V-3 Fe, alloys) could be used to predict their flow stress at strain rates up to 1000/s. First, we established from Figures 2 and 3 that when the low strain rate constitutive parameters were used as input codes in DEFORM-3D for uniaxial compression test simulation, the peak flow stress values were comparable with the experimentally derived peak stress. Previous authors reported similar results [24; 25; 26], where the flow stress obtained at low strain rates from DEFORM-3D simulations matched the experimental values. The largest difference in the peak stress values was observed at the highest strain rate of 10/s, but this was expected since simulations may not fully represent all the experimental conditions that influence the results. For example, in this study, the friction coefficient was kept constant at 0.3, but under experimental conditions, it changes with temperature, strain, and strain rate [27; 28]. Hence, slight deviations are expected between the experimentally determined \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Strain Rate** **(I/s)**} & \multirow{2}{*}{**Ln Strain Rate** **(I/s)**} & **Simulated Peak** **Stress** & **Experimental** **Stress** * & **Difference** **(\%)** \\ \cline{3-5}  & & **900 \({}^{\circ}\)C** & **900 \({}^{\circ}\)C** & **(\%)** \\ \hline
0.1 & \(-2.302585\) & 89.8 & 88 & 2.05 \\ \hline
1 & 0 & 137.1 & 138 & 0.65 \\ \hline
10 & 2.3025851 & 196 & 243 & 19.3 \\ \hline
20 & 2.9957323 & 217.6 & 247.8 & 12.2 \\ \hline
50 & 3.9120230 & 246.3 & 262.7 & 6.2 \\ \hline
100 & 4.6051702 & 293.3 & - & - \\ \hline
1000 & 6.9077553 & 351.8 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Peak flow stress obtained under DEFORM-3D simulation and the Gleeble experiment for Ti-6 Al-4V.