## 3 Results
### Experimental Validation of Flow Stress Predicted by DEFORM-3D Simulation  
The flow stress obtained from uniaxial compression testing at high strain rates of 20 to 1000/s at two different temperatures for the three different titanium alloys is shown in Figure 4. As expected in materials with positive strain rate sensitivity, flow stress increased with increasing strain rate and decreasing deformation temperatures [17; 18; 19; 20]. The flow curves show continuous flow softening after the peak stress was attained. This suggests  
Figure 3: Simulated peak stress vs. linear strain rate at 800 and 900 \({}^{\circ}\)C for (**a**) Ti-4.5 Al-1V-3 Fe; (**b**) Ti-6 Al-1V-3 Fe; and (**c**) Ti-6 Al-4V.  
either geometric dynamic recrystallization of elongated grains or deformation-induced defects like cracking as the possible softening mechanism [17; 18; 20]. To confirm this trend, limited experimental uniaxial compression tests were performed at a deformation temperature of 900 \({}^{\circ}\)C and two strain rates (20 and 50/s) on the commercial-grade Ti-6 Al-4V alloy. The corresponding optical micrographs of post-deformed samples were analyzed (Figure 5). The stress-strain curve shows continuous flow softening accompanied by flow oscillation. Flow oscillation is not observed in the DEFORM-3D-generated data in Figure 4, which could be because only the peak stress values were used to determine the simulation's constitutive constants. Should the constants be derived at incremental strain, the oscillations obtained experimentally may have been seen in the simulation results. [PERSON] et al. [24] reported that using constitutive constants obtained at 0.35 strain intervals from a physical model improved the flow stress generated by the FEM. The corresponding optical images (Figure 5b,c) show uniformly refined grains (diameter is \(\sim\)12 \(\upmu\)m) compared with preform microstructures in previous work [17; 20]. The uniformly refined grains confirmed the dynamic recrystallization of the complex initial microstructure, particularly the elongated \(\alpha\)-Ti grains during deformation. These features support the flow oscillations seen at 20 and 50/s, and the absence of deformation-induced defects indicates that the continuous softening was due to geometric dynamic recrystallization of the elongated \(\alpha\)-Ti grains. Extensive details on the microstructural evolution during the deformation of the Ti-6 Al-4V alloy at strain rates of 0.1 to 10/s have been reported previously [20].  
Figure 4: Flow stress obtained from DEFORM-3D simulation at high strain rates for **(a)** Ti-4.5 Al-1V-3 Fe at 800 \({}^{\circ}\)C; **(b)** Ti-4.5 Al-1V-3 Fe at 900 \({}^{\circ}\)C; **(c)** Ti-6 Al-1V-3 Fe at 800 \({}^{\circ}\)C; **(d)** Ti-6 Al-1V-3 Fe at 900 \({}^{\circ}\)C; **(e)** Ti-6 Al-4V at 800 \({}^{\circ}\)C; and **(f)** Ti-6 Al-4V at 900 \({}^{\circ}\)C.  
To validate the simulation results, the peak stress obtained from the Gleeble experiment and that of the DEFORM-3D simulation were compared, and the peak stress values were similar. The difference in the peak flow stress values was 15% for a strain rate of 20/s and 6% for a 50/s strain rate, respectively (Table 3). This difference is lower than the \(\sim\)19% obtained for a much lower strain rate of 10/s. These trends indicate that, in the absence of SHPB, high strain rate uniaxial compression data can be obtained from DEFORM-3D simulation in as much as the constitutive constants have been established from experimental data at lower strain rates.  
Figure 5: (**a**) The uncorrected flow stress of commercial Ti-6 Al-4V obtained from the Gleeble 3500 uniaxial compression experiment and corresponding optical images at (**b**) 20/s; and (**c**) 50/s strain rates.