## 2 Materials and Methods
### High Strain Rate Experimental Test  
The compression split Hopkinson pressure bar (SHPB) test was used in the present research for high strain rate tests. The tests were conducted at the Armaments Corporation of South Africa (ARMSCOR) laboratories in Pretoria. A typical schematic diagram of the SHPB apparatus is shown in Figure 3. The SHPB experimental setup normally consists of a gas gun/cannon, the incident, transmitter, and striker bars as shown in Figure 3. The SHPB test specimen is normally sandwiched between the incident and transmitter bars. During testing, the striker bar is fired from the gas gun/pneumatic launcher and impacts the free end of the incident bar at a high velocity. The impact of the striker bar on the incident bar sends a compressive wave towards the sandwiched specimen. Upon reaching the specimen, the incident wave becomes partially reflected due to impedance mismatch of the bar-sample interface, and partially transmitted to the transmitter bar. The wave reflections occur continuously across the length of the sample until the stress build-up is sufficient to cause plastic strain [30; 31]. The strain in the incident and transmitter bars is measured by the strain gauges that are attached at the mid points of the surface of each bar so that the incident and reflected waves do not overlap [30]. The equations for determining the samples stress (\(\sigma_{s}\)), strain (\(\varepsilon_{s}\)) and strain rate (\(\dot{\varepsilon}_{s}\)) from the wave signal are based on the theory of one-dimensional elastic wave propagation in a cylindrical specimen, and are as follows [29; 31; 30]:  
\[\sigma_{s}=EA_{0}\varepsilon_{t}/A_{s} \tag{1}\]  
\[\varepsilon_{s}=2C_{0}/l_{s}\int_{0}^{t}\varepsilon_{r}dt \tag{2}\]  
\[\dot{\varepsilon_{s}}=2\varepsilon_{r}C_{0}/l_{s} \tag{3}\]  
where the symbols \(A_{0}\), \(A_{s}\), \(l_{s}\), \(C_{0}\) and \(E\) stand for the cross-sectional area of the bars, initial cross section area of the specimen, length of the specimen, bars longitudinal wave velocity and [PERSON]'s modulus of the bars, respectively. It is important to note that \(C_{0}\) is the pressure bars' longitudinal wave velocity, a function of the elastic modulus and density (\(\rho\)) of the material (\(C_{0}=\sqrt{E/\rho}\)). These are input parameters of the SHPB test. In the present study, the incident and transmitter bars used for testing of the Ti6 Al4V(ELI) alloy specimen were made of tool steel and were 2000 mm long with a diameter 20 mm. The striker bar was made of the same material and same diameter as the pressure bars but  
Figure 3: Schematic diagram of the SHPB apparatus in which symbols \(\varepsilon_{i}\), \(\varepsilon_{r}\) and \(\varepsilon_{t}\) denote the incident, reflected and transmitted waves. was 500 mm long. The data acquisition system consisted of strain gauges with a gauge factor of 1.88, calibrated voltage of 1.00 V, an amplifier and a data acquisition card fixed in a computer. Hottinger Baldwin Messtechnik GmbH (HBM) strain gauges were arranged in a full Wheatstone bridge configuration to eliminate the effects of bending and only measured the axial strain. The strain gauges were glued at the centre of the incident and transmitter bars (1000 mm from each end) before being wired to the data acquisition card in the computer. A high-speed camera and velocity sensors were used to measure the velocity of the projectile (striker bar) just before it struck the incident bar. To minimize friction and therefore maintain a uniaxial state of compression, lithium based NLGI 3 grease (Castrol WB) was used to lubricate the interface between the pressure bars and the test specimen. The approach adopted in performing the SHPB high temperature experiments was to heat each test specimen alone in a furnace to the desired temperature, and then bring the bars into contact with the specimen just before impact.