## 3 Results and Discussion
### Quasi-Static Mechanical Properties  
Figure 11 shows the measured stress-strain curves of the three microstructures of LPBF Ti6 Al4V(ELI) at various levels of quasi-static strain rate and at ambient temperature. The values of yield stress (YS) and ultimate compressive stress (UCS) obtained for the three forms of material at each strain rate is summarised in Figure 12. As seen from these figures, the values of yield and flow stresses increased with an increase in strain rate. However, it is interesting to note that in Figure 11a the effect of strain rate on yield and flow stress was more significant in samples C as compared with samples D and E, especially between the curves for the tests conducted at strain rates of 0.001 s\({}^{-1}\) and 0.005 s\({}^{-1}\). One possible reason for this observation is the fine microstructure of samples C reported in Figures 4a and 5a. The fine grain sizes in this form of the alloy would lead to a decrease in the distance in which mobile dislocations have to travel before encountering serious obstacles, thereby enhancing the strain sensitivity of the materials. Figure 10: Typical values of the global Schmid factor for pyramidal <\(\infty\)> slip systems of the \(\alpha\)-phase for the load applied along the build orientation in samples (**a**) C, (**b**) D and (**c**) E, while (**d**) shows the statistical distribution of the values obtained in each form of material. Figure 11: The stress–strain curves of samples (**a**) C, (**b**) D and (**c**) E at various strain rates, while (**d**), (**e**) and (**f**) show the comparison of the flow stress curves of these different samples at strain rates of 0.1 s\({}^{-1}\), 0.005 s\({}^{-1}\) and 0.001 s\({}^{-1}\), respectively. Figure 12: Comparison of (**a**) the yield and (**b**) ultimate compressive stress of various forms of LPBF Ti6 Al4V(ELI) at different levels of strain rate. In other words, dislocations in fine \(\alpha\)-laths encounter obstacles such as the grain boundaries and local misorientations observed in Figure 5, generally after travelling only a short distance. This increases the chances of a material to encounter a serious pile-up of dislocation and a consequently high increase in strength as the strain rate increases. At the same strain rate, the difference in flow stress curves among these different samples seen in Figure 11d-f, and the values of obtained yield and ultimate compressive stresses presented in Figure 12 are considered to be significant. The order of the strength of the material from the highest to the lowest is seen to be in samples C, D and E. This variation in the flow stress curves of these various forms of LPBF Ti6 Al4V(ELI) was ascribed to differences in microstructure and microtexture among these samples. The microstructure of samples C presented in Figures 4 and 5 consisted of fine lamellar microstructure with the average thickness of \(\alpha\)-laths being 2.5 \(\upmu\)m. These \(\alpha\)-grains are also randomly oriented as discussed in Figure 5, which hinders slip transfer between neighbouring grains during plastic deformation. Moreso, the microstructure of samples group C largely consisted of \(\alpha\)-lath grains, each with an area less than 5 \(\upmu\)m\({}^{2}\). The small grains are associated with large networks of grain boundaries as seen in Figure 5b, which are barriers to dislocation motion, thus increasing the strength of the materials. The grain boundary strengthening (\(\sigma_{d}\)) is usually described in terms of the well-known Hall-Petch relationship, which is of the form \(\sigma_{d}=K_{hp}d^{-\frac{1}{2}}\)[35]. The symbol \(K_{hp}\) denotes the Hall-Petch constant, which is a material constant that arises due to stress concentration against grain boundaries emanating from accumulation of dislocations. When enough stress is generated against such grain boundaries, dislocation sources are activated in the adjacent grains.