## 3 Results and Discussion
### Quasi-Static Mechanical Properties
For the lamellar type of microstructure shown in Figures 4 and 5, the parameter \(d\) is usually taken as the shortest distance that dislocations have to move before encountering obstacles, which is usually the thickness of the \(\alpha\)-lath in these microstructures. Thus, taking \(K_{hp}\) as 328 \(MPa\mu\)m\({}^{\frac{1}{2}}\) for Ti6 Al4V(ELI) [36], the average thickness of the \(\alpha\)-laths noted in Figures 4 and 5 would contribute a stress of about 207.45 MPa, 133.91 MPa and 109.33 MPa to the yield stress, for samples C, D and E, respectively. These values explain the observations made in Figures 10 and 12. It is worth noting that the studies have shown that there is a limit of grain size for which the Hall-Petch relationship can be used [37]. The literature has shown that when the average grain size of a material decreases to approximately 40 nm, the inelastic deformation mechanisms start to change from dislocation-based to grain-boundary-based deformation. The grain boundary deformation mechanisms include grain boundary sliding and dislocation absorption at grain boundaries, which lead to softening and, thus, decrease in flow stress [38; 39]. The lower yield and flow stress in samples E was also ascribed to the presence of parallel \(\alpha\)-laths, characterised by LAGBs between them as seen in Figure 5f, which could suggest ease of slip transfer between adjacent grains. The strain hardening of the different microstructures of LPBF Ti6 Al4V(ELI) at different quasi-static strain rates is summarised in Figure 13.  
It is noted in Figure 13 that these different microstructures exhibited noticeable strain hardening at different levels of strain rate, for the larger part of the flow stress curve. From the plotted curves in Figure 13, at the initial stage of plastic deformation, the strain hardening rapidly decreased quasi-linearly with the increase in strain, suggesting that the flow stress increased at a decreasing rate as the level of strain rose at this stage. The strain hardening rate was the highest at the stage of initial plastic strain (0-0.04) as a result of initial high density of free dislocations in these microstructures, and hence high rates of accumulation and multiplication within this range of plastic strain. The strain hardening at this stage was also attributed to the interaction of dislocations amongst themselves or with other defects, such as LAGBs and HAGBs described and discussed in Figure 5b,d,f. The decrease in strain hardening rate with increasing strain was ascribed to the formation of dislocation forests and more ordered dislocation substructures as plastic strain increased [40]. The effects of strain rate on strain hardening was significant in samples C as observed in Figure 13a, where the strain hardening was higher at low strain rate and lower as test strain rate increased. However, as seen in Figure 13b,c, the strain hardening curves of samples D and E, respectively, were largely overlapping at the three quasi-static test strain rates. One possible reason for the observation made for samples C was the fine microstructure and extended large network of HAGBs observed in this material in Figure 5b. As the largest portion of the microstructure in samples C was occupied by grains with small areas (\(<\)4.96 \(\upmu\)m\({}^{2}\)), any change in strain rate would cause an instantaneous accumulation of dislocations, increasing the yield stress but at the cost of post-yield strain hardening. After this early stage of strain hardening, as the plastic deformation progresses, the straining hardening effect is seen to continue decreasing, and eventually maintains a relatively steady state in all test samples and at all test strain rates, as observed in Figure 13a-c. The relatively steady state of strain hardening is due to the balance between dislocation accumulation and dislocation annihilation (balance of strain hardening and softening).