## 3 Results
### High Strain Rate Behaviour of Various Forms of DMLS Ti6 Al4V(ELI) Alloy
#### 3.3.2 Strain Rate Sensitivity
In fact, for \(\alpha\)-lathes with small thicknesses, it means that dislocations inside them move a shorter distance before encountering obstacles (grain boundaries), thus increasing the material's potential of encountering serious dislocation pile ups and hence a higher value of the parameter \(m\). It is important to note here that a high strain rate sensitivity index could mean that the material exhibits a dramatic increase in strength with increase in strain rate, which is consistent with the results presented in Figures 7-9. The calculated values of the strain rate sensitivity index \(m\) shown in Table 4 and Figure 11d do not follow the analogy of grain size described in the preceding paragraph, namely that the strain rate sensitivity increases with decrease in grain size. At any given temperature, samples D (average lathes thickness 6 \(\upmu\)m) have the highest strain rate parameter, showing the material to be more sensitive to high strain rate and temperature than the other two types of samples. On the other hand, samples C (average lathes thickness of 2.5 \(\upmu\)m) show the lowest response to high strain rate and temperature depicted by a lower value of \(m\). Samples E with the largest average \(\alpha\)-thickness have higher values of \(m\) at all temperatures and strain rates than samples C, but lower than those of samples D.  
A previous study by [PERSON] et al. [37] attributed opposite/reverse grain size dependence on strain rate sensitivity of copper at high strain rate because of a change in deformation mechanisms from obstacle-controlled plasticity to a combination of obstacle and dislocation drag controlled plasticity. A similar case was reported elsewhere in Lesuer [38] for close packed structures. At high strain rates the interactions of mobile dislocations with phonons and electrons slow down the motion of dislocations and therefore more force is \begin{table}
\begin{tabular}{c c c c c c} \hline
**Test Temperature** & **25 \({}^{\circ}\)C** & \multicolumn{2}{c}{**200 \({}^{\circ}\)C**} & \multicolumn{2}{c}{**500 \({}^{\circ}\)C**} \\ \hline
**Alloy** & \(m\) & \(R^{2}\) & \(m\) & \(R^{2}\) & \(m\) & \(R^{2}\) \\ \hline C & 0.21 & 0.94 & 0.22 & 0.85 & 0.26 & 0.89 \\ D & 0.22 & 0.96 & 0.30 & 0.97 & 0.34 & 0.85 \\ E & 0.21 & 0.89 & 0.28 & 0.97 & 0.32 & 0.99 \\ \hline \end{tabular}
\end{table} 
Table 4: Correlation coefficient (\(R^{2}\)) of the log-log plots of true stress and strain rate, and strain rate sensitivity (\(m\)) for samples C, D and E at various test temperatures. required to deform the material. Generally, a shock wave acting on a material crystal lattice generates mechanical waves within the crystal structure. The unit of vibrational energy that arises from oscillating atoms within the crystal is referred to as a phonon. The Orowan relation [39] can be used to derive pure drag plasticity for a material, from the relationship of the strain rate (\(\dot{e}\)), mobile dislocation density (\(\rho_{m}\)) and velocity of dislocations (\(v\)) as:  
\[\dot{e}=\frac{vb\rho_{m}}{M} \tag{5}\]  
where \(M\) is the Taylor factor. The average dislocation velocity as described in Frost and Ashby [40] can be expressed as:  
\[v=\frac{\sigma_{drag}b}{M\mu_{d}} \tag{6}\]  
where \(\sigma_{drag}\), \(b\) and \(\mu_{d}\) are the viscous drag flow stress due to the dislocation drag effect, Burgers vector and drag coefficient, respectively. Dislocation density can be assumed to be proportional to the reciprocal of the grain size (\(d\)) (taking this as represented by the lathe thickness in the case of DMLS Ti6 Al4V(ELI)). Furthermore, the mobile dislocation density is part of the total dislocation density, and the scale factor or this proportionality can be assumed constant for the three material variants C, D and E. With these assumptions, Equations (5) and (6) can be combined to give:  
\[\sigma_{drag}=\frac{\dot{e}\mu_{d}M^{2}d}{b^{2}} \tag{7}\]  
For polycrystals, the Taylor factor, \(M\) varies from grain to grain due to their differences in texture with reference to the loading axis.