# Drill Hole Orientation: Its Role and Importance on the Compression Response of Pure Magnesium
## 3 Results and Discussions
### Simulation Results
#### 3.1.2 Development of Plastic Zones  
While a pictorial representation of the shear stress region provides valuable insight into the ideal drill hole orientation in compression, a quantitative representation can be obtained by studying the development of plastic zones within the sample. The development of this plastic zone is, in turn, crucial to the deformation behaviour, as well as the load-bearing capacity of a sample. In general, the presence of a drill hole is expected to act as a precursor for the weakening of the structure and the plastic zone is expected to first develop around these drill holes as they represent regions of stress concentrations. However, [PERSON] et al. [36] showed that the size of the hole dictates the load-bearing capacity analogous to how the size, radius, and position of a crack determines the time to failure in components. Hence, to make a comparison of load-bearing capacities between the three orientations, the plastic zone volumes were evaluated at 9000 N, a load that is halfway between elastic zone and load at failure (as detailed in Section 2.1.1). At this load, the true strain in monolithic magnesium was found to be around 9% and hence, plastic zone volumes above 9% strain were compared and the same is presented in Table 1.  
Figure 5: Maximum shear stress plots at 9000 N for (**A**) vertical drill hole orientation, (**B1,B2**) angular drill hole orientation and (**C1,C2,C3**) horizontal drill hole orientation. Initial impressions from Table 1 are that both angular and horizontal drill hole orientations experience significantly larger plastic zone volumes above the critical strain of 9% when compared to the monolithic and vertically drilled hole. This was evident even in the shear stress plots in the earlier section. The vertical drill hole orientation observes a larger plastic zone volume above 9% strain when compared to monolithic condition while having a lower total volume as the drill hole, by itself, introduces a stress concentration and the area around the hole, therefore, observes higher stresses and strains which was absent in the monolithic condition. The angular drill hole orientation sees the largest plastic zone volume above this critical strain while having the lowest total volume. So, one may jump to the conclusion that the angular drill hole scenario presents the worst-case scenario as a higher percentage of its volume sees large plastic strains. However, these values do not give a complete picture of the load-bearing capacity of these drill orientations. While visual understanding of plastic zone development is difficult to report with incremental loads, an easier way to quantify and understand this plastic zone development is to measure what part of the volume has exceeded the corresponding strain limit at any given load. To do so, the true strains in the monolithic magnesium sample were evaluated at loads of 1500 N increments and the plastic zone volume above these strains for each drill hole orientation were arrived at before comparison. Using this method, the development of plastic zone volume is presented in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Drill Hole Orientation** & **Plastic Zone Volume above 9\% Strain** & **Total Volume** \\ \hline No Drill (Monolithic) & 58.80 mm\({}^{3}\) & 402 mm\({}^{3}\) \\ \hline Vertical Drill & 68.47 mm\({}^{3}\) & 388 mm\({}^{3}\) \\ \hline Angular Drill & 107.29 mm\({}^{3}\) & 384 mm\({}^{3}\) \\ \hline Horizontal Drill & 102.60 mm\({}^{3}\) & 388 mm\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Plastic zone volume above 9% strain observed at various drill hole orientations. Figure 6: Development of plastic zone volume with increasing load for different drill hole orientations.