## 3 Results and Discussion
### Stress Results
Furthermore, the trend line for these three materials is very consistent, but stainless steel austenitic AISI 316L (annealed) have surpassed the upper limit of the material yield strength. In Figure 8b, it is evident that the stress experienced by Annealed Steel Austenitic AISI 316L exceeds its material's yield strength. Conversely, the stress in the titanium alloy remains below its material's yield strength. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pitch** & **Simulation** & **10 Thread** & **15 Thread** & **20 Thread** \\ \hline \multirow{3}{*}{0.25 mm} & Stainless steel austenitic AISI 316L (annealed) & 649.4 & 547.1 & 357.0 \\  & Titanium commercial purity Grade 4 (annealed) & 491.6 & 399.4 & 345.5 \\  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 484.5 & 398.0 & 342.6 \\ \hline \multirow{3}{*}{0.30 mm} & Stainless steel austenitic AISI 316L (annealed) & 458.4 & 408.8 & 337.4 \\  & Titanium commercial purity Grade 4 (annealed) & 442.3 & 370.6 & 312.0 \\  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 448.5 & 373.2 & 307.3 \\ \hline \multirow{3}{*}{0.35 mm} & Stainless steel austenitic AISI 316L (annealed) & 414.6 & 378.1 & 309.1 \\  & Titanium commercial purity Grade 4 (annealed) & 390.3 & 363.3 & 296.3 \\  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 390.3 & 363.4 & 295.0 \\ \hline \multirow{3}{*}{0.40 mm} & Stainless steel austenitic AISI 316L (annealed) & 423.8 & 367.8 & 339.40 \\  & Titanium commercial purity Grade 4 (annealed) & 408.6 & 356.0 & 334.60 \\ \cline{1-1}  & Titanium alpha beta alloy Ti-6 Al-4V (annealed) & 409.7 & 360.4 & 333.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Stress simulation results. Figure 7: Graph for stress vs. thread engagement: (a) pitch 0.25 mm; and (b) pitch 0.30 mm. Based on simulations, the finite element analysis (FEA) simulations could consistently highlight the threaded area as the critical point of contact. Maximum stress is consistently localized within this threaded region across all scenarios, underscoring its significance as a focal point for stress concentration. As evident from Table 7 and the trend lines in Figures 7 and 8 illustrating the relationship between tensile stress and thread engagement, a consistent pattern emerges where increased thread engagement correlates with lower stress levels. This trend is attributed to the effective dispersion of stress across a larger area with higher thread engagement, consequently reducing stress concentration in specific regions and lowering the risk of failure. Additionally, the stress pattern observed in the thread of the annealed Stainless Steel Austenitic AISI 316L is particularly noteworthy. In all simulated specimens, the maximum stress in the annealed Stainless Steel Austenitic AISI 316L surpasses its material's yield strength. This finding suggests that the material may not meet the required conditions for the motorized intramedullary leg-lengthening nail. In Figures 9-11, a clear trend emerges where finer pitch threads experience higher stress levels. The finer pitch leads to a decrease in the contact area of the thread, resulting in a smaller area for load concentration, consequently elevating stress within the thread. Stress concentration significantly impacts the reliability and safety of threaded connections, especially when loads are applied to segments with finer contact areas. These concentrated stress points are prone to material deformation, yielding, and in extreme cases, failure. In Figures 9 and 10, the AISI 316L with a pitch of 0.25 mm shows a noticeably higher von Mises stress. This phenomenon is attributed to the reduced contact area resulting from the smaller pitch size and limited thread engagement. Conversely, larger pitch threads offer a key advantage in the form of a broader contact area, facilitating a more even distribution of applied loads across the threads. This broader contact area reduces stress concentrations in the threaded connection, enhancing its robustness and reducing susceptibility to failure due to extreme stress concentrations.