## 3 Results and Discussion  
The new methodology was used to predict screw self-loosening under external cyclic loading for the dental implant under study, and the experimental tests were carried out to support the simplified \begin{table}
\begin{tabular}{c c c c} \hline \hline
**T1 6A1 4V ELI (TI GR5)** & \multicolumn{2}{c}{**TI CP4**} \\ \hline
**Composition** & **Wt.\%** & **Composition** & **Wt.\%** \\ \hline Al & 5.5–6.5 & N(max) & 0.05 \\ V & 3.5–4.5 & C(max) & 0.08 \\ Fe(max) & 0.25 & Fe(max) & 0.5 \\ O(max) & 0.13 & O(max) & 0.4 \\ C(max) & 0.08 & H(max) & 0.0125 \\ N(max) & 0.05 & - & - \\ H(max) & 0.012 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical composition of materials used in implant and prosthetic component manufacturing process. Figure 8: (a) Boundary conditions of the finite element (FE) model of the dental implant under study; (b) mesh. model and verify the results. Thus, the critical external load \(F_{crit}\) for which screw self-loosening occurs was evaluated following the methodology in Figure 3: an external load \(F\) was applied in the FE model, from this analysis \(F_{a}\) and \(F_{e}\) force reactions were obtained in the screw head and using the developed Equation (8) \(T_{L}\) loosening torque value was achieved. The procedure was repeated iteratively by increasing the value of \(F\) until \(T_{L}\) falls to zero. As mentioned, three different tightening torques (10, 15 and 20 Ncm) were studied, and the obtained \(F_{crit}\), \(F_{a}\) and \(F_{e}\) values for which self-loosening occur are shown in Table 2.  
Then, the next step was to experimentally verify the values of the theoretically evaluated external forces \(F_{crit}\) that cause self-loosening for the three initial tightening torques. The mean values of \(T_{Li}\) obtained from measurements were 7.45, 11.6 and 16.0 Ncm with standard deviations of 0.4, 0.5 and 0.6 Ncm for the 10, 15 and 20 Ncm tightening torques, respectively. Figure 9 shows the scatter in untightening torques measured for each tightening torque. Then, 1000 cycles were applied in the experiment using the external loads close to the theoretical values \(F_{crit}\) shown in Table 2. At the end of the 1000 cycles, \(T_{Lf}\) was measured and compared with \(T_{Li}\) through the 2\(\sigma\) criterion mentioned. Figure 10 shows the experimental results: tests where self-loosening occurred are marked with an 'x' symbol, while 'o' marks the tests with no loosening. Following the staircase method, the external load to cause self-loosening in the experimental setup (\(F_{exp}\)) is calculated as the average of the values indicated with black markers in Figure 10 while the grey markers are discarded. Table 3 summarizes the values of \(F_{exp}\), their corresponding standard deviations \(\sigma_{exp}\) and the difference between the experimental (\(F_{exp}\)) and theoretical (\(F_{crit}\)) results. Furthermore, it has been appreciated that in the case under study, the presented methodology shows a constant relation between the external load at which self-loosening occurs and the tightening torque \(\frac{F_{crit}}{T_{T}}\) as it can be deducted from Table 2. Experimental results were used to validate this statement, calculating the parameter \(\frac{F}{T_{T}}\) for all the tests performed. Figure 10 shows not only the external load at which self-loosening occurred in each experimental test (primary axis) but also the parameter \(\frac{F}{T_{T}}\) calculated for each test (secondary axis). All the experimental results, except the ones discarded \begin{table}
\begin{tabular}{c c c c} \hline \hline \(T_{T}\) (Ncm) & \(F_{crit}\) (N) & \(F_{a}\) (N) & \(F_{e}\) (N) \\ \hline
10 & 64.5 & 217.7 & 36.1 \\
15 & 96.7 & 326.1 & 53.7 \\
20 & 128.3 & 433.9 & 72.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated load values that cause self-loosening in the dental implant under study using the methodology. Figure 9: Box and whisker plot of all untightening operations performed before cyclic loading.