## 3 Results and Discussion
Additionally, the treatment with the lowest least square means (LSM) was the sample 4_50_1, which, in combination with the almost inexistent higher break cycle levels (Figure 4), leads to the conclusion that it was the most vulnerable to premature rupture and had the poorest resistance to stress. These observations are mostly caused by the improving effect of the MMT addition on the structure and tensile properties of starch films at these levels of incorporation [34; 37]. Also, the high glycerol content (%wt) based on dry starch weakens tensile properties through a reduction in intramolecular forces inside the amylose matrix induced by glycerol, which acts as a secondary plasticizer, leading to lower tensile strength, eventually [34; 38]. Additionally, the very low starch concentration of this treatment reflects a weak amylose matrix, which, of course, has an impact on a film's integrity and stiffness, as has also been observed in the literature [39]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Sample ID** & & & **LSM** & **Lower 95\%** & **Upper 95\%** \\ \hline
7\_35\_10.5 & A & & 1.77 & 1.71 & 1.83 \\
7\_35\_1 & B & & 1.62 & 1.54 & 1.69 \\
7\_50\_1 & C & & 1.44 & 1.35 & 1.53 \\
7\_50\_10.5 & & D & 1.24 & 1.16 & 1.32 \\
4\_50\_1 & & D & 1.10 & 1.00 & 1.19 \\ \hline \end{tabular}
\end{table} 
Table 4: [PERSON]’s grouping of sample IDs based on the error mean square of the ANOVA regression model. Samples not sharing the same letter are significantly different. Figure 5: Mean changes and 95% confidence intervals of the log tensile quotient vs. sample ID along with the 5 increasing levels of log exact break time and the 3 increasing levels of break cycle. Error bars denote the 95% confidence intervals and means; those whose intervals do not overlap differ significantly. Finally, an attempt was made to configurate the prediction profile of the most resistant sample (7_35_10.5) according to the log tensile quotient by entering the log exact break time 4.73 and increasing the level of the break cycle from 1 to 6 (Table 5). In general, the decreasing trend of the log tensile quotient, which indicates the mechanical resistance of films, in high log exact break times and break cycles is possibly attributed to the material fatigue effect after cyclic loads at a fixed frequency. This process, which generally comprises two steps, namely, initiation and propagation, involves changes on the microstructural level of the material, such as the generation of microcracks or other inhomogeneities, which occur at very low stress levels and, of course, below the ultimate tensile strength. Subsequently, the evolution and spread of these microflaws in the remaining material through repeated stretch cycles induces the weakening of the integrity and strength of the material and, inevitably, its fracture at low stress levels [40; 41]. Figure 6: Reliability of the regression model (red line \(\pm\) 95% confidence band) explaining total variation. (**a**) Plot of actual vs. predicted values of the log tensile quotient. (**b**) Plot of residuals vs. predicted values of the log tensile quotient. As discussed in the Introduction, data from fatigue tests have been modeled using other methods, such as the reliability testing method or the finite element numerical analysis method. Definitely, these methods analyze events at a microscale level using elaborate approaches, such as continuum damage mechanics, cohesive zone model elements and truss elements [42], and generate valuable data that can correlate microstructures with material behaviors. It should be mentioned, though, that statistical analysis is not necessarily applied to validate the reliability of these complicated models. In this study, we presented a simplistic and readily understandable approach that could be used as a tool to quickly produce information on fatigue behavior related to sample composition and experimental factors without requiring expertise in modeling, specialized software and computing power.