## 3 Results and Analysis
### Fatigue Test
#### 3.3.3 Fatigue Limit Through Infrared Thermography and Volumetric Dissipated Energy
Therefore, these data can be fit to the exponential equation (Equation (1)), considering a dependent variable, the volumetric dissipated energy, and an independent variable, the stress ratio (\(\sigma_{\text{max}}/\sigma_{\text{ut}}\)), in order to obtain faster convergence during the fitting. Table 5 shows the fitting parameter for the volumetric dissipated energy over the stress ratio (\(\sigma_{\text{max}}/\sigma_{\text{ut}}\)), and Figure 9 shows the data with the fitted curves. The data fits well to the three-parameter exponential model for all laminates, having a correlation coefficient over 0.91, which is better than for the thermography data; even the [90\({}^{\circ}\)]\({}_{4}\) laminate shows good fitting. The fatigue limits found are in a wide range (Table 6); although the stress versus number of cycles data fits well to the Weibull equation for unidirectional composites, this fatigue limit value may be overestimated, since there will always be a process of progressive damage at lower repetitive loads, causing there to be no long-term fatigue limit for [0\({}^{\circ}\)]s, which was confirmed by [PERSON] et al. on flax/epoxy composites [2]; furthermore, for the [0/90]s composites, the Weibull fitting coefficient parameter does not make sense; therefore, the Weibull equation should be used with caution. On the other hand, with the Basquin equation, and considering that the fatigue limit occurs at 2 \(\times\) 10\({}^{6}\) cycles, the fatigue limit has good agreement with the bilinear fitting method for the [0\({}^{\circ}\)]s; meanwhile, a low fatigue limit was found by the exponential method (thermography and volumetric dissipated energy). Starting from the conclusion of [PERSON] et al., the fatigue limit for unidirectional composites may occur at/over 10\({}^{8}\) cycles; therefore, the fatigue limit estimated by the exponential method would be in the correct range. Using the found Basquin parameters with 10\({}^{8}\) cycles for [0\({}^{\circ}\)]s, the estimated fatigue limits are 0.25\({}_{\text{ut}}\) MPa, which is near to the values found by the exponential method. On the other hand, for the basket weave and \begin{table}
\begin{tabular}{c c c c c} \hline
**Laminate** & **a** & **b (\(\times\)10\({}^{-4}\))** & **c (\(\times\)10\({}^{-4}\))** & **R\({}^{2}\)** \\ \hline
[0\({}^{\circ}\)]s & 16.72 & 48.7 & 3.03 & 0.936 \\
[0\({}^{\circ}\)/90\({}^{\circ}\)]s & 30.52 & 43.2 & 51.11 & 0.870 \\ Basket weave warp & 148.15 & 51.3 & 41.00 & 0.974 \\ Basket weave weft & 110.21 & 51.1 & \(-\)49.30 & 0.964 \\
[+45\({}^{\circ}\)/\(-\)45\({}^{\circ}\)]s & 143.43 & 43.1 & 106.65 & 0.806 \\
[90\({}^{\circ}\)]\({}_{4}\) & - & - & - & - \\ \hline \end{tabular}
\end{table} 
Table 4: Three-parameter exponential fitting coefficients for temperature variation over maximum stress. \begin{table}
\begin{tabular}{c c c c c} \hline
**Laminate** & **a (\(\times\)10\({}^{-3}\))** & **b (\(\times\)10\({}^{-2}\))** & **c (\(\times\)10\({}^{-4}\))** & **R\({}^{2}\)** \\ \hline
[0\({}^{\circ}\)]s & 23.82 & 132.52 & 120.90 & 0.941 \\
[0\({}^{\circ}\)/90\({}^{\circ}\)]s & 189.59 & 55.65 & 45.10 & 0.975 \\ Basket weave warp & 809.00 & 38.35 & 27.60 & 0.988 \\ Basket weave weft & 363.90 & 51.11 & 0.687 & 0.981 \\
[+45\({}^{\circ}\)/\(-\)45\({}^{\circ}\)]s & 404.28 & 36.51 & 10.70 & 0.916 \\
[90\({}^{\circ}\)]\({}_{4}\) & 6.93 & 56.23 & 2.295 & 0.980 \\ \hline \end{tabular}
\end{table} 
Table 5: Three-parameter exponential fitting coefficients for volumetric dissipated energy over stress ratio (\(\sigma_{\text{max}}/\sigma_{\text{ut}}\)). \([+45/-45]_{\text{s}}\) laminates, the fatigue limits estimated by the bilinear and exponential methods are nearby. For the long term, laminated with fibers off-axis to the loading direction, failures at the matrix and interface are dominant; therefore, if the load is not enough to reach the stress to cause failure in the matrix and the interface, the stress applied would be under the fatigue limit; therefore, no material separation would happen.