## 3 Results and Analysis
### Fatigue Test
#### 3.3.3 Fatigue Limit Through Infrared Thermography and Volumetric Dissipated Energy  
In order to consider the fatigue loads during the process of designing structures and/or mechanical components, the fatigue limit is the key parameter. Nonetheless, using the classical fatigue test can be time-consuming and costly; thus, a technique like infrared thermography is a good alternative. Data generated during the fatigue tests (surface temperature versus maximum stress) can be fit using two lines (bilinear), where the criteria to select the range of data to fit it is the correlation coefficient (R\({}^{2}\)), i.e., R\({}^{2}\) should be the highest in both fitting equations [13; 22]. The fatigue limit can be found with the intercept of both fitted lines. An alternative method is using the equation proposed by [PERSON] et al. [13], where the data can be fit using a three-parameter exponential as in Equation (1):  
\[y=a\cdot e^{(b\cdot x-\frac{1}{b\cdot x})}+c\cdot x \tag{1}\]  
where \(y\) can be the temperature variation or the volumetric dissipated energy due to the maximum fatigue stress applied (\(\sigma_{\text{max}}\) or \(\sigma_{\text{max}}/\sigma_{\text{ut}}\)) and a, b, and c are the fitting parameters. In this method, the fatigue limit is found by determining the minimum radius of curvature of the fitted curve, and the value can be approximated by Equation (2). \[R_{p}=\frac{1}{k}=\left|\frac{\left(1+y^{\prime}\right)^{3/2}}{y^{\prime \prime 2}}\right| \tag{2}\]  
Figure 8 shows the data obtained for the studied laminates. It is exciting that [0\({}^{\circ}\)]s and basket weave warp and weft show similar high temperatures, around 12 \({}^{\circ}\)C, even if the applied maximum stress is lower for the case of basket weave laminates. Furthermore, a clear trend is observed for all laminates except for the [90\({}^{\circ}\)]4; this can be explained with the high rate of failure nucleation at the matrix-fiber interface since the load is applied transversally to the fiber direction. According to the linear fitting, at higher stress with high temperature, results present a high correlation coefficient R\({}^{2}\) (over 0.93); however, at lower stress, high variability of the temperature is observed, and as a consequence, a low correlation coefficient is found. In materials like flax/PLA composites, their properties are highly affected by factors like reinforcement properties, fiber-matrix interaction, porosity, loading, geometry, and environmental conditions; this, at the end, is reflected with high variability in the temperature at lower stress applied, even though the environmental conditions may have a huge impact. The exponential equation was fitted considering the temperature variation over the maximum stress applied; this was in order to obtain convergence in a reasonable time. The  
Figure 8: Surface temperature over the maximum stress applied: (**a**) data and bilinear fitting for [0\({}^{\circ}\)]\({}_{8}\) and [0\({}^{\circ}\)/90\({}^{\circ}\)]\({}_{8}\), (**b**) data and exponential fitting for [0\({}^{\circ}\)]\({}_{8}\) and [0\({}^{\circ}\)/90\({}^{\circ}\)]\({}_{8}\), (**c**) data and bilinear fitting for basket weave warp and weft, (**d**) data and exponential fitting for basket weave warp and weft, (**e**) data for [+45\({}^{\circ}\)/ -45\({}^{\circ}\)]\({}_{8}\) and [90\({}^{\circ}\)]\({}_{8}\) and (**f**) data and exponential fitting for [+45\({}^{\circ}\)/ -45\({}^{\circ}\)]\({}_{8}\) and [90\({}^{\circ}\)]\({}_{8}\). data fits the exponential equation well for all laminates except for the [90\({}^{\circ}\)]\({}_{4}\) laminates. The three parameters and the correlation coefficient are shown in Table 4.  
On the other hand, dissipated energy can be used to determine the fatigue limit [22]. The volumetric dissipated energy was estimated at each cycle from the stress and strain values recorded during tests. Assuming that the dissipated energy reaches stabilization in the same range that the temperature did, the average dissipated energy can be related to the stress ratio.