Fatigue Life (Limit) Analysis Through Infrared Thermography on Flax/PLA Composites with Different Reinforcement Configurations

Featured Application

The results of this work can be used as a guideline to estimate fatigue limit of green composites using different methods as a function of fiber architecture.

Abstract

This paper presents the fatigue limit of flax/PLA composites with different fiber reinforcement architectures. The configurations of the analyzed flax/PLA composites are [0°]₈, [0°/90°]_s, [+45°/−45°]_s, [90°]₄, stacking sequences, and basket weave laminates. The methods used to estimate the fatigue limit are the fitting of stress versus number of cycles data using Weibull and Basquin equations, the surface thermographic technique with bilinear and exponential models to analyze the evolution of temperature increment, and volumetric dissipated energy. According to the results found, superficial temperature and the maximum strain reached stabilization over 2000 cycles for σ_max/σ_ut < 0.7, which was used to determine cyclic stress–strain curves and the fatigue limit. The cyclic stress–strain shows a nonlinear behavior for all laminates, having a good correlation to the Ramberg–Osgood model. Furthermore, having the stabilized temperature and volumetric dissipated energy, the exponential model was used to evaluate the fatigue limit and compared to the values found by Basquin and bilinear models. The fatigue limit found by Basquin and bilinear models shows conservative values compared to the exponential models. The results also show that temperature measurement using infrared thermography is quite sensitive to the environmental temperature variation, especially at low stress applied, and finally, the comparison of these methods on different reinforcement configurations provides a guide to select a proper technique in each case.

1. Introduction

During the last few years, natural-fiber-based composites have been extensively implemented in different industries and engineering applications [1,2] due to advantages like low cost, lower density, excellent mechanical properties, and lower hazard impact during manufacturing and handling [3,4]. On the other hand, among the all-natural fibers, flax fibers are the most explored and used reinforcement for many different polymers (epoxy and polyester, among others) according to the literature and the industry [4,5,6,7,8].

During the last decade, flax fibers have been explored as reinforcement for biodegradable polymers such as polylactic acid (PLA), showing promising characteristics. Even though different properties have been studied in static and dynamic regimes at experimental levels and with mathematical models, information about their properties under fatigue loading conditions is still very limited. Determining fatigue properties is time-consuming and resource-intensive, as the sample must be subjected to repetitive loading up to failure, and the tests must be repeated at different stress levels to build the stress–fatigue life curve [2]. In order to simplify the study and reduce the time, different methods have been developed and implemented, such as nondestructive evaluation (NDE) methods (optical, thermal, electromagnetic, ultrasound, acoustic emission, X-ray, and others) [9,10]. Especially for the fatigue limit, the surface temperature measured by the thermographic technique is one of the most efficient methods, which was implemented and validated on metals and composites [11,12,13,14,15]. According to the reported studies, using the thermography technique, the time to complete the entire campaign to determine the fatigue limit may reduce drastically, since it requires around 6000 cycles (20 min considering a loading rate of 5 Hz) to reach stabilization on each sample [16,17].

During the fatigue damage process (fatigue test under load control), three main stages are presented: the initial stage is usually related to the microstructural reorganization and microcrack initiation, which is characterized by sudden increment in the deformation and temperature; the second stage is related to the crack development on the fiber–matrix interface and in the matrix, where a stable damage progression is presented with a low increment rate of deformation and a stable temperature; the final stage is usually relatively short in the number of cycles, which is characterized with high local increment in the temperature (crack tip area) and large deformation on the sample [14]. In order to estimate the fatigue limit, the second stable stage can be used. Using the superficial temperature and the stress ratio (σ_max/σ_ut), Huang consolidated and validated three methods [13]: maximum angle change, minimum curvature radius, and bilinear method. According to the result found by Huang, maximum angle change is quite sensitive to the data quality, even failing the estimation if the data error is over 10%; this method is more suitable for metals than composites. On the other hand, the minimum curvature radius method requires a larger amount of data, and even with that, the result is conservative. The last method combines the bilinear and Luong’s methods, having a good correlation with all available data, although it is not conservative in determining the fatigue limit [13].

On the other hand, the natural fiber structure is unique and complex, presenting three main parts: primary cell wall, secondary cell wall, and lumen. The secondary cell wall is the main part responsible for carrying the load; in this wall, cellulose microfibers present a helical shape following the fiber axis, and the lower the microfibril angle, the higher the fiber stiffness. According to the literature, the microfibril angle on flax fiber ranges from 8° to 11° [18,19]; throughout the loading process, especially at low strain rates or cyclic loads, microfibril orientation can be rearranged, reducing the microfibril angle even lower [20]. Furthermore, during the fatigue loading on natural fiber composites, not only does microfiber rearrangement occur, but also the bundle of fibers is rearranged, which makes the behavior even more complex.

Although composites using unidirectional flax fibers have been widely studied, there is still a lack of deep knowledge about the fatigue response of composites with multidirectional laminates and/or fibers with a basket weave arrangement, especially when using a completely biodegradable polymer like PLA as the matrix of the composite material. The main objective of this study is to evaluate the fatigue limit using the infrared thermography and the volumetric dissipated energy approaches; laminated flax/PLA biocomposite samples with [0°]₈, [0°/90°]_s, [+45°/−45°]_s, and [90°]₄ orientations and basket weave laminated samples were studied.

2. Materials and Methods

2.1. Reinforcement and Matrix

Reinforcement materials included cross-stitched unidirectional flax fiber (Ecotechnilin FLAXDRYTM-UD 180) and unprocessed flax fabrics arranged in a basket weave configuration (approximate area density of 500 g/m²). Polylactic acid pellets (NaturePlast PLI 005) were used as the matrix.

2.2. Laminate Manufacturing Process

Laminates were manufactured using the thermo-compression technique, where the PLA sheets were manufactured according to the method described by Jiao-Wang et al. [21]. In order to avoid the influence of the moisture, PLA sheets and flax fiber fabrics were dried at 60 °C over 12 h. Then, PLA sheets were alternately stacked with flax fabrics. With the target temperature set at 180 °C, the PLA/flax combination preform was placed between the heating plates and maintained for two minutes (preheating process) with an initial pressure of 0.02 MPa.

Afterward, the pressure was increased at a rate of 0.01 MPa/s up to 0.25 MPa for [90°]₄, [0°/90°]_s, and [+45°/−45°]_s and up to 2 MPa for [0°]₈, then maintained for an additional four minutes. For the basket weave laminate, the pressure was increased at a rate of 0.07 MPa/s up to 8 MPa, and the pressure was also maintained for four minutes. Immediately after pressure release, the flax/PLA laminate was removed from the heating plates and cooled down at room temperature. Fiber direction in each laminate and the nomenclature used are shown in Figure 1.

To evaluate the volume fraction and degree of crimp of the fibers of the manufactured laminates, a couple of samples were randomly selected from each type of laminate; thereafter, they were embedded in epoxy resin; afterward, they were polished to a mirror surface. Micrography images were obtained using the Olympus GX51 optical microscope, and the images (minimum of 5 images) were analyzed using the Stream Basic V.2.1 software from Olympus to determine the fiber volume fraction and the degree of crimp.

2.3. Tensile Quasistatic and Fatigue Tests

Sample dimensions for the tensile quasistatic and fatigue tests are 20 mm wide and 170 mm long; the sample’s thickness was measured with a micrometer. Afterwards, test specimens were randomly selected for static and fatigue tests. Due to the gauge length of the extensometer (50 mm), the free sample length (grip to grip) distance was set to 70 mm. Tests were conducted using a servo-hydraulic MTS Landmark testing system with a load cell of 100 kN. For the static test, displacement control was configured at 2.1 mm/min (strain rate ~0.0005 1/s) and six samples were tested for each stacking sequence. On the other hand, fatigue tests were conducted under sinusoidal load control with a frequency of 5 Hz and a stress ratio of 0.1 (σ_min/σ_max). In order to cover the whole stress spectrum, nine stress levels were used (σ_max/σ_ut = 0.8, 0.7, 0.6, 0.5, 0.4, 0.35, 0.3, 0.25, and 0.2), and five samples were tested at each stress level.

2.4. Infrared Thermography

During the fatigue tests, the superficial temperature was monitored by using an infrared thermographic camera Fluke Ti450 (Fluke, Everett, WA, USA) (320 × 240 pixels), with a sampling rate of nine frames per second and a material emissivity of 0.9. The generated data was saved in .IS3 format; afterward, the generated files were handled using SmartView Classic 4.4 software from Fluke in order to obtain the temperature matrix in the interest zone. Furthermore, considering the environment temperature variation, a guard sample (without load) was placed beside the tested samples as a reference. Figure 2 shows the experimental setup for the fatigue test, where the small image on the left side is the amplified view of the sample, the reference sample and the extensometer used.

3. Results and Analysis

3.1. Volume Fraction and Degree of Crimp

Table 1. Fiber volume fraction of the manufactured laminates.

	Volume Fraction (vf)	Standard Deviation (SD)
[0°/90°]s, [90°]4, and [+45°/−45°]s	0.3722	0.0148
[0°]8	0.4613	0.0309
Basket weave warp	0.3733	0.0285
Basket weave weft	0.2417	0.0173

shows the average value and the standard deviation of the fiber volume fraction of the laminates. Since the manufacturing parameters used were the same for [0°/90°]_s, [90°]₄, and [+45°/−45°]_s laminates, they were grouped as one set of data to obtain the average volume fraction, and the result shares similarity with the one reported in the previous work [22]. Unidirectional [0°]₈ laminate shows a higher volume fraction due to the higher pressure applied during the manufacturing stage; however, a higher standard deviation is observed for this case. On the other hand, due to the particular woven pattern of the basket weave reinforced laminate, it displays two volume fractions, in which the warp direction shows a higher volume fraction than the weft; overall, the fiber volume fraction of basket weave laminate is around 0.615, which is also similar to the one reported by Jiao-Wang et al. [21].

Furthermore, fiber crimp and maximum waviness angle were determined for the basket weave reinforced laminates (micrographs of the basket weave laminates are shown in Figure 3). Results show higher crimp along the warp direction than the weft direction, as expected, and the values are 7.16% and 3.15% for the warp and weft directions, respectively; these results are similar to the results reported by Jiao-Wang et al. [21]. On the other hand, the maximum angle of waviness found in this study was 19.38° and 12.35° for the warp and weft directions, respectively.

3.2. Quasistatic Tensile Test

Figure 4 shows the representative stress–strain curves for the different studied laminates. UD laminates loaded along the fiber direction show better stiffness and strength ([0°]₈ and [0°/90°]_s) than the rest. On unidirectional fiber laminates, there is a minimum degree of waviness of the fibers due to the cross-stitched threads, and combined with the microfibril angle, this can trigger the rearrangement of the reinforcement and matrix during the loading process; therefore, the stress–strain curve is not perfectly linear as observed for [0°]₈, which was reported and analyzed in the previous study [22], and similar behavior was also found in flax/epoxy composites [2,23,24,25]. On the other hand, since half the laminas are in the transversal direction on [0°/90°]_s, progressive failure at the 90° lamina may happen; a pronounced nonlinear stress–strain curve is observed, especially over 0.0085 strain, which is the strain to failure reported for [90°]₄. When the fibers are transversally oriented to the loading direction, the fiber–matrix interface is the weakest area; therefore, sudden failure happens, which is observed on the strain curve (Figure 4). The laminate with a [+ 45°/−45°]_s fiber orientation presents two clear stages, which can be delimited by ε_cr = 0.011. First, before reaching ε_cr, stable fiber–matrix interaction would happen. Then, after ε_cr, the fiber–matrix interface starts to slide (due to the dominant shear stress at 45°); a similar behavior was observed in Kevlar and carbon fiber composites [26,27].

For basket weave laminates, the waviness of the fibers has a significant effect on the stress–strain curve; the degrees of crimp and angle of waviness are lower in the weft direction compared to the warp direction; therefore, higher stiffness and strength are expected along the weft direction, even though the fiber volume fraction is lower (Figure 4). Furthermore, since the angles of waviness are 19.38° and 12.35° for the warp and weft directions, respectively, a nonlinear stress–strain is observed.

Table 2. Summary of the mechanical properties obtained from the static tests.

Laminate	Initial Modulus (GPa)	Tensile Strength (MPa)	Strain to Failure (mm/mm)
[0°]8	20.99 ± 0.60	218.02 ± 8.20	0.0162 ± 0.0007
[0°/90°]s	14.24 ± 1.714	134.31 ± 11.55	0.0163 ± 0.0026
Basket weave warp	9.01 ± 0.337	88.05 ± 4.28	0.0333 ± 0.0036
Basket weave weft	10.56 ± 0.54	100.40 ± 6.31	0.0206 ± 0.0011
[+45°/−45°]s	6.37 ± 1.108	74.90 ± 11.50	0.0847 ± 0.0276
[90°]4	6.49 ± 1.655	34.70 ± 3.77	0.0077 ± 0.00151

summarizes the tensile test mechanical properties of the laminate under study.

3.3. Fatigue Test

3.3.1. S-N Curve

During the loading process, any misalignment of the reinforcement to the loading direction significantly affects the stiffness and strength, which was observed during tensile tests. Furthermore, during repetitive loading, fibers tend to align to the loading direction in each loading cycle, accelerating the permanent damage process and even drastically reducing the fatigue limit (endurance limit). On the other hand, performing the fatigue test to build stress–number of cycles (S-N) curves for six groups of samples is time-consuming and technically not feasible; moreover, in composites with reinforcement alignment off-axis, it is complex to determine the fatigue limit since the S-N curve keeps reducing (over 10⁶ cycles). Therefore, only for [0°]₈ and [0°/90°]_s were tests performed in order to build S-N curves; on the rest of the samples, the tests were stopped after 6000 cycles, which is the number of cycles to reach the stabilization temperature and maximum strain.

Figure 5 shows the experimental S-N data and fitted curves using the Basquin (${\sigma }_{max}={\sigma }_f{N}_f^b$) and Weibull ($\left({\sigma }_{max}-{\sigma }_{\infty }\right)/\left({\sigma }_{ut}-{\sigma }_{\infty }\right)=e^{(-\alpha {(\log (N_f))}^{\beta })}$) models [22,28]. The fitting parameters for [0°]₈ are α = 0.00216, β = 4.10, and σ_∞ = 105.20 MPa, with R² = 0.82 for the Weibull model and σ_f = 390.33 MPa, b = −0.0947 with R² = 0.841 for the Basquin model. For [0°/90°]_s, the parameters are α = 0.00159, β = 1.706, and σ_∞ = −2709.3 MPa with R² = 0.92 for the Weibull model and σ_f = 223.18 MPa, b = −0.1072 with R² = 0.911 for the Basquin model. An advantage of the Weibull model is the ability to determine the fatigue limit (σ_∞); this works only if there is a clear trend, which happens in the case of unidirectional fiber composites loaded in the fiber direction; this is corroborated for the [0°]₈ laminates with σ_∞ = 105.20 MPa. On the contrary, for [0°/90°]_s, the σ_∞ value is inconsistent (negative value), which means that the fatigue limit is more complex to establish and the Weibull model is inadequate in this case. However, using the Basquin model and considering that the fatigue limit occurs at 2 × 10⁶ cycles [2,29], the limit for [0°/90°]_s is 47.11 MPa. During the fatigue process, the damage rate is stable in the second stage, with microcrack nucleation at the interface, followed by crack development along the matrix; however, this mechanism is typically for UD lamina loaded axially. In lamina with loading off-axis to the reinforcement direction, complete fiber–matrix and/or lamina–lamina interface separation would happen during the first or second stage of damage; therefore, lasting to the fatigue limit was not possible, which happened to the [0°/90°]_s in this study, unless predefined values are established (2 × 10⁶ cycles).

3.3.2. Strain Ratcheting and Cyclic Stress–Strain Curves

Figure 6 shows the maximum strain measured over the number of cycles. It is evident that for a low stress ratio (σ_max/σ_ut) below 0.6, the strain stabilization reaches around 2000 cycles for all laminates. On the other hand, laminates with off-axis reinforcement to the load direction show earlier failure for 0.7 and 0.8 stress ratios. Moreover, higher strain is observed for [+45°/−45°]_s, basket weave warp, and basket weave weft, which is reasonable due to the stress level and failure mode.

Stabilization of strain is directly related to the second stage of the damage, where the crack development occurs; therefore, considering the maximum strain (maximum strain from the hysteresis loop) and the applied stress at ~2000 cycles, an approximate cyclic stress–strain plot can be built.

Figure 7 shows the cyclic stress–strain curves for the studied laminates. Analogous to the results from static tests, the curves are nonlinear, and due to the similarity of the trend of the data observed to the one found in metals, a nonlinear stage power law (${\epsilon }_p={{\displaystyle \frac{\sigma }{E}}+\left({\displaystyle \frac{\sigma }{K\prime }}\right)}^{1/n\prime }$) model (Ramberg–Osgood) can be adapted, where E is the modulus and $K\prime$ and $n\prime$ are the coefficient and exponent of the power law. Moreover, fitted curves were also included in the plot (Figure 7). The fitted coefficient and exponent are detailed in the

Table 3. Cyclic stress–strain power law model parameters for the studied laminates.

Laminate	$\mathit{K}\mathit{\prime }$	$\mathit{n}\mathit{\prime }$	R2
[0°]8	796.79	0.3703	0.92
[0°/90°]s	644.38	0.4266	0.91
Basket weave warp	259.90	0.3603	0.87
Basket weave weft	338.93	0.3759	0.88
[+45°/−45°]s	259.82	0.3850	0.61
[90°]4	425.08	0.5466	0.79

, demonstrating a good correlation coefficient for [0°]₈, [0°/90°]_s, basket weave warp, and basket weave weft (R² > 0.87). However, [+45°/−45°]_s shows poor agreement with R² = 0.61. Although for [90°]_4, the R² = 0.79, due to the dispersed strain and stress values, the obtained parameters should be taken with caution. These cyclic stress–strain curves allow the building of hysteresis loop curves for damage analysis in composites.

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 (R²), i.e., R² 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 Huang et al. [13], where the data can be fit using a three-parameter exponential as in Equation (1):

$$y=a·e^{\left(b·x-{\displaystyle \frac{1}{b·x}}\right)}+c·x$$

(1)

where $y$ can be the temperature variation or the volumetric dissipated energy due to the maximum fatigue stress applied (σ_max or σ_max/σ_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).

$$R_{\rho }={\displaystyle \frac{1}{k}}=\left|{\displaystyle \frac{{\left(1+y\prime \right)}^{3/2}}{{y″}^2}}\right|$$

(2)

Figure 8 shows the data obtained for the studied laminates. It is exciting that [0°]₈ and basket weave warp and weft show similar high temperatures, around 12 °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°]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 R² (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 data fits the exponential equation well for all laminates except for the [90°]₄ laminates. The three parameters and the correlation coefficient are shown in

Table 4. Three-parameter exponential fitting coefficients for temperature variation over maximum stress.

Laminate	a	b (×10−4)	c (×10−4)	R2
[0°]8	16.72	48.7	3.03	0.936
[0°/90°]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°/−45°]s	143.43	43.1	106.65	0.806
[90°]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. 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 (σ_max/σ_ut), in order to obtain faster convergence during the fitting.

Table 5. Three-parameter exponential fitting coefficients for volumetric dissipated energy over stress ratio (σ_max/σ_ut).

Laminate	a (×10−3)	b (×10−2)	c (×10−4)	R2
[0°]8	23.82	132.52	120.90	0.941
[0°/90°]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°/−45°]s	404.28	36.51	10.70	0.916
[90°]4	6.93	56.23	2.295	0.980

shows the fitting parameter for the volumetric dissipated energy over the stress ratio (σ_max/σ_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°]₄ laminate shows good fitting.

The fatigue limits found are in a wide range (

Table 6. Fatigue limit determined according to the Weibull, Basquin, bilinear, and exponential models; values in brackets are the fatigue limit in MPa.

Laminate	Fatigue Limit (MPa)
	Exp. Weibull	Exp. Basquin (2 × 106 Cycles)	Thermography		Volumetric Dissipated Energy
			Bilinear Model	Exponential Model	Exponential Model
[0°]8	0.48 (105.2)	0.45 (98.7)	0.44 (96.8)	0.23 (49.1)	0.18 (39.6)
[0°/90°]s	-	0.35 (47.1)	0.40 (54.0)	0.41 (54.9)	0.43 (57.4)
Basket weave warp	-	-	0.46 (40.5)	0.49 (43.1)	0.55 (48.1)
Basket weave weft	-	-	0.47 (47.6)	0.44 (44.0)	0.46 (46.1)
[+45°/−45°]s	-	-	-	0.69 (52.0)	0.65 (48.5)
[90°]4	-	-	-	-	0.43 (14.8)

); 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°]₈, which was confirmed by Jeannin 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 × 10⁶ cycles, the fatigue limit has good agreement with the bilinear fitting method for the [0°]₈; meanwhile, a low fatigue limit was found by the exponential method (thermography and volumetric dissipated energy). Starting from the conclusion of Jeannin et al., the fatigue limit for unidirectional composites may occur at/over 10⁸ cycles; therefore, the fatigue limit estimated by the exponential method would be in the correct range. Using the found Basquin parameters with 10⁸ cycles for [0°]₈, the estimated fatigue limits are 0.25σ_ut MPa, which is near to the values found by the exponential method. On the other hand, for the basket weave and [+45/−45]_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. However, in composites with fibers aligned to the loading direction, fiber ratcheting due to microfibril alignment would happen, even if the stress applied is lower; therefore, the fatigue limit would be lower, as observed for the [0°]₈ using the exponential method, which was also reported by [29], where they found that samples loaded along the fiber direction present a lower fatigue limit. Although this is not evident for the [0°/90°]_s, due to half of the laminas being transversely oriented to the loading direction, mixed-mode damage would happen; therefore, a higher fatigue limit is found. For [90°]₄, due to the high variability of the temperature at low stress applied, it was not possible to apply the thermography method to determine the fatigue limit, while volumetric dissipation energy fits well to the exponential equation.

During the fatigue test, superficial temperature attains stabilization around 2000 cycles for applied stress lower than 0.6 or even 0.7 from σ_ut; although an apparent stabilization is reached, this temperature may drop, which may happen due to the environment temperature changes or even with the small airflow around, the inherent variability of the laminate properties notwithstanding. These small changes may have a huge impact on the surface temperature of the tested samples at low stress; therefore, high variation in the result is observed, which was found in this study. Therefore, in the thermography method, tests must be performed under different levels of stress at low stress in order to increase the resolution and reduce the variability, which at the end increases the duration of the measurement and the total cost. On the other hand, using a calibrated extensometer and with a sufficient rate of data acquisition, the volumetric dissipation energy is an alternative, showing low variability even at low stresses.

4. Conclusions

Fatigue tests were performed on flax/PLA laminates with different lamina configurations ([0°]₈, [0°/90°]_s, basket weave, [+45°/−45°]_s, and [90°]₄) with the purpose of determining the fatigue limit using different methods; these are the main conclusions:

Temperature measurement using infrared thermography is quite sensitive to the environmental temperature variation, especially at low stress applied, where stabilization temperature is below 1.5 °C; therefore, tests must be performed at different load ratios, which in the end increase the testing cost.

The Weibull equation fits well to the fatigue life when the load is applied to the fiber direction [0°]₈; however, the estimated fatigue limit is overestimated or even fails to evaluate composites with laminas in different directions; therefore, the Weibull equation should be used with caution.

Temperature and the maximum strain reach stabilization over 2000 cycles for σ_max/σ_ut < 0.7, which is convenient to evaluate the fatigue limit; furthermore, the use of the thermographic bilinear method to evaluate only the fatigue limit is not recommended, since the results depend on the range of data used to fit both lines, even more so with the high variability of the temperature at low stress applied, which can misinterpret the values obtained.

According to the results, the volumetric dissipated energy is an alternative, and together with the thermography method, results found can be corroborated, especially at lower stress applied. Furthermore, fatigue limits were found for the studied laminates, showing a low fatigue limit (0.18 to 0.23σ_ut) for laminates with reinforcement in the loading direction, contrary to the rest of the laminates, which show a higher fatigue limit.

A cyclic stress–strain curve was established based on the strain measurement during the test and fitted to the Ramberg–Osgood model, which can be used to build loading hysteresis.

The results found in this study can be used to design components where the tensile-tensile cyclic loading is applied; however, the overall mean stress effect is missing. Therefore, future works should focus on the study of composites with different mean stress levels and build the Haigh diagram.