Random vibration-based progressive fatigue damage monitoring in thermoplastic coupons: a preliminary investigation

In recent years there has been an increasing trend towards the utilization of composites, particularly thermoplastics, in various components of aerostructures. The prelusion of such materials has underscored the significance of investigating their fatigue behavior and developing reliable methods for detecting fatigue damage. In this context, vibration-based techniques hold significant potential as they leverage the inherent excitation provided by in-flight noise and turbulence. This study aims at assessing the progressively accumulated fatigue damage in thermoplastic coupons via random vibration signals while accounting for operational and inter-structural uncertainties. The experimental process consists of preliminary tension and fatigue tests, interrupted fatigue tests, C-Scan inspection tests, and non-contact random vibration tests. Consecutive fatigue states are obtained by performing fatigue tests at intervals of 10 000 cycles for a population of 7 coupons. At each interruption, ultrasonic C-Scan and vibration inspection tests are performed, allowing for the visualization of fatigue damage and random vibration signal analysis. Welch Power Spectral Density estimates are employed and are shown to have good potential for distinguishing among different fatigue states despite the inevitable population and experimental uncertainty. Furthermore, fatigue damage is found to progress symmetrically and laterally along the free edges of the test coupons, which is explained by the free edge effect.


Introduction
In the last decade, thermoplastics are increasingly replacing thermosets in aerospace applications mainly due to their recyclability and weldability [1].Modern aerospace structures are designed using the damage tolerance philosophy [2].This presupposes very good knowledge of the fatigue behaviour of structural materials and the development of reliable fatigue damage diagnosis methods.Yet, as of this date, fatigue behaviour of thermoplastics has not been thoroughly studied.The same is true for the use of random vibration-based methods for automated and potentially in-flight condition monitoring and prognosis during the structure's lifecycle [3][4][5].Random vibration based diagnostic technology is of particular interest in this context as it may be based on naturally available, or artificially enhanced, vibration response signals for continuously monitoring developing fatigue damage in-flight, without interrupting regular service.Several studies on the application of vibration based Structural Health Monitoring (SHM) methods aiming at damage assessment and prognosis for composite structures have been reported.One of the first studies suggested empirical models established by empirical relations of natural frequencies and damping ratios for damage assessment and fatigue life prediction [6].In [7] 4 different damage metrics based on Frequency Response Functions (FRFs) and global modal parameters are suggested for damage assessment and categorization.In [8] non-destructive methods (DIC, X-ray) and non-contact vibration tests are combined for damage detection and localization.Strain maps and modal properties are extracted, which lead to prediction of damage initiation.In [9] Fourier Analysis, C-Scan, and multiphysics finite element modelling are used for damage detection, and quantification.Good capability for the assessment of delamination of different sizes and depths is observed, and by analysing the measured operational vibration shapes quantification of the delamination extent is achieved.In [10] FRFs, C-Scan inspection tests, and modal parameters are used for damage detection, localization, and quantification.Damage metrics are shown to be sensitive to different types of damage and fiber orientation.Damage severity is also assessed while localization is based on C-Scans.In [11] AutoRegressive (AR) modelling, a Multiple Model (MM) detection method, and Power Spectral Density (PSD) estimates are employed.Detection and classification of damage states, with 100% and 96% accuracy, respectively, are achieved, while localization is based on C-Scan images.In [12] an experimental study, focusing on prognosis of damage growth through Lamb waves and X-Ray is presented and correlation between damage growth and damage assessment is achieved.It is noteworthy that none of the reported works has considered progressive fatigue damage in thermoplastics.The aim of the present study is the progressive fatigue damage monitoring in thermoplastics using coupons and random vibration signals.The experimental procedure, which integrates mechanical fatigue tests, C-scan tests, and random vibration tests, is applied to a population of 7 nominally identical thermoplastic coupons under interrupted fatigue.An important and innovative aspect of the work is that it accounts for two important types of inevitable uncertainty: inter-coupon (that is population uncertainty) and inter-experiment (operational) uncertainty (among experiments with the same coupon).

The experimental procedure
A flowchart of the experimental procedure is depicted in Figure 1.Preliminary tension tests are first conducted in order to assess the basic mechanical properties of the materials.Then, a series of fatigue tests are conducted to obtain the average fatigue life of the coupons.Having the results from the preliminary tension and fatigue tests, the fatigue loading parameters and the interruption intervals of fatigue loading are determined.The main experimental series consists of interrupted fatigue tests with intermediate ultrasonic C-scans and random vibration tests.The testing parameters are also provided in Figure 1.

Materials and specimens
The coupons are of dimensions 250  × 25  × 2.24  and the bonded tabs of 50  × 25  × 2.24  (Figure 2).The coupons and the tabs are made of thermoplastic TC 1225 LM PAEK prepreg plies with a fiber volume fraction of 66%.The 0.14 mm-thick plies are stacked in a quasiisotropic stacking sequence with a lay-up of [-45/0/45/90]2s.Following the preliminary fatigue tests, interrupted fatigue tests were conducted with a step of 10 000 cycles and the same fatigue loading parameters of Table 1 until coupon failure.As already noted, 7 coupons are subject to interrupted fatigue.

Ultrasonic C-scans
At each fatigue test interruption, C-Scan inspections are conducted using a 5 MHz sensor, pulse echo settings and reference (pristine) coupon to characterize fatigue damage.The tests are controlled via the ULTRAWIN software.

Random vibration tests
The random vibration tests are based on acoustic zero-mean and constant (in all cases) variance white random excitation digitally generated at 12.8  and used for driving a set of speakers while the coupon is suspended via elastic chords simulating free-free boundary conditions; a photo of the experimental setup is provided in Figure 4.A reflective surface is attached in the middle of the coupon

Results from the interrupted fatigue tests
The failure cycles for the 7 coupons are indicated in Figure 5, where significant dispersion is observed (standard deviation  of 46 040 cycles, with the ± range depicted on each bar).
Figure 5. Failure cycles for each coupon (interrupted fatigue tests).

Fatigue delamination propagation
The progressive damage C-Scans for coupon #3, which failed at 131 300 cycles, are shown in Figure 6.The lateral and symmetric damage in the two free edges is evident.Although the dispersion of the failure cycles is quite intense among the coupons, the damage evolution is qualitatively similar for all of them, but the rate is quite distinct.
The percentage of damaged surface, based on the C-Scan images, is presented in Figure 7 based on an 8-bit rbg color map.In the initial (10 000 and 20 000) cycles, the damage exhibits a gradual progression.Yet, upon reaching the critical threshold of 30 000 cycles, a noticeable increase in damage evolution occurs across multiple layers.It is worth noting that this crucial aspect, although not discernible from the C-Scan images, becomes evident through the interrupted fatigue tests.

Random vibration analysis
The vibration signal average sample variance for the Healthy State and each Fatigue State (FS) is depicted in Figure 8 (average over all experiments performed for each State for all 7 coupons; the values being normalized by the Healthy State average sample variance).Based on it, a slight increase in the vibration average sample variance is observed after FS4.This is quite plausible; yet it cannot be suggested as a reliable Fatigue State indicator in practice not only because the increase is rather limited (and not totally consistent among the coupons) even under constant excitation level, but mainly because (unlike with the present laboratory tests) in practical operation the vibration variance will depend upon the totally uncontrolled and unobservable in-flight excitation level.Welch-based Power Spectral Density (PSD) estimates (which reflect the underlying structural dynamics as affected by each Fatigue State) are subsequently obtained based on the random vibration velocity signals (signal and estimation details in Table 2).The compounded experimental and population uncertainty in the PSD estimates is, for the 7 Healthy State coupons, depicted in Figure 9 and is quite significant.This uncertainty is evident not only in the PSD level at each specific frequency, but also in the translation of the resonant frequency values observed.The latter is relatively 'small' for the first two resonant frequencies, but rather pronounced for the resonant frequency at 3.4  (the uncertainty zone for it extends for about 200 ).The fatigue effect on the Welch PSD estimates is, for coupon #3, depicted in Figure 10.Although dependency of all resonant frequencies on the Fatigue State is evident, the dependency of the resonant frequency at 3.4  is most dramatic (and beyond the uncertainty range associated with the Healthy State).More specifically, this resonant frequency decreases significantly with increasing fatigue cycles (Fatigue State).This signifies the importance of the effects of fatigue on the structural dynamics and is promising for properly inferring the Fatigue State based on random vibration signals -and it is important to note that it is independent of the excitation level.On the other hand, the (experimental procedure related) uncertainty present is, again, significant and has to be properly accounted for.

Figure 1 .
Figure 1.Flowchart of the experimental procedure.

Figure 2 .
Figure 2. Dimensions of coupons 2.2.Mechanical tests The tension tests are conducted according to the ASTM standard D3039 and the fatigue tests according to the ASTM standard D3479.A photo of a mounted coupon during a tension test is shown in Figure 3(a).The load-displacement curves, as extracted from the tension tests, are shown in Figure 3(b).The average maximum load is 51.35 kN, the longitudinal stiffness is 59.75 MPa, and the tensile strength is 935.11MPa.The coupons exhibited brittle behavior and their fracture was abrupt.The fatigue tests are conducted using a frequency of 5 Hz, a stress ratio of 0.1 and maximum stress of   = 0.6  .The fatigue loading parameters are listed inTable 1.The average fatigue life is 106 612 cycles.
-based vibration velocity measurement via the Polytec OFV-505 laser doppler vibrometer and a controller, while the vibration velocity is recorded via a National Instruments NI-9230 unit.Each experiment is 1  long with the sampling frequency being 12.8 .70 distinct experiments (each with a distinct of the white noise acoustic excitation) are run for the Healthy State of each coupon, and, subsequently, 35 distinct experiments (also with distinct white noise acoustic excitation realization each time) are run for each Fatigue State (FS) of each coupon.

Figure 4 .
Figure 4. Photo of the random vibration test set-up.

Figure 6 .
Figure 6.C-Scan inspection tests for coupon #3 at different cycles: Lateral and symmetric damage at the free edges.

Figure 8 .
Figure 8. Random vibration tests: Vibration signal average sample variance for the Healthy State and each Fatigue State (average over all experiments performed for each State for all 7 coupons; all values normalized by the average sample Healthy State variance).

Figure 9 .
Figure 9. Random vibration tests: Welch PSD estimates for all Healthy State coupons (70 experiments per coupon for all 7 coupons).

Figure 10 .
Figure 10.Random vibration tests: Fatigue effects on Welch PSD estimates for coupon #3 (70 curves/experiments for the Healthy State and 35 for each Fatigue State).4. Concluding remarks A preliminary investigation on random vibration-based progressive fatigue damage monitoring for thermoplastic structures has been carried out.The work has been based on  nominally identical coupons subjected to interrupted (every 10 000 cycles) fatigue damage, with C-scans and random vibration tests implemented.The main conclusions of the study may be summarized as follows: (i) As evident from the C-scans, fatigue leads to symmetric lateral damage (combination of extensive matrix cracking and delamination), which is explained via the edge effect.(ii) Progressive fatigue damage has been shown to have serious effects on the dynamics, which are reflected on the random vibration PSD estimates.These effects are promising for inferring the Fatigue State from measured random vibration signals.(iii) The percentage decrease (although not totally monotonic) of a resonant frequency with increasing fatigue damage further solidifies the expectation for reliable vibration-based Fatigue State inference.(iv) An obstacle to overcome for achieving this goal is the significant experimental and population (inter-coupon) uncertainty.
* Force Controlled

Table 2 .
Random vibration tests: Signal and Welch PSD estimation parameters.
The percentage difference (with respect to the Healthy State) of the average (over all experiments per state for all 7 coupons) resonant frequency of 3.4  versus the Fatigue State is depicted in Figure11.Evidently, this difference clearly follows (although not totally monotonically) the Fatigue State evolution, thus signifying the fact that it may be potentially effective as a Fatigue State indicator.