
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

72553
10.1038/s41598-024-72553-2
Article
Damage source localisation in complex geometries using acoustic emission and acousto-ultrasonic techniques: an experimental study on clear aligners
Barile Claudia 1
Cianci Claudia 1
Paramsamy Kannan Vimalathithan 1
Pappalettera Giovanni giovanni.pappalettera@poliba.it

1
Pappalettere Carmine 1
Casavola Caterina 1
Laurenziello Michele 2
Ciavarella Domenico 2
1 https://ror.org/03c44v465 grid.4466.0 0000 0001 0578 5482 Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Bari, Italy
2 https://ror.org/01xtv3204 grid.10796.39 0000 0001 2104 9995 Dipartimento di Medicina Sperimentale e Clinica, Università di Foggia, Foggia, Italy
14 9 2024
14 9 2024
2024
14 2146725 1 2024
9 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Passive non-destructive evaluation tools such as acoustic emission (AE) testing and acousto-ultrasonics (AU) approach present a complex problem in damage localisation in complex and nonhomogeneous geometries. A novel AU-guided AE frequency interpretation approach is proposed in this research work which aims at overcoming this limitation. For the experimental evaluation, the damage sources from a geometrically complex clear dental aligners are tested under cyclic compression load and their origins are evaluated. Despite the rapid worldwide diffusion of the clear aligners, their mechanical behaviour is poorly investigated. In this work, the frequency characteristics of the artificially simulated stress wave, generated from different dental positions of the clear aligners, are studied using the AU approach. These frequency characteristics are then used to analyse the AE signals generated by these aligners when subjected to cyclic compressive loading. In addition, the time domain characteristics of the AE signals are studied using their Time of Arrival (ToA). The Akaike Information Criterion (AIC) is used to estimate the ToA. These frequency and time domain characteristics of the AE signals are used to estimate the local damage origin in the clear dental aligners. This will help in identifying localised damage sources during the usage period of the aligners. Experimental results revealed significant damages in the left maxillary premolar and right maxillary third molar of the aligners.

Keywords

Acoustic emission
Acousto-ultrasonics
Fractographic analysis
Clear dental aligners
Frequency analysis
Time of arrival
Subject terms

Biomedical engineering
Mechanical engineering
http://dx.doi.org/10.13039/501100003407 Ministero dell’Istruzione, dell’Università e della Ricerca D93C23000100001 issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The wide availability of data processing and signal processing algorithms, supported by powerful hardware has made Acoustic Emission (AE) technique one of the formidable Non-Destructive Evaluation (NDE) tools. In particular, the growth of the AE technique over the last decade has been exponential1–3. Despite this tremendous growth, research into the propagation of acoustic waves in complex shapes and structures is very limited. Designing acoustic wave propagation in a non-homogeneous medium of complex geometry is quite challenging. In addition, the classification of damage sources based on source location is complex4.

Over the years, several methods have been developed to classify damage sources and localise the sources of acoustic emission. Among them, the triangulation principle5, the Akaike Information Criterion (AIC)6,7 to estimate the arrival time, and the sideband peak frequency8 are successful in source localisation. Signal-based approaches such as time–frequency analysis, frequency-based analysis9–11, and parameter-based approaches such as data classification and clustering are used for damage source classification12–14. Some research is aimed at bridging the gap between the signal-based and parameter-based approaches by using information-theoretic parameters such as entropy and complexity indices for the same11,13. Extensive research has been carried out over the years to improve the applicability of these techniques to inhomogeneous materials8,15. Nevertheless, their applications are limited to structures with geometrical regularity. This is due to the lack of information on the characteristics of the AE signals from damage sources in a geometrically irregular structure.

Acousto-ultrasonics (AU) is one of the simplest yet efficient approaches to characterising the propagation of acoustic waves. This approach can be described as an AE simulation with an ultrasonic source. The acoustic waves are typically associated with the spontaneously released stress waves that accompany the plastic deformation or crack growth in material. The AU approach differs in the sense that the artificial stress waves are induced in the material. In this approach, an artificially simulated stress waves by exciting a piezoelectric crystal with a voltage burst and are propagated through a material and recorded using an AE sensor (typically piezoelectric sensors). The recorded acoustic waves reveal the information about the propagation path. Based on this approach, a qualitative information about the propagating medium and its influence on the characteristics of the acoustic waves can be extracted16,17. Thus, in this research work, the AU approach is used contemporarily with the AE testing to characterise the damage sources in a complex geometry.

The test material in this study is one of the fast-growing orthodontic devices, the clear dental aligners. Recent research has shown that a significant number of adult patients are reluctant to undergo conventional orthodontic treatment for malocclusion because it is less aesthetically pleasing18,19. Clear dental aligners are designed based on the dental alignment of the patients obtained by a cast or an intra-oral scanner. Their design is pre-programmed to move the misaligned tooth or group of teeth into the desired position in small increments20,21. These aligners are used for a short period of time (usually between 7 and 14 days) and are replaced constantly. The pre-designed increments are designed to distribute the forces in constant gradual increments that realign the teeth22,23. The mechanical performance of the thermoformed aligners is susceptible to the degradation due to the thermal stress induced during the manufacturing process and the occlusal forces during their use. Although there has been some research into the various mechanical properties of aligner materials such as polyurethane (PU), polyethylene terephthalate (PET), PET-glycol modified (PET-g), polycarbonate, polyethylene, and polypropylene, very few research works have reported on the actual mechanical performance of the aligner itself24–28. This means that the available mechanical performance studies are mostly on the test specimens in the form of thin plates, dog bone specimens, or thin discs. It is therefore essential to understand the mechanical behaviour of these aligners under load and to identify the source origin of the damage.

The objective of this research work is to use the acousto-ultrasonics and the acoustic emission techniques to classify the damage sources in thermoformed clear dental aligners. The dental aligners are cyclically loaded for 22,500 cycles and their mechanical performance and damage sources are analysed using AE testing. AE testing is based on the analysis of stress waves generated by the damage sources of a material/structure under load. It is essential to have a prerequisite information on the frequency components of the stress waves that may be generated by the dental aligners. Since there are no previous studies available on this particular topic and designing the propagation of acoustic waves in complex geometry is quite difficult, the AU approach is used in this study.

First, the frequency characteristics of the propagating acoustic waves in the complex geometry of the aligners are studied using the AU approach based on Hsu–Nielsen tests. Then, using the information from the AU approach, the damage sources are classified using the AE signals generated by the clear dental aligners under cyclic loading. The characteristics of the AE signals are studied in their frequency domain using Fast Fourier Transform (FFT) and in their time domain using Akaike Information Criterion (AIC). Finally, the results are validated using microscopic analysis of the tested aligners. In short, this work uses an integrated acoustic emission and acousto-ultrasonic test method for evaluating the damage source origin in otherwise complex component.

Materials and methods

Preparation of clear dental aligners

Dental alignment of a patient is reconstructed in 3D using 3Shape OrthoAnalyzer® software with the permissible accuracy of 6.9 μm. (Note: No experiments were conducted on the patient; a written consent was signed by the patient to acquire their dental record. This study was reported following the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guidelines for observational studies29. All the procedures of this research protocol adhered to the Declaration of Helsinki of 1975, as revised in 2008). A solid cast of the dental alignment is then reconstructed in the Liquid Crystal HR2 3D Printer (Photocentric Ltd.) using daylight hard resin.

The clear dental aligners are prepared using this cast by thermoforming processing in Erokodent® Erkoform 3D vacuum machine. Medical grade polyurethane (PU) and polyethylene terephthalate—glycol modified (PET-g) sheets of 0.75 mm thickness from two suppliers, Bart Medicals Ltd., (commercial name Ghost Aligner®) and Dentsply Sirona Inc. (commercial name Essix ACE plastic), respectively, are used as the base materials. These thermoplastic sheets are thermoformed over the hard resin cast by first heating the sheets with a medium wave infrared heater, that heats the discs to 160 °C at a pressure of 0.8 bar and then by applying vacuum. The prepared aligners are named after their base materials as TPET-G and TPU (T refers to the thermoformed thermoplastic).

Denominations for the tooth positions

Since the objective of the study is to locate the damage sources in the dental positions of the clear aligners, a standard denomination system is used for the different tooth positions of the thermoformed aligners. The tooth positions are named according to the dental notations of ISO 3950—Dentistry—Designation system for teeth and areas of the oral cavity standard. The tooth numbers and their position in the oral cavity of the upper and lower jaws are presented in Table 1. For the convenience of the readers, a figure representing the different dental nominations of the maxillary arch is given in Sect. S1 of the Supplementary file.Table 1 Tooth denomination according to ISO 3950 standard.

Upper left	Upper right	
18	17	16	15	14	13	12	11	21	22	23	24	25	26	27	28	
48	47	46	45	44	43	42	41	31	32	33	34	35	36	37	38	
Lower left	Lower right	

The tooth numbers from the table can be read as follows: 11 and 21 are the maxillary central incisors in left and right jaws, respectively and 18 and 28 are the maxillary third molars in the left and right jaws, respectively.

Acousto-ultrasonic test

As explained briefly in the Introduction section the Acousto-Ultrasonic test is based on inducing stress waves through the material and their recording by a piezoelectric sensor. Hsu-Nielsen source (mechanical pencil with brittle graphite lead) is used as the source to simulate stress waves to the aligner, since it produces a burst like signal that resembles growing crack signals in thin plates30. Moreover, the signal generated by this source generates a wide frequency response, which is useful for the analysis31–33. The piezoelectric sensor used in this study is a lightweight miniature PICO sensor (Physical Acoustics) with an operating frequency up to 750 kHz and resonant frequencies at 250 kHz and 550 kHz. The sensor signals are amplified by 40 dB and registered in a PAC PCI-2 data acquisition system at a sample rate of 2 MHz. The waveforms are recorded for a length of 2048 samples with a pre-trigger of 512 samples. The pre-trigger instructs the data acquisition system the length of the continuous waveform to be recorded before the threshold exceeding sample point. Therefore, the time-domain parameters extracted from the waveforms are pre-trigger dependent. In this study, since the waveforms are recorded at a sample rate of 2 MHz, waveforms of length 1.024×10-3 s are recorded with a pre-trigger of 0.256×10-3 s.

The sensor is held firmly onto the cast by a mechanical clip. A thin layer of silicone grease is applied between the sensor surface and the cast to ensure good acoustic coupling. The position of the sensor is close to the third molar position (see Supplementary S1 for tooth positions and the position of the sensor). This position is selected since it is the flattest position on the dental cast where the sensor makes full contact with the surface.

The cast and the aligners are mounted on a Universal Testing machine (in order to simulate the same conditions as the cyclic loading described in the subsequent sections), INSTRON 3344 with a 1 kN load cell. The upper and lower casts are held firmly at a constant pressure of 10 MPa. The test is carried out in two modes: without the aligners (propagation test on the casts) and with the aligners, in order to understand the attenuation and dispersion of the acoustic waves propagating through the casts from the aligners. First, the casts are brought into contact with a minimum compressive load of 5 N (approx.) to ensure that there are no vibrations or external interferences during the AU test. Then, for the second mode, the clear dental aligner is mounted on the upper cast and the same procedure is followed as before.

The AU test is performed on six different teeth positions: tooth 18, 14, 11, 21, 24 and 28, the maxillary third molars, the maxillary first premolars, and the maxillary central incisors. The acoustic events are generated from the flat mid position of each tooth positions (refer to Supplementary S1 section for more information). The AU test is repeated 3 times for each tooth position, simulating 3 signal acoustic event each time.

Cyclic compression tests

The mechanical performance of the dental aligners is studied under cyclic loading. The cyclic test is designed to simulate the occlusal forces acting on the aligner during the swallowing action during the aligner usage. The tests are conducted in a load-controlled mode with the cyclic compression load is applied at a frequency of f = 0.25 cycles/s. The loading stages of a single cycle are as follows:Stage 1 Compression load ramped up from 0 to 50 N in 1 s.

Stage 2 Dwell time of 1 s with the compression load 50 N.

Stage 3 Compression load ramped down from 50 to 0 N in 1 s.

Stage 4 Dwell time of 1 s at 0 N.

For the convenience of the readers, a schematic representation of the loading cycles is presented in the Supplementary file under the Sect. S2.

It is reported that the maximum occlusal forces exerted on the jaws of a human during a swallowing action is 50 N34–36. Similarly, the maximum duration of the occlusal contact lasts for a maximum of 1 s during swallowing34. Based on these factors, the compression load and dwell time for the cyclic compression loads are selected. The test is repeated for 22,500 cycles, which relates to the average swallowing action in two weeks period, which is also the average usage time of the clear aligners25,37. It is reported that there is no certain median value on the number of swallows even on healthy human population. Both early and recent studies report that a healthy human swallows between 203 and 1008 times a day38,39. For favourable testing conditions to evaluate the mechanical performance under real usage conditions, in the present study, the number of swallows is set to be 1500 times per day for the usage time of 15 days of the aligner.

To simulate the oral environment during the cyclic test, the aligner is made to be in contact with artificial saliva solution (The chemical composition of the artificial saliva solution used is provided in Supplementary S3) during the entirety of the test. For that, a sponge is impregnated with the artificial saliva solution and placed in a manner that it does not impend the loading while staying in contact with the aligner. The entire setup is enclosed by cellulose hydrate film. The test setup of the dental aligner cast, and the final test setup is presented in Fig. 1a,b, respectively.Fig. 1 (a) Test setup showing the casts and the aligner. (b) Final test setup including sponge, envelope for saliva, and AE sensor.

The energy absorbed by the aligners at different cycles and their respective stiffness values are calculated from the hysteresis curve of load–displacement curves. The energy absorbed is the total area enclosed by the hysteresis loop, while the stiffness is calculated from the slope of the curve during the loading stage.

Optical microscopy

For fractographic analysis on the tested aligners, the damaged surfaces are observed under optical microscope (NIKON SMZ800), which has a maximum magnification of ×6.3. The aligners are cleaned with acetone and dried before observing under the microscope with a white light source being used for illumination.

Results

Propagation of acoustic waves through the dental aligners

Representative AE waveforms in their time domain propagated through the dental cast (without the dental aligner) and their respective frequency domain characteristics (FFT results) are presented in Fig. 2a,b, respectively.Fig. 2 (a) Acoustic waves propagated through the hard dental cast, represented in their time-domain and (b) their frequency characteristics in the FFT spectrum.

The sensor is placed close to the third molar (tooth 18) and the peak amplitudes of the simulated AE signals from these positions are higher than those from other positions. Particularly, the AE signals from the incisors (teeth 11 and 21) are very low. The greater attenuation in signal propagation as the distance between the source and the sensor increases is expected4,40.

The frequency components of the propagated signals are centred between the 100 and 200 kHz frequency bands. The peak frequencies of the signals from teeth 18 and 28, respectively are, 123 kHz and 185 kHz. A trend can be seen in the frequency domain. The peak frequency shifts towards the higher frequency at different teeth positions. For example, the peak frequency of the AE signals from tooth 24 is 169 kHz. On the other hand, signals from the incisors (teeth 11 and 21) show a large amount of dispersion. Comparing the results of Fig. 2a,b, it can be observed that apart from the attenuation due to the propagating distance of the AE signals, a large amount of dispersion is also observed when the location of the AE source is far away from the sensor. This can be attributed to both the inhomogeneity of the propagating medium and the complex propagation path4,16,17. Nevertheless, it can be ascertained that the central frequencies of the propagated AE waves are between 100 and 200 kHz.

The AU test is continued with the aligners, TPET-G and TPU positioned on the upper cast. The frequency characteristics of the acoustic waves propagated through these aligners are compared with those propagated through the dental cast alone (without the aligners in place). This gives a clear indication on how the propagation of the acoustic waves is affected when these aligners are mounted.

The frequency characteristics of the AE waves simulated from the maxillary third molars (teeth 18 and 28) are presented in Fig. 3a,b, maxillary first premolars (teeth 14 and 24) in Fig. 3c,d, and central incisors (teeth 11 and 21) in Fig. 3e,f, respectively.Fig. 3 Frequency characteristics of the acoustic waves propagated through the aligners compared with the ones propagated through the Dental Cast; simulated from (a) Tooth 18, (b) Tooth 28, (c) Tooth 14, (d) Tooth 24, (e) Tooth 11, and (f) Tooth 21 Positions.

The difference in amplitude of the propagated waves from symmetrical teeth positions such as 18/28, 14/24 and 11/21 is because the sensor is positioned in a non-axisymmetric position, as explained in the previous section. Therefore, this difference in amplitudes is not considered for discussion.

When the acoustic waves are propagated through the dental aligners, a large amount of attenuation can be observed in both the cases, teeth 18 and 28. The spectral amplitude of the signals dropped from 8.5×10-3 a.u. to 3.2×10-3 in TPET-G and 2.7×10-3 in TPU (see Fig. 2a). However, there is little to no dispersion in the low frequency components. In fact, the peak frequencies are still around 125 kHz. On the other hand, the high frequency components completely vanishes when the acoustic waves are simulated through the aligners. The spectral amplitudes of the frequency components above 250 kHz completely vanishes. This is not due to the attenuation of these low magnitude/high frequency components because the low magnitude/low frequency components (even below 50 kHz) are preserved. Similar observations can be made also in Fig. 2b where the acoustic waves are generated from the tooth 28. The high frequency components above 250 kHz vanishes entirely, large attenuations and little to no dispersion is observed in the frequency components between 100 and 200 kHz.

Similar to the propagation characteristics from the maxillary third molars, the frequency components above 250 kHz vanish when the acoustic waves are propagated from teeth 14 and 24. A significant amount of attenuation can also be observed here in Fig. 3c,d between the acoustic waves propagated through the cast and the aligners. Little to no dispersion is observed, however. Also in this case, the significant frequency components of the propagated waves lie between 100 and 200 kHz.

The large amount of attenuation in the propagated acoustic waves are observed even in the absence of the aligners in Fig. 2a,b, due to the propagating distance between the source location and the sensor. Although the major frequency components lie between 100 and 200 kHz, a definite frequency peak could not be identified as in the other two cases. Now, the waves propagated through the aligners have attenuated even further, particularly in TPET-G (see Fig. 3e,f). It can be surmised that in the dental aligners when the source location is far away from the sensors, particularly in the central incisors, the propagated acoustic waves cannot be taken into consideration for analysis. This means that, if the damage sources are located at the central incisors during the mechanical loading of the aligners, a large amount of attenuation and dispersion can be expected from the propagated acoustic waves. It can even vanish if their amplitude is very low.

Of course, this can be rectified by placing multiple sensors at different dental positions. However, the complex geometry of the cast and its irregular surface does not permit positioning of multiple sensors.

Cyclic test results

The cyclic test results are presented and discussed in this research in terms of the energy absorption and stiffness changes in the aligners for all the loading cycles. For each cycle, the load–displacement hysteresis curve is extracted. Energy absorbed by the aligner is calculated as the area within the hysteresis loop and the stiffness is calculated as the first slope of the bilinear stiffening in the loading phase of the hysteresis curve. For the sake of brevity, the hysteresis curves are not presented here. They can be found in the Supplementary file under Sect. S4. For detailed information about the mechanical performance of the aligners, the readers are requested to refer to the authors’ previous article41.

The energy absorbed by the aligners at different loading stages and the respective variation in their stiffness are calculated from the hysteresis curves and the results are presented in Fig. 4a,b.Fig. 4 Mechanical performance of the clear dental aligners: (a) energy absorbed and (b) stiffness during the cyclic compression test.

In Fig. 4a, the energy absorbed by TPET-G is relatively lower than that of TPU. The energy absorbed by TPET-G increases from 3.6 Nmm in cycle 100 to 4.52 Nmm in cycle 4000. Beyond that, the average absorbed by TPET-G is around 4.6 Nmm, and it remains almost stable until the end of the test (22,500 cycles). In TPU, the energy absorbed dropped sharply after the first 200 cycles from 6.8 to 5.6 Nmm and it remains relatively stable until cycle 9000 (average energy absorbed is 5.95 Nmm). Post cycle 9000, the energy absorbed increases slightly to 6.4 Nmm and beyond that there is a steep decrease. The energy absorbed at cycle 17,000 is in fact 2.6 Nmm, which is lower than the average energy absorbed by TPET-G.

The stiffness of TPET-G remains relatively stable compared to TPU in Fig. 4b, where the stiffness increases steeply up until cycle 17,000 and stablishes until the end of the test.

Fractographic results using optical microscopy

The inner surface of the clear dental aligners after the compression cyclic tests are tested under optical microscope (NIKON SMZ800). The fractographic analysis is carried out on different dental positions of the aligners. The teeth which have shown significant damages are presented in this section.

Several small cracks of length less than 1 mm and some strain hardened regions are found in the aligners, which could have arisen during the thermoforming process. In Supplementary S5, a microscopic image of untested aligner is presented to observe the effects of the thermoforming process.

The fractographic images of TPET-G and TPU aligners at different tooth positions are presented in Figs. 5 and 6, respectively.Fig. 5 Microscopic images of TPET-G taken from different dental positions. (a) Tooth 14; (b) Tooth 18; (c) Tooth 26 and (d) Tooth 27.

Fig. 6 Microscopic images of TPU taken from different dental positions. (a) Tooth 17; (b) Tooth 18; (c) Tooth 21 and (d) Tooth 27.

Acoustic emission results from the cyclic compression tests

The AE signals from the cyclic compression tests on the aligners are recorded using the same piezoelectric sensor used in the AU test. The AE signals are recorded in burst-mode of acquisition with each ‘hit’ is recorded when it crosses the detection threshold of 26 dB. The signals are registered at a sample rate of 2 MHz, similar to the procedure followed during the AU test. Similarly, the signals are recorded for a length of 1024 µs with a pre-trigger of 256 µs.

Based on the frequency information obtained from the AU results in “Fractographic results using optical microscopy” section, it can be assumed that in the recorded AE signals, the significant frequency components may lie between 100 and 200 kHz.

The AE analysis is made in two different modes: in the frequency domain using the peak frequency of the signal FFT and in the time domain using the Time of Arrival (ToA) picked by Akaike Information Criterion (AIC). AIC is quite popular in estimating the ToA of signals (any non-stationary data in general) and the procedure is explained by several authors. The detailed procedure about AIC is reported by Kitagawa and Akaike7. A brief description on the ToA calculation procedure with an example signal from the TPU dental aligner is presented in the Supplementary Sect. S6. It should be noted that the ToAs calculated in this study are pre-trigger dependent, similar to any other time domain descriptor. However, this does not affect the damage source analysis since it is not used as a standalone descriptor. The damage source analysis is performed by integrating the time domain and frequency domain descriptors with the AU test results.

The characteristics of the AE signals generated from TPET-G and TPU are compared with their mechanical characteristics (energy absorbed) and are presented respectively in Figs. 7 and 8.Fig. 7 Energy absorbed by TPET-G during the cyclic compression test compared with the AE signal characteristics: (a) peak frequency and (b) ToA.

Fig. 8 Energy absorbed by TPU during the cyclic compression test compared with the AE signal characteristics: (a) peak frequency and (b) ToA.

Discussion

The frequency characteristics of the AE signals generated during the compression cycle test can be estimated approximately through the results of the AU test. The frequency characteristics of the acoustic waves not only depends on the propagating medium but also on the damage source and the characteristics of the sensor used. Hsu–Nielsen source is often used to emulate the acoustic waves generated from the damage sources such as crack growth in polymer-based materials. Based on this and the results of the AU test, it can be surmised that the damage sources in dental aligners might generate acoustic waves of significant frequency components centred between 100 and 200 kHz. Moreover, if the damage sources are from the central incisors (or generally far away from the sensor location), the acoustic waves generated from these sources may go unaccounted for. Despite this shortcoming, the expected frequency components of the acoustic waves generated from the damage sources are approximated using the AU approach.

However, in Figs. 7a and 8a, there are several AE signals that have frequencies above 400 kHz. In TPET-G, these signals appear in two distinct zones with varying frequencies: one around Cycle 450 and the other around Cycle 22,500 (at the end of the test). Their time and frequency domain characteristics are analysed. The results showed that the signals that have frequencies above 400 kHz are generally high frequency noise, and therefore, these results are presented in Supplementary Sect. S7. Similar observations are observed also in the AE data collected from TPU, where most of these noise signals appear at the end of the test (although a countable number of them sporadically appears in other cycles).

Towards the mechanical test results, which consequently generated the AE signals, the TPET-G and TPU aligners are significantly different in terms of their energy absorption characteristics and stiffness behaviour.

Generally, in thermoplastic composites, under cyclic loading, the energy absorbed during the initial cycles is due to large (strain) deformation. This can explain the initial increase in the energy absorbed by both the aligners, which is observed in Fig. 4a. The large strain deformation in these thermoplastics is typically followed by strain hardening42–46. During the strain hardening stage, the energy absorbed by the aligners and their stiffness are expected to remain stable. It is observed in TPET-G, where the average stiffness after cycle 8000 (until the end of the test—cycle 22,500) is 162.2 ± 4.3 N/mm (see Fig. 4b). However, this phenomenon is not observed in TPU. In fact, the energy absorbed by the TPU aligner decreases steeply after 17,000 cycles while the stiffness increases exponentially between cycles 5000 and 17,000. After this, it remains more or less stable. Why the energy absorbed decreases steeply at 17,000, while the stiffness increases exponentially up to the same cycle? Possibly, the energy absorbed by this aligner is released by a local failure and the strain hardening is localised to a smaller region to the vicinity of this failure. Therefore, the stiffness increases exponentially up to cycle 17,000. It can be assumed that the energy absorbed by the TPU is released rapidly by some major damage (such crack nucleation or crack growth). In merit of validating these observations, the fractographic results of the tested aligners must be discussed.

Minor cracks and small chip formation can be found in teeth 26 and 27, respectively (see Fig. 5c,d). There are two possible sources for the minor cracks and the chip formation in the molar region: one is the cracks formed due to the thermal stress induced during the thermoforming process and the other is the sliding occlusal contacts made by the hard dental cast on the mandibular arch47. The sliding occlusal contact could be the source for the chip formation on tooth 27 in Fig. 5d. Strain hardened regions (whitening) are found in tooth 18 (Fig. 5b). The thermal stress may be induced on the aligners during the thermoforming process, which resulted in local strain hardened regions. Only one major crack of length greater than 1 mm is observed in this aligner, which is at tooth 14 (see Fig. 5a). This crack is located adjacent to some other minor cracks. This shows that despite the formation of this one major crack, the energy absorbed by this aligner, or its stiffness remains highly unaffected. Nevertheless, they appear to not have affected the energy absorbed by the TPET-G aligner.

In TPU, however, a large crack of length exceeding 3.50 mm is observed in tooth 27 (Fig. 6d). This crack is adjacent to three other cracks of length, which originates from the apex of the crown of the tooth propagating along the stretch marks of the strain hardened regions. This possibly resulted from the sliding occlusal contacts between the hard dental cast and the aligner. The presence of this crack clearly shows that the energy absorbed by this aligner during its initial loading stages is released during the crack growth. Possibly, at cycle 17,000, the amount of energy released during this crack growth is quite high, which resulted in the steep decrease in the energy absorbed by this aligner. The presence of localised crack and the strain hardened region in the vicinity of the cracks confirms the assumptions made in earlier in this section regarding the damage sources in TPU dental aligners.

Apart from this major crack, similar to TPET-G, several minor cracks and strain hardened regions are also observed in TPU. Particularly, they are observed in teeth 17 (Fig. 6a), 18 (Fig. 6b) and 21 (Fig. 6c). The comparison between the mechanical results and fractographic analysis explained the occurrence of damages and their dental location. However, it still remains unclear at which cycle these cracks starts to initiate. They probably initiated from the minor cracks formed during the thermoforming process, but at which cycle they begin to nucleate remains unanswered. For this, the acoustic waves propagated from these aligners are analysed and discussed in the next section.

The number of AE events generated from TPET-G is much lower than that of TPU. It is evident from the microscopic results that the TPU suffered most damage with cracks of length greater than 3.5 mm and other minor cracks propagating towards the strain hardening region (see Fig. 6). TPET-G, on the other hand, suffered less damage and consequently, less generation of AE signals. The stability in the energy absorption characteristics also concur with these observations. The distribution of peak frequencies of the AE signals from TPET-G are presented in Fig. 7a. Their distribution can be found in four specific regions: one between cycles 5000 and 10,000 and the other from 17,000 to the end of the test, and two others highly localised at Cycle 450 and Cycle 22,500, respectively. As mentioned earlier, it is established that the latter two localised distributions are possibly noise. Therefore, the discussion is kept only for the former two regions. The first region between cycles 5000 and 10,000 signifies that a crack begins to propagate at cycle 5000 and it continues until cycle 10,000 where it stops to grow further. It begins to grow again at 17,000 cycles and extends until the end of the test. How can it be ascertained that these signals are generated from the same crack? Comparing the peak frequency of these AE signals with the results from the AU tests, it can be observed that the stress waves generated from different dental positions have different frequencies, due to the dispersion. Since the peak frequencies are localised around 125 kHz, it can be assumed that they are generated by the same damage source. Few sample FFT results of the AE signals from these two regions are presented in Supplementary Sect. S7. Their frequency characteristics share similarity with the AE signals propagated through the dental cast. Moreover, the ToA of the AE signals in Fig. 7b also shows similar values. The average ToA of the AE signals recorded from TPET-G is 3.09±0.07×10-4 s. These results can be used to draw a safe conclusion that these signals are possibly generated from a same source.

The only major damage source observed in TPET-G in the fractographic analysis is in tooth 14 (left maxillary premolar). The peak frequency of the stress wave generated from tooth 14 during the AU test (see Fig. 3c) is around 120 kHz, similar to the peak frequencies of AE signals generated during the cyclic loading of TPET-G. Therefore, it is safe to assume that the damage source in TPET-G is left maxillary premolar (tooth 14), which generated AE signals at frequencies around 125 kHz at two different periods of the cyclic tests: between cycles 5000–10,000 and between cycles 17,000–22,500.

In TPU, the presence of several cracks results in the large amount of AE signal generation. Between cycles 1000 and 14,000, a significant number of AE signals with peak frequencies around 125 kHz is recorded (see Fig. 8a). Another group of AE signals with peak frequencies between 150 and 200 kHz are recorded from 7500 cycles up to 17,000 cycles. After 17,000 cycles, there is an idle period of about 2500 cycles, where no AE signals are recorded (see Fig. 8a). Now, the signals with the peak frequencies around 125 kHz can be associated with cracks in the left maxillary premolars, similar to that of TPET-G. The second group of signals from 7500 cycle possibly could be the one observed in tooth 27. This is established based on several factors. First, this can be established by comparing the frequency characteristics of the stress waves generated from right maxillary third (tooth 28) in the AU test (see Fig. 3b). Second, the fractographic analysis shows the presence of multiple large cracks in tooth 27 (see Fig. 6d). Third, the ToA of these signals in Fig. 8b has an average of 3.1±0.08×10-4 s, which may infer that these signals could possibly be generated from the same source (similar to the observations made in TPET-G). These conclusions are not drawn solely from one result but rather by integrating all the aforementioned three results. And finally, the energy absorbed by TPU drops suddenly at cycle 17,000. These observations conclude that the crack in tooth 27 of TPU began to grow steadily from cycle 7500 and terminated at cycle 17,000 by releasing a large amount of energy. This is followed by an idle period where no AE signals being generated. The FFT results of these signals are also presented in the Supplementary Sect. S7 for verification.

The ToA and the frequency bands of the AE signals aid in identifying the two distinct damage sources in TPU. The presence of other frequencies such as one around 50 kHz and some other signals above 200 kHz could possibly be generated due to the friction between the cracked PU elements of the aligner. The FFT of these signals are presented in the Supplementary Sect. S7, which confirms that their frequency features do not resemble the propagated signals in the AU test. At this moment, it can only be assumed that it is not generated from the crack growth event. Further analysis may be required to understand their source.

Conclusion

The damage sources in two different clear dental aligners, TPET-G and TPU are localised by using AE technique and AU approach. Generally, it is highly difficult to evaluate damage sources in a complex geometry using AE testing. However, in this research work, first, the characteristics of stress wave propagation in the aligners are studied using the AU approach. Based on these results, the AE signal analysis is designed. The frequency characteristics of the AE signals generated during the cyclic loading of the aligners and their ToA are able to locate the damage sources at different dental positions. These results are validated by the fractographic analysis of the aligners. Nevertheless, the conclusions are drawn based on the results obtained by using one sensor. In the future work, this approach could be extended to adapt multiple sensors and a profound damage analysis.

Supplementary Information

Supplementary Information.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-72553-2.

Acknowledgements

One of the Authors (Vimalathithan Paramsamy Kannan) acknowledges the support of the following: Funder: Project funded under the National Recovery and Resilience Plan (PNRR), Mission 4 Component 2 Investment 1.4—Call for tender No. 3138 of December 16, 2021 of Italian Ministry of University and Research funded by the European Union—NextGenerationEU. Award Number: CNMS denominato MOST, Concession Decree No. 1033 of June 17, 2022 adopted by the Italian Ministry of University and Research, CUP: D93C22000410001, Spoke 14” Hydrogen and New Fuels”. One of the Authors (Cianci Claudia) acknowledges that this work was partly supported by the Italian Ministry of University and Research under the Programme “Department of Excellence” Legge 232/2016 (Grant No. CUP—D93C23000100001)”.

Author contributions

Claudia Cianci—Methodology, Validation, Investigation, Formal Analysis, Data Curation, Writing—Original Draft, Writing—Review and Editing; Claudia Barile—Methodology, Validation, Investigation, Formal Analysis, Writing—Review and Editing; Vimalathithan Paramsamy Kannan—Conceptualization, Methodology, Validation, Investigation, Software, Formal Analysis, Data Curation, Writing—Original Draft, Writing—Review and Editing; Giovanni Pappalettera—Conceptualization, Methodology, Validation, Investigation, Formal Analysis, Writing—Review and Editing, Supervision; Caterina Casavola—Resources; Carmine Pappalettere—Conceptualization; Domenico Ciavarella—Conceptualization, Methodology, Resources, Writing—Review and Editing, Supervision; Michele Laurenziello—Conceptualization, Methodology, Resources, Writing—Review and Editing.

Data availability

The datasets generated during and/or analysed during the current study are not publicly available due to ongoing investigations but are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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