Thermo-mechanical characterization of NiTi orthodontic archwires with graded actuating forces

Thermo-mechanical characterization of NiTi orthodontic archwires with graded actuating forces

journal of the mechanical behavior of biomedical materials 107 (2020) 103747 Contents lists available at ScienceDirect Journal of the Mechanical Beh...

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journal of the mechanical behavior of biomedical materials 107 (2020) 103747

Contents lists available at ScienceDirect

Journal of the Mechanical Behavior of Biomedical Materials journal homepage: http://www.elsevier.com/locate/jmbbm

Thermo-mechanical characterization of NiTi orthodontic archwires with graded actuating forces ~es a, E. Camacho a, A. Lopes a, A. P. Freitas Rodrigues a, b, *, F.M. Braz Fernandes a, R. Magalha c d e S. Paula , R. Basu , N. Schell a

CENIMAT/I3N, Materials Science Department, NOVA School of Science and Technology, Universidade NOVA de Lisboa, Caparica, Portugal CEMMPRE, Mechanical Engineering Department, University of Coimbra, Coimbra, Portugal Mechanical Engineering and Materials Department-SE-4, Instituto Militar de Engenharia–IME, Rio de Janeiro, Brazil d School of Metal Construction Skills, Bhartiya Skill Development University Jaipur, India e Helmholtz-Zentrum Geesthacht, Institute of Materials Research, HZG, Geesthacht, Hamburg, Germany b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Orthodontic archwires Mechanical behavior Phase transformation temperature Functionally graded

Functionally graded NiTi orthodontic archwire was tested to assess the evolution of the actuation force as a function of the temperature. Varying actuation forces on the same orthodontic wire allow the optimization of repositioning of the different types of teeth, according its radicular support. The wire was separated into three segments: Incisive, Premolar and Molar. The functionally graded NiTi orthodontic archwire segments have distinct structural and mechanical behavior as confirmed by differential scanning calorimetry, synchrotron-based X-ray diffraction, and thermomechanical analysis. The mechanical behavior was analyzed by three-point bending tests at four different temperatures (5, 20, 25 and 37 � C). In parallel, three-point bending tests were performed by TMA analysis in a temperature range from 5 � C (from cold water) to 40 � C (hot meal). This study showed the comparison of the different segments on the same archwire, providing a better understanding of the behavior of these functionally graded materials.

1. Introduction Since the beginning of the orthodontic archwire manufacturing back in the 70’s, these have become more complex and convenient for different clinical cases. The orthodontic archwires are used to move the teeth with a low and continuous force. When a force is applied, the or­ thodontic archwire needs to display an elastic behavior during a period of weeks to months. Moreover, different stages (initial, intermediate or final) of the orthodontic treatment require different orthodontic arch­ wires (Melsen et al., 2007) (Proffit et al., 2013). NiTi orthodontic archwires are the most commonly used archwires at initial stage of orthodontic treatment (leveling and alignment) due to their unique properties: the shape memory effect and superelasticity (Evans and Durning, 1996). (T. Saburi, 1998) (Melsen et al., 2007) (Riley and Bearn, 2009) (Proffit et al., 2013) These functional properties are attributed to a martensitic transformation. This transformation may be thermal or stress-induced, and it may take place directly from austenite (parent phase with B2 cubic symmetry; space group Pm3m) to

martensite (product phase with B19’ monoclinic symmetry; space group P21 =m) or may go through an intermediate phase, the R-phase (trigonal symmetry; space group P3) (Otsuka and Ren, 2005). Stress-induced martensite (SIM) promotes the superelasticity and thermal-induced martensite (TIM) promotes the shape memory effect. Therefore, martensitic transformations in NiTi alloys present both thermal and mechanical hysteresis. As known (Frenzel et al., 2010), Ni content can control these functional properties: Ni-rich and equiatomic NiTi alloys display the superelastic effect close to room temperature and above it and Ti-rich NiTi alloys display the shape memory effect above room temperature. When the material is cooled from austenite (A) domain, the martensite (M) starts forming at a given temperature (Ms temperature). The transformation from austenite to martensite is referred to as direct transformation and finishes at martensite finish temperature (Mf tem­ perature). Thus, when the material at low-temperature phase (M) is heated up to a given temperature, the austenite phase starts to be formed; this temperature is known as temperature and the

* Corresponding author. CENIMAT/I3N, Materials Science Department, NOVA School of Science and Technology, Universidade NOVA de Lisboa, Caparica, Portugal. E-mail address: [email protected] (P.F. Rodrigues). https://doi.org/10.1016/j.jmbbm.2020.103747 Received 31 January 2020; Received in revised form 17 March 2020; Accepted 20 March 2020 Available online 4 April 2020 1751-6161/© 2020 Elsevier Ltd. All rights reserved.

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transformation finishes when the Af temperature is reached. This transformation is referred to as reverse transformation. Even when the material is deformed in the martensitic domain up to a certain extent (in most cases up to 10%), this deformation can be retained by the material, as long as the martensitic stability temperature range is maintained. However, the material starts recovering the original shape when it is heated above As temperature. When Af is reached, the recovery by shape memory effect should have finished: thermally-induced martensite (Otsuka and Ren, 2005). On the other hand, the stress-induced martensitic transformation, which promotes the superelastic effect, occurs when a stress is applied to the material within a given range of temperature where austenite is thermally stable. The deformation during loading may be recovered after complete removal of the applied stress, up to 10% strain (Dolce and Cardone, 2001) (Otsuka and Ren, 2005) (Ohara, 2016). The conventional superelastic NiTi orthodontic archwires show a homogeneous composition along the wire. However, the forces required to move the teeth are different for the incisor, premolar and molar teeth. It is known that to have different actuating forces on the same wire it is necessary that the wire displays a structural gradient across its length. It is possible to produce this functional gradient by changing the Ni/Ti ratio in the austenite matrix, mainly through heat treatment, such as annealing, that promotes the Ni4Ti3 precipitate formation. This precip­ itation induces a local change of the Ni/Ti ratio in the surrounding matrix and, as a consequence, modifies the transformation temperatures range and the loading and unloading plateaus of the stress-strain curves during the superelastic regime (Y. Suzuki, 1998) (Otsuka and Ren, 2005). Taking into account the structural gradient, some manufacturers (Dentsply - GAC, 2008) use the localized heat treatments to produce this effect and obtain the archwires that display different actuating forces across the same archwire (Mahmud et al., 2007) (Bashir S. Shariat a et al., 2017) (Braz Fernandes et al., 2019) (Karami et al., 2020).. Due to high capacity of functionally graded materials in solving complex problems such as requiring a wider controllable range of temper­ ature/stress range (Bataillard et al., 1998), they also have been used for engineering applications in thermal, structural, optical and electronic materials (Miyamoto et al., 1999). In the literature, few studies reported the investigation about the functionally graded orthodontic archwires (Mullins et al., 1996) (Mehta, 2015) (Freitas Rodrigues, 2018). Mullins et al., 1996 reported that these archwires apply low and gentle forces in the incisive teeth, increasing the forces across the premolars up to the molars’ teeth. This force begins at 0.8 N and increases up to 3 N, in order to provide the appropriate force to each tooth, promoting the comfort of the patient (Mullins et al., 1996). Miura (1991) patented a thermally graded NiTi archwire (Bio­ Force archwires by GAC Dentsply) with the following heat treatment configuration at 500 � C: molar region heat treated for 5 min, premolar during 15–60 min and posterior region during 1–2.5 h (Miura, 1991) (Mehta, 2015). However, there is a gap in the literature about the effect of the heat treatment temperature on structural gradient and corresponding me­ chanical behavior of functionally graded NiTi orthodontic archwires. The superelastic behavior can be analyzed by three-point bending test at different temperatures, comparing the plateau during unloading that has been defined as the superelastic actuation region during the orthodontic treatment. Several studies reported investigations about the mechanical behavior of superelastic and thermal active orthodontic archwires (Mullins et al., 1996) (Iijima et al., 2002) (Parvizi and Rock, 2003) (Mallory et al., 2004) (Juvvadi et al., 2010) (Peres et al., 2012). The information about the mechanical behavior at different tem­ peratures is important because the oral temperature presents wide variation during the day due to the ingestion of hot and cold food and drinks, and also due to the fact that different areas in the oral cavity present different temperatures. Therefore, the structural characteristics of the orthodontic archwire can be changed (Sakima et al., 2006). Moore

et al. investigated the temperature variation at archwire position adja­ cent to maxillary right central incisor and first premolar. They reported that the temperatures ranged from 5.6 to 58.5 � C (median 34.9 � C) at incisor and from 7.9 to 54 � C (median 35.6 � C) at the premolar (Moore, 1999). The synchrotron radiation-based X-ray diffraction (SR-XRD) may be used to understand the structural characteristics of the commercial or­ thodontic archwire because this technique allows for a precise mea­ surement in the analyzed samples. Using high energy X-rays, it is possible to work in transmission mode. The Differential Scanning Calorimetry (DSC) techniques allows to check its transformations characteristics. Combining the SR-XRD anal­ ysis with the DSC provides a better understanding of the materials behavior during mechanical tests performed at different temperatures. The aim of this study was to investigate the temperature dependence of mechanical properties (three-point bending test) of different seg­ ments of the same orthodontic functionally graded archwire in order to provide a better understanding of their functional behavior. 2. Material and methods 2.1. Material In this investigation, a class of functionally graded NiTi orthodontic archwire (NiTi orthodontic Archwire – BioForce Dentsply GAC Inter­ national, Inc., Central Islip, NY, USA) with 0.4 � 0.4 mm was analyzed. In order to investigate the variable actuating forces in the same wire, the orthodontic archwire was separated into three parts, as shown in Fig. 1. 2.2. Methods The transformation temperatures of the different segments were characterized by Differential Scanning Calorimetry (DSC) following the ASTM F2004-05 standard. Two thermal cycles from 150 � C to þ150 � C and þ5 to þ40 � C with heating/cooling rate of 10 � C/min were used. The transformation temperatures were determined using the tangent method. The second DSC cycle was used to clarify the interpretation of TMA tests (run from þ5 to þ40 � C) in a narrower temperature range which is closer to the working temperature range. SR-XRD was used to determine the existing phases in each archwire segment at room temperature. The experiment was performed in transmission mode, at beamline P07 High Energy Materials Science (HEMS) of Petra III/DESY, using a wavelength of 0.124 Å (98 keV). A beam spot of 200 � 200 μm2 was used to scan the wire along its length (40 mm to ensure the analysis of the three segments - S01, S02 and S03 with the spacing distance of 1 mm) and a 2D detector PerkinElmer was

Fig. 1. – Scheme of the segments S01, S02, S03 of the studied orthodontic archwire.Dimensions in mm. 2

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placed at 1.65 m from the sample. The raw 2D images were treated using the Fit2D program in order to calculate the individual XRD patterns by integration from 0 to 360� along the azimuthal angle (Hammersley et al., 1996; Oliveira et al., 2016). For the SR-XRD measurement, the identification of the diffraction peaks was based on the ICDD database. The thermomechanical analysis (TMA) was performed using a PT 1600 from Linseis in all segments (S01, S02 and S03) within the tem­ perature range from þ5 to þ40 � C, using a heating/cooling rate of 1 K/ min. The tests were run in three-point bending mode, using a support span of 9 mm and an actuation force following a triangular waveform (frequency of 0.01 Hz); the force ranged from 100 to 1250 mN, in order to accommodate the different deformation characteristics of the austenite (higher temperature range) and R-phase (lower temperature range). The maximum deflection of the wires (at different temperatures) ranged from 100 μm to 750 μm. In order to simulate the orthodontic treatment in an oral environ­ ment and the simulated force exerted on a lingually displaced maxillary lateral incisor (International Organization for Standardization. ISO 15841: Dentistry – wires for use in orthodontics. Geneva: ISO; 2006., n. d.) (ISO 15841), a three-point bending test was carried out for each section of specimen wire. The tests were performed at different tem­ peratures: 5 � C, 20 � C (commonly room temperature in the orthodontic room), 25 � C (conventional room temperature) and 37 � C (human body temperature). The wire was heated/cooled for 5 min to reach the test temperature. The length size of each wire segment, 15 mm, was chosen in agreement with ISO 15841:2006 (International Organization for Standardization. ISO 15841: Dentistry – wires for use in orthodontics. Geneva: ISO; 2006., n.d.). All samples were loaded with the same pro­ tocol on a tensile machine (Shimadzu AG-50kNG equipped with a 500 N load cell). The measurement was performed by immersion in a water bath with a controlled temperature. Each wire was first loaded to a deflection of 2 mm and then unloaded at a rate of 0.5 mm/min. The displacements of 1.0, 0.75 and 0.5 mm upon unloading were used as references for the measurement of the actuation forces, as shown in Fig. 2. Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) was used to assess the micromorphological and compositional characteristics of the archwire segments. The Scanning Electron Microscopy (FEI Quanta-3D field emission gun-scanning elec­ tron microscope (FEG-SEM) study of the samples was performed, coupled with an SD-EDS Detector (X-Max 80, Oxford Instruments) for compositional analysis. The acceleration voltage was maintained at 15 keV for all the segments. Before examination by SEM, samples were cut, polished and then chemically etched (15 vol% HF þ 45 vol% HNO3 þ 40 vol% H2O) in order to remove surface oxides and the deformation layer.

3. Results and discussion 3.1. Structural characterization To understand the characteristics of the commercial orthodontic archwire at room temperature and to analyze the influence of the tem­ perature and applied stress, SR- XRD, EDS were used. Fig. 3a shows the superimposition of the X-ray diffraction patterns obtained at room temperature along 40 mm of the wire covering S02 and part of the neighboring S01 and S03 regions, with the spacing distance of 1 mm. Fig. 3b shows 3 representative X-ray patterns, one for each segment: S01 (green), S02 (blue) and S03 (red). Diffractograms obtained at S03 are well indexed by the B2 austenitic phase. The B2 peak was observed with different intensities along the functionally graded wire and the R-phase is identified at segments S01 and S02. Ni4Ti3 diffraction peaks were observed in the S01 region. These observations support the existence of a functional gradient throughout the length of the wire. The average Ni/Ti ratio in the matrix segments of the wire changes from 1.076 (S01) to 1.252 (S03) with an average value of 1.18 � 0.11 (Table 1). The decreasing content of Ni on the matrix from S03 to S01 is related to the localized heat treatment that gives graded functional characteristics. The formation of the Ni-rich precipitates (Ni4Ti3) during such heat treatment decreases the Ni content in the matrix. SEM observations of S01, S02 and S03 region of the orthodontic archwire are depicted in Fig. 4. Each section (S01, S02 and S03) had a similar characteristic surface structure. This observation shows that there are second phases in the B2 matrix. EDS analysis revealed that the composition of the lens-like phase precipitates (highlighted by letter a) was Ni-rich, thus suggesting the Ni4Ti3 presence. In addition, it was observed the presence of oxides that can be associated with Ni2Ti4O (highlighted by letter b) and carbides that can be associated with TiC (highlighted by letter c), which are often present in these materials, due to the processing history (Y. Suzuki, 1998). Fig. 5 shows the load-deflection curves for the test of three segments at room temperature (20 � C). At room temperature, the three segments present some unrecovered deformation decreasing from S01 to S03, in agreement with the decreasing presence of the R-phase, also from S01 to S03. There is a clear difference between the mechanical behavior of the different segments. According to the EDS measurement (Table 1), the S03 specimen shows the highest Ni content on the matrix, which is confirmed by a typical mechanical behavior for the austenitic alloy. It can be seen that the upper plateau increases from S01 to S03, as a result of the increasing Ni content and corresponding decreasing trans­ formation temperatures; thus, for the same Clausius-Clapeyron ratio, a decreasing transformation temperature should give rise to increasing critical stress for the stress-induced martensitic transformation (Otsuka and Ren, 2005). Again, these observations support the existence of a functional gradient along the wire (Nespoli et al., 2015). 3.2. Thermal and thermomechanical analysis Fig. 6 depicts the DSC charts of the three segments for the broader temperature range ( 150 to þ150 � C). The S03 shows the Af near room temperature while S01 and S02 segments are slightly above that. All the curves on heating presented Af temperatures lower than 37 � C (human body temperature), indicating the capability of actuation via the superelastic effect during orthodontic treatment. The DSC results show a two-step transformation during the cooling, suggesting that B2↔R and R↔B19’ transformation occurred. For all archwire segments, the presence of intermediate R-phase is in agree­ ment with other studies (Bradley et al., 1996) (Mehta, 2015). On heating, S01 and S02 segments show only one transformation peak, suggesting that B19’ ↔ B2 transformation took place in one step.

Fig. 2. – Displacements (0.5, 0.75 and 1.0 mm) analyzed in the deflection curve (inclination of the deactivation curve - superelastic behavior). 3

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Fig. 3. SR-XRD patterns at room temperature for the three segments along the wire length. a) superimposition of the XRD patterns of all scans along the wire to observe the graded functionally wire. b) diffraction patterns for the three segments to compare the phases present at room temperature.

superelasticity effect). Moreover, during heating, this deflection ampli­ tude rate starts increasing up to a maximum that occurs at a temperature above 25 � C for the S02 and S03 segments. These results are confirmed by the mechanical tests that show that S01 and S02 segments have relatively lower actuating forces than the S03 segment, as evidenced in Fig. 5.

Table 1 The matrix chemical composition of orthodontic archwire (atomic percent [at %]) measured by energy-dispersive X-ray analysis. Segments S01 S02 S03

Chemical Composition

Ni/Ti ratio

Ni [at%]

Ti [at%]

51.82 54.96 55.59

48.18 45.04 44.41

1.076 1.220 1.252

3.3. Evolution of the actuation force x temperature The analyzed points of the displacement (0.5, 0.75 and 1.0 mm) are the points related to the clinically advisable rate of biological tooth movement in 4–5 weeks after implementation of the archwires (Pilon

S03 heating curve shows a peak on the onset side which would indicate the presence of two steps: B19’ → R-phase → B2, which is in agreement with the literature (Bradley et al., 1996) (Brantley and Eliades, 2001). Other studies (Brantley et al., 2003) (Nespoli et al., 2015) also used DSC measurements to show the R-phase transition. They observed a broad­ ening of the heating peak and suggested a mixture of the phases (B2 R–B190 ) in the archwire segments. To clarify the transformation characteristics, a DSC analysis was performed in the range from 5 to 40 � C (Fig. 7) where only the B2↔Rphase transformation is taking place, as shown in Table 2. The results show a trend of decreasing transformations temperature ranging from S01 to S03 qualitatively similar to the literature (Mehta, 2015). Considering the R-phase presence, three-point bending results per­ formed by TMA are plotted together with the second DSC test (þ5 to þ40 � C cycle) as shown in Fig. 7; the temperature range 5–40 � C has been chosen to have a narrower temperature range closer to working temperature of the archwire and also to have the R-phase transformation peak well centered both in cooling and heating. The three-point bending test for all three segments shows that the deflection of the wire remains constant at the highest temperature range (above 30 � C) where the austenite is thermally stable (full recovery of the deformation by

Fig. 5. – Plot of representative load-deflection data for the three segments tested at room temperature.

Fig. 4. - Scanning electron micrographs of the three segments of the wire. 4

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The results for 20 � C will be discussed taking into consideration the fact that this is common room temperature in the orthodontic clinical room. As mentioned before, this measurement was performed by im­ mersion in a water bath with a controlled temperature. S01 section did not display a significant actuation force. A light actuating force was just observed for the S03 and S02. This indicates that the deformation is easier at this temperature and can be bent into desirable shapes with no risk of permanent deformation. The range of the actuating forces (superelastic behavior) is: S01 is null, S02 from 0.05 to 0.46 N and S03 from 0.5 to 0.95 N (Fig. 8 f). The results for the different segments tested at 5 � C shows no unloading plateaus and increasing unrecovered deformation from S03 to S01. This suggests that all the segments were not in the fully austenitic field. In general, the manufacturing of NiTi orthodontic archwires goes through a complex metallurgical process. Chemical composition, heat treatments, and thermomechanical processes all influence the properties of the wires. The different segments of the NiTi orthodontic archwire used in this study show: 1) different structural characteristics; 2) distinct phase transformation temperatures; 3) different load-deflection curves for all the tested conditions. The samples showed a superelastic behavior at 37 � C (body tem­ perature simulation), as well as at 25 � C. At 37 � C, the actuation forces may be considered light and practically constant during unloading in the range from 1 mm to 0.5 mm. All the segments showed the typical plateau for superelasticity. The section S03 as the molar segment, S02 as the premolar segment, and S01 as the incisive segment, showed a decreasing actuating force with an average of the actuating forces ranging from 2 N (S03), 1.3 N (S02) down to 0.7 N (S01). Similar behavior is reported in the literature (Mehta, 2015). The lower load levels correlated with the Af temperatures suggest that the actuating force levels at which the superelastic effect occurs are lower for the segments of the wire which have higher Af temperatures. The different behavior of each segments evaluated in this study is a

Fig. 6. a) DSC curves of three segments. Room temperature is highlighted by the black line.

et al., 1996) (Proffit et al., 2013). For this reason, all the values reported here represent data from the force-displacement curves during the unloading portion in the range 0.5–1.0 mm. These curves are depicted in Fig. 8 (a), (b) and (c). Fig. 8 (d), (e) and (f) depict the variation of actuating forces as a function of displacements along the superelastic lower plateau of each segment at the tested temperatures. During the orthodontic treatment, 37 � C is the most important actuation temperature. Thus, the discussion about tests at 37 � C will be presented first. The results at this temperature show that the range of actuating forces is significant for all the segments. None of the segments showed unrecovered deformation after the three-point bending test. Higher actuating force for the unloading superelastic plateau was recorded for the S03 segment compared to the S01 and S02 segments. For S03, the forces varied from 1.92 to 2.09 N, for S02 from 1.28 to 1.43 N and for the S01 segment from 0.56 to 0.88 N (Fig. 8d). As expected, the molar segment yielded higher actuating force values. The results at 25 � C are similar to those obtained at 37 � C since the Af is close to this temperature. For 25 � C, lower actuating forces are observed when compared to the corresponding actuating forces at 37 � C. At 25 � C there is also full recovery of the deformation (superelastic behavior). The range of the actuating forces (superelastic behavior) is as follows: S01 from 0.14 to 0.48 N, S02 from 0.90 to 1.24 N and S03 from 0.79 to 1.11 N (Fig. 8e).

Table 2 -Phase transformation temperatures in � C. Cooling S01 S02 S03

Heating

Rs

Rf

As

Af

21.5 20.8 20.0

19.3 17.7 14.6

21.4 19.4 15.3

23.7 22.7 22.0

Fig. 7. - DSC and three-point bending (TMA) results for the three segments of the archwire. 5

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Fig. 8. – Force x Stroke curves for the three segments of the archwire (a) S01, (b) S02, (c) S03 at four temperatures (5, 20, 25 and 37 � C). Actuation forces as a function of displacement during unloading at 37 � C (d), 25 � C (e), 20 � C (f).

direct consequence of the localized heat treatment carried on in distinct regions of the archwire (Mehta, 2015). Extrapolating these results to a clinical situation, it can be suggested that when the patient ingests warm drinks the force delivered by these archwires will overall increases stimulating the right tooth movement. This increase of the actuating force will be more notorious for S03, compared to S02 or S01. Conversely, cold drinks reduce the force delivered by these archwires, providing greater patient comfort. Due to adequate actuating force delivered in each archwire segments this can promotes the reduction of the number of archwire changes along the alignment stage of the orthodontic treatment. Orthodontic archwires with homogeneous structure will have uniform actuating forces along the full length; adapting the actuation force to the speci­ ficity of each type of tooth will require more archwire setting changes during the alignment stage of the orthodontic treatment (Evans and Durning, 1996). (Mullins et al., 1996) (Proffit et al., 2013) (Mehta, 2015).

- At the human body temperature, the archwire shows the superelastic behavior for all the segments; - Clinically, the temperatures of 5 � C and 20 � C are interesting because at these temperatures the formability is higher, making it easier to correctly shape the archwire before its insertion in the patient’s mouth. The increase of the temperature is necessary to achieve the superelastic effect since Af is above room temperature. At human body temperature all the segments are fully austenitic. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement P. Freitas Rodrigues: Writing - original draft, Data curation. F.M. Braz Fernandes: Supervision, Funding acquisition, Methodology, ~es: Writing - review Validation, Writing - review & editing. R. Magalha & editing, Funding acquisition. E. Camacho: Data curation, Software, Visualization. A. Lopes: Data curation, Visualization. A.S. Paula: Su­ pervision. R. Basu: Data curation, Resources. N. Schell: Resources, Data curation.

4. Conclusions It is expected that functionally graded orthodontic archwire may show the shape memory effect and may generate continuous and light forces in different ways for each tooth. The following conclusions can be drawn from this work: - The functional gradient is clearly put in evidence by SR-XRD; - The orthodontic archwire tested has different mechanical properties along the length of the wire; - The analysis of the phase trans­ formation temperatures of all the three segments of the orthodontic wire show that all Af temperatures are below oral/body temperature; - There are significant differences of the actuating forces during unloading (lower superelastic plateaus) when comparing the different segments of the archwire at different temperatures;

Acknowledgments P.F.R., F.M.B.F., E.C., A.L. acknowledge the funding of CENIMAT/ I3N by COMPETE 2020, through FCT, under the project UID/CTM/ 50025/2013. P.F.R acknowledge the funding of CEMMPRE by Project PTDC/CTM-CTM/29101/2017 – POCI-01-0145-FEDER-029101 funded by FEDER funds through COMPETE2020 - Programa Operacional ~o (POCI) and by national funds Competitividade e Internacionalizaça 6

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Journal of the Mechanical Behavior of Biomedical Materials 107 (2020) 103747

(PIDDAC) through FCT/MCTES. This research is sponsored by FEDER funds through the program COMPETE – Programa Operacional Factores ~o de Competitividade – and by national funds through FCT – Fundaça para a Ci^encia e a Tecnologia –, under the project UID/EMS/00285/ 2019.“A.S.P, and P.R. acknowledge the funding of CAPES (APQ-1 2009/ 02 E-26/110.414/2010, APQ-1 2011-2 E-26/110.269.2012, E-26/ 111.435/2012 – CsF/Brazil – BEX 11943-13-0) and CNPq (research ~o productivity scholarship PQ-2 – Process 307798/2015-1). Dr. Joa Pedro Oliveira, UNIDEMI-Universidade Nova de Lisboa for the collab­ oration during SR-XRD analysis. The authors acknowledge the Dentsply GAC International, Inc., Central Islip, NY, USA.

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