- Email: [email protected]
Finite element analysis comparing WaveOne, WaveOne Gold, Reciproc and Reciproc Blue responses with bending and torsion tests
Author’s Accepted Manuscript Finite element analysis comparing WaveOne, WaveOne Gold, Reciproc and Reciproc Blue responses with bending and torsion tests María Prados-Privado, Rosa Rojo, Carlos Ivorra, Juan Carlos Prados-Frutos www.elsevier.com/locate/jmbbm
PII: DOI: Reference:
S1751-6161(18)31297-9 https://doi.org/10.1016/j.jmbbm.2018.10.016 JMBBM3030
To appear in: Journal of the Mechanical Behavior of Biomedical Materials Received date: 5 September 2018 Revised date: 4 October 2018 Accepted date: 5 October 2018 Cite this article as: María Prados-Privado, Rosa Rojo, Carlos Ivorra and Juan Carlos Prados-Frutos, Finite element analysis comparing WaveOne, WaveOne Gold, Reciproc and Reciproc Blue responses with bending and torsion tests, Journal of the Mechanical Behavior of Biomedical Materials, https://doi.org/10.1016/j.jmbbm.2018.10.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Finite element analysis comparing WaveOne, WaveOne Gold, Reciproc and Reciproc Blue responses with bending and torsion tests María Prados-Privado 1,2,#,*, Rosa Rojo 3 , Carlos Ivorra 2, and Juan Carlos Prados-Frutos 3,# Department of Continuum Mechanics and Structural Analysis. Higher Polytechnic School, Carlos III University, Avenida de la Universidad, 30. 28911, Leganés, Madrid, Spain. 2 ASISA Dental. Research Department. C/ José Abascal, 32. 28003, Madrid, Spain. 3 Department of Medicine and Surgery, Faculty of Health Sciences, Rey Juan Carlos University, Avda. Atenas s/n, 28922, Alcorcón, Madrid, Spain. * Correspondence: [email protected]; Tel.: +34-916-249-500 1
# Equal contribution
Abstract: To evaluate the bending and torsional properties of four nickel-titanium endodontic files, we simulated and compared WaveOne® primary size 25 with 0.07 taper, WaveOne Gold® primary size 25 with 0.07 taper, Reciproc® primary size 25 with 0.08 taper, and Reciproc Blue® primary size 25 with 0.08 taper. Three-dimensional models were created using computer-aided design software and numerically analyzed in ANSYS® Workbench. Boundary conditions for the numerical analyses were based on the ISO 3630-1 specifications. The highest stress levels were recorded for WaveOne® and Reciproc®. Numerical results of the bending test showed that WaveOne Gold® is 86 % more flexible than WaveOne® with a deflection of 3 mm. Reciproc Blue® was 42.31 % more flexible than Reciproc® file with a deflection of 3 mm. The WaveOne® instrument withstood the highest stress under the torsion test, followed by Reciproc®, then Reciproc Blue® files. The stress under torsion in the WaveOne® and WaveOne Gold® files is reduced in a 51%. Regarding Reciproc® and Reciproc Blue® files, the stress under torsional moments remains very similar. Our results exposed a considerable difference in terms of stress tolerance between WaveOne® and WaveOne Gold®. However, Reciproc® files demonstrated a similar stress distribution. The results obtained through finite element analysis suggest that thermal treatment of files might improve their flexibility, increasing resistance during the preparation of highly curved canals. Also, the values obtained regarding the improvement of flexibility were in accordance with the manufacturer claims. Keywords: bending resistance; endodontic file; finite element analysis; nickel titanium; thermal treatment
1. Introduction Endodontic treatment is a clinical intervention that aims to treat infections in the root canal of the tooth. This treatment involves a reciprocating motion which reduce the stress on the files and allows clinicians to use only a single instrument for root canal preparation [1]. This motion has a better root preparation than rotary motion and reduced the cyclic and torsional fatigue [2]. Compared with the continuous rotation of the endodontic files and independently of other variables such as the angle of curvature, the rotation speed or the surface characteristics of the NiTi instruments, the reciprocating movement improves the resistance to cyclic and torsional fatigue [2,3]. It also allows the clinician to perform root canal preparation better and with a unique instrument [1,3]. WaveOne® and Reciproc® files use reciprocating motion in which the direction of rotation alternates between counterclockwise and clockwise direction, and the use of WaveOne Gold® and Reciproc Blue® has been commercialized with improvements in behavior to the fatigue of the instruments.
Metals 2018, 8, x FOR PEER REVIEW
2 of 15
This procedure employs endodontic instruments composed of nickel-titanium (NiTi) alloy [4]. Rotary files are commonly made of NiTi alloy because this material is flexible, super elastic, and has excellent shape memory [5], demonstrating a nonlinear elastic behavior that allows the material to undergo high deformation without plastic residual-strain after stress removal. Rotary NiTi instruments have more advantages than stainless steel instruments as they require less procedural time and produce less canal aberrations [4]. The differences in the mechanical properties between rotary instruments are due to the variation in materials, geometrical factors such as pitch length, taper or conicity, cross-sectional shapes, and manufacturing conditions used [6]. All these characteristics affect clinical performance. From a mechanical point of view, NiTi alloys seem to be better suited than stainless steel for the complex anatomy of root canals. This has been clinically verified by studies like the one published by Pettiette et al. where a NiTi alloys had a better clinical prognosis in endodontics compared with the use of stainless steel [7]. Nickel-titanium files were introduced to avoid unwanted changes in the morphology of root canals caused by stainless steel files [8]. From the clinical point of view both instruments obtain outcomes in terms of success, amount of residual bacteria and similar cleaning capacity. However, NiTi files are associated with lower canal transportation and apical extrusion [9]. The mechanical properties of NiTi rotary files, including flexibility and torsional resistance, are fundamental requirements of endodontic instruments for successful use [10]. Good flexibility is crucial to maintain the shape of root canals; an acceptable torsional resistance reduces the probability of the occurrence of the intracanal separation [11]. The super-elastic behavior of NiTi depends on the crystallographic phases and the thermal, mechanical, and chemical treatments to which the alloy has been subjected. This alloy used in endodontic treatment contains approximately, 55 wt % Ni and 45 wt % Ti [12]. One method of increasing the efficiency of NiTi rotary files is improving the manufacturing process. The NiTi alloy has three different microstructure phases that are temperature-dependent: austenite, martensite, and R-phase [13]. R-phase and martensitic NiTi are soft and ductile and can be easily deformed, whereas austenitic NiTi is strong and hard [14]. The mechanical properties of nickel-titanium alloys and, in particular, super-elasticity and shape memory, are influenced by heat treatment conditions [15,16]. The transformation temperature at which the crystal structure changes from austenite to martensite or vice versa affects to super-elasticity and shape memory properties. The rotary files have a better super-elasticity if the NiTi alloy is fully austenite whereas, in case of full martensite, the rotary instruments have a better shape memory property [10,16,17]. Manufacturers have introduced several thermally treated NiTi alloys to optimize the microstructure and transformation behavior [18]. This behavior is due to a reversible solid-state transformation from the parent phase austenite to a new crystallographic structure called martensite [4]. Unfortunately, these heat treatments are unknown due to the protection of intellectual property and they have not been divulged by manufacturers [19]. From a clinical point of view, the fracture of the files is an event that should be considered to avoid performing the complicated technique of removing the separated instrument, subject to considerable risks, especially in the apical third [20]. The prevalence of fracture in rotating nickel titanium instruments is in the range of 0.4 to 5% [21]. Different manufacturers have made various modifications to the alloys to reduce the probability of fracture. The ISO 3630-1 guideline details [22] the conditions required for in vitro tests of endodontic treatment. Torsional stiffness and bending flexibility are the two most essential properties required in any rotary file, which determines file performance in clinical use [23]. These two properties have been studied extensively and have been described as two of the most important causes of fracture [24]. Because these experimental tests are very expensive, among other factors, a finite element analysis is a good alternative for studying the mechanical behavior of endodontic instruments. Some studies have analyzed the influence of instrument geometry on flexibility and torsional stiffness by
Metals 2018, 8, x FOR PEER REVIEW
3 of 15
using finite element analysis [25,26], but no studies have compared the mechanical behavior of WaveOne Gold® and Reciproc Blue® files using a numerical analysis. As WaveOne Gold® and Reciproc Blue® have now been commercialized, only some in vitro studies have been published regarding the mechanical behavior of these rotary files [27,28]. However, from the best of our knowledge, no numerical studies in the literature have analyzed and compared the behavior of WaveOne Gold®, Reciproc Blue® and their former instruments. Therefore, the contribution of this paper is that the bending and torsional resistance of WaveOne Gold® and Reciproc Blue® are analyzed. The aim of this study was to evaluate the mechanical behavior of four commercially available instruments using the finite element method and compare the numerical results between them. 2. Materials and Methods 2.1. Endodontic instruments analyzed The most widely known NiTi file systems are WaveOne® (Dentsply Maillefer, Ballaigues, Switzerland) and Reciproc® (VDW, Munich, Germany), which are made of M-Wire alloy [29,30]. The WaveOne® file has a convex triangular cross-sectional design [31]. WaveOne Gold Primary® has a cross-section with a parallelogram structure with two cutting edges, but the most important modification is the alloy employed, which is based on heating the file and then slowly cooling it [31]. Reciproc® files have an S-shaped cross section with two cutting edges. Reciproc Blue® also has a heat treatment. Figure 1 details the three types of NiTi rotary instruments examined in this study.
Figure 1. Endodontic instruments: (a) WaveOne®; (b) WaveOne Gold®; (c) Reciproc® and Reciproc Blue®.
2.2. Finite element model 2.2.1. Three-dimensional model
Metals 2018, 8, x FOR PEER REVIEW
4 of 15
Three-dimensional (3D) models were created using the computer-assisted design (CAD) software SolidWorks® 2016 (Dassault Systèmes, SolidWorks Corp., Concord, MA, U.S.). Then, all models were imported to the ANSYS® Workbench 16 (Canonsburg, PA, U.S.) where the simulation was computed. 2.2.2. Material properties WaveOne® and Reciproc® files are composed of NiTi alloy. The mechanical parameters of this super-elastic alloy are detailed in Table 1 [4]. Table 1. Parameters used to describe nickel-titanium (NiTi) super-elastic behavior, obtained from de Arruda Santos et al. [4].
Parameter
(
)
Description
Value
Austenite elasticity Austenite Poisson’s ratio Martensite elasticity Martensite Poisson’s ratio Transformation strain
42530 MPa 0,33 12828 MPa 0,33 10 %
loading Start of transformation loading End of transformation loading
(
)
unloading Start of transformation unloading End of transformation unloading End of martensitic elastic regime
6.7 492 MPa 630 MPa 6.7 192 MPa 97 MPa 1200 MPa
WaveOne Gold® and Reciproc Blue® files are made of NiTi alloy through a thermal treatment process. The files were analyzed with two different temperatures and their corresponding material properties because the temperature at which the heat treatment is performed is unknown. Two temperatures were used in this study: 700º and 800 ºC. The material properties after thermal treatment at those temperatures were obtained from Safdel et al. from hot compression tests, at different temperatures, under the strain rate of 0.001 s–1 [32]. These two temperatures resulted in the improvement in the flexibility that the manufacturer details.
(a)
(b)
Figure 2. Material properties after thermal treatment (a) at 700 ºC and (b) at 800 ºC
2.2.3. Boundary conditions The boundary conditions used to simulate the behavior of the endodontic instruments aligned with the ISO 3630-1 specifications [22]. For the bending resistance test, the file was held 3 mm from the tip, preventing any displacement in the x, y, and z-axes. The shaft was deflected until a 45°
Metals 2018, 8, x FOR PEER REVIEW
5 of 15
inclination. This procedure was performed in x and y directions, taking into account eventual differences resulting from bending orientation. Figure 3 represents these conditions.
Figure 3. Boundary condition for bending test.
For the torsion resistance test, the endodontic instrument was held three mm from the tip and a clockwise torsional moment of 0.3 Ncm [4,25] was applied, as shown in Figure 4.
Figure 4. Boundary condition for torsion test.
2.2.4. Mesh Mesh generation was performed in ANSYS® Workbench 16 (Canonsburg, PA, U.S.). All endodontic files were meshed with a fine mesh and all regions of stress concentration that were of interest were manually refined. The convergence criterion involved a change in von Mises stress in the model of less than 5 % [33]. The element type employed in all analyzed was SOLID187. Table 2. Number of nodes and elements.
WaveOne® WaveOne Gold® Reciproc® Reciproc Blue®
Number of nodes
Number of elements
24,256 31,343 36,758 32,904
12,371 19,420 24,254 21,490
3. Results 3.1. Bending resistance test Figure 5 illustrates the bending deformation with displacement in the y-axis and shows the von Mises stress distributions in the cross-section at three mm from the tip for each instrument. A maximum stress of 1146 MPa appeared at one vertex of the triangle in the WaveOne® file. The behavior of the WaveOne Gold® and Reciproc Blue® files was analyzed with two different temperatures. Figure 5 demonstrates that the thermal treatment at 800 ºC caused a higher maximum von Mises stress than the thermal treatment at 700 ºC. In both cases, maximum stress was lower than those withstood by WaveOne® file under the same conditions. The von Mises stress for WaveOne Gold® instrument was 26 % lower than that obtained by the WaveOne® file, under the same boundary conditions.
Metals 2018, 8, x FOR PEER REVIEW
6 of 15
Figure 5. Results of bending test analysis in y-axis: von Mises stress distribution (MPa) in the cross-section at 3 mm from the tip.
A maximum stress of 942 MPa appeared in Reciproc® file. The highest stress appeared near the corner of the S-shaped section. The von Mises stress for the Reciproc Blue® instrument at 700 ºC was 35% lower than obtained in the Reciproc® file under the same boundary conditions. The values of the bending moment detailed in Table 3 were obtained by multiplying the registered bending force by the distance between the point at which the force was applied and the fixed tip of the instrument. Table 3. Bending resistance test results summary at 700 ºC.
Deflection (mm) 1 2 3 Maximum stress (MPa)
WaveOne®
Bending at 700 ºC (Ncm) WaveOne Δ (%) Reciproc® Gold®
Reciproc Blue®
Δ (%)
0.05 0.04 0.15
0.18 0.4 1.1
97.22 90.00 86.36
0.09 0.51 0.9
0.17 0.88 1.56
47.06 42.05 42.31
1146.6
847.35
–26.10
942.48
614.21
–34.83
As shown in Table 3, with a deflection of three mm, the WaveOne Gold® file at 700ºC was 86.36 % more flexible than the WaveOne® file. Reciproc Blue® with the same deflection and tempered treatment was 42.31 % more flexible than the Reciproc® file. Flexibility decreased as deflection increased in both cases. Table 4 summaries bending resistance results at 800 ºC. In view of these results, the maximum stress for both WaveOne Gold® and Reciproc Blue® were higher than those recorded in the same rotary files at 700 ºC. The improvement in bending resistance at 800 ºC was also worse than found in the same instruments at a lower temperature. Table 4. Bending resistance test results summary at 800 ºC.
Metals 2018, 8, x FOR PEER REVIEW
Deflection (mm) 1 2 3 Maximum stress (MPa)
WaveOne®
7 of 15
Bending at 800 ºC (Ncm) WaveOne Δ (%) Reciproc® Gold®
Reciproc Blue®
Δ (%)
0.05 0.04 0.15
0.18 0.14 0.49
72.22 71.43 69.39
0.09 0.51 0.9
0.12 0.65 1.14
33.33 27.45 26.67
1146.6
864.3
–24.58
942.48
835.15
–11.39
Figure 6 details the stress distribution along the body of the instruments. Stress in all rotary files was concentrated around three mm from the tip.
Figure 6. Stress distribution along the body of the instruments.
Figure 7 illustrates the von Mises stress distributions in the cross-section three mm from the tip for each instrument when the displacement was applied along the x-axis.
Metals 2018, 8, x FOR PEER REVIEW
8 of 15
Figure 7. Stress distribution pattern of the bending test analysis along the x-axis for the cross-section three mm from the tip.
3.2. Torsion resistance test Figure 8 illustrates the von Mises stress distribution in the cross-section three mm from the tip for each instrument analyzed in this study.
Metals 2018, 8, x FOR PEER REVIEW
9 of 15
Figure 8. von Mises stress (MPa) after torsion resistance test.
The Maximum stress in the WaveOne Gold® instrument was lower than those recorded for the WaveOne® file under the torsional test. In this case, the maximum stress was similar at both temperatures, but thermal treatment at 700 ºC resulted in the lowest stress. For Reciproc Blue®, the maximum stress recorded with heat treatment was similar to that recorded in the instrument without thermal treatment. In view of torsional test simulations, the stress pattern highly depended on the cross-section geometry. In the case of the Reciproc® files, the temperature was a secondary factor in stress distribution. Figure 9 represents the stress distribution in the body of the rotary file after the torsion resistance test. The stress was concentrated near the place where the file was fixed and decreased as it moved away from the point of support, at three mm from the tip.
Figure 9. Stress distribution in the body of the instrument after the torsion resistance test.
Metals 2018, 8, x FOR PEER REVIEW
10 of 15
Table 5 summaries torsional results at 700 ºC. As shown in Table 5, the difference of stresses in the WaveOne® and WaveOne Gold® files with each of torsional moments remains constant. In this case, the stress on file with the heat treatment is reduced in a 51%. Regarding Reciproc® and Reciproc Blue® files, the stress under torsional moments remains very similar. Table 5. Torsional test results summary at 700 ºC.
Torsion at 700ºC
Maximum stress [MPa]
Torsional moment [Ncm]
WaveOne®
WaveOne Gold®
Δ(%)
Reciproc®
Reciproc Blue®
Δ(%)
0,1 0,2
330,05 660,09
160,95 321,69
-51,23% -51,27%
226,23 452,46
221,7 444,96
-2,04% -1,69%
0,3
990,14
481,98
-51,32%
678,69
669,75
-1,32%
4. Discussion This study analyzed and compared the flexibility and torsion resistance of four different endodontic instruments via finite element analysis. The boundary conditions imposed to simulate the behavior of the endodontic instruments were in accordance with the ISO 3630-1 specifications [22]. To perform the numerical study, it was necessary to introduce the values of the material properties of the NiTi. Because of the intellectual property, the temperature of the heat treatment was unknown, and the studies were carried out with different temperatures (700 and 800ºC). Once the results were obtained, the flexibility in each file was checked and compared with what the manufacturer claims. Finally, a torsional test was also carried out. The material properties of NiTi alloy were obtained from the literature, although the detailed thermomechanical process was unknown due to the protection of intellectual property [10]. The transformation temperature is one of the crucial factors influencing the mechanical properties of NiTi alloys and resulting in differences in their bending properties [34,35]. WaveOne Gold® and Reciproc Blue® files were thermally treated. Because the thermal treatment temperature was unknown, two different temperatures were simulated, and the file flexibility differences were measured both with and without thermal treatment. To the best of our knowledge, no numerical studies in the literature have analysed the bending and torsional resistance of WaveOne Gold® and Reciproc Blue®. Several NiTi alloy thermomechanical procedures were used with the aim of improving the flexibility of NiTi files [36,37]. The main finding in our study was that the new WaveOne Gold® and Reciproc Blue® files with super-elastic properties were studied at different temperatures for their treatment of nickel titanium tempering through finite elements. We verified that the results offered by the manufacturers are compatible with those obtained. WaveOne® and Reciproc® recorded the highest stress levels, close to the plastic regime of martensite (1200 MPa), as demonstrated by the stress distribution results. This value aligns with those obtained for RaCe (FKG Dentaire, La-Chaux-de-Fonds, Switzerland) size 25 with 0.06 taper and PTU F1 (DentsplyMaillefer, Ballaigues, Switzerland) in a bending resistance test [4]. Notably, the nonlinearity of the curves in both bending and force occurred because of the large displacements [38]. The numerical results from the bending test showed that WaveOne Gold® is 86 % more flexible than WaveOne® with a deflection of three mm at 700 ºC. Reciproc Blue® is 42.31 % more flexible than the Reciproc® file with a deflection of three mm at 700 ºC. The manufacturer claims that their Gold files are 80 % more flexible than the standard instrument, and Blue files are 40 % more flexible than Reciproc®. However, the values obtained for the same test at 800 ºC did not approach the values stated by the manufacturer. The highest temperature resulted in improvements in flexibility below 70 % for the WaveOne and 27 % for the Reciproc.
Metals 2018, 8, x FOR PEER REVIEW
11 of 15
The von Mises stress distribution patterns were affected by the cross-section geometry and the material properties. According to the results in Figure 5, stress concentrated in the area at the corner of the triangle, whereas the rest of the geometries distributed the stresses more uniformly. In Figure 7, the stress distribution pattern was quite similar in the x and y directions for the WaveOne® and Reciproc® files. However, a considerable difference was observed in this pattern when the orientations of WaveOne Gold® and Reciproc Blue® were changed. In Figure 6, the stress in all rotary files concentrated around three mm from the tip, although after the torsional test, stress concentrated near the place where the file was fixed and decreased moving away from the point of support at three mm from the tip. Cyclic fatigue failures in WaveOne Gold, Reciproc®, and Reciproc Blue® appeared in different analyses are in accordance with the area where the maximum stress was experienced in this study [39,40]. The WaveOne® instrument experienced the highest stress under the torsion test, followed by Reciproc® and Reciproc Blue® files. WaveOne Gold® files experienced the least stress. Stress values obtained in this study are comparable with those obtained by other analyses with similar conditions [41]. Torsional stiffness of endodontic instruments is also associated with cutting efficiency [4]; however, it could not be evaluated through this numerical analysis. Thermally treated files experienced lower stress values than common nickel titanium files, which means that they have a greater resistance to torsion and better cutting efficiency [5,42]. Considerable differences in terms of stresses were found between WaveOne® and WaveOne Gold®; however, stress in Reciproc files were quite similar. Kim et al. reported that stress levels in instruments under torsion were influenced by many factors, such as the geometry of the cross-section, area of the continuous inner core, radial land, and peripheral surface ground [41]. The influence of the combination of these aspects on the stress distribution along the endodontic instruments under torsion remains uncertain. This study shows that the effect of the alloy is less important in this type of test than the cross-section geometry. Several differences were observed in the design and materials used in fabrication of endodontic files that considerably influence file properties. Therefore, clinical must understand the properties and the differences of these materials to select the system that accomplishes the optimum clinical results. This study has some limitations and assumptions. The geometry of the endodontic files was created using CAD software according to the specifications detailed by the manufacturer. This limitation is consistent with other numerical studies [5]. The use of a simplification in the cross-section geometry also aligns with other numerical studies [43]. Another limitation is the treatment process assumption, as well as the percentage of austenite and martensite. In this case, the material properties were obtained from hot compression tests at different temperatures of 700 and 800 ºC under a strain rate of 0.001 s–1 [32]. From the best of our knowledge, no numerical studies in the literature have analysed WaveOne Gold® and Reciproc Blue® behavior, but our results are comparable with those obtained through in vitro tests under similar conditions [41].
5. Conclusions The results obtained through finite element analysis suggest that thermal treatment of files might improve their flexibility, increasing resistance for the preparation of curved canals. However, according to the results obtained in the bending resistance test, considering the limitations of the study, the improvements in the flexibility mentioned by the manufacturer are obtained with a heat treatment at 700 ºC. With the assumptions and limitations of this study and in view of the results obtained, we conclude that WaveOne Gold® has better clinical behavior.
Metals 2018, 8, x FOR PEER REVIEW
12 of 15
Future work in this area could include a probabilistic approach to study the long-term behavior of endodontic instruments. With this approach, authors should be able to provide principal statistics of fatigue life and the probability of failure associated with each cycle load. Acknowledgments: The work was supported by Grant A-274 (Rey Juan Carlos University– Neodent) and Grant A-285 (Rey Juan Carlos University – Proclinic SA). Conflicts of Interest: The authors declare no conflict of interest.
References 1.
Alcalde, M. P.; Duarte, M. A. H.; Bramante, C. M.; de Vasconselos, B. C.; Tanomaru-Filho, M.; Guerreiro-Tanomaru, J. M.; Pinto, J. C.; Só, M. V. R.; Vivan, R. R. Cyclic fatigue and torsional strength of three different thermally treated reciprocating nickel-titanium instruments. Clin. Oral Investig. 2018, 22, 1865–1871, doi:10.1007/s00784-017-2295-8.
2.
Karataş, E.; Arslan, H.; Büker, M.; Seçkin, F.; Çapar, I. D. Effect of movement kinematics on the cyclic fatigue resistance of nickel-titanium instruments. Int. Endod. J. 2016, 49, 361–364, doi:10.1111/iej.12453.
3.
Ferreira, F.; Adeodato, C.; Barbosa, I.; Aboud, L.; Scelza, P.; Zaccaro Scelza, M. Movement kinematics and cyclic fatigue of NiTi rotary instruments: a systematic review. Int. Endod. J. 2017, 50, 143–152, doi:10.1111/iej.12613.
4.
de Arruda Santos, L.; López, J. B.; de Las Casas, E. B.; de Azevedo Bahia, M. G.; Buono, V. T. L. Mechanical behavior of three nickel-titanium rotary files: A comparison of numerical simulation with bending and torsion tests. Mater. Sci. Eng. C 2014, 37, 258–263, doi:10.1016/j.msec.2014.01.025.
5.
El-Anwar, M. I.; Yousief, S. A.; Kataia, E. M.; El-Wahab, T. M. A. Finite Element Study on Continuous Rotating versus Reciprocating Nickel-Titanium Instruments. Braz. Dent. J. 2016, 27, 436–441, doi:10.1590/0103-6440201600480.
6.
Melo, M. C. C.; Pereira, E. S. J.; Viana, A. C. D.; Fonseca, A. M. A.; Buono, V. T. L.; Bahia, M. G. A. Dimensional characterization and mechanical behaviour of K3 rotary instruments. Int. Endod. J. 2008, 41, 329–338, doi:10.1111/j.1365-2591.2007.01368.x.
7.
Pettiette, M. T.; Delano, E. O.; Trope, M. Evaluation of success rate of endodontic treatment performed by students with stainless-steel K-files and nickel-titanium hand files. J. Endod. 2001, 27, 124–7.
8.
Pedrinha, V. F.; Brandão, J. M. da S.; Pessoa, O. F.; Rodrigues, P. de A. Influence of File Motion on Shaping, Apical Debris Extrusion and Dentinal Defects: A Critical Review. Open Dent. J. 2018, 12, 189– 201, doi:10.2174/1874210601812010189.
9.
Del Fabbro, M.; Afrashtehfar, K. I.; Corbella, S.; El-Kabbaney, A.; Perondi, I.; Taschieri, S. In Vivo and In Vitro Effectiveness of Rotary Nickel-Titanium vs Manual Stainless Steel Instruments for Root Canal Therapy: Systematic Review and Meta-analysis. J. Evid. Based Dent. Pract. 2018, 18, 59–69, doi:10.1016/j.jebdp.2017.08.001.
10.
Zhou, H.; Peng, B.; Zheng, Y.-F. An overview of the mechanical properties of nickel-titanium endodontic instruments. Endod. Top. 2013, 29, 42–54, doi:10.1111/etp.12045.
11.
Yared, G.; Kulkarni, G. K.; Ghossayn, F. An in vitro study of the torsional properties of new and used K3 instruments. Int. Endod. J. 2003, 36, 764–769, doi:10.1046/j.1365-2591.2003.00732.x.
12.
Thompson, S. A. An overview of nickel-titanium alloys used in dentistry. Int. Endod. J. 2000, 33, 297–310.
13.
Shen, Y.; Zhou, H.; Zheng, Y.; Peng, B.; Haapasalo, M. Current Challenges and Concepts of the Thermomechanical Treatment of Nickel-Titanium Instruments. J. Endod. 2013, 39, 163–172, doi:10.1016/j.joen.2012.11.005.
Metals 2018, 8, x FOR PEER REVIEW
14.
13 of 15
Shim, K.-S.; Oh, S.; Kum, K.; Kim, Y.-C.; Jee, K.-K.; Chang, S. W. Mechanical and Metallurgical Properties of Various Nickel-Titanium Rotary Instruments. Biomed Res. Int. 2017, 2017, 1–13, doi:10.1155/2017/4528601.
15.
Kuhn, G.; Jordan, L. Fatigue and Mechanical Properties of Nickel-Titanium Endodontic Instruments. J. Endod. 2002, 28, 716–720, doi:10.1097/00004770-200210000-00009.
16.
Hayashi, Y.; Yoneyama, T.; Yahata, Y.; Miyai, K.; Doi, H.; Hanawa, T.; Ebihara, A.; Suda, H. Phase transformation behaviour and bending properties of hybrid nickel?titanium rotary endodontic instruments. Int. Endod. J. 2007, 40, 247–253, doi:10.1111/j.1365-2591.2007.01203.x.
17.
Viana, A. C. D.; Chaves Craveiro de Melo, M.; Guiomar de Azevedo Bahia, M.; Lopes Buono, V. T. Relationship between flexibility and physical, chemical, and geometric characteristics of rotary nickel-titanium instruments. Oral Surgery, Oral Med. Oral Pathol. Oral Radiol. Endodontology 2010, 110, 527–533, doi:10.1016/j.tripleo.2010.05.006.
18.
De-Deus, G.; Silva, E. J. N. L.; Vieira, V. T. L.; Belladonna, F. G.; Elias, C. N.; Plotino, G.; Grande, N. M. Blue Thermomechanical Treatment Optimizes Fatigue Resistance and Flexibility of the Reciproc Files. J. Endod. 2017, 43, 462–466, doi:10.1016/j.joen.2016.10.039.
19.
Testarelli, L.; Plotino, G.; Al-Sudani, D.; Vincenzi, V.; Giansiracusa, A.; Grande, N. M.; Gambarini, G. Bending Properties of a New Nickel-Titanium Alloy with a Lower Percent by Weight of Nickel. J. Endod. 2011, 37, 1293–1295, doi:10.1016/j.joen.2011.05.023.
20.
McGuigan, M. B.; Louca, C.; Duncan, H. F. Clinical decision-making after endodontic instrument fracture. BDJ 2013, 214, 395–400, doi:10.1038/sj.bdj.2013.379.
21.
McGuigan, M. B.; Louca, C.; Duncan, H. F. Endodontic instrument fracture: causes and prevention. BDJ 2013, 214, 341–348, doi:10.1038/sj.bdj.2013.324.
22.
International Organization for Standardization ISO 3630-1:2008 Preview Dentistry -- Root-canal instruments -- Part 1: General requirements and test methods; 2008;
23.
Basheer Ahamed, S. B.; Vanajassun, P. P.; Rajkumar, K.; Mahalaxmi, S. Comparative Evaluation of Stress Distribution in Experimentally Designed Nickel-titanium Rotary Files with Varying Cross Sections: A Finite Element Analysis. J. Endod. 2018, 44, 654–658, doi:10.1016/j.joen.2017.12.013.
24.
Ha, J.-H.; Lee, C.-J.; Kwak, S.-W.; El Abed, R.; Ha, D.; Kim, H.-C. Geometric Optimization for Development of Glide Path Preparation Nickel-Titanium Rotary Instrument. J. Endod. 2015, 41, 916–919, doi:10.1016/j.joen.2015.01.025.
25.
Bonessio, N.; Pereira, E. S. J.; Lomiento, G.; Arias, A.; Bahia, M. G. A.; Buono, V. T. L.; Peters, O. A. Validated finite element analyses of WaveOne Endodontic Instruments: a comparison between M-Wire and NiTi alloys. Int. Endod. J. 2015, 48, 441–450, doi:10.1111/iej.12333.
26.
Montalvão, D.; Shengwen, Q.; Freitas, M. A study on the influence of Ni-Ti M-Wire in the flexural fatigue life of endodontic rotary files by using Finite Element Analysis. Mater. Sci. Eng. C. Mater. Biol. Appl. 2014, 40, 172–9, doi:10.1016/j.msec.2014.03.061.
27.
Özyürek, T.; Uslu, G.; Gündoğar, M.; Yılmaz, K.; Grande, N. M.; Plotino, G. Comparison of cyclic fatigue resistance and bending properties of two reciprocating nickel-titanium glide path files. Int. Endod. J. 2018, 51, 1047–1052, doi:10.1111/iej.12911.
28.
Alcalde, M. P.; Duarte, M. A. H.; Bramante, C. M.; de Vasconselos, B. C.; Tanomaru-Filho, M.; Guerreiro-Tanomaru, J. M.; Pinto, J. C.; Só, M. V. R.; Vivan, R. R. Cyclic fatigue and torsional strength of three different thermally treated reciprocating nickel-titanium instruments. Clin. Oral Investig. 2017, doi:10.1007/s00784-017-2295-8.
Metals 2018, 8, x FOR PEER REVIEW
29.
14 of 15
Özyürek, T.; Yılmaz, K.; Uslu, G. Shaping Ability of Reciproc, WaveOne GOLD, and HyFlex EDM Single-file
Systems
in
Simulated
S-shaped
Canals.
J.
Endod.
2017,
43,
805–809,
doi:10.1016/j.joen.2016.12.010. 30.
Bürklein, S.; Benten, S.; Schäfer, E. Shaping ability of different single-file systems in severely curved root canals of extracted teeth. Int. Endod. J. 2013, 46, 590–597, doi:10.1111/iej.12037.
31.
Adıgüzel, M.; Capar, I. D. Comparison of Cyclic Fatigue Resistance of WaveOne and WaveOne Gold Small, Primary, and Large Instruments. J. Endod. 2017, 43, 623–627, doi:10.1016/j.joen.2016.11.021.
32.
Safdel, A.; Zarei-Hanzaki, A.; Shamsolhodaei, A.; Krooß, P.; Niendorf, T. Room temperature superelastic responses of NiTi alloy treated by two distinct thermomechanical processing schemes. Mater. Sci. Eng. A 2017, 684, 303–311, doi:10.1016/j.msea.2016.12.047.
33.
Freitas-Júnior, A. C.; Rocha, E. P.; Bonfante, E. A.; Almeida, E. O.; Anchieta, R. B.; Martini, A. P.; Assunção, W. G.; Silva, N. R. F. A.; Coelho, P. G. Biomechanical evaluation of internal and external hexagon
platform
three-dimensional
switched finite
implant-abutment element
connections:
analysis.
Dent.
An
Mater.
in
vitro
2012,
laboratory 28,
and
e218–e228,
doi:10.1016/j.dental.2012.05.004. 34.
Ebihara, A.; Yahata, Y.; Miyara, K.; Nakano, K.; Hayashi, Y.; Suda, H. Heat treatment of nickel-titanium rotary endodontic instruments: effects on bending properties and shaping abilities. Int. Endod. J. 2011, 44, 843–849, doi:10.1111/j.1365-2591.2011.01891.x.
35.
Miyai, K.; Ebihara, A.; Hayashi, Y.; Doi, H.; Suda, H.; Yoneyama, T. Influence of phase transformation on the torsional and bending properties of nickel-titanium rotary endodontic instruments. Int. Endod. J. 2006, 39, 119–126, doi:10.1111/j.1365-2591.2006.01055.x.
36.
Gao, Y.; Gutmann, J. L.; Wilkinson, K.; Maxwell, R.; Ammon, D. Evaluation of the Impact of Raw Materials on the Fatigue and Mechanical Properties of ProFile Vortex Rotary Instruments. J. Endod. 2012, 38, 398–401, doi:10.1016/j.joen.2011.11.004.
37.
Lopes, H. P.; Gambarra-Soares, T.; Elias, C. N.; Siqueira, J. F.; Inojosa, I. F. J.; Lopes, W. S. P.; Vieira, V. T. L. Comparison of the Mechanical Properties of Rotary Instruments Made of Conventional Nickel-Titanium Wire, M-Wire, or Nickel-Titanium Alloy in R-Phase. J. Endod. 2013, 39, 516–520, doi:10.1016/j.joen.2012.12.006.
38.
Montalvão, D.; Alçada, F. S. Numeric Comparison of the Static Mechanical Behavior between ProFile GT and ProFile GT Series X Rotary Nickel-Titanium Files. J. Endod. 2011, 37, 1158–1161, doi:10.1016/j.joen.2011.05.018.
39.
Gündoğar, M.; Özyürek, T. Cyclic Fatigue Resistance of OneShape, HyFlex EDM, WaveOne Gold, and Reciproc Blue Nickel-titanium Instruments. J. Endod. 2017, 43, 1192–1196, doi:10.1016/j.joen.2017.03.009.
40.
Keskin, C.; Inan, U.; Demiral, M.; Keleş, A. Cyclic Fatigue Resistance of Reciproc Blue, Reciproc, and WaveOne Gold Reciprocating Instruments. J. Endod. 2017, 43, 1360–1363, doi:10.1016/j.joen.2017.03.036.
41.
Kim, H. C.; Kim, H. J.; Lee, C. J.; Kim, B. M.; Park, J. K.; Versluis, A. Mechanical response of nickel-titanium instruments with different cross-sectional designs during shaping of simulated curved canals. Int. Endod. J. 2009, 42, 593–602, doi:10.1111/j.1365-2591.2009.01553.x.
42.
He, R.; Ni, J. Design Improvement and Failure Reduction of Endodontic Files through Finite Element Analysis:
Application
to
V-Taper
File
Designs.
J.
Endod.
2010,
36,
1552–1557,
doi:10.1016/j.joen.2010.06.002. 43.
Tsao, C. C.; Liou, J. U.; Wen, P. H.; Peng, C. C.; Liu, T. S. Study on bending behaviour of nickel-titanium rotary endodontic instruments by analytical and numerical analyses. Int. Endod. J. 2013, 46, 379–388,
Metals 2018, 8, x FOR PEER REVIEW
doi:10.1111/iej.12025.
15 of 15
PII: DOI: Reference:
S1751-6161(18)31297-9 https://doi.org/10.1016/j.jmbbm.2018.10.016 JMBBM3030
To appear in: Journal of the Mechanical Behavior of Biomedical Materials Received date: 5 September 2018 Revised date: 4 October 2018 Accepted date: 5 October 2018 Cite this article as: María Prados-Privado, Rosa Rojo, Carlos Ivorra and Juan Carlos Prados-Frutos, Finite element analysis comparing WaveOne, WaveOne Gold, Reciproc and Reciproc Blue responses with bending and torsion tests, Journal of the Mechanical Behavior of Biomedical Materials, https://doi.org/10.1016/j.jmbbm.2018.10.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Finite element analysis comparing WaveOne, WaveOne Gold, Reciproc and Reciproc Blue responses with bending and torsion tests María Prados-Privado 1,2,#,*, Rosa Rojo 3 , Carlos Ivorra 2, and Juan Carlos Prados-Frutos 3,# Department of Continuum Mechanics and Structural Analysis. Higher Polytechnic School, Carlos III University, Avenida de la Universidad, 30. 28911, Leganés, Madrid, Spain. 2 ASISA Dental. Research Department. C/ José Abascal, 32. 28003, Madrid, Spain. 3 Department of Medicine and Surgery, Faculty of Health Sciences, Rey Juan Carlos University, Avda. Atenas s/n, 28922, Alcorcón, Madrid, Spain. * Correspondence: [email protected]; Tel.: +34-916-249-500 1
# Equal contribution
Abstract: To evaluate the bending and torsional properties of four nickel-titanium endodontic files, we simulated and compared WaveOne® primary size 25 with 0.07 taper, WaveOne Gold® primary size 25 with 0.07 taper, Reciproc® primary size 25 with 0.08 taper, and Reciproc Blue® primary size 25 with 0.08 taper. Three-dimensional models were created using computer-aided design software and numerically analyzed in ANSYS® Workbench. Boundary conditions for the numerical analyses were based on the ISO 3630-1 specifications. The highest stress levels were recorded for WaveOne® and Reciproc®. Numerical results of the bending test showed that WaveOne Gold® is 86 % more flexible than WaveOne® with a deflection of 3 mm. Reciproc Blue® was 42.31 % more flexible than Reciproc® file with a deflection of 3 mm. The WaveOne® instrument withstood the highest stress under the torsion test, followed by Reciproc®, then Reciproc Blue® files. The stress under torsion in the WaveOne® and WaveOne Gold® files is reduced in a 51%. Regarding Reciproc® and Reciproc Blue® files, the stress under torsional moments remains very similar. Our results exposed a considerable difference in terms of stress tolerance between WaveOne® and WaveOne Gold®. However, Reciproc® files demonstrated a similar stress distribution. The results obtained through finite element analysis suggest that thermal treatment of files might improve their flexibility, increasing resistance during the preparation of highly curved canals. Also, the values obtained regarding the improvement of flexibility were in accordance with the manufacturer claims. Keywords: bending resistance; endodontic file; finite element analysis; nickel titanium; thermal treatment
1. Introduction Endodontic treatment is a clinical intervention that aims to treat infections in the root canal of the tooth. This treatment involves a reciprocating motion which reduce the stress on the files and allows clinicians to use only a single instrument for root canal preparation [1]. This motion has a better root preparation than rotary motion and reduced the cyclic and torsional fatigue [2]. Compared with the continuous rotation of the endodontic files and independently of other variables such as the angle of curvature, the rotation speed or the surface characteristics of the NiTi instruments, the reciprocating movement improves the resistance to cyclic and torsional fatigue [2,3]. It also allows the clinician to perform root canal preparation better and with a unique instrument [1,3]. WaveOne® and Reciproc® files use reciprocating motion in which the direction of rotation alternates between counterclockwise and clockwise direction, and the use of WaveOne Gold® and Reciproc Blue® has been commercialized with improvements in behavior to the fatigue of the instruments.
Metals 2018, 8, x FOR PEER REVIEW
2 of 15
This procedure employs endodontic instruments composed of nickel-titanium (NiTi) alloy [4]. Rotary files are commonly made of NiTi alloy because this material is flexible, super elastic, and has excellent shape memory [5], demonstrating a nonlinear elastic behavior that allows the material to undergo high deformation without plastic residual-strain after stress removal. Rotary NiTi instruments have more advantages than stainless steel instruments as they require less procedural time and produce less canal aberrations [4]. The differences in the mechanical properties between rotary instruments are due to the variation in materials, geometrical factors such as pitch length, taper or conicity, cross-sectional shapes, and manufacturing conditions used [6]. All these characteristics affect clinical performance. From a mechanical point of view, NiTi alloys seem to be better suited than stainless steel for the complex anatomy of root canals. This has been clinically verified by studies like the one published by Pettiette et al. where a NiTi alloys had a better clinical prognosis in endodontics compared with the use of stainless steel [7]. Nickel-titanium files were introduced to avoid unwanted changes in the morphology of root canals caused by stainless steel files [8]. From the clinical point of view both instruments obtain outcomes in terms of success, amount of residual bacteria and similar cleaning capacity. However, NiTi files are associated with lower canal transportation and apical extrusion [9]. The mechanical properties of NiTi rotary files, including flexibility and torsional resistance, are fundamental requirements of endodontic instruments for successful use [10]. Good flexibility is crucial to maintain the shape of root canals; an acceptable torsional resistance reduces the probability of the occurrence of the intracanal separation [11]. The super-elastic behavior of NiTi depends on the crystallographic phases and the thermal, mechanical, and chemical treatments to which the alloy has been subjected. This alloy used in endodontic treatment contains approximately, 55 wt % Ni and 45 wt % Ti [12]. One method of increasing the efficiency of NiTi rotary files is improving the manufacturing process. The NiTi alloy has three different microstructure phases that are temperature-dependent: austenite, martensite, and R-phase [13]. R-phase and martensitic NiTi are soft and ductile and can be easily deformed, whereas austenitic NiTi is strong and hard [14]. The mechanical properties of nickel-titanium alloys and, in particular, super-elasticity and shape memory, are influenced by heat treatment conditions [15,16]. The transformation temperature at which the crystal structure changes from austenite to martensite or vice versa affects to super-elasticity and shape memory properties. The rotary files have a better super-elasticity if the NiTi alloy is fully austenite whereas, in case of full martensite, the rotary instruments have a better shape memory property [10,16,17]. Manufacturers have introduced several thermally treated NiTi alloys to optimize the microstructure and transformation behavior [18]. This behavior is due to a reversible solid-state transformation from the parent phase austenite to a new crystallographic structure called martensite [4]. Unfortunately, these heat treatments are unknown due to the protection of intellectual property and they have not been divulged by manufacturers [19]. From a clinical point of view, the fracture of the files is an event that should be considered to avoid performing the complicated technique of removing the separated instrument, subject to considerable risks, especially in the apical third [20]. The prevalence of fracture in rotating nickel titanium instruments is in the range of 0.4 to 5% [21]. Different manufacturers have made various modifications to the alloys to reduce the probability of fracture. The ISO 3630-1 guideline details [22] the conditions required for in vitro tests of endodontic treatment. Torsional stiffness and bending flexibility are the two most essential properties required in any rotary file, which determines file performance in clinical use [23]. These two properties have been studied extensively and have been described as two of the most important causes of fracture [24]. Because these experimental tests are very expensive, among other factors, a finite element analysis is a good alternative for studying the mechanical behavior of endodontic instruments. Some studies have analyzed the influence of instrument geometry on flexibility and torsional stiffness by
Metals 2018, 8, x FOR PEER REVIEW
3 of 15
using finite element analysis [25,26], but no studies have compared the mechanical behavior of WaveOne Gold® and Reciproc Blue® files using a numerical analysis. As WaveOne Gold® and Reciproc Blue® have now been commercialized, only some in vitro studies have been published regarding the mechanical behavior of these rotary files [27,28]. However, from the best of our knowledge, no numerical studies in the literature have analyzed and compared the behavior of WaveOne Gold®, Reciproc Blue® and their former instruments. Therefore, the contribution of this paper is that the bending and torsional resistance of WaveOne Gold® and Reciproc Blue® are analyzed. The aim of this study was to evaluate the mechanical behavior of four commercially available instruments using the finite element method and compare the numerical results between them. 2. Materials and Methods 2.1. Endodontic instruments analyzed The most widely known NiTi file systems are WaveOne® (Dentsply Maillefer, Ballaigues, Switzerland) and Reciproc® (VDW, Munich, Germany), which are made of M-Wire alloy [29,30]. The WaveOne® file has a convex triangular cross-sectional design [31]. WaveOne Gold Primary® has a cross-section with a parallelogram structure with two cutting edges, but the most important modification is the alloy employed, which is based on heating the file and then slowly cooling it [31]. Reciproc® files have an S-shaped cross section with two cutting edges. Reciproc Blue® also has a heat treatment. Figure 1 details the three types of NiTi rotary instruments examined in this study.
Figure 1. Endodontic instruments: (a) WaveOne®; (b) WaveOne Gold®; (c) Reciproc® and Reciproc Blue®.
2.2. Finite element model 2.2.1. Three-dimensional model
Metals 2018, 8, x FOR PEER REVIEW
4 of 15
Three-dimensional (3D) models were created using the computer-assisted design (CAD) software SolidWorks® 2016 (Dassault Systèmes, SolidWorks Corp., Concord, MA, U.S.). Then, all models were imported to the ANSYS® Workbench 16 (Canonsburg, PA, U.S.) where the simulation was computed. 2.2.2. Material properties WaveOne® and Reciproc® files are composed of NiTi alloy. The mechanical parameters of this super-elastic alloy are detailed in Table 1 [4]. Table 1. Parameters used to describe nickel-titanium (NiTi) super-elastic behavior, obtained from de Arruda Santos et al. [4].
Parameter
(
)
Description
Value
Austenite elasticity Austenite Poisson’s ratio Martensite elasticity Martensite Poisson’s ratio Transformation strain
42530 MPa 0,33 12828 MPa 0,33 10 %
loading Start of transformation loading End of transformation loading
(
)
unloading Start of transformation unloading End of transformation unloading End of martensitic elastic regime
6.7 492 MPa 630 MPa 6.7 192 MPa 97 MPa 1200 MPa
WaveOne Gold® and Reciproc Blue® files are made of NiTi alloy through a thermal treatment process. The files were analyzed with two different temperatures and their corresponding material properties because the temperature at which the heat treatment is performed is unknown. Two temperatures were used in this study: 700º and 800 ºC. The material properties after thermal treatment at those temperatures were obtained from Safdel et al. from hot compression tests, at different temperatures, under the strain rate of 0.001 s–1 [32]. These two temperatures resulted in the improvement in the flexibility that the manufacturer details.
(a)
(b)
Figure 2. Material properties after thermal treatment (a) at 700 ºC and (b) at 800 ºC
2.2.3. Boundary conditions The boundary conditions used to simulate the behavior of the endodontic instruments aligned with the ISO 3630-1 specifications [22]. For the bending resistance test, the file was held 3 mm from the tip, preventing any displacement in the x, y, and z-axes. The shaft was deflected until a 45°
Metals 2018, 8, x FOR PEER REVIEW
5 of 15
inclination. This procedure was performed in x and y directions, taking into account eventual differences resulting from bending orientation. Figure 3 represents these conditions.
Figure 3. Boundary condition for bending test.
For the torsion resistance test, the endodontic instrument was held three mm from the tip and a clockwise torsional moment of 0.3 Ncm [4,25] was applied, as shown in Figure 4.
Figure 4. Boundary condition for torsion test.
2.2.4. Mesh Mesh generation was performed in ANSYS® Workbench 16 (Canonsburg, PA, U.S.). All endodontic files were meshed with a fine mesh and all regions of stress concentration that were of interest were manually refined. The convergence criterion involved a change in von Mises stress in the model of less than 5 % [33]. The element type employed in all analyzed was SOLID187. Table 2. Number of nodes and elements.
WaveOne® WaveOne Gold® Reciproc® Reciproc Blue®
Number of nodes
Number of elements
24,256 31,343 36,758 32,904
12,371 19,420 24,254 21,490
3. Results 3.1. Bending resistance test Figure 5 illustrates the bending deformation with displacement in the y-axis and shows the von Mises stress distributions in the cross-section at three mm from the tip for each instrument. A maximum stress of 1146 MPa appeared at one vertex of the triangle in the WaveOne® file. The behavior of the WaveOne Gold® and Reciproc Blue® files was analyzed with two different temperatures. Figure 5 demonstrates that the thermal treatment at 800 ºC caused a higher maximum von Mises stress than the thermal treatment at 700 ºC. In both cases, maximum stress was lower than those withstood by WaveOne® file under the same conditions. The von Mises stress for WaveOne Gold® instrument was 26 % lower than that obtained by the WaveOne® file, under the same boundary conditions.
Metals 2018, 8, x FOR PEER REVIEW
6 of 15
Figure 5. Results of bending test analysis in y-axis: von Mises stress distribution (MPa) in the cross-section at 3 mm from the tip.
A maximum stress of 942 MPa appeared in Reciproc® file. The highest stress appeared near the corner of the S-shaped section. The von Mises stress for the Reciproc Blue® instrument at 700 ºC was 35% lower than obtained in the Reciproc® file under the same boundary conditions. The values of the bending moment detailed in Table 3 were obtained by multiplying the registered bending force by the distance between the point at which the force was applied and the fixed tip of the instrument. Table 3. Bending resistance test results summary at 700 ºC.
Deflection (mm) 1 2 3 Maximum stress (MPa)
WaveOne®
Bending at 700 ºC (Ncm) WaveOne Δ (%) Reciproc® Gold®
Reciproc Blue®
Δ (%)
0.05 0.04 0.15
0.18 0.4 1.1
97.22 90.00 86.36
0.09 0.51 0.9
0.17 0.88 1.56
47.06 42.05 42.31
1146.6
847.35
–26.10
942.48
614.21
–34.83
As shown in Table 3, with a deflection of three mm, the WaveOne Gold® file at 700ºC was 86.36 % more flexible than the WaveOne® file. Reciproc Blue® with the same deflection and tempered treatment was 42.31 % more flexible than the Reciproc® file. Flexibility decreased as deflection increased in both cases. Table 4 summaries bending resistance results at 800 ºC. In view of these results, the maximum stress for both WaveOne Gold® and Reciproc Blue® were higher than those recorded in the same rotary files at 700 ºC. The improvement in bending resistance at 800 ºC was also worse than found in the same instruments at a lower temperature. Table 4. Bending resistance test results summary at 800 ºC.
Metals 2018, 8, x FOR PEER REVIEW
Deflection (mm) 1 2 3 Maximum stress (MPa)
WaveOne®
7 of 15
Bending at 800 ºC (Ncm) WaveOne Δ (%) Reciproc® Gold®
Reciproc Blue®
Δ (%)
0.05 0.04 0.15
0.18 0.14 0.49
72.22 71.43 69.39
0.09 0.51 0.9
0.12 0.65 1.14
33.33 27.45 26.67
1146.6
864.3
–24.58
942.48
835.15
–11.39
Figure 6 details the stress distribution along the body of the instruments. Stress in all rotary files was concentrated around three mm from the tip.
Figure 6. Stress distribution along the body of the instruments.
Figure 7 illustrates the von Mises stress distributions in the cross-section three mm from the tip for each instrument when the displacement was applied along the x-axis.
Metals 2018, 8, x FOR PEER REVIEW
8 of 15
Figure 7. Stress distribution pattern of the bending test analysis along the x-axis for the cross-section three mm from the tip.
3.2. Torsion resistance test Figure 8 illustrates the von Mises stress distribution in the cross-section three mm from the tip for each instrument analyzed in this study.
Metals 2018, 8, x FOR PEER REVIEW
9 of 15
Figure 8. von Mises stress (MPa) after torsion resistance test.
The Maximum stress in the WaveOne Gold® instrument was lower than those recorded for the WaveOne® file under the torsional test. In this case, the maximum stress was similar at both temperatures, but thermal treatment at 700 ºC resulted in the lowest stress. For Reciproc Blue®, the maximum stress recorded with heat treatment was similar to that recorded in the instrument without thermal treatment. In view of torsional test simulations, the stress pattern highly depended on the cross-section geometry. In the case of the Reciproc® files, the temperature was a secondary factor in stress distribution. Figure 9 represents the stress distribution in the body of the rotary file after the torsion resistance test. The stress was concentrated near the place where the file was fixed and decreased as it moved away from the point of support, at three mm from the tip.
Figure 9. Stress distribution in the body of the instrument after the torsion resistance test.
Metals 2018, 8, x FOR PEER REVIEW
10 of 15
Table 5 summaries torsional results at 700 ºC. As shown in Table 5, the difference of stresses in the WaveOne® and WaveOne Gold® files with each of torsional moments remains constant. In this case, the stress on file with the heat treatment is reduced in a 51%. Regarding Reciproc® and Reciproc Blue® files, the stress under torsional moments remains very similar. Table 5. Torsional test results summary at 700 ºC.
Torsion at 700ºC
Maximum stress [MPa]
Torsional moment [Ncm]
WaveOne®
WaveOne Gold®
Δ(%)
Reciproc®
Reciproc Blue®
Δ(%)
0,1 0,2
330,05 660,09
160,95 321,69
-51,23% -51,27%
226,23 452,46
221,7 444,96
-2,04% -1,69%
0,3
990,14
481,98
-51,32%
678,69
669,75
-1,32%
4. Discussion This study analyzed and compared the flexibility and torsion resistance of four different endodontic instruments via finite element analysis. The boundary conditions imposed to simulate the behavior of the endodontic instruments were in accordance with the ISO 3630-1 specifications [22]. To perform the numerical study, it was necessary to introduce the values of the material properties of the NiTi. Because of the intellectual property, the temperature of the heat treatment was unknown, and the studies were carried out with different temperatures (700 and 800ºC). Once the results were obtained, the flexibility in each file was checked and compared with what the manufacturer claims. Finally, a torsional test was also carried out. The material properties of NiTi alloy were obtained from the literature, although the detailed thermomechanical process was unknown due to the protection of intellectual property [10]. The transformation temperature is one of the crucial factors influencing the mechanical properties of NiTi alloys and resulting in differences in their bending properties [34,35]. WaveOne Gold® and Reciproc Blue® files were thermally treated. Because the thermal treatment temperature was unknown, two different temperatures were simulated, and the file flexibility differences were measured both with and without thermal treatment. To the best of our knowledge, no numerical studies in the literature have analysed the bending and torsional resistance of WaveOne Gold® and Reciproc Blue®. Several NiTi alloy thermomechanical procedures were used with the aim of improving the flexibility of NiTi files [36,37]. The main finding in our study was that the new WaveOne Gold® and Reciproc Blue® files with super-elastic properties were studied at different temperatures for their treatment of nickel titanium tempering through finite elements. We verified that the results offered by the manufacturers are compatible with those obtained. WaveOne® and Reciproc® recorded the highest stress levels, close to the plastic regime of martensite (1200 MPa), as demonstrated by the stress distribution results. This value aligns with those obtained for RaCe (FKG Dentaire, La-Chaux-de-Fonds, Switzerland) size 25 with 0.06 taper and PTU F1 (DentsplyMaillefer, Ballaigues, Switzerland) in a bending resistance test [4]. Notably, the nonlinearity of the curves in both bending and force occurred because of the large displacements [38]. The numerical results from the bending test showed that WaveOne Gold® is 86 % more flexible than WaveOne® with a deflection of three mm at 700 ºC. Reciproc Blue® is 42.31 % more flexible than the Reciproc® file with a deflection of three mm at 700 ºC. The manufacturer claims that their Gold files are 80 % more flexible than the standard instrument, and Blue files are 40 % more flexible than Reciproc®. However, the values obtained for the same test at 800 ºC did not approach the values stated by the manufacturer. The highest temperature resulted in improvements in flexibility below 70 % for the WaveOne and 27 % for the Reciproc.
Metals 2018, 8, x FOR PEER REVIEW
11 of 15
The von Mises stress distribution patterns were affected by the cross-section geometry and the material properties. According to the results in Figure 5, stress concentrated in the area at the corner of the triangle, whereas the rest of the geometries distributed the stresses more uniformly. In Figure 7, the stress distribution pattern was quite similar in the x and y directions for the WaveOne® and Reciproc® files. However, a considerable difference was observed in this pattern when the orientations of WaveOne Gold® and Reciproc Blue® were changed. In Figure 6, the stress in all rotary files concentrated around three mm from the tip, although after the torsional test, stress concentrated near the place where the file was fixed and decreased moving away from the point of support at three mm from the tip. Cyclic fatigue failures in WaveOne Gold, Reciproc®, and Reciproc Blue® appeared in different analyses are in accordance with the area where the maximum stress was experienced in this study [39,40]. The WaveOne® instrument experienced the highest stress under the torsion test, followed by Reciproc® and Reciproc Blue® files. WaveOne Gold® files experienced the least stress. Stress values obtained in this study are comparable with those obtained by other analyses with similar conditions [41]. Torsional stiffness of endodontic instruments is also associated with cutting efficiency [4]; however, it could not be evaluated through this numerical analysis. Thermally treated files experienced lower stress values than common nickel titanium files, which means that they have a greater resistance to torsion and better cutting efficiency [5,42]. Considerable differences in terms of stresses were found between WaveOne® and WaveOne Gold®; however, stress in Reciproc files were quite similar. Kim et al. reported that stress levels in instruments under torsion were influenced by many factors, such as the geometry of the cross-section, area of the continuous inner core, radial land, and peripheral surface ground [41]. The influence of the combination of these aspects on the stress distribution along the endodontic instruments under torsion remains uncertain. This study shows that the effect of the alloy is less important in this type of test than the cross-section geometry. Several differences were observed in the design and materials used in fabrication of endodontic files that considerably influence file properties. Therefore, clinical must understand the properties and the differences of these materials to select the system that accomplishes the optimum clinical results. This study has some limitations and assumptions. The geometry of the endodontic files was created using CAD software according to the specifications detailed by the manufacturer. This limitation is consistent with other numerical studies [5]. The use of a simplification in the cross-section geometry also aligns with other numerical studies [43]. Another limitation is the treatment process assumption, as well as the percentage of austenite and martensite. In this case, the material properties were obtained from hot compression tests at different temperatures of 700 and 800 ºC under a strain rate of 0.001 s–1 [32]. From the best of our knowledge, no numerical studies in the literature have analysed WaveOne Gold® and Reciproc Blue® behavior, but our results are comparable with those obtained through in vitro tests under similar conditions [41].
5. Conclusions The results obtained through finite element analysis suggest that thermal treatment of files might improve their flexibility, increasing resistance for the preparation of curved canals. However, according to the results obtained in the bending resistance test, considering the limitations of the study, the improvements in the flexibility mentioned by the manufacturer are obtained with a heat treatment at 700 ºC. With the assumptions and limitations of this study and in view of the results obtained, we conclude that WaveOne Gold® has better clinical behavior.
Metals 2018, 8, x FOR PEER REVIEW
12 of 15
Future work in this area could include a probabilistic approach to study the long-term behavior of endodontic instruments. With this approach, authors should be able to provide principal statistics of fatigue life and the probability of failure associated with each cycle load. Acknowledgments: The work was supported by Grant A-274 (Rey Juan Carlos University– Neodent) and Grant A-285 (Rey Juan Carlos University – Proclinic SA). Conflicts of Interest: The authors declare no conflict of interest.
References 1.
Alcalde, M. P.; Duarte, M. A. H.; Bramante, C. M.; de Vasconselos, B. C.; Tanomaru-Filho, M.; Guerreiro-Tanomaru, J. M.; Pinto, J. C.; Só, M. V. R.; Vivan, R. R. Cyclic fatigue and torsional strength of three different thermally treated reciprocating nickel-titanium instruments. Clin. Oral Investig. 2018, 22, 1865–1871, doi:10.1007/s00784-017-2295-8.
2.
Karataş, E.; Arslan, H.; Büker, M.; Seçkin, F.; Çapar, I. D. Effect of movement kinematics on the cyclic fatigue resistance of nickel-titanium instruments. Int. Endod. J. 2016, 49, 361–364, doi:10.1111/iej.12453.
3.
Ferreira, F.; Adeodato, C.; Barbosa, I.; Aboud, L.; Scelza, P.; Zaccaro Scelza, M. Movement kinematics and cyclic fatigue of NiTi rotary instruments: a systematic review. Int. Endod. J. 2017, 50, 143–152, doi:10.1111/iej.12613.
4.
de Arruda Santos, L.; López, J. B.; de Las Casas, E. B.; de Azevedo Bahia, M. G.; Buono, V. T. L. Mechanical behavior of three nickel-titanium rotary files: A comparison of numerical simulation with bending and torsion tests. Mater. Sci. Eng. C 2014, 37, 258–263, doi:10.1016/j.msec.2014.01.025.
5.
El-Anwar, M. I.; Yousief, S. A.; Kataia, E. M.; El-Wahab, T. M. A. Finite Element Study on Continuous Rotating versus Reciprocating Nickel-Titanium Instruments. Braz. Dent. J. 2016, 27, 436–441, doi:10.1590/0103-6440201600480.
6.
Melo, M. C. C.; Pereira, E. S. J.; Viana, A. C. D.; Fonseca, A. M. A.; Buono, V. T. L.; Bahia, M. G. A. Dimensional characterization and mechanical behaviour of K3 rotary instruments. Int. Endod. J. 2008, 41, 329–338, doi:10.1111/j.1365-2591.2007.01368.x.
7.
Pettiette, M. T.; Delano, E. O.; Trope, M. Evaluation of success rate of endodontic treatment performed by students with stainless-steel K-files and nickel-titanium hand files. J. Endod. 2001, 27, 124–7.
8.
Pedrinha, V. F.; Brandão, J. M. da S.; Pessoa, O. F.; Rodrigues, P. de A. Influence of File Motion on Shaping, Apical Debris Extrusion and Dentinal Defects: A Critical Review. Open Dent. J. 2018, 12, 189– 201, doi:10.2174/1874210601812010189.
9.
Del Fabbro, M.; Afrashtehfar, K. I.; Corbella, S.; El-Kabbaney, A.; Perondi, I.; Taschieri, S. In Vivo and In Vitro Effectiveness of Rotary Nickel-Titanium vs Manual Stainless Steel Instruments for Root Canal Therapy: Systematic Review and Meta-analysis. J. Evid. Based Dent. Pract. 2018, 18, 59–69, doi:10.1016/j.jebdp.2017.08.001.
10.
Zhou, H.; Peng, B.; Zheng, Y.-F. An overview of the mechanical properties of nickel-titanium endodontic instruments. Endod. Top. 2013, 29, 42–54, doi:10.1111/etp.12045.
11.
Yared, G.; Kulkarni, G. K.; Ghossayn, F. An in vitro study of the torsional properties of new and used K3 instruments. Int. Endod. J. 2003, 36, 764–769, doi:10.1046/j.1365-2591.2003.00732.x.
12.
Thompson, S. A. An overview of nickel-titanium alloys used in dentistry. Int. Endod. J. 2000, 33, 297–310.
13.
Shen, Y.; Zhou, H.; Zheng, Y.; Peng, B.; Haapasalo, M. Current Challenges and Concepts of the Thermomechanical Treatment of Nickel-Titanium Instruments. J. Endod. 2013, 39, 163–172, doi:10.1016/j.joen.2012.11.005.
Metals 2018, 8, x FOR PEER REVIEW
14.
13 of 15
Shim, K.-S.; Oh, S.; Kum, K.; Kim, Y.-C.; Jee, K.-K.; Chang, S. W. Mechanical and Metallurgical Properties of Various Nickel-Titanium Rotary Instruments. Biomed Res. Int. 2017, 2017, 1–13, doi:10.1155/2017/4528601.
15.
Kuhn, G.; Jordan, L. Fatigue and Mechanical Properties of Nickel-Titanium Endodontic Instruments. J. Endod. 2002, 28, 716–720, doi:10.1097/00004770-200210000-00009.
16.
Hayashi, Y.; Yoneyama, T.; Yahata, Y.; Miyai, K.; Doi, H.; Hanawa, T.; Ebihara, A.; Suda, H. Phase transformation behaviour and bending properties of hybrid nickel?titanium rotary endodontic instruments. Int. Endod. J. 2007, 40, 247–253, doi:10.1111/j.1365-2591.2007.01203.x.
17.
Viana, A. C. D.; Chaves Craveiro de Melo, M.; Guiomar de Azevedo Bahia, M.; Lopes Buono, V. T. Relationship between flexibility and physical, chemical, and geometric characteristics of rotary nickel-titanium instruments. Oral Surgery, Oral Med. Oral Pathol. Oral Radiol. Endodontology 2010, 110, 527–533, doi:10.1016/j.tripleo.2010.05.006.
18.
De-Deus, G.; Silva, E. J. N. L.; Vieira, V. T. L.; Belladonna, F. G.; Elias, C. N.; Plotino, G.; Grande, N. M. Blue Thermomechanical Treatment Optimizes Fatigue Resistance and Flexibility of the Reciproc Files. J. Endod. 2017, 43, 462–466, doi:10.1016/j.joen.2016.10.039.
19.
Testarelli, L.; Plotino, G.; Al-Sudani, D.; Vincenzi, V.; Giansiracusa, A.; Grande, N. M.; Gambarini, G. Bending Properties of a New Nickel-Titanium Alloy with a Lower Percent by Weight of Nickel. J. Endod. 2011, 37, 1293–1295, doi:10.1016/j.joen.2011.05.023.
20.
McGuigan, M. B.; Louca, C.; Duncan, H. F. Clinical decision-making after endodontic instrument fracture. BDJ 2013, 214, 395–400, doi:10.1038/sj.bdj.2013.379.
21.
McGuigan, M. B.; Louca, C.; Duncan, H. F. Endodontic instrument fracture: causes and prevention. BDJ 2013, 214, 341–348, doi:10.1038/sj.bdj.2013.324.
22.
International Organization for Standardization ISO 3630-1:2008 Preview Dentistry -- Root-canal instruments -- Part 1: General requirements and test methods; 2008;
23.
Basheer Ahamed, S. B.; Vanajassun, P. P.; Rajkumar, K.; Mahalaxmi, S. Comparative Evaluation of Stress Distribution in Experimentally Designed Nickel-titanium Rotary Files with Varying Cross Sections: A Finite Element Analysis. J. Endod. 2018, 44, 654–658, doi:10.1016/j.joen.2017.12.013.
24.
Ha, J.-H.; Lee, C.-J.; Kwak, S.-W.; El Abed, R.; Ha, D.; Kim, H.-C. Geometric Optimization for Development of Glide Path Preparation Nickel-Titanium Rotary Instrument. J. Endod. 2015, 41, 916–919, doi:10.1016/j.joen.2015.01.025.
25.
Bonessio, N.; Pereira, E. S. J.; Lomiento, G.; Arias, A.; Bahia, M. G. A.; Buono, V. T. L.; Peters, O. A. Validated finite element analyses of WaveOne Endodontic Instruments: a comparison between M-Wire and NiTi alloys. Int. Endod. J. 2015, 48, 441–450, doi:10.1111/iej.12333.
26.
Montalvão, D.; Shengwen, Q.; Freitas, M. A study on the influence of Ni-Ti M-Wire in the flexural fatigue life of endodontic rotary files by using Finite Element Analysis. Mater. Sci. Eng. C. Mater. Biol. Appl. 2014, 40, 172–9, doi:10.1016/j.msec.2014.03.061.
27.
Özyürek, T.; Uslu, G.; Gündoğar, M.; Yılmaz, K.; Grande, N. M.; Plotino, G. Comparison of cyclic fatigue resistance and bending properties of two reciprocating nickel-titanium glide path files. Int. Endod. J. 2018, 51, 1047–1052, doi:10.1111/iej.12911.
28.
Alcalde, M. P.; Duarte, M. A. H.; Bramante, C. M.; de Vasconselos, B. C.; Tanomaru-Filho, M.; Guerreiro-Tanomaru, J. M.; Pinto, J. C.; Só, M. V. R.; Vivan, R. R. Cyclic fatigue and torsional strength of three different thermally treated reciprocating nickel-titanium instruments. Clin. Oral Investig. 2017, doi:10.1007/s00784-017-2295-8.
Metals 2018, 8, x FOR PEER REVIEW
29.
14 of 15
Özyürek, T.; Yılmaz, K.; Uslu, G. Shaping Ability of Reciproc, WaveOne GOLD, and HyFlex EDM Single-file
Systems
in
Simulated
S-shaped
Canals.
J.
Endod.
2017,
43,
805–809,
doi:10.1016/j.joen.2016.12.010. 30.
Bürklein, S.; Benten, S.; Schäfer, E. Shaping ability of different single-file systems in severely curved root canals of extracted teeth. Int. Endod. J. 2013, 46, 590–597, doi:10.1111/iej.12037.
31.
Adıgüzel, M.; Capar, I. D. Comparison of Cyclic Fatigue Resistance of WaveOne and WaveOne Gold Small, Primary, and Large Instruments. J. Endod. 2017, 43, 623–627, doi:10.1016/j.joen.2016.11.021.
32.
Safdel, A.; Zarei-Hanzaki, A.; Shamsolhodaei, A.; Krooß, P.; Niendorf, T. Room temperature superelastic responses of NiTi alloy treated by two distinct thermomechanical processing schemes. Mater. Sci. Eng. A 2017, 684, 303–311, doi:10.1016/j.msea.2016.12.047.
33.
Freitas-Júnior, A. C.; Rocha, E. P.; Bonfante, E. A.; Almeida, E. O.; Anchieta, R. B.; Martini, A. P.; Assunção, W. G.; Silva, N. R. F. A.; Coelho, P. G. Biomechanical evaluation of internal and external hexagon
platform
three-dimensional
switched finite
implant-abutment element
connections:
analysis.
Dent.
An
Mater.
in
vitro
2012,
laboratory 28,
and
e218–e228,
doi:10.1016/j.dental.2012.05.004. 34.
Ebihara, A.; Yahata, Y.; Miyara, K.; Nakano, K.; Hayashi, Y.; Suda, H. Heat treatment of nickel-titanium rotary endodontic instruments: effects on bending properties and shaping abilities. Int. Endod. J. 2011, 44, 843–849, doi:10.1111/j.1365-2591.2011.01891.x.
35.
Miyai, K.; Ebihara, A.; Hayashi, Y.; Doi, H.; Suda, H.; Yoneyama, T. Influence of phase transformation on the torsional and bending properties of nickel-titanium rotary endodontic instruments. Int. Endod. J. 2006, 39, 119–126, doi:10.1111/j.1365-2591.2006.01055.x.
36.
Gao, Y.; Gutmann, J. L.; Wilkinson, K.; Maxwell, R.; Ammon, D. Evaluation of the Impact of Raw Materials on the Fatigue and Mechanical Properties of ProFile Vortex Rotary Instruments. J. Endod. 2012, 38, 398–401, doi:10.1016/j.joen.2011.11.004.
37.
Lopes, H. P.; Gambarra-Soares, T.; Elias, C. N.; Siqueira, J. F.; Inojosa, I. F. J.; Lopes, W. S. P.; Vieira, V. T. L. Comparison of the Mechanical Properties of Rotary Instruments Made of Conventional Nickel-Titanium Wire, M-Wire, or Nickel-Titanium Alloy in R-Phase. J. Endod. 2013, 39, 516–520, doi:10.1016/j.joen.2012.12.006.
38.
Montalvão, D.; Alçada, F. S. Numeric Comparison of the Static Mechanical Behavior between ProFile GT and ProFile GT Series X Rotary Nickel-Titanium Files. J. Endod. 2011, 37, 1158–1161, doi:10.1016/j.joen.2011.05.018.
39.
Gündoğar, M.; Özyürek, T. Cyclic Fatigue Resistance of OneShape, HyFlex EDM, WaveOne Gold, and Reciproc Blue Nickel-titanium Instruments. J. Endod. 2017, 43, 1192–1196, doi:10.1016/j.joen.2017.03.009.
40.
Keskin, C.; Inan, U.; Demiral, M.; Keleş, A. Cyclic Fatigue Resistance of Reciproc Blue, Reciproc, and WaveOne Gold Reciprocating Instruments. J. Endod. 2017, 43, 1360–1363, doi:10.1016/j.joen.2017.03.036.
41.
Kim, H. C.; Kim, H. J.; Lee, C. J.; Kim, B. M.; Park, J. K.; Versluis, A. Mechanical response of nickel-titanium instruments with different cross-sectional designs during shaping of simulated curved canals. Int. Endod. J. 2009, 42, 593–602, doi:10.1111/j.1365-2591.2009.01553.x.
42.
He, R.; Ni, J. Design Improvement and Failure Reduction of Endodontic Files through Finite Element Analysis:
Application
to
V-Taper
File
Designs.
J.
Endod.
2010,
36,
1552–1557,
doi:10.1016/j.joen.2010.06.002. 43.
Tsao, C. C.; Liou, J. U.; Wen, P. H.; Peng, C. C.; Liu, T. S. Study on bending behaviour of nickel-titanium rotary endodontic instruments by analytical and numerical analyses. Int. Endod. J. 2013, 46, 379–388,
Metals 2018, 8, x FOR PEER REVIEW
doi:10.1111/iej.12025.
15 of 15