Methods for manufacturing or modifying NiTi alloy endodontic instruments

Abstract

The present invention relates to a method for manufacturing or modifying endodontic instruments made from NiTi alloys, including heat treatment. The present invention further relates to endodontic instruments preferably obtained by the method, having excellent properties in terms of cyclic fatigue recovery.

Description

[Technical field]

[0001] The present invention relates to the technical field of instruments for use in dentistry, more particularly to endodontic instruments for root canal treatment. [Background technology]

[0002] In root canal treatment, endodontic instruments are used to clean and enlarge the elongated tapered root canal. In order for the file to conform to the shape of the root canal, it must be flexible. It has been proposed to use superelastic files. Typically, to obtain superelasticity, nickel-titanium alloys (NiTi) are used, which may be, for example, 55% nickel and 45% titanium by weight (EP 1 745 757). However, the file must also meet high expectations in terms of stress and strain resistance and cyclic fatigue.

[0003] One of the most important properties of endodontic files for root canal treatment is their good resilience to cyclic fatigue. If an endodontic file breaks when rotating in a curved root canal, removal of the fragments is difficult and time-consuming, and the associated health risks to the patient are considerable.

[0004] In order to obtain high resistance to torsional breakage, to maintain the shape when splitting and to provide a sharp cutting edge, it has been proposed in the art to treat endodontic instrument blanks of NiTi alloys at a temperature of about 500°C for 1-2 hours (EP 1 753 361). In the same publication it has also been proposed to apply a coating by deposition, which essentially involves a heat treatment.

[0005] EP 3 375 557 discloses blanks for endodontic instruments which are subjected to a surface treatment (electrical discharge machining). Such EDM processes inherently involve the generation of heat. However, the heat input time is short and the method is selected for its effect on the surface properties of the file.

[0006] Thus, although heat treatment of endodontic file blanks is known in the art, the cyclic fatigue resistance of such files is still insufficient. In particular, if the blanks are subjected to only short temperature cycles of about 1 hour, the cyclic fatigue properties of the blanks remain unchanged or even deteriorate compared to untreated files. This may be due to harmful oxidation of the file's surface, low phase transition temperatures, and / or structural defects of the material. Summary of the Invention [Problem to be solved by the invention]

[0007] It is therefore an object of the present invention to overcome the shortcomings of endodontic instruments known in the art, and more specifically, to provide a method of manufacturing or modifying endodontic instruments made from superelastic NiTi alloys that are more resilient to cyclic fatigue and therefore easier, longer lasting and safer to use in root canal treatment. [Means for solving the problem]

[0008] This object is achieved by the method and endodontic instrument claimed in the claims. The method relates to manufacturing or modifying an endodontic instrument made from a nickel-titanium alloy (hereinafter NiTi alloy). The method includes performing a heat treatment, - providing a NiTi endodontic instrument made of a shape memory alloy, preferably having superelastic properties at 25°C; - heating the endodontic instrument to a first temperature range of 550°C to 625°C, preferably 560°C to 610°C, more preferably 260°C to 600°C, even more preferably 570°C to 590°C; - maintaining the endodontic instrument at a first temperature range for a first period of time between 20 minutes and 90 minutes, preferably between 30 minutes and 70 minutes, and more preferably between 45 minutes and 60 minutes; Next, - allowing the endodontic instrument to cool to a second temperature range, between 400°C and 549°C, preferably between 450°C and 530°C, and more preferably between 475°C and 515°C; - maintaining the endodontic instrument in a second temperature range for a second period of at least 180 minutes, preferably between 190 and 300 minutes, more preferably between 210 and 270 minutes, even more preferably between 220 and 260 minutes; Includes.

[0009] NiTi endodontic instruments with superelastic properties are made from alloys known in the art. The titanium alloys can be selected from, for example, alpha-titanium alloys, beta-titanium alloys, alpha-beta-titanium alloys, and nickel-titanium alloys. Non-limiting examples of α-titanium alloys, β-titanium alloys, and α-β-titanium alloys for use in this embodiment of the invention include Ti-5AI-2.5Sn α alloy; Ti-5Al-2.5Sn-ELI (low O2) α alloy; Ti-3Al-2.5V α alloy; Ti-5Al-5Zr-5Sn α alloy; Ti-6Al-2Cb-1Ta-0.8Mo α alloy; Ti-5Al-5Sn-2Zr-2Mo-0.25Si near α alloy; Ti-6Al-2Nb-1Ta-1Mo near α alloy; Ti-8Al-1Mo-1V near α alloy; Ti-6Al-2Sn-4Zr-2Mo near α alloy; Ti-6Al-2Sn-1.5Zr-1Mo-0.35Bi-0.1 Si near α alloy. Near α alloy; Ti-2.25-Al-11Sn-5Zr-1Mo-0.2Si Near α alloy; Ti-3Al-2.5V α-β alloy; Ti-10V-2Fe-3Al α-β alloy; Ti-5AI-2Sn-2Zr-4Mo-4Cr α-β alloy; Ti-6Al-2Sn-4Zr-6Mo α-β alloy; Ti-4Al-4Mn α-β alloy;Ti-6Al-2Sn-2Zr-2Mo-2Cr-0.25Si α-β alloy;Ti-4Al-3Mo-1V α-β alloy;Ti-6Al-2Sn-4Zr-6Mo α-β alloy;Ti-11 Sn-5Zr-2AI-1 Mo α-β alloy;Ti-6AI-4V The titanium alloys used in the shanks are α-β alloys; Ti-6Al-4V-ELI (low O2) α-β alloys; Ti-6Al-6V-2Sn-0.75Cu α-β alloys; Ti-7Al-4Mo α-β alloys; Ti-6Al-2Sn-4Zr-2Mo α-β alloys; Ti-,5Al-1.5Fe-1.5Cr-1.5Mo α-β alloys; Ti-8Mn α-β alloys; Ti-8Mo-8V-2Fe-3Al β alloys; Ti-11.5Mo-6Zr-4.5Sn β alloys; Ti-3Al-8V-6Cr-4Mo-4Zr β alloys; and Ti-3Al-13V-11Cr β alloys (numbers are weight percent). The titanium alloys used in the shanks can contain 54 to 57 weight percent nickel and 43 to 46 weight percent titanium.The NiTi alloy may or may not contain a stabilizing amount of a metal selected from molybdenum, tin, bismuth, tantalum, vanadium, zirconium, niobium, chromium, cobalt, nickel, manganese, iron, aluminum, copper, and / or lanthanum.

[0010] It has been shown that by heat treatment, excellent cyclic fatigue properties and excellent tensile strength of the finished device can be achieved. Heat treatment requires at least two processing steps at different temperatures: the first step of heat treatment is carried out at a relatively high temperature, and the second step of heat treatment is carried out at a significantly lower temperature but for a longer period of time. The steps are required in combination to achieve the improved results of the present invention. The treatment shifts the transition temperature of the alloy to above 37°C, corrects defects in the microstructure of the material and relieves stresses. The alloy is homogenized. Crack initiation and propagation are reduced and the material is better suited to compensate mechanical loads. The overall effect of heat treatment in the first and second temperature ranges is a substantial increase in the resistance of the finished device to cyclic fatigue.

[0011] Preferably, the working part of the endodontic instrument in the unloaded state is substantially linear, and in particular, the endodontic instrument does not have a bent, curved or helical shape in the unloaded state. By unloaded state, it is meant that no mechanical force is applied to the instrument. It is not the function of either the first or second step of heat treatment to deflect a part of the endodontic file and / or to orient a part of the endodontic file in a predetermined non-linear shape. In particular, neither the first nor the second step of heat treatment is performed such that the files are placed in a shaping section of a mold for receiving a part of a conventional file, thus forcing them into a curved, helical, corkscrew shape, etc.

[0012] In a preferred embodiment, after maintaining the endodontic instrument in the second temperature range, the endodontic instrument is allowed to cool to a third temperature range of 250°C to 350°C, preferably 275°C to 325°C, over a period of 90 minutes to 150 minutes, preferably over a period of 110 minutes to 130 minutes. It is particularly preferred that the cooling rate is kept constant, i.e. has a substantially constant value between 0.2°C / min and 3.3°C / min, with a variation of ±30% or less. The controlled cooling can support homogeneous phase transition temperatures across the length and cross-section of the finished material.

[0013] After heat treatment, the endodontic instruments are preferably allowed to cool in air at ambient conditions, i.e. at a temperature of 25°C and 1000 bar. The endodontic instruments may also be quenched by placing them in a liquid bath, preferably water. However, cooling in ambient air has proven slightly better in terms of the resistance of the resulting instruments to cyclic fatigue.

[0014] The heat treatment step occurring at least in the first temperature range is preferably carried out in a vacuum or in an inert gas atmosphere. More precisely, whenever the endodontic instruments are kept at a temperature of 550°C or higher, an inert gas atmosphere, for example argon, krypton, xenon, radon or vacuum, is maintained to prevent the surface of the file from oxidizing.

[0015] The temperature over time within the first specified range and the second specified range may be constant, increasing, decreasing or curving with one or several local maxima or minima. However, it is preferred that the endodontic instrument is kept at a first substantially constant temperature during the first period of time and / or at a second substantially constant temperature during the second period of time. It is particularly preferred that the instrument is maintained at a first constant temperature, for example 575°C (±2°C) during the first period of time, and at a second constant temperature, for example 500°C (±2°C) during the second period of time.

[0016] One aspect of the invention relates to an endodontic instrument obtainable by the method described above, which has several advantageous properties: in particular, it has a high resistance to cyclic fatigue and is able to fully compensate mechanical strains by deformation.

[0017] Preferably, the above-mentioned endodontic instruments in the unloaded state are substantially straight, and in particular the working parts of the endodontic instruments do not have a bent, curved or helical shape in the unloaded state. Due to the materials and methods used, the endodontic files have adequate flexibility to accommodate curved root canals, so that no predefined shaping is necessary.

[0018] One aspect of the present invention relates to an endodontic instrument, preferably obtained by the above method, having a mean cycles to failure of at least 4000, preferably at least 4300, more preferably at least 4500.

[0019] "Average" is understood to be the arithmetic mean. The number of cycles to failure is measured by rotating the sample in a curved groove machined from a stainless steel block and covered with a glass plate until the sample breaks. The groove had a width b of 1.5 mm, a depth d of 2 mm, a total length L1+B+L2 of 2.1 cm, L1 of 10.5 mm, L2 of 3 mm, a curvature of 60° and an arc length B with a radius of curvature R of 8.25 mm. The file was attached to the end motor and introduced maximally into the stainless steel tube while not touching the front end of the tube. The test was carried out at 20 ° C and a rotation speed of 500 rpm. The number of rotations was counted by optical means (monitored through a glass plate that laterally closes the stainless steel groove).

[0020] In one aspect of the invention, an endodontic instrument comprises: - has only been subjected to a heat treatment step occurring within a first temperature range, or - has been subjected only to a heat treatment step occurring within a second temperature range, Calculated from the cyclic fatigue values ​​in the same file, The performance in cyclic fatigue tests is improved by at least 20%, preferably by at least 25%.

[0021] Such a device can be obtained by the method described above. In particular, the endodontic instrument has pseudoplastic behavior at room temperature of 25° C. and superelastic behavior at temperatures above the phase transition temperature of the endodontic instrument. The endodontic instrument has a phase transition temperature of at least 37° C., preferably at least 40° C., more preferably 45-70° C., measured according to the flexion and free recovery test method according to ASTM F2082 / F2082M.

[0022] In the bend and free recovery test method based on ASTM F2082 / F2082M, the file is cooled to its nominally fully martensite phase. The file is then deformed and its wider proximal end is fixed in a holder. The specimen is heated to its fully austenitic phase in ambient air. During heating, the movement of a marker applied to the tip of the specimen is measured and plotted against the specimen temperature. A temperature increase (1 K / min) is applied until the file has fully recovered to its initial shape. The austenite finish temperature (A f (Definition according to Standard Terminology for NiTi Shape Memory Alloys, F2005-05(2015)) is measured using the 90% Recoverable Deformation Method. Unless otherwise specified herein, the parameters according to ASTM F2082 / 2082M apply.

[0023] The phase transition temperature describes the excellent ability of the alloy to compensate for mechanical loads by deformation, especially at the relevant temperatures present during root canal treatment.

[0024] The present invention can be better understood based on the following examples and figures. The examples are presented to further illustrate the invention and are not intended to limit it. [Brief description of the drawings]

[0025] [Figure 1]This is the temperature profile over time for a simple run of the file "500C_75min". [Diagram 2] 1 is a profile of temperature over time during simple processing of file "500_300" under controlled cooling. [Diagram 3] 13 is a profile of temperature over time for treatment in the first and second temperature ranges "575_500_300" under controlled cooling. [Figure 4a] FIG. 1 is a front view of the measurement setup for cyclic fatigue testing grooves. [Figure 4b] FIG. 13 is a top view of the measurement tube setup for the cyclic fatigue test groove. [Diagram 5] 1 shows the results of a cycle fatigue test (Example 1). [Figure 6] FIG. 13 is a DSC diagram of untreated NiTi control wire. [Figure 7] FIG. 14 DSC diagram of NiTi wire subjected to simple treatment (600° C. for 1 h). [Figure 8] Figure 14 DSC diagram of NiTi wire subjected to temperature treatment in the first and second temperature ranges (600°C for 1 hour, followed by exposure to 500°C for 3.5 hours, cooling to 300°C over 2 hours). [Figure 9] 13 is a profile of temperature over time for processing a second batch of file "575_500_300_long" at a first and second temperature range. [Figure 10] This is the temperature profile over time for a brief run of the second batch of file, "500C_300_long". [Figure 11] 13 shows the results of cyclic fatigue testing of files from the second batch (Example 2). [Figure 12] This is the result of tensile stress. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] Example 1 Sixty HyFlex CM files were prepared from Coltene (size / taper 30 / 0.04) NiTi alloy with superelastic properties. The files had a working portion extending from the distal end of the shank along the axial length of the shank in which at least one cutting blade was provided in a helical shape. The files were manufactured by milling. The manufacturing included some cold working, but may also include an annealing step.

[0027] An ensemble of 10 files each was placed in a titanium container (grade 1). Two titanium containers (i.e., 20 files) were placed in a quartz holder and covered with getter material. Subsequently, the three quartz holders were individually placed in a vacuum furnace for processing, as shown in Figures 1-3. The pressure in the furnace was increased to 3 × 10 -3 The pressure was lowered to 100 bar and the sample was placed under an argon gas flow of 0.2 L / min.

[0028] Twenty files 500C_75min were held at 500 °C for 75 min, 10 of them were rapidly quenched in water immediately after heat treatment, and 10 of them were cooled in ambient air (Figure 1).

[0029] Twenty files 500_300 were held at 500 °C for 4 h and then cooled to 300 °C over 2 h at a constant cooling rate of 1.7 °C / min. Ten of them were quenched in water immediately after heat treatment and ten of them were cooled in ambient air (Figure 2).

[0030] Twenty files 575_500_300 were held at 575°C for 45 min, cooled to 500°C over 15 min, held at 500°C for 4 h, and cooled to 300°C over 2 h at a constant cooling rate of 1.7°C / min. Ten of the files were quenched in water immediately after heat treatment and ten of them were cooled in ambient air (Figure 3).

[0031] Cyclic fatigue was measured by rotating the samples in a curved groove machined from a stainless steel block and covered with a glass plate until the sample broke. The groove had a width b of 1.5 mm, a depth d of 2 mm, a total length L1+B+L2 of 2.1 cm, L1 of 10.5 mm, L2 of 3 mm, a curvature of 60° and an arc length B with a radius of curvature R of 8.25 mm. Figure 4a is a schematic front view of a stainless steel block 1 with a curved groove 3. The glass plate is not shown in Figure 4a. Figure 4b is a top view of a stainless steel block 1 with a groove 3 with dimensions b and d. A glass plate 2 is attached to cover the entire extension of the groove 3 machined from the stainless steel block. A file is attached to the end motor and introduced maximally into the stainless steel groove covered with a glass plate while avoiding touching the front end of the tube. The test was performed at 20 °C and a rotation speed of 500 rpm. The number of rotations was counted by optical means (monitoring through a glass plate 2 laterally closing the stainless steel channel).

[0032] As can be seen from Figure 5, files that underwent a brief treatment at 500°C for only 75 minutes (500C_75min) performed poorly in the cyclic fatigue tests, averaging 444 cycles to failure (quench in water; 500C_75min_W), or 446 cycles to failure (cooling in ambient air; 500C_75min_A). Files that underwent a brief treatment at 500°C for 4 hours with controlled cooling to 300°C (500_300) performed significantly better, averaging 3583 cycles to failure (quench in water; 500_300_W), or 3634 cycles to failure (cooling in ambient air; 500_300_A).

[0033] However, files subjected to combined heat treatment in the first and second temperature ranges (575_500_300) performed significantly better. Samples quenched in water failed after an average of 5315 cycles (575_500_300_W). Samples quenched in air failed after an average of 5450 cycles (575_500_300_A). This corresponds to an improvement in resistance to cyclic fatigue of at least 48%, calculated from the cyclic fatigue values ​​of the best comparison groups (500_300 quenched in water / air, respectively). Quenching in ambient air generally improved the performance of the files in the cyclic fatigue tests compared to files quenched in water.

[0034] The dramatic improvement in resistance to cyclic fatigue of file 575_500_300 cannot be explained by mere stress relaxation over time in heat treatment. This effect may be the result of the combined effect of Ni-rich Ni4Ti3 precipitation, reduction of microstructural defects, and homogenized microstructure. Thermal characterization of NiTi wires by differential scanning calorimetry (DSC) confirms that heat treatment influences the phase transition temperatures of the alloy. The untreated alloy is austenitic / superelastic at room temperature (Figure 6). The NiTi alloy subjected to 600°C for 60 min shows a more obvious phase transition peak, occurring at a relatively low temperature (Figure 7). In contrast, NiTi alloys subjected to heat treatment in the first and second temperature ranges according to the invention (1 hour at 600°C, followed by 3.5 hours exposure at 500°C, cooling to 300° over 2 hours) show well-defined peaks and a significant shift in the phase transition temperatures to values ​​of approximately 60°C (austenitic transformation) and 20°C (martensitic transformation; Figure 8). It should be noted that the DSC measurements merely show the effect of heat treatment on the phase transition behavior of the alloy. For the purposes of the present invention, the superelastic and pseudoplastic properties of the endodontic instruments are characterized by the bending and free recovery principle.

[0035] Example 2 A second batch of 20 HyFlex CM files from Coltene (size / taper 30 / 0.04) NiTi alloy with superelastic properties was prepared. As in the previous example, the files had a working portion extending from the distal end of the shank along the axial length of the shank in which at least one cutting blade was provided in a helical shape. The files were manufactured by milling. The manufacturing included some cold working, but may also include an annealing step.

[0036] An ensemble of 10 files each was placed in two titanium containers (grade 1). The titanium containers were placed in quartz holders and covered with getter material (grade 1). The quartz holders were then individually placed in a vacuum furnace for processing, as shown in Figures 6 and 7. The pressure in the furnace was increased to 3 × 10 -3 The pressure was lowered to 100 bar and the sample was placed under an argon gas flow of 0.2 L / min.

[0037] Ten files, "575_500_300_long", were held at 575°C for 45 minutes, cooled to 500°C over 15 minutes, held at 500°C for 4 hours, and cooled to 300°C over 2 hours at a constant cooling rate of 1.7°C / min. They were quenched in water immediately after heat treatment while still located in the titanium container. The temperature is plotted over time in Figure 9.

[0038] Ten files, "500_300_long", were held at 500°C for 5 hours and cooled to 300°C over 2 hours at a constant cooling rate of 1.7°C / min. They were quenched in water immediately after heat treatment while still located in the titanium container. The temperature is plotted over time in Figure 10.

[0039] Cyclic fatigue was measured by rotating the samples in a tube made of stainless steel until fracture, as described above for Example 1.

[0040] As can be seen from Figure 11, files that underwent a simple treatment at 500°C for 5 hours with controlled cooling to 300°C (500_300_long) performed reasonably well, averaging 2908 cycles to failure. In contrast, files that underwent a combined heat treatment in the first and second temperature ranges (575_500_300_long) performed significantly better. Samples failed after an average of 4567 cycles. This corresponds to an improvement in resistance to cyclic fatigue of at least 55%, calculated from the cyclic fatigue values ​​of the comparison group (500_300_long).

[0041] To complement the characterization of the modified alloys, uniaxial tensile tests were performed. Thus, nine pseudoelastic NiTi wires of 120 mm were investigated for their tensile resistance.

[0042] Each of the three wire sets was heat treated in a furnace as follows. -500°C for 4 hours (including rapid heating from room temperature to the target temperature over 30 minutes), followed by cooling to 300°C over 2 hours (000_000_N); -600°C for 1 hour (600_060_V); -575°C for 45 min, then cool to 500°C over 15 min, hold the wire at 500°C for 4 h, then cool to 300°C over 2 h (575_conti_N); The inert atmosphere (Ar flow) was maintained only during the initial treatment (if any) at elevated temperatures above 570° C. After removing the wire from the furnace, the wire was left to cool in ambient air.

[0043] Tensile tests were performed according to ASTM F2616 and the draw speed settings were adapted to the values ​​recommended in the publication SFB 459 (Sonderforschungsbereich der Ruhr-Universitaet Bochum).

[0044] The results of the uniaxial tensile tests are shown in Figure 12. As can be seen from the plot, the reference wire (000_000_N) treated at 500 °C for 4 h and cooled to 300 ° over 2 h remains rigid at ambient temperature. In contrast, the set of samples that underwent heat treatment at high temperature reached more than 80% elongation before the sample slipped / ruptured. The sample that underwent only high temperature treatment (600 °C for 1 h; 600_060_V, dashed line) is able to compensate the mechanical strain to some extent by deformation. However, the sample that underwent high temperature treatment (575 °C for 45 min) and this treatment was followed by a milder heat treatment at 500 °C for 3.5 h (controlled cooling to 300 ° over 2 h; 575_conti_N, dotted line) was best able to compensate the mechanical strain by deformation.

[0045] It can be concluded that only materials subjected to stepwise composite heat treatments in different temperature ranges provide an optimal balance between microstructural homogeneity and material tensile strength, thus allowing excellent resistance to cyclic fatigue, resistance to crack initiation / propagation, and sufficient compensation against mechanical loading.

Claims

1. 1. A method of manufacturing or modifying an endodontic instrument made from a NiTi alloy by performing a heat treatment, comprising: - Providing a NiTi endodontic instrument made of a shape memory alloy; - heating the endodontic instrument to a first temperature range, between 550°C and 625°C; maintaining the endodontic instrument in the first temperature range for a first time period from -20 minutes to 90 minutes; Next, - allowing the endodontic tool to cool to a second temperature range, between 400°C and 549°C; - maintaining the endodontic instrument in the second temperature range for a second period of at least 180 minutes; A method comprising:

2. The method of claim 1 , wherein the working portion of the endodontic instrument in an unloaded state is straight.

3. The heat treatment is 2. The method of claim 1, further comprising the step of: - after maintaining the endodontic instrument in the second temperature range, allowing the endodontic instrument to cool to a third temperature range of 250°C to 350°C.

4. The method according to any one of claims 1 to 3, wherein the endodontic instrument after the heat treatment is cooled in air.

5. The method according to any one of claims 1 to 4, wherein at least said steps occurring at least partially within said first temperature range are carried out in a vacuum or in an inert gas atmosphere.

6. The method according to any one of claims 1 to 5, wherein the endodontic instrument is kept at a first constant temperature during the first period of time and / or at a second constant temperature during the second period of time.

7. An endodontic instrument obtained by the method of any one of claims 1 to 6, having pseudoplastic behavior at room temperature and at a phase transition temperature of at least 37°C, as measured according to the flexion and free recovery test method based on ASTM F2082 / F2082M.

8. The endodontic instrument of claim 7 wherein the instrument in an unloaded state is straight.

9. 9. The endodontic instrument of claim 7 or 8, wherein the endodontic instrument has a mean cycles to failure of at least 4000, which is the arithmetic mean of the number of revolutions the endodontic instrument is rotated in a curved stainless steel channel covered with a glass plate until it breaks, and the mean cycles to failure is determined from 10 endodontic instruments.

10. - has only been subjected to said heat treatment steps occurring within said first temperature range, or - only subjected to said heat treatment steps occurring within said second temperature range, The cyclic fatigue values ​​of NiTi endodontic instruments made of shape memory alloys were calculated. Improved performance in cyclic fatigue tests by at least 20%; The cycle fatigue value in the cycle fatigue test was measured by rotating the sample in a curved groove machined from a stainless steel block and covered with a glass plate until the sample broke; The groove has a width b of 1.5 mm, a depth d of 2 mm, a total length L1+B+L2 of 2.1 cm, L1 being 10.5 mm, L2 being 3 mm, a curvature of 60° and an arc length B with a radius of curvature R of 8.25 mm; An endodontic instrument according to any one of claims 7 to 9, wherein the cyclic fatigue value indicates the number of cycles to failure.

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