**1. Introduction**

Due to iatrogenic procedural errors associated with the material stiffness of stainless-steel instruments, nickel–titanium (NiTi) material was introduced in the production of endodontic files [1]. The main characteristics of NiTi rotary instruments include memory shape, superior elasticity, and a centered canal preparation. In particular, the elastic flexibility of NiTi instruments is two to three times higher than that of stainless-steel instruments due to their lower modulus of elasticity [2,3]. The material properties of NiTi and stainlessness rotary files are presented in Table 1 [4].

Despite the elastic flexibility of NiTi rotary systems, instrument fracture has been reported [5,6]. The failure of rotary NiTi files can be either flexural (cyclic) or torsional [7]. The majority of studies have shown that cyclic fatigue (CF) fracture occurs when an instrument is flexed in the maximum curvature region of the canal while rotating freely, resulting in repeated tension–compression cycles [6,8]. The tension occurs on the part of the instrument on the outside of the curve, whereas the compression occurs on the other part on the inside of the curve. Therefore, these repeated cycles, caused by the rotation of the instrument within the curved canal, result in instrument fracture due to the increase in the cyclic fatigue of the instrument over time. Torsional fatigue occurs when an instrument tip is locked in a canal, while the body continues to rotate. Therefore, fracture of the tip becomes unpreventable when the torque exerted by the handpiece exceeds the elastic limit of the metal [8]. However, one of the limitations in in vitro studies of the cyclic fatigue behavior of NiTi instruments is the difficulty of assessing the clinical relevance of published tests results, where there are several factors, including torsional fatigue, at play at the same time.


**Table 1.** Properties of NiTi and stainless steel rotary files.

The mechanical behavior and elastic flexibility of the NiTi alloy were improved by changing the transformation behavior of the alloy through heat treatment [9]. The NiTi alloy contains three microstructural phases (austenite, martensite, and R phase). Instruments in the martensite phase can be soft, ductile, and easily deformed and can recover their shape upon heating above the transformation temperature. Compared with conventional super-elastic NiTi, which shows a finish temperature of 16–31 ◦C [7,9], controlled memory wire and M-wire instruments show increased austenite transformation finish temperatures of approximately 55 and 50 ◦C, respectively [10]. Therefore, at body temperature, the conventional super-elastic NiTi file has an austenite structure, whereas an NiTi file with thermal processing is essentially in the martensite phase [9].

ProTaper Universal (PTU) and ProTaper Gold (PTG) rotary instruments possess the same geometries; however, PTG instruments have been metallurgically enhanced through heat-treatment technology in an attempt to improve flexibility, resistance to CF, and durability [7,11]. ProTaper Next (PTN) instruments are made of M-wire, which is fabricated by the thermomechanical processing of NiTi wire blanks [5]. In addition, fracture resistance has been improved in PTN instruments due to the unique asymmetrical rotary motion and reduced contact points between the instrument and root canal walls [5].

In the endodontic literature, rotational bending is applied to test for CF in NiTi rotary instruments. Several devices and methods have been used to evaluate the in vitro CF fracture resistance of NiTi rotary endodontic instruments [8]. In addition to two important parameters used to determine the shape of the root canal, i.e., the angle and radius of curvature [6], some studies have reported that the results obtained might be unreliable and inconsistent if the established device parameters do not follow each instrument's morphologic and geometric features [8]. To overcome this problem, multiple devices with artificial canals that have dimensions that exceed those of the tested instruments by 0.1–0.3 mm have been used [12–14].

No previous study has compared the CF resistance of all the ProTaper instruments among the three different generations. Therefore, the aim of the present study was to assess the CF behavior of the PTU, PTG, and PTN NiTi rotary files.

#### **2. Materials and Methods**

#### *2.1. Preparation of Artificial Canals*

The laser micromachining technique was used to machine artificial canals in stainless-steel plates with dimensions of 100 mm × 50 mm × 10 mm. Machining was performed using the LASERTEC 40 (Deckel Maho Gildemeister, Hamburg, Germany), which consists of a Q-switched Neodynium-doped Yttrium Aluminum Garnt (Nd: Y3Al5O12 (Nd: YAG)) laser operating at a wavelength of 1064 nm with a maximum average power of 30 W.

The artificial canal to be machined was modeled using CATIA V5® software (Dassault Systèmes, Version 5, Vélizy, France), and laser path programming was performed with a Standard Triangle

Language file of the proprietary machine software. After the laser process parameters were established, the laser was focused on the workpiece with the aid of a galvano scanner, and the canal was then machined layer by layer [15].

The artificial canals were machined in stainless-steel blocks with dimensions corresponding to the dimensions of the instrument tested: +0.1 mm in width and +0.2 mm in depth, with an angle of curvature of 45◦, a radius of curvature of 5 mm, and a center of curvature 5 mm from the tip of the instrument [6,8] (Figure 1).

**Figure 1.** Custom-made stainless-steel blocks with dimensions corresponding to the dimensions of ProTaper Next (PTN) (**A**), ProTaper Gold (PTG), and ProTaper Universal (PTU) (**B**): +0.1 mm in width and +0.2 mm in depth, with an angle of curvature of 45◦, a radius of curvature of 5 mm, and a center of curvature 5 mm from the tip of the instrument. (**C**) Two-dimensional draft of artificial canal for PTU F1 instrument.

The dimensions of the PTU and PTG instruments were recorded according to the manufacturer as shown in Table 2. The actual dimension for the PTN from the manufacturer along with the maximum diameters of the PTN instruments measured using Digimizer® software (MedCalc Software, version 4.5., Ostend, Belgium) are shown in Table 3.


**Table 2.** Dimensions of PTU and PTG from the manufacturer.

**Table 3.** Dimensions of the PTN from the manufacturer.


#### *2.2. Cyclic Fatigue Testing*

Fifteen rotary instruments of each type (PTU S1, S2, F1, F2, and F3, PTG S1, S2, F1, F2 and F3, and PTN X1, X2, and X3), totaling 195 instruments of 25 mm in length, were used in this study.

Stainless-steel blocks were attached to a main frame to which a mobile support for the handpiece was connected. The dental handpiece was mounted on a mobile device that allowed for the simple placement of each instrument inside the artificial canal as shown in Figure 2. To prevent the instruments from slipping out and to allow for observation of the instruments, the artificial canals were covered with glass.

**Figure 2.** CF testing device illustrating positioning of dental handpiece, NiTi rotary instrument, and stainless steel block.

A pilot study was conducted to confirm the reliability of the CF device. All of the instruments were rotated at the speed recommended by the manufacturer (300 rpm) until fracture. The artificial canals were lubricated with synthetic oil (3-In-One Multi-Purpose Oil, WD-40®, San Diego, CA, USA) to reduce the friction of the tested file against the artificial canal walls. The motor and timer were then simultaneously activated. During each test, the instrument was monitored and visualized through the glass until fracture occurred, and the time to fracture was registered in seconds. Figure 3 shows the rotary files before and after fracture. The fractured surface was examined using SEM (JEOL 6360LV Scanning Electron Microscope, Tokyo, Japan) after preparation with ≥99.8% ethanol.

**Figure 3.** ProTaper Next X3 before (**a**) and after (**b**) fracture.

Statistical analysis of the empirical data is essential for the proper interpretation and prediction of results. There are many statistical methods such as analysis of variance (ANOVA), regression analysis, and correlation for analyzing data and representation of results [16]. Reports are available on the use of statistical methods for cyclic fatigue failure analysis [17] and fatigue life prediction [18].

In this work, one-way ANOVA and Tukey's tests were performed to analyze and compare the means. Statistical significance was set at *P* < 0.05. Weibull reliability analysis was performed and the probability of survival was calculated for the tested instruments.
