Influence of Cross-Section and Pitch on the Mechanical Response of NiTi Endodontic Files under Bending and Torsional Conditions-A Finite Element Analysis

Abstract

In this article, the effects of cross-section and pitch on the mechanical response of NiTi endodontic files is studied by means of finite element analyses. The study was conducted over a set of eight endodontic rotary files, whose geometry was obtained from combinations of two cross-sections (square and triangular) and four pitches. Each file was subjected to bending and torsional analyses, simulating the testing conditions indicated in the ISO 3630 Standard, in order to assess their stiffness and mechanical strength. The results indicate that endodontic files with a square cross-section have double the stiffness of those with triangular cross-sections, both in terms of bending and torsion. For both loading modes, endodontic files with a triangular cross-section can undergo larger deformations before overload failure than those with a square cross-section: up to 20% more in bending and 40% in torsion. Moreover, under equivalent boundary conditions, endodontic files with triangular cross-sections present a higher fatigue life than those with square cross-sections: up to more than 300% higher for small pitches. The effect of pitch on the stiffness and strength of the file is smaller than that of the cross-section shape, but smaller pitches could be beneficial when using a triangular cross-section, as they increase the bending flexibility, fatigue life, and torsion stiffness. These results suggest a clinical recommendation for the use of files with a triangular-shaped cross-section and a small pitch in order to minimize ledging and maximize fatigue life. Finally, in this study, we reveal the sensitivity of the orientation of files with respect to the bending direction, which must be taken into account when designing, reporting, and interpreting test results under such loading conditions.

Keywords: cross-section; endodontic file; finite element analysis; flexural bending; pitch; stress distribution; torsion.

Figure A1

Algorithm to search for the maximum von Mises ${\sigma }_{ij}$ stress in the analysis frame after the array $\mathsf{\Sigma }$ is created.

Figure 1

Geometries of the analyzed endodontic files: endodontic files with square cross-section (a); endodontic files with triangular cross-section (b); normalized square cross-section (c); and normalized triangular cross-section (d).

Figure 2

Sample stress–strain curve for NiTi material.

Figure 3

Devices used for torsion (a) and bending (b) analyses.

Figure 4

Definition of the finite element model.

Figure 5

The von Mises stress plots for the bending analysis of endodontic files with $p_z=4\mathrm{mm}$ and $\phi =0^{\circ }$.

Figure 6

Bending moment–rotation relationships for the bending analysis of endodontic files with $p_z=4\mathrm{mm}$: squared cross-section (a) and triangular cross-section (b).

Figure 7

Bending analysis: effect of the pitch on the maximum rotation (a) and maximum applied torque (b) when the end of the martensitic elastic regime is reached.

Figure 8

Bending analysis: bending stiffness of the endodontic rotary files with (a) square and (b) triangular cross-section.

Figure 9

Bending analysis: effect of the pitch on the maximum principal strain (a) and the expected number of cycles (b) when the rotated angle is ${\theta }_x={20}^{\circ }$.

Figure 10

The von Mises stress plots for the torsional analysis of endodontic files with $p_z=4\mathrm{mm}$.

Figure 11

Torque–rotation relationships for the torsional analysis of endodontic files with different axial pitch: squared cross-section (a) and triangular cross-section (b).

Figure 12

Torsional analysis: effect of the pitch on the applied torque (a) and rotation (b) when the end of the martensitic elastic regime is reached.

Figure 13

Torsional analysis: torsion stiffness of the endodontic rotary files with (a) square and (b) triangular cross-section.