|Year : 2007 | Volume
| Issue : 4 | Page : 112-118
|Stress distribution in rotary nickel titanium instruments - a finite element analysis
Vinoo Subramaniam, R Indira, MR Srinivasan, P Shankar
Department of Conservative Dentistry and Endodontics, Ragas Dental College and Hospital, Uthandi, Chennai, India
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| Abstract|| |
Nickel Titanium endodontic instruments facilitates instrumentation of curved canals. Continuous unidirectional rotation causes development of complex stresses in nickel titanium rotary instruments. The distribution of torsional anti bending stresses depends primarily on the cross sectional design and mass of the instrument to be cut. The finite element analysis is aimed to study and compare stress distribution and behavior of two rotary instruments, protaper and profile. The stress induced phase transformation of nickel titanium alloy is also studied by Finite Element Model, this model when simulated properly shows better understanding of stress analysis than other methods.
The analyses are made by applying a concentrated torsional and bending moment to the protaper and profile instrument models. Under equal loads, protaper model showed uniform stress distribution and less elasticity compared to profile model. Profile model is more elastic but, showed stress peaks between flutes.
|How to cite this article:|
Subramaniam V, Indira R, Srinivasan M R, Shankar P. Stress distribution in rotary nickel titanium instruments - a finite element analysis. J Conserv Dent 2007;10:112-8
|How to cite this URL:|
Subramaniam V, Indira R, Srinivasan M R, Shankar P. Stress distribution in rotary nickel titanium instruments - a finite element analysis. J Conserv Dent [serial online] 2007 [cited 2022 Jan 28];10:112-8. Available from: https://www.jcd.org.in/text.asp?2007/10/4/112/43028
| Introduction|| |
Advances in technology and techniques have made contemporary endodontic procedures more pleasant and predictable with a success rate of 95%. These results achieved by root canal treatment depend critically on the method of instrumentation and on the instruments used for shaping the canals. In 1960, introduction of Nickel-Titanium alloy by W.F.Buehler at the Naval Ordnance Laboratory has revolutionized Metallurgy. Ni-Ti alloy is found to have unique properties like super elasticity and shape memory, which will preserve the canal geometry during cleaning and shaping  . The super elasticity of nickel titanium allows deformation of as much as 8% strain to be fully recoverable compared to a maximum of less than 1% with stainless steel ,
Investigations in the use of nickel-titanium rotary files have shown that they cause significantly less root canal transportation by remaining more centered in the root canal, remove less dentin, and produce a rounder root canal preparation than do stainless-steel or nickel-titanium hand files  .
The stresses to which a nickel-titanium, mechanically driven instrument is subjected are different from the stresses, which a manual instrument undergoes. The nickel-titanium, mechanically driven instrument when subjected to continuous rotation, undergoes unidirectional torque inducing constant stress and strain to the files  . This subjects the instrument to a constant and variable strain depending on the canal curvature and the hardness of the dentin to be removed. It is therefore of determinant importance to manufacture rotary endodontic instruments that are not only elastic but also strong. Cross section of the instrument is extremely important because it directly determines torsional and bending properties of the instrument  .
This study was aimed to compare torsional and bending stresses in two simulated models of nickel-titanium rotary instruments, Protaper and Profile using Finite Element Model. These two instruments were taken because these represents the generation of triple helix and triple u cross sectioned instruments respectively.
| Materials and Methods|| |
The instruments analyzed in this study were protaper and profile. Finite Element Method requires modeling of the instruments to be analyzed  .
CATIA modeling software was used to digitally draw the characteristic solid cross sections [Figure 1]. The cross sections of Protaper and Profile are inscribed with in cylinders of equal diameter and length.
The geometric models of Protaper and Profile are made by rotating the characteristic cross section through 360 degrees over a length [Figure 2]. This procedure ignored the variations in taper of the Protaper and Profile instruments in clinical use.
These images of Protaper and Profile are now transferred to ANSYS Finite Element Method Software. The models thus transferred are divided into discrete hexahedral elements. The total numbers of elements are 3750 for Protaper and 3600 for Profile [Figure 2].Material properties of the instruments like Young's Modulus, Poisson's Ratio and elastic limit were incorporated. The ANSYS program is now defined with all properties. The instrument is divided into finite elements; in all axes X, Y and Z. The nodes were then defined.
The surrounding conditions, force and moments were fixed. In both cases, the model was blocked at one end and was loaded with a concentrated torsional or bending moment at other end.
| Mechanical Properties|| |
The instruments, Protaper and Profile are made of nickel-titanium alloy whose mechanical behavior is highly non-linear  . The mechanical behavior of this alloy is represented by the graph of stress against strain. The characteristics curve of material can be divided into three parts. The crystalline structure of the alloy changes with force. (Graph 1).
The first part is linear, where the alloy is in a more stable crystalline phase of the austenitic type. The second part of graph is also linear but almost flat. In this phase the material is in transition from austenitic to Martensitic phase. This phase describes behavior specific to the material analyzed; a very small stress produces large strain. This characteristic of the material is identified as super-elasticity  . The third part of the graph is highly non-linear and alloy is characterized by a Martensitic type phase. This last part of the graph has the typical characteristics of a stress-strain diagram of a metal, with an elastic zone, a yield point and a breaking point. The different cross-sectional designs of nickel titanium rotary instruments have an effect on their flexibility and other physical properties.
| Results|| |
The results of the analyses were obtained by applying a concentrated torsional and bending moment to the protaper and profile finite element models. These analyses do not take into account the forces applied to two models by any external structure like dentin.
| Torsional Behavior|| |
A torsional load of 0 to 2.5 N/mm 2 was applied to both protaper and profile models in four increments. Stress values increase radially outwards from the center of the model to the periphery.
The central core of protaper model was subjected to less stress, with values between 0 and 200 N/mm in all four force levels [Figure 3] this was represented by blue and light blue colored areas in the model. The external part of the model operates in the super-elastic field with stress values above 250 N/mm. This was represented by light blue and green areas. Less stress accumulation was observed in between flutes of protaper model compared to profile model.
The core of profile model was subjected to less stress, with values between 0 and 200 N/mm in all four force levels [Figure 3] was represented by blue and lightblue colored areas in the model. In this area, the material is entirely in the austenitic phase. When stresses were increased the material transformed in to super elastic state. The external part of the model operates in the super-elastic field with stress values above 400 N/mm. This was represented by green and yellow areas. Peak stress concentration was observed between flutes as red areas. In this area, the material is in the martensitic phase and has lost the property of super elasticity.
| Bending Behavior|| |
A bending load of 4.5 N/mm 2 was applied [Figure 4] to both protaper and profile models in four increments. In both Protaper and profile, stress values increase as the distance from the neutral bending plane increases. These stresses may be of the tensile or the compression type, depending on the position with respect to the neutral plane. The applied bending moment being equal, the model with the protaper section showed lower stress values.
The central part of the protaper model is characterized by stress values between 0 and 200 N/mm indicated by blue and light blue areas [Figure 4].In this area, the material is entirely in the austenitic phase. Extending toward the outer surface of the models the stress value rises from 200 N/mm to 500 N/mm. This is indicated by green regions characterized by super elasticity. Outer surface of the model shows stress peaks indicated by yellow color characteristic of martensitic phase.
The central part of the profile model showed stress values between 0 and 200 N/mm indicated by blue and light blue areas [Figure 4]. In this area, the material is entirely in the austenitic phase. Extending toward the outer surface of the models, the stress value rises when higher loads are applied. Peak stress concentration was observed between flutes as red areas. In this area, the material is in the martensitic phase and has lost the property of super elasticity. This stress peak varies in position within the flutes as the position of the cross-section varies.
| Rigidity Curves of Protaper and Profile|| |
The bending and torsional rigidity of the models analyzed depends on the crystalline phase of the material in the different parts of the model and thus on the stress conditions generated by the applied load. This is represented in the graph of stiffness against moment. (Graph 2)
The first part of the curves of protaper and profile are horizontal. The crystal structures of the instruments are in austenitic phase. The displacement of the moment applied varies linearly with the load. In this part of the curve, the difference in rigidity between the two models is only due to the different moment of inertia of the two cross-sections. Moment of inertia is bending fracture resistant factor. The model with the protaper cross section has the higher moment of inertia and thus the greater bending rigidity.
When the bending moment is increased, the material of the more external part of the crosssection of the models is subjected to higher stress values typical of the transition from austenitic to martensitic phase In this transition phase the material behaves in a super-elastic fashion, and the bending rigidity of the two models varies as the proportion of material in the super-elastic field varies. This corresponds to the second part of the curve. Thus the different behavior of the two models of protaper and profile can be attributed to the different geometry of the cross-sections.
In the third part of the curve bending rigidity tends to become almost constant again when most of the material is in the martensitic phase. The different bending rigidity values of the two models are again chiefly due to the different moments of inertia of the two cross-sections.
The central part of the graph indicates that the material is in transition from the austenitic to the martensitic phase. The transition from the first part of the curve, to the third part of the curve, occurs more rapidly for Profile cross section. The portion of material operating in the super-elastic field is quickly reduced as the applied load increases. In the case of Protaper cross-section, this transition phase is much more gradual. It shows a more gradual transition of the material from the austenitic to the martensitic phase as the applied load increases. The Protaper model with convex cross-section is thus characterized by the presence of an extended superelastic phase for a wider range of loads than Profile model with concave cross section.
| Discussion|| |
The manufacturing of endodontic instruments using super elastic nickel-titanium alloys have provided an important development in the techniques of cleaning and shaping of the root canal system. The improved flexibility of instruments made of nickel titanium has been shown to produce improved preparation shapes compared to stainless steel  .
Inspite of the evident advantages of this technique, Ni-Ti rotary instruments may undergo failure by fatigue when used in curved canals due to the tension /compression cycles to which they are subjected when flexed in the region of maximum curvature of the canals. This metal fatigue eventually leads to cumulative micro structural changes that ultimately lead to failure of the instrument  .
Failure of the endodontic rotary instruments can occur under two circumstances: torsional fracture and bending or flexural fracture  . Torsional fracture occurs when a part of the instrument is locked in a canal while the shaft continues to rotate, exceeding the torsional limit Flexural fatigue is synonymous with metal fatigue. When an instrument is rotating around the curve, it is compressed on the inner side of the curve and stretched on the outer side of the curve. With every 180 degrees of rotation, the instrument flexes and stretches over and over again, resulting in cyclic fatigue and, eventually, fractures. The larger sized or greater taper file sustains more compressive and tensile forces due to increased metal mass , .
The present simulated study compares torsional and bending stresses in two simulated models of nickel titanium rotary instruments: Protaper and Profile using Finite Element Method.
The cross-sections of Protaper and Profile [Figure 1], have markedly different geometrical properties. Protaper has an area almost 30% greater than Profile.
The Protaper instruments demonstrate a convex, triangular cross-section  The Profile instrument demonstrates a concave; U shaped cross section . It has a 20-degree negative rake angle at the cutting edge and flat radial lands to cut dentin in a planing motion. These configurations prevent the instrument from screwing into the canal while rotating. The radial lands also add peripheral mass that contributes significantly to the strength of the instrument. The U-shaped grooves provide the space to accommodate dentin shavings while planing of the canal wall. The noncutting tip and symmetric radial lands allow the file to remain self-centered as it rotates through 360 degrees, theoretically decreasing the potential for canal transportation and procedural errors to occur.
The stresses that are generated in the models analyzed, during a torsional or bending moment, are not constant and they vary with the applied load. This variation corresponds to the crystalline phases of the alloy, which shows a nonlinear behavior , . Comparing the bending rigidity graphs of the two models, the three crystalline phases characteristics of the alloy are recognized (Graph 2). The first horizontal phase corresponds to the austenitic phase, second phase corresponds to super elastic phase and third phase is martensitic  . The horizontal part of the graph representing austenitic phase is located lower in the Profile model indicating low stiffness compared to protaper. The geometric characteristic of profile cross-section makes it more elastic  .
The different behavior of the two models in the transformation phase from austenite to martensite is very unique. This transformation phase is ideal for working with mechanically driven rotary instruments, giving them the characteristic of super-elasticity without excessive stress  . Young's modulus of the transformation phase is lower than that of the Martensitic phase , and the instrument in this phase transformation would be more flexible  .
The bending rigidity curve of the Profile model (Graph 2) shows that this model shifts rapidly from the austenitic phase to the martensitic phase. In profile model the transformation phase is short. The transformation behavior of the protaper model is different. Here the changeover from the austenitic phase to the Martensitic phase is gentle and the part of the graph corresponding to this transformation is long. This indicates that, under similar loading conditions, the protaper model works for a longer time in the super-elastic phase, which gives maximum performance and high resistance to fracture. The Profile is more elastic but accumulates high stress more rapidly, because the transformation phase is so short that the model frequently has to operate in the martensitic phase  (Graph 2).
| Conclusion|| |
From the results of the present study it may be inferred that
- Distribution of torsional and bending stresses was uniform in protaper model compared to profile model.
- Protaper model is stiffer than profile model because 30% more mass has been incorporated in the protaper design compared to profile. This increase in mass enhances its use in narrow canals where high stresses are generated during instrumentation because of radicular anatomy and dentin hardness.
- Profile model is more flexible than protaper model because of its design. But it exhibits high stress concentration between flutes.
- The bending rigidity graph of protaper model (graph 2) exhibits super elastic phase transformation from austenite to martensite for an extended period of time. Hence the protaper instrument can operate with high loads in super elastic phase with out accumulating high stresses and this enhances its fracture resistance. Profile model has a very short super elastic transformation phase. It undergoes transformation in to martensitic phase quickly and accumulates high stresses, which reduces its fracture resistance.
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Department of Conservative Dentistry and Endodontics, Ragas Dental College and Hospital, Uthandi, Chennai
Source of Support: None, Conflict of Interest: None
[Figure 1], [Figure 2], [Figure 3], [Figure 4]
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