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The European Journal of Orthodontics Advance Access originally published online on September 5, 2006
The European Journal of Orthodontics 2007 29(1):8-13; doi:10.1093/ejo/cjl038
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© The Author 2006. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved.
The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact journals.permissions@oxfordjournals.org.

Improvement of pseudoelasticity and ductility of Beta III titanium alloy—application to orthodontic wires

P Laheurte*, A Eberhardt**, MJ Philippe* and L Deblock***

* LETAM (CNRS—UMR 7078), Université de Metz
** LPMM (CNRS—UMR 7554), ENIM Metz
*** Private practice, Vandoeuvre-les-Nancy, France

Address for correspondence Dr P. Laheurte, LETAM/ISGMP, Université de Metz, Ile du Saulcy, 57 000 Metz, France. E-mail: laheurte{at}letam.sciences.univ-metz.fr


   Summary
Top
 Summary
Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
The pseudoelasticity of metastable Beta III titanium alloy (TMATM) used for orthodontic applications is obtained by cold wiredrawing. This wire has higher rigidity than cold-drawn NiTi (NitinolTM, superelastic NiTi SE) and lower recoverable deformation. The low ductility value of Beta III is due to the deformation imposed by wiredrawing. The aim of this research was to improve the behaviour of this alloy by modifying the microstructural parameters to decrease the rigidity and increase the recoverable deformation and ductility of the alloy. The effects of second phase precipitate, grain size, and deformation on the wire mechanical properties were also examined.

The isothermal precipitation of alpha ({alpha}) or omega ({omega}isoth) phases precludes the expression of the pseudoelastic effect. The presence of an {omega}isoth phase considerably increases fracture strength, whereas the {alpha} phase strongly decreases the ductility and adversely affects the strain recovery ({varepsilon}r).

To control the grain size, the growth of the recrystallized grains was studied by considering several parameters, which are known to have an influence on grain size, including the cold rolled strain, the temperature, the time of annealing, and the initial grain size. A structure with coarse grains, quenched from a temperature higher than the beta transus (Tß), associated with a plastic pre-deformation, contributed to an improved pseudoelastic behaviour, due to the presence of a reversible martensite phase ({alpha}'') induced by the pre-deformation.


   Introduction
Top
 Summary
 Introduction
Materials and methods
 Results
 Discussion
 Conclusions
 References
 
The desirable properties of an orthodontic wire depend on the requirements set by mechanotherapy at a specific treatment stage, and thus, selection of the appropriate wire is often complex. Criteria such as the degree of torque control, the desired load-deflection ratio, and the need for a specified elastic or plastic zone must be taken into account in the process.

In general, three factors determine the rigidity of the wire: the length, the cross-section, and the elastic modulus of the alloy. The traditional method to modify the rigidity consists of varying the dimensions of the wire by engaging incrementally larger cross-section wires in the slot, or adjusting the configuration of the loops. The use of materials with a low elastic modulus, such as titanium alloys, was introduced as an alternative way to advance treatment, namely, ‘variable modulus orthodontics’ (Goldberg et al., 1977Go; Burstone and Goldberg, 1979, 1980GoGo; Goldberg and Burstone, 1979Go; Burstone, 1981Go). The use of alloys with different rigidities provides a range of force during deactivation, which is independent of the wire cross-section.

Figure 1 illustrates the behaviour of an ‘ideal’ archwire providing a constant force throughout treatment, which coincides with the concept of optimal tooth movement. The behaviour of archwire A (Figure 1) during deactivation shows a variation of force which requires reactivation of the archwire in order to reach the desired tooth position. A compromise between the two extreme situations consists of using a lower rigidity wire (wire B, Figure 1). The variation of force however is lower and thus, the archwire requires less frequent activation.


Figure 1
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  		Figure 1 Wire rigidity on dental displacement—‘ideal’ wire with constant force (A) and with two different rigidities (B).

 
To meet clinical needs, various alloys have been introduced, presenting a force-deflection curve depicted in Figure 2. Stainless steel, which constitutes the most common alloy, possesses a high rigidity, and is characterized by an apparent elasticity modulus of 210 GPa. The titanium alloys for use in orthodontics include the cold-drawn Beta III developed by Burstone and Goldberg (1980Go, TMATM) and nickel-titanium (NiTi). The latter are also used in a strong, cold work-hardened form (NitinolTM) and in austenitic form, which provide superelasticity. NiTi wires, and especially NiTi superelastic (SE), present a substantial recovery strain (Table 1), where the unloading secant modulus (Es) is 20 GPa and its behaviour resembles that of bone during loading. NiTi wires are not weldable, have minimal ductility, and are used in pre-formed arches. However, the presence of the high Ni concentration in NiTi alloys raises some concerns about potential allergencity or toxicity of this wire. Therefore, the introduction of a nickel-free, low-stiffness pseudoelastic wire, with improved formability that can be joined with other wires or auxiliaries, would be of great value to the practising orthodontist.


Figure 2
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  		Figure 2 Tensile diagram showing the apparent modulus (Etg), unloading secant modulus (Es), recoverable strain ({varepsilon}r), and strain to fracture ({varepsilon}m).

 

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  		Table 1 Qualitative evaluation of NiTi and Beta III wire for orthodontic use.

 
While Beta III alloy does not contain nickel and has good weldability, its performance for recoverable deformation is inferior and it has a higher unloading Es compared with NiTi. The pseudoelasticity of Beta III titanium alloy obtained by cold working (wiredrawing) as shown in Figure 2 corresponds to a mechanism of selective reorientation of the martensite variant (Duerig and Zadno, 1990Go; Laheurte et al., 2005Go). For orthodontic applications, a significant recoverable deformation and a low unloading Es are desirable.

The purpose of this study was to modify the wire properties and obtain a beta titanium wire with improved pseudoelasticity through the variation of the phases of the wire alloy.


   Materials and methods
Top
 Summary
 Introduction
 Materials and methods
Results
 Discussion
 Conclusions
 References
 
As-received Beta III alloy was wiredrawn to segments of 0.43 x 0.63 mm. Treatment solutions and isothermal precipitation of the {alpha} or {omega} phases were carried out in vacuum quartz tube. Heat treatment for 1 hour at 800°C [above the beta transus (Tß) = 760°C] was followed by quenching with water. The average grain size (range 6–100 µm) of wires was obtained by thermomechanical treatment. To control the grain size in the wire, the normal growth of the recrystallized grains was studied by taking into account several parameters known to have an influence on grain size: the cold rolled strain, the temperature and time of annealing, and the initial grain size. The influence of these parameters was evaluated using an experimental design presented previously (Laheurte et al., 2004bGo). The tensile tests were carried out on a tensile testing machine (Zwick France sarl, Roissy Airport Ch. de Gaulle Cedex, France) in the form of loading–unloading cycles with increasing deformations to fracture. The resultant strain was measured by an extensometer (Zwick France sarl) with a gauge length of 20 mm at a strain rate of 4 x 10–3 s–1.


Characterization in tension

The apparent tangent modulus (Etg), the yield strength {sigma}e0.2%, and the ductility (elongation to fracture) are represented in Figure 3. In the relevant literature (Shastry and Goldberg, 1983Go; Goldberg and Shastry, 1984Go), the yield strength/modulus of elasticity ratio ({sigma}e 0.2%/Etg as shown in Figure 2) is often used as an index of the use of an orthodontic wire. However, this elastic strain does not sufficiently account for the action of the wire. It has been proposed (Laheurte et al., 2004aGo) that the wire should be characterized by Es and the recoverable strain ({varepsilon}r) on the unloading curve (Figure 2).


Figure 3
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  		Figure 3 Tensile diagrams of principal orthodontic wires, and compared with bone Es = secant modulus.

 

   Results
Top
 Summary
 Introduction
 Materials and methods
 Results
Discussion
 Conclusions
 References
 

Effect of precipitation treatment on pseudoelastic behaviour

The tensile test to fracture (Figure 4a) and at 2 per cent with unloading (Figure 4b) carried out for various heat treatments were compared with the drawn state (1). State (2) is obtained after water quenching from 800°C, while states (3) and (4) correspond to an ageing of 30 minutes at 550°C and 350°C, respectively. This process results in a precipitation of 40 per cent of {alpha} phase and 50 per cent of {omega}isoth phase (Laheurte, 2003Go). In the quenched state, the ductility was 25–27 per cent, while both the unloading Es and the recoverable deformation were lower relative to the as-received specimens (Table 2). The precipitation of the {omega}isoth and {alpha} phases during ageing, and states 3 and 4, considerably increased the ultimate tensile strength. The very low ductility, which was present in state 3, confirmed the brittleness due to the {omega}isoth phase. The {alpha} phase strongly decreased ductility and did not improve the {varepsilon}r compared with the as-received cold drawn. The unloading Es was higher than that of the cold-drawn state.


Figure 4
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  		Figure 4 Influence of heat treatment on (a) ductility and (b) the recoverable strain and unloading secant modulus.

 

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  		Table 2 Mechanical characteristics after imposed deformation of 2 per cent or after fracture (average of three tests and standard deviation).

 

Effect of uniaxial pre-deformation on pseudoelastic behaviour

After quenching, the recrystallized beta grains had an average size of 22 µm. When the deformation increased from 0 to 15 per cent, the Es decreased from 37 to 25 GPa (Figure 5). The unloading curve showed an elastic pattern for the first cycle but deviated from linearity for the following cycles. {varepsilon}r increased with the imposed deformation. This variable is the sum of the elastic strain ({varepsilon}elast) and the deformation ({varepsilon}M) due to the variant reorientation of the martensite.


Figure 5
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  		Figure 5 Influence of plastic pre-deformation (0 1, and 15 per cent) on the recoverable strain {varepsilon}r = {varepsilon}M + {varepsilon}elast and on the unloading secant modulus (rectangular wires 0.63 x 0.43 mm).

 

Effect of the grain size

{varepsilon}r and the reduction of the Es increased with grain size (Figure 6a,b). For small grain sizes, no hysteresis was apparent and the {varepsilon}r was purely elastic. The grain boundaries constituted obstacles for growth and propagation of the martensite variants and their mobility during unloading.


Figure 6
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  		Figure 6 Influence of grain size on (a) recoverable strain and (b) unloading secant modulus.

 

Comparison of a structure optimized with a cold work-hardening structure

By combining grain growth and plastic deformation, a significant decrease in the Es and an increase of {varepsilon}r were obtained. Figure 7a shows the optimized structure of Beta III wire with the other wires and, in particular, the Beta III cold work-hardened wire. The unloading Es varied from 40 to 21 GPa and the maximum {varepsilon}r from 3 to 4 per cent leading to increased ductility in the order of 100 per cent (Figure 7b), relative to the as-received, cold-drawn form (Laheurte et al., 2003Go). Scanning electron micrographs (Figure 8a,b) illustrate the greater aptitude for the formation of loops with low curvature radii for the optimized structure compared with the cold work-hardening structure (presence of cracks). The bending test (Figure 9) with a configuration resembling that of clinical conditions showed that the unloading Es was decreased by 40 per cent, corresponding to a maximum deflection of 1.5 mm (Table 3).


Figure 7
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  		Figure 7 Comparison of unloading secant modulus (Es) and recoverable strain ({varepsilon}r) of principal alloys with optimized Beta III: (a) {varepsilon}r and Es modulus and (b) strain to fracture.

 

Figure 8
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  		Figure 8 Scanning electron micrograph of Beta III alloy (x200) after bending at 180 degrees: (a) optimized structure and (b) cold wiredrawing. Note the presence of cracks (arrow).

 

Figure 9
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  		Figure 9 Beta III characteristic of bending test: loading–unloading cycles for three imposed deflexions at 0.5, 1, and 1.5 mm (wire 0.17 x 0.25 inch, distance between the two brackets 14 mm).

 

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  		Table 3 Optimized structure of Beta III—characteristic of bending test: unloading forces for three deformations (wire 0.17 x 0.25 inch, distance between the two bracket 14 mm).

 

   Discussion
Top
 Summary
 Introduction
 Materials and methods
 Results
 Discussion
Conclusions
 References
 
The precipitation of the {alpha} phase involves enrichment in ß-stabilizing elements of the ß phase. The latter, which is more mechanically stable, deforms without ß to {alpha}'' (reversible martensitic transformation). These results are in agreement with Shastry and Goldberg (1983)Go and Goldberg and Shastry (1984)Go, who studied Beta III wire alloys for orthodontic application.

For the 800°C heat treatment regimen, the increase of the average grain size and pre-deformation lead to a higher {varepsilon}r and a lower unloading Es. X-ray diffraction studies of wires with coarse grains, plastically deformed by 12 per cent in tension, have revealed the presence of the stress-induced orthorhombic martensitic {alpha}'' phase, retained by the plastic deformation. In these alloys, the grain boundaries act as obstacles to martensite variant growth and decrease their mobility during unloading (Laheurte et al., 2005Go).

Moreover, the ‘slip’ deformation is generally accompanied by twinning in the structures with small grains and by twinning and martensitic transformation in structures with coarse grains. The reduction of the unloading Es is due to an increase in the {varepsilon}r, which is the sum of elastic strain and variant reorientation of martensite induced by deformation. When the imposed deformation increases, the elastic strain remains effectively constant, whereas the {varepsilon}r attributed to variant reorientation increases. This is in accordance with previous research indicating that the volume fraction of martensite does not change in an unloading–loading loop (Laheurte, 2003Go). However, for grains sizes obtained after heat treatment at 900°C, oxidation (residual oxygen and reduction of tube SiO2 by Ti) is responsible for the loss of ductility, the hardening of the alloy, and pseudoelastic degradation. The pseudoelastic degradation of the behaviour and ductility is really the result of a chemical modification of the material at 900°C treatment.


   Conclusions
Top
 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
References
 
The findings show that the presence of an {alpha} or {omega}isoth second phase, resulting from isothermal treatment or an insufficient cooling rate, decreases the ductility and pseudoelastic behaviour of beta titanium alloy. For an alloy quenched at a higher temperature than the Tß, the plastic deformation and grain size growth results in an increase in the {varepsilon}r and a decrease in the unloading Es, leading to a significant improvement in the mechanical properties of the alloy.


   References
Top
 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 

    Burstone CJ. (1981) Variable modulus orthodontics. American Journal of Orthodontics 83:374–381.[CrossRef]

    Burstone CJ and Goldberg AJ. (1979) Patent No 7906380, USA.

    Burstone CJ and Goldberg AJ. (1980) Beta titanium: a new orthodontic alloy. American Journal of Orthodontics 77:121–132.[CrossRef][Web of Science][Medline]

    Duerig TW and Zadno R. (1990) An engineer's perspectives of pseudoelasticity. In Duerig TW (Ed.). Engineering aspect of SMA(Butterworth-Heinemann Publishers, London) pp. 369–393.

    Goldberg AJ and Burstone CJ. (1979) An evaluation of beta titanium alloys for use in orthodontic appliances. Journal of Dental Research 58:593–599.[Abstract/Free Full Text]

    Goldberg AJ and Shastry CV. (1984) Age hardening of orthodontic beta titanium alloys. Journal of Biomedical Materials Research 18:155–163.[CrossRef]

    Goldberg AJ, Vanderby R, Burstone CJ. (1977) Reduction in the modulus of elasticity in orthodontic wires. Journal of Dental Research 56:1227–1231.[Abstract/Free Full Text]

    Laheurte P. (2003) Contribution à l'étude du comportement pseudoélastique d'un alliage de titane bêta métastable—applications aux arcs orthodontiques. Thesis, University of Metz, France.

    Laheurte P, Eberhardt A, Philippe MJ, Deblock L. (2003) Fil en alliage de titane bêta pour l'orthodontie et procédé d'obtention d'un tel fil. Patent No 03 15094, University of Metz.

    Laheurte P, Eberhardt A, Philippe MJ, Deblock L. (2004a) Caractéristiques comparées des fils orthodontiques de Bêta III: proposition d'un nouveau critère de choix. Revue d' Orthopédie Dento-Faciale 38:205–220.

    Laheurte P, Eberhardt A, Philippe MJ, Deblock L. (2004b) Etude de la croissance des grains recristallisés dans l'alliage de titane Bêta III. La Revue de Métallurgie 12:1021–1026.

    Laheurte P, Eberhardt A, Philippe MJ. (2005) Influence of the microstructure on the pseudoelasticity of a metastable beta titanium alloys. Materials Science and Engineering A 396:223–230.[CrossRef]

    Shastry CV and Goldberg AJ. (1983) The influence of drawing parameters on the mechanical properties of two beta-titanium alloys. Journal of Dental Research 62:1092–1097.[Abstract/Free Full Text]


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