INFLUENCE OF SHAPE MEMORY PROPERTIES ON

Materials Science Forum Vols. 706-709 (2012) pp 514-519 Online available since 2012/Jan/03 at www.scientific.net © (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/MSF.706-709.514

INFLUENCE OF SHAPE MEMORY PROPERTIES ON SLIDING RESISTANCE IN FIXED ORTHODONTIC APPLIANCES Laurence Jordan1-2, Pascal Garrec1-2 and Frédéric Prima1 1 2

Group of Structural Metallurgy, UMR 7045, University Pierre & Marie Curie, Paris, France Faculty of Odontology, Rothschild Hospital AP-HP, University Paris-Diderot, Paris, France. [email protected], [email protected]; [email protected]

Keywords: Orthodontic archwire; friction; resistance of sliding; shape memory alloys; β-titanium.

Introduction Tooth movements in an orthodontic treatment are the result of an applied force system, wirebracket-ligature, and the response of the bone tissue. Starting an orthodontic treatment, it is necessary to exercise a sufficient initial force and then to maintain to obtain a continuous tooth movement. Orthodontic wires, which generate the biomechanical forces, usually transfer forces through brackets to trigger tooth movement. In the case of excessive forces of friction, they are behaving as an opposing force with respect to the movement of the tooth, making it sometimes slower or incontrollable [1]. Kusy and Whitley [2] defined the resistance to sliding (RS) of an archwire-bracket couple as the combined effect of 3 components: classical friction (FR), elastic binding (BI) and physical notching (NO). The first effect, classical friction (FR) is due to contact of the wire with bracket surfaces and evaluated by the product of the normal force (FN) and the coefficient of friction (µ) between two surfaces, FN corresponds to ligation force on a bracket (Fig. 1a). Elastic binding (BI) is created when the contact between the wire and the corners of the bracket bends the wire. In this case, the angle between the wire and the bracket reaches a critical angle (θc). Under this condition, FN from ligature and FBI, force of bending of the wire in the edges of the bracket participate in the friction (Fig. 1b). Notching (NO) is created when permanent deformation of the wire occurs at the wirebracket corner interfaces (formation of notches) and tooth movement stops. Thus, the mechanical phenomena controlling RS are important to investigate because a variable percentage of the applied force is lost instead of moving tooth. Indeed, Proffit [3] reported that 50 per cent of the force necessary to initiate tooth movement is required to overcome the retarding force generated between bracket, archwires and ligatures.

Fig. 1: Resistance of sliding between wire and bracket. In a, the angle is inferior at critical angle, the applied force (F) is equal in classical friction (FR), FN is the force due to the ligature. In b, the wire begins to bend on the corner of bracket; the angle is equal or superior at critical angle. BI adds up to FR. FBI increases with angle between archwire and bracket. Recently, the orthodontists used new kind of brackets, “self-ligating brackets”, which allowed a decrease of the friction force during sliding phases of orthodontic treatment compared with conventional bracket [4,5,6]. With reduced friction, the force needed to produce orthodontic movement can be light and allowed more physiologically tooth movement. Self-ligating brackets do All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 82.123.219.171, Chimie-ParisTech, Paris, France-27/08/14,08:44:01)

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not require a ligature, but have an inbuilt mechanism that can be opened and closed to secure the archwire. They can be divided into 2 main categories, active and passive according to their mechanisms of closure. The active self-ligating brackets have a spring clip to press the wire and the passives do not apply a ligation force to the archwire because the slide covers only the slot. The aim of this study was to measure, in vitro, the resistance to sliding generated by various combinations of wire/bracket and particularly shape memory wires with increasing contact angle between archwire and bracket in an experimental model with 5 nonaligned conventional or passive self-ligating brackets.

Materials and methods Two different edgewise brackets (stainless steel), mandibular central incisor bracket, 0.56 x 0.711 mm (0.022x0.028 in) slot were used in testing: • Passive self-ligating bracket (SLB) with a prescribed torque of -1° and +2° of angle (does’nt exist in 0° and 0° angle): Damon3MX (SDS Ormco, Glendora, Calif); • Conventional brackets (CB) with a prescribed torque and angle at 0°: Orthos (Ormco) ligated with stainless steel ligatures (Preformed 0.254 mm (0.010 in); Ormco). Four types of straight wires (150 mm) with a cross-sectional dimension of 0.457 x 0.635 mm (0.018 x 0.025 in) were tested: • Stainless Steel (SS) wire: Orminox (Ormco); • β-titanium wire: Bendalloy (RMO, Denver, Colorado); • Shape memory alloy (SMA) type NiTiCu wire: NiTiCopper35 (Ormco); • Shape memory alloy type NiTi wire: NeoSentalloyF100 (GAC International, Central Islip, NY). The two kinds of shape memory alloys wires were examined with differential scanning calorimetry (DSC Model 822e, Mettler-Toledo Inc., Columbus, OH, USA) to determine phases present and transformation temperatures at a cooling/heating rate of 5°C/min, the thermograms were carried out in an interval of temperature of + 60°C and -100°C. The experimental device (Fig. 2) is constituted by aluminium bars, on which are bonded five aligned brackets from the same production. The middle bracket (the 3rd) is on a mobile part to vary angle between bracket and wire. To make sure of the alignment of each bracket, a SS wire of 0.533 x 0.711 mm (0.021 x 0.028 in) is placed in the slot of bracket during the bonding. The interbracket distance was 6 mm between the middle of slot of each bracket.

Fig. 2: Experimental device.

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The bars is vertically fixed to the transverse beam of a universal testing machine (GT-Test GmbH, model 112, Erkrath, Germany), the tested wire was perfectly in the axis of the load cell (20 Newton) at a rate of 2 mm per minute in standard compressive mode. The wire-bracket couples were tested at θ values of 0 °, 3 °, 6 °, 9 ° and 12 ° for shape memory alloys; 0 °, 3 °, 6 °, 9 ° for the β-titanium and 0 °, 3 °, 6 ° for the stainless steel to stay in the elastic deformations for every sort of alloys. For each value, the brackets were slid 4 mm along the archwire. The frictional force was three times measured at an ambient temperature of 24°C in dry state. For each set of θ values tested, averaging values and standard deviations of forces were measured during the last 90 s drawing a plot of θ versus resistance of sliding. Results The DSC diagram obtained (Fig. 3) on heating or cooling showed peaks related with the martensitic transformation. The phenomena were exothermic on cooling and endothermic on heating. The DSC curves of the NiTi wire (NeoSentalloy F100®) showed two martensitic transformations on cooling: austenite/R-phase and R-phase/martensite. On heating, the reverse transformation was directly martensite/austenite. The NiTiCu wire (NiTiCopper35®) was characterized by a direct and reverse transformation austenite/martensite.

Fig. 3: DSC diagram of NiTi and NiTiCu wires. At experimental temperature, the NiTi wire was biphased R-phase/austenite and the NiTiCu wire was austenitic.

The resistance of sliding (N) for the conventional brackets (CB) was nearly constant value below 3° but increases above this angle as the θ value increases (Table 1). Table 1: Averages and standard deviations of resistance of sliding (N) for the different couples wire/bracket at different angles. Bracket SS wire NiTiCu wire NiTi wire β-Ti wire θ SLB 0° CB 0.0490±0.0088 0.3573±0.0211 0.1780±0.0080 0.0347 ± 0.0042 SLB 0.3725±0.0280 0.3647±0.0196 0.3236±0.0118 0.0948±0.0055 3° CB 0.2303±0.1097 0.5001±0.0244 0.3495±0.1209 0.1580±0.0123 SLB 6.5250±0.0513 4.5408±0.1447 4.6643±0.0525 1.1071±0.0568 6° CB 2.4796±0.0518 3.6115±0.0877 3.1555±0.0512 1.2241±0.0278 SLB 12.0140±0.2469 5.4285±0.3083 2.8146±0.1979 9° CB 6.0025±0.1071 4.9354±0.2501 2.8273±0.0306 SLB 7.3871±0.7710 5.4629±0.6949 12° CB 6.4103±0.2924 4.4636±0.2096


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The passive self-ligating brackets (SLB) exhibited no RS below 3° because the wire was not restrain and didn’t keep in brackets. At 3°, except SS wire, all the wires showed a lowest RS in the SLB with regard to CB. Above 3°, for the two kinds of brackets, the RS increased as the θ value between the bracket and the wire increased (Table 1). The graph below (Fig. 4) showed a superimposing of averages of the resistance of sliding of each couple wire-bracket at different angles: Above 3°, RS increased with θ. This increase varied greatly between different couples. The resistance of sliding for SS, β-Ti or NiTiCu were higher in selfligating brackets than that in conventional brackets. For NiTi alloy, the RS were similar in both brackets but at 12°, RS for SLB became higher with regard to CB.

b a Fig. 4: In a, plot of averages of resistance of sliding of different wires as function of θ for conventional brackets (CB) and self-ligating brackets (SLB). In b, details of RS below 3° were represented for conventional brackets.

Discussion The angle (θ) at which the wire first contacts the edges of the slot is called the critical angle (θc). This angle was calculated from the average values of slot of brackets, width and size of wires and was approximately between 2.9 and 3.5° [7,8]. This critical angle defined two different behaviours, visible on figure 4. Below θc, the resistance of sliding (RS) was a constant value for each couple bracket-wire that depended on the ligation force and only classical friction (FR) contributed to RS. Above θc, the RS increased as the angle increased too and both FR and elastic binding (BI) contributed to the RS. Below θc RS depended on classical friction force (FR) and is given by the equation (1) in which FN was the applied normal force (ligation force) and µ, the coefficient of friction: FR = FN x µ

(1)

The coefficients of friction of the stainless steel and the NiTi alloys are similar and lower than the beta-titanium alloy one [9,10]. The passive self-ligating bracket exhibited no friction below 3°, it is like a tube. The differences between RS for the conventional bracket and the self-ligating bracket at 3° (Fig. 4a) were due to the level of normal force that was highest in the conventional bracket. The difference between RS for the beta-titanium wire and the others wires was cause by the differences in the amount of coefficient of friction (Fig. 4b).

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Above θc Both classical friction (FR) and elastic binding (BI) contributed to resistance of sliding above critical angle. FR was a component that depended solely on the ligation force. The BI component, however, contributed an additional amount of resistance that depended in part on the angle value imposed between wire and bracket but also on the elastic properties of the wires (elastic modulus). Indeed, Zufall and Kusy [11] proposed a formula (2) to calculate the normal force caused by binding (FBI):    FBI = 16 × E × I  + BI  × sin(θ − θ c ) width × (2 × IBD − width )   E: elastic modulus; I: moment of inertia of wire;

(2)

width: average width of bracket; IBD: interbracket distance.

The influence of bending component of the wire (elastic modulus) in RS became greater as the wire-bracket angle increased to the detriment of classical friction [12, 13]. Above 3° (Fig. 4a) with SLB, elastic binding (BI) generated resistance of sliding and thus the elastic modulus (E) of each wire played a dominating role. Stainless steel wire had a higher modulus of elasticity (180 GPa) than a β–titanium wire (65 GPa) [10]. For the same geometry, a SS wire also had a greater stiffness than a β–Ti wire. Above θc, the SS wire appears to have a greater FBI to the edges of a bracket than a β–Ti wire. The increase of the slope of the β–Ti wire from 6 ° to 9° with SLB was perhaps due by the beginning of plastic bending. With the conventional bracket (Fig. 4a), both classical friction (FR) and elastic binding (BI) contributed to resistance of sliding. At 6°, RS of stainless steel wire was less high than RS of β–Ti wire. Certainly, at this angle, the coefficient of friction (µ) was a component more important than the bending of the wires (BI) in the resistance of sliding. But, the resistance of sliding for shape memory alloys were drastically lower or equivalent to β–Ti wire for a given θ while the elastic modulus had the same values (65 GPa in austenitic phase). Below 6°, RS were equivalent between β–titanium and NiTiCu wires for the two kinds of brackets but above this angle, RS increases less quickly for NiTiCu alloys, the behaviour is not linear any more. And, the resistance of sliding of NiTi wires in conventional or self-ligating bracket were very weak. At experimental temperature (Fig. 3), the NiTi wire crystallised in a R-phase, which presents an elastic modulus lower than austenitic structure and facilitated the martensitic transformation at small angles. So, the resistance of sliding of this alloy is the lowest. While NiTiCu wire is at room temperature in austenite phase, its elastic modulus was identical to that of β–titanium wire. When the angle increased (> 6°), the martensitic transformation took place by the deformation of the wire, the modulus fell and the behaviour of this wire tended to that of NiTi. During martensitic transformation (forward and reverse), the elastic modulus was not constant and decreased greatly [14]. Thus, the mechanical behaviour of superelastic alloys (NiTi and NiTiCu) was largely dependent on the martensitic transformation; the most favourably orientated variants along the direction of the strain were selected. The resistance of sliding above critical angle depended essentially of value of angle between wire and bracket and value of elastic modulus of the wire, so the slope of curves was linear. But, with shape memory alloys, the slope of curves was connected to martensitic transformation characteristics during superelasticity. Thus the increase of FBI per degree (θ) (equation 2) was not linearly because the pseudomodulus largely decrease during martensitic transformation. Conclusion Below critical angle, with SLB, the almost all applied force was transferred to the tooth to produce movement. Under these circumstances, conventional brackets, although they were ligated and thus a normal force (ligation) was active to the wire, beyond critical angle between wire and bracket, could produce the same amount of sliding. In this case, the elastic property (elastic modulus)


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became an important factor for the level of resistance of sliding. Alloys with light elastic modulus seemed more appropriate for the leveling and aligning stages of orthodontic treatment. Among these, the advantage of shape memory alloys was related to the superelastic property: the martensitic transformation was characterized by a large decrease of elastic pseudomodulus and allowed a light resistance to sliding with a high deformation capacity. The relative importance of binding in resistance of sliding varied mainly with wire alloy as angle between wire-bracket increased. Wire alloy seemed be more important than bracket material even if the resistance of sliding could be also affected by bracket design. Summary Shape memory alloys such as NiTi alloys display great interest in dentistry because of their peculiar elastic properties. In orthodontic treatments, to obtain an efficient tooth movement, it is necessary to control sliding mechanics. Tooth movement is accomplished by guiding the tooth along continuous archwire in an orthodontic bracket. However, friction is generated between the bracket and the wire, resulting in an additional resistance against the teeth movement. As a consequence, a greater force is required to overcome this friction stress. The purpose of this study was to measure the frictional forces generated by various combinations of brackets and orthodontic wires (SS, β-Ti, NiTi, NiTiCu) and evaluated at several angles in an experimental apparatus. Our results showed that the archwire mechanical properties (especially elastic properties) appeared to be a factor that can significantly influence the friction, which depends both on surface and mechanical properties. When sliding occurs in active configuration, friction increases proportionally with the angle value and depends first on the stiffness of wires. With conventional alloys, stiffness is directly related to elastic modulus. But shape memory alloys are characterized by a martensitic transformation. When the formation of stress-induced martensite occurs, the elastic deformation becomes non-linear characterized by a great decreasing of the pseudomodulus of elasticity. So, even if the angle value between archwire and bracket is significant, the friction appears moderate because of superelasticity effect. Then, coefficient of friction and orthodontic wire stiffness are the two critical factors influenced the friction generated when an orthodontic wire slides through non-aligned brackets. The lowest resistance of sliding occurs with NiTi alloys and the highest with β-Ti. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

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Influence of Shape Memory Properties on Sliding Resistance in Fixed Orthodontic Appliances 10.4028/www.scientific.net/MSF.706-709.514