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Fabrication of a new composite orthodontic archwire and validation by a bridging micromechanics model

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Fabrication of a new composite orthodontic archwire and validation by a bridging micromechanics model
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  Biomaterials 24 (2003) 2941–2953 Fabrication of a new composite orthodontic archwire andvalidation by a bridging micromechanics model Zheng-Ming Huang a, *, R. Gopal b , K. Fujihara b , S. Ramakrishna b , P.L. Loh c ,W.C. Foong c , V.K. Ganesh c , C.L. Chew c a Department of Engineering Mechanics, Tongji University, 1239 Siping Road, Shanghai 200092, People’s Republic of China b Biomaterials Laboratory, Division of Bioengineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore c Faculty of Dentistry, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore Received 30 September 2002; accepted 27 January 2003 Abstract A new technique based on tube shrinkage is proposed for the fabrication of composite archwires. Compared with a traditionalpultrusion method, this new technique can avoid any fiber damage during the fabrication and can provide the archwire with arequired curvature in its final clinical usage. The present paper focuses on the technique development and mechanical design andvalidation in terms of constituent materials by using a micromechanics bridging model. Prototype archwire has been fabricatedusing fiberglass and an epoxy matrix, with a wire diameter of 0.5mm and a 45% fiber volume fraction. Tensile and three-pointbending tests have shown that the mechanical performance of the prototype composite archwire is comparable to that of a clinicalNi–Ti archwire. Another purpose of the present paper is to provide an efficient procedure for a critical design of compositearchwires. For this to be possible, the ultimate load especially flexural load carrying ability of the composite archwire must beassessed from the knowledge of its constituent properties. However, difficulty exists in doing this, which comes from the fact that thefailure of the utmost filament of the composite archwire subjected to initially the maximum bending stress does not imply itsultimate failure. Additional higher loads can still be applied and a progressive failure process is generated. In this paper, the circulararchwire was discretized into a number of parallel laminae along its axis direction, and the bridging micromechanics modelcombined with the classical lamination theory has been applied to understand the progressive failure process with reasonableaccuracy. Only the constituent fiber and matrix properties are required for this understanding. Nevertheless, the ultimate bendingstrength cannot be obtained only based on a stress failure criterion. This is because neither the first-ply nor the last-ply failurecorresponds to the ultimate failure. An additional critical deflection (curvature) condition must be employed also. By using both thestress failure and the critical deflection conditions, the predicted load-deflection up to the ultimate failure agrees well with themeasured data. Thereafter, different mechanical performances of composite archwires can be tailored before fabrication by choosingsuitable constituent materials, their contents, and the archwire diameters. Several design examples have been shown in the paper. r 2003 Published by Elsevier Science Ltd. Keywords:  Biocomposite; Archwire; Strength design; Ultimate failure; Critical deflection; Sample fabrication 1. Introduction Orthodontics is a branch of dentistry, dealing with thegrowth, guidance, correction, and maintenance of thedento–facial complex. The orthodontic practice involvesthe application of corrective appliances, commonlycalled braces, to move teeth. Main components of thebrace (a fixed appliance) are brackets and archwires, asshown in Fig. 1. Patients receiving orthodontic treat-ment are most concerned with their esthetic appearance.Current materials in orthodontic applications aremainly metals, such as Stainless Steel, Co–Cr alloyand titanium alloy, which have color incomparable withteeth. In order to improve the appearance of fixedorthodontic appliances, and thus to increase patientacceptance, several aesthetic materials have been used asan alternative to metals in bracket manufacture (Fig. 2).A further improvement would require the use of anaesthetic archwire [1].Archwires, ideally, are designed to move teeth withlight continuous forces. They are placed through the *Corresponding author. E-mail address:  huangzm@mail.tongji.edu.cn (Z.-M. Huang).0142-9612/03/$-see front matter r 2003 Published by Elsevier Science Ltd.doi:10.1016/S0142-9612(03)00093-0  brackets and retained in position using ligatures andelastic modules (Fig. 1). The archwire should behaveelastically over the period of usage, ranging from weeksto months. The duration of use varies with the stage of treatment, namely, initial, intermediate and final stagesof the treatment, and no single archwire is best for allthe stages. Springback, stiffness, formability, resiliencemodulus, biocompatibility and low friction are desirablecharacteristics of an archwire for optimum mechanicalperformance during the treatment [2]. It has beenrecognized that an optimal archwire can be developedusing composite technology made from continuousfibers and polymer matrix [1,3–7]. This is because the polymer matrix material, which is available fromnumerous candidates, can offer the aesthetic feature of the composite archwire. On the other hand, the variousmechanical properties of the wires at different stages canbe achieved by choosing suitable fiber material, fibercontent, and fiber arrangement pattern. For example, bychanging the fiber diameter and the number of filaments, stiffness properties of the wires can bespecifically tailored to allow good engagement betweenthe wire and the bracket slot from the initial to the finalstage [8].Most composite archwires reported in the literaturehave been fabricated by virtue of pultrusion methods[3–8]. A sketch of such a pultrusion process is shown inFig. 3. The continuous fiber yarn, such as transparentbio-fiberglass or ceramic fiber bundle, is impregnated ina resin path, which is later drawn through a curing die.Pultrusions with small, clinically relevant round orrectangular cross-sections potentially can be prepared ascontinuous lengths of wires and subsequently formedinto individualized appliances [9]. However, it has been recognized that two drawbacks can be involved with apultrusion process. The first is that the fiber filamentsmay be readily damaged during the pultrusion. As thecomposite archwire is a primary load-carrying element,its fiber volume fraction has to be made relatively high.The extra polymer resin contained in the impregnatedfiber bundle must be squeezed out before the bundle canbe introduced into the die channel, which has a diameterof about 0.5mm for a round wire. Thus, the fiberdamages can occur at the entrance of the die. Thesecond drawback is that the composite archwire thusfabricated is a straight cylinder, which is generally notpreferred in a clinical application.In order to eliminate both of the aforementionedshortcomings involved with a pultrusion, we havedeveloped a new method for the fabrication of acomposite archwire. It is essentially based on tube-shrinkage. Instead of using a curing die, the resin-impregnated yarn is introduced into a plastic tube,which is heat-shrinkable. As the inner diameter of thetube is larger than that of the yarn, the fiber damagescan be controlled to minimum. Once heated, the tubeshrinks and pushes the extra resin out of the entrance.Before the resin is completely cured at an elevatedtemperature such as in an oven, the tube containing theresin-impregnated fiber bundle is put into a mould witha desired curvature as well as cross-sectional (round orrectangular) shape. A resulting archwire prototype isshown in Fig. 4, which is a curved form more appro-priate for the clinical application.Photo micrograph of the newly developed archwireprototype samples indicated that the fiber filamentarrangements were uniform on the cross-section andthere were negligibly small voids as well as other defects.Fiber content of the archwire was determined through acombustion (resin burn out) method and a 45% fibervolume fraction was realized. These results show that Fig. 2. Comparison between metal and aesthetic brackets.Fig. 3. A schematic pultrusion process for fabrication of compositearchwires.Fig. 1. Fixed orthodontic appliances (braces). Z.-M. Huang et al. / Biomaterials 24 (2003) 2941–2953 2942  the tube-shrinkage technique is feasible for the fabrica-tion of composite archwires. Experimental characteriza-tion for the prototype samples of a specific size (i.e.diameter) and fiber content has been carried out throughtensile and three-point bending tests. The test data havebeen compared with those of a clinically used Ni–Ti(Reflex s wire; TP Orthodontics, Inc.) metal archwire. Ithas been found that the mechanical performance of theprototype composite archwire is comparable to that of the metal wire.Another purpose of the present paper is to provide auseful design procedure for composite archwires. As thearchwires will be used as primary load-carrying ele-ments, their strength (tensile and especially bendingstrength) properties must be targeted by the design. Arational estimation on the stiffness and strength of theresulting composite archwire in terms of its constituentmaterials and contents and the wire diameter is essentialfor the efficient design. This is accomplished in the paperby making use of a bridging micromechanics model [10]and the classical lamination theory. The circular wirecylinder is imaginatively separated along the axisdirection into a number of lamina layers, all of whichhave the same mechanical properties but differentwidths. When the wire is subjected to a lateral (bending)load, each of the discretized layers carries a differentload share, whose determination is based on the classicallamination theory. The stress resultants of all the laminalayers must be balanced with the externally applied load(moment) on the wire cross-section. The analysis foreach individual lamina is performed using the bridgingmodel, from which the internal stresses in the constitu-ent fiber and matrix materials are expressed in terms of the load shared by the lamina. In this way, themechanical response of the lamina and further of thewhole archwire is understood from the knowledge of theconstituent responses. The efficiency of the theoreticalanalysis is verified through experiments. The estimatedstiffness and strength properties of the compositearchwire with some specific fiber volume fraction andwire diameter agree favorably with the measured data.Design diagrams for the archwire stiffness and strengthversus the fiber volume fractions and the wire diametersare then made and are reported in the paper. Thesediagrams can be helpful for the development of composite archwires used at different stages. 2. Experimental detail  2.1. Materials The prototype composite archwire was made of aunidirectional (UD) fiber reinforced composite cylinder.The reinforcement used was a bundle of several E-glassfiber yarns, each containing 200 fiber filaments (thefilament diameter=9 m m, Unitica Glass Fiber, Japan).With this limited number of filaments in a fiber yarn, thediameter and the fiber content of the resulting compositearchwire can be tailored by choosing suitable number of yarns. A mixture consisting of 68wt% of an epoxy resin,R50, and 32wt% of a hardener, H64, provided byChemicrete Enterprise Pte Ltd. (Singapore) was used asthe matrix material in the present study. It should benoted that although epoxy resins have not beenacknowledged as fully biocompatible they are muchcheaper than more clinical such as dental resins. On theother hand, mechanical functions of the two types of resins (epoxy and dental resins) in the resultingcomposite wires should not have significant difference,as the mechanical properties of the composite wires areessentially controlled by the fiber properties, fibercontent, and the fiber reinforcement pattern. Thus, inour first stage of technical development, the use of theepoxy resin is reasonable. The glass fibers are biocom-patible, and can be used in later clinical development.  2.2. Fabrication The new technique, which has been used to directlyfabricate curved archwires, is based on tube-shrinkage.For the fabrication of a prototype composite archwire, ahand-processing method (Fig. 5) was used, and is brieflydescribed as follows. A number of resin-impregnatedfiberglass yarns (7 yarns in the present study) weregathered together, and were introduced into a plastic(polyolefin) tube, which is heat shrinkable (Fig. 5(a)). Asthe inner diameter (1mm inner and 1.5mm outerdiameters) of the tube was larger than that of thegathered yarn bundle, fiber damages could be controlledto minimum at this stage. In the next step, a heatingelement (an electronic soldering iron) was applied to thetube from one end (at the top grip) to the other (atthe bottom grip), as shown in Fig. 5(b). Meanwhile, theheated tube shrank, pushing the extra resin out of the bottom end of the tube. Then, the shrunk tube withthe resin-impregnated fiber yarn bundle inside wasloaded into the female part of a mould (Fig. 5(c)),which has the required curvature of the archwire, before Fig. 4. Prototype of a curved composite archwire. Z.-M. Huang et al. / Biomaterials 24 (2003) 2941–2953  2943  being put into an oven (Fig. 5(d)) of 100  C for fastercuring. It took about 1h for the resin-impregnated yarnbundle to be completely cured. Finally, the tube wascarefully removed and the composite archwire resulted.With this kind of fabrication process, the aforemen-tioned two drawbacks related with the pultrusionmethod (Fig. 3) can be overcome. The fabricatedprototype composite archwire had a diameter of 0.5mm.As in subsequent theoretical simulation and designthe in situ constituent properties are important, flat purematrix panels were also fabricated through resin castingand cured at the 100  C oven. The panels had a nominalthickness of 4.5mm. They were then cut into uniaxiallytensile, uniaxially compressive, and four-point bendingtest specimens according to relevant ASTM standards,respectively, using a water-cooled diamond saw.  2.3. Characterization In order to investigate the quality of the developedcomposite archwire, its cross-section was examined. Thecomposite wire segment was embedded in a Co-castresin and polished. The polished cross-section wasobserved under an optical microscope (OlympusBX51) with 100 times magnification. A typical photomicrograph of the archwire cross-section is shown inFig. 6. From the figure, we can clearly see that the glassfiber filaments were uniform on the whole cross-section,and there were only negligibly small voids both fromamount and from size viewpoints. No other significantdefect existed. The fiber volume fraction of the samplecomposite archwire was measured through a combus-tion method, and an averaged value of about 0.45 hasbeen found.Tensile and three-point bending (Fig. 7) tests werecarried out for the sample archwire (remember: the wirediameter was 0.5mm and the fiber volume fraction was45%) developed above. Currently, there is no specificstandard for the characterization of an archwire.However, the span size of the three-point bending testwas chosen in accordance with the distance of twoadjacent brackets fixed on the teeth (Fig. 1). This size isusually 14mm [6,7], and is in the range specified byASTM D 790 standard, with respect to the wirediameter. Typical load-deflection curve up to failure isshown in Fig. 8. Fig. 5. Schematic show of fabrication for composite archwire by tubeshrinkage.Fig. 6. Optical cross-section micrograph of a sample compositearchwire (100   magnification) with a fiber volume fraction of 45%.Fig. 7. Three-point-bending test of a composite archwire.   Fig. 8. Three-point bending results of a composite wire (0.5mmdiameter) and a Ni–Ti wire (0.406mm diameter). Z.-M. Huang et al. / Biomaterials 24 (2003) 2941–2953 2944  As aforementioned, a different stage orthodontictreatment generally uses a different archwire. Ourpresent target is at the initial stage (taking about 3–4months), and thus a clinically used Ni–Ti archwire(Reflex s wire, TP Orthodontic, Inc.) was also tested.The Reflex wires are highly flexible for the alignment of teeth, which is employed at the initial stage treatment(lasting for 3–4 months). They are also less expensivethan other wires, and hence are widely used in practice.The metal wire test results are also plotted in Fig. 8 forcomparison. Although the composite archwire has aslightly larger diameter (0.5mm) than that (0.016in, i.e.0.406mm) of the Ni–Ti wire, the bending behavior of the former is highly superior to that of the latter. Testingdata for the archwires of these two materials aresummarized in Table 1. It is seen that the presentcomposite archwire is comparable in stiffness andstrength to those of the Ni–Ti archwire. Further increasein the stiffness and strength of the composite archwirecan be expected with the increase of its fiber volumefraction, or the number of yarns contained in the tube.  2.4. Constituent properties For subsequent simulation and design purpose, theconstituent fiber and matrix properties must be speci-fied. In the present case, both the E-glass fiber and theepoxy matrix can be considered as isotropic materials.Moreover, the fiber is regarded as linearly elastic untilrupture.In general, it is difficult to measure directly themechanical properties of a fiber material. From thematerial data sheet provided by the supplier, the fiberused has some comparable mechanical parameters tothose of the Silenka E-glass 1200tex given in Ref. [11].Thus, the elastic properties of the fiber were taken fromRef. [11] and are listed in Table 2. These parameters are considered to be the same until rupture at both tensionand compression. The fiber tensile and compressivestrengths, however, were retrieved from the uniaxialtensile and compressive strengths of a UD compositeprovided in Ref. [11], using the formulae given in Ref.[12]. The back calculated fiber strengths are summarizedin Table 2. It is noted that compared with the data(2150MPa) provided in Ref. [11], only a slight amend-ment (being 2100MPa, see Table 2) has been made forthe fiber tensile strength.In contrast with the fiber properties, the monolithicmatrix properties are easily measurable. As the compo-site archwire is mainly subjected to flexural loads, thebending behavior of the pure matrix must be under-stood. Four-point bending tests were carried out. Inorder to differentiate the mechanical properties of thepure matrix under tension from those under compres-sion, strain gauges have also been used to record thestrains at the top and bottom surfaces of the beam, andonly a marginal difference between the tensile and thecompressive responses has been recognized. The com-pressive stress–strain curve of the epoxy matrix is stifferthan the tensile stress–strain curve. Four linear segmentswere used to approximately represent the stress–strain(or load-deflection) responses of the matrix material.Based on these representations, the matrix hardeningmodulus at any load level was found to be E  m  ¼ ð E  mT  Þ i  ;  when  ð s mY Þ i   1 p s me p ð s mY Þ i   with  ð s mY Þ 0  ¼  0 ; E  m  ¼ ð E  mT  Þ 4 ;  when  s me X ð s mY Þ 4 ; where the tangential moduli and the critical stressescorresponding to tension and compression are summar-ized in Table 3. The remaining question is how to definethe matrix tensile and compressive strengths underbending. The bending test only determined one of thesetwo strengths. To resolve the problem, uniaxial tensile(Fig. 9) and compressive tests have also been performedfor the pure matrix specimens. It was found that thematrix has a uniaxial tensile strength of 42.6MPa and auniaxial compressive strength of 63MPa. In otherwords, the uniaxial compressive strength of the matrix Table 1Measured properties of archwiresMaterials Diameter, d   (mm)Fiber volumefraction,  V  f  Tensile modulus, E   (GPa)Tensile strength, s u  (MPa)Bending modulus, E  b  (GPa)Bending strength, s b  (MPa)GF/epoxy 0.5(0.005) a 0.45(0.001) 31.2(1.8) 890(45.3) 31.8(2.1) 881.5(69.8)Ni–Ti 0.36 — — — 38.9 804 a Standard deviation.Table 2Mechanical properties of E-glass fibers [9] E  f 11  (GPa)  n f 12  E  f 22  (GPa)  G  f 12  (GPa)  n f 23  s f u  (MPa)  s f u ; c  (MPa)74 0.2 74 30.8 0.2 2100 1320 Z.-M. Huang et al. / Biomaterials 24 (2003) 2941–2953  2945
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