0099-2399/88/1407-0346/$02.00/0
`JOURNAL OF ENDODONTICS
`Copyright © 1988 by The American Association of Endodontists
`
`Printed in U.S.A.
`VoL. 14, No. 7, JULY 1988
`
`An Initial Investigation of the Bending and
`Properties of Nitinol Root Canal Files
`
`Harmeet Walia, BDS, MDS, MS, MS, William A. Brantley, BS, MS, PhD, and Harold Gerstein, BS, DDS
`
`Root canal files in size #15 ahd triangular cross(cid:173)
`sections were fabricated from 0.020-inch diameter
`arch wires of Nitinol, a nickel-titanium orthodontic
`alloy with a very low modulus of elasticity. A unique
`manufacturing process was used in which the fluted
`structure of a K-type file was machined directly on
`the starting wire blanks. The Nitinol files were found
`to have two to three times more elastic flexibility in
`bending and torsion, as well as superior resistance
`to torsional fracture, compared with size # 15 stain(cid:173)
`less steel files manufactured by the same process.
`The fracture surfaces for clockwise and counter(cid:173)
`clockwise torsion were observed with the scanning
`electron microscope and exhibited a largely flat
`morphology for files of both alloy types and torsional
`testing modes. It was possible to permanently pre(cid:173)
`curve the Nitinol files in the manner often used by
`clinicians with stainless steel files. These results
`suggest that the Nitinol files may be promising for
`the instrumentation of curved canals, and evalua(cid:173)
`tions of mechanical properties and in vitro cutting
`efficiency are in progress for size #35 instruments.
`
`It is well known by clinicians that inadvertent procedural
`errors can occasionally arise during the instrumentation of
`curved canals. These misfortunes include ledge or zip forma(cid:173)
`tion, perforation of the canal, and separation or fracture of
`the instrument (1). As a consequence, the root canal mor(cid:173)
`phology is adversely altered, a violation of the basic principle
`that endodontic preparation is to retain the original shape of
`the canal. Clinicians have adopted various methods to circum(cid:173)
`vent problems with the preparation of curved canals, such as
`precurving instruments and using a telescopic filing technique
`(1-3). Weine (4) has suggested that clinicians might remove
`the tips of instruments at chairside to make intermediate sizes
`for use in the preparation of curved canals.
`The procedural errors which may occur during the instru(cid:173)
`mentation of curved canals have a common genesis: the basic
`stiffness of the stainless steel alloys (5) utilized for the manu(cid:173)
`facture of root canal files and reamers. Moreover, there is a
`substantial rise in instrument stiffness with increasing instru(cid:173)
`ment size (6). For example, with the stainless steel files and
`reamers, the smaller sizes of instruments have considerably
`
`346
`
`greater flexibility and can conform much better to the mor~
`phology of curved canals.
`While manufacturers have recently marketed a number of
`new instruments based upon different cross-sectional shapes,
`design concepts, and fabrication procedures, in a quest for
`improved cutting efficiency (7) and flexibility (8), all of these
`brands have been fabricated from stainless steel. In this article
`we report the first use of an entirely new metallurgical system,
`Nitinol nickel-titanium orthodontic wire alloy (9), for the
`fabrication of endodontic files. The Nitinol alloy has a very
`low modulus of elasticity, only one-fourth to one-fifth the
`value for stainless steel, and a very wide range for elastic
`deformation.
`The purposes of this initial study were to investigate the
`feasibility of manufacturing root canal files from Nitinol and
`to evaluate the bending and torsional properties of these
`instruments. The results of our laboratory study suggest the
`possibility of a new generation of files, possessing a degree of
`flexibility which may be ideally suited for instrumenting
`curved canals.
`
`MATERIALS AND METHODS
`
`Standard preformed Nitinol arch wire blanks, 0.020 inch
`in diameter, were obtained (Unitek Corp., Monrovia, CA),
`and two 2-inch straight segments from each arch wire were
`used for instrument fabrication. A unique file manufacturing
`process was used (Quality Dental Products, Johnson City,
`TN), in which the fluted cross-sectional shape was machined
`directly on the wire blank, rather than the conventional ( 10)
`manufacturing procedure of twisting the ground and tapered
`blank. For this initial feasibility study, experimental Nitinol
`root canal files were fabricated in size # 15 and triangular
`cross-sections, for comparison to size # 15 stainless steel files
`with the same cross-sectional shape and manufactured by the
`same process, which served as the controls.
`The Nitinol and stainless steel files were evaluated in the
`three mechanical testing modes of cantilever bending, clock(cid:173)
`wise torsion, and counterclockwise torsion, following the ex(cid:173)
`perimental methods previously used by Krupp et al. (8).
`Values of bending and torsional moment were measured with
`a sensitive torque meter (model 783-C-1; Power Instruments,
`Inc., Skokie, IL), using a manual-loading experimental pro(cid:173)
`cedure and an apparatus based upon the original form of
`American Dental Association specification no. 28 ( 11 ). All
`specimens were subjected to bending or twisting at a point 3
`
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`Vol. 14, No.7, July 1988
`
`Nitinol Root Canal Files
`
`347
`
`mm from the apex of the instrument. For the bending tests,
`the specimens were loaded at 1 0-degree increments to a total
`angular deflection of90 degrees. The specimens for the clock(cid:173)
`wise and counterclockwise torsion tests were loaded at 45-
`degree increments to an angular deflection of 360 degrees and
`thereafter at 90-degree increments until instrument fracture.
`There were five specimens or replications in each test group,
`and values of moment at each bend angle or twist angle were
`averaged and plotted to obtain graphical representations of
`mechanical behavior. From these graphs it was possible to
`compare the important practical mechanical properties of the
`Nitinol and stainless steel files: the relative flexibility and the
`resistance to fracture in torsion. In addition, scanning electron
`microscopic (SEM) photographs were obtained for files in the
`as-received condition to observe the effects of the manufac(cid:173)
`turing process and after torsional failure ·to compare the
`fracture surface morphologies for the two groups of files.
`
`RESULTS
`
`Scanning electron microscopic photographs of the tip and
`body regions are shown in Figs. 1 and 2 for the as-received
`Nitinol files and in Figs. 3 and 4 for the as-received stainless
`steel files. The rounded or Roane (12) tip design, the machin(cid:173)
`ing marks along the faces of the flutes, and the ridges of
`permanently deformed metal (rollover) along the cutting
`edges are characteristic features of the proprietary manufac(cid:173)
`turing process for these instruments. The extent of metal
`rollover was much less for the stainless steel files, which were
`subjected by the manufacturer to an electropolishing proce(cid:173)
`dure, than for the Nitinol files which were not electropolished.
`The Nitinol files had considerably greater elastic flexibility
`
`FIG 2. SEM photograph of the body region of a size #15 Nitinol file.
`The machining marks and the ridge of permanently deformed metal
`along the cutting edge are evident at this higher magnification.
`
`FIG 3. SEM photograph of the tip region of a size #15 Quality Dental
`Products stainless steel file. A round~d tip design is used for both
`the stainless steel and Nitinol instruments.
`
`than the stainless steel files in all three testing modes of
`bending, clockwise torsion, and counterclockwise torsion
`(Figs. 5 to 7). This follows from a comparison of the slopes
`of the initial, approximately linear, portions of these plots;
`the slope is two to three times greater for the stainless steel
`files. The initial slopes of the two plots in Figs. 5 to 7 cannot
`be compared with precision because there is some arbitrary
`judgment in how these curves should be drawn for the lowest
`moment values. The pointer on the torque meter obscures
`
`FIG 1. Scanning electron microscopic photograph of the tip region of
`a size #15 Nitinol file. The information on all of the legends for the
`SEM photographs is as follows, from left to right: accelerating voltage
`in kV; magnification; exposure number; scale marker for indicated
`distance in micrometers (original magnification x271 ).
`
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`348 Waliaetal.
`
`FIG 4. SEM photograph of the body region of a size #15 Quality
`Dental Products stainless steel file. An electropolishing procedure,
`not utilized for the Nitinol files, was used to reduce the machining
`damage on the stainless steel file surfaces.
`
`20
`
`Size No. 15
`Bending
`
`Stainless Steel
`
`e 0
`I
`E
`.3
`1-z w
`~ 10
`0
`~
`(!) z
`15
`z
`w
`Ill
`
`Journal of Endodontics
`
`The forms of the bending curves in Fig. 5 indicate that
`permanent deformation of the 3-mm apicalregions of the
`stainless steel files began at a bend angle of approximately 30
`degrees, but that the apical regions of the Nitinol files were
`undergoing largely elastic deformation even at bend angles of
`90 degrees. The latter was supported by visual observations
`of the Nitinol files after unloading, where very little, if any,
`permanent bends were evident.
`The Nitinol files also exhibited considerably greater resist(cid:173)
`ance to fracture in torsion than the stainless steel files. For
`
`20
`
`Size No. 15
`Clockwise Torsion
`
`e 0
`
`I
`E
`.3
`1-z w
`~
`0
`~
`
`...J < z
`
`0
`(j)
`0:
`0
`1-
`
`180
`
`360
`
`540
`
`720
`
`900
`
`ANGULAR DEFLECTION (deg)
`
`FIG 6. Clockwise torsion test results for the size #15 Nitinol and
`stainless steel files .
`
`e 0
`I
`E
`.3
`1-z w
`~
`0
`~
`...J < z
`
`0
`(j)
`a:
`0
`1-
`
`Nitinol
`
`90
`
`180
`
`270
`
`360
`
`450
`
`ANGULAR DEFLECTION (deg)
`
`FIG 7. Counterclockwise torsion test results for the size #15 Nitinol
`and stainless steel files. The two initial data points for the Nitinol files
`could not be determined with the torque meter, and the two plots
`have been drawn to intersect the origin. Both of these considerations
`are less pronounced in Figs. 5 and 6.
`
`Nitinol
`
`20
`
`Size No. 15
`Counterclockwise Torsion
`
`30
`
`60
`
`90
`
`ANGULAR DEFLECTION (deg)
`
`FIG 5. Cantilever bending test results for the size #15 Nitinol and
`stainless steel files. The data points in this figure and in Figs. 6 and
`7 correspond to average moment values for groups of five instru(cid:173)
`ments at the indicated bend or twist angles.
`
`the reading of bending or torsional moments less than 0.05
`inch-oz (3.60 gm-cm). Consequently, the passive position
`(zero moment value) and the corresponding location for zero
`angular deflection cannot be determined directly in an exper(cid:173)
`iment. For convenience, all of the graphical plots have been
`drawn to intersect the origin. This extrapolation appears to
`be more satisfactory for the bending plots (Fig. 5) and clock(cid:173)
`wise torsion plots (Fig. 6) than for the counterclockwise
`torsion plots (Fig. 7).
`
`PGR2015-00019 - Ex. 1033
`US ENDODONTICS, LLC., Petitioner
`
`

`
`Vol. 14, No.7, July 1988
`
`Nitinol Root Canal Files
`
`349
`
`clockwise torsion (Fig. 6), the size # 15 Nitinol files were
`capable of undergoing a mean value of 21h revolutions before
`fracturing, while the stainless steel ftles fractured after a mean
`value of 1% revolutions. The general appearances of the two
`clockwise torsion plots in Fig. 6 are very similar. The relatively
`extensive, nearly horizontal, portions of these two graphs
`indicate that the apical regions for both groups of files under(cid:173)
`went substantial permanent torsional deformation before frac(cid:173)
`turing. An interesting point is that for clockwise twist angles
`exceeding 270 degrees the Nitinol files developed approxi(cid:173)
`mately 10 to 20% higher torsional moment than did the
`stainless steel files.
`For counterclockwise torsion (Fig. 7), the Nitinol files
`experienced largely elastic deformation before fracturing at a
`mean value of 450 degrees angular deflection ( 11/4 revolu(cid:173)
`tions). The stainless steel files fractured at a mean value of
`225 degrees (between 1h and 3f4 revolution), and the counter(cid:173)
`clockwise torsion plot for these instruments displayed a defi(cid:173)
`nite, although not an extensive, horizontal region correspond(cid:173)
`ing to. permanent deformation from 13 5 to 225 degrees. When
`the differing scales of Figs. 6 and 7 and the uncertainty of
`extrapolation to zero moment values are considered, it can
`be seen that the counterclockwise torsion plots are quite
`similar to the corresponding clockwise torsion plots over the
`same range of angular deflection.
`The SEM photographs of the fracture surfaces for the
`Nitinol and stainless steel files after torsional failure showed
`essentially the same general characteristics (Figs. 8 to 11 ). The
`clockwise torsional fracture surfaces for the Nitinol (Fig. 8)
`and stainless steel (Fig. 9) instruments were largely flat and
`inclined to the axes of the files; non planar regions of fracture
`were observed near corners of the triangular cross-sections.
`The counterclockwise torsional fracture surfaces for both the
`Nitinol (Fig. 1 0) and stainless steel (Fig. 11) files were quite
`flat and differed little in appearance.
`
`FIG 9. SEM photograph of the 3-mm apical region of a size #15
`stainless steel file which has been tested to fracture in clockwise
`torsion.
`
`FIG 10. SEM photograph of the 3-mm apical region of a size #15
`Nitinol file which has been tested to fracture in counterclockwise
`torsion.
`
`DISCUSSION
`
`This initial study has demonstrated that root canal files
`fabricated from Nitinol orthodontic wires possess very prom(cid:173)
`ising bending and torsional properties. Our experimental re(cid:173)
`sults indicate that for size # 15 the new metallurgical files have
`superior mechanical properties to the stainless steel files which
`were manufactured by the same process of directly machining
`the flutes forK-type instruments.
`
`FIG 8. SEM photograph of the 3-mm apical region of a size #15
`Nitinol file which has been tested to fracture in clockwise torsion.
`
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`

`
`350 Waliaetal.
`
`FtG 11. SEM photograph of the 3-mm apical region of a size #15
`stainless steel file which has been tested to fracture in counterclock(cid:173)
`wise torsion.
`
`The outstanding elastic flexibility of the Nitinol files is a
`consequence of the very low elastic modulus of these nickel(cid:173)
`titanium alloys. Although there are complexities introduced
`by the fluted and tapered cross-sections, the slopes of the
`initial elastic, approximately linear, regions of the bending
`and torsion plots should be proportional to the modulus of
`elasticity in tension (Young's modulus) and the modulus of
`elasticity in torsion (shear modulus), respectively, of the Ni(cid:173)
`tinol and stainless steel alloys ( 13). Experimental measure(cid:173)
`ments have shown that the modulus of elasticity in tension
`for Nitinol orthodontic wires is only about one-fourth to one(cid:173)
`fifth that for stainless steel orthodontic wires ( 14 ). Although
`experimental values of shear modulus are not available for
`these two orthodontic alloys, it can be readily shown that the
`shear modulus has approximately 40% of the value of Young's
`modulus for a given metal ( 15). Consequently, the shear
`modulus for the Nitinol orthodontic alloy should also have a
`value of about one-fourth to one-fifth that for the stainless
`steel wire alloy used to fabricate the root canal files. As
`previously noted, the slopes of the initial linear portions of
`the bending and torsion plots for the Nitinol files in Figs. 5
`to 7 are approximately one-half to one-third the values of the
`corresponding slopes for the stainless steel files. The discrep(cid:173)
`ancy between the observed and theoretically predicted relative
`slopes is attributed to the difficulty in drawing the exact forms
`of the bending and torsion plots at small values of angular
`deflection, particularly for the Nitinol files, and perhaps to
`small differences in cross-sectional dimensions of the nomi(cid:173)
`nally same size # 15 instruments. The dependence of instru(cid:173)
`ment stiffness on size has been discussed by Craig et al. (6).
`The resistance to torsional fracture for the experimental
`Nitinol root canal files was clearly superior to the behavior of
`the control stainless steel files manufactured by the same
`process in size #15 (Figs. 6 and 7). Comparison of the present
`data to the results of a previous extensive study (8) in our
`
`Journal of Endodontics
`
`laboratory on several brands of K-type files indicates that the
`process of machining the fluted structure does ~ret appear to
`have substantial adverse effects on the tendency of the files in
`size # 15 to fracture during torsion testing.
`Standard K-type root canal files were not used as controls
`in our study because extensive data for bending and torsional
`properties from seven different brands in size # 15 were avail(cid:173)
`able from the recent investigation by Krupp et al. (8) and
`because we needed control files fabricated by the same process
`used for the experimental Nitinol files. It was found that the
`stainless steel control files manufactured by Quality Dental
`Products yielded graphical plots of bending moment and
`torsional moment versus angular deflection that were similar
`to plots for the Kerr K-Flex and Whaledent brands in the
`same size which had been previously (8) evaluated. Because
`careful attention in the present study was directed to locating
`the D3 position in the test grips and to maintaining the proper
`instrument test spans for the bending and torsion experi(cid:173)
`ments, five replications in each group of Nitinol and stainless
`steel files were found to be sufficient. The five individual
`values of bending or torsional moment at each value of
`angular deflection generally did not differ much, with coeffi(cid:173)
`cients of variation (ratio of standard deviation to mean value)
`typically about 10%. Krupp et al. (8) had previously found
`that a sample size of five for each group of instruments was
`adequate for similar carefully performed bending and torsion
`tests with our manually loaded torque meter apparatus.
`The superior torsional ductility, or resistance to fracture,
`of the Nitinol root canal files, compared with the stainless
`steel instruments evaluated in this study, was an unanticipated
`result. It is well known that orthodontists experience consid(cid:173)
`erable difficulty with the placing of permanent bends in the
`very flexible Nitinol alloy (9), and we have felt that the
`conventional process ( 10) of twisting the ground and tapered
`wire blank might not be feasible for the fabrication of K-type
`root canal files from Nitinol. However, the inherent torsional
`ductility of this nickel-titanium alloy is evident from the
`clockwise torsion plot of Fig. 6, and the SEM photographs
`(Figs. 1 and 2) of the metal rollover ridges along the cutting
`edges of the flutes further attest to the capability of Nitinol
`for permanent deformation. Substantial permanent tensile
`deformation of Nitinol arch wires was also observed in a
`previous study ( 14) in our laboratory on the bending and
`tensile properties of orthodontic wires. The likelihood of
`ductility for Nitinol had been implied from the tabulated
`mechanical property information in the earlier review article
`by Civjan et al. ( 16), who discussed some potential dental
`applications for these nickel-titanium alloys. The authors
`suggested that 60-Nitinol, which is much harder than the 55-
`Nitinol orthodontic wire alloy (9), would have excellent char(cid:173)
`acteristics for endodontic i:J?.struments, but they did not pro(cid:173)
`vide any further discussion of this application.
`With Nitinol root canal files, the endodontist may choose
`to alter some of the clinical procedures presently used with
`stainless steel files in the preparation of curved canals. Because
`of the pronounced "elastic memory" characteristics of this
`alloy, the clinician may not consider it necessary to precurve
`Nitinol files to conform to the morphology of curved root
`canals. Nonetheless, we have found that the size #15 Nitinol
`files can be precurved, so this capability is available for these
`experimental instruments.
`
`PGR2015-00019 - Ex. 1033
`US ENDODONTICS, LLC., Petitioner
`
`

`
`Vol. 14, No.7, July 1988
`
`Research is continuing on the new metallurgical files, with
`studies of bending and torsional properties and the evaluation
`of in vitro cutting efficiency for size #35 files, fabricated from
`special 0.031-inch large diameter Nitinol wires (Unitek
`Corp.). Attention is also being directed. to whether some
`electropolishing technique exists for removal of the heavily
`deformed metal along the cutting edges, although an alterna(cid:173)
`tive approach may be the use of an improved procedure for
`machining the flutes (Derek Heath, Quality Dental Products,
`personal communication).
`It may be noted that our present investigations using Ni(cid:173)
`tinol as a new metallurgical file alloy represent only a first
`approach into an entirely new field of endodontic research.
`Other nickel-titanium orthodontic wire alloys have recently
`been described ( 17, 18), and manufacturers have introduced
`several new wire brands, for which superelastic behavior and
`other outstanding mechanical properties are claimed. More(cid:173)
`over, it is possible to alter the superelastic force delivery of
`the Japanese NiTi wire alloy (and perhaps for other p.ew wire
`brands as well) by means of an appropriate heat treatment
`(18). It would be worthwhile to evaluate root canal files
`fabricated from some of these recently introduced nickel(cid:173)
`titanium alloys, as well as from beta titanium, an orthodontic
`wire alloy having excellent ductility and a modulus of elastic(cid:173)
`ity intermediate in value to stainless steel and Nitinol ( 19). It
`would be particularly interesting also to compare the proper(cid:173)
`ties of root canal files fabricated by both the conventional
`process (10) forK-type instruments and the technique in the
`present investigation of machining the fluted structure on the
`wire blanks for new alloy systems other than stainless steel
`where both manufacturing procedures are feasible. With ap(cid:173)
`propriate choice of alloy type and cross-sectional shape, one
`or more series of root canal files possessing a wide range in
`flexibility and other properties may be possible.
`
`CONCLUSIONS
`
`The Nitinol files were observed to have two to three times
`the elastic flexibility of the stainless steel files as well as
`superior resistance to fracture in clockwise torsion and coun(cid:173)
`terclockwise torsion. It was possible to precurve the size # 15
`Nitinol files in a manner similar to that generally favored by
`clinicians for the instrumentation of curved root canals, al(cid:173)
`though a precurving technique may be deemed unnecessary
`with these very flexible files. The extraordinary flexibility of
`these instruments is a result of the very low values of modulus
`of elasticity in tension and shear modulus of the Nitinol alloy
`compared with values for the wrought stainless steel alloys
`currently used in the manufacture of root canal files. The
`superior fracture resistance of the Nitinol instruments was
`attributed to the ductility of this nickel-titanium alloy, which
`was evident in the clockwise torsional behavior and scanning
`electron microscopic photographs of the machined surfaces
`of the files. The present results suggest that Nitinol endodontic
`
`Nitinol Root Canal Files
`
`351
`
`files may have particular promise for the clinical preparation
`of curved root canals, and studies are currently underway to
`evaluate the mechanical properties and the in vitro cutting
`efficiency for size #35 instruments.
`
`We wish to express our gratitude to Derek Heath, President of Quality
`Dental Products, and to Jerry Arpaio, retired Vice-President for Research and
`Development, for fabricating the Nitinol files, contributing numerous helpful
`discussions on the manufacture of root canal files, and providing the stainless
`steel instruments that served as the controls for this study. We also want to
`thank 'the Unitek Corporation for contributing the Nitinol arch wires and Mary
`Kastern for expert graphics assistance in preparing the drawings for the bending
`and torsion plots.
`
`Dr. Walia is assistant professor, Department of Endodontics, Marquette
`University School of Dentistry, Milwaukee, WI. Dr. Brantley is professor and
`chairman, Department of Dental Materials, and director, Dental Graduate
`Studies, Marquette University School of Dentistry. Dr. Gerstein was formerly
`professor and chairman, Department of Endodontics, Marquette University
`School of Dentistry. For additional information, contact Dr. Brantley, Depart(cid:173)
`ment of Dental Materials, Marquette University School of Dentistry, 604 North
`16th Street, Milwaukee, WI 53233.
`
`References
`
`1. Weine FS, Kelly RF, Lio PJ. The effect of preparation procedures on
`original canal shape and on apical foramen shape. J Endodon 1975;1 :255-62.
`2. Ingle Jl, Mullaney TA, Grandich RA, Tainter JF, Fahid A. Endodontic
`cavity preparation. In: Ingle Jl, Tainter JF, eds. Endodontics. 3rd ed. Philadel(cid:173)
`phia: Lea & Febiger, 1985:200-1.
`3. Walton RE. Histologic evaluation of different methods of enlarging the
`pulp canal space. J Endodon 1976;2:304-11.
`4. Weine FS. Endodontic therapy. 3rd ed. St. Louis: CV Mosby, 1982;290-
`
`3.
`
`5. Phillips RW. Skinner's science of dental materials. 8th ed. Philadelphia:
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`6. Craig RG, Mcilwain ED, Peyton FA. Comparison of theoretical and
`experimental bending and torsional moments of endodontic files and reamers.
`J Dent Res 1967;46:1 058-63.
`7. Newman JG, Brantley WA, Gerstein H. A study of the cutting efficiency
`of seven brands of endodontic files in linear motion. J Endodon 1983;9:316-
`22.
`8. Krupp JD, Brantley WA, Gerstein H. An investigation of the torsional and
`files. J Endodon
`bending properties of seven brands of endodontic
`1984;1 0:372-80.
`9. Andreasen GF, Morrow RE. Laboratory and clinical analyses of nitinol
`wire. Am J Orthod 1978;73:142-51.
`1 0. Heuer MA. Instruments and materials. In: Cohen S, Burns RC, eds.
`Pathways of the pulp. 3rd ed. St. Louis: CV Mosby, 1984:428-31.
`11. Council on Dental Materials and Devices. New ADA specification no.
`28 for endodontic files and reamers. J Am Dent Assoc 1976;93:813-8.
`12. Roane JB, Sabala CL, Duncanson MG: The "balanced force" concept
`for instrumentation of curved canals. J Endodon 1985;11 :203-11.
`13. Popov EP. Introduction to mechanics of solids. Englewood Cliffs, NJ:
`Prentice-Hall, 1968:145-62.
`14. Asgharnia MK, Brantley WA. Comparison of bending and tension tests
`for orthodontic wires. Am J Orthod 1986;89:228-36.
`15. Dieter GE. Mechanical metallurgy. 2nd ed. New York: McGraw-Hill,
`1976:49-52.
`16. Civjan S, Huget EF, DeSimon LB. Potential applications of certain
`nickel-titanium (Nitinol) alloys. J Dent Res 1975;54:89-96.
`17. Burstone CJ, Qin B, Morton JY. Chinese NiTi wire-a new orthodontic
`alloy. Am J Orthod 1985;87:445-52. ·
`18. Miura F, Magi M, Ohura Y, Hamanaka H. The super-elastic property of
`the Japanese NiTi alloy wire for use in orthodontics. Am J Orthod Dentofac
`Orthop 1986;90:1-1 0.
`19. Burstone CJ, Goldberg AJ. Beta titanium: a new orthodontic alloy. Am
`J Orthod 1980;77:121-32.
`
`PGR2015-00019 - Ex. 1033
`US ENDODONTICS, LLC., Petitioner