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Elastic properties of alternative versus single-stranded leveling archwires
ORIGINAL ARTICLE
Elastic properties of alternative versus singlestranded leveling archwires Brian K. Rucker, BS,a and Robert P. Kusy, MS, PhDa-d Chapel Hill, NC The strength, stiffness, and range of single-stranded stainless steel (SS) and superelastic nickel-titanium (NiTi) archwires were compared with those of alternative leveling products, including nylon-coated and multistranded wires. Wire cross-sections were photographed after being potted in polymer, ground, and polished. Because the rectangular wires had rounded or beveled corners, gravimetric measurements and specific gravity calculations quantified the actual polygonal cross-sectional areas versus the ideal rectangular cross-sectional areas. Beveling reduced the cross-sectional areas by 7% to 8%; this decreased the wire stiffnesses by 15% to 19%. Using a testing machine, we measured the yield strengths, the elastic limits, and the ultimate tensile strengths in tension, and wire stiffnesses in 3-point bending. From cyclic loading tests, the elastic limits of the superelastic NiTi wires were approximately 90% and 45% of their ultimate tensile strengths for the round and rectangular wires, respectively. Using the measurements of the mechanical properties and geometric parameters of each wire, we computed the elastic property ratios (EPRs) versus a 16-mil (0.41 mm) NiTi wire. The single-stranded NiTi wires outperformed the alternative wires, whose EPRs varied from 0.05 to 0.32 for strength, from 0.11 to 1.55 for stiffness, and from 0.10 to 0.80 for range. Based on the current study and a review of the orthodontic literature, few superelastic wires are activated sufficiently in vivo to exhibit superelastic behavior. Therefore, the EPR data reported here for superelastic wires truly represent their performance in most clinical situations. (Am J Orthod Dentofacial Orthop 2002;122:528-41)
L
ight orthodontic forces produce the same amount of tooth movement as heavier forces and are physiologically more acceptable.1 Once forces were applied in the hundreds of grams, but today these forces probably are only tens of grams.2 For the initial leveling and aligning stages of orthodontic treatment, practitioners still use traditional archwires made from stainless steel (SS) or conventional nickel-titanium (NiTi) that is martensite stabilized. Additionally, pseudoelastic (so-called superelastic) NiTi alloys are engineered to provide a constant force during tooth movement. Alternative leveling products include multistranded NiTi wires that deliver ultra-low forces and esthetically pleasing products such as glass-fiber composites and polymer-coated wires. The ideal properties of leveling archwires include high strength to prevent permanent deformation, low From the University of North Carolina, Chapel Hill. a Department of Biomedical Engineering. b Department of Orthodontics. c Dental Research Center. d Curriculum in Applied and Material Sciences. Reprint requests to: Robert P. Kusy, University of North Carolina, Building 210-H, Room 313, Chapel Hill, NC 27599; e-mail, [email protected]. Submitted, January 2002; accepted, March 2002. Copyright © 2002 by the American Association of Orthodontists. 0889-5406/2002/$35.00 ⫹ 0 8/1/127292 doi:10.1067/mod.2002.127292
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stiffness to deliver low forces per unit of deactivation, and high range to maximize activations.3 Because a decrease in stiffness is often accompanied by a decrease in strength, a practitioner typically selects a leveling archwire with the lowest stiffness that retains acceptable strength. The elastic properties of strength, stiffness, and range can be calculated for linear elastic materials (eg, SS) in single4 and multistranded5-8 configurations. To best aid the orthodontist in wire selection, these properties are reported as relative values called elastic property ratios (EPRs). Such EPRs are calculated versus a common wire; this permits comparing any 2 wires. With linear elastic models, the properties of conventional NiTi wires also were reported, although this alloy displays some nonlinear elastic behavior.8 However, EPR calculations for superelastic NiTi alloys might require redefining some terms in the earlier models. A survey of the properties of superelastic wires in vitro is necessary because some researchers concluded that few of these wires actually exhibit superelastic properties.9-12 Those laboratory findings were supported by clinical studies in which no significant differences of tooth migration were observed among superelastic NiTi wires, comparable conventional NiTi wires, and multistranded SS counterparts.13-15 The current study compares the EPRs of single-
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Fig 1. Wire inventory divided into 3 basic experimental groups: group 1 features wires with similar overall wire diameters; group 2 compares SS cores of polymer-coated wires with single-stranded SS wires; group 3 compares braided wire configurations with corresponding single-stranded wires. For these groups of SS and NiTi wires, EPRs were computed versus single-stranded 16-mil NiTi wire (not shown) (1 mil ⫽ 0.001 in ⫽ 0.0254 mm).
stranded SS and NiTi archwires to those of alternative leveling products that include nylon-coated SS wires and multistranded SS and NiTi wires. Gravimetric measurements and specific gravity calculations determine the actual cross-sectional areas and area moments of inertia for the archwires with nominal rectangular dimensions, many of which have rounded or beveled edges.2,9,16-18 Tensile tests measure the yield strengths, elastic limits, and ultimate tensile strengths; flexural tests measure the wire stiffnesses. The EPRs of each wire can be determined from the measurements of mechanical properties and geometric parameters. For the superelastic wires, the reported EPRs apply only to their behaviors in the initial linear elastic region. The tensile and flexural data will be considered alongside current findings in the orthodontic literature9-15 to
speculate how often superelastic wires demonstrate superelastic behavior in clinical settings. MATERIAL AND METHODS
Single-stranded SS and superelastic NiTi archwires provided controls for 3 basic experimental groups (Fig 1). The multistranded SS and superelastic NiTi archwires had coaxial and braided configurations (Table I). The coaxial configuration had 6 strands twisted around an inner strand (groups 1 and 2), and the braided configuration had 9 strands that were swaged into rectangular cross-sections (group 3). The configurations of the nylon-coated wires (groups 1 and 2) included 1 with a single-stranded SS core, marketed as an esthetic orthodontic wire, and 1 with a coaxial SS core, used elsewhere.
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Table I. Average dimensions for stainless steel (SS) and nickel titanium (NiTi) wires including overall wire diameter (D), inner strand diameter (di), outer strand diameter (do), helix angle (␣), base (b), and height (h) Actual dimensions* Configuration Single-stranded Single-stranded Single-stranded Coaxial Braided Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Coaxial Braided
Alloy
Nominal dimensions (mil)
SS SS SS SS SS Whole wire Single-stranded SS core Whole wire Coaxial SS core NiTi NiTi NiTi NiTi NiTi
12† 18‡ 17 ⫻ 25§ 17.5㛳 17 ⫻ 25† 18¶ 9¶ 18# 12# 16** 18** 17 ⫻ 25** 18†† 17 ⫻ 25†
D (mil)
di (mil)
do (mil)
12.10 17.98 18.05 17.47 8.75 17.87 10.87 15.86 17.43 17.55
7.14
5.27
3.39
3.74
5.82
6.21
␣ (°) 90 90 90 59.8 90 90 90 90 83.5 90 90 90 74.9 90
b (mil)
h (mil)
16.77
24.34
17.18
24.61
17.14
24.91
17.45
24.70
*1 mil ⫽ 0.001 inch ⫽ 0.0254 mm. †SDS Ormco, Glendora, Calif. ‡GAC International, Islandia, NY. §3M Unitek Corporation, Monrovia, Calif. 㛳Highland Metals, San Jose, Calif. ¶American Orthodontics, Sheboygan, Wis. #Rio Grande, Albuquerque, NM. **Dentaurum, Inc., Newtown, Pa. ††Strite Industries Limited, Cambridge, Ontario, Canada.
To determine archwire dimensions, we measured (⫾ 0.01 mil) each outer strand diameter (do) and axial displacement per twist of a wire strand (ᐉ*) at 5 locations using the optics of a Kentron microhardness tester (Kent Cliff Labs, Peekskill, NY). Each overall wire diameter (D), inner strand diameter (di), base (b), and height (h) were measured (⫾ 0.05 mil) 5 times with a digital micrometer (-Mate, Sony Magnescale America, Orange, Calif) (1 mil ⫽ 0.001 in ⫽ 0.0254 mm). The helix angles (␣) of the outer twisted strands were calculated by5,6 ␣ ⫽ tan⫺1{ᐉ*/[(D⫺do)]}
(1)
Cross-sectional geometries were determined by carefully cutting and potting small segments of archwires in epoxy or polyester resins. These specimen cylinders were ground with wet carbide papers and polished with levitated 1.0 and 0.3 m alumina. Each transverse section of wire was viewed with bright-field reflected light microscopy (Zeiss Universal Microscope, Oberkuchen, Germany) and photographed with Type 331 film (Polaroid-Land, Cambridge, Mass). For the gravimetric measurements and specific gravity (SG) calculations, each wire length was
measured (⫾ 0.5 mil) 5 times with calipers (Fowler Tools and Instruments, Boston, Mass). Samples were cleaned with methanol and weighed (⫾ 0.1 mg) 5 times with a digital balance (Sartorius, Goettingen, Germany). Because many rectangular archwires are fabricated by rolling round wire through a Turk’s head,16 the cross-sections of these wires have polygonal shapes in which the corners are rounded or beveled.2,9,16-18 Therefore, the ratio of the calculated SG (based on actual weight and rectangular dimensions) to the SG reported in the metallurgical literature was assumed to equal the ratio of the polygonal to the rectangular cross-sectional areas. By modeling the polygonal cross-sections,19 each polygonal area moment of inertia (Ipoly.) was calculated by using the corresponding relative SG, b, and h (Fig A and Appendix). The reported SG values are 7.965 g/cm3 for SS alloys typically used to produce archwires (eg, types 301, 302, 304, and 316L)20 and 6.50 g/cm3 for 55/45 NiTi.21 Tensile tests were conducted with a mechanical testing machine (Instron, Canton, Mass) with a 500-kg load cell and capstan grips at a 2 mm/min crosshead speed. Three samples were activated for each wire type. To measure the ultimate tensile strength (UTS), each
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Table II. Maximum force (P) and number of wires (n) simultaneously tested per distance between outer supports (L1) that meet the 3-point bending criteria
Alloy
Nominal dimensions (mil)
L1 (cm)
n
Maximum P (N)*
SS SS SS SS SS Single-stranded SS core Coaxial SS core NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi
12 18 17 ⫻ 25† 17 ⫻ 25‡ 17.5 8.75 10.87 16 16 18 18 17 ⫻ 25† 17 ⫻ 25† 17 ⫻ 25‡ 17 ⫻ 25‡ 18 18
0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 1.27 0.89 1.27 0.89 1.27 0.89 1.27 0.89 1.27
1 1 1 1 2 1 7 1 2 1 1 1 1 1 1 4
1.29 1.29 1.29 1.29 1.11 0.73 1.18 1.29 1.71 1.29 1.25 1.29 1.84 1.29 1.84 1.11
Configuration Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Coaxial
- Not possible -
*1N ⫽ 0.102 kg force. †Tested in flatwise orientation. ‡Tested in edgewise orientation.
sample was loaded to failure and the maximum stress noted. To measure the 0.1% yield strengths (YS), each sample was preloaded to 1 kg, mounted with a 1.27-cm 10% extensometer, and activated to failure. A best-fit line superposed these elastic traces, and parallel lines established the 0.1% yield points. The elastic limits (EL), which are the greatest stresses that materials can withstand without showing permanent sets after deactivation,22 were measured with a 1.27-cm 50% extensometer by cyclically activating the NiTi wires to a designated stress level and observing any signs of cold working (ie, permanent plastic deformation). With the same machine, wires were tested in 3-point bending with a distance between outer supports (L1) of 0.89 or 1.27 cm. With a 500-kg load cell with a 200-g full-scale sensitivity, the force-deflection curves were maintained at a slope of 45° to 75° by varying the crosshead speed and the chart paper speed. Each Young’s modulus (E) was calculated by23 E ⫽ L13P/48␦Itotaln
(2)
in which P, ␦, Itotal, and n are the force applied to the beam, the deflection of the activated beam, the total area moment of inertia, and the number of wires simultaneously tested, respectively. For the singlestranded wires, Itotal ⫽ D4/64. For the coaxial wires,7 Itotal ⫽ (di4 ⫹ 6do4 )/64 in which the helical spring
shape factor5,6 is ⫽ 2sin␣(2 ⫹ ␥cos2␣) and ␥ is Poisson’s ratio, which was assigned the values of 0.28 for SS24 and 0.34 for NiTi.21 At present, the Itotal for braided wires cannot be calculated directly because of strand asymmetry along the length. Due to the great difference between the physical properties of polymeric and metallic materials,25 only the SS cores of the nylon-coated wires were required to calculate the crosssectional area and Itotal for these wires. With custom software, the n and maximum P in equation (2) were calculated for each 3-point bending arrangement according to the following criteria: the total wire deflection was ⱕ 0.05L1, the wire deflection due to gravity was ⱕ 0.0005␦, and the machine deflection was ⱕ 0.005␦ (Table II).23 The n and maximum P values were calculated for the SS wires assuming E ⫽ 199 gigapascals (GPa)8 and for NiTi wires assuming E ⫽ 44.4 GPa.23 For the braided wires, the n and maximum P were estimated at 1 and 1 newton (N), respectively. Each EPR value was calculated versus a 16-mil NiTi wire and considered under the same testing arrangement—ie, the same clinical situation.4 By fitting a linear regression to each data set, a correlation coefficient was calculated (Lotus Freelance Graphics, Cambridge, Mass) to determine the statistical probability based on the number of data points.
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Fig 2. Cross-sections of rectangular archwires. Wires were transversely potted in polymer, ground, and polished. Based on calculated specific gravities of single-stranded SS (a) and NiTi (d) wires (Table III), between 1.7% and 2.0% of actual rectangular areas were missing from each corner. However, even the sides of NiTi wire (d) appear somewhat rounded. Strands of braided wires displayed various cross-sectional patterns, 2 examples of which are shown for the SS [(b) and (c)] and NiTi [(e) and (f)] wires, respectively. RESULTS
In general, the dimensional and weight measurements of wires were reported only as means because 1 SD was within about 3% of each corresponding mean. Specifically, the D, b, and h measurements were as much as 3.1% larger and 3.2% smaller than their corresponding nominal dimensions (Table I). The nylon-coated wires with a nominal D of 18 mil had 8.75-mil single-stranded SS cores or 10.87-mil coaxial SS cores (Fig 1, groups 1 and 2). For the single-stranded rectangular wires, the SS
wires appeared to fit the polygonal model (Fig A in Appendix) more accurately than the NiTi wires for which not only the corners but also the entire crosssections were rounded (Fig 2, top frames). Although the cross-sections of the braided wires varied along the length of the archwire, the strands of both alloys appeared to alternate between a few general wire configurations (Fig 2, middle and bottom frames). Beveling of the braided wires was not considered because neither the Itotal nor the Ipoly. of these wires was calculated from their dimensions.
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Table III.
Calculated specific gravities (SG) for round, rectangular, and braided archwires
Configuration
Alloy
Nominal dimensions (mil)
Single-stranded Single-stranded Braided Single-stranded Single-stranded Braided
SS SS SS NiTi NiTi NiTi
12 17 ⫻ 25 17 ⫻ 25 16 17 ⫻ 25 17 ⫻ 25
Actual dimensions (mil)
Length (in)
Weight (g)
Calculated SG (g/cm3)
Relative SG (%)*
12.07 16.91 ⫻ 24.52 17.39 ⫻ 24.43 15.97 17.20 ⫻ 25.02 17.55 ⫻ 24.76
11.4330 11.5278 2.0195 11.4507 11.5318 0.7763
0.1700 0.5801 0.0830 0.2427 0.4877 0.0271
7.930 7.406† 5.900† 6.457 5.997† 4.900†
99.6 93.0 74.1 99.3 92.3 75.4
*Relative SG ⫽ (calculated SG)/(reported SG) ⫻ 100% where reported SG of SS and NiTi alloys equal 7.965 g/cm3 and 6.50 g/cm3, respectively.20,21 †Calculated SG assumed actual rectangular dimensions. Table IV. Radius of rounded archwire corner (R) and area moments of inertia of polygonal (Ipoly.) versus rectangular (Itotal) cross-sections*
Configuration
Alloy
Nominal dimensions (mil)
Single-stranded Single-stranded Single-stranded Single-stranded
SS SS NiTi NiTi
17 ⫻ 25‡ 17 ⫻ 25§ 17 ⫻ 25‡ 17 ⫻ 25§
R (mil)
Ipoly. ⫻ 1017 (m4)
Itotal ⫻ 1017 (m4)
Relative I (%)†
5.78 5.78 6.19 6.19
337 696 362 749
398 839 435 919
84.6 83.0 83.3 81.5
*See Fig A and particularly eqs. (A3) and (A4) in Appendix. †Relative I ⫽ (Ipoly.)/(Itotal) ⫻ 100%. ‡Computed in flatwise orientation. §Computed in edgewise orientation.
Round, single-stranded SS and NiTi archwires were used as controls for making SG determinations because their cross-sectional areas are easily computed; both calculated SG values were within 0.7% of their reported values (Table III). For the single-stranded 17 ⫻ 25-mil SS wire, the relative SG of 93.0% suggested that 1.75% of the actual rectangular cross-sectional area was missing from each of the 4 corners (Figs 2, a, and A). By substituting the b and h (Table I) and relative SG (Table III) for this wire into equations (A3) and (A4) of the Appendix, the Ipoly. values were approximately 85% and 83% of the corresponding rectangular Itotal in the flatwise and edgewise orientations, respectively (Table IV). Similarly for the single-stranded 17 ⫻ 25-mil NiTi wire, the relative SG of 92.3% (Table III) suggested that approximately 1.93% of the actual rectangular cross-sectional area was missing from each corner (Figs 2, d, and A). The Ipoly. values for the NiTi wire were approximately 83% and 82% of the corresponding rectangular Itotal in the flatwise and edgewise orientations, respectively (equations (A3), (A4), and Table IV). The 9 strands of the SS and NiTi braided wires accounted for 74.1% and 75.4% of the areas defined by their rectangular dimensions, respectively (Fig 2, b, c, e, f, and Table III).
For the SS wires, YS varied from 1.01 to 2.37 GPa and UTS varied from 1.29 to 2.56 GPa (Table V). For the NiTi wires, YS varied from 0.18 to 0.49 GPa, and UTS varied from 0.80 to 1.67 GPa. The ratio of YS/UTS averaged 0.83 and 0.29 for the SS and NiTi wires, respectively. To compute the strengths of the rectangular and braided wires (Fig 1, group 3), the cross-sectional areas were based on the relative SG values (Table III). Although the nylon material was ignored in computing the cross-sectional areas of the coated wires (Fig 1, groups 1 and 2), the YS value of each coated versus uncoated wire agreed to within 1 SD. From the clinical perspective, the forces at the 0.1% yield points were listed, which equal YS times cross-sectional area (1 N ⬵ 100 g). To determine the E of the rectangular wires, each Itotal in Table VI was assigned the corresponding Ipoly. value (Table IV). When the SS wires were tested in a 3-point bending arrangement with L1 ⫽ 0.89 cm, E varied from 177 to 217 GPa. The NiTi wires were tested with L1 ⫽ 0.89 cm or with L1 ⫽ 1.27 cm, if they could meet the criteria detailed in the “Material and Methods” section (Table II). The individual E values of these NiTi wires varied from 32.1 to 60.2 GPa.
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Table V.
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
Forces at 0.1% yield point, 0.1% yield strengths (YS), elastic limit (EL), and ultimate tensile strengths
(UTS)
Configuration Single-stranded Single-stranded Single-stranded Coaxial Braided Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Coaxial Braided
Alloy
Nominal dimensions (mil)
Force at YS (N)*
YS (GPa)*
EL (GPa)
UTS (GPa)*
YS/UTS
EL/UTS
SS SS SS SS SS Whole wire Single-stranded SS core Whole wire Coaxial SS core NiTi NiTi NiTi NiTi NiTi
12 18 17 ⫻ 25 18 17 ⫻ 25 18 8.75 18 10.87 16 18 17 ⫻ 25 18 17 ⫻ 25
128 ⫾ 5 310 ⫾ 12 432 ⫾ 17 167 ⫾ 4 212 ⫾ 14 92.0 ⫾ 8.1 82.4 ⫾ 2.5 82.7 ⫾ 5.4 80.1 ⫾ 3.4 57.1 ⫾ 1.5 76.7 ⫾ 7.1 86.7 ⫾ 6.3 50.3 ⫾ 1.2 37.7 ⫾ 0.3
1.72 ⫾ 0.07 1.89 ⫾ 0.07 1.54 ⫾ 0.06 1.12 ⫾ 0.02 1.01 ⫾ 0.07 2.37 ⫾ 0.21 2.12 ⫾ 0.07 1.95 ⫾ 0.13 1.89 ⫾ 0.08 0.44 ⫾ 0.01 0.49 ⫾ 0.05 0.31 ⫾ 0.02 0.36 ⫾ 0.01 0.18 ⫾ 0.00
—† —† —† —† —† —† —† —† —† 1.23‡ 1.59‡ 0.46‡ 1.12‡ 0.72‡
2.28 ⫾ 0.08 2.33 ⫾ 0.03 1.95 ⫾ 0.01 1.52 ⫾ 0.00 1.29 ⫾ 0.01 2.56 ⫾ 0.14 2.40 ⫾ 0.01 2.28 ⫾ 0.01 2.11 ⫾ 0.04 1.44 ⫾ 0.01 1.67 ⫾ 0.03 1.00 ⫾ 0.03 1.24 ⫾ 0.01 0.80 ⫾ 0.00
0.75 0.81 0.79 0.74 0.78 0.93 0.88 0.86 0.90 0.31 0.29 0.31 0.29 0.23
—† —† —† —† —† —† —† —† —† 0.85‡ 0.95‡ 0.46‡ 0.90‡ 0.90‡
*Data listed as mean ⫾ 1 SD. †Not tested. ‡Values calculated in Discussion section.
Young’s modulus of elasticity (E) based on stiffness measurements in 3-point bending and Itotal calculations*
Table VI.
Configuration Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Braided Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Braided
Alloy
Nominal dimensions (mil)
L1 (cm)
Stiffness ⫻ 105 (N-m2)
Itotal ⫻ 1017 (m4)
E (GPa)
SS SS SS SS SS SS Single-stranded SS core Coaxial SS core NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi
12 18 17 ⫻ 25† 17 ⫻ 25‡ 18 17 ⫻ 25‡ 8.75 10.87 16 16 18 18 17 ⫻ 25† 17 ⫻ 25† 17 ⫻ 25‡ 17 ⫻ 25‡ 18 17 ⫻ 25‡
0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 1.27 0.89 1.27 0.89 1.27 0.89 1.27 0.89 0.89
8.67 40.5 73.1 134 2.80 7.72 2.12 0.482 4.79 4.30 6.06 6.92 21.6 21.8 43.7 43.4 0.665 2.11
43.8 214 337 696 13.2 36.0§ 12.0 2.65 129 129 189 189 362 362 749 749 19.8 53.8§
198 190 217 193 212 196§ 177 182 37.0 33.3 32.1 36.7 59.6 60.2 58.4 57.9 33.6 34.5§
*For single-stranded rectangular wires, Itotal was assigned corresponding Ipoly value (see Table IV). †Tested in flatwise orientation. ‡Tested in edgewise orientation. §Values calculated in Discussion section.
DISCUSSION Superelasticity
Although the superelastic behavior of NiTi wires can easily be demonstrated in the laboratory, some
researchers speculate that these behaviors are rarely, if ever, achieved in clinical situations. For example, superelasticity has little or no clinical importance for torque applications because at least 45° of activation
American Journal of Orthodontics and Dentofacial Orthopedics Volume 122, Number 5
was required to show a deactivation plateau.9 In 3-point bending, Tonner and Waters10 found that superelastic wires required at least 2 mm of deflection to exhibit a plateau region; consequently, such wires can produce a reasonably constant force only when a tooth is grossly misaligned. In a similar study, Segner and Ibe11 showed that many superelastic archwires exhibit no superelastic properties or, at least, had no advantage over conventional NiTi materials. Wires that did show superelasticity required at least 1 mm of tooth displacement and a force level at the plateau region that was often above 4.9 N (⬵ 500 g). By simulating 1 and 2 mm malocclusions with 20° angulation, Schumacher et al12 measured maximum vertical forces of 3.8 N (⬵ 390 g).12 In the present study, the minimum tensile force that was required to reach a superelastic plateau (SP) equaled 37.7 N (⬵ 3850 g) for the braided NiTi wire (Table V). Admittedly, clinical applications result in more complex combinations of stresses (first and second order bending, third order torsion, and mesiodistal tension). However, in vivo studies13-15 suggest that either superelasticity was not demonstrated during the cases or NiTi wires that are behaving superelastically affect tooth migration no differently than conventional NiTi wires. Because the physical properties reported here assume linear elasticity, the data are correct only for the initial linear portion of the force-deflection curve, which apparently applies to most clinical situations. Nonetheless, generalizations can be made about the elastic properties of NiTi wires in the plateau region.
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Fig 3. Results of tensile tests. Strand dimension represents wire configuration, ie, overall wire diameter, outer strand diameter, or base dimension. Shown are 0.1% yield strengths (YS) for the SS (■) and NiTi (Œ) wires and ultimate tensile strengths (UTS) for SS (䊐) and NiTi (‚) wires. No correlation was evident between stress and strand dimension.
Strength
Regarding the YS (■, Œ) and UTS (䊐, ⌬) data for the SS and NiTi wires, respectively, no correlation existed between stress and strand dimension (Fig 3). The YS values of the NiTi wires were consistently lower than those of the SS wires, however. For each alloy, the braided wires had the lowest YS and UTS (Table V). Although the YS values of the NiTi wires indicated the initial force levels of each SP in tension (Table V), the true elastic behaviors of these wires were determined by incremental cyclic loading.22 One set of these tests is illustrated for the 16-mil NiTi wire when loaded 3 times to 1.31 GPa (Fig 4). In the first cycle, a portion of the austenitic (A) phase was transformed to the martensitic (M) phase through cold working. A second cycle further transformed the A phase and eliminated the SP; that is, a conventional NiTi wire was produced by the third loading cycle. For the 16-mil NiTi wire, a series of cyclic loading tests determined the EL (Fig 5), which equaled approximately EL/UTS ⫻ 100% ⫽ 1.23/1.44 ⫻ 100% ⫽ 85% of its UTS, versus the yield
Fig 4. Activation and deactivation curves for 16-mil superelastic NiTi wire. After applying 5 N preload to straighten sample, extensometer was mounted, and stress of 1.31 GPa was cyclically applied 3 times to same wire. On activation, stress-strain curve displayed linear elasticity in austenitic (A) and martensitic (M) regions; relatively constant force appeared in SP region. Because wire was activated above its elastic limit, permanent plastic deformation (ie, cold working) and loss of superelasticity occurred by third cycle.
stress (YS/UTS ⫻ 100% ⫽ 0.44/1.44 ⫻ 100% ⫽ 31%; Table V). Similarly for the 18-mil NiTi wire, EL equaled approximately 1.59/1.67 ⫻ 100% ⫽ 95% of its UTS versus the yield stress (0.49/1.67 ⫻ 100% ⫽
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Fig 5. Series of tests to determine elastic limit of 16-mil NiTi wire. At stress of 1.23 GPa or less, small amount of hysteresis after each cycle resulted from mechanical tolerances and some work of transformation. At stress of 1.31 GPa, substantial amount of hysteresis on first 2 cycles signified cold working (Fig 4). At stresses of 1.38 GPa or more, just 1 cycle transformed nearly all of A phase to M phase and thereby eliminated superelasticity. Based on these results, elastic limit was assigned 1.23 GPa, albeit true value is between 1.23 and 1.31 GPa.
29%; Table V). The round wires therefore had poor formability. In contrast, the rectangular NiTi wires had good formability with a EL/UTS ⫻ 100% ⫽ 0.46/ 1.00 ⫻ 100% ⫽ 46% (Table V). Because the braided (Fig 2, b, c, e, f) and coaxial NiTi wires were made from round strands, the EL values were assigned 90% of their corresponding UTS values (Table V). To compute each EPR, the stress at the proportional limit (Table I in Rucker and Kusy7) was assigned the corresponding EL for the NiTi wires and YS for the SS wires. For multistranded wires, choosing between the tensile properties of whole wires versus individual wire strands provides an interesting dilemma because both can be clinically important. The EPR values presented here are based on whole wire performance, which is most relevant when forces are distributed– eg, certain wire positions in bracket engagements and soft food boli during mastication. In contrast, strand strength is most important when considering concentrated forces such as those from the corners or edges of orthodontic appliances, opposing tooth cusps, or hard food boli. Modulus
Equation (2) can be rearranged to express Itotal as a function of wire stiffness by using a linear equation of the form Y ⫽ mX ⫹ B (ie, L13P/48␦n ⫽ EItotal ⫹ B).
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
For the SS wires (Table VI), the slope of the linear regression line, which equals E, had a slope of 196 GPa (Fig 6). An apparent Itotal can then be determined for the SS braided wire (Fig 1, group 3) from its wire stiffness value via the regression line equation. Substituting its wire stiffness of 7.72 ⫻ 10⫺5N-m2, the apparent Itotal value equals 36.0 ⫻ 10⫺17m4 in the edgewise orientation (Table VI). With the same nominal dimensions, the relative Itotal of the braided rectangular wire to the single-stranded rectangular wire equals (36.0/696) ⫻ 100% ⫽ 5.17% (Tables IV and VI). These findings compare favorably with previous relative Itotal values (admittedly for 8-strand braids) of 3% to 7% based on frictional measurements of archwires in elastic binding26 and Burstone’s materialstiffness numbers of 4% to 8%.27 For wires of equal length, the stiffness of this SS braided wire is more than 19 times less than a single-stranded SS wire with the same dimensions. Such a drastic decrease in stiffness is not intuitive based on a relative SG of 74.1% (Table III). The braided wire performs in flexure more like 9 independent strands rather than a cohesive group of strands (Fig 2, b and c). For the nylon-coated wires (Fig 1, groups 1 and 2), flexural tests in 3-point bending suggest E values that are 2 to 3 times higher than those of the SS cores alone. Because the load-deflection slopes of the corresponding coated and noncoated wires were indistinguishable in tensile tests, this discrepancy was caused presumably because the nylon compressed or adhered to the steel outer supports of the bending apparatus. Various lubricants did not correct this problem. The E of NiTi alloys reportedly equals 31 to 35 GPa for the M phase and 84 to 98 GPa for the A phase,28 and measurements using archwires typically vary between 33 and 55 GPa.23,29,30 When our stiffnesses were plotted against Itotal for the NiTi wires (Table VI), E equaled 34.5 GPa for the round wires (Œ) and 55.5 GPa for the rectangular wires (⌬) (Fig 7). X-ray diffractometry* identified the relative proportions of the A phase in 4 NiTi wire samples with a conventional NiTi wire as a control, which presumably represented 100% M phase (Fig 8). (See Tables 4.15 through 4.23 of Brantley and Eliades13 for related discussion.) Because the peaks of the 3 superelastic NiTi wires were similar, no correspondence existed between E and the presence of the A phase. Interestingly, in bending tests, the round superelastic wires had the same E as conventional NiTi wires, but, in tension, the E in the A region was clearly greater than in the M *The x-ray diffractometer (Model PW1729, Philips Analytical, Almelo, The Netherlands) had a Cu source, a Ni filter, a solid-state Si detector, and a 0.2-mm aperture slit, and operated at 50kV and 20mA.
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Fig 6. Flexural data of SS wires when distance between outer supports (L1) equaled 0.89cm. Slope of linear regression line equals Young’s Modulus of Elasticity (E), which was 196 GPa with probability, P ⬍ .001. For single-stranded rectangular wire, total area moments of inertia (Itotal) were assigned corresponding polygonal area moments of inertia (Ipoly.) (Table IV and Appendix). Itotal of braided wire cannot be calculated directly, so wire stiffness value from Table VI was substituted into linear regression line to find apparent Itotal value (see insert detailing bottom left corner of plot).
Fig 7. Flexural data of NiTi wires. Round (Œ) and rectangular (⌬) wires were tested when L1 equaled 0.89 or 1.27 cm. For round wires, E equaled 34.5 GPa with P ⬍ .01. Based on Ipoly. values for single-stranded rectangular wire (Table IV and Appendix), E equaled 55.5 GPa with P ⬍ .001. Apparent Itotal of braided wire was indirectly calculated with linear regression line for round wires (see insert detailing bottom left corner of plot).
region (Fig 4). Both techniques ideally should generate the same result for a homogeneous material. In tension, all material is tested under the same stress, whereas in bending a combination of tensile and compressive stresses is concentrated on the outer fibers of the wire. Accordingly, measurements of E in bending might be
affected by a heterogeneous distribution of phases and preferred orientation of crystals during fabrication. Because the NiTi braided wires were formed from round strands (Fig 2, e and f), the regression line for the round wires was used to find the apparent Itotal of the braided wire via the regression equation. Substituting
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Fig 8. Typical x-ray diffractometry data of 4 different NiTi archwires. A peak for (110) plane was essentially absent for conventional NiTi control, which was assumed to equal 100% M. On average, similar amounts of A were present in round, rectangular, and braided wires.
the wire stiffness of 2.11 ⫻ 10⫺5N-m2, the apparent Itotal value equals 53.8 ⫻ 10⫺17m4 in the edgewise orientation (Table VI). Compared with the singlestranded wire of the same nominal dimensions (Tables IV and VI), the relative Itotal is (53.8/749) ⫻ 100% ⫽ 7.18%. Elastic property ratios
The behaviors of superelastic NiTi wires can be divided into 3 distinct regions31 (Fig 9): (1) the A region in which the elastic properties can be predicted from linear elastic models, where the E measurements for these archwires typically vary from 33 to 55 GPa23,29,30; (2) the SP region in which wires deliver a nearly constant force over a span of strains or activations, the breadth of which depends on the initial content of the A phase (Fig 4); and (3) the M region in which the magnitudes of E should be less than those of the A region and typically equal 31 to 35 GPa.28 Here, the elastic behavior can be predicted by a linear elastic model, too. The EPR values in Table VII, which apply to the A region of Figure 9, were calculated by using the corresponding wire dimensions (Table I), strengths
Fig 9. Idealized activation and deactivation curves for superelastic NiTi wire. Slope of curve in A region is E, whereas Eeff. defines secant modulus of wire being deactivated from M region into SP region. In qualitative terms, Eeff. is identical to E at lower activations but decreases as wire traverses SP region. Quantifying Eeff. would require stress-strain data for particular wire and present amount of wire activation. Stiffness is inversely proportional to range, to which strain is related.
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Table VII.
Elastic property ratios (EPRs) of archwires versus 16-mil NiTi wire*
Archwire
EPRs
Group†
Configuration
Alloy
Nominal dimensions (mil)
EPRStrength
EPRStiffness
EPRRange
Control
Single-stranded
NiTi
16
1.0
1.0
1.0
1
Nylon-coated Coaxial Nylon-coated Coaxial Single-stranded Single-stranded
Coaxial SS core NiTi Single-stranded SS core SS NiTi SS
18 Wire 18 18 Wire 17.5 18 18
0.05 0.12 0.32 0.08 1.72 2.24
0.11 0.15 0.47 0.62 1.43 8.93
0.45 0.80 0.68 0.13 1.20 0.25
2
Nylon-coated Nylon-coated Single-stranded
Coaxial SS core Single-stranded SS core SS
10.9 Core 8.75 Core 12
0.05 0.32 0.62
0.11 0.47 1.91
0.45 0.68 0.32
3
Braided Braided Single-stranded Single-stranded
NiTi SS NiTi SS
17 ⫻ 25 17 ⫻ 25 17 ⫻ 25 17 ⫻ 25
0.16 0.15 1.38 4.39
0.41 1.55 9.58 29.6
0.39 0.10 0.14 0.15
*EPR values of rectangular wires were computed in edgewise orientation. †See Fig 1.
(Table IV), and E values (Table VI). In group 1 (Fig 1), the alternative wires had EPRStrength values from 0.05 to 0.32 (the last of which equaled only 32% of the 16-mil NiTi wire’s ability to resist permanent deformation), EPRStiffness values from 0.11 to 0.62, and EPRRange values from 0.13 to 0.80. Consequently for leveling treatments, the elastic properties of round multistranded wires are inferior to single-stranded NiTi wires. Compared with the 12-mil SS wire in group 2 (Fig 1), both nylon-coated wires had higher ranges at the cost of lower strengths (Table VII). This is representative of elastic properties as a function of size: a decrease in wire diameter generally results in a decrease in strength, a decrease in stiffness, and an increase in range. In group 3 (Fig 1), the braided wires had low strengths (EPRStrength ⬍ 0.17) and ranges (EPRRange ⬍ 0.40) (Table VII). Although the braided wires had substantially lower stiffnesses than the corresponding single-stranded rectangular wires, these stiffnesses most likely fall between those of 14-mil and 18-mil single-stranded NiTi wires. Overall, no alternative wire matched either the strength or the range of the single-stranded NiTi wires. Because in some cases NiTi wires might function superelastically, generalizations are needed to evaluate the elastic properties of strength, stiffness, and range when wires are operating in the SP region (Fig 9). First, the strengths of these materials are based on the limits of elastic behavior. Therefore, whether
operating in the SP region (a nonlinear elastic region) or exclusively in the A region (a linear elastic region), the strength of a wire remains proportional to YS for SS alloys and to EL for NiTi alloys. Second, the stiffnesses, which are proportional to E, are trivial in the SP region based on linear elastic models as these stiffnesses approach or equal zero. This dilemma can be addressed by assigning an apparent or effective E (Eeff.), which is defined by the slope of the line that connects the origin to a point on the deactivation curve in Figure 9. In clinical practice, this construction represents the mean value of stiffness (ie, the mean force per unit of deactivation achieved) that a tooth experiences. Quantifying Eeff. is challenging and requires knowledge of the forcedeflection characteristics and current deactivation of the wire. In clinical terms, Eeff. actually decreases as the amount of activation increases, ie, as the SP region is traversed. Third, the range increases as Eeff. decreases. Defining the range of NiTi wires in the SP region is not necessary, however, because more range than a clinician can use is often available– even in the A region. Fortunately, as the accuracy of the overall linear elastic model decreases, so does the likelihood that wires will be clinically used at these ranges. As a result, the present EPR values predict the behavior of superelastic NiTi wires for most clinical cases, too.
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CONCLUSIONS
evaluation of mechanical properties and comparison with titanium alloy alternatives. Angle Orthod 1987;57:18-32. Rucker BK, Kusy RP. Theoretical investigation of elastic flexural properties for multistranded orthodontic archwires. J Biomed Mater Res 2002;62:338-49. Rucker BK, Kusy RP. Elastic flexural properties of multistranded stainless steel versus conventional nickel titanium archwires. Angle Orthod 2002;72:302-9. Meling TR, Ødegaard J. On the variability of cross-sectional dimensions and torsional properties of rectangular nickel-titanium arch wires. Am J Orthod Dentofacial Orthop 1998;113: 546-57. Tonner RIM, Waters NE. The characteristics of super-elastic Ni-Ti wires in three-point bending. Part I: the effect of temperature. Eur J Orthod 1994;16:409-19. Segner D, Ibe D. Properties of superelastic wires and their relevance to orthodontic treatment. Eur J Orthod 1995;17:395402. Schumacher HA, Bourauel C, Drescher D. Deaktivirungverhalten und effektivitat verschiedener orthodontischer nivellierungsbogen– eine dynamische analyse der kraftsysteme. Fortschr Kieferorthop 1992;53:273-85. Brantley WA, Eliades T. Orthodontic materials: scientific and clinical aspects. Stuttgart (Germany): Thieme; 2001. p. 91-9. Evans TJW, Jones ML, Newcombe RG. Clinical comparison and performance perspective of three aligning arch wires. Am J Orthod Dentofacial Orthop 1998;114:32-9. Cobb HW III, Kula KS, Phillips C, Proffit WR. Efficiency of multi-strand steel, superelastic Ni-Ti and ion-implanted Ni-Ti archwires for initial alignment. Clin Orthod Res 1998;1:12-9. Sebanc J, Brantley WA, Pincsak JJ, Conover JP. Variability of effective root torque as a function of edge bevel on orthodontic arch wires. Am J Orthod 1984;86:43-50. Sernetz F. Der einflub der kantenverrundung auf das biegeverhalten orthodontischer vierkantdrahte. Kieferorthop 1998;12: 61-8. Siatkowski RE. Loss of anterior torque control due to variations in bracket slot and archwire dimensions. J Clin Orthod 1999;33: 508-10. Kusy RP, Mims L, Whitley JQ. Mechanical characteristics of various tempers of as-received cobalt-chromium archwires. Am J Orthod Dentofacial Orthop 2001;119:274-91. Harvey PD, editor. Engineering properties of steel. Metals Park (Ohio): American Society for Metals; 1982. p. 253-99. Jackson CM, Wagner HJ, Wasilewski RJ. 55-Ninitol–the alloy with a memory: its physical metallurgy, properties, and applications. Report SP 5110. Washington, D.C.: NASA; 1972. p. 23, 39. Greener EH, Harcourt JK, Lantenschlager EP. Materials science in dentistry. Baltimore: Williams & Wilkins; 1972. p. 47. Kusy RP, Stush AM. Geometric and material parameters of nickel-titanium and a beta-titanium orthodontic archwire alloy. Dent Mater 1987;3:207-17. Nielsen LE. Mechanical properties of polymers. New York: Reinhold; 1962. p. 7. Askeland DR. The science of engineering and materials. 3rd ed. Boston: PWS Publishing; 1994. p. 363, 498. Rucker BK, Kusy RP. Resistance to sliding of stainless steel multistranded archwires and comparison to single-stranded leveling wires. Am J Orthod Dentofacial Orthop 2002;122:73-83. Burstone CJ. Variable-modulus orthodontics. Am J Orthod 1981;80:1-16.
Compared with the elastic properties of singlestranded NiTi wires, none of the alternative leveling wires can compete. This outcome is independent of whether the wires are clinically operating in the austenitic region or in the SP region. Compared with the elastic properties of single-stranded SS wires, the alternative wires had low strengths, albeit sometimes superior stiffnesses and ranges. For NiTi wires, the elastic properties of strength and range are based on elastic limit measurements, which can be 3 to 4 times higher than the corresponding yield strengths. In the initial austenitic region, E is sometimes, as expected, higher for superelastic NiTi wires than for conventional NiTi wires. Consequently, for 2 wires with equal dimensions in bending, the superelastic NiTi wire might be stiffer than the conventional NiTi wire. Beveling and rounding of rectangular archwires can impact the flexural properties. For example, an 8% decrease in cross-sectional area (ie, 2% from each corner) results in nearly a 20% decrease in stiffness. In flexure, the braided wires behave more like small single-stranded wires that deflect independently than like a cohesively swaged, welded, or soldered collection of strands. Based on the present force levels of the SPs measured along with other reported bench and clinical findings, NiTi wires do not usually exhibit superelastic behaviors in vivo. Consequently, conventional NiTi wires often perform as well as superelastic NiTi wires. Under most situations, the elastic properties of superelastic NiTi wires might be based on linear elastic models. The authors thank Dr Nalin R. Parikh in the Department of Physics for the use of the x-ray diffractometer and SDS Ormco, GAC International, 3M Unitek, Highland Metals, American Orthodontics, Dentaurum, and Strite Industries Limited for wire donations.
7.
8.
9.
10.
11.
12.
13. 14.
15.
16.
17.
18.
19.
20. 21.
22. REFERENCES 1. Viazis AD. Atlas of advanced orthodontics. Philadelphia: W. B. Saunders; 1998. p. 51-2. 2. Thurow RC. Edgewise orthodontics. 4th ed. St Louis: Mosby; 1982. p. 46, 106. 3. Proffit WR. Contemporary orthodontics. 3rd ed. St Louis: Mosby; 2000. p. 528-9. 4. Kusy RP, Greenberg AR. Effects of composition and cross section on the elastic properties of orthodontic archwires. Angle Orthod 1981;51:325-41. 5. Kusy RP, Dilley GJ. Elastic property ratios of a triple-stranded stainless steel arch wire. Am J Orthod 1984;86:177-88. 6. Kusy RP, Stevens LE. Triple-stranded stainless steel wires:
23.
24. 25. 26.
27.
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28. Kusy RP. A review of contemporary archwires: their properties and characteristics. Angle Orthod 1997;67:197-208. 29. Tonner RIM, Waters NE. The characteristics of super-elastic Ni-Ti wires in three-point bending. Part II: intra-batch variation. Eur J Orthod 1994;16:421-5. 30. Asgharnia MK, Brantley WA. Comparison of bending and tension tests for orthodontic wires. Am J Orthod 1986;89:228-36. 31. Kousbroek R. Shape memory alloys. In Ducheyne P, Hastings GW, editors. Metal and ceramic biomaterials. Volume II: Strength and surface. Boca Raton (Fla): CRC Press; 1984. p. 73-4.
The area missing from the ideal rectangular crosssection is modeled by removing each corner defined by a square with side 2R minus a circle with radius R (Fig A). Based on the value of equation (A1) for a particular wire, a corresponding R is solved through iterations of the following equation: (Polygonal area)/(Rectanglular area) ⫽ [bh⫺(4R2⫺R2)]/(bh)⫽ [bh⫺R2(4⫺)]/(bh) (A2)
APPENDIX
Because rectangular archwires have beveled edges due to manufacturing techniques,2,9,16-18 the crosssectional areas of the resulting polygons are less than the actual rectangular dimensions (Fig 2). The polygonal shapes can be modeled by circumscribing a circle with radius R in a square on each corner of the rectangular cross-section (Fig A).19 Assuming a consistent cross-sectional shape over the length of the wire, the ratio of the calculated SG to the reported SG (as derived from the metallurgical literature) defines the ratio of the polygonal to the rectangular cross-sectional areas (Table III): relative SG ⫽(polygonal area)/(rectanglular area) (A1)
The R is then used to compute the area moments of inertia for the polygon (Ipoly.):19 Ipoly. ⫽ b3h/12 – 0.03018R4 – 0.8584R2(b/2 – 0.2234R)2 (A3) for wires in the flatwise orientation and Ipoly. ⫽ bh3/12 – 0.03018R4 – 0.8584R2(h/2 – 0.2234R)2 (A4) for wires in the edgewise orientation.
Fig A. Basic constructions to model polygonal shapes of actual crosssections of archwires having ideal nominal rectangular dimensions.
Elastic properties of alternative versus singlestranded leveling archwires Brian K. Rucker, BS,a and Robert P. Kusy, MS, PhDa-d Chapel Hill, NC The strength, stiffness, and range of single-stranded stainless steel (SS) and superelastic nickel-titanium (NiTi) archwires were compared with those of alternative leveling products, including nylon-coated and multistranded wires. Wire cross-sections were photographed after being potted in polymer, ground, and polished. Because the rectangular wires had rounded or beveled corners, gravimetric measurements and specific gravity calculations quantified the actual polygonal cross-sectional areas versus the ideal rectangular cross-sectional areas. Beveling reduced the cross-sectional areas by 7% to 8%; this decreased the wire stiffnesses by 15% to 19%. Using a testing machine, we measured the yield strengths, the elastic limits, and the ultimate tensile strengths in tension, and wire stiffnesses in 3-point bending. From cyclic loading tests, the elastic limits of the superelastic NiTi wires were approximately 90% and 45% of their ultimate tensile strengths for the round and rectangular wires, respectively. Using the measurements of the mechanical properties and geometric parameters of each wire, we computed the elastic property ratios (EPRs) versus a 16-mil (0.41 mm) NiTi wire. The single-stranded NiTi wires outperformed the alternative wires, whose EPRs varied from 0.05 to 0.32 for strength, from 0.11 to 1.55 for stiffness, and from 0.10 to 0.80 for range. Based on the current study and a review of the orthodontic literature, few superelastic wires are activated sufficiently in vivo to exhibit superelastic behavior. Therefore, the EPR data reported here for superelastic wires truly represent their performance in most clinical situations. (Am J Orthod Dentofacial Orthop 2002;122:528-41)
L
ight orthodontic forces produce the same amount of tooth movement as heavier forces and are physiologically more acceptable.1 Once forces were applied in the hundreds of grams, but today these forces probably are only tens of grams.2 For the initial leveling and aligning stages of orthodontic treatment, practitioners still use traditional archwires made from stainless steel (SS) or conventional nickel-titanium (NiTi) that is martensite stabilized. Additionally, pseudoelastic (so-called superelastic) NiTi alloys are engineered to provide a constant force during tooth movement. Alternative leveling products include multistranded NiTi wires that deliver ultra-low forces and esthetically pleasing products such as glass-fiber composites and polymer-coated wires. The ideal properties of leveling archwires include high strength to prevent permanent deformation, low From the University of North Carolina, Chapel Hill. a Department of Biomedical Engineering. b Department of Orthodontics. c Dental Research Center. d Curriculum in Applied and Material Sciences. Reprint requests to: Robert P. Kusy, University of North Carolina, Building 210-H, Room 313, Chapel Hill, NC 27599; e-mail, [email protected]. Submitted, January 2002; accepted, March 2002. Copyright © 2002 by the American Association of Orthodontists. 0889-5406/2002/$35.00 ⫹ 0 8/1/127292 doi:10.1067/mod.2002.127292
528
stiffness to deliver low forces per unit of deactivation, and high range to maximize activations.3 Because a decrease in stiffness is often accompanied by a decrease in strength, a practitioner typically selects a leveling archwire with the lowest stiffness that retains acceptable strength. The elastic properties of strength, stiffness, and range can be calculated for linear elastic materials (eg, SS) in single4 and multistranded5-8 configurations. To best aid the orthodontist in wire selection, these properties are reported as relative values called elastic property ratios (EPRs). Such EPRs are calculated versus a common wire; this permits comparing any 2 wires. With linear elastic models, the properties of conventional NiTi wires also were reported, although this alloy displays some nonlinear elastic behavior.8 However, EPR calculations for superelastic NiTi alloys might require redefining some terms in the earlier models. A survey of the properties of superelastic wires in vitro is necessary because some researchers concluded that few of these wires actually exhibit superelastic properties.9-12 Those laboratory findings were supported by clinical studies in which no significant differences of tooth migration were observed among superelastic NiTi wires, comparable conventional NiTi wires, and multistranded SS counterparts.13-15 The current study compares the EPRs of single-
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Fig 1. Wire inventory divided into 3 basic experimental groups: group 1 features wires with similar overall wire diameters; group 2 compares SS cores of polymer-coated wires with single-stranded SS wires; group 3 compares braided wire configurations with corresponding single-stranded wires. For these groups of SS and NiTi wires, EPRs were computed versus single-stranded 16-mil NiTi wire (not shown) (1 mil ⫽ 0.001 in ⫽ 0.0254 mm).
stranded SS and NiTi archwires to those of alternative leveling products that include nylon-coated SS wires and multistranded SS and NiTi wires. Gravimetric measurements and specific gravity calculations determine the actual cross-sectional areas and area moments of inertia for the archwires with nominal rectangular dimensions, many of which have rounded or beveled edges.2,9,16-18 Tensile tests measure the yield strengths, elastic limits, and ultimate tensile strengths; flexural tests measure the wire stiffnesses. The EPRs of each wire can be determined from the measurements of mechanical properties and geometric parameters. For the superelastic wires, the reported EPRs apply only to their behaviors in the initial linear elastic region. The tensile and flexural data will be considered alongside current findings in the orthodontic literature9-15 to
speculate how often superelastic wires demonstrate superelastic behavior in clinical settings. MATERIAL AND METHODS
Single-stranded SS and superelastic NiTi archwires provided controls for 3 basic experimental groups (Fig 1). The multistranded SS and superelastic NiTi archwires had coaxial and braided configurations (Table I). The coaxial configuration had 6 strands twisted around an inner strand (groups 1 and 2), and the braided configuration had 9 strands that were swaged into rectangular cross-sections (group 3). The configurations of the nylon-coated wires (groups 1 and 2) included 1 with a single-stranded SS core, marketed as an esthetic orthodontic wire, and 1 with a coaxial SS core, used elsewhere.
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Table I. Average dimensions for stainless steel (SS) and nickel titanium (NiTi) wires including overall wire diameter (D), inner strand diameter (di), outer strand diameter (do), helix angle (␣), base (b), and height (h) Actual dimensions* Configuration Single-stranded Single-stranded Single-stranded Coaxial Braided Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Coaxial Braided
Alloy
Nominal dimensions (mil)
SS SS SS SS SS Whole wire Single-stranded SS core Whole wire Coaxial SS core NiTi NiTi NiTi NiTi NiTi
12† 18‡ 17 ⫻ 25§ 17.5㛳 17 ⫻ 25† 18¶ 9¶ 18# 12# 16** 18** 17 ⫻ 25** 18†† 17 ⫻ 25†
D (mil)
di (mil)
do (mil)
12.10 17.98 18.05 17.47 8.75 17.87 10.87 15.86 17.43 17.55
7.14
5.27
3.39
3.74
5.82
6.21
␣ (°) 90 90 90 59.8 90 90 90 90 83.5 90 90 90 74.9 90
b (mil)
h (mil)
16.77
24.34
17.18
24.61
17.14
24.91
17.45
24.70
*1 mil ⫽ 0.001 inch ⫽ 0.0254 mm. †SDS Ormco, Glendora, Calif. ‡GAC International, Islandia, NY. §3M Unitek Corporation, Monrovia, Calif. 㛳Highland Metals, San Jose, Calif. ¶American Orthodontics, Sheboygan, Wis. #Rio Grande, Albuquerque, NM. **Dentaurum, Inc., Newtown, Pa. ††Strite Industries Limited, Cambridge, Ontario, Canada.
To determine archwire dimensions, we measured (⫾ 0.01 mil) each outer strand diameter (do) and axial displacement per twist of a wire strand (ᐉ*) at 5 locations using the optics of a Kentron microhardness tester (Kent Cliff Labs, Peekskill, NY). Each overall wire diameter (D), inner strand diameter (di), base (b), and height (h) were measured (⫾ 0.05 mil) 5 times with a digital micrometer (-Mate, Sony Magnescale America, Orange, Calif) (1 mil ⫽ 0.001 in ⫽ 0.0254 mm). The helix angles (␣) of the outer twisted strands were calculated by5,6 ␣ ⫽ tan⫺1{ᐉ*/[(D⫺do)]}
(1)
Cross-sectional geometries were determined by carefully cutting and potting small segments of archwires in epoxy or polyester resins. These specimen cylinders were ground with wet carbide papers and polished with levitated 1.0 and 0.3 m alumina. Each transverse section of wire was viewed with bright-field reflected light microscopy (Zeiss Universal Microscope, Oberkuchen, Germany) and photographed with Type 331 film (Polaroid-Land, Cambridge, Mass). For the gravimetric measurements and specific gravity (SG) calculations, each wire length was
measured (⫾ 0.5 mil) 5 times with calipers (Fowler Tools and Instruments, Boston, Mass). Samples were cleaned with methanol and weighed (⫾ 0.1 mg) 5 times with a digital balance (Sartorius, Goettingen, Germany). Because many rectangular archwires are fabricated by rolling round wire through a Turk’s head,16 the cross-sections of these wires have polygonal shapes in which the corners are rounded or beveled.2,9,16-18 Therefore, the ratio of the calculated SG (based on actual weight and rectangular dimensions) to the SG reported in the metallurgical literature was assumed to equal the ratio of the polygonal to the rectangular cross-sectional areas. By modeling the polygonal cross-sections,19 each polygonal area moment of inertia (Ipoly.) was calculated by using the corresponding relative SG, b, and h (Fig A and Appendix). The reported SG values are 7.965 g/cm3 for SS alloys typically used to produce archwires (eg, types 301, 302, 304, and 316L)20 and 6.50 g/cm3 for 55/45 NiTi.21 Tensile tests were conducted with a mechanical testing machine (Instron, Canton, Mass) with a 500-kg load cell and capstan grips at a 2 mm/min crosshead speed. Three samples were activated for each wire type. To measure the ultimate tensile strength (UTS), each
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Table II. Maximum force (P) and number of wires (n) simultaneously tested per distance between outer supports (L1) that meet the 3-point bending criteria
Alloy
Nominal dimensions (mil)
L1 (cm)
n
Maximum P (N)*
SS SS SS SS SS Single-stranded SS core Coaxial SS core NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi
12 18 17 ⫻ 25† 17 ⫻ 25‡ 17.5 8.75 10.87 16 16 18 18 17 ⫻ 25† 17 ⫻ 25† 17 ⫻ 25‡ 17 ⫻ 25‡ 18 18
0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 1.27 0.89 1.27 0.89 1.27 0.89 1.27 0.89 1.27
1 1 1 1 2 1 7 1 2 1 1 1 1 1 1 4
1.29 1.29 1.29 1.29 1.11 0.73 1.18 1.29 1.71 1.29 1.25 1.29 1.84 1.29 1.84 1.11
Configuration Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Coaxial
- Not possible -
*1N ⫽ 0.102 kg force. †Tested in flatwise orientation. ‡Tested in edgewise orientation.
sample was loaded to failure and the maximum stress noted. To measure the 0.1% yield strengths (YS), each sample was preloaded to 1 kg, mounted with a 1.27-cm 10% extensometer, and activated to failure. A best-fit line superposed these elastic traces, and parallel lines established the 0.1% yield points. The elastic limits (EL), which are the greatest stresses that materials can withstand without showing permanent sets after deactivation,22 were measured with a 1.27-cm 50% extensometer by cyclically activating the NiTi wires to a designated stress level and observing any signs of cold working (ie, permanent plastic deformation). With the same machine, wires were tested in 3-point bending with a distance between outer supports (L1) of 0.89 or 1.27 cm. With a 500-kg load cell with a 200-g full-scale sensitivity, the force-deflection curves were maintained at a slope of 45° to 75° by varying the crosshead speed and the chart paper speed. Each Young’s modulus (E) was calculated by23 E ⫽ L13P/48␦Itotaln
(2)
in which P, ␦, Itotal, and n are the force applied to the beam, the deflection of the activated beam, the total area moment of inertia, and the number of wires simultaneously tested, respectively. For the singlestranded wires, Itotal ⫽ D4/64. For the coaxial wires,7 Itotal ⫽ (di4 ⫹ 6do4 )/64 in which the helical spring
shape factor5,6 is ⫽ 2sin␣(2 ⫹ ␥cos2␣) and ␥ is Poisson’s ratio, which was assigned the values of 0.28 for SS24 and 0.34 for NiTi.21 At present, the Itotal for braided wires cannot be calculated directly because of strand asymmetry along the length. Due to the great difference between the physical properties of polymeric and metallic materials,25 only the SS cores of the nylon-coated wires were required to calculate the crosssectional area and Itotal for these wires. With custom software, the n and maximum P in equation (2) were calculated for each 3-point bending arrangement according to the following criteria: the total wire deflection was ⱕ 0.05L1, the wire deflection due to gravity was ⱕ 0.0005␦, and the machine deflection was ⱕ 0.005␦ (Table II).23 The n and maximum P values were calculated for the SS wires assuming E ⫽ 199 gigapascals (GPa)8 and for NiTi wires assuming E ⫽ 44.4 GPa.23 For the braided wires, the n and maximum P were estimated at 1 and 1 newton (N), respectively. Each EPR value was calculated versus a 16-mil NiTi wire and considered under the same testing arrangement—ie, the same clinical situation.4 By fitting a linear regression to each data set, a correlation coefficient was calculated (Lotus Freelance Graphics, Cambridge, Mass) to determine the statistical probability based on the number of data points.
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Fig 2. Cross-sections of rectangular archwires. Wires were transversely potted in polymer, ground, and polished. Based on calculated specific gravities of single-stranded SS (a) and NiTi (d) wires (Table III), between 1.7% and 2.0% of actual rectangular areas were missing from each corner. However, even the sides of NiTi wire (d) appear somewhat rounded. Strands of braided wires displayed various cross-sectional patterns, 2 examples of which are shown for the SS [(b) and (c)] and NiTi [(e) and (f)] wires, respectively. RESULTS
In general, the dimensional and weight measurements of wires were reported only as means because 1 SD was within about 3% of each corresponding mean. Specifically, the D, b, and h measurements were as much as 3.1% larger and 3.2% smaller than their corresponding nominal dimensions (Table I). The nylon-coated wires with a nominal D of 18 mil had 8.75-mil single-stranded SS cores or 10.87-mil coaxial SS cores (Fig 1, groups 1 and 2). For the single-stranded rectangular wires, the SS
wires appeared to fit the polygonal model (Fig A in Appendix) more accurately than the NiTi wires for which not only the corners but also the entire crosssections were rounded (Fig 2, top frames). Although the cross-sections of the braided wires varied along the length of the archwire, the strands of both alloys appeared to alternate between a few general wire configurations (Fig 2, middle and bottom frames). Beveling of the braided wires was not considered because neither the Itotal nor the Ipoly. of these wires was calculated from their dimensions.
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Table III.
Calculated specific gravities (SG) for round, rectangular, and braided archwires
Configuration
Alloy
Nominal dimensions (mil)
Single-stranded Single-stranded Braided Single-stranded Single-stranded Braided
SS SS SS NiTi NiTi NiTi
12 17 ⫻ 25 17 ⫻ 25 16 17 ⫻ 25 17 ⫻ 25
Actual dimensions (mil)
Length (in)
Weight (g)
Calculated SG (g/cm3)
Relative SG (%)*
12.07 16.91 ⫻ 24.52 17.39 ⫻ 24.43 15.97 17.20 ⫻ 25.02 17.55 ⫻ 24.76
11.4330 11.5278 2.0195 11.4507 11.5318 0.7763
0.1700 0.5801 0.0830 0.2427 0.4877 0.0271
7.930 7.406† 5.900† 6.457 5.997† 4.900†
99.6 93.0 74.1 99.3 92.3 75.4
*Relative SG ⫽ (calculated SG)/(reported SG) ⫻ 100% where reported SG of SS and NiTi alloys equal 7.965 g/cm3 and 6.50 g/cm3, respectively.20,21 †Calculated SG assumed actual rectangular dimensions. Table IV. Radius of rounded archwire corner (R) and area moments of inertia of polygonal (Ipoly.) versus rectangular (Itotal) cross-sections*
Configuration
Alloy
Nominal dimensions (mil)
Single-stranded Single-stranded Single-stranded Single-stranded
SS SS NiTi NiTi
17 ⫻ 25‡ 17 ⫻ 25§ 17 ⫻ 25‡ 17 ⫻ 25§
R (mil)
Ipoly. ⫻ 1017 (m4)
Itotal ⫻ 1017 (m4)
Relative I (%)†
5.78 5.78 6.19 6.19
337 696 362 749
398 839 435 919
84.6 83.0 83.3 81.5
*See Fig A and particularly eqs. (A3) and (A4) in Appendix. †Relative I ⫽ (Ipoly.)/(Itotal) ⫻ 100%. ‡Computed in flatwise orientation. §Computed in edgewise orientation.
Round, single-stranded SS and NiTi archwires were used as controls for making SG determinations because their cross-sectional areas are easily computed; both calculated SG values were within 0.7% of their reported values (Table III). For the single-stranded 17 ⫻ 25-mil SS wire, the relative SG of 93.0% suggested that 1.75% of the actual rectangular cross-sectional area was missing from each of the 4 corners (Figs 2, a, and A). By substituting the b and h (Table I) and relative SG (Table III) for this wire into equations (A3) and (A4) of the Appendix, the Ipoly. values were approximately 85% and 83% of the corresponding rectangular Itotal in the flatwise and edgewise orientations, respectively (Table IV). Similarly for the single-stranded 17 ⫻ 25-mil NiTi wire, the relative SG of 92.3% (Table III) suggested that approximately 1.93% of the actual rectangular cross-sectional area was missing from each corner (Figs 2, d, and A). The Ipoly. values for the NiTi wire were approximately 83% and 82% of the corresponding rectangular Itotal in the flatwise and edgewise orientations, respectively (equations (A3), (A4), and Table IV). The 9 strands of the SS and NiTi braided wires accounted for 74.1% and 75.4% of the areas defined by their rectangular dimensions, respectively (Fig 2, b, c, e, f, and Table III).
For the SS wires, YS varied from 1.01 to 2.37 GPa and UTS varied from 1.29 to 2.56 GPa (Table V). For the NiTi wires, YS varied from 0.18 to 0.49 GPa, and UTS varied from 0.80 to 1.67 GPa. The ratio of YS/UTS averaged 0.83 and 0.29 for the SS and NiTi wires, respectively. To compute the strengths of the rectangular and braided wires (Fig 1, group 3), the cross-sectional areas were based on the relative SG values (Table III). Although the nylon material was ignored in computing the cross-sectional areas of the coated wires (Fig 1, groups 1 and 2), the YS value of each coated versus uncoated wire agreed to within 1 SD. From the clinical perspective, the forces at the 0.1% yield points were listed, which equal YS times cross-sectional area (1 N ⬵ 100 g). To determine the E of the rectangular wires, each Itotal in Table VI was assigned the corresponding Ipoly. value (Table IV). When the SS wires were tested in a 3-point bending arrangement with L1 ⫽ 0.89 cm, E varied from 177 to 217 GPa. The NiTi wires were tested with L1 ⫽ 0.89 cm or with L1 ⫽ 1.27 cm, if they could meet the criteria detailed in the “Material and Methods” section (Table II). The individual E values of these NiTi wires varied from 32.1 to 60.2 GPa.
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Table V.
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
Forces at 0.1% yield point, 0.1% yield strengths (YS), elastic limit (EL), and ultimate tensile strengths
(UTS)
Configuration Single-stranded Single-stranded Single-stranded Coaxial Braided Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Coaxial Braided
Alloy
Nominal dimensions (mil)
Force at YS (N)*
YS (GPa)*
EL (GPa)
UTS (GPa)*
YS/UTS
EL/UTS
SS SS SS SS SS Whole wire Single-stranded SS core Whole wire Coaxial SS core NiTi NiTi NiTi NiTi NiTi
12 18 17 ⫻ 25 18 17 ⫻ 25 18 8.75 18 10.87 16 18 17 ⫻ 25 18 17 ⫻ 25
128 ⫾ 5 310 ⫾ 12 432 ⫾ 17 167 ⫾ 4 212 ⫾ 14 92.0 ⫾ 8.1 82.4 ⫾ 2.5 82.7 ⫾ 5.4 80.1 ⫾ 3.4 57.1 ⫾ 1.5 76.7 ⫾ 7.1 86.7 ⫾ 6.3 50.3 ⫾ 1.2 37.7 ⫾ 0.3
1.72 ⫾ 0.07 1.89 ⫾ 0.07 1.54 ⫾ 0.06 1.12 ⫾ 0.02 1.01 ⫾ 0.07 2.37 ⫾ 0.21 2.12 ⫾ 0.07 1.95 ⫾ 0.13 1.89 ⫾ 0.08 0.44 ⫾ 0.01 0.49 ⫾ 0.05 0.31 ⫾ 0.02 0.36 ⫾ 0.01 0.18 ⫾ 0.00
—† —† —† —† —† —† —† —† —† 1.23‡ 1.59‡ 0.46‡ 1.12‡ 0.72‡
2.28 ⫾ 0.08 2.33 ⫾ 0.03 1.95 ⫾ 0.01 1.52 ⫾ 0.00 1.29 ⫾ 0.01 2.56 ⫾ 0.14 2.40 ⫾ 0.01 2.28 ⫾ 0.01 2.11 ⫾ 0.04 1.44 ⫾ 0.01 1.67 ⫾ 0.03 1.00 ⫾ 0.03 1.24 ⫾ 0.01 0.80 ⫾ 0.00
0.75 0.81 0.79 0.74 0.78 0.93 0.88 0.86 0.90 0.31 0.29 0.31 0.29 0.23
—† —† —† —† —† —† —† —† —† 0.85‡ 0.95‡ 0.46‡ 0.90‡ 0.90‡
*Data listed as mean ⫾ 1 SD. †Not tested. ‡Values calculated in Discussion section.
Young’s modulus of elasticity (E) based on stiffness measurements in 3-point bending and Itotal calculations*
Table VI.
Configuration Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Braided Nylon-coated Nylon-coated Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Single-stranded Coaxial Braided
Alloy
Nominal dimensions (mil)
L1 (cm)
Stiffness ⫻ 105 (N-m2)
Itotal ⫻ 1017 (m4)
E (GPa)
SS SS SS SS SS SS Single-stranded SS core Coaxial SS core NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi NiTi
12 18 17 ⫻ 25† 17 ⫻ 25‡ 18 17 ⫻ 25‡ 8.75 10.87 16 16 18 18 17 ⫻ 25† 17 ⫻ 25† 17 ⫻ 25‡ 17 ⫻ 25‡ 18 17 ⫻ 25‡
0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 1.27 0.89 1.27 0.89 1.27 0.89 1.27 0.89 0.89
8.67 40.5 73.1 134 2.80 7.72 2.12 0.482 4.79 4.30 6.06 6.92 21.6 21.8 43.7 43.4 0.665 2.11
43.8 214 337 696 13.2 36.0§ 12.0 2.65 129 129 189 189 362 362 749 749 19.8 53.8§
198 190 217 193 212 196§ 177 182 37.0 33.3 32.1 36.7 59.6 60.2 58.4 57.9 33.6 34.5§
*For single-stranded rectangular wires, Itotal was assigned corresponding Ipoly value (see Table IV). †Tested in flatwise orientation. ‡Tested in edgewise orientation. §Values calculated in Discussion section.
DISCUSSION Superelasticity
Although the superelastic behavior of NiTi wires can easily be demonstrated in the laboratory, some
researchers speculate that these behaviors are rarely, if ever, achieved in clinical situations. For example, superelasticity has little or no clinical importance for torque applications because at least 45° of activation
American Journal of Orthodontics and Dentofacial Orthopedics Volume 122, Number 5
was required to show a deactivation plateau.9 In 3-point bending, Tonner and Waters10 found that superelastic wires required at least 2 mm of deflection to exhibit a plateau region; consequently, such wires can produce a reasonably constant force only when a tooth is grossly misaligned. In a similar study, Segner and Ibe11 showed that many superelastic archwires exhibit no superelastic properties or, at least, had no advantage over conventional NiTi materials. Wires that did show superelasticity required at least 1 mm of tooth displacement and a force level at the plateau region that was often above 4.9 N (⬵ 500 g). By simulating 1 and 2 mm malocclusions with 20° angulation, Schumacher et al12 measured maximum vertical forces of 3.8 N (⬵ 390 g).12 In the present study, the minimum tensile force that was required to reach a superelastic plateau (SP) equaled 37.7 N (⬵ 3850 g) for the braided NiTi wire (Table V). Admittedly, clinical applications result in more complex combinations of stresses (first and second order bending, third order torsion, and mesiodistal tension). However, in vivo studies13-15 suggest that either superelasticity was not demonstrated during the cases or NiTi wires that are behaving superelastically affect tooth migration no differently than conventional NiTi wires. Because the physical properties reported here assume linear elasticity, the data are correct only for the initial linear portion of the force-deflection curve, which apparently applies to most clinical situations. Nonetheless, generalizations can be made about the elastic properties of NiTi wires in the plateau region.
Rucker and Kusy 535
Fig 3. Results of tensile tests. Strand dimension represents wire configuration, ie, overall wire diameter, outer strand diameter, or base dimension. Shown are 0.1% yield strengths (YS) for the SS (■) and NiTi (Œ) wires and ultimate tensile strengths (UTS) for SS (䊐) and NiTi (‚) wires. No correlation was evident between stress and strand dimension.
Strength
Regarding the YS (■, Œ) and UTS (䊐, ⌬) data for the SS and NiTi wires, respectively, no correlation existed between stress and strand dimension (Fig 3). The YS values of the NiTi wires were consistently lower than those of the SS wires, however. For each alloy, the braided wires had the lowest YS and UTS (Table V). Although the YS values of the NiTi wires indicated the initial force levels of each SP in tension (Table V), the true elastic behaviors of these wires were determined by incremental cyclic loading.22 One set of these tests is illustrated for the 16-mil NiTi wire when loaded 3 times to 1.31 GPa (Fig 4). In the first cycle, a portion of the austenitic (A) phase was transformed to the martensitic (M) phase through cold working. A second cycle further transformed the A phase and eliminated the SP; that is, a conventional NiTi wire was produced by the third loading cycle. For the 16-mil NiTi wire, a series of cyclic loading tests determined the EL (Fig 5), which equaled approximately EL/UTS ⫻ 100% ⫽ 1.23/1.44 ⫻ 100% ⫽ 85% of its UTS, versus the yield
Fig 4. Activation and deactivation curves for 16-mil superelastic NiTi wire. After applying 5 N preload to straighten sample, extensometer was mounted, and stress of 1.31 GPa was cyclically applied 3 times to same wire. On activation, stress-strain curve displayed linear elasticity in austenitic (A) and martensitic (M) regions; relatively constant force appeared in SP region. Because wire was activated above its elastic limit, permanent plastic deformation (ie, cold working) and loss of superelasticity occurred by third cycle.
stress (YS/UTS ⫻ 100% ⫽ 0.44/1.44 ⫻ 100% ⫽ 31%; Table V). Similarly for the 18-mil NiTi wire, EL equaled approximately 1.59/1.67 ⫻ 100% ⫽ 95% of its UTS versus the yield stress (0.49/1.67 ⫻ 100% ⫽
536 Rucker and Kusy
Fig 5. Series of tests to determine elastic limit of 16-mil NiTi wire. At stress of 1.23 GPa or less, small amount of hysteresis after each cycle resulted from mechanical tolerances and some work of transformation. At stress of 1.31 GPa, substantial amount of hysteresis on first 2 cycles signified cold working (Fig 4). At stresses of 1.38 GPa or more, just 1 cycle transformed nearly all of A phase to M phase and thereby eliminated superelasticity. Based on these results, elastic limit was assigned 1.23 GPa, albeit true value is between 1.23 and 1.31 GPa.
29%; Table V). The round wires therefore had poor formability. In contrast, the rectangular NiTi wires had good formability with a EL/UTS ⫻ 100% ⫽ 0.46/ 1.00 ⫻ 100% ⫽ 46% (Table V). Because the braided (Fig 2, b, c, e, f) and coaxial NiTi wires were made from round strands, the EL values were assigned 90% of their corresponding UTS values (Table V). To compute each EPR, the stress at the proportional limit (Table I in Rucker and Kusy7) was assigned the corresponding EL for the NiTi wires and YS for the SS wires. For multistranded wires, choosing between the tensile properties of whole wires versus individual wire strands provides an interesting dilemma because both can be clinically important. The EPR values presented here are based on whole wire performance, which is most relevant when forces are distributed– eg, certain wire positions in bracket engagements and soft food boli during mastication. In contrast, strand strength is most important when considering concentrated forces such as those from the corners or edges of orthodontic appliances, opposing tooth cusps, or hard food boli. Modulus
Equation (2) can be rearranged to express Itotal as a function of wire stiffness by using a linear equation of the form Y ⫽ mX ⫹ B (ie, L13P/48␦n ⫽ EItotal ⫹ B).
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
For the SS wires (Table VI), the slope of the linear regression line, which equals E, had a slope of 196 GPa (Fig 6). An apparent Itotal can then be determined for the SS braided wire (Fig 1, group 3) from its wire stiffness value via the regression line equation. Substituting its wire stiffness of 7.72 ⫻ 10⫺5N-m2, the apparent Itotal value equals 36.0 ⫻ 10⫺17m4 in the edgewise orientation (Table VI). With the same nominal dimensions, the relative Itotal of the braided rectangular wire to the single-stranded rectangular wire equals (36.0/696) ⫻ 100% ⫽ 5.17% (Tables IV and VI). These findings compare favorably with previous relative Itotal values (admittedly for 8-strand braids) of 3% to 7% based on frictional measurements of archwires in elastic binding26 and Burstone’s materialstiffness numbers of 4% to 8%.27 For wires of equal length, the stiffness of this SS braided wire is more than 19 times less than a single-stranded SS wire with the same dimensions. Such a drastic decrease in stiffness is not intuitive based on a relative SG of 74.1% (Table III). The braided wire performs in flexure more like 9 independent strands rather than a cohesive group of strands (Fig 2, b and c). For the nylon-coated wires (Fig 1, groups 1 and 2), flexural tests in 3-point bending suggest E values that are 2 to 3 times higher than those of the SS cores alone. Because the load-deflection slopes of the corresponding coated and noncoated wires were indistinguishable in tensile tests, this discrepancy was caused presumably because the nylon compressed or adhered to the steel outer supports of the bending apparatus. Various lubricants did not correct this problem. The E of NiTi alloys reportedly equals 31 to 35 GPa for the M phase and 84 to 98 GPa for the A phase,28 and measurements using archwires typically vary between 33 and 55 GPa.23,29,30 When our stiffnesses were plotted against Itotal for the NiTi wires (Table VI), E equaled 34.5 GPa for the round wires (Œ) and 55.5 GPa for the rectangular wires (⌬) (Fig 7). X-ray diffractometry* identified the relative proportions of the A phase in 4 NiTi wire samples with a conventional NiTi wire as a control, which presumably represented 100% M phase (Fig 8). (See Tables 4.15 through 4.23 of Brantley and Eliades13 for related discussion.) Because the peaks of the 3 superelastic NiTi wires were similar, no correspondence existed between E and the presence of the A phase. Interestingly, in bending tests, the round superelastic wires had the same E as conventional NiTi wires, but, in tension, the E in the A region was clearly greater than in the M *The x-ray diffractometer (Model PW1729, Philips Analytical, Almelo, The Netherlands) had a Cu source, a Ni filter, a solid-state Si detector, and a 0.2-mm aperture slit, and operated at 50kV and 20mA.
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Rucker and Kusy 537
Fig 6. Flexural data of SS wires when distance between outer supports (L1) equaled 0.89cm. Slope of linear regression line equals Young’s Modulus of Elasticity (E), which was 196 GPa with probability, P ⬍ .001. For single-stranded rectangular wire, total area moments of inertia (Itotal) were assigned corresponding polygonal area moments of inertia (Ipoly.) (Table IV and Appendix). Itotal of braided wire cannot be calculated directly, so wire stiffness value from Table VI was substituted into linear regression line to find apparent Itotal value (see insert detailing bottom left corner of plot).
Fig 7. Flexural data of NiTi wires. Round (Œ) and rectangular (⌬) wires were tested when L1 equaled 0.89 or 1.27 cm. For round wires, E equaled 34.5 GPa with P ⬍ .01. Based on Ipoly. values for single-stranded rectangular wire (Table IV and Appendix), E equaled 55.5 GPa with P ⬍ .001. Apparent Itotal of braided wire was indirectly calculated with linear regression line for round wires (see insert detailing bottom left corner of plot).
region (Fig 4). Both techniques ideally should generate the same result for a homogeneous material. In tension, all material is tested under the same stress, whereas in bending a combination of tensile and compressive stresses is concentrated on the outer fibers of the wire. Accordingly, measurements of E in bending might be
affected by a heterogeneous distribution of phases and preferred orientation of crystals during fabrication. Because the NiTi braided wires were formed from round strands (Fig 2, e and f), the regression line for the round wires was used to find the apparent Itotal of the braided wire via the regression equation. Substituting
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Fig 8. Typical x-ray diffractometry data of 4 different NiTi archwires. A peak for (110) plane was essentially absent for conventional NiTi control, which was assumed to equal 100% M. On average, similar amounts of A were present in round, rectangular, and braided wires.
the wire stiffness of 2.11 ⫻ 10⫺5N-m2, the apparent Itotal value equals 53.8 ⫻ 10⫺17m4 in the edgewise orientation (Table VI). Compared with the singlestranded wire of the same nominal dimensions (Tables IV and VI), the relative Itotal is (53.8/749) ⫻ 100% ⫽ 7.18%. Elastic property ratios
The behaviors of superelastic NiTi wires can be divided into 3 distinct regions31 (Fig 9): (1) the A region in which the elastic properties can be predicted from linear elastic models, where the E measurements for these archwires typically vary from 33 to 55 GPa23,29,30; (2) the SP region in which wires deliver a nearly constant force over a span of strains or activations, the breadth of which depends on the initial content of the A phase (Fig 4); and (3) the M region in which the magnitudes of E should be less than those of the A region and typically equal 31 to 35 GPa.28 Here, the elastic behavior can be predicted by a linear elastic model, too. The EPR values in Table VII, which apply to the A region of Figure 9, were calculated by using the corresponding wire dimensions (Table I), strengths
Fig 9. Idealized activation and deactivation curves for superelastic NiTi wire. Slope of curve in A region is E, whereas Eeff. defines secant modulus of wire being deactivated from M region into SP region. In qualitative terms, Eeff. is identical to E at lower activations but decreases as wire traverses SP region. Quantifying Eeff. would require stress-strain data for particular wire and present amount of wire activation. Stiffness is inversely proportional to range, to which strain is related.
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Table VII.
Elastic property ratios (EPRs) of archwires versus 16-mil NiTi wire*
Archwire
EPRs
Group†
Configuration
Alloy
Nominal dimensions (mil)
EPRStrength
EPRStiffness
EPRRange
Control
Single-stranded
NiTi
16
1.0
1.0
1.0
1
Nylon-coated Coaxial Nylon-coated Coaxial Single-stranded Single-stranded
Coaxial SS core NiTi Single-stranded SS core SS NiTi SS
18 Wire 18 18 Wire 17.5 18 18
0.05 0.12 0.32 0.08 1.72 2.24
0.11 0.15 0.47 0.62 1.43 8.93
0.45 0.80 0.68 0.13 1.20 0.25
2
Nylon-coated Nylon-coated Single-stranded
Coaxial SS core Single-stranded SS core SS
10.9 Core 8.75 Core 12
0.05 0.32 0.62
0.11 0.47 1.91
0.45 0.68 0.32
3
Braided Braided Single-stranded Single-stranded
NiTi SS NiTi SS
17 ⫻ 25 17 ⫻ 25 17 ⫻ 25 17 ⫻ 25
0.16 0.15 1.38 4.39
0.41 1.55 9.58 29.6
0.39 0.10 0.14 0.15
*EPR values of rectangular wires were computed in edgewise orientation. †See Fig 1.
(Table IV), and E values (Table VI). In group 1 (Fig 1), the alternative wires had EPRStrength values from 0.05 to 0.32 (the last of which equaled only 32% of the 16-mil NiTi wire’s ability to resist permanent deformation), EPRStiffness values from 0.11 to 0.62, and EPRRange values from 0.13 to 0.80. Consequently for leveling treatments, the elastic properties of round multistranded wires are inferior to single-stranded NiTi wires. Compared with the 12-mil SS wire in group 2 (Fig 1), both nylon-coated wires had higher ranges at the cost of lower strengths (Table VII). This is representative of elastic properties as a function of size: a decrease in wire diameter generally results in a decrease in strength, a decrease in stiffness, and an increase in range. In group 3 (Fig 1), the braided wires had low strengths (EPRStrength ⬍ 0.17) and ranges (EPRRange ⬍ 0.40) (Table VII). Although the braided wires had substantially lower stiffnesses than the corresponding single-stranded rectangular wires, these stiffnesses most likely fall between those of 14-mil and 18-mil single-stranded NiTi wires. Overall, no alternative wire matched either the strength or the range of the single-stranded NiTi wires. Because in some cases NiTi wires might function superelastically, generalizations are needed to evaluate the elastic properties of strength, stiffness, and range when wires are operating in the SP region (Fig 9). First, the strengths of these materials are based on the limits of elastic behavior. Therefore, whether
operating in the SP region (a nonlinear elastic region) or exclusively in the A region (a linear elastic region), the strength of a wire remains proportional to YS for SS alloys and to EL for NiTi alloys. Second, the stiffnesses, which are proportional to E, are trivial in the SP region based on linear elastic models as these stiffnesses approach or equal zero. This dilemma can be addressed by assigning an apparent or effective E (Eeff.), which is defined by the slope of the line that connects the origin to a point on the deactivation curve in Figure 9. In clinical practice, this construction represents the mean value of stiffness (ie, the mean force per unit of deactivation achieved) that a tooth experiences. Quantifying Eeff. is challenging and requires knowledge of the forcedeflection characteristics and current deactivation of the wire. In clinical terms, Eeff. actually decreases as the amount of activation increases, ie, as the SP region is traversed. Third, the range increases as Eeff. decreases. Defining the range of NiTi wires in the SP region is not necessary, however, because more range than a clinician can use is often available– even in the A region. Fortunately, as the accuracy of the overall linear elastic model decreases, so does the likelihood that wires will be clinically used at these ranges. As a result, the present EPR values predict the behavior of superelastic NiTi wires for most clinical cases, too.
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CONCLUSIONS
evaluation of mechanical properties and comparison with titanium alloy alternatives. Angle Orthod 1987;57:18-32. Rucker BK, Kusy RP. Theoretical investigation of elastic flexural properties for multistranded orthodontic archwires. J Biomed Mater Res 2002;62:338-49. Rucker BK, Kusy RP. Elastic flexural properties of multistranded stainless steel versus conventional nickel titanium archwires. Angle Orthod 2002;72:302-9. Meling TR, Ødegaard J. On the variability of cross-sectional dimensions and torsional properties of rectangular nickel-titanium arch wires. Am J Orthod Dentofacial Orthop 1998;113: 546-57. Tonner RIM, Waters NE. The characteristics of super-elastic Ni-Ti wires in three-point bending. Part I: the effect of temperature. Eur J Orthod 1994;16:409-19. Segner D, Ibe D. Properties of superelastic wires and their relevance to orthodontic treatment. Eur J Orthod 1995;17:395402. Schumacher HA, Bourauel C, Drescher D. Deaktivirungverhalten und effektivitat verschiedener orthodontischer nivellierungsbogen– eine dynamische analyse der kraftsysteme. Fortschr Kieferorthop 1992;53:273-85. Brantley WA, Eliades T. Orthodontic materials: scientific and clinical aspects. Stuttgart (Germany): Thieme; 2001. p. 91-9. Evans TJW, Jones ML, Newcombe RG. Clinical comparison and performance perspective of three aligning arch wires. Am J Orthod Dentofacial Orthop 1998;114:32-9. Cobb HW III, Kula KS, Phillips C, Proffit WR. Efficiency of multi-strand steel, superelastic Ni-Ti and ion-implanted Ni-Ti archwires for initial alignment. Clin Orthod Res 1998;1:12-9. Sebanc J, Brantley WA, Pincsak JJ, Conover JP. Variability of effective root torque as a function of edge bevel on orthodontic arch wires. Am J Orthod 1984;86:43-50. Sernetz F. Der einflub der kantenverrundung auf das biegeverhalten orthodontischer vierkantdrahte. Kieferorthop 1998;12: 61-8. Siatkowski RE. Loss of anterior torque control due to variations in bracket slot and archwire dimensions. J Clin Orthod 1999;33: 508-10. Kusy RP, Mims L, Whitley JQ. Mechanical characteristics of various tempers of as-received cobalt-chromium archwires. Am J Orthod Dentofacial Orthop 2001;119:274-91. Harvey PD, editor. Engineering properties of steel. Metals Park (Ohio): American Society for Metals; 1982. p. 253-99. Jackson CM, Wagner HJ, Wasilewski RJ. 55-Ninitol–the alloy with a memory: its physical metallurgy, properties, and applications. Report SP 5110. Washington, D.C.: NASA; 1972. p. 23, 39. Greener EH, Harcourt JK, Lantenschlager EP. Materials science in dentistry. Baltimore: Williams & Wilkins; 1972. p. 47. Kusy RP, Stush AM. Geometric and material parameters of nickel-titanium and a beta-titanium orthodontic archwire alloy. Dent Mater 1987;3:207-17. Nielsen LE. Mechanical properties of polymers. New York: Reinhold; 1962. p. 7. Askeland DR. The science of engineering and materials. 3rd ed. Boston: PWS Publishing; 1994. p. 363, 498. Rucker BK, Kusy RP. Resistance to sliding of stainless steel multistranded archwires and comparison to single-stranded leveling wires. Am J Orthod Dentofacial Orthop 2002;122:73-83. Burstone CJ. Variable-modulus orthodontics. Am J Orthod 1981;80:1-16.
Compared with the elastic properties of singlestranded NiTi wires, none of the alternative leveling wires can compete. This outcome is independent of whether the wires are clinically operating in the austenitic region or in the SP region. Compared with the elastic properties of single-stranded SS wires, the alternative wires had low strengths, albeit sometimes superior stiffnesses and ranges. For NiTi wires, the elastic properties of strength and range are based on elastic limit measurements, which can be 3 to 4 times higher than the corresponding yield strengths. In the initial austenitic region, E is sometimes, as expected, higher for superelastic NiTi wires than for conventional NiTi wires. Consequently, for 2 wires with equal dimensions in bending, the superelastic NiTi wire might be stiffer than the conventional NiTi wire. Beveling and rounding of rectangular archwires can impact the flexural properties. For example, an 8% decrease in cross-sectional area (ie, 2% from each corner) results in nearly a 20% decrease in stiffness. In flexure, the braided wires behave more like small single-stranded wires that deflect independently than like a cohesively swaged, welded, or soldered collection of strands. Based on the present force levels of the SPs measured along with other reported bench and clinical findings, NiTi wires do not usually exhibit superelastic behaviors in vivo. Consequently, conventional NiTi wires often perform as well as superelastic NiTi wires. Under most situations, the elastic properties of superelastic NiTi wires might be based on linear elastic models. The authors thank Dr Nalin R. Parikh in the Department of Physics for the use of the x-ray diffractometer and SDS Ormco, GAC International, 3M Unitek, Highland Metals, American Orthodontics, Dentaurum, and Strite Industries Limited for wire donations.
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22. REFERENCES 1. Viazis AD. Atlas of advanced orthodontics. Philadelphia: W. B. Saunders; 1998. p. 51-2. 2. Thurow RC. Edgewise orthodontics. 4th ed. St Louis: Mosby; 1982. p. 46, 106. 3. Proffit WR. Contemporary orthodontics. 3rd ed. St Louis: Mosby; 2000. p. 528-9. 4. Kusy RP, Greenberg AR. Effects of composition and cross section on the elastic properties of orthodontic archwires. Angle Orthod 1981;51:325-41. 5. Kusy RP, Dilley GJ. Elastic property ratios of a triple-stranded stainless steel arch wire. Am J Orthod 1984;86:177-88. 6. Kusy RP, Stevens LE. Triple-stranded stainless steel wires:
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28. Kusy RP. A review of contemporary archwires: their properties and characteristics. Angle Orthod 1997;67:197-208. 29. Tonner RIM, Waters NE. The characteristics of super-elastic Ni-Ti wires in three-point bending. Part II: intra-batch variation. Eur J Orthod 1994;16:421-5. 30. Asgharnia MK, Brantley WA. Comparison of bending and tension tests for orthodontic wires. Am J Orthod 1986;89:228-36. 31. Kousbroek R. Shape memory alloys. In Ducheyne P, Hastings GW, editors. Metal and ceramic biomaterials. Volume II: Strength and surface. Boca Raton (Fla): CRC Press; 1984. p. 73-4.
The area missing from the ideal rectangular crosssection is modeled by removing each corner defined by a square with side 2R minus a circle with radius R (Fig A). Based on the value of equation (A1) for a particular wire, a corresponding R is solved through iterations of the following equation: (Polygonal area)/(Rectanglular area) ⫽ [bh⫺(4R2⫺R2)]/(bh)⫽ [bh⫺R2(4⫺)]/(bh) (A2)
APPENDIX
Because rectangular archwires have beveled edges due to manufacturing techniques,2,9,16-18 the crosssectional areas of the resulting polygons are less than the actual rectangular dimensions (Fig 2). The polygonal shapes can be modeled by circumscribing a circle with radius R in a square on each corner of the rectangular cross-section (Fig A).19 Assuming a consistent cross-sectional shape over the length of the wire, the ratio of the calculated SG to the reported SG (as derived from the metallurgical literature) defines the ratio of the polygonal to the rectangular cross-sectional areas (Table III): relative SG ⫽(polygonal area)/(rectanglular area) (A1)
The R is then used to compute the area moments of inertia for the polygon (Ipoly.):19 Ipoly. ⫽ b3h/12 – 0.03018R4 – 0.8584R2(b/2 – 0.2234R)2 (A3) for wires in the flatwise orientation and Ipoly. ⫽ bh3/12 – 0.03018R4 – 0.8584R2(h/2 – 0.2234R)2 (A4) for wires in the edgewise orientation.
Fig A. Basic constructions to model polygonal shapes of actual crosssections of archwires having ideal nominal rectangular dimensions.