INTRODUCTION

During the early leveling stages of orthodontic treatment, more physiologically acceptable tooth movement can be achieved if light, continuous forces are used rather than heavier, intermittent forces.1 Low-stiffness wires are used to deliver these light forces, typically single-stranded nickel titanium (NiTi) wires or multistranded stainless steel (SS) wires. Linearly elastic materials that include SS and conventional NiTi, which is stabilized martensite, deliver forces that are proportional to the amount of activation.2 These forces decrease as the teeth move and the wires deactivate. Alternatively, pseudoelastic (so-called “superelastic”) NiTi archwires are now available3 that deliver a nearly constant force over a span of activations—ideally those that occur between office visits. However, some superelastic NiTi products have tested comparable to conventional NiTi wires,4 and only in certain instances have superelastic NiTi wires significantly outperformed multistranded SS wires in clinical trials.3 As the properties of NiTi alloys are dependent on small changes in composition, Bourauel et al5 found that superelastic NiTi appliances from the same package displayed extreme changes in force delivery. Consequently, some practitioners do not employ superelastic wires during orthodontic treatment; instead, they use the more traditional and proven leveling tools of conventional NiTi and multistranded SS wires.

A recent investigation that modeled the elastic properties (ie, strength, stiffness, and range) of linearly elastic archwires found that: (1) the three-strand twisted and coaxial wire configurations indeed attain the best elastic properties among basic multistranded geometries, and (2) multistranded SS archwires often matched the elastic properties of conventional NiTi leveling wires.6 These findings were based on several assumptions, two of which were that there was no strand interaction (eg, interstrand friction) during flexure and that the stress at the proportional limit, which represents the limit of the elastic region, followed the theoretical values for SS and conventional NiTi alloys as defined in the metallurgical literature.7 These important assumptions must be properly addressed to ensure the validity of the model and to accurately compare the elastic properties of currently available leveling wires.

In the present investigation flexural tests were performed to compare the measured and calculated stiffnesses of the multistranded wires. A strong correlation indicated that strand interaction was negligible and that Young's modulus of elasticity (E) for SS was correct and indeed constant for even the heavily drawn strands of coaxial wires. This data was combined with known E data for conventional NiTi wires.8 The 0.1% yield strengths (σ_YS), which approximate the proportional limits, were measured for the SS wires and wire strands. Since σ_YS can be considerably affected by drawing ratios and thermal history,9 the σ_YS values for the individual wire strands may be considerably different from those of the larger single-stranded wires. Although the reported values and techniques for measuring the σ_YS for conventional NiTi wires vary substantially,10–12 proper evaluations for NiTi alloys require cyclic loading.13,14 After verifying the assumptions of the model with the results of these tests, the E, σ_YS, and geometric parameters for each archwire were used to compare the measured properties of commercial leveling wires to their theoretical values. Specific clinical questions were then addressed by determining whether the multistranded SS wires had geometric and physical properties that maximized their effectiveness as leveling appliances, and whether improvements were required in order for the multistranded SS wires to compete with conventional NiTi wires.

MATERIALS AND METHODS

Three-stranded (triple) and six-stranded coaxial (coax) SS archwires, each from four manufacturers, were compared to single-stranded (single) SS and conventional NiTi leveling wires.

Each outer strand diameter (d_o) and axial displacement per twist of a wire strand (ℓ*) was measured (± 0.01 mil) at five locations using the optics of a Kentron microhardness tester (Kent Cliff Labs, Peekskill, New York) (Figure 1). Each inner strand diameter (d_i) and overall wire diameter (D) was measured (± 0.05 mil) at five locations using a digital micrometer (μ–Mate; Sony Magnescale America Inc, Orange, Calif). The helix angles (α) of the outer twisted strands were calculated by equation 112:

View Figure

• Download as Powerpoint
• Download Figure

Using an Instron mechanical testing machine (Instron Corp, Canton, Mass) in a three-point bending arrangement, the triple wires were tested with a distance between outer supports (L₁) of 12.5 mm and the coax wires were tested with L₁ = 8.9 and 12.5 mm (cf, Figure 1). The force-deflection curves were maintained at a slope of 45 degrees to 75 degrees using a 500 kg load cell with a 200 g full-scale sensitivity. Each E was calculated by equation 212:

in which P, δ, I_total, and n are the force applied to the beam, the deflection of the beam under load, the total area moment of inertia, and the number of wires simultaneously tested, respectively. Note that equation 2 assumes no strand interaction and applies only to linear elastic materials. For the triple wires,12 I_total = 3d_o⁴κπ/64 in which the helical spring shape factor is κ = 2sinα/(2 + γcos²α) and γ is Poisson's ratio, which is assigned the value of 0.28 for SS.15 For the coax wires,6 I_total = (d_i⁴ + 5d_o⁴κ)π/64. The n and maximum P in equation (2) were governed by the following criteria: the total wire deflection was ≤ 0.05L₁; the wire deflection due to gravity was ≤ 0.0005δ; and, the machine deflection was ≤ 0.005δ.8

Tensile tests were conducted with the Instron machine using a 500 kg load cell, capstan grips with a nip-to-nip distance of 60 mm, and a 2 mm/min crosshead speed. Three samples were tested for each wire type and the results averaged. To measure the ultimate tensile strength (σ_UTS), each sample was loaded to failure and the maximum stress was noted. To measure the 0.1% yield stress (σ_YS), each sample was preloaded to 1kg, mounted with a 12.5 mm extensometer that was capable of a 10% maximum strain and loaded to failure. The extensometer was attached to only the single wires and the straight inner strands of the coax wires, since straightening the twisted stands of the triple wires could alter their tensile properties. A best-fit line was drawn over the elastic loading trace and a parallel line was drawn to establish the 0.1% yield point. To measure the elastic limit (σ_EL), which is the greatest stress a material can withstand without showing any permanent set when the load is removed,14 the NiTi wires were preloaded, mounted with the extensometer and cyclically loaded to a specific stress until evidence of cold-working (ie, plastic deformation) was observed. A new as-received wire was used for each iteration.

After a linear regression was fitted to the experimental data using statistical software, the corresponding correlation coefficient and the number of data points determined a probability.

RESULTS

The α values averaged 72° and 54° for the triple and coax wires, respectively, and varied from 49° to 82° (Table 1). Note that α = 90 degrees for single wires.

TABLE 1. Helix Angles (α) of Stainless Steel Archwires*

View Fullscreen

The d_i, d_o, σ_YS, and σ_UTS values were reported as only mean values because their standard deviations were < 5% of each mean (Table 2). For the coax wires, the d_i values were up to 40% larger but only 3% smaller than the corresponding d_o values.

TABLE 2. The Diameters of the Inner (d_i) and Outer (d_o) Strands, 0.1% Yield Stresses (σ_YS), and Ultimate Tensile Strengths (σ_UTS) of Single-Stranded, Triple, and Coax Stainless Steel Archwires*

View Fullscreen

When flexural tests were performed on 38 coax and triple wires (Figure 2), the slope of the linear regression line (E = 199 GPa) had a high correlation coefficient (r = .99) and a highly significant probability (P < .001). This data appeared to be independent of both wire configuration and L₁.

View Figure

• Download as Powerpoint
• Download Figure

For the SS wires, σ_YS varied from 1.41 to 2.34 GPa, and the σ_UTS values varied from 1.51 to 2.68 GPa (cf, Table 2). Neither the σ_YS nor σ_UTS values strongly correlated with strand diameter (ie, d_i for the single or coax wires and d_o for the triple wires (Figure 3, top frames). The ratio of σ_YS to σ_UTS averaged 0.81 for the single wires and 0.88 for the coax wires.

View Figure

• Download as Powerpoint
• Download Figure

For the NiTi wires, the σ_EL values that averaged 1.10 GPa were as much as 80% higher than the corresponding σ_YS determinations (Table 3). The σ_EL values did not strongly correlate with strand diameter, and the σ_UTS values were nearly constant (cf, Figure 3, bottom frames). To measure the σ_EL of the 16 mil NiTi wires (Figure 4), plastic deformation was not evident when a wire was cyclically loaded four times to 1.19 GPa. When a new wire was tested at 1.23 GPa or higher, deformation was conspicuous on the first cycle, whereas the next three cycles showed the smaller and relatively constant amounts of hysteresis due to mechanical testing. For conventional NiTi wires in tension, both the stress (related to the strength property) and strain (related to the range property) are substantially higher for σ_EL than for σ_YS (Figure 5).

TABLE 3. The d_i, σ_YS, σ_EL*, and σ_UTS of Single Conventional Nickel Titanium Archwires†

View Fullscreen

View Figure

• Download as Powerpoint
• Download Figure

View Figure

• Download as Powerpoint
• Download Figure

DISCUSSION

Elastic property ratios

For the SS wires, the elastic property ratios (EPRs) were initially calculated (Table 4) using the corresponding α (cf, Table 1) and σ_YS (cf, Table 2) values and E was assigned the value of 199 GPa (cf, Figure 2). The σ_YS values were used to estimate the σ_PL values (see Table 16). Previous work showed that the ratio of σ_YS/σ_UTS for SS wires generally increased as the strand diameter decreased (eg, 70% to 80% for single wires).16 Since here the ratio of σ_YS/σ_UTS averaged 0.81 and 0.88 for single and coax wires, respectively (cf, Table 2), the σ_YS of each triple wire was assigned 85% of the average σ_UTS of the wire's strands. The EPRs for the SS wires were averaged among manufacturers for each wire size and type. To compute the EPRs of the conventional NiTi wires, the σ_EL values were used to estimate the σ_PL values and E was assigned the value of 44.4 GPa.8 Because stiffness is often the first consideration in wire selection,17,18 wires in Table 4 are listed by increasing stiffness. The multistranded wires had EPR_Stiffness values that varied from 0.27 (coax 15.5 mil wire) to 1.9 (triple 21.5 mil wire); that is, the multistranded wires had from approximately one-third to twice the stiffness of a 16 mil NiTi wire. All multistranded wires that had stiffnesses lower than a 16 mil NiTi wire (EPR_Stiffness ≤1.0) had low strengths (EPR_Strength ≤0.31). The ranges of the multistranded wires (0.24 ≤EPR_Range ≤0.43) were basically no higher than that of the single 12 or 14 mil SS wires. Separate nomograms are plotted for each nominal diameter to compare visually the performances of commercial triple and coax SS wires to alternative leveling archwires (Figures 6–9). For the same D, the coax wire had noticeably lower stiffness and strength than the triple wire.

TABLE 4. Average Elastic Property Ratios (EPRs) of Commercial SS and Conventional NiTi Archwires Versus a NiTi 16 mil Wire*

View Fullscreen

View Figure

• Download as Powerpoint
• Download Figure

Previous findings

Regarding strength, the σ_YS of wires can differ noticeably between manufacturers and even between wire sizes within a product line due to strain hardening during the wire-drawing process.9 Based on various modes of bending and tensile tests performed on as-received products, σ_YS averaged 1.95 GPa and E averaged 188 GPa for SS archwire111619–21; whereas, σ_YS averaged 0.45 GPa and E averaged 37 GPa for NiTi archwires.810,11 About a three-fold increase was noted between the current σ_EL values (Table 3) and these reported σ_YS values for NiTi. This discrepancy arises because previous investigators measured the yield strengths assuming that conventional NiTi follows linear elasticity.

Regarding stiffness, several archwires have been studied by various investigators.171822,23 Each column in Table 5 was normalized by the stiffness value of the 16 mil NiTi wire that was reported in each particular investigation. Compared to previous results, the current EPR_Stiffness values were surprisingly similar given the variability in E measured on SS archwires (96 to 232 GPa).10,11 Stiffness, the product of E times I, can be measured from the slope of a load-deflection curve in the elastic region assuming linear elasticity. Consequently, relative stiffnesses can be measured without knowing the absolute values of E (a material parameter) or I (a geometric factor). However, the present expressions that model the elastic properties wires depend wholly on strand symmetry and non-interaction. Because engineering mechanics still lacks a systematic approach to predict the properties of wires having braided-, soldered-, or swaged-strand configurations, orthodontics cannot calculate the elastic properties of those wires either.

TABLE 5. Elastic Property Ratio for Stiffness (EPR_Stiffness) of Leveling Archwires in Current and Previous Investigations Versus a 16 mil NiTi Wire*

View Fullscreen

Regarding range, few data are available because direct measurements are difficult and arbitrarily defined. Ingram et al24 determined relative range by wrapping wires around mandrels of decreasing diameter until a minimum amount of permanent set was achieved. As helix angles were not noted, the reported range values for the triple and coax wires depended on the manufacturer. For multistranded wires, these ranges were generally greater than the single SS wires and always less than the single NiTi wires. The corresponding values in this study were mostly the same as the single SS leveling wires (cf, Figures 6–9 and Table 4).

CONCLUSIONS

Conventional nickel titanium (NiTi) archwires display nonlinear elasticity to the extent that traditional yield strength determinations, which assume linear elasticity, can grossly underestimate the elastic properties of strength and range.

Multistranded stainless steel (SS) archwires do not match the strength and range of conventional NiTi wires because they are fabricated with SS alloys that possess moderately high yield strengths.