Comparative range of orthodontic wires

Comparative range of orthodontic wires Stephen B. Ingram, Jr., B.S.M.E., D.M.D., David P. Glpe, B.A., MA., and Richard J. Smith, D.M.D., Ph.D.* Baltimore,

Md., and St. Louis, MO.

ADA specification No. 32 for determining the range (elastic limit) of orthodontic wires uses the bending of a wire section treated as a cantilever beam. An alternative method for defining the range of orthodontic wires proposed by Waters (1981) is to wrap wire sections around mandrels of varying. diameters and measure the deformation imparted after unwrapping. Four brass mandrels with a total of 46 test diameters ranging from 3.5 to 60.0 mm were used in this study. Wire sections 9 cm in length were rolled on the mandrel with a hand lathe. The mandrel cross section required to produce a predetermined amount of deformation (2 mm arc height for a 5 cm chord) was defined as the yield diameter for that particular wire. No individual wire was tested twice so as to avoid introduction of strain history. Test samples of.488 different orthodontic wires supplied by nine commercial distributors were evaluated (a total of 4,747 samples)., Stainless steel wires of identical dimensions had a large variation in range, depending on the state of strain hardening and heat treatment. For example, 0.020 inch round wire had yield diameters ranging from 22.8 mm for Australian special plus orange (TP Laboratories) to 42.9 mm for Nubryte gold (G.A.C. International). Chromium cobalt wires had less range than stainless steel before heat treatment, but increased greatly in range after heat treatment. Nitinol (Unitek) had the greatest range of all wires tested (yield diameter of 8.7 mm for 0.016 inch Nitinol). Multistranded stainless steel wires had yield diameters between 9.0 and 14.0 mm. (AM J ORTHOD DENTOFAC ORTHOP 90: 296-307, 1986.) Key words: Orthodontic

wires, range, elastic limit, bending test, heat treatment

D

uring the past decade, there has been a remarkable increase in the physical properties of the wires available to orthodontists. With the development of chromium-cobalt, nickel-titanium, and titaniummolybdenum alloys, and the production of round and rectangular multibraided wires by several different methods of wrapping 3,5,6,8, or 9 strands of stainless steel, the orthodontist is presented with a wide variety of options. It is difficult to gain clinical experience with the possible applications of so many different wires, and clinical judgments of the “feel” of a wire can be particularly misleading with wires that have variable relationships among the basic physical properties of strength, stiffness, and range.’ Of these basic properties, But-stone’ has argued that stiffness, or load-deflection rate, is the most important variable in clinical wire selection and he has presented a method to compare the stiffnesses of different orthodontic wires. In this article we evaluate a second physical property of orthodontic wires-their range, which is also deFrom the Departments of Orihcdontics. University of Maryland Dental School, and Washington University School of Dental Medicine. *Professor and Chairman, Department of Orthodontics, Professor of Biomedical Science and Pathology, Washington University School of Dental Medicine. 296

scribed in the literature as the maximum flexibility, the range of activation, the range of deflection, the working range, or the maximum elastic deflection. Range is a measure of how far a wire can be deformed without exceeding the limits of the material. It is a measure of distance without regard to the force that is required to accomplish the deflection.’ Several studies have reported on selected aspects of range in some of the newer wires, such as Nitinol and TMA, and have compared these materials to stainless steel or to each other.3“’ Information on the range of multiple-strand wires has been determined by engaging the wires in a standardized set of irregular teeth for subjective comparisons of the amount of permanent deformation. “Jo In this study we describe the development of a reproducible, accurate, and clinically relevant method to determine range of orthodontic wires, and then use that method to compare a large variety of the wires presently available to orthodontists. MATERIALS AND METHODS

The process of engaging an arch wire in the brackets of malaligned teeth can be expressed as bending the wire about arcs of circles of varying diameters, depending upon the degree of irregularity and the inter-

Volume 90 Number 4

bracket distance (Fig. 1). The minimum diameter bend that a wire can negotiate and still return to a nearly straight condition is defined in this study as its yield diameter. Thus, the smaller the yield diameter of the wire, the greater is its range. Yield diameters were determined by a modification of the mandrel test proposed by Waters. I4 To test preformed arch wires, the requirement for straight sections of wire 10 inches long was reduced to a section 9 cm long with a straight section of 6.5 cm. The failure mode was also redefined from 0.1% yield to a fixed amount of curvature, so that multistranded and solid wires could be subjected to a common test. Because titanium alloy wires do not exhibit a distinct yield point, selection of any yield criterion is arbitrary. A different yield criterion could alter the relative range of wires. To check for straightness prior to the bending test, sections of wire at least 9 cm long were placed on 1 mm graph paper mounted on a flat surface. Wires with greater than 0.5 mm deviation over their entire length were straightened. These wires were used only when completely straight sections could not be obtained from the manufacturer. A 120” bend was placed in both ends of the wire in opposite directions, using the smallest barrel of Tweed loop pliers. Careful attention was paid to keep rectangular wires on plane and to avoid distortion of the straight section. Preformed arches were cut at the midline and the anterior portion straightened, but only the previously straight posterior section was used for measuring yield diameter. One end of the wire was placed in a small hole (Fig. 2) drilled into a brass mandrel at 120” to the tangent and an appropriate weight was suspended from the wire using the bend at the other end (Fig. 3). An appropriate weight was defined as a weight sufficient to maintain contact of the wire with the mandrel as the wire was wrapped. Although the exact weight was recorded for each wire, this weight was not critical. Doubling of the weight produced identical yield diameters for a series of test wires. The suspended wire was wound about the mandrel at a speed of approximately one revolution per second using a hand lathe, held for 10 seconds, and unwound at the same rate. Careful attention was paid to keep rectangular wires in plane. A few wires proved to be impossible to test in the edgewise direction without twisting. Each wire was wrapped only once so as not to introduce strain history. Forty-six different mandrel diameters from 3.5 to 60.0 mm were available (Fig. 4). The actual tolerance of each mandrel diameter proved to be within ?O.OOl inch. The hand lathe was a converted Redding case trimmer. Immediately after unwinding, the wire was examined for curvature under a lighted magnifying glass

Comparative range of orthodontic wires 297

Fig. 1. In clinical conditions the deflection of orthodontic wires usually involves bending rather than tension or compression. Clinical bends can be equated with a bend around a circle of a specific diameter.

( X 3). The objective was to select the mandrel diameter that resulted in the arc of a 5 cm chord having a height of 2 mm (Fig. 5). From one to ten samples of a wire were needed to find the one or two mandrel diameters that approximated the yield criterion. After the correct size mandrel diameter was selected, additional samples were tested until three separate pieces of the wire were deformed to the test criterion. If no mandrel diameter produced the desired result, three trials each of the two mandrel diameters that bracketed the test criterion were selected and an interpolated mandrel diameter was calculated. Arc heights were measured to nearest ‘/4 mm with a one-half millimeter steel rule recessed in a piece of 1 mm graph paper mounted on a flat surface. Wires within 1 cm of the end that engaged the mandrel or within 1.5 cm of the end from which the weight was suspended were not measured (Fig. 5). Rectangular wires were tested in the edgewise (1’) and ribbonwise (2”) directions. Chromium-cobalt-nitinol (Cr-Co-Ni) wires were tested as delivered and after heat treatment in a baffled furnace at 900” F for 20 minutes. This extended time for heat treatment was used to ensure that all material in the furnace reached the target temperature. Samples of 488 different orthodontic wires from nine orthodontic companies (a total of 4,747 samples) were tested. All testing was performed by one or both of two operators, whose techniques were standardized to ensure consistent measurements.

298 Ingram, Gipe, and Smith

Am. J. Orthod.

Dentofac. Orthop. October 1986

Fig. 2. One end of the wire is placed in a small hole drilled in the mandrel at each test diameter.

Fig. 3. Each wire is wound on the mandrel. A weight is used to keep the wire in contact with the mandrel.

RESULTS

The results are summarized in Tables I through V. The numbers in the body of each table represent yield diameters in millimeters; the numbers along the top of the tables represent wire dimensions in inches. The smaller the yield diameter, the greater the range. Some results are also illustrated graphically. In these graphs yield diameter is plotted along the vertical axis and wire size along the horizontal axis. The box diagrams forming the background of each graph show the range of yield diameter for all of the solid stainless steel wires of that particular size. The bottom of the line extending down from each box is the lowest yield diameter for a stainless steel wire of that size; the top of the line extending above is the highest value. The bottom, middle, and top lines of the box itself indicate the yield diameters at the 25th, 5Oth, and 75th percentiles, respectively. From Table I, it can be seen that at all available

sizes the round stainless steel wire with the greatest range tested is Dentaurum Remainium super special heat treated.* TP Australian special plus (orange)t also has a large range. The wire exhibiting the lowest range varied with size, beginning with American Grthodontics standard* at 0.014 inch, followed by Lancer Pacific sterling spring extra resilient9 at 0.016 inch, Lancer Pacific sterling spring resilient§ at 0.018 inch, and G.A.C. Nubryte gold11at 0.020 inch. It is interesting that manufacturers’ claims of increasing range could not always be confirmed. For stainless steel wire of a given size, a manufacturer producing, for example, several different resiliencies, gold tones, or spring hard-

*Dentaumm Inc., Newton, Pa. tTP Labnratories, Inc., Lapmte, Ind. $American Orthodontics Corp., Sheboygan, Wis. &ancer Pacific, Inc., Carlsbad, Calif. 1IG.A.C. International, Inc., Commack, N.Y.

Comparative

Volume 90 Number 4

range of orthodontic

wires

299

Fig. 4. The four mandrels used to test all wires have a total of 46 test diameters ranging from 3.5 to 60.0 mm.

Fig. 5. A wire deformed to the yield criterion. See text for discussion.

enings is in effect claiming increasing range for the heat-treated wires. An examination of Table I shows that this is often not the case. As seen from Table II, the 0.016 x 0.022 inch wire with the greatest range in the edgewise (1”) direction is Unitek H-T II* with a yield diameter of 31.4 mm; a close second is Masel golden? with a yield diameter of 32.0 mm. The wire with the smallest range is again Lancer Pacific sterling spring extra resilient with a yield diameter of 50.7 mm. The range of a rectangular wire should be independent of the dimension not being tested. Thus, 0.016 x 0.022 inch, 0.017 x 0.022 *Unitek Corporation, Monrovia, tMase1 Co., Inc., Bristol, Pa.

Calif.

inch, and 0.018 x 0.022 inch should all have the same yield diameter in the 1” direction, if the alloy, state of heat treatment, and strain hardening are identical. The dimension tested is listed at the bottom of Table II. A comparison of how closely the yield diameters match for any one brand name wire at the same dimension is one indication of the quality control exercised in the manufacture of that wire. Some of the rectangular wires could not be tested in the edgewise (1”) dimension because the wire twisted on the mandrel when it was wrapped. In these cases no yield diameter is recorded for the 1” direction. Table III shows some interesting properties of the round titanium alloy and multistranded stainless steel wires. The wires as a group have low stiffness and high

300

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Gipe, and Smith

Dentofac.

Orthop. October 1986

Table I. Comparative range of round steel orthodontic wires Wire dimension (in)

American Orthodontics (mm) Standard Gold tone Super gold tone Dentaurum (mm) Remanium spring hard Remanium extra spring hard Remanium super spring hard Remanium super special heat treated G.A.C. International (mm) Nubtyte standard Nubtyte gold Lancer Pacific (mm) Sterling spring resilient Sterling spring extra resilient Masel (mm) Resilient Golden Ormco (mm) Round Rocky Mountain/Orthodontics (mm) Tru-Chrome TP Laboratories (mm) Australian regular white Australian regular plus green Australian special black Australian special plus orange Unitek (mm) Resilient Hi-T II

0.010

0.012

0.014

0.016

0.018

0.020

14.0 -

21.5 -

37.0 29.6 23.3

31.4 32.5 26.0

32.8 21.3 30.8

35.5 37.0 38.0

-

24.8 21.0 -

25.0 18.0

30.0 32.0 29.0 19.2

29.5 26.8 21.4

40.5 30.0 22.3

21.9 -

26.0 31.0

29.3 28.9

30.7 27.2

34.0 42.9

22.0 28.0

26.0 33.3

33.2 33.5

31.4 30.5

-

-

-

24.4 20.0

25.6 20.0

30.7 25.0

30.8 25.1

33.4 27.0

-

18.0

18.0

21.7

24.0

25.1

17.9

21.0

23.0

26.0

21.7

30.8

-

-

26.0 28.0 25.2 18.2

32.0 29.5 26.8 19.3

30.5 30.7 27.3 22.8

34.4 31.5 29.6 22.8

-

18.4 -

18.0 22.5

23.3 25.8

23.7 25.3

29.2 25.5

19.5

range as compared with solid stainless steel. According to standard engineering formulas, the range of a solid wire is expected to decrease as its size increases.‘,‘5.‘6 The results indicate that this is not the case with these low stiffness wires. Range appears to be independent of wire size and nearly constant for a particular wire configuration. For example, the yield diameters for American Orthodontics Co-Ax vary only from 11.2 to 10.0 mm and the largest size has slightly greater range than the smallest size (Fig. 6). Although Unitek’s Nitinol has the greatest range of any wire tested (Fig. 7), most of the multistranded wires have similar ranges. All of the multistranded wires have greater range than Grmco* TMA except for Ormco spiral wire. The properties of rectangular titanium alloy and multistranded stainless steel wires are similar to their round counterparts (Table IV). All of these rectangular wires have greater range and less stiffness’ than solid *Ormco Corp., Glendora, Calif.

0.022

stainless steel. Again, range appears to be independent of wire size. For example, the range of 0.021 x 0.025 inch Ormco Force 9 is greater than 0.016 x 0.022 inch Force 9. Unitek’s Nitinol has the greatest range of the rectangular low stiffness wires, but Ormco’s D-rect and Force 9 also have exceptional ranges. TMA has less range and more stiffness* than Nitinol, D-rect, and Force 9, but slightly greater range than G.A.C. Quad Cat and the Dentaurum stranded rectangular wires. The data in Table V show that nonheat-treated chromium cobalt orthodontic wires generally have less range than stainless steel wires of comparable size, but that the range can be greatly increased by heat treatmerit, confirming previous observations. ” For example, American Orthodontics multiphase blue 0.016 x 0.022 inch tested in the ribbonwise direction (2”) increases in range from a yield diameter of 38 mm to one of 27 mm by heat treatment. This represents a change from approximately the 95th percentile to the 5th percentile as compared with available stainless steel sam-

Volume 90 Number 4

Comparative

70

70

60

60

I

Size

(in.)

Fig. 6. For Figs. 6 through 9, yield diameter of various wires is plotted against a background of box diagrams showing the range of yield diameters for solid stainless steel wires of that size (see text for additional details). In Fig. 6, all round multistranded wires fall within the shaded area except for Masel Penta-One 0.015 inch (point l), American Orthodontics twist wire 0.021 inch (point 2) American Orthodontics Co-Ax 0.021 inch (point 3), and all sizes of Ormco spiral wire (open circles).

ples (Fig. 8). Similar effects following heat treatment were documented for Rocky Mountain* Elgiloy blue (Fig. 9). DISCUSSION

Although the range of any orthodontic wire is affected by many factors, including the wire size and shape, the modulus of elasticity of the material, and the design of the orthodontic appliance, any test for range is essentially a test for elastic limit so far as an individual wire is concerned. l8 To date, there is no consensus as to an appropriate definition of elastic limit for orthodontic purposes. The most common method for determining elastic limit is to stress a cylindric specimen in tension and then determine the point of flexure by plotting a stress-strain *Rocky

MountainiOlthodontics,

Denver,

Cola.

wires

301

-

I -

Wire

range of orthodontic

I ,014

I ,016

I 018

I .020

Wire Size (in.) Fig. 7. Solid circles show yield diameters for Ormco TMA and the open circles for Unitek Nitinol. The background boxes show the variability of round stainless steel wires for each diameter.

diagram. When the material does not exhibit a discrete yield point, 0.1%14 and 0.2%19 retained strain is assumed to be the elastic limit. However, this test method is probably not the most appropriate for orthodontic wires because it tests the material in tension, whereas orthodontists primarily stress wire in bending. Two different methods to determine elastic limit in bending have been used (Fig. 10). The first involves fabrication of a cantilever beam from a straight piece of wire that is then loaded at its free end until an arbitrary amount of permanent deformation occurs. ADA specification No. 32 requires this type of test using a one-inch cantilever section and 0.05 radians (2.9”) deformation.*’ However, a one-inch test specimen proves to be too long for existing instrumentation to consistently measure the extremely light forces generated by flexing small stainless steel wire (less than 0.012 inch) and all of the multistranded and titanium alloy wires. Brantley and associates” report that test results using cantilever sections of Y2inch, 1 inch, and 2 inches differ by more than 100’S, even though elastic limit is a function of the material and not length dependent. The second method of testing a wire in bending

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Am. J. Orthod.

Dent&c. Orthop. October 1986

Table II. Comparative range of rectangular stainless steel orthodontic wires Wire dimension (in) 0.916

American Orthodontics (mm) Gold tone Dentaurum (mm) Rcmeium spring bard Remanium extra spring hard G.A.C. Internat~omd (mm) Nqbryte standxd Nubryte gold Lancer Pacific (mm) Sterling spring resilient Sterling spring extra resilient Masel (mm) Resilient Golden Qrmco (mm) Edgewise Rocky MountainlOrthodontics (mm) Tru-Chrome Unitek (mm) Standard Resilient Hi-T II DIMENSIONTESTED(in)

0.016 x 0.022

0.017

0.017 x 0.022

0.017 x 0.025

1”

2”

0.;17

I”

I”

25.3

40.0

38.0

25.1

29.0

21.5

-

38.1

30.4 29.3

40.9

33.0

38.0

is.0

30.0 32.5

40.7 36.0

34.0 31.0

44.0 38.0

34.0 28.9

36.8 39.7

41.2 34.0

32.4 34.0

35.0 32.5

42.1 31.4

34.0 35.3

40.7 47.0

33.2 35.5

30.5 26.8

50.7

30.5 32.0

39.7 42.0

31.7 34.4

38.0

35.5 33.3

36.0 24.4

35.3 26.0

40.0 28.0

44.0

32.0

39.3

41.2 26.5

45.0 36.7

32.0 28.6

21.1

39.1

34.0

34.0

40.1

35.6

-

29.7

30.9

42.7

36.6

30.0

41.7

34.0

43.3

32.5

21.4 31.3 29.7 0.016

39.8 36.7 31.4 0.022

29.0 32.0 25.7 0.016

31.1 32.0 -

34.6 33.6 29.5 0.022

28.0 32.5 26.0 0.017

38.5 0.025

29.6 29.1 29.0 0.017

44.0

0.017

2”

2”

Table III. Comparatjve range of round titanium alloy and multistrqnded steel wires Wire dimension (in) 0.015

American Orthodont@s (mm) Co-Ax Twist Dentaurum (mm) Bntatlex G.A.C. Internatiorql (mm) Pentacat Wildcat Lancer Pacific (mm) Swiss strand Masel (mm) Penta-One Ormco (mm) Respond Spiral Rocky MountainlOrthodont~cs (mm) T&Flex TP Laboratories (mm) Co-Ax Ormco TMA (mm) Unitek Nitinol (mm)

0.017

0.019

0.021 o&5

0.04’ss

0.016

0.04r75

0.018

o.oqrg5

11.2 11.0

-

10.0 12.8

-

10.8 15.2

10.7 18.0

11.2

-

11.8

-

12.1

12.9

-

12.7 -

10.6 10.6

-

14.4 12.2

15.5 13.4

10.1

-

10.6

-

12.5

13.4

14.0

-

12.1

-

11.0

13.2

10.9 21.0

-

10.7 21.5

-

12.2 21.0

12.7 26.0

9.8

-

10.3

-

11.2

12.6

-

11.2 17.0 8.7

-

10.2 14.1 8.7

-

-

9.9

Comparative range of orthodontic wires 303

Volume 90 Number 4

Wire dimension (in) 0.018

0.018 x 0.022

0.h

1”

2"

0.018

x 0.025

0.019

2"

0.;19

I”

0.019 x 0.025 1”

0.021

2"

0.021 x 0.025 1”

o.t21

2"

0.0215 x 0.028 1”

2"

-

-

-

32.0

29.0

-

28.8

-

55.6

41.0

-

33.1 33.5

41.0 37.0

34.5 32.0

46.0 44.0

36.0 33.3

35.6 32.0

44.0

35.6 36.3

40.0

42.0

40.0

-

38.0 50.0

30.9 42.0

35.5 38.0

-

-

42.0 46.3

35.0 36.6

-

43.3 48.8

36.5 38.0

-

-

42.5

43.0

36.5 38.0

-

41.1 45.0

32.6 32.6

49.1 48.0

36.0 34.0

-

-

-

-

45.3 44.0

41.1 36.0

-

-

35.6 31.4

38.5 34.0

28.8 29.4

41.4 35.2

36.0 26.0

-

49.6 34.4

38.0 29.8

-

41.3 38.2

34.0 31.0

-

-

32.3

36.7

33.0

-

-

30.3

39.0

37.0

41.2

45.3

-

40.9

34.0

43.4

34.0

34.0

-

-

-

41.5

38.0

-

-

-

36.0 35.3 31.2

30.5 j3.7 27.0

39.5 38.0

31.0 32.6

28.9 34.5

37.6 35.3 26.7

34.0 35.5

-

40.8 35.7 28.8

42.7 41.7

-

30.0 36.7 33.8

34.6 33.6

-

38.0 38.4 39.0

35.1

-

0.022

0.018

0.018

0.025

0.018

0.019

0.025

37.6

-

0.019

0.021

31.7

40.0

34.7

0.025

-

0.021

0.028

0.0215

Ttible IV. Com@rative range of rectangular titanium alloy and rhuitistranded wires Wire dimension (in) 0.016 x

0.017 0.025

0.022

x

0.018 0.025

1”

2"

I”

2"

23.0

20.0

26.0

25.2

21.7

12.3 13.6 22.0

10.9 11.7 17.2 10.2

x

Oil9 0.025

x

0.021 0.025

x

I”

2"

I0

2"

I”

2"

20.1

-

-

-

-

30.1

26.4

24.9

20.7

-

-

23.5

20.7

-

-

14.7 14.3 -

12.9 11.6 11.6

12.9 14.0 -

11.6 13.3 10.5

12.2 15.3 21.5 -

11.1 14.0 17.7 12.0

12.5 11.7 21.0 15.0

11.7 11.8 19.8 11.0

Dent&rum (mm) Multistranded

rehngular

G.A.C. Intkrnational(mm) Quad Cat

Ormco (mm) D-ECi. Force9

Ormco ThfA (mm) Unitek Nitinol (mm)

-

involves wrapping a straight wire around a mandrel and then in some way measuring the amount of curvature imparted to the *ire after unwrapping.14~22~23 If the wire diameter (or thickness for rectangular wires) and mandrel diameter are known, the elastic limit can be calculated (except in the case of multistranded wires). ‘4.23 The eiastic limit of almost all structural material,

including stainless steel, is lower in tension than it is in compression. ‘Iherefore, in a bending test, permanent deformation wili occur first at the tension side of the wire. This is at the very outside of the wire as it is being wrapped around the mandrel. Because the tensile stress produced by the deadweight used to keep the wire in contact with the mandrel is additive to the tensile

304

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October 1986

Table V. Comparative range of chromium cobalt orthodontic wires Wiredimension (in)

0.016 x

0.010 American Oythodontics (mm) Multiphase (blue) As delivered After heat treatment Dentaurum (mm) Remaloy soft As delivered After heat treatment Remaloy spring hard As delivered After heat treatment G.A.C. International (mm) Bioloy (blue) As delivered After heat treatment Bioloy (yellow) As delivered After heat treatment Ormco (mm) Azura As delivered After heat treatment Rocky MountainlOrthodontics (mm) Elgiloy soft (blue) As delivered After heat treatment Elgiloy resilient (red) As delivered After heat treatment

0.014

0.016

0.018

-

40.0

40.8

-

44.0 -

-

-

-

-

-

-

0.022

x 1”

2"

50.3

37.6 22.9

48.0 31.0

38.0 27.0

-

-

47.0 30.0

53.0 35.6

45.0 38.0

35.0 22.0

36.7 24.0

-

-

-

-

-

-

-

40.3 32.0

-

-

-

-

-

-

-

35.6 27.5

44.0 34.0

36.7 28.0

-

-

-

-

-

39.7 31.2

45.6 39.0

40.3 32.0

-

-

-

-

-

40.6 25.8

51.0 34.0

43.0 27.7

24.0

28.0 18.4

29.7 19.7

-

-

-

-

19.3 13.0

-

stress produced by bending (Fig. 1 l), it is necessary to evaluate the contributions of each of these sources of tensile stress to wire failure. With 0.016-inch diameter steel wire, the maximum elastic strain at the failure site where permanent deformation occurs is calculated as followsz3: wax

0.020

0.016 0.016

S = Ey

where S = stress, E = modulus of elasticity = 25 X lo6 psi,24 and y = strain = 1.36 x 10e2. Substituting values into this equation indicates the stress produced by bending: S = 25 X lo6 psi X 1.36 x lo-* S = 34 X lo4 psi

R = R+~

where R = radius of the wire = 0.008 inch = 0.2 mm, r = radius of the mandrel = 14.5 mm and y max = maximum elastic strain. Substituting values into this equation, 0.2 = 1.36 x 1O-2 ymax = 0.2 + 14.5

The stress produced by the above strain is calculated from the equation:

The tensile stress produced by the deadweight is calculated by the formula:

where F = the deadweight (a maximum of 350 g was used for 0,016 diameter round wire) and A = a crosssectional area of the wire, resulting in a value of: s=

350 g = 0.38 n(0.008 in)’

x

104 psi

Volume 90 Number 4

Comparative

Wire

0.017 x 0.022 0.017 x 0.017

0.017 x 0.025

dimension

0.018 x 0.022

1”

2”

I”

2”

46.7 34.0

40.4 32.0

37.0

52.7 38.5

43.6 31.6

-

0.019 x 0.025 0.019 x 0.026

lo

2”

I”

2”

41.6 30.0

50.0 35.8

42.9 32.0

56.7 38.0

56.0 40.0

45.5 31.0

54.0 39.0

46.7 32.0

-

-

-

-

-

-

-

-

-

-

-

-

-

49.0 38.0

-

d2 + h2 2h

305

wires

(in)

0.018 x 0.025

0.021 x 0.025

0.021 x 0.028

IQ

2”

1”

2”

1”

2”

46.2 28.0

-

-

56.0 36.8

47.5 32.0

-

-

58.0 47.0

50.0 36.0

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

61.0 52.0

53.2 41.0

-

-

-

-

58.0 52.0

52.0 43.0

-

-

-

-

-

-

-

-

-

-

-

49.0 -

40.3 31.5

-

-

48.0 46.0

46.0 33.8

52.0 44.0

42.9 37.0

50.0 44.9

50.8 41.5

-

-

45.0 32.0

59.6 39.0

41.6 30.5

53.3 37.3

44.2 32.0

58.0 40.0

45.3 33.2

58.0 39.2

55.2 31.3

52.7 38.8

45.3 34.4

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Therefore, the tensile stressproduced by the deadweight is only 1.1% of the tensile stress produced by bending at the failure site. The mandrel test as described in this study comes close to producing the theoretically desired test stress of pure bending. Furthermore, unlike cantilever tests,*’ the results of the mandrel test are independent of the length of the test specimen, provided that the minimum length is met. Longer test specimens would merely produce a greater portion of a circle with the same radius (15.725 cm) when tested at their yield diameters. The selected yield criterion, a 2 mm deformation in a 5 cm chord, is consistent with standard engineering criteria of 0. 1%14to 0.2%19 strain in defining an elastic limit. With 0.016 inch stainless steel wire, this yield criterion produces a recovery strain of 0.1% . Referring to Fig. 12: r,=-=

of orthodontic

range

(2.5 cm)* + (0.2 cm)’ = 15 725 cm 0.4 cm

For 0.016 inch diameter wire: R 0.2 mm Ylec= -R + rrs = 0.2 mm + 157.125 mm = 0.00127 where r,, = radius of curvature after recovery, d = 1/2 chord, h = 1 height from chord to inner circumference, yrec = recovery strain, and R = radius of round wire or Y2 height of a rectangular wire. Testing a wire at mandrel diameters larger than its yield diameter typically produced little or no permanent deformation and the wire returned to its previously straight condition. Nevertheless, subsequent tests on these wires were not recorded because strain history had been introduced. It is not necessarily true that the wire with the greatest range is the best choice for every clinical situation. Burstonez5 has pointed out that while great range and low stiffness may be useful in the active components of an appliance being used to move teeth, the reactive

306 Ingram, Gipe, and Smith

Am. J. Orthod.

Dentofac. Orthop. October 1986

Flg. 10. The elastic limit in bending can be determined from a cantilever test or a mandrel test. See text for further discussion.

Fig. 9. American Orthodontics multiphase blue without heat treatment (open circles) and after heat treatment (closed circles). The background boxes show the variability of rectangular solid stainless steel wires for each wire size.

70 -

P ;

60

-

50

-

40-

r E I ; .E F

3o

20

10

-

-

Fig. 9. Rocky Mountain Orthodontics Elgiloy blue without heat treatment (open circles) and after treatment (closed circles). The background boxes are the same as in Fig. 8.

components, in which the orthodontist does not want movement, would be better controlled with low-range, high-stiffness wire. Perhaps most important, the new materials and manufacturing techniques can effectively change the relationship between range and stiffness that orthodontists have come to expect from clinical experience with solid stainless steel. Thus, because of their high range of activation, these wires can still have relatively high magnitudes of total stored energy even with their lower stiffnesses (load-deflection rates). The clinician can be misled into fully engaging a large deflection and thereby delivering an excessive force. REFERENCES 1. Thurow RC: Edgewise orthodontics, ed 4. St. Louis, 1982, The C. V. Mosby Company. 2. Burstone CJ: Variable-modulus orthodontics. AM J ORTHOD 80: l-16, 1981. 3. Drake SR, Wayne DB, Powers JM, Asgar K: Mechanical properties of orthodontic wires in tension, bending, and torsion. AM J ORTHOD 82: 206-210, 1982. 4. Kusy RP: Comparison of nickel-titanium and beta-titanium wire sires to conventional orthodontic arch wire materials. AM J ORTHOD 79: 625-629,

1981.

5. Lopez I, Goldberg J, Burstone CJ: Bending characteristics of nitinol wire. AM J ORTHOD 75: 569-575, 1979. 6. Andreasen GF, Morrow RE: Laboratory and clinical analysis of nitinol wire. AM J ORTHOD 73: 142-151, 1978. 7. Goldberg AJ, Burstone CJ: An evaluation of beta titanium alloys for use in orthodontic appliances. J Dent Res 58: 593-599, 1979. 8. Andreasen G: A clinical trial of alignment of teeth using a 0.0 19 inch thermal nitinol wire with a transition temperature range between 31” C and 45” C. AM J ORTHOD 78: 528-537, 1980. 9. Burstone CJ, Goldberg AJ: Beta titanium: A new orthodontic alloy. AM J ORTHOD 77: 121-132, 1980. 10. Kusy RP, Greenberg AR: Comparison of elastic properties of

Comparative

Volume 90 Number 4

range of orthodontic

wires

307

TENSION

NEUTRAL

AXIS

BENCWG STRESS

DEAD

WEIGHT

STRESS

TOTAL STRESS

Fig. 11. In a mandrel bending test, the wire fails in tension. The tension from the deadweight adds to the tension from bending. As discussed in the text, the deadweight contributes only about 1% of the tensile stress at the failure site.

Fig. 12. The test criterion of 2 mm height to the arc of a 5 cm chord produces a recovery strain of 0.1% for 0.016 inch wire. See text for discussion. nickel-titanium and beta titanium arch wires. AM J ORTHOD 82: 199-205, 1982. 11. Bachman J: Torquing of stainless steel and Nitinol wires. Em J Orthod 5: 167-169, 1983. 12. Andreasen GF, Barrett RD: An evaluation of cobalt-substituted nitinol wire in orthodontics. AM J ORTHOD 63: 462-470, 1973. 13. Barrowes KJ: Archwire flexibility and deformation. J Clin Ortbod 16: 803-811, 1982. 14. Waters NE: An improved method for the yield in bending of straight orthodontic wires. Br J Orthod 8: 89-98, 1981. 15. Burstone CJ, Baldwin JJ, Lawless DT: The application of continuous forces to orthodontics. Angle Orthod 31: 1-14, 1961. 16. Nikolai RI: Bioengineering analysis of orthodontic mechanics, Philadelphia, 1985, Lea & Febiger. 17. Waters NE, Houston WJB, Stephans CD: The heat treatment of wires: a preliminary report. Br J Orthod 3: 217-222, 1976. 18. Timoshenko S: Strength of materials, ed 3. Princeton, New Jersey, 1956, Van Nostrand. 19. Marin AG, Sauer AF: Strength of material, ed 2. New York, 1964, The Macmillan Company. 20. New American Dental Association specification No. 32 for orthodontic wires not containing precious metals. J Am Dent Assoc 95: 1169-1171, 1977.

21. Brantley WA, Augat WS, Myers CL, Winders RV: Bending deformation studies of orthodontic wires. J Dent Res 57: 609615, 1978. 22. Waters NE: A method for characterizing the elastic deformability of orthodontic wires. Dent Pratt 22: 289-295, 1972. 23. Waters NE, Stephans CD, Houston WJB: Physical characteristics of orthodontic wires and archwires-part 1. Br J Orthod 2: 1524, 1975. 24. Goldberg AJ, Vanderby R Jr, Burstone CJ: Reduction in the modulus of elasticity in orthodontic wires. J Dent Res 56: 12271231, 1977. 25. Burstone CJ: Application of bioengineering to clinical orthodontics. In Graber TM, Swain BF (editors): Orthodontics: Current principles and techniques. St. Louis, 1985, The C. V. Mosby Company, pp 193-227. Reprint requests to: Dr. Richard J. Smith Department of Orthodontics Washington University School of Dental Medicine 4559 Scott Avenue St. Louis, MO 63110