Frictional coefficients of ion-implanted alumina against ion-implanted beta-titanium in the low load, low velocity, single pass regime

Dent Mater 8:167-172, May, 1992

Frictional coefficients of ion-implanted alumina against ion-implanted beta-titanium in the low load, low velocity, single pass regime R.P.Kusy ~, E.J. Tobin 2, J.Q. Whitley 1, P. Sioshansi 2 Departments of Orthodontics and Biomedical Engineering, Dental Research Center, Universityof North Carolina, Chapel Hill, NC, USA 2Spire Corporation, Bedford, MA, USA

Abstract. The frictional coefficients were measured for four wire alloys against the flats of polycrystalline alumina cylinders using a low load, low velocity, single pass device. Ion-implantations of titanium into polycrystalline alumina flats and nitrogen into betatitanium wires reduced the static and kinetic coefficients from 0.50 and 0.44 before implantation to 0.20 and 0.25 after implantation, respectively. These results are similar in magnitude to frictional coefficients for unimplanted, control couples of stainless steel, cobalt-chromium, and nickel titanium wires against polycrystalline aluminaflats. For orthodontic applications, we conclude that more efficient and reproducible appliances can be engineered for tooth movement if ion-implantation is used to reduce the abrasion of beta-titanium by polycrystalline alumina.

INTRODUCTION Numerous devices have been designed to measure friction and wear (Blau, 1989). In most of the applications, devices such as the pin-on-disk, the block-on-ring, and the flat-on-flat designs have been extensively used to evaluate the tribological properties of couples that are subjected to high Hertzian stresses, sliding wear, high running speeds, and/or multiple passes (Dickson, 1979; DeVries et al., 1981; Clark et al., 1983; Sliney et al., 1986; Deadmore and Sliney, 1988). Applications exist in dental medicine, however, where only low loads, low velocities, and/or a single pass are required (Hartley et al., 1973; Powers et al., 1983; Kusy and Whitley, 1989). Under these conditions, no break-in, run-in, or wear-in phenomena can occur (Blau, 1989). As in many other fields, applications for ceramic products are being found in orthodontics. Because of their desirable aesthetic properties, ceramic brackets are being selected regardless of the disadvantages of the much lower fracture toughness of ceramics compared to that of steel [polycrystalline alumina (3.0-5.3 MPa'm 1/2) and sapphire (2.4-4.5 MPa'm 1/2) versus stainless steel (80-95 MPa'm1% (Scott, 1988). In addition, the coefficients of kinetic friction of stainless steel against polycrystalline alumina (~K= 0.18) are greater than those values that have been measured for 18-8 stainless steel against 18-8 stainless steel (~K -- 0.13) (Kusy and Whitley, 1990a; 1990b). In this paper a low load, low velocity, single pass device is used to measure the effects of ion-implantation on the frictional coefficients for ceramic-metal couples. This laboratory device was chosen over a pin-on-disk device because it better simulates the clinical situation that exists, when teeth have to be moved by an arch wire sliding through a bracket slot.

MATERIALS AND METHODS Ceramic-Metal Couples. Polycrystalline alumina cylinders (Ceradyne, Inc., Costa Mesa, CA, USA; nominally 99.8+% pure and 1.27 cm high x 0.635 cm diameter) were faced with a 320 grit diamond sectioning saw and ground with 600 grit carbide paper. During the finishing process, the reflectance of each cylinder was periodically measured by a heliumneon laser (Fig. 1) (Whitleyet al., 1987; Tanner, 1976). From a plot of the quotient of the reflected sample light (IX)and its incident beam (Io) versus the cosine squared of the incidence angle of the light (a = 84, 82, 80, 78, and 76°), the optical RMS roughnesses were determined from the slope (Fig. 2) (Kusy et al., 1988; Hensler, 1972). When nominal RMS roughnesses of 0.22-0.25 ~m were attained, cylinders were set aside from which matched sets were later chosen (Fig. 3). The primary opposing material in this study was a stabilized beta phase alloy of titanium having a nominal composition-- 79Ti, 11Mo, 6Zr, and 4Sn w/o (Ormco Corp., Glendora, CA, USA). These rectangular arch wires 0.43 m m x 0.63 mm (0.017 in x 0.025 in) were evaluated in the as-received state in which the optical RMS roughness measurements equaled 0.14 }~m. Beta-titanium was chosen as the opposing material because, in similar applications that used 18-8 stainless steel cylinders, the titanium alloy had the highest coefficients of friction and was most susceptible to adhesive wear via cold welding (Kusy and Whitley, 1990a). Three other wires, each 0.45 mmx 0.63 mm (0.018 in x 0.025 in) in cross section, were evaluated against polycrystalline aluminacylinders: 18-8 stainless steel (Unitek Corp., Monrovia, CA, USA; nominally 71Fe, 18Cr, 8Ni, and < 0.2C w/o), cobaltchromium (Rocky Mountain Orthodontics, Denver, CO, USA; nominally 40Co, 20Cr, 15Ni, and 15Fe w/o), and nickel titanium (Unitek Corp.; nominally 55Ni and 45Ti w/o). These three alloys represent alternative wires that orthodontists may use to move teeth. Ion-Implantation. In addition to the control couples that were composed of polycrystalline alumina and four metallic alloys, two ion-implanted couples were evaluated: one in which titanium ions (Ti+) were implanted into the alumina but the beta-titanium wire alloy remained unchanged, and a second in which the Ti + implantation of the alumina was opposed by a nitrogen ion (N ÷) implantation of a beta-titanium alloy. In both cases, specimens were subjected to multiple implantations (five) in a Varian 350D ion-implanter (Table 1) (Sioshansi, 1987). As a result, very high and relatively constant concentrations of ion species were predicted within

Dental Materials~May 1992 167

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only a few tens of nanometers from the surface (Figs. 4 and 5). Previous experiences had shown that deeper implantations, which were acceptable for couples that can wear-in (Sioshansi et al., 1985), are not as effective in low load, low velocity, single pass applications (Kusy and Andrews, 1990). Measurement of Friction. The frictional coefficients were measured by a device, the prototype ofwhich was first reported by Greenberg and Kusy in 1979. In this flat-on-flat contact friction device, the coaxial springs (S) transmit the force by a moveable piston to the flats of cylinders (F), which are in contact with a rectangular wire (W) (Fig. 6). The normal force is measured by a force transducer (TN). The flats on the cylinders are drawn past the 12.7 cm long wire, which is clamped to the load cell transducer (Tp) of the screw-driven testing machine, at a rate of 1.0 cm/min under prevailing atmospheric conditions at 34°C. Static and kinetic drawing forces (P) were determined from the initial rise on the chart curve and by averaging the digitally stored plateau region of each force vs. distance (P vs. 8) trace, respectively (cf Fig. 7, "static" and "kinetic"). From the free-body diagram (Fig. 8), these forces are divided by two and plotted as the frictional force (f = P/2) versus the normal force (N) (Greenberg and Kusy, 1979). The slopes of the regression curves from at least one observation of five normal forces (nominally 0.2, 0.4, 0.6, 0.8, and 1.0 kgf) yield values for the static and kinetic coeffi168 Kusy et aL/Frictional coefficients of ion-implanted alumina

cients of friction (1.ls and ~K, respectively). From the computation of each correlation coefficientand the number of observations, the level of significance was obtained for which a relationship existedbetween normal and frictional forces. The ranges Ofpsand PKare also reported for each couple based upon the quotient of each frictional force divided by its corresponding normal force. This method of analysis is equivalent to determining the range of the slopes of five fvs. N lines that are formed from each respective (N,f) coordinate and the origin. RESULTS Plots of P vs. 8 showed that, on average, both the static and kinetic coefficients of friction decreased somewhat when the alumina flats alone were implanted, but decreased more after both the flats and beta-titanium wires were implanted (Fig. 7). When data from the other four normal forces were evaluated TABLE 1: IMPLANTATION PARAMETERS Substrate

Polycrystalline Alumina

Beta-Titanium Alloy

Ion Exposure Specie Sequence

Ionization Energy (keV)

Dose (ions/cm 2)

Ti+

1 2 3 4 5

180 120 80 50 30

8.0 5.0 3.0 2.0 1.5

x x x x x

1016 1016 1016 1018 1016

N+

1 2 3 4 5

190 120 60 30 15

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beta-titanium wires, which have been subjected to specific flat/wire treatments. Samples were tested in air at 34°C using a 800 g normal force, after cleaning the loadbearing surfaces with 95 v/v % ethanol. (1 N = 0.1 kgf)

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similarly and plots of fvs. N generated, the static and kinetic coefficients of friction displayed linear behavior and extrapolated close to origin (Figs. 9 and 10). With regard to specific flat/wire treatments, the slopes of the control/control and the Ti+/control couples were similar. However, the slopes of the Ti+/N+ implantation of the polycrystalline alumina/betatitanium couple were significantly different from the other couples. In the worst case, the static coefficients based upon the slopes decreased from 0.59 (control/control) to 0.20 (Ti+/ N+). Similarly, the kinetic coefficients based upon the slopes decreased from 0.47 (control/control) to 0.25 (Ti+/N+). As Figs. 11 and 12 show, this best Ti+/N + couple compares favorably with control couples in which stainless steel, cobalt-chromium, or nickel titanium wires have been substituted for the beta-titanium wire. These frictional coefficients, as well as the results for several other couples, are summarized in Table 2 (static) and Table 3 (kinetic) along with their correlation coefficients. In all cases, a relationship between normal force and frictional force was indicated (p < 0.05). With one exception, all of the frictional coefficients based upon the slopes were within the ranges of frictional coefficients, which were based on the point-by-point analysis of each frictional force and its corresponding normal force.

DISCUSSION Using a pin-on-disc apparatus and a single implantation of a mixed N2+/N+ beam with an energy of 90 keV and a dose of 3.5 x 1017 ions/cm 2, Oliver et al. (1984) studied the wear and frictional behavior of four ferrous alloys, a hard chromium plating, and a titanium alloy. In three cases, they found that

= ~/2 N

Fig. 8. Free body diagram of the forces off the flats and its opposing wire during friction testing.

nitrogen implantation: caused considerable scatter while increasing the frictional coefficients (Armco iron); resulted in no highly significant change in friction or wear (52100 bearing steel); or improved wear without significantly changing the friction (hard chromium plating). In the other three cases, some improvements of the frictional coefficients were seen, however. When the 12T martensitic stainless steel was implanted, a small but probably insignificant decrease in friction was observed along with a corresponding fourfold reduction in wear rate. In the last two cases, which are most similar to the present alloys under investigation, the unimplanted type 304 austenitic stainless steel exhibited a frictional coefficient that decreased from 0.17 to 0.12 with runin, while its implanted counterpart maintained a constant intermediate value of 0.15. These values are comparable with results obtained previously in this laboratory for unimplanted stainless steel (Kusy and Whitley, 1990b). For the Ti-6A1-4V alloy, the frictional coefficients decreased from 0.48 to 0.15 as the wear rate was reduced by more than one hundred-fold. In a second study, Pons et al. (1987) used a pin-on-disc apparatus at a rotating speed of 10 rpm and Hertzian pressures of 0.8, 1.1, and 1.4 x 107 Pa to investigate the wear of an as-rolled Ti6A1-4V alloy. Unlike the first study, the N + ions were implanted at three energies in order to obtain a flat concentration profile: 20, 70, and 90 keV. Regardless of the contact load, the initial frictional coefficients were high for both the control and 2 w/o loadings (PK = 0.40) but decreased for the 10-44 w/o loadings (PK = 0.26). Dental Materials~May 1992 169

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Fig. 11. Comparison of the static frictional force (f) versus normal force (N) plots for Ti + implanted polycrystalline alumina flats against N + implanted beta-titanium wires ( A , --) and three control couples that substitute stainless steel (- - -), cobaltchromium (. . . . ), and nickel titanium (. . . . . . ) arch wires to slide against unimplanted polycrystalline alumina flats. (1 N = 0.1 kgf)

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The aforementioned two references confirm that improved wear performance is not a sufficient condition to presume that frictional coefficients have also been reduced. Careful analyses of these and other papers (Oliver etal., 1984; Pons etal., 1987; Singer, 1984; Iwaki, 1987; Dillichetal., 1984; McHargue, 1986) often show such variable results that no general relationship can be adduced. Fortunately for N + implanted titanium alloys, a positive correlation exists between wear rate and frictional coefficients (Oliver etal., 1984; Pons et at., 1987). In those papers, a ratio of one-half to over three was realized between the unimplanted versus the implanted kinetic coefficients compared to ratios of about three and two for the present static and kinetic values, respectively (Figs. 9 and 10; Tables 2 and 3). Additional investigators have reportedly seen similar decreases in frictional coefficients by factors of two to four and concomitant reductions in wear by factors of 400 to 500 (McHargue, 1986). The substantial increases in PK that were noted during run-in or the formation of a bilayer, which allowed the substrate to extrude under the applied loads, are not important because the present application is only concerned with a low load, low velocity, single pass regime. The five multiple implantations that bring the Ti + implanted polycrystalline alumina and the N + implanted beta-titanium alloy to within just a fraction of the wavelength of light from the surface are credited with the superior frictional coefficients. When the frictional coefficients of the N + implanted betatitanium and the Ti+ implanted polycrystalline alumina couple were compared with the control/control couples of 18-8 stain-

170 Kusyetal./Frictionalcoefficientsofion-implantedalumina

O

I

0

r

I

0.2 0.4 0.6 0.8 Normal Force, N (kgf)

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Fig. 12. Same as Fig. 11, except kinetic frictional force (f) is plotted as the ordinate. (1 N = 0.1 kgf)

less steel, cobalt-chromium, or nickel titanium alloys against polycrystalline alumina, the frictional coefficients were no longer so very different (Figs. 11 and 12). Specifically, as the plowing tendency ofthe rough and sometimes faceted alumina surface (Kusy and Whitley, 1990a; 1990b) was reduced from the hardening afforded by the ion-implanted layer on the titanium-rich alloy(Dearnaleyand Peacock, 1984; Kembaiyan et al., 1990; Martin and McKenzie, 1990), the values Ofps and PKbased upon the slopes were reduced from 0.59 and 0.47 to 0.20 and 0.25 (Tables 2 and 3). Moreover, as the magnitude of the frictional coefficients decreased, the periodicity of the Ti+/control couple (Fig. 7, middle trace) reduced markedly with the addition ofN + implantation to the beta-titanium wire (Fig. 7, lower trace). Although not yet attempted, similar treatments of other titanium alloys (e.g., the present nickel titanium alloy) should reduce the frictional coefficients to values that are comparable with stainless steel and cobaltchromium alloys. Then, not only could beta-titanium be substituted for stainless steel arch wires in orthodontic treatment plans that require the retraction of central and lateral incisors, but also nickel titanium could have frictional characteristics during early aligning procedures that would be more comparable with stainless steel alternatives. Although the present coefficients of friction are not nearly as good as the values for control couples composed of PTFE against PTFE (Ps = 0.05 and PK = 0.04) (Kusy and Whitley, 1990b) or 18-8 stainless steel against stainless steel (Ps = 0.12 and PK= 0.14)

TABLE 2:

Wire Alloy

Beta-Titanium

Stainless Steel

SUMMARY OF STATIC COEFFICIENTS OF FRICTION AGAINST POLYCRYSTALLINE ALUMINA FLATS Treatment* Frictional Coefficient Correlation Number of Probability Coefficient Data Points (p)++ Flat Wire Slope+ Range # (n)** Control Control 0.59 0.30- 0.77 0.98 15 < 0.001 Control Control 0.41 0.43 - 0.61 0.99 5 < 0.01 Ti + Control 0.43 0.35- 0.52 0.95 5 < 0.02 Ti + N+ 0.20 0.17- 0.23 0.95 5 < 0.02 Control Ti +

Control Control

0.23 0.14

0.17 - 0.36 0.12- 0.16

0.96 0.95

15

< 0.001

5

< 0.02

Control

Control

0.24

0.20 - 0.45

0.98

15

< 0.001

Control Ti+ For footnotes see Table 3

Control Control

0.30 0.43

0.18- 0.38 0.36 - 0.43

0.97 1.00

15 5

< 0.001 < 0.01

Cobalt-Chromium Nickel Titanium

TABLE 3:

Wire Alloy

Beta-Titanium

SUMMARY OF KINETIC COEFFICIENTS OF FRICTION AGAINST POLYCRYSTALLINE ALUMINA FLATS Treatment* Frictional Coefficient Correlation Number of Probability Coefficient Data Points (p)++ Flat Wire Slope + Range # (n)** Control Control 0.47 0.24- 0.49 0.99 15 < 0.001 Control Control 0.41 0.38- 0.49 0.97 5 < 0.01 Ti + Control 0.38 0.32- 0.39 0.98 5 < 0.01 Ti + N+ 0.25 0.17- 0.28 0.92 5 < 0.05

Stainless Steel

Control Ti +

Control Control

0.19 0.15

0.13- 0.23 0.13- 0.16

0.96 0.98

15 5

< 0.001 < 0.01

Cobalt-Chromium

Control

Control

0.20

0.18- 0.23

1.00

15

< 0.001

Nickel Titanium

Control Control 0.28 0.24- 0.30 1.00 15 < 0.001 Ti + Control 0.43 0.37- 0.47 0.98 5 < 0.01 * For ion-implanted flats or wires, see Table 1 for parameters. + These frictional coefficients were based on the regression analysis of frictional force versus normal force. # These frictional coefficients were based on point-by-point analysis of each frictional force and its corresponding normal force. ** The number of data points represents the number of normal force-frictional force combinations that were grouped for each regression analysis. ++ The probability that a relationship exists between the normal and frictional forces is derived from the correlation coefficient and the number of data points (Young, 1962).

(Kusy and Whitley, 1990a; 1990b), our implantation procedure achieved parity with other control couples that are considered acceptable alternatives with polycrystalline alumina. One can envision that, in time, future orthodontic treatment plans could control tooth motion by implanting selected surfaces of an arch wire or its brackets. Thereby, some segments might be allowed to slide, while others might bind as plowing or stick-slip (Czichos, 1978; Thompson and Robbins, 1990) phenomenon was increased.

ACKNOWLEDGMENT

This work was supported, in part, by an SBIR Phase I Grant No. DE08622 from NIH-NIDR. The assistance of Mr. Thuan N. Phan, who was supported by the Minority Research Apprentice Program, is also gratefully recognized. Received June 4, 1991/Accepted October 22, 1991 Address correspondence and reprint requests to: Robert P. Kusy Building #210-H, Room #313 University of North Carolina Chapel Hill, NC 27599-7455

REFERENCES

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