Elastic properties of translucent polycrystalline cubic boron nitride as characterized by the dynamic resonance method

Diamond and Related Materials 8 (1999) 1522–1526 www.elsevier.com/locate/diamond

Elastic properties of translucent polycrystalline cubic boron nitride as characterized by the dynamic resonance method Mark P. D’Evelyn a, *, Takashi Taniguchi b a General Electric Corporate Research and Development, P. O. Box 8, Schenectady, NY 12301, USA b National Institute for Research in Inorganic Materials, 1-1 Namiki Tsukuba, Ibaraki 305, Japan Accepted 30 November 1998

Abstract Cubic boron nitride (cBN ) is second only to diamond in a number of extreme material properties, and its performance exceeds diamond in many applications involving contact with ferrous alloys and/or high temperatures. However, its properties are less well understood. We have sintered cBN powder (2–4 mm or 8–12 mm particle size) into pure, translucent, polycrystalline compacts by pressing at a pressure of 7.7 GPa and temperatures from 2100 to 2350°C without any sintering agent. We have determined the Young’s modulus E, shear modulus G, and Poisson’s ratio n of a number of translucent polycrystalline cBN compacts, in the form of free-standing disks, using the dynamic resonance method. The measured values for E, G, and n lay in the ranges of 665– 895 GPa, 295–405 GPa, and 0.11–0.15, respectively, depending on the grain size of the cBN starting material and the sintering temperature. These values may be compared with the theoretical values of E, G, and n for pure, equiaxed, cBN of 909 GPa, 405 GPa, and 0.12, respectively. Combining the Young’s modulus with previous Vickers hardness measurements, the fracture toughness K of well-sintered translucent PCBN is evaluated as 6.8 MPa m1/2. The dependence of the elastic properties on the IC synthesis conditions is discussed in the context of the microstructure and of related material properties. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Cubic boron nitride; Dynamic resonance method; High pressure high temperature; Young’s modulus

1. Introduction Cubic boron nitride (cBN ) is the second hardest material known, after diamond, and is superior to diamond in several respects: a higher oxidation resistance, greater chemical resistance to ferrous alloys such as steels and nickel-based superalloys, and electronic properties that are readily amenable to both p- and n-type doping [1]. Commercial cBN products are available in the form of mesh-sized crystals and polycrystalline compacts; however, most polycrystalline cBN (PCBN ) products also contain significant volume fractions of a binder phase. Several methods of producing dense, sintered, translucent cBN bodies without additional sintering agents have been reported [2–6 ]. These methods involve either the direct conversion of deoxidized hexagonal BN (hBN ) to cBN at 7.7 GPa and a temperature between * Corresponding author. Fax: +1 518 387 7563. E-mail address: [email protected] (M.P. D’Evelyn)

2000 and 2500°C [2,3,6 ] or direct sintering of cBN powder at 7.7 GPa and a temperature above 2000°C [4,5]. Control of the grain size appears to be easier when cBN powder is used as the starting material [5]. Pure-phase polycrystalline cBN may prove to have superior properties in some applications, and also provides an opportunity to better understand the properties of cBN, which are not as well established as those of diamond. Previous work established that the density and hardness of translucent PCBN was optimized for reaction temperatures in the range of 2000–2350°C. However, no information was available on the elastic properties of the material as a function of the grain size of the starting material and the sintering temperature. In this paper we report the determination of the Young’s modulus, shear modulus, and Poisson’s ratio of translucent PCBN as a function of synthesis conditions using the dynamic resonance method, use the results to evaluate the fracture toughness, and analyze the modulus results in terms of the microstructure and related material properties.

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2. Experimental details Six free-standing PCBN disks were synthesized using a high pressure high temperature method described in detail elsewhere [4,5]. Briefly, cBN powder in sizes of 2–4 or 8–12 mm (SBNT grade, Showa Denko, Tokyo, Japan) was used as the starting material. The powders were fired at 1000°C under a vacuum of 3×10−3 Pa to remove adsorbed water, then were placed in a Ta capsule. Sintering was performed at 7.7 GPa at temperatures between 2100 and 2350°C for 15 min in a modified belt-type apparatus with a bore diameter of 32 mm. The temperature was estimated from the relationship between input power and cell temperature previously determined using a W–5%Re/W–26%Re thermocouple, uncorrected for the effect of pressure on the e.m.f. These syntheses were performed about a year after the previously reported studies [4,5], with a different wattage/temperature calibration, and the temperatures are estimated to have a long-term reproducibility of about ±25–50°C, typical for high pressure high temperature work. After the high pressure treatment, the Ta foil was removed using an HF/HNO acid treatment. 3 The cBN specimens were then ground into disks approximately 0.3 mm thick and 6 mm in diameter. The elastic properties of each disk were measured using the impulse dynamic resonance method [7–9]. This method is applicable to disks as well as to freestanding rectangular bars, has been proposed as an annex to ASTM Standard C1259 [10], and has recently been applied to the characterization of disks of polycrystalline diamond and cubic boron nitride [11] and CVD diamond [12]. Accurate equations relating the resonant frequencies of free-standing disks to their elastic constants were first derived by Martincek [13], and a more refined set of tables was calculated by Glandus [14,15]. These equations are believed to be accurate to approximately 1% or better for a wide range of specimen geometries and elastic constants. The mode with the lowest frequency, the fundamental torsional vibration, has bisecting nodal lines and is illustrated in Fig. 1a. The flexural vibration is a biaxial drumhead mode with a nodal circle occurring at 68.1% of the disk diameter [13–15], as illustrated in Fig. 1b. The equations relating the Young’s modulus and shear modulus to the torsional and flexural frequencies, f and f , respectively, are summarized below. In these T F equations d is the diameter of the disk, t is the thickness, and r is the density. The Poisson’s ratio is derived directly from the ratio of the flexural and torsional frequencies and t/d by interpolation from tabulated values [13–15]. Once the value of n is evaluated, the Young’s modulus is calculated from E=

3 2

p2r(1−n2)

A B CA B A B D d2 2 t

f

F K F

2

+

f 2 T . K T

(1)

Fig. 1. Schematic illustration of ringing measurements on (a) the torsional mode or (b) the flexural mode of a disk. The flexural vibration is a biaxial drumhead mode with a nodal circle at 0.681 of the diameter of the part.

The numerical factors K and K depend weakly on n F T and the t/d ratio and are calculated by interpolation from tabulated values [14,15]. For the parts analyzed here, K and K in Eq. (1) were approximately equal to F T 8.4 and 5.8, respectively. The value of the shear modulus then follows from G=

E 2(1+n)

.

(2)

Finally, the bulk modulus [16 ] is calculated as B=

EG 9G−3E

.

(3)

The procedures for the dynamic resonance experiments were the same as those described in detail elsewhere [11]. Briefly, the specimens were fixtured on tensioned cotton threads or foam buttons and excited by bouncing a hollow zirconia bead on the edge or center to excite the torsional or flexural modes, respectively, as illustrated in Fig. 1. The ringing signal was detected by a microphone and preamplifier and analyzed using a digital oscilloscope with fast Fourier transform capability. Each specimen was weighed on a precision

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balance, its diameter was measured using a micrometer, and its thickness was measured at five points using a digital thickness gauge with a precision of ±1 mm. The measured thicknesses varied by 1–9 mm over each disk, i.e. were uniform to 0.3–3%. The edges of some of the specimens were slightly chipped, leading to some uncertainty in the effective thickness.

3. Results A total of six translucent, polycrystalline cBN specimens were tested, yielding flexural and torsional frequencies between 130 and 250 kHz. The Poisson’s ratio, Young’s modulus, shear modulus, and bulk modulus were then calculated for each specimen using Eqs. (1)– (3), and the results are summarized in Table 1. Ideally, the uncertainties in the results would be determined from replicate measurements. Only one specimen was fabricated for each reaction condition, however, and therefore we can only make estimates. The uncertainties in the frequencies were about ±1 kHz, or ±0.5–1%, and the main source of error was probably the thickness [11,17]. The densities, based on the measured weights, thicknesses, and diameters, were slightly below values measured directly by the Archimedes method [5], probably because of the presence of some small chips along the edges of the disks. We have estimated the uncertainties in the elastic properties by calculating the change in values produced by substituting the effective thickness calculated from the Archimedesmeasured density [5] for the measured thickness. The measured results, together with the error bars estimated in this way, are plotted in Fig. 2. The errors were largest for the disks sintered at 2200°C, for which the chipping was somewhat more pronounced. For comparison, we have also included theoretical values for pure, equiaxed cBN, calculated [11] by performing an orientational average of single-crystal elastic constant data [18]. Briefly, the orientation-averaged shear modulus G 9 is determined by solving the Hershey–

Fig. 2. Dependence of the Young’s modulus E ( left scale, filled symbols) and shear modulus G (right scale, open symbols) on sintering temperature at 7.7 GPa. Grain size of cBN powder raw material was 2–4 mm (circles) or 8–12 mm (triangles). The theoretical values of E (909 GPa) and G (405 GPa) for pure, equiaxed PCBN are indicated by the arrows.

Kro¨ner–Eshelby equation [19,20] 8G 9 3+(9B+4C∞)G 9 2−3c (B+4C∞)G 9 −6Bc C∞=0 (4) 44 44 where B is calculated directly from the single-crystal elastic stiffness constants as (c +2c )/3 [16 ] and 11 12 C∞=(c −c )/2. Inserting the elastic stiffness constants 11 12 for cBN (c =820 GPa; c =190 GPa; c =480 GPa 11 12 44 [18]) into Eq. (4) and numerically solving, we obtain B=400 GPa and G 9 =405 GPa. From the equations relating B, G, E, and n [11,16 ], we obtain E9 =909 GPa and n: =0.121. These values are included in Table 1 and Fig. 2. 4. Discussion The Young’s modulus and shear modulus attained their maximum values for sintering temperatures of 2200 and 2350°C for starting cBN particle sizes of 2–4 or 8– 12 mm, respectively. At a sintering temperature T of S 2100°C the modulus values were significantly less, suggesting incomplete sintering. Sintering appears to be

Table 1 Summary of measured properties of translucent polycrystalline cBN disks, as a function of grain size and sintering temperature (T ). Tabulated s values include the weight, diameter (d ), thickness (t), density (r), torsional ( f ) and flexural ( f ) frequencies, Young’s modulus (E), shear modulus T F (G), Poisson’s ratio (n), and bulk modulus (B) Grain size (mm)

T (°C ) S

Weight (g)

d (mm)

t (mm)

r (g cm−3)

f (kHz) T

f (kHz) F

E (GPa)

G (GPa)

n

B (GPa)

2–4 2–4 2–4 8–12 8–12 8–12 Theoretical

2100 2200 2300 2100 2200 2350

0.0248 0.0253 0.0255 0.0263 0.0246 0.0266

5.64 5.66 5.69 5.75 5.73 5.72

0.295 0.306 0.291 0.301 0.290 0.308

3.37 3.28 3.44 3.37 3.29 3.36 3.49

149.0 169.0 151.5 137.0 146.0 161.1

219.0 243.8 219.5 198.5 216.0 234.0

766 894 849 665 790 853 909

337 402 380 297 345 380 405

0.137 0.111 0.117 0.118 0.145 0.122 0.121

352 383 370 290 371 376 400

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complete at 2200°C when starting with 2–4 mm cBN powder, whereas with 8–12 mm cBN powder an additional 150°C increased the modulus values further. These trends are in excellent agreement with previous results on directly sintered cBN, where the density, Vickers hardness, and fracture toughness attained their maximal values near 2200–2300°C, and the optimum conditions occurred at slightly higher temperature for 8–12 mm cBN starting material relative to that with 2–4 mm cBN [4,5]. By analogy with these results, the apparent decrease in E and G as T is increased from 2200 to S 2300°C with 2–4 mm cBN ( Fig. 2) is probably real. The peak in material properties occurred at temperatures roughly 50°C higher in the previous studies [4,5] than in the present work, but the difference may not be significant because of uncertainty in the temperature calibrations (ca. ±25–50°C ). The present work utilized a slightly longer sintering time (15 versus 10 min), but the effect of additional sintering time is unlikely to be as important as a 50°C change in the process temperature. The fracture toughness K of ceramic materials can IC be evaluated using the so-called indentation microfracture method, wherein the lengths of median/radial-type cracks associated with Vickers indentations are measured as a function of applied load [21–24]. In the formulation which has been most widely applied to superhard materials [3,5,25,26 ], the fracture toughness is evaluated from K =A(E/H )1/2P/C3/2 (5) IC 0 where A=0.016±0.004 [24], H is the hardness, P is the applied load, and C is the crack length. 0 In a previous study of translucent PCBN [5], wellsintered material produced from 2–4 or 8–12 mm cBN powder was found to have a hardness of approximately 49 GPa. Assuming that the ratio E/H is constant, the fracture toughness is proportional to P/C3/2 which was 0 found to achieve a maximum of 100 MPa m1/2 for optimally sintered translucent PCBN [5]. The very similar functional dependence of E (present work) and H [5] on sintering temperature indicates that the assump-

tion of a constant E/H ratio is indeed valid. Taking the average of the maximum Young’s modulus values measured with PCBN synthesized from 2–4 and 8–12 mm cBN, 874 GPa, and combining this value with the previously measured values of H and P/C3/2 we obtain 0 from Eq. (5) a value of K =6.8 MPa m1/2 for optimally IC sintered translucent PCBN. This value is above that reported for single-crystal cBN, 2.8 MPa m1/2 [27], and within the range of values measured for PCBN with binders, 5.5–10.8 MPa m1/2 [11,28–30]. Previous studies of the microstructure of directly sintered cBN [4,5] provide further insight into the physical basis for the trends in modulus values observed in the present study. For T of 2100°C or less fracture S was predominantly inter-granular, indicating relatively weak bonding between the grains [4,5]. Weak intergranular bonding must also be responsible for the decreased modulus values at T =2100°C. At T = S S 2350°C, fracture was predominantly trans-granular, indicating stronger bonding, and little grain growth had occurred [4,5], consistent with a modulus and hardness close to that of ideal cBN. At higher temperature some grain growth occurred, decreasing the fracture toughness, and residual pores were also observed [4,5]. Similar factors were probably responsible for the slight decrease in modulus values at 2300°C with the 2–4 mm cBN starting material ( Table 1, Fig. 2). The elastic properties of disks sintered under optimum conditions (2200°C for 2–4 mm; 2350°C for 8– 12 mm) are close to the theoretical values for pure, equiaxed cBN and are also in excellent agreement with previous measurements on nearly pure-phase PCBN, as summarized in Table 2, including the longitudinal speedof-sound measurements of Gilmore [31] and the acoustic interferometry measurements of Manghnani [32]. The near-convergence of the measured values to the theoretical values is a strong indication that bonding between cBN grains in the optimum-sintered material is strong and that there are a minimal number of voids. The discrepancies between the measurements are well within the variation produced by different synthesis conditions ( Table 1) and uncertainties in the measurements them-

Table 2 Comparison of elastic properties of PCBN measured in the present work with previous measurements on pure-phase and commercial-grade PCBN. Borazon (BZN ) is a trademark of GE Superabrasives Sample

Author(s)

Vol.% cBN

E (GPa)

G (GPa)

n

PCBN, 2–4 mm, T =2200°C S PCBN, 8–12 mm, T =2350°C S PCBN, pure phase PCBN, pure phase BZN 6000A BZN 7000A BZN 8100A Theoretical

This work This work Gilmore [31] Manghnani [32] D’Evelyn and Zgonc [11] DZ [11] DZ [11] DZ [11]

~100 ~100 ~99 ~99 90 80 60 100

894 853 890 847 737 709 648 909

402 380

0.111 0.122

378 318 309 275 405

0.121 0.158 0.147 0.176 0.121

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selves (Fig. 2); the uncertainty in the theoretical values is probably 10–40 GPa [11]. The addition of a matrix phase, as in commercial products, improves tool performance in many applications but substantially decreases the Young’s modulus and shear modulus ( Table 2), as would be expected from the decreased cBN-to-cBN bonding. In conclusion, we have determined the effect of sintering temperature on the elastic properties of pure, translucent polycrystalline cBN using the dynamic resonance method. At the optimum sintering temperatures of 2200°C for 2–4 mm cBN or 2350°C for 8–12 mm cBN powders, the Young’s modulus, shear modulus, and Poisson’s ratio are very close to the theoretical values of pure, equiaxed cBN and the fracture toughness is 6.8 MPa m1/2. At lower process temperatures the modulus values are lower, apparently due to incomplete sintering, while at higher temperatures the modulus values are reduced by grain growth.

Acknowledgement M.P.D. thanks Dr. Curt Johnson for the use of his equipment.

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