ISSN 10634576, Journal of Superhard Materials, 2014, Vol. 36, No. 2, pp. 65–81. © Allerton Press, Inc., 2014. Original Russian Text © Yu.V. Milman, 2014, published in Sverkhtverdye Materialy, 2014, Vol. 36, No. 2, pp. 3–23.

PRODUCTION, STRUCTURE, PROPERTIES The paper is dedicated to memory of Prof. Silvana Lux of Johannesburg (South African Republic), a prominent researcher in the field of powder metallurgy and hard alloys, whose talent and managerial abilities have made pos sible joint investigations of researchers from Ukraine and SAR.

The Effect of Structural State and Temperature on Mechanical Properties and Deformation Mechanisms of WC–Co Hard Alloy Yu. V. Milman Frantsevich Institute for Materials Science Problems, National Academy of Sciences of Ukraine, vul. Krzhizhanovs’kogo 3, Kiev, 03680 Ukraine email: [email protected] Received September 3, 2013

Abstract—The publications reporting systematic investigations of the effect of structural state of WC–Co hard alloys (the cobalt binder content, WC grains size and contiguity) and temperature on mechanical properties and deformation mechanisms have been reviewed and generalized. The ductile–brittle transi tion, strain hardening, special features of WC–Co alloys deformations in various temperature ranges, and specificity of mechanical properties of the alloys with submicron WC grains have been discussed. DOI: 10.3103/S1063457614020014 Keywords: WC–Co hard alloy, hardness, yield strength, ultimate strength, strain hardening, temperature of the ductile–brittle transition, plastic deformation mechanism.

1. INTRODUCTION For many decades WC–Co hard alloy is one of the basic tool materials. In operation a tool may be essen tially heated but for many years systematic studies of the influences of a temperature, cobalt binder content, and size of WC grains on the alloy mechanical properties, mechanisms of deformation and fracture were not conducted. A number of papers, which dealt with this problem, were prepared with my participation and pub lished in different journals [1–7]. In these studies the features of the deformation and fracture processes of WC–Co alloys like ductile–brittle transition, strain hardening, dependence of plasticity prior to failure and characteristics of alloys plasticity, which is defined by indentation, on the alloy structure and temperature, were considered for the first time [1–7]. A change of the mechanism of WC–Co alloys deformation in various temperature regions and the features of a hightemperature deformation in alloys with nanosized WC grains are also discussed. The results obtained in the above studies are generalized in the present paper. 2. MECHANICAL PROPERTIES OF A WC SINGLE CRYSTAL WC tungsten carbide has a hexagonal structure with crystal lattice parameters a = 2.906 Å and c = 2.837 Å [8]. WC is a unique refractory compound, which combines high hardness (HV ≈ 17 GPa), high Young modulus (E ≈ 720 GPa), and a high for refractory compounds characteristic of plasticity (δH ≈ 0.82), which is defined by indentation. The characteristic of plasticity, δH, is defined as the ratio of the plastic deformation degree to the total deformation in indentation and may characterize the plasticity of materials that exhibit brittle frac ture during standard mechanical tests [9–12]. 65

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Mechanical properties of a WC single crystal (0001) were studied in [7] in comparison with other refractory compounds and properties of WC–6Co and WC–15Co1 hard alloys. In the same study the properties of a WC single crystal were compared with properties of a WC grain in a hard alloy. It is seen from Fig. 1 that the temperature dependence of hardness, HV, of WC is of the same mode as of other refractory compounds: the hardness increases as the temperature decreases according to the exponential dependence at high temperatures and according to the linear dependence at low temperatures. The activation energy of dislocations movement in WC is U ≈ 1.8 eV [7], which approaches the activation energy of dislocations movement in Si, Ge, and other covalent crystals and refractory compounds. The tem perature dependence of WC–Co alloys exhibits somewhat other mode. In Fig. 2 the plasticity characteristic, δH, of WC is compared with δH of other refractory compounds in a wide temperature range. HV, GPa 18

δH 1.0

16 0.8

14 12

0.6 10 8 0.4 6 4

0.2

2

0

200

400 600 800 Temperature, °C

1000

Fig. 1. Temperature dependence of WC single crystal hardness as compared with hardness of single crystals of WC (䊊), WC–6Co (䊉), WC–15Co (䉱).

0

250 500 750 Temperature, °C

1000

1250

Fig. 2. Temperature dependence of the plasticity charac teristic δH of a WC single crystal as compared with δH of other refractory compounds and alloys: WC (䊊), TiC (䉭), B4C (ⵧ), NbC (䉫), WC–6Co (䉬), WC–15Co (䉱), B4C + 40ZrB2 (䊏).

Though at room temperature δH of WC is below the critical value of 0.9, at which the plasticity shows up during a tensile test [9, 10], the δH of WC is essentially higher than of TiC, B4C, and NbC. At the local indentation loading glide lines are observed around the imprint in a WC single crystal and radial microcracks are absent (Fig. 3). Just the increased plasticity of WC in local loading is responsible for an enhanced efficiency of its operation in a cobalt binder as compared, e.g., with TiC, ZrC, and NbC, though single crystals of these carbides exhibit higher hardness at room temperature than WC (HV = 22 GPa of ZrC and HV = 24 GPa of ZrC and NbC). Thanks to the WC plasticity at local loading, the stress concentration in the head of dislocation piledup groups in a cobalt binder may partially relax in a WC particle not inducing the crack formation. Because of the aforesaid a successful replacement of WC in hard alloys by other more brittle (though harder) refractory com pound seems unlikely. As is seen from Fig. 2, the dÍ value of WC–Co hard alloys at 20°C is somewhat lower than of a WC single crystal (as a result of a decrease of the Young modulus), but essentially higher than in the majority of refractory compounds. 1

The alloy composition is given in wt %. JOURNAL OF SUPERHARD MATERIALS

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50 μm

Fig. 3. Glide lines around the imprint in a WC single crystal at an indentation load of 50 N.

By nanoindentation it was shown in [7] that a WC grain in a hard alloy has slightly lower HV and E values than a WC single crystal. However, the δH plasticity characteristic of a grain is even somewhat higher than that of a single crystal. In [13] the nanohardness was studied at the same lot of WC single crystals, which was used in [7] to deter mine hardness. In this case at the indentation load P = 5 mN, the nanohardness was H = 39.8 GPa, i.e., exceeded the macrohardness more than by a factor of 2 (see Fig. 1). It is also shown in [13] that as P decreases further, an abrupt increase of H should be observed. 3. EFFECT OF THE TEMPERATURE, PHASE COMPOSITION AND STRUCTURAL STATE ON WC–Co ALLOYS HARDNESS WC–Co hard alloys are usually twophase, they consist of WC grains and a cobalt binder. Typical structures of the alloys are given in Fig. 4.

0.25 μm

1 μm

(a) (b) Fig. 4. Microstructures of the WC–Co alloy: d = 0.328 μm, Vm = 10 vol % (a), d = 1.32 μm, Vm = 16 vol % [5] (b).

The data that were earlier published in the literature [14, 15] on hightemperature hardness of WC–Co alloys showed that hardness of these materials monotonically decreases with the temperature increase in the 20–1000°C range and that hardness of alloys with coarse WC grains is lower than hardness of alloys with fine grains. A detail study of the effect of WC grain size and the amount of cobalt binder on hightemperature hardness and the first study of the lowtemperature (to –196°C) hardness of WC–Co alloys were reported in [1, 2]. JOURNAL OF SUPERHARD MATERIALS

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Alloys with concentration of the cobalt binder of 6, 10, and 15 wt %, i.e., 10, 16, and 24 vol %, the mean size of WC grains varied from 0.30 to 3.55 mm were studied. Table 1 gives characteristics of alloys studied in [1, 2]. Typical temperature dependences of alloys hardness are shown in Fig. 5. These results are in good agreement with results obtained by other researchers [14, 15]. Table 1. Compositions of the WC–Co alloys under study Characteristics Co, wt % Vm (Co), vol % Meansize of a grain d, μm

N6 6 10 0.54

N10 10 16 0.47

N15 15 24 0.48

HV, GPa 30

S6 6 10 1.26

Alloys S10 10 16 1.20

S15 15 24 1.05

G6 6 10 2.62

G10 10 16 2.28

G15 15 24 2.00

HV, GPa 30

25

25

20

20

15

15

10

10

5

5 0

0 –200

0

200 400 600 Temperature, °C (a)

800

1000

–200

0

200 400 600 Temperature, °C (b)

800

1000

HV, GPa 30 25 20 15 10 5 0 –200

0

200 400 600 800 1000 Temperature, °C (c) Fig. 5. Temperature dependences of hardness of WC–Co alloys having different grain sizes (N (a), S (b), G (c)) and different cobalt binder content 6 (䊊, 䊉), 10 (䊐, 䊏), 15 (䉭, 䉱) wt %; the indentation load being 60 N (䊉, 䊏, 䉱) and 200 N (䊊, 䊐, 䉭); the alloys designations see in Table 1.

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To the best of our knowledge the results of measuring hardness at belowroom temperature have no analogs in the literature. To interpret the results obtained in [2], we used the equation H = HWCVWCC + Hm(1 – VWCC),

(1)

proposed by Lee and Gurland [16]. In this equation H is the hardness of the WC–Co alloy, HWC is the hardness of a WC polycrystal, Hm is the hardness of a cobalt binder in the WC–Co alloy, C is the contiguity of WC grains, VWC is the WC volume fraction in the WC–Co alloy. It is experimentally shown in [16] that HWC and Hm in Eq. (1) should allow for a grain size and are described by Hall–Petch equations: HWC = H0WC + K0WCd–1/2;

(2)

Hm = H0m + K0mλ–1/2,

(3)

here d is the mean size of a WC grain, λ is the mean glide line in a cobalt binder. The H0WC, K0WC, H0m, and K0m parameters at room temperature were found in [17]: HWC = 1350 + 21d–1/2; Hm = 130 + 16λ–1/2. As is shown in [16], between d and λ parameters there is the following relation V λ = m d . ( 1 – Vm ) ( 1 – C )

(4)

The WC grains contiguity, C, varies with the cobalt binder content of the alloy, but depends on the grain size slightly [16]. As is shown in [2], one may assume with a sufficient accuracy that C ≈ 0.6 for all alloys considered in this study. In this case there is a linear relation between λ and d λ = Bd,

(5)

V where B = m , i.e., B = 0.28, 0.48, and 0.79 at Vm = 0.10, 0.16, and 0.24, respectively. ( 1 – Vm ) ( 1 – C ) With the use of expressions (1)–(5) it was shown in [2] that the Hall–Petch relation should be true for a WC–Co alloy as well H = H0 + Kyd–1/2,

(6)

where H0 = H0WCVWCC + H0m(1 – VWCC),

(7)

Ky = K0WCVWCC + K0m(1– VWCC)B–1/2.

(8)

As it follows from Fig. 6, the experimental data sufficiently well verify the correctness of the Hall–Petch relation (6) for the studied alloys with three different concentrations of cobalt binder. A successful use of Eq. (1) to describe the structure effect on the hardness of WC–Co alloys indicates that in indentation the direct contact of a diamond indenter with the sample surface results in the fact that plastic deformation occurs in both phases WC and Co of the alloy at all the studied temperatures. Based on the experimental data obtained, in [1] the H0 and Ky parameters in Eq. (6) were defined. Tem perature dependences of H0 and Ky parameters are presented in Fig. 7. It follows from the figure that H0 parameter decreases with increasing temperature. In the –196–600°C temperature range the Ky parameter depends slightly on the temperature and as the temperature further increases, the parameter decreases essen tially. It should be noted that the H0 parameter as well as the alloys hardness H considerably increase as the temperature decreases to –196°C. The effect of the cobalt binder on the H0 and Ky parameters at 20°C are given in Fig. 8 according to the results reported in [1, 2]. It is seen that as the cobalt concentration increases, both parameters decrease. JOURNAL OF SUPERHARD MATERIALS

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HV, GPa 25

25

20

20

15

15

10

10

5

5

0 15

20

25

30 35 40 –1/2 –1/2 d , mm (a)

45

0 15

50

20

25

30–1/2 35 –1/2 40 d , mm (b)

45

50

HV, GPa 25

20

15

10

5

0 15

20

25

30 35 40 45 50 –1/2 , mm (c) Fig. 6. Hall–Petch relations for WC–Co alloys with different cobalt binder content: Vm = 10 (a), 16 (b), 24 (c) wt %; test tem peratures: 196 (䊏), 20 (䊐), 200 (䊉), 300 (䊊), 400 (䉱), 500 (䉭), 600 (䉲), 700 (䉮), 800 (䉬), 900 (䉫) °C. –1/2

d

The experimental results shown in Figs. 7 and 8 in combination with Eq. (6) make it possible to sufficiently exactly calculate the temperature dependence of hardness of WC–Co alloys having different WC grain sizes and different concentrations of the cobalt binder, and to develop alloys with the specified hardness. 4. MECHANICAL PROPERTIES OF WC–Co ALLOYS IN A BENDING TEST Let us consider the results of mechanical tests of WC–Co alloys described in [3–5]. Table 2 shows the phase compositions, mean size of WC grains d, mean width of a cobalt interlayer, λ, con tiguity C, and mechanical properties of the studied alloys. The threepoint bending tests were conducted on 35 × 4.5 × 1.2 mm samples recording the curves of a load P and bending deflection f. The rate of the bending knife motion was 1.7 × 10–6 m/s, which afforded the extension rate in a surface layer v = 7 × 10–5s–1. The tests were carried out in a vacuum of 10–3 Pa in the tem perature range 20–1000°C using a rigid tensile machine of the Instron type, the heating was produced by tung sten heaters. It is seen from Table 1 that the main attention was given to the alloys having micron and submi cron WC grains. The yield strength σs = σ0.01 and ultimate strength σf were calculated from the deformation curves. As the plasticity characteristic we used the tensile deformation of sample surface prior to failure δ in JOURNAL OF SUPERHARD MATERIALS

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bending test and the plasticity characteristic found by indentation δH (see section 2). As the deformation tem perature of WC–Co alloys changes, the ductilebrittle transition is observed. We defined the physical temper ature of cold brittleness Tdp as the maximum temperature, at which δ = 0, and conventional temperature of cold brittleness Tdp, at which δ = 0.1% (see Table 2). 3/2

H0, GPa 12

Ky, MN/m 12

10

10

8

8

6

6

4

4

2

2

0 –200 0 200 400 600 800 1000 200 400 600 800 1000 Temperature, °C Temperature, °C (b) (a) Fig. 7. Temperature dependences of H0 (a) and Ky (b) parameters in the Hall–Petch relation (Eq. 6) for WC–Co alloys having different concentrations of a cobalt binder: Vm = 10 (䊊), 16 (ⵧ), 24 (䉭) wt %. 0

8

14

7

12

6 H0, GPa

5 8

4 6

3

3/2

10 Ky, MN/m

0 –200

4

2

2

1 0

0 8

10

12

14

16 18 Vm, %

20

22

24

26

Fig. 8. H0 and Ky parameters in the Hall–Petch relation vs. cobalt binder concentrations at temperatures of 20 (䊉, 䉱) and 600 (䊊, 䉭) °C.

The temperature dependences of σs and σf are given in Fig. 9. In this figure the temperatures of cold brit tleness Tdp are also shown. The temperature dependences of the plasticity characteristics δ and δH are dem onstrated in Fig. 10 [5]. It is seen that δ > 0 is inherent in alloys at comparatively high temperatures only. At room temperature δ = 0 for all alloys studied, while the δH has values other than zero at all temperatures and allows us to compare the alloy plasticity. It follows from Figs. 9 and 10 and Table 2 that at room temperature a decrease of the grain size results in a decrease of δH. A decrease in the grain size leads also to an increase of yield strength σs (Fig. 9) and cold brit

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tleness Tdp (Figs. 9 and 10). However, at high temperatures (800 and 1000°C) the plasticity of alloys with sub micron WC grains turns out to be increased. Table 2. Grain size d, Co concentration, contiguity C, mean width of cobalt interlayer λ, hardness HV, temperatures of the ductile–brittle transitions Tdp and Tdc, ultimate strength σf and plasticity characteristics δH of WC–Co alloys [5] Alloy characteristics d, μm Co, wt % C λ, mm HV, GPa (at P = 50 N) Tdp, °C Tdc, °C σf, GPa δH

S6 1.30 6 0.60 0.36 16.8 300 700 2.61 0.739

S10 1.32 10 0.70 0.84 15.2 250 600 2.74 0.737

S15 1.30 15 0.58 0.98 13.6 200 450 2.63 0.752

NY6 0.328 6 0.57 0.08 22.5 550 650 2.39 0.678

Alloy NY10 0.397 10 0.52 0.16 19.3 ~ 300 580 3.56 0.701

NY15 0.350 15 0.45 0.20 16.3 ~ 300 570 2.79 0.719

NY6A 0.292 6 0.55 0.07 24.3 700 820 0.91 0.630

NY10A 0.293 10 0.60 0.14 19.0 400 615 1.66 0.703

NY15A 0.304 15 0.63 0.26 16.6 400 605 0.65 0.712

4.0

3.5

3.5

3.0

3.0

2.5

1.5

1.0

σf, σs, GPa

σf, σs, GPa

2.5

2.0 Tdp S15 Tdp S10

2.0 1.5

Tdp NY10 Tdp NY15

1.0 Tdp NY6

Tdp S6

0.5

0.5

0 0 200 400 600 800 T, °C 400 600 800 T, °C (a) (b) Fig. 9. Temperature dependences of ultimate strength σf (䊊, ⵧ, 䉫) and yield strength σs (䊉, 䊏, 䉬); Tdp is the temperature of a ductilebrittle transition: alloys S6 (䊊, 䊉), S10 (䊐, 䊏), S15 (䉫, 䉬) (a) and NY6 (䊊, 䊉), NY10 (䊐, 䊏), NY15 (䉫, 䉬) (b) (Table 2) [5].

0 –200

0

200

It is seen from Fig. 11 that the dependence of σs on grain size d may be described by the Hall–Petch rela tion at 600 and 800°C. As the cold brittleness temperature, Tdp, of a number of alloys is above 400°C, we failed to check the correctness of the Hall–Petch relation at this and lower temperatures. At 1000°C the Hall–Petch relation (see Fig. 11b) is not true. In [4] this fact is attributable to the grain boundary sliding, which is espe cially essential for alloys with submicron WC grains. The ultimate strength, σf , depends slightly on the temperature at T < Tdp (see Fig. 9), which corresponds to the Ioffe theory of cold brittleness [18]. At T < Tdp the σf value abruptly decreases with increasing temper ature, reflecting a decrease of the yield strength, σs. It is worth noting a high σf value in the temperature range of brittle fracture at T < Tdp. It is seen from Fig. 9 that at room temperature σf = 3.56 GPa of an alloy with a mean grain size d = 0.35 mm and σf = 2.74 GPa if d = 1.3 mm (both results are obtained for the most strong alloys with 10 wt % concentration of the cobalt JOURNAL OF SUPERHARD MATERIALS

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binder). Such high strength values are due to a high degree to the plasticity of WC grains at local loading (see above). Just this type of loading is characteristic of the effect of dislocation pileups in the plastic cobalt binder on a grain. The plasticity of WC grains in local loading allows one to partially relax stresses in the head of a dislocation pileup and decrease the concentration of stresses on a grain. In this case the initiation and open ing of cracks is hampered and an increased efficiency of a WC–Co alloy is attained. As is seen from the results presented, in the temperature region T < Tdp in alloys with submicron WC grains (d = 350 nm) the σf value is essentially higher than in alloys with micron grains. However, in alloys with the finest grains d = 300 nm the plasticity characteristic, δH, essentially reduces and as a result the bending strength decreases. At the same time the hardness of these alloys is the highest (see Table 2). 4.1. DuctileBrittle Transition and Plasticity in WC–Co Alloys At room temperature in standard mechanical tests like the tension or bending the WC–Co alloys are brittle. As the temperature increases, these materials exhibit some plasticity prior to failure (see Fig. 10). For a description of the ductile–brittle transition in WC–Co alloys, the Ioffe theory of the cold brittleness [18] may be used. According to this theory, as the temperature decreases, the yield strength increases quicker than the ultimate strength. The intersection of two curves σs(T) and σf(T) just is the temperature of the ductilebrittle transition, Tdp. This conception was first used to describe the cold brittleness in steels, and later in other bcc metals [19] and ceramics [19, 20]. It was found that the porosity decreases σf quicker than σs and because of this an increase of the porosity brings about an increase of Tdp [21]. It is likely that the ductilebrittle transition in WC–Co alloys was first studied in [3–5], where two temper atures of cold brittleness, Tdp and Tdc, were defined. The Tdp values of different alloys are given in Fig. 9, and both temperatures of the ductilebrittle transition in Table 2, from which it follows that a decrease in the grain size results in the essential increase of Tdp and Tdc. As the cobalt concentrations increases, these temperatures decrease. The minimum Tdp (200°C) is observed for the S15 alloy, and maximum (700°C) for the NY6A alloy having the finest grains and lowest cobalt binder δ, %

δ, %

0.4

0.4 0.2 δH 0.9

0 200

400

600

T, °C

δ, %

δH

5

0.9

δ, %

0

200

600 T, °C

400

5

4

4

0.8

3

δH 0.7

0.8

3 δH

2

δ

2

δ 1

0.7

1

0 0 T, °C 0 200 400 600 800 T, °C 600 800 (b) (a) Fig. 10. Temperature dependences of δ and δH of alloys S6 (䊉), NY6 (䉱), NY6A (䉬), alloys compositions according to Table 2 [5]. 200

400

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0.8

0.4 δ, %

δH 0

200

400

600 T, °C

0.9

5

4 δ 0.8

3

δH

2

0.7

1

0

σs, GPa

200

400

600 800 (c) Fig. 10. (Contd.)

T, °C

0

σs, GPa 0.8

0.6

2

0.4

1

0.2

0 1.2 1.6 2.0 0.8 1.2 1.6 2.0 –1/2 –1/2 –1/2 –1/2 d , mm d , mm (a) (b) Fig. 11. Yield strength σs vs. mean WC grain size d in the σsd–1/2 coordinates at 600 (䊉, 䊏, 䉱) (a), 800 (䊊, 䊐, 䉭) and 1000 (䊉, 䊏, 䉱) (b) °C [5]; the Co concentrations are 6 (䊊, 䊉), 10 (䊐, 䊏), 15 (䉭, 䉱) wt %. 0.8

concentration. For the majority of the studied alloys the Tdc = (600–700°C). The plasticity in bending of the alloys under study is detected at T > Tdp. The temperature dependence of δ and δH is shown in Fig. 10. The increase of the cobalt content of an alloy results in an increase in d and δH in all the temperature range studied. The effect of the grain size on the plasticity is more complicated. At low temperatures the S alloys have higher JOURNAL OF SUPERHARD MATERIALS

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plasticity as compared with the NY and NYA alloys having submicron grains. However, as the temperature increases, the plasticity of the NY and NYA alloys increases faster and at 800 and 1000°C their plasticity is higher than of the S alloys. Moreover, the NYA alloys, in which grain size is finer than in NY, have the higher plasticity than that of the NY alloys. In [20, 21] an equation was derived that describes the dependence of plasticity prior to failure d on porosity θ for sintered materials: 3 δ = δ k exp ⎛ –  Bθ⎞ . ⎝ 2 ⎠

(9)

Here δk is the plasticity of a porefree (compact) material. The value of the constant B = 4.3 was calculated based on the data of Šalak et al. [22, 23] for porous iron. Later in [21] it was shown that the same B value in Eq. (9) is true for a SiC porous ceramics. The Eq. (9) was derived based on the Cope concept, where as a model a metal–ceramic composite was chosen on the assumption that only interlayers of a ductile matrix between hard particles (or pores) deform [24]. The influences of pores and the second phase on the material strength properties differ greatly. However, the models of a porous body and body with hard particles of the second phase in a description of plasticity prior to failure are virtually identical. According to both models, the fracture is preceded by the plastic deformation only of a part of the material volume between particles or pores. For this reason the use of Eq. (9) to describe the dependence of plasticity δ on cobalt contents of WC–Co hard alloys becomes possible, assuming that θ = VWC, where VWC is the volume fraction of WC particles. Sufficiently reliable experimental data on the δ(VWC) dependence at 800 and 1000°C were obtained in [4, 5]. As is seen in Fig. 12, Eq. (9) is applicable to the description of the δ(VWC) dependence. Really, according to Eq. (9), ln(δ) depends linearly on VWC and at 800°C B ≈ 4.3 for S and NY alloys (see Fig. 12). However, at 1000°C the δ(VWC) dependences for NY and especially for NYA alloys are weaker. This fact as well as a high plasticity of NY and NYA alloys at this tem perature may be because in this case the basic deformation mechanism is a grain boundary sliding. ln(δ, %) 1.5 1 1.0 2 0.5

4

B = 4.3

5 6

3

0

–0.5

–1.0 0.75

0.80

0.85

0.90

VWC

Fig. 12. Dependence of plasticity before fracture δ on volume fraction VWC of WC grains: (1) NYA, 1000°C, B = 2.0; (2) NY, 1000°C, B = 3.0; (3) S, 1000°C, B = 4.8; (4) NYA, 800°C, B = 4.8; (5) NY, 800°C, B = 4.3; (6) S, 800°C, B = 4.4; B is the constant from Eq. (9) [5].

4.2. Strain Hardening of WC–Co Alloys In analysis of the stress–deformation (σ–ε) curves of WC–Co alloys, it was found in [3] that the alloys are characterized by parabolic strain hardening since the moment of the plastic flow beginning. Because of this, σ–ε curves may be approximated according to the Ludwik equation [25]: JOURNAL OF SUPERHARD MATERIALS

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σ = σ s + Nε p . n

(10)

Here σs is the lowest yield strength, εp is the plastic deformation, N is the coefficient of the strain hardening, n is the strainhardening exponent. With the dislocation mechanism of the deformation of a singlephase material [19] N = αGb

1 ⁄ 2 –1 ⁄ 2

ᐉ

,

(11)

where a is the constant approximately equal to 1; G is the shear modulus, b is the Burgers vector, l is the mean length of glide plane, n ≈ 0.5. Figure 13 shows typical stress–deformation curves of WC–Co alloys in loga rithm coordinates log(σ–σs)–logεp at 800 and 1000°C, where the plasticity is sufficient for a reliable deter mination of N and n values. It is seen from Fig. 13 that the experimental points really well lay onto a straight line, which gives a possibility to use Eq. (10) to define N and n values. Table 3 lists the experimentally found N and n values of the S, NY, and NYA alloys. It is seen from the table that at 800°C the n value is near 0.5 for all the alloys under study.

1.0 1.0

σ − σS, GPa

0.5

σ − σS, GPa

0.5

0.2

0.1

0.05

0.1

0.2 0.5 0.1 1.0 εp, % 0.5 1.0 εp, % (a) (b) Fig. 13. Stress–deformation curves for WC–Co alloys in the log(σ–σs)–logεp coordinates: alloys S6 (䊊, 䊉), S10 (䉭, 䉱), S15 (䉫, 䉬) (a) and NY6 (䊊, 䊉), NY10 (䉭, 䉱), NY15 (䉫, 䉬) (b) at 800 (䊊, 䉭, 䉫) and 1000 (䊉, 䉱, 䉬) °C (see Table 2) [5]. 0.1

0.2

The N value of WC–Co alloys is anomalously high. Thus, even at room temperature N = 0.65 GPa for Mo and N ≤ 0.55 GPa for steels. In the case of WC–Co the N value is close to 10 GPa at 800°C, though it is known that the N value decreases with increasing temperature because of a decrease in α and G. At 1000°C n ≈ 0.5 for S alloys only, while for alloys NY and NYA n < 0.5. For NYA alloys, where grains are finer than in NY alloys, the n value is the minimum. The N value at 1000°C also decreases and for NYA alloys it is lower than for NY. It is seen from Fig. 14, strain hardening coefficient N decreases with increasing cobalt content of the alloy. At 800°C the N values in the S and NY alloys differ slightly, while at 1000°C this difference is essential. This feature of the strain hardening of WC, NY, and NYA alloys with nanosized grains may be caused by grain boundary sliding in the course of the deformation. The N value was calculated in [4] using Eq. (11) and invoking the Lee and Gurland concept (see Eqs. (1)– (3)) taking into account the fact that WC alloys are twophase. To calculate the N value, the following equation (at α = 1) was derived 1⁄2

N = α Gm bm λ

1⁄2

1⁄2 d ( 1 – V WC C ) + G WC b WC ⎛  ⎞ ⎝ 4⎠

–1 ⁄ 2

V WC C ,

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where Gm and bm are the shear modulus and Burgers vector of the cobalt matrix, GWC and bWC are the same for WC particles. In this equation the length of the glide plane was taken as equal to λ (the mean width of an interlayer) for a cobalt matrix and d/4 for WC particles. The ratio of the N experimental value to calculated Ncalc value is shown in Table 3. Table 3. Coefficient of the strain hardening N, strain hardening exponent n in Eq. (10) and the ratio of the N experimental value to the Ncalc calculated value T, °C 800

1000

Characteristic of alloys N, GPa n N/Ncalc N, GPa n N/Ncalc

S6 13.1 0.49 2.5 4.4 0.48 0.89

S10 10.6 0.48 2.1 3.2 0.50 0.64

S15 7.7 0.45 1.9 1.85 0.52 0.46

Alloy NY10 9.9 0.49 1.3 1.17 0.38 0.16

NY6 15.7 0.45 1.6 1.9 0.41 0.20

NY15 7.2 0.47 1.1 1.01 0.37 0.15

NY6A – – – 0.92 0.37 0.09

NY10A 8.1 0.43 0.82 0.74 0.34 0.07

NY15A 5.1 0.42 0.56 0.52 0.32 0.06

N, GPa 16 14 12 10

800°C

8 6 4 1000°C 2 0

5

15 %, Со

10

Fig. 14. Strain hardening coefficients N vs. Co contents of S (䊉), NY (䉱), NYA (䉬) alloys at 800 and 1000°C.

It follows from Table 3 that with the “normal” dislocation mechanism (at 800°C for all alloys and at 1000°C for the S alloys) the N/Ncalc ratio in the order of magnitude is close to 1. However, for NY and espe cially NYA alloys at 1000°C, where hypothetically the grain boundary sliding takes place, the N/Ncalc ratio is essentially lower, i.e., the strain hardening is weaker. For alloys with submicron grains the strainhardening exponent, n, turns out to be essentially lower than 0.5, which is also indicative of the presence of the deforma tion mechanism in addition to the dislocation sliding. Most likely it is a grain boundary sliding. The data calculated by Eq. (12) indicate that heavy strain hardening of WC–Co alloys at the normal dis location mechanism of the deformation (without the grain boundary sliding) is caused by the following rea sons: a high shear modulus G of WC particles, small width of the cobalt binder interlayer, λ, and small grains of WC particles. 5. CONCLUSIONS The results that have been obtained in [1–7] contributed greatly to the physics of the deformation and for mation of mechanical properties (hardness, strength, yield strength, plasticity, strain hardening, and cold brit tleness) of WC–Co alloys in a wide (–196–1000°C) temperature range. JOURNAL OF SUPERHARD MATERIALS

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Tungsten carbide WC is a unique refractory compound, in which high hardness and plasticity have been combined at a local loading. The plasticity characteristic of a WC single crystal defined by indentation [9, 10] is δH = 0.82, which is much higher than that of other refractory compounds. It has been found that just the increased plasticity at a local loading affords an enhanced efficiency of its operation in a cobalt binder as com pared, e.g., with TiC, ZrC, and NbC, despite the fact that single crystals of these carbides at room temperature exhibit higher hardness than WC. It has been shown that the behavior of WC–Co hard alloys in mechanical testing is characterized by the existence of a ductilebrittle transition. The physical temperature of the transition, Tdp, is 200–300°C for alloys with WC grains of micron sizes and 600–700°C for alloys with submicron sizes of grains. However, the high plasticity prior to failure has been exhibited by all alloys only at temperatures exceeding 600–700°C. At room temperature the elongation before fracture is δ = 0 for all alloys studied, while plasticity characteristic δH, which is defined by indentation has finite values at all temperatures and allows us to compare plasticity of alloys. Ultimate strength value σf at room temperature is high (up to 3.5 GPa) and slowly decreases with increas ing temperature up to 600°C and then more sharply. At T > 600°C the σf value depends on temperature approximately as yield strength σs does. It has been found that the yield strength (defined for a very small (0.01%) deformation degree) rapidly increases with temperature decrease below 1000°C and in the intersection of σs(T) and σf(T) curves the duc tilebrittle transition takes place. An increase of the cobalt content of a WC–Co alloy brings about an increase of plasticity δ before fracture at temperatures above Tdp and plasticity characteristic δH over whole temperature range under study. An equa tion describing the dependence of δ on the Co concentration at temperatures above Tdp has been proposed. At temperatures below 800°C alloys with WC micron grains exhibit a higher plasticity than alloys with sub micron grains. However, the plasticity of alloys with submicron grains increases quicker with temperature increase and at 800 and 1000°C a high plasticity has been observed in alloys with finer WC grains (NY and NYA). WC–Co alloys are characterized by a high strain hardening even at 800 and 1000°C, which may be attrib utable to a high shear modulus, G, of the WC phase, low mean value of the free path of dislocations in the glide plane for a cobalt binder, and small WC particles. It has been shown that in a wide temperature range from –196 to 1000°C hardness of WC–Co alloys may be described by the equation of the Hall–Petch type. The coefficients of this equation in the above tempera ture range have been defined, which makes it possible to calculate hardness at the known grain size and cobalt binder concentration. The results reported in [1–7] give ground to expect that the deformation of WC–Co alloys in indentation differs essentially from the deformation in mechanical tests. In measuring hardness the direct contact of a dia mond indenter with the sample surface, in which the most part is occupied by the solid WC phase, causes the plastic deformation to occur in both phases (WC and Co) at all temperatures under study. Therefore, to describe the effect of the structural state on the hardness of WC–Co alloys is possible only if mechanical prop erties of both phases are allowed for. At the same time the results obtained give ground to consider three temperature ranges with different mechanisms of deformation at standard mechanical tests of bulk samples of WC–Co alloys: –lowtemperature range (< 600–800°C). During mechanical tests the macroscopic plastic deformation occurs in a cobalt binder only, which is responsible for a very low plasticity prior to failure. However, in this temperature range the WC–Co alloys exhibit high resistance to fracture σf, which offers their increased effi ciency. The high σf in this temperature range is largely caused by some plasticity of WC grains at their local loading; –mediumtemperature range (from 600–800 to 1000°C). The plastic deformation occurs not only in a binder, but also in a WC skeleton, which results in a very strong strain hardening; – hightemperature range (1000°C and partially from 800°C for alloys with submicron WC grains). Grain boundary sliding (which is characteristic of superplastic deformation) is the primary deformation mechanism for alloys with submicron WC grains. The existence of this mechanism is confirmed by low yield strength and its decrease with decreasing WC grain, high plasticity prior to failure, low coefficient and exponent of strain hardening. It is not improbable that low deformation rate at mechanical tests (7 × 10–5 s–1) contributed to a manifestation of the grain boundary sliding. JOURNAL OF SUPERHARD MATERIALS

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It has been found that the use of alloys with submicron WC grains (d = 300 nm) allows an essential increase of WC–Co alloys hardness, but in this case the alloy plasticity characteristic, δH, decreases. The analysis of the literature on studies deformation mechanisms and mechanical properties of WC–Co published in recent years [26–48] shows a considerable interest in the alloys with nanosized and submicron WC grains [29–37]. In particular, the occurrence of an additional deformation mechanism, namely, grain boundary sliding, has been verified [32]. At the same time a number of problems of the physics of strength of WC–Co alloys investigated in [1–7] and generalized in this study have not been further elaborated in the above publications. This refers to the following scientific results: – ductilebrittle transition and temperature of cold brittleness WC–Co alloys; – features of strain hardening of WC–Co alloys; – difference of deformation mechanisms of WC–Co alloys during indentation and mechanical tests for tension and bending; – change of deformation mechanisms of WC–Co alloys as the temperature changes; – studies of plasticity of WC–Co alloys over a wide temperature range not only according to standard char acteristic of plasticity before fracture δ (which in testing for tension and bending in a rather wide temperature range equals zero), but with the use of plasticity characteristic δH, which is defined by indentation [9–12] and exhibits a finite value at all temperatures. A derivation of an equation for the dependence δ on the volume frac tion of WC grains in an alloy; – studies of the hardness of WC–Co alloys having WC grains of different sizes and different concentrations of cobalt binder at low temperatures (to –196°C); – determination of H0 and Ky constants to describe the hardness dependence on the size of WC grains using an equation of the Hall–Petch type (Eq. (6)) in a wide temperature range (–196–900°C) and at differ ent concentrations of cobalt binder. Thus, publications [1–7] are of crucial scientific importance for further development of the above direc tions. The author thanks his colleagues, Chugunova, S.I.,Goncharuk, V.A., and Goncharova, I.V., researchers of the Institute for Materials Science Problems, National Academy of Sciences of Ukraine, for their cooperation in studies of Physics of hard alloys strength. REFERENCES 1. Milman, Yu.V., Luyckx, S., and Northrop, J.T., Influence of temperature, grain size, and cobalt content on the hard ness of WC/Co alloys, Int. J. Refract. Met. Hard Mater., 1999, vol. 17, nos. 1–3, pp. 39–44. 2. Milman, Yu.V., Chugunova, S., Goncharuck, V., Luyckx, S., and Northrop, J.T., Low and high temperature hardness of WC–6 wt % Co alloys, Ibid., 1997, vol. 15, pp. 97–101. 3. Milman, Yu.V., Luyckx, S., Goncharuck, V.A., and Northrop, J.T., Mechanical properties in bending tests and mechanical behaviour of submicron and micron WC–Co grades at elevated temperatures, 15th Int. Plansee Seminar, Reutte, 2001, G. Kneriger, P. Rödhammer, and H. Wildner, Eds., Reutte: Plansee Holding AG, 2001, vol. 2 (P/M Hard Mat.), pp. 75–90. 4. Milman Yu. V., Luyckx S., Goncharuck, A.V., and Northrop, J.T., Results from bending tests on submicron and micron WC–Co grades at elevated temperatures, Int. J. Refract. Met. Hard Mater., 2002, vol. 20, pp. 71–79. 5. Milman, Yu.V., Luyckx, S., Goncharuck, V.A., Chugunova, S.I., Goncharova, I.V., and Northrop, J.T., Mechanical properties and mechanism of deformation of WC–Co hard alloys in a wide temperature range, Electron microscopy and strength of materials, 2001, issue 11, pp. 164–176. 6. Milman, Yu.V., Chugunova, S.I., Goncharova, I.V., and Luyckx, S., Determination of ductility and stressstrain curve of WCbased hard metals by indentation method, Sci. Sintering, 1997, vol. 29, no. 3, pp. 155–161. 7. Milman, Yu.V., Luyckx, S., Chugunova, S.I., Goncharova, I.V., and Dub, S.N., Peculiarities of plastic deformation of WC single crystal, in Proc. Int. Conf. on Science for Materials in the frontier of Centuries: Advantages and Challenges, Kyiv, Ukraine, 4–8 Nov., 2002, pp. 556–557. 8. Luyckx, S., Slip system of tungsten carbide crystal at room temperature, Acta Met., 1970, vol. 18, pp. 233–236. 9. Milman, Yu.V., Galanov, B.A., and Chugunova, S.I., Plasticity characteristic obtained through hardness measure ment, Acta Met. Mater., 1993, vol. 41, no. 9, pp. 2523–2532. 10. Milman, Yu.V., Plasticity characteristic obtained by indentation, J. Phys. D: App. Phys., 2008, vol. 41, art. 074013. 11. Milman, Yu.V., Dub, S., and Golubenko, A., Plasticity characteristic obtained through instrumental indentation, Mater. Res. Soc. Symp. Proc., 2008, vol. 1049, pp. 123–128. 12. Milman, Yu.V., Chugunova, S.I., and Goncharova, I.V., Plasticity defined indentation and theoretical plasticity of materials, Izvestiya RAS, Ser. Physics, 2009, vol. 73, no. 9, pp. 1282–1289. JOURNAL OF SUPERHARD MATERIALS

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13. Milman, Yu.V., Golubenko, A.A., and Dub, S.N., Indentation size effect in nanohardness, Acta Materialia, 2011, vol. 59, pp. 7480–7487. 14. Lee, M., Hightemperature hardness of tungsten carbide, Metall. Mater. Trans. A, 1983, vol. 14, no. 8, pp. 1625– 1629. 15. Laugier, M.T., Elevated temperature properties of WC–Co cemented carbides, Mater. Sci. Eng. A, 1988, vol. 105– 106, pp. 363–367. 16. Lee, H.C. and Gurland, J., Hardness and deformation of cemented tungsten carbide, Ibid., 1978, vol. 33, pp. 125– 133. 17. Sigl, L.S. and Exner, H.E., The flow stress and hardness of metalreinforced brittle composites, Ibid., 1989, vol. 108, pp. 121–129. 18. Ioffe, A.F., Izbrannye trudy, T. 1 (Selected papers, vol. 1), Leningrad: Nauka, 1974. 19. Trefilov, V.I., Milman, Yu.V., and Firstov, S.A., Fisicheskie osnovy prochnosti tugoplavkikh metallov (Physical princi ples of strength of refractory metals), Kiev: Naukova Dumka, 1975. 20. Ristich, M. M., Trefilov, V.I., Milman, Yu.V., Gridneva, I.V., and Duzhevich, D., Structure and mechanical properties of sintered materials, Beograd, Serbia: Izd. Serbian Acad. Sci. and Arts, 1992. 21. Milman, Yu.V., Chugunova, S.I., Goncharova, I.V., Chudoba, T., Lojkowski, W., and Gooch, W., Temperature dependence of hardness in siliconcarbide ceramics with different porosity, Int. J. Refract. Met. Hard Mater., 1999, vol. 17, no. 5, pp. 361–368. 22. Milman, Yu.V., Ivashchenko, R. K., and Zakharova, N. P., Mechanical properties of sintered materials. II. The effect of porosity on the plasticity of powder alloys, Powder Metallurgy and Metal Ceramics, 1991, vol. 30, no. 3, pp. 93– 100. 23. Šalak, A., Miloškovich, V., Dudrova, E., and Rudnayova, E., The dependence of mechanical properties of sintered iron compacts upon porosity, Powder Metal. Int., 1974, vol. 6, pp. 128–132. 24. Cope, L.H., The mechanical properties of nuclear cermets, Metallurgia, 1965, vol. 72, pp. 165–171. 25. Ludwik, P., Elemente der technolgyschen Mechanik, Berlin: Springer, 1909. 26. Novikov, N.V., Bondarenko, V.P., and Golovchan, V.T., HighTemperature Mechanical Properties of WC–Co Hard Metals (Review), J. Superhard Mater., 2007, vol. 29, no. 5, 261–280. 27. Fang, Z.Z., Wang, X., Ryu, T., Hwang, K.S., and Sonh, H.Y., Synthesis, sintering, and mechanical properties of nanocrystalline cemented tungsten carbide—A review, Int. J. Refract. Met. Hard Mater., 2009, vol. 27, no. 2, pp. 288–299. 28. Upadhyaya, G.S., Materials science of cemented carbides—an overview, Materials & Design, 2001, vol. 22, no. 5, pp. 483–489. 29. Shi, X.L., Shao, G.O., Duan, X.L., Yuan. R.Zh., and Lin, H.H., Mechanical properties, phases and microstructure of ultrafine hardmetals prepared by WC–6.29Co nanocrystalline composite, Mater. Sci. Eng. A, 2005, vol. 392, nos. 1–2, pp. 335–339. 30. Jia, K., Fischer, T.E., and Gallois, B., Microstructure, hardness, and toughness of nanostructured and conventional WC–Co composites, Nanostruct. Mater., 1998, vol. 10, no. 5, pp. 875–891. 31. Mahmoodan, M., Aliakbarzaden, H., and Shahri, F., Effect of Cr3C2 and VC on the mechanical and structure prop erties of sintered WC–10 wt % Co nanopowders, World J. Nano Sci. Eng., 2013, vol. 3, pp. 35–39. 32. Richter, V. and Ruthendorf, M.V., On hardness and toughness of ultrafine and nanocrystalline hard materials, Int. J. Refract. Met. Hard Mater., 1999, vol. 17, nos. 1–3, pp. 141–152. 33. Sivaprahasam, D., Chandrasekar, S.B., and Sundaresan, R., Microstructure and mechanical properties of nanocrys talline WC–12Co consolidated by spark plasma sintering, Ibid., 2007, vol. 25, no. 2, pp. 144–152. 34. Carroll, D.F., Sintering and microstrutural development in WC/Cobased alloys made with superfine WC powder, ibid., 1999, vol. 17, nos. 1–3, pp. 123–132. 35. Kim, H.Ch., Oh, D.Y., and Shon, I.S., Sintering of nanophases WC–15 vol.%Co hard metals by rapid sintering process, Ibid., 2004, vol. 22, nos. 4–5, pp. 197–203. 36. Jia, Ch., Sun, L., Tang, H., and Qu, X., Hot pressing of nanometer WC–Co powder, ibid., 2007, vol. 25, no. 1, pp. 53–56. 37. Qiao, Zh., Ma, X., Zhao, W., Tang, H., and Zhao, B., Nanostructured novel cemented hard alloy obtained by mechanical alloying and hotpressing sintering and its applications, J. Alloys Comp., 2008, vol. 562, nos. 1–2, pp. 416–420. 38. Shourong L., Microstructure parameters of WC–Co cemented carbide, Transactions of Materials and Heat Treat ment, 2005, vol. 01, http://en.cnki.com.cn/Article_en/CJFDTOTALJSCL200501014.htm 39. Kurlov, A.S. and Rempel, A.A., Effect of cobalt powder morphology on the properties of WC–Co hard alloys, Inter metallic Mater., 2013, vol. 49, no. 9, pp. 956–960. 40. Xu, Y., Zhang, Y., Hao, S.Z., Parroud, O., Li, M.C., Wang, H.H., Grosdidier, T., and Dong, C., Surface microstruc ture and mechanical property of WC–6% Co hard alloy irradiated by high current pulsed electron beam, Appl. Surf. Sci., 2013, vol. 279, pp. 137–141. JOURNAL OF SUPERHARD MATERIALS

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41. Engqvist, H., Jacobson, S., and Axen, N., A model for the hardness of cemented carbides, Wear, 2002, vol. 252, nos. 5–6, pp. 384–393. 42. Lu, Sh.P. and Kwon, O.Y., Microstructure and bonding strength of WC reinforced Nibase alloy brazed composite coating, Surf. Coat. Techn., 2002, vol. 153, no. 1, pp. 40–48. 43. Fang, Zh.Z., Correlation of transverse rupture strength of WC–Co with hardness, Int. J. Refract. Met. Hard Mater., 2005, vol. 23, no. 2, pp. 119–127. 44. Uglov, V.V., Anishchik, V.M., Astashynski, V.M., Cherenda, N.N., Gimro, I.G., Kovyazo, A. V., Modification of WC hard alloy by compressive plasma flow, Surf. Coat. Techn., 2005, vol. 200, nos. 1–4, pp. 245–249. 45. Shon, I.J., Jeong, I.K., Ko, I.Y., Doh, J.M., and Woo, K.D., Sintering behavior and mechanical properties of WC–10Co, WC–10Ni and WC–10Fe hard materials produced by highfrequency induction heated sintering, Ceram. Int., 2009, vol. 35, no. 1, pp. 339–344. 46. Lin, Ch., Kny, E., Yuan, G., and Djuricic, B., Microstructure and properties of ultrafine WC–0.6VC–10Co hard metals densified by pressureassisted critical liquid phase sintering, J. Alloys Comp., 2004, vol. 383, nos. 1–2, pp. 98– 102. 47. Shourong, L., Evaluating principle for hardness of WC–Co alloy by magnetism, Cemented Carbide, 2003, 02. http://en.cnki.com.cn/Article_en/CJFDTOTALYZHJ200302000.htm 48. Baoqi, S., Study of strength and structure of WC–Co hard alloy (III), Rare Metals and Cemented Carbides, 2004, 03. http://en.cnki.com.cn/Article_en/CJFDTOTALXYJY200403012.htm Translated by G. Kostenchuk

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