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Residual stresses in cemented carbides — An overview Aaron Krawitz a, Eric Drake b,⁎ a b

University of Missouri, Columbia, MO, USA Rice University, Houston, TX, USA

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 18 June 2014 Accepted 16 July 2014 Available online xxxx

Thermal residual stresses in cemented carbide composites are large, interact with applied stresses, and affect deformation and toughness. Their magnitudes are high (e.g., +2 GPa for Co and −0.4 GPa for WC in WC–10 wt.% Co) and their distributions are complex. Magnitudes depend on expansion coefﬁcients, binder content and particle size; distribution depends on particle angularity — wide ranges of local values occur in both phases. The response of WC-based cemented carbides to applied uniaxial compression and tension is profoundly inﬂuenced by thermal residual stresses. They account for long-observed non-linearity at very low strains, plasticityinduced relaxation, unusual Poisson's ratio behavior, and changes in density with loading. Mechanical response is also asymmetric and a function of load direction and history. The response to cyclic loading gives insight into the role of thermal residual stresses in the toughness of these materials, known for their high toughness considering their high hardness. Results for WC–Co and WC–Ni systems are presented. These studies substantially depend on the application of neutron diffraction: neutrons facilitate good bulk sampling of the volumetric thermal residual stresses in the presence of heavy elements and the use of in situ measurements; diffraction enables each phase to be monitored independently. Results show a complex plasticity behavior that comprises a primary source of toughening characteristic in cemented carbides. However, it is now clear that assumptions implicit in the application of fracture mechanics to cemented carbides, including far-ﬁeld linear elasticity and isotropy are not valid. The emergent view of cemented carbide mechanics seems to require a new, non-linear-elastic model of toughness behavior in these materials, both in terms of bulk “continuum” response and response in the presence of defects. Moreover, such models, if they are to provide accuracy, must also take into account the documented anisotropic relaxation and plasticity effects and their sensitivity to load directionality and history. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Residual stress Neutron diffraction Cemented carbide composites Mechanical behavior

Contents Introduction . . . . . . . . . . . Method of measurement . . . . . Bulk thermal residual microstresses Magnitude . . . . . . . . . . Composition . . . . . Temperature . . . . . Particle size . . . . . . Distribution . . . . . . . . . Interaction with external loads . . . Monotonic loading . . . . . . Compression . . . . . Tension . . . . . . . . Cyclic loading . . . . . . . . Repeated loading . . . Stepped loading . . . .

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⁎ Corresponding author. E-mail address: [email protected] (E. Drake).

http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018 0263-4368/© 2014 Elsevier Ltd. All rights reserved.

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

Role of residual stresses in mechanical behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

relation that applies for microstresses, namely that the force exerted by each phase must balance for equilibrium:

Introduction Thermal residual stresses in cemented carbides are established between the binder and hard phases upon cooling from liquid or solid phase sintering temperatures. They arise due to the difference in thermal expansion between the metal binder and the refractory carbide. Such stresses are classiﬁed as thermal residual microstresses, or Type II residual stresses. Type I residual stresses are macrostresses that equilibrate over the length scale of a part. They arise from thermal and/or deformation treatments that subject the part to macroscale differences in thermal or mechanical treatment. Type III stresses are very short range and result from plastic deformation, usually the strain ﬁelds associated with dislocations. Though Type II stresses in cemented carbide composites are created during cooling after liquid phase or solid state sintering and are ubiquitous in these materials, their role in material performance is not straightforward. Interest in these stresses largely derives from their huge levels. The values are high in the metal binder phase due to the small volume fraction present and the constraint provided by the surrounding carbide particles. An estimate may be obtained from the misﬁt strain in a spherical WC particle in an inﬁnite matrix comprised of the average composite values of thermal expansion and elastic constants. Using values shown in Table 1, results are shown in Table 2 for WC–Co composites using Gurland's approach [1]. The thermal stress in a sphere of WC surrounded by a sphere of material representing the average properties of the composite for a speciﬁed composition is given by:

σ WC

0 0 0

2EWC Ecomp αcomp −αWC ΔT ¼ 1 þ νcomp EWC þ 2ð1 − 2υWC ÞEcomp

ð1Þ

f Co σ Co þ f WC σ WC ¼ 0

ð3Þ

where fi and σ i are the volume fraction and average stress, respectively, of the ith phase [3,4]. Though Gurland's formulation is for an elastic system, the values in Table 2 are lower than those measured, though actually quite close. However, the actual values depend on more than just the relative amounts of the two phases and an effective set-up temperature. Factors such as cooling rate, carbide size, carbide shape, in situ binder yield strength, and the point-to-point distribution of local stress in both the particles and binder are not addressed by such analytical relations. As will be seen, carbide size can have a large effect on the thermal stress magnitude and distribution. The stress magnitude increases as the particle size decreases due to the greater constraint of the binder phase through the reduced binder mean free path. Also, the distribution of stress within the carbide particles and matrix is substantial and important. It is due to the angular shape of the particles, the crystallography of the hexagonal WC, and the variable binder distances of the complex microstructure. The range of stress around the mean values in the binder and carbide is signiﬁcant. This has been investigated in a preliminary way using FE analysis and “real,” two-dimensional microstructure meshes, and documented through diffraction peak shape effects. Finally, the interaction of the residual stresses with applied load has been explored. The response to uniaxial tension and compression has been studied in detail, as well as the effects due to cyclic loading. This work suggests an important contribution to the unusual toughness of cemented carbide composites. Method of measurement

where E is the Young's modulus, α is the linear coefﬁcient of thermal expansion, ν is the Poisson's ratio, and the comp values for the composite are given by: Ecomp ¼

f WC f Co þ EWC ECo

−1 ð2Þ

αcomp ¼ f WC αWC þ f Co αCo f ν f ν νcomp ¼ Ecomp WC WC þ Co Co EWC ECo

The method of choice for these studies is neutron diffraction. Diffraction provides independent views of the response of the binder and carbide phases, and their response to in situ loading. Neutrons overcome the absorption effects caused by the use of X-rays in the presence of the heavy metal tungsten. The application of diffraction methods to stress measurement in cemented carbides and the particular use of neutrons are treated in an antecedent publication [5]. Bulk thermal residual microstresses

where f is the volume fraction. Stresses for Co may be obtained by exchanging the WC subscripts for Co subscripts in Eq. (1). The values shown in Table 2 have been shown to be reasonable compared to those measured in typical materials. Thus, for a WC–10 wt.% Co sample, values of + 2061 MPa for Co and − 407 MPa for WC were obtained using neutrons [2]. The Co values are obtained from the force balance

Neutron diffraction measurements have often been made using model WC–Ni cemented carbides. This is because Ni is a very good neutron scatterer (see Table 3) and has a stable fcc structure over a wide range of temperature. Co, on the other hand, scatters neutrons poorly and tends to stay in the high temperature fcc structure upon cooling rather than transforming to the room temperature hcp phase due to the sluggish fcc-to-hcp transformation. The reasoning was that the fundamental responses of the composites would more clearly reveal

Table 1 Some room temperature properties of WC, Co and Ni. Properties

WC

Co

Ni

E (GPa) K (GPa) G (GPa) ʋ α (°C−1) × 106 ρ (Mg/m3)

672 397 292 0.25 6.2 15.7

200 185 76 0.32 13.8 8.8

207 192 79 0.31 13.3 8.9

Table 2 Thermal residual stresses using Gurland's method [1]. Wt. fraction Co

Vol. fraction Co

σCo (MPa)

σWC (MPa)

.05 .10 .20

.086 .165 .308

+2222 +1840 +1305

−209 −364 −581

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

Neutronsa

X-raysb

Z

b (10−12 cm)

μ l (cm−1)

t90% (cm)

f (10−12 cm)

μ l (cm−1)

t90% (cm)

C Al Co Ni W

0.6646 0.3449 0.250 1.03 0.477

0.98 0.10 3.89 2.10 1.45

2.35 23.0 0.59 1.10 1.59

1.00 2.58 5.94 6.24 17.62

15.8 133.9 2857 434 3251

1.46 1.72 8.06 5.31 7.08

a b

× × × × ×

10−1 10−2 10−4 10−3 10−4

Thermal neutrons with a wavelength of 0.1798 nm. Copper Kα X-rays with a wavelength of 0.154178 nm (average of Kα1 and Kα2).

4000

Thermal residual stress (MPa)

Table 3 Comparison of neutron and X-ray scattering and absorption. The scattering powers of neutrons (b) and X-rays (f) are given in scattering length units for direct comparison. μl is the linear absorption coefﬁcient and t90% is the thickness to absorb 90% of the incident beam intensity at normal incidence.

3

themselves with respect to effects of binder content, carbide particle size, temperature, stress distribution, and interaction with external loads. In fact, studies have also been performed on WC–Co materials and are included here.

9.2 vol.% Ni

3000

Ni 2000 29 vol.% Ni

1000

0

9.2 vol.% Ni

-1000

-2000

29 vol.% Ni

0

200

WC 400

600

800

1000

T (K) Fig. 2. Thermal residual stress from 100 K to 900 K for samples of WC–9.2 vol.% Ni and WC–29 vol.% Ni [10]. The stresses are elastic and reversible with heating and cooling.

Magnitude Composition The role of composition is shown in Fig. 1, for both WC–Co [6,7] and WC–Ni [8,9] material. The square symbols are from samples of a different source than the triangle symbols. However, the WC particle sizes are all about 1 μm. The “x” symbols are calculated values using Eqs. (1) and (3), and a temperature drop of 800 K from the sintering temperature. The calculated values show the proper functional form for variation of binder content over a wide range (about 5 to 50%). Differences in processing and even differences in binder (Co and Ni) do not make much difference. The cooling rates are slow because the samples have sufﬁcient mass that heat is removed slowly. The ΔT was chosen to best ﬁt the data and is high even though Eq. (1) is an all elastic formulation. The constraint imposed by the ﬁne scale three-dimensional microstructure is hard to capture in analytical (or even ﬁnite element) formulations, and in general an artiﬁcially high set-up T is needed. This issue will be addressed again below.

Temperature Samples of WC–9.2 vol.% Ni and WC–29 vol.% Ni were measured in the temperature range 100 K to 900 K [10]. The resultant thermal stresses are shown in Fig. 2. The set-up temperature is about 900 K. The stresses are elastic so the curves are reversible with thermal cycling, though low level damage likely accrues. This would eventually manifest as a change in peak shape, particularly for the binder, which would indicate an accumulating plastic damage in the binder and a concomitant relaxation in the elastic thermal stress state, which would shift the peaks of both phases. These data also show the effect of composition discussed above. The residual stresses for these materials are very high because the WC particle size is 0.5 μm; see Particle size section. Mari et al. measured stress as a function of temperature in WC– 11 wt.% (17.8 vol.%) Co, and followed two heating-cooling cycles from room temperature to 1273 K [11,12]. Above about 1000 K, the cell parameter of Co increases due to solubility of W and C, not due to residual stress. The observed hysteresis between heating and cooling is attributed to a “difference in heating and cooling kinetics of solution–precipitation.

4000

Binder Thermal residual stress (MPa)

Thermal residual stress (MPa)

3000 3000 2000 1000

0 -1000 -2000

WC 0

10

20

30

40

50

60

Volume percent binder Fig. 1. Compilation of many WC-based cemented carbides, all with approximately 1 μm WC particles. The experimental values are for WC–Ni (upward triangles) [9] and WC–Co (squares) [6,7] and downward triangles [8]. The “x” symbols are calculated values using Eq. (1). Experimental binder stress values are calculated using Eq. (3).

Coarse WC Medium WC Fine WC Ultrafine WC Coarse Co Medium Co Fine Co Ultrafine Co

Co 2000

1000

0

-1000 10

WC 20

30

40

50

60

Volume % Co Fig. 3. The strong effect of carbide particle size on the thermal residual stress for a matrix of WC–Co samples [6,7].

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

These important studies indicate the complexity of the systems at temperatures where diffusional changes can occur. Particle size The variation of the thermal residual stress with binder content and carbide particle size for a series of WC–Co composites is shown in Fig. 3 [6,7]. Composites with 10, 20 and 40 wt.% Co (16.4, 30.6 and 54.0 vol.% Co, respectively) and four particle sizes were measured for thermal stress. The particle sizes are ultraﬁne (0.6 μm), ﬁne (1.0 μm), medium (3 μm) and coarse (5 μm). Two effects are represented. First, as the amount of a phase increases, its average residual stress decreases to satisfy the force balance. This composition effect has been discussed above. Second, for a given composition, as the WC particle size decreases, the stress magnitude in both phases increases. The effect is stronger as the amount of Co decreases. For example, as the WC particle size is reduced from 5 μm to 0.6 μm for WC–10 wt.% Co, the thermal stress in the Co increases from 1500 MPa to 2600 MPa, and, for WC–40 wt.% Co, the change is from about 400 MPa to 1000 MPa. The mean free paths in the Co binder range from 6.3 μm for coarse WC (5 μm) and 54.0 vol.% Co to 0.2 μm for ultraﬁne WC (0.6 μm) and 16.4 vol.% W [6,7]. This very strong particle size effect has not, to our knowledge, been analytically modeled.

a

Peak breadth ( s)

4

40

29 vol.% Ni

30

9 vol.% Ni

20 WC powder

10 0

b

200

400 600 T (K)

1000

800

1000

80

Distribution

9 vol.% Ni

Peak breadth ( s)

The residual thermal stress values are averages over the volume of the sample. Fig. 4 shows how the breadths of diffraction peaks from each phase, WC 101 and Ni 311, vary with T for the samples shown in Fig. 2 [10]. These values are the Gaussian component of the peak breadths and are a measure of the range of elastic stresses in the sample. They are directly compared with breadths of the same peaks from annealed, stress-free WC and Ni powders, which do not change with T and represent the instrumental breadth plus any minor broadening sources in the annealed powder material. The breadth values are in microseconds as the data was taken at a pulsed source. This breadth versus T response is elastic, that is, the broadening is due to the distribution of elastic strain that exists in the irradiated volume. As the mean stress increases, the distribution broadens, and this effect is essentially reversible over a small number of cycles. However, many thermal cycles would lead to irreversible changes, though such an experiment has yet to be done. Finally, it is noted that if the Ni content increases, the stress in WC decreases and vice versa. The elastic strain distribution cannot be directly converted to a stress distribution [13]. However, bounds can be set between pure deviatoric and pure hydrostatic limits. It has been shown that the stress state is close to the deviatoric (lower) bound in similar WC–Ni material [13]. For the cemented carbides shown in Figs. 6 and 8, the room temperature thermal stresses in the WC phase are about −300 MPa and −800 MPa for the 9.2 vol.% Ni and 29 vol.% Ni composites, respectively. The deviatoric standard deviations are about 400 MPa and 800 MPa, respectively. It seems clear that the range of stress in WC ranges from very high compression to signiﬁcant tension. Conversely, the binder stress ranges from compression to very high tension. It is apparent from the foregoing that diffraction and the sampling capability of neutrons offer an unprecedented view of the micro- and macrobehavior of cemented carbides. However, the quantiﬁcation and roles of microscale plasticity behavior in these composites have awaited the application of microstructural FEM. Such work allows independent assessment of both elastic and plastic strain components developing during thermal and mechanical loadings. Such modeling would enable both prediction of macroscopic response and interpretation/validation of diffraction results. Finite element studies were conducted to gain insight into diffraction results, using a series of WC–Ni cemented carbides that were both modeled, and physically produced and measured [14,15]. The meshes employed were two-dimensional plane stress elastic models

800

60

29 vol.% Ni

40

Ni powder

20

0

200

400

600

T (K) Fig. 4. Variation of peak breadth for WC–9.2 vol.% Ni and WC–32 vol.% Ni sample as a function of T. These are the same samples as shown in Fig. 2. (a) WC 201 peak; (b) Ni 311 peak.

based on real microstructures. These model results corroborated both the diffraction mean stresses in WC and Ni and the observed broad distributions, including regions of tension and extreme compression in WC and regions of compression and extreme tension in Ni. They also provided insights into how these distributions develop and resolve on the scale of the microstructures, for example, showing highest tensile stresses in WC at corners and near WC/Ni interfaces. Compressive areas in Ni were less widespread as the WC content increases, occurring in narrow Ni bands between WC grains. This is because the mean binder stress becomes increasingly tensile for high carbide-fraction material, which is the usual case. Interaction with external loads Monotonic loading Compression Applied stress interacts with the thermal residual stress in cemented carbide composites. Fig. 5 shows the axial response of the Ni phase in WC–20 wt.% Ni as well as the macroscopic stress–strain curve for

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

a

0

0

Macro σ−ε

Ni Applied stress (MPa)

Applied stress (MPa)

5

-500

-1000

-500

Axial

-1000

Transverse

-1500

-1500

Ni

-2000

-4000

-2000

0

2000

Strain (με) -6000

-4000

-2000

0

Strain (με ) Fig. 5. The macroscopic (elastic–plastic) load–unload stress–strain curves and the Ni phase load-unload (elastic-only) stress–strain curves for WC–20 wt.% Ni in the axial direction [9].

uniaxial compression to −2000 MPa [9]. The Ni curve shows only the elastic strain while the composite curve shows the sum of the elastic and plastic strain response. Both curves show nonlinearity from less than 0.2% strain. However, the accumulation of total strain increases in the composite while the elastic strain rate decreases in the Ni. Upon unloading, the composite sample is shorter by more than 0.3% while the elastic strain in the Ni has actually increased by almost 0.1%. Elastic strain changes in both the axial and transverse directions are shown in Fig. 10 for the Ni phase. These are the responses of the Ni phase during uniaxial compression to 2000 MPa for (1) WC–5 wt.% Ni, (2) WC–10 wt.% Ni, and (3) WC–20 wt.% Ni. The transverse response for WC–5 wt.% Ni (Fig. 6 (a)) shows that the accumulation of positive Poisson strain slows down and actually begins to reverse at the end of the load cycle. After unloading, there is a net reduction in transverse strain and a net increase in axial strain. The increase in axial strain is due to the Poisson effect that results from the (greater) decrease in transverse strain. This trend increases in the 10% Ni and 20% Ni composites, where plasticity in the Ni is greatly increased. As for the 5% Ni material, the transverse strain magnitude in the 10% Ni and 20% Ni composites initially increases due to the axial compression, then decreases. The decrease is so great that the strain goes below the initial value for both compositions. It is emphasized that these changes are relative to the starting values of thermal residual strain, and are the same in all directions when averaged over all diffracting grains. The Poisson reaction in the axial direction leads to an increase in the mean Ni strain in that direction even though there is an overall reduction in the thermal residual stress. The mechanics of the thermal stress relaxation is shown schematically in Fig. 7. The applied uniaxial compressive strain opposes the mean tensile residual stress in the axial direction (Fig. 7(a)). However, in the transverse direction, the applied Poisson strain is tensile and adds to the thermal residual strain in the Ni. This leads to preferential ﬂow of the Ni in the transverse direction and asymmetric relaxation of the thermal residual stress. The transverse relaxation, in turn, induces a Poisson expansion in the axial direction, as indicated in Fig. 7(b). For the WC–20 wt.% Ni composite, the result is reduction in the transverse and axial thermal residual stresses by −523 and −227 MPa, respectively. Thus, the relaxed residual stress state becomes cylindrical and, for the WC–20 wt.% Ni sample, is + 1778 MPa in the axial direction and + 1482 MPa in the transverse direction. To summarize, upon uniaxial compressive loading/unloading, the thermal

b Applied stress (MPa)

-8000

0

Ni -500

Axial -1000

Transverse

-1500

-2000

-4000

-2000

0

2000

Strain (με)

c

0

Ni Applied stress (MPa)

-2000

-500

Axial

-1000

Transverse -1500

-2000

-4000

-2000

0

Strain (με) Fig. 6. The Ni phase load–unload stress–strain curves in the axial and transverse directions due to uniaxial compression in (a) WC–5 wt.% Ni, (b) WC–10 wt.% Ni, and (c) WC–20 wt.% Ni.

residual stress in the Ni phase decreases in both the axial and transverse directions, but does so asymmetrically; the decrease is greater in the transverse direction. The elastic strain in the Ni phase, however, decreases in the transverse direction but increases in the axial direction, due to the Poisson effect. Macroscopic load–unload stress–strain curves of WC–10 wt.% Ni for −500 and −2000 MPa are shown in Fig. 8(a). An enlarged plot of the − 500 MPa load–unload sequence is shown in Fig. 8(b). This is shown to emphasize that nonlinearity begins very

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

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A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

a Applied stress (MPa)

0

-500

-1000 -500 load -500 unload

-1500

-2000 load -2000 unload

-2000

-4000

a) Applied composite uniaxial compressive strain.

Applied stress (MPa)

b

b) Resulting relaxation of thermal residual strain for Ni. Fig. 7. Schematic response of WC–Ni to uniaxial compression. (a) Applied strain to composite in the axial and transverse directions. (b) Anisotropic relaxation response of the thermal residual stress for the Ni phase.

early in the loading cycle. By −500 MPa, a clear hysteresis is present. This is due to the interaction between the applied stress and the thermal residual stress. It can be shown that composite density is not conserved when the thermal residual stress levels decrease in the WC and Ni phases. The forces remain balanced but the density actually increases upon relaxation of the initial thermal stress. This is because, upon relaxation of the thermal residual stresses in the Ni and WC, the decrease of the Ni phase volume is greater than the increase of the WC-phase volume so that the density of the composite increases. Tension The application of uniaxial tension also creates an asymmetric relaxation of the thermal residual stress, but in the opposite sense of that for compression. This is shown schematically in Fig. 9. In this case, the applied axial tension leads to preferential ﬂow of the Ni in the axial direction because the applied strain adds to the positive residual strain in this direction. In the transverse direction, the applied Poisson compressive strain is now negative and opposes the mean Ni thermal residual strain, which is tensile (positive). The result is the greater relaxation of the thermal residual stress in the axial direction than in the transverse direction. In this case, the change in elastic strain in the Ni is negative in the axial direction and positive in the transverse direction. The situation is illustrated for a WC–10 wt.% Ni composite that was subjected to a +1500 MPa tensile stress, the highest value that could be obtained without fracture (Fig. 10) [16]. The response of the Ni phase is shown in Fig. 10(a). For comparison, Ni-phase curves are

-2000 Strain (με)

0

0

-100

-200

-300

-400

-500 -1000

-500

Strain (με)

0

Fig. 8. The WC–10 wt.% Ni macroscopic load–unload stress–strain curves of (a) −500 MPa and −2000 MPa loadings and (b) enlargement of −500 MPa load–unload. Note that the 0 load level is actually −10 MPa in order to keep tension on the sample. This is true in all plots but is visible here due to the expanded scale.

shown for loading to −1000 MPa (Fig. 10(b)). The relaxation asymmetry is reversed for tensile versus compressive loading. The macroscopic load–unload stress–strain curves for WC–10 wt.% Ni to +1500 MPa are shown in Fig. 11(a). The corresponding curve for WC–10 wt.% Ni loaded to −1000 MPa is shown in Fig. 11(b). (The macroscopic load–unload stress–strain curves to − 500 and − 2000 MPa are shown in Fig. 8.) The reverse nature of the relaxation asymmetry is clearly shown. For the − 1000 MPa case, the composite has already been subjected to three load–unload cycles to −500 MPa, which induced some plasticity. Thus, the effect should be somewhat stronger than it appears. To summarize, upon uniaxial tensile loading/unloading, the thermal residual stress in the Ni phase decreases in both the axial and transverse directions, but does so asymmetrically: the decrease is greater in the axial direction. The elastic strain in the Ni phase, however, decreases in the axial direction but increases in the transverse direction, due to the Poisson effect. In both the compressive and tensile cases, the applied plastic strain is opposed by the change in Ni strain due to relaxation of some of the thermal residual stress. However, for applied uniaxial compression, it is the tensile Poisson reaction of the Ni elastic strain that opposes the applied compression while, for applied uniaxial tension, it is the direct reduction of the Ni elastic strain that opposes the applied uniaxial tension. This suggests, as is observed, that the overall macroscopic length change will be greater for applied compression.

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

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a) Applied uniaxial tensile strain.

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b) Resulting relaxation of thermal residual strain. Fig. 9. Schematic response of WC–Ni to uniaxial tension. (a) Applied strain to composite in the axial and transverse directions. (b) Anisotropic relaxation response of the thermal residual strain for the Ni phase.

Cyclic loading Repeated loading The effect of repeatedly loading a cemented carbide was studied using a WC–10 wt.% Ni sample subjected to 100 cycles of uniaxial compression from − 10 to − 2500 MPa [17]. Diffraction data were taken during load–unload cycles 1, 2, 3, 10, 25, 50 and 100. The macroscopic response of the Ni phase for cycles 1 and 100 is shown in Fig. 12. The changes occurring in the Ni phase are shown in Fig. 13. The relaxation process is best seen as a function of the number of cycles (Fig. 14). Most of the change occurs during the ﬁrst three cycles, with a stable state reached after about 10 cycles. Although the relaxation stabilizes rather early in the process, there is still a hysteresis present in both the axial and transverse directions. Most of the composite volume does not yield but rather is elastically strained under load. This creates a range of strain in the sample that contributes to a strain variance (peak broadening) that is reversed upon unloading. The peak breadth responses follow a similar pattern and, after 10 cycles, are about 75% of the starting values, that is, they narrow because the mean thermal residual stress decreases [17]. Stepped loading The stepped loading response of WC–Ni helps explain the response of the composite in service, and in accounting for the unusual toughness of cemented carbides (Fig. 15). The hysteresis closes signiﬁcantly after

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Fig. 10. The Ni phase load–unload stress–strain curves for WC–10 wt.% Ni under (a) 1500 MPa tension and (b) −1000 MPa compression.

three cycles but, if the load is subsequently increased, the process begins again, as shown by the ﬁrst cycles to −1000 and −2000 MPa following the initial loading to −500 MPa. A component in service would be able to absorb additional energy through the plastic deformation/relaxation process in regions where it experienced an increase in load as well as through the ongoing hysteresis process. Role of residual stresses in mechanical behavior Long-recognized but unexplained mechanical behavior anomalies of cemented carbides are now attributable to the inﬂuences of residual stresses, including small-strain yielding and plasticity-induced relaxation. The absence of linear elastic load response of commercial WC–Co grades is perhaps the principal observation. Felgar and Lubahn measured samples in both tension and compression [18]. Nonlinearity in tension was observed at strains as low as 0.1%, as well as nonlinear responses, that were termed “anelastic”, in both tension and compression. These behaviors, identical to those seen herein, are due to thermal stress relaxation and the volumetric, asymmetric nature of the response of the system to applied stress. Another example is that pre-loading in compression has been observed to increase density and cause asymmetric Palmqvist crack lengths [19]. Both are due to the asymmetric stress relaxation that results from the interaction of nonuniform applied strains with the preexisting thermal residual stresses. In general, the longer Palmqvist cracks are in the direction of higher residual stress while the shorter ones are in the direction that has experienced greater

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

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A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

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Fig. 11. The macroscopic load–unload stress–strain curves for WC–10 wt.% Ni for (a) +1500 MPa tension and (b) −1000 MPa compression.

relaxation. Finally, variation in Poisson's ratio was observed during uniaxial compressive loading [20]. Speciﬁcally, the initial value of Poisson's ratio in a WC–15.6 wt.% Ni sample began decreasing with the onset of load for the two load cycles measured. This is due to the greater stress relaxation in the directions normal to the compression axis. Poisson's

Fig. 13. The Ni phase response in WC–10 wt.% Ni after 1 and 100 cycles of repeated compression loading to −2500 MPa. (a) Axial direction. (b) Transverse direction.

ratio ν = εx/εz and the transverse direction x experiences a higher degree of strain relaxation than the direction of compressive loading, z. The plasticity behavior appears to comprise a primary source of toughening characteristic of cemented carbides. This suggests the feasibility of sufﬁciently realistic and scaled-up microstructural modeling,

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Number of cycles Fig. 14. Strain relaxation versus number of cycles for WC–10 wt.% Ni under repeated uniaxial compression to −2500 MPa.

Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

A. Krawitz, E. Drake / Int. Journal of Refractory Metals and Hard Materials xxx (2014) xxx–xxx

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applied loading produce differing responses. Bulk plasticity behavior diminishes with cyclic loading, but is reactivated when applied stress exceeds previous values.

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Fig. 15. Stepped loading of WC–10 wt.% Ni: three cycles to −500 MPa then three cycles to −1000 MPa then three cycles to −2000 MPa. The loading cycles are represented by solid lines; the unloading cycles are represented by dashed lines.

which would provide predictive capability for mechanical response of cemented carbide composites in terms of composition, microstructure, and thermal and load history. Toughness, perhaps the most important attribute of cemented carbides, and the one that distinguishes them from other engineering materials at equivalent hardness levels, has been quantiﬁed by fracture toughness testing based on linear elastic fracture mechanics [21–24]. Much effort has been given to explaining and predicting observed toughness in terms of microstructural parameters and in situ elastic/plastic behavior of the binder and carbide phases [21,22,24,25]. However, assumptions implicit in this approach including far-ﬁeld linear elasticity and isotropy are not valid for cemented carbides. The emergent view of cemented carbide mechanics seems to require a new, non-linearelastic model of toughness behavior in these materials, both in terms of bulk “continuum” response and response in the presence of defects. Moreover, such models, if they are to provide accuracy, must also take into account the documented anisotropic relaxation and plasticity effects and their sensitivity to load directionality and history. Conclusions Thermal residual stresses are high in cemented carbides, with binder in mean tension and the carbide in mean compression. The initial residual stress state is a function of composition; temperature and temperature history; and, carbide particle size, distribution and shape. The stress distributions in the binder and carbide phases are extremely broad. Applied stress interacts with residual stress causing localized binder plasticity and thermal stress relaxations. Cumulative relaxation is anisotropic on the macroscale and accordingly, tensile and compressive

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Please cite this article as: Krawitz A, Drake E, Residual stresses in cemented carbides — An overview, Int J Refract Met Hard Mater (2014), http://dx.doi.org/10.1016/j.ijrmhm.2014.07.018

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