Materials Science and Engineering A 383 (2004) 390–398
Apparent viscosity of W–Cu powder compacts during sintering F. Doré a , C.L. Martin b , C.H. Allibert a,∗ a b
LTPCM (UMR 5614 CNRS-INPG), BP 75 38402 Saint Martin d’Hères, France GPM2 (UMR 5010 CNRS-INPG), BP 46, 38402 Saint Martin d’Hères, France Received 7 July 2003; received in revised form 11 May 2004
Abstract The apparent rigidity of W–Cu (35 vol.%) powder compacts during sintering is characterised from the determination of axial viscosity by dilatometry under sequential loading. The study is carried out on composite powders containing submicron size phases, in the temperature range 1020–1100 ◦ C in which a significant shrinkage is evidenced by conventional dilatometry. When the sintering bodies density increases from 0.5 to 0.74dth , the axial viscosity increases from 103 to 13 × 103 MPa s in solid state and from 0.5 × 103 to 4 × 103 MPa s when Cu is liquid. These rather low values do not indicate the formation of a rigid W particle network. From about 1060 to 1100 ◦ C, the rapid shrinkage, the low axial viscosity and the significant microstructure change support a densification process by rearrangement by viscous flow. © 2004 Elsevier B.V. All rights reserved. Keywords: W–Cu; Densification; Apparent viscosity; Processes
1. Introduction W–Cu materials consist of a mixture of almost pure W and Cu phases . Powder metallurgy processes, mainly liquid phase sintering (LPS) or infiltration, are used to obtain dense materials with an homogeneous distribution of the W and Cu phases. In the LPS process, densification results from overlapping stages of rearrangement and of microstructure evolution, both leading to a denser packing of the solid grains [2,3]. Rearrangement of the solid–liquid-pore mixture occurs by liquid flow towards pores and into the grain boundaries of the solid particles. Microstructural evolution proceeds from the coarsening of the solid particles by dissolution–precipitation or from the shrinkage of the solid phase network. In W–Cu alloys, liquid Cu exhibits a good wetting of the surface of the W particles  provided that no oxygen contamination of the W surface takes place. Rearrangement is possible but with a limited efficiency as liquid Cu does not penetrate into the W grain boundaries. The negligible W solubility in Cu  precludes a significant contribution of the dissolution–precipitation process. Therefore, the W–Cu
densification is expected to involve mainly rearrangement and the shrinkage of the W network. From the comparison between the densification predicted by a theoretical approach and the one determined experimentally on co-milled W and Cu powders, Johnson and German  propose that the dominant shrinkage mechanism is the solid-state sintering of the W skeleton in presence of liquid Cu. These authors  predict that this process produces efficient densification of particles with sufficiently small size. They show that the sintering of W–20% Cu1 from fine (0.23 m) co-milled powders leads to a final density of up to 0.95dth after 60 min at 1400 ◦ C. The study of similar co-milled powders containing 20–80% Cu also leads Upadhyaya and German  to conclude to the dominant contribution of the solid-state sintering of the W skeleton. For these authors, the W network should be formed below the Cu melting. In both studies, the major part of the shrinkage is observed above Cu melting. A rather different behaviour is reported for the sintering of composite powders with submicron size phases synthesised by coreduction of mixed W and Cu oxides [7–13] or by high energy co-milling of W and Cu powders . A strong shrinkage occurs in a limited temperature range around the Cu melting point. In some cases, a density of up to 0.95dth is reached already in solid
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0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.05.050
All the phase fractions noted % are volume fractions.
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state . The efficient and rapid densification at a temperature close to the equilibrium Cu melting point is likely to result from rearrangement by viscous flow. As expected from the physicochemical properties of the material, rearrangement and solid-state sintering of the W network are shown to produce the densification of W–Cu compacts. However, the rearrangement contribution is different in the various studied powders. This contribution is likely related to the deformation of the W skeleton. Few data are available on the apparent rigidity of the W skeleton that depends on the microstructure and on the interface chemistry of the W–Cu-pores mixture. The purpose of the present work is to characterise the deformation capability of the W network during the sintering of W–Cu powders with composition W–35% Cu. The studied powders consist of mixed W and Cu phases with submicron size and contain a very low impurity level. The characterisation is based on the determination of an apparent viscosity by using dilatometry with sequential loading during isothermal treatments. The apparent viscosity is evaluated at temperatures where a significant shrinkage occurs. These temperatures, on both side of the Cu melting point, are previously determined by conventional dilatometry.
2. Experimental 2.1. Materials The study was carried out on the powders referred to as H∗ and H, that consist of particles containing a mixture of W and Cu phases. The powders were synthesised by coreduction of W and Cu oxides, mixed without milling, in proportion corresponding to the compositions reported in Table 1. In the two powders, the Cu content corresponds to a volume fraction of 35% and the main impurities (Fe, Ni) that could act as sintering activators have a very low level. The powders are spherical granules (Fig. 1) limited by rather dense outer shells and containing aggregates. Both shells and aggregates consist of mixed phases of W and Cu. The W crystallite size calculated from X-ray peak broadening is about 200 and 250 nm for H∗ and H, respectively. The slight differences between the two powders concern the particle size distributions and the SBET values (Table 2). The particle size distribution is tighter and includes a larger fraction of fine sizes and the mean size is slightly smaller in H∗ than in H. The aggregate size evaluated from SBET and by scanning electron microscopy (SEM) is slightly smaller for H∗ Table 1 Contents (wt.%) in Cu and in major impurities in the powder H∗ and H synthesised by Eurotungstene Poudres
Fig. 1. SEM (BSE mode) images of the powder H∗ : (a) spherical particles and (b) aggregates inside the particles. The aggregates contain mixed W and Cu phases too small to be differentiated.
(0.5 m) than for H (0.8 m). The powders were pressed as cylinders (10 mm in diameter, 5–7 mm in length (lo )) by uniaxial compaction to reach the green relative density 0.49– 0.52dth . For these powders, the synthesis process, the compaction behaviour, the sintered density achieved by treatments at 1000–1200 ◦ C and some results of shrinkage rates were described in previous papers [12,13]. 2.2. Experimental techniques The shrinkage behaviour was studied using two types of dilatometry equipments. In conventional dilatometry, the specimen was maintained by the push rod on the reference Table 2 Geometrical characteristics of the powders SBET (m2 g−1 )
D, m (laser granulometry)
F. Dor´e et al. / Materials Science and Engineering A 383 (2004) 390–398
3. Shrinkage behaviour
Fig. 2. SEM image of the microstructure of H∗ after dilatometry under loading at 1060 ◦ C showing Cu (dark grey) spread on W grains (light grey). Pores are black.
plane, the specimen and pusher axis were horizontal. The pressure applied by the pusher was approximately 6 kPa. The length variation of the samples was measured during thermal cycles completed under hydrogen flow. Dilatometry with sequential loading was performed with the device similar to that used for the viscosity determination of WC–Co compacts . In this case, both the axis of the specimen and the axis of the pusher were vertical. The pressure exerted by the pusher was reduced (0.6 kPa) since the specimen was partly maintained by gravity. Controlled loads were applied for selected periods during the isothermal step. The treatments were carried out under flow of a mixture argon–hydrogen (10%). The thermal cycles used in both types of experiments were heating at 5 K min−1 followed by one or several successive isothermal steps at temperatures in the range 1020–1200 ◦ C, separated by heating at 5 K min−1 . The elimination of the oxygen amount in the starting powder is required for the Cu spreading on the W grain surface. After treatment at 1200 ◦ C, temperature leading to almost complete densification, the oxygen content was 0.007 wt.% in the conventional dilatometer and 0.017% in the dilatometer with sequential loading. At lower temperature, porosity in the samples was still high and the oxygen content was not analysed as it should have accounted for the oxygen amount adsorbed on the surface of the open pores after cooling. The absence of oxygen contamination was deduced from the microstructure showing the perfect Cu spreading (Fig. 2) on the surface of the W grains. It was also indicated by the close density values reached after a similar treatment in conventional or loaded dilatometry. The density of the samples studied by dilatometry was determined by geometrical measurements and by the Archimedes technique. As the size scales are very different for porosity, for the particles and for the W or Cu phases, porosity was observed by optical microscopy and some information on the microstructure was obtained by SEM.
The dilatometric curves related to H∗ for a continuous heating to 1110 ◦ C followed by a plateau at this temperature are reported in Fig. 3. The linear shrinkage l/lo becomes significant at about 1020 ◦ C, and increases drastically from 1060 to 1110 ◦ C followed by a more gradual increase during the first 60 min at this temperature (Fig. 3a). In the temperature range 1060–1110 ◦ C, the linear shrinkage rate d(l/lo )/dt (Fig. 3b) exhibits a peak with a maximum at about 5 K above the equilibrium Cu melting point. The behaviour recorded for H is similar but the maximum shrinkage rate at the peak is smaller. The significant shrinkage observed in a tight temperature range on both sides of the Cu melting indicates a rearrangement starting in the solid state. To check for the possible development of a W skeleton, shrinkage was also studied for a cycle including three successive steps of 60 min at 1020, 1060 and 1090 ◦ C. The temperatures of the two first steps (1020 and 1060 ◦ C) are lower than the equilibrium melting point of Cu. The temperature of the last step (1090 ◦ C) corresponds to the maximum of the shrinkage rate peak. The shrinkage and the shrinkage rate produced by the three steps treatment and by the con-
Fig. 3. Comparison of the shrinkage measured by conventional dilatometry for a continuous heating at 1110 ◦ C and for the three-step treatment. (a) Linear shrinkage, (b) linear shrinkage rate. The temperatures ((䉫) 1020 ◦ C, (䊐) 1060 ◦ C, () 1090 ◦ C, (䊊) 1110 ◦ C) are marked on the continuous heating and three-step curves.
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tinuous heating at 1110 ◦ C are reported in Fig. 3a and b for H∗ . Fig. 3 shows that densification rate is significantly reduced but densification is not stopped by the intermediate steps and shrinkage re-starts at each temperature jump. The network expected to form between the W particles during the early stage of sintering is not rigid. The same trend was observed for H . During continuous heating, densification is coherent with a rearrangement process by viscous flow. During the step–treatment, the rearrangement capability of the particles may have been affected by the W network development induced by intermediate holdings.
4. Apparent viscosity 4.1. Principle of the determination In order to get some more insight into the sintering behaviour of the powder, it is important to characterize the rigidity of the network formed by the particles. The apparent viscosity of the particle packing provides such information and is attainable during sintering by using dilatometry with sequential loadings. The technique consists in applying an axial load on the specimen while it is sintering. The comparison of the axial strain rates measured without any load (free sintering) and with a load applied on the specimen allows evaluating the viscosity of the specimen during the sintering process. During a loading sequence, the dilatometer measures the total axial strain rate. Considering only irreversible strains that are of interest for sintering, the axial strain rate can be decomposed in two terms: vp
˙ sz + ε˙ z ε˙ tot z =ε ε˙ sz
(1) vp ε˙ z
where is the axial strain rate due to free sintering and the additional viscoplastic strain rate due to the load on the specimen. Knowing the load applied σ z on the specimen, and assuming a Newtonian behaviour, the axial viscosity, vp ηz , can be evaluated from the measure of ε˙ z : σz ηz = vp (2) ε˙ z Obviously, Eq. (2) is rather simplistic for describing the complex rheological behaviour of a sintering body. More sophisticated laws could be used, such as a Bingham’s law that enables introducing a minimum stress required to initiate flow . However, once viscoplastic flow is well established, as it is the case in our experiments when the load is applied, the simple Newtonian law given by Eq. (2) is sufficient to interpret the experimental data in terms of an apparent viscosity. Furthermore, in this work we limit the mechanical characterisation of the sintering body to a particular space direction (z). When the full constitutive behaviour of the sintering body is needed, both deviatoric and hydrostatic viscosities must be determined. An example of the full constitutive behaviour of the sintering body required for sim-
ulating distortion during sintering is given by Gillia et al. [15,17]. Here a simple compression test in the dilatometer provides enough qualitative information concerning the W network formed during sintering. The measured viscosity is the axial viscosity referred to as ηz . 4.2. Main parameters acting on apparent viscosity A sintering body is a packing of rigid particles filled with porosity. The axial viscosity ηz mainly depends on the volume fraction and on the rigidity of the solid particles and on the type of contacts generated between particles. Several models [18,19] relate the effective viscosity ηeff to the relative density of the sintering body. At a given temperature, the exponential increase of ηeff with relative density proposed by Bouvard and Meister  was shown for mixtures WC–Co . In the present study, the material contains the W rigid phase, deformable Cu and porosity. Below its melting point, Cu is expected to contribute to the viscosity of the sintering body. The axial viscosity ηz will be represented versus relative density, that represents the fraction of the solid phases. When Cu is liquid, its contribution to viscosity may be neglected: it will be examined if the volume fracW of the W rigid phase in the mixture W–Cu-pore tion XV is the pertinent parameter to describe the viscosity evolution. The temperature of sintering is a major parameter for densification and shrinkage was observed mainly during the first 60 min of isothermal steps (Fig. 3). The axial viscosity will be determined along isothermal holdings (60 min) at the temperatures where densification starts (1020 ◦ C), where a drastic acceleration occurs (1060 ◦ C) and close to the maximum (1100 ◦ C) shrinkage rate. 4.3. Technique of measurement and validity The cycle with five unloaded–loaded sequences used to get the axial viscosity at different relative densities during an isothermal period is shown in Fig. 4. The typical evolution of the axial strain rate during a loading sequence is indicated in Fig. 5. Intermittent loadings were applied to minimize the effects of external loadings on the sintering body. Fig. 5 shows that indeed after removal of the load, the free sintering curve is retrieved. Hence short loadings are not expected to disturb irreversibly the specimen and several unloaded–loaded sequences can be used to probe the sintering body during one thermal cycle. The values of the shrinkage rate are close to those measured by conventional dilatometry. Unfortunately, the intermittent loadings scheme cause transients. Such transients were observed with a comparable order of magnitude by other researchers . We believe that these transients come from the transitory squeezing of the Cu soft phase in between the W grains when the load is applied instantaneously. After some time, the soft Cu phase comes back to a geometrical configuration close to the one before the loading and a steady state is reached. vp ε˙ z is computed at this point. In a single test, the result-
F. Dor´e et al. / Materials Science and Engineering A 383 (2004) 390–398 1.0E+04
axial viscosity (MPa s)
H*1060 10 KPa 8.0E+03
H*1060 15 KPa H*1060 19 KPa c1
H*1060 19 KPa c2 H*1060 19 KPa c3
Fig. 4. Typical thermomechanical cycle used during dilatometry with sequential loadings. Four of five short loading sequences are used during a cycle. The loads are 75, 110 and 145 g corresponding respectively to axial stresses of 10, 15 and 19 kPa at 1020 and 1060 ◦ C and 45 g (6 kPa) at 1100 ◦ C.
ing dilatometric curves give both the axial strain rate due vp to free sintering, ε˙ sz , and the additional strain-rate, ε˙ z , due to the load. The axial viscosity can be derived quite simply (Eq. (2)) provided that the behaviour of the sintering body can be considered as Newtonian. To check that the Newtonian behaviour can be assumed, the axial viscosity of the specimen was evaluated at 1060 ◦ C for three values (45, 110 and 145 g) of applied loads corresponding to 10, 15 and 19 kPa pressures, respectively. Moreover, several series of measurements were performed at 1020, 1060 and 1100 ◦ C for a constant applied load to estimate the uncertainties of the technique. At 1060 ◦ C, all the results of axial viscosity versus relative density are reported in Fig. 6. For a given density, the values of axial viscosity determined from three series at 19 kPa are rather dispersed.
Fig. 6. Axial viscosity values at 1060 ◦ C determined from three series of experiments under 19 kPa and from two series at 10 and 15 kPa, respectively. At 1060 ◦ C the results are rather dispersed and for a given density, the viscosity values determined from different loads are of the same order.
The values measured for the lower applied loads (10, 15 kPa) are in the same range as those obtained for the higher load vp and the shrinkage rate ε˙ z is roughly proportional to the applied load. Hence the Newtonian assumption is realistic considering the other uncertainties of the technique. The different experiments performed at 1020 ◦ C for 19 kPa and at 1100 ◦ C for 6 kPa display a much higher reproducibility (Fig. 7). This is explained from the temperature dependence of the shrinkage rate. In the ranges around 1020 or 1100 ◦ C the shrinkage rate does not change too rapidly with temperature, so a small temperature variation does not affect too much the microstructure of the sintering body. Between about 1060 and 1090 ◦ C the increase of shrinkage rate is drastic and a very small difference between either the experimental temperatures or the specimen microstructures can explain the rather dispersed values obtained at 1060 ◦ C.
Fig. 5. Evolution of the axial strain rate ε˙ tot z during a loading sequence. Applying an additional load (here 19 kPa) results in an increase of the strain-rate. vp vp ε˙ z represents the difference between the characteristic curves for the specimens during free sintering and sintering under load. ε˙ z is calculated once the loaded curve has attained a steady-state.
F. Dor´e et al. / Materials Science and Engineering A 383 (2004) 390–398 1.2E+04
1.0E+04 H* 1020˚C H* 1060˚C H* 1100˚C
H* 1060˚C axial viscosity (MPa s)
1.0E+04 axial viscosity (MPa s)
H* 1060˚C after step 1020˚C
0.6 relative density
Fig. 7. Comparison of the axial viscosity determined during isothermal treatments at 1020, 1060 and 1100 ◦ C. The results at 1020 and 1060 ◦ C account from three series of experiments, those at 1100 ◦ C account for two series of experiments.
4.4. Apparent viscosity evolution with temperature The variations of ηz versus the density determined for H∗ at 1020, 1060 and 1100 ◦ C are shown in Fig. 7. The comparison of the results obtained at 1060 and 1100 ◦ C for a given relative density evidences the significant decrease of the viscosity of the sintering body produced by the Cu melting. At 1100 ◦ C, in mixtures where Cu is liquid, the viscosity increase with density is very limited. The density (0.74dth ) and consequently the volume fraction of the W rigid phase (∼0.48) obtained after 60 min at 1100 ◦ C, could be too low for obtaining the significant increase expected for ηz . At 1060 ◦ C, the viscosity increase with density is more pronounced. At the lowest temperature (1020 ◦ C), at which densification is not detectable during the isothermal holding, ηz increases drastically. This leads to assume that a particles network with strong cohesion may be formed during solid-state sintering. This network should not impede the further densification at higher temperature, as observed in the 3 steps unloaded experiment (Fig. 1). To examine the evolution of such a network, a step test was carried out in dilatometry under load. The specimen was subjected to a first isothermal holding at 1020 ◦ C for 60 min followed by a second isothermal holding at 1060 ◦ C for 60 min. During the two isothermal steps, the specimen was sequentially loaded axially to measure its viscosity. As shown in Fig. 8, the isothermal holding at 1020 ◦ C has no great influence on the apparent viscosity at 1060 ◦ C and does not hinder sintering at this temperature. 4.5. Powder and density effects The axial viscosity of powder H is compared to that of H∗ in Fig. 9. At 1060 ◦ C, the values are in the same range for H
Fig. 8. Comparison of the viscosity values determined at 1060 ◦ C after direct heating and after a previous step at 1020 ◦ C.
and H∗ . At 1100 ◦ C, the higher values determined for H correspond to a stronger effect of density. The higher apparent rigidity observed for H is not related to the W grain size, of the same order in H and H∗ . A more detailed microstructure characterisation is required to find which of the microstructure parameters determine the lower deformation capability of H that also corresponds to a lower sintered density  and to a lower shrinkage rate . As observed in the WC–Co system , the representation of the axial viscosity increase versus sintered density by a simple exponential law is correct for H and H∗ at 1060 ◦ C and is very good for H at 1100 ◦ C. For H∗ , the axial viscosity increase is limited in the range of sintered density reached at 1100 ◦ C and such an exponential representation was not attempted.
1.E+04 y = 13.24e9.06x R2 = 0.94
H 1060˚C axial viscosity (MPa s)
H* 1060˚C H 1100˚C
y = 3.00e12.00x R2 = 0.93 y = 0.85e12.50x R2 = 1.00
Fig. 9. Evolution of the axial viscosity vs. relative density for H and H∗ at 1060 and 1100 ◦ C. The experimental results are correctly represented by an exponential variation for H and for H∗ at 1060 ◦ C. For H∗ at 1100 ◦ C the axial viscosity increase is limited and this representation was not attempted.
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5. Discussion 5.1. Possible origin of the transient ηz jump at 1020 ◦ C The drastic but transient ηz jump at 1020 ◦ C (Fig. 7) cannot originate from a W skeleton that should not collapse at higher temperature. It might result of gas overpressure into pores but this effect is not evidenced by the results. At this temperature, porosity in the material is mainly open, and no distortion of the sample shape is displayed. Moreover, close shrinkage results are provided by conventional dilatometry under hydrogen flow, a gas that is easily eliminated as its diffusivity is much higher than that of argon. It is proposed that the transient rigidity increase without shrinkage results of the solid Cu flow that forms a continuous Cu network binding the W grains and that produces the local densification of aggregates with simultaneous coarsening of the larger pores. This assumption is based on literature data related to solid-state rearrangement in W–Cu [4,20–22]. Solid Cu wetting on the W surface is possible as the surface energies γ SV are lower for Cu than for W [20,4]. At 1050 ◦ C the spreading on W grains and the filling of fine pores by solid Cu were effectively observed in model experiments . The Cu transport in various W–Cu compacts was shown to generate dense W–Cu aggregates separated by pores without overall densification . Such processes are not directly demonstrated by the very fine microstructure at 1020 ◦ C (Fig. 10a). The Cu continuous network expected to form is difficult to evidence. Cells of mixed W and Cu phases are effectively present among W grains either dispersed or forming chains covered by Cu (Fig. 10b) but they likely originate from the original powder. However, the proposed scheme is consistent with the evolution of porosity distribution (Fig. 11). After 60 min at 1020 ◦ C coarse pores (10–20 m) are localised around rather dense cells. After direct heating at 1060 ◦ C pores are more homogeneously distributed in the sample and their size distribution is extended towards finer values. Obviously, the quantitative analysis of the evolution of the microstructure and of the pore size distribution is required to assert that the viscosity jump at 1020 ◦ C is related to the
Fig. 11. Optical micrographs showing porosity: (a) after 60 min at 1020 ◦ C and (b) after direct heating at 1060 ◦ C.
formation of a Cu network. Whatever its origin, the rigidity peak at 1020 ◦ C does not affect the apparent viscosity at higher temperature. 5.2. Apparent viscosity values The values of axial viscosity ηz deduced from the dilatometry experiments range from 0.5 × 103 to 4 × 103 MPa s when Cu is liquid and from 103 to 13 × 103 MPa s in the solid state. The only literature data that could be directly compared to these results are those measured by the same technique on cemented carbides  that also consist of a WC rigid phase, a deformable Co binder and porosity. In the temperature range 1100–1325 ◦ C in which the mechanical behaviour of Co is expected close to that of Cu at 1020–1060 ◦ C, ηz increases from 0.6 × 103 to 40 × 103 MPa s as density increases from 0.55 to 0.95dth . These values, slightly higher than those presently measured, can be due to the fraction of the deformable phase (22% Co) lower than that in W–Cu (35% Cu). The few other data found in the literature [8,15] concern the effective viscosity ηeff also termed bulk viscosity. By analogy with linear elasticity and assuming linear viscous behaviour, ηeff is related to ηz by: ηeff =
Fig. 10. SEM images at two magnifications of the microstructure of H∗ after 60 min at 1020 ◦ C: (a) general microstructure and (b) dense W–Cu packing and W grains dispersed or linked in chains.
ηz 3(1 − 2νvp )
where νvp is viscous Poisson ratio (3)
For a material rather similar to W–Cu, the results of Gillia et al.  evaluate vp from 0.05 to 0.15 in the density domain 0.6–0.8dth . Therefore, ηeff and ηz are of the same order and their comparison is of interest. In the solid state, the ηeff values were calculated from the models [18,19] for pure Cu and W. The models assume that contacts are rigid necks between particles and relate the contact size to that of particles. The W phase size in H∗ and H is about 0.3–0.6 m at sintering temperature. The ηeff values calculated for a particle size of 0.6 m and a density of 0.5dth are some hundred Pascal second and 106 MPa s for Cu and W, respectively. Ob-
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viously, ηz of the mixture W–Cu is in this extremely large range. At a temperature where Cu is liquid, the effective viscosity was evaluated by Panichkina et al.  for the material W–Cu (22%) using both a theoretical and an experimental approach. First, the deformation rate ε˙ sz was calculated from a mechanism of grain boundary sliding, as proposed by Ashby and Verall  for a polycrystalline solid and was assumed to correspond to viscous flow: πδgb Dgb σ 100σΩ ε˙ = = D with D + = D v eff eff ηeff LDv RTL2 (4) where σ is the applied stress, Ω the molar volume, R the gas constant, T the temperature, L the particle size, Dv the volume diffusion, Dgb the grain boundary diffusion coefficient and δgb the grain boundary width. The values selected for Dgb and δgb correspond to grain boundaries consisting of a liquid Cu film. In the second approach, the porosity decrease measured as a function of the sintering time was expressed using the classical formalism of viscous flow: 9γsv t 9γsv t Θ − Θ0 = exp − ≈ 1− (5) 4Lηeff 4Lηeff where Θ, Θ0 are the final and initial porosity, γ SV the surface energy and t the sintering time. At 1200 ◦ C, for a material with a W grain size (0.6 m) and a density range 0.7–0.8dth close to that presently investigated, the calculated and experimental values of ηeff are 46 × 103 (Eq. (4)) and 16 × 103 MPa s (Eq. (5)), respectively. The same magnitude range provided by the two approaches suggests that the mechanism of grain boundary sliding can be involved. Our results are consistent with those of Panichkina et al. . Effectively, when the viscosity variW , the η values measured for ation is represented versus XV z ∗ ◦ H at 1100 C and deduced from  are located on a unique curve (Fig. 12) that is correctly fitted by an exponential inW . Introducing the relation between XW crease of ηz with XV V and sintered density, this law is used to predict the axial viscosity increase with density for H∗ at 1100 ◦ C.
Fig. 12. Axial viscosity vs. W volume fraction and vs. sintered density at 1100 ◦ C. The values of H∗ and that from  are located on the same curve representing the increase of axial viscosity vs. W volume fraction. This curve is used to predict the exponential increase of axial viscosity of H∗ vs. density. The ηz value deduced from ηeff for 88% W and 0.7dth  assumes νvp = 0.15.
hardly develop during a continuous heating or isothermal steps at temperature below or slightly higher than the Cu melting. Neither is there any rigid skeleton detected from the microstructures (Fig. 13) showing that the packing formed by W particles at 1060 ◦ C is partly deformed at 1100 ◦ C. At 1060 ◦ C, the microstructure (Fig. 13a) consists of three types of “motifs” that are likely to originate from the initial particle packing. These “motifs” are dense cells of W
5.3. Features and evolution of the W skeleton In the material presently investigated, the W content W from 0.32 to 0.49 in the density (65%) corresponds to XV range 0.5–0.75dth . This fraction is lower than the solid fraction (0.74) forming the close packing of a fcc crystal structure. However, it is expected sufficient to generate a continuous W skeleton as Upadhyaya and German  showed that the shape of compacted W–Cu mixtures, with a W grain size close to that of H∗ or H is retained by sintering at 1400 ◦ C for a W fraction as low as 22%. The very low ηeff values measured at the beginning of the isothermal steps indicate that any rigid W network could
Fig. 13. SEM images at two magnifications of the microstructure of H∗ after 60 min: (a) at 1060 ◦ C and (b) at 1100 ◦ C.
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and Cu phases coming from the aggregates in the granules, Cu coated W grains either dispersed or linked as “chains”, formed by the particle shells and flattened by compaction. At 1100 ◦ C (Fig. 13b), the main “motifs” are still detectable but the more homogeneous phase distribution and the fragmented and curved “W chains” evidence the modification of the W packing. In the densification range investigated, the shrinkage rate, the microstructure change and the viscosity evolution indicate the main contribution of rearrangement. The axial viscosity increase versus sintered density leads to expect that the continuous W skeleton should form for density larger than 0.7–0.85dth and that the sintering of the W network can become effective above this density range. These conclusions are applicable to the studied powders that contain a significant Cu amount in which the W grains are rather unevenly distributed. The rather high deformation capability of these materials could result of the low W–W contact number and/or of the slow development of W grain boundaries from W–W contacts during sintering. Hence, the higher rigidity of H could originate from more W grain boundaries formed already in the chains and cells of the powder granules. These assumptions will be checked in the future from the fine scale characterisation of the W packing microstructure.
6. Conclusion The axial viscosity ηz is determined experimentally during the sintering of a powder material W–Cu (35%) that consists of a W rigid phase, deformable Cu and pores. The results evidence the significant ηz decrease with increasing temperature and a limited ηz increase with relative density. Below the Cu melting, ηz increases drastically with time at 1020 ◦ C while no shrinkage occurs, but decreases again on further heating. The ηz increase at low temperature can be attributed to the formation of a Cu network around the W grains that collapses at higher temperature by Cu flow in larger and farther pores. In solid state, the ηz values – 103 to 13 × 103 MPa s in the density domain 0.5–0.7dth – are consistent with those measured  on a material WC–Co with a rather similar structure (WC rigid phase, deformable Co and pores). The Cu melting induces a significant decrease of the axial viscosity −0.5 × 103 to 4 × 103 MPa s from 0.5 to 0.74dth . At 1100–1200 ◦ C, the present results and the published data  on the alloy W–22% Cu are located on a unique curve showing the exponential increase of ηz versus the volume fraction of W rigid phase in the mixture W–liquid Cupores.
For the W content and the microstructure of the material presently studied, the decrease of ηz with temperature does not indicate the formation of a W rigid skeleton during the early sintering stages, as proposed in the literature . Instead, and according to the dilatometry results and the microstructure change, we propose that the major part of the shrinkage occurs by rearrangement by viscous flow. In the future, the fine scale microstructure and shrinkage kinetics will be studied to check if the process is controlled by sliding at grain boundaries as proposed by Panichkina et al. .
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