To investigate the effects of different HIP parameters on the densification process, the densification behavior is discussed by analyzing the relative density distribution at typical moments and law curve of special nodes. Finally, the optimal HIP parameters are obtained, and the correctness of the simulation results is verified by experiments.
Due to the uneven density distribution of compact during the densification process, the overall density of compact is difficult to characterize the densification law. Consequently, five key points are taken from the edge to the centre on the powder alloy compact shown in figure 7, and the densification pattern of these five nodes during the HIP process is studied separately. It comprehensively reflects the densification of different parts in the process of powder densification, which is convenient to investigate the densification law of compact under different HIP parameters.
After the HIP simulations for each scheme are completed, the M33 scheme (900 °C/90 MPa) is selected in table 2 to analyse the degree of densification of the compact at different moments. The relative density distributions of the compact at different moments under M33 scheme are analysed.
Table 2. Optimizing programs of HIP process parameters for W-Cu alloy powder.
Pressure/MPaTemperature/°C708090100110120800M11M12M13M14M15M16850M21M22M23M24M25M26900M31M32M33M34M35M36950M41M42M43M44M45M46100M51M52M53M54M55M56The relative density distributions of the compact at different moments during HIP process under the M33 scheme (900 °C/90 MPa) are shown in figure 6. Under the M33 scheme, when the HIP process is carried out at 1.0 h (2500 incremental steps), the temperature and pressure are increased to 600 °C and 60 MPa, respectively, and there is yet no significant densification behaviour in the compact. When the HIP process is carried out at 1.5 h (i.e., the temperature and pressure are increased to the holding temperature and pressure, respectively), a significant densification behaviour occurs in the compact, and the relative density at the edge and the centre reached 97.24% and 86.96%, respectively. Hereafter, when the HIP process is carried out at 2.5 h, the heat preservation and pressure preservation have been completed, and the maximum relative density is 98.93%, which is distributed near the edge of compact, and the minimum relative density is 89.45%, which is distributed near the centre of compact. Finally, when the HIP process is carried out at 4 h, the whole HIP process has been completed, and the relative density of the minimum density area of the compact has reached 89.96%.
Figure 6. Relative density distributions of compact at different times during HIP under M33 scheme (900 °C/90 MPa).
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Standard image High-resolution imageThe results of relative density distribution in figure 6 show that different regions within the compact have different relative densities. Consequently, five key points has been taken to explore relative density distribution of compact from the edge to near the central axis. The five density measurement points selected from the compact are shown in figure 7. After 4 h of HIP, the relative density of the point 1 has reached more than 99%, while the point 5 has only reached 90%, and the relative density of the remaining points is distributed between 90% and 99%. In addition, the area near the edge of the compact first approaches complete densification, and the area near the axis of the compact finally approaches complete densification. In other words, when point 5 is fully dense, the whole compact is fully dense. Therefore, only the relative density at point 5 needs to be measured and the relative density at that point 5 is employed as the reference point for optimization. It is worth noticing that the relative density of the whole compact is full dense when the relative density at point 5 achieves 96% or more.
Figure 7. The diagram of measurement points and densification curves of different points of compact under program M33 scheme (900 °C/90 MPa).
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Standard image High-resolution imageFurthermore, the densification curve of the compact shows an 'S' shape as the HIP process proceeds shown in figure 7. At the initial stage of HIP, the relative density decreases slightly due to the increase in temperature, which causes the expansion of the plastic can and the compact. Hereafter, as the temperature and pressure increase, the compact reaches a rapid densification phase, which causes the movement and rearrangement of the larger particles and the filling of larger pores, with a rapid increase in relative density. During the pressure preservation stage, the compact undergoes viscoelastic deformation, the remaining small pores and defects in the compact are filled by extrusion, and the tendency of increasing relative density slows down. When the temperature and pressure are unloaded, the relative density of the compact increases by diffusion and creep.
To analyse the effects of HIP process parameters on the densification process of W-Cu powders, the process parameters (holding temperature, holding pressure, holding time) of HIP have been studied separately in this section to investigate the influence and law of each parameter on the densification process during the HIP process.
The variation of relative density for W-Cu compact with pressure at point 5 under different temperatures for holding time of 1 h is shown in figure 8(a), indicating that relative density at the edge of compact increases with pressure increasing. Obviously, there is a significant effect of temperature on the relative density of the compact after HIP. For example, the relative density at the edge of compact is 87% at 800 °C and 99.5% at 1000 °C under the pressure of 70 MPa and holding time of 1 h. It is worth noticing that the relative density at the edge of all compacts has achieved about 99%. Moreover, it can be seen from figure 8(a) that the higher the holding temperature, the higher the densification rate. This is because the higher the temperature of W-Cu powder during heat preservation, the lower the tensile strength of the particles is. Under the same pressure, the particles are more prone to plastic deformation and brittle fracture, forming smaller particles and filling more pores, which leads the compact denser. In addition, the viscosity between the powders decreases with the increase of temperature, so the smaller pressure can make the particles fracture into smaller particles, and the relative density reach the theoretical terminal density value in advance. The results are in accordance with Murray's terminal density theory, where the effects of HIP temperature on relative density increase exponentially and are more significant than the effects of pressure on relative density.
Figure 8. Relative density of point 5 after keeping at different HIP parameters: (a) relative density of point 5 after keeping at different temperatures for holding time of 1 h, (b) relative density of point 1 after keeping at different pressures holding time of 1 h and (c) relative density of point 5 after keeping under holding times of 1-2.5 h.
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Standard image High-resolution imageThe variation of relative density for compact with temperature under different pressures for holding time of 1 h is shown in figure 8(b). During the HIP densification process of W-Cu powders, the effects of pressure on density are smaller compared to the effects of temperature on density. The relative density of compact is 87.1% under low pressure of 70 MPa and 99% under pressure of 120 MPa at 800 °C, which increases by 8.7%. In addition, at lower temperatures, the densification rate varies almost linearly with temperature before the plastic deformation of the powder particles occurs, which increases rapidly due to the rearrangement, the translation and rotation of the powder particles under pressure. When the temperature reaches above 900 °C, the densification rate decreases, and the densification rate varies nonlinearly with temperature. However, the higher the pressure after 900 °C, the lower the densification rate, which means that a right pressure must be chosen within a certain temperature range. If a higher pressure is chosen, the densification rate decreases during the plastic deformation phase and the overall densification time increases. If a smaller pressure is chosen, the time of the particle rearrangement phase is increased. Therefore, it is important to select the appropriate HIP pressure for the densification rate of W-Cu powder without considering the holding time.
Figure 8(c) shows the variation of relative density for compact at point 5 with pressure under different holding time, indicating that the relative density of W-Cu powder increases with increasing holding time and that a longer holding time results in less pressure being required to achieve the same relative density, and the results show that there is likeness compared with the law that the higher the temperature, the smaller the holding pressure required to reach the same relative density. Consequently, the heat preservation and pressure preservation stage are the most important process in the densification process of powders, which can prevent the arc ablation of high voltage electrical contacts due to those tiny pores and defects, and is also the core technology to improve the service life of powder alloy. To prepare dense W-Cu alloy products, the holding stage is crucial, where the densification rate is slow, but the densification density is close to complete densification. In other words, extending the holding time during the HIP densification process can further improve the densities of the compact and the properties of the W-Cu alloy products. Therefore, based on the analysis of the numerical simulation results, the holding time of WCu30 can be 1.5 h to 2.5 h under the premise of ensuring the qualified performance of the products, without considering the influences of temperature and pressure.
According to the results from section 4.1.2, when a lower holding temperature (800 °C) is chosen, a higher holding pressure (120 MPa) is required to bring the compact close to full density, while when a lower holding pressure (70 MPa) is chosen, a higher holding temperature (1000 °C) is required to bring the compact close to full compaction. Consequently, the three parameters (holding pressure, holding temperature and holding time) of the HIP process are optimized simultaneously in this section. The crossover schemes are shown in table 2, where are 120 schemes for the HIP process according to the permutations of five temperature values and six pressure values set by the initial and boundary conditions, plus four holding times. In these schemes, the minimum holding temperature, minimum holding pressure and minimum holding time are optimized according to the densification law of section 4.1.2, using the relative density of compact at the point 5 as the target value for optimization.
As shown in figure 9, the surfaces of relative density versus holding temperature and holding pressure are plotted using the response surface methodology (RSM), based on the data from the simulation results of the schemes in table 2, with surfaces stacked under holding time of 1–2.5 h. The relative density of the point 5 changes less with the holding temperature when the holding time is 1 h, which is because the holding time is too short, the temperature and pressure act almost exclusively on the edge of compact. When the temperature and pressure act on the point 5, the effect has been significantly reduced, resulting in smaller effects of holding temperature on the relative density in the central region of compact. It can be seen from figure 9 that when the holding temperature exceeds 900 °C, the higher the holding temperature, the smaller the holding pressure required if the compact achieves the same relative density. Moreover, the relative density of compact above 96% in the figure 9 corresponds to a wide range of holding temperatures and pressures. When the holding temperature is higher than 900 °C and the holding pressure reaches 100 MPa, the relative density of compact is 95% to 97%, but not all of them reach above 96% when the holding time is 1.5 h. However, when the holding time is 2 h under holding temperatures of 900 ∼1000 °C and holding pressures of 100 ∼120 MPa, the relative density of compact can reach 96%∼98%. In addition, when the holding time is 2.5 h, the relative density of compact can reach 96% of the holding temperature and holding pressure ranges are the widest, but the holding time is the longest.
Figure 9. Contour maps of relative density of compact at point 5 at different holding times.
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Standard image High-resolution imageIn summary, in the HIP scheme of W-Cu alloy powder, the relative density can reach more than 96% in the following parameters: holding temperatures of 900 ∼1000 °C, holding pressures of 100 ∼120 MPa, holding times of 1.5 ∼2.5 h. Table 3 shows the relative density of point 1, 2, 3, 4 and 5 under the three optimized parameters schemes. According to the principle of energy saving and high efficiency, the optimized solutions is holding temperature of 950 °C, holding pressure of 110 MPa and holding time of 2 h. Figures 10(a)–(d) shows the relative density of the compact after HIP for holding times of 0.5, 1, 2 and 3 h under the optimized scheme of (950 °C/110 MPa). From figure 10(e), the overall relative density of the compact can reach more than 96% at 4h of HIP. From figure 10(f), the relative density of point 5 can reach more than 96% when HIP process is carried out for 4 h. According to the law described in section 4.1.1, the relative density of the whole compact has reached more than 96%.
Table 3. Relative density of five points under three kinds of optimized parameter programs (%).
SchemeP1P2P3P4P5900 °C/100MPa/1.5h99.4997.4293.8793.1692.94950 °C/100MPa/2h99.9999.9198.3697.3897.031000 °C/100MPa/2.5h10010010099.9999.89Figure 10. Relative density distributions (a-e) of compact for different times of HIP process and the variation (f) of relative density of different points with time under program M45 scheme (950 °C/110 MPa).
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Standard image High-resolution imageThe compact after HIP is shown in figure 11. The compact is cut into 2 mm thick slices along the axial direction, and five sampling points are marked in the simulation. Five specimens are taken out from these five points, and the relative density is measured by Archimedes drainage method. Hereafter, the average relative density is calculated as follows:
where is the density of distilled water. The relative density results of the experiment and simulation are comparatively analysed, as shown in table 4.
Figure 11. Compact after HIP: (a) with can and (b) without can.
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Standard image High-resolution imageTable 4. Experimental and simulated relative density of compact at different point (%).
SchemeP1P2P3P4P5AverageSimulation99.9999.8398.0897.3097.0398.45Experiment10010098.696.495.898.16Error/%0.010.170.530.931.280.30As shown in table 4, the average relative error in relative density between the simulation and experiment is 0.30%. There is no significant difference between the experimental results and the simulation results of the compact in terms of the relative density, which indicate that the numerical model is reasonable.
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