2020 Volume 61 Issue 7 Pages 1381-1386
Die-casting is widely applied to the production of automotive components because of its high productivity for manufacturing complex-shaped castings. However, since molten metal is injected into a cavity at high speed and it solidified rapidly under high pressure in this process, many casting defects are liable to occur. Although the most frequent internal defect is gas entrapment, shrinkage porosity also forms in the thick-wall portions of die castings. In order to avoid shrinkage porosity, there is a need to feed adequate molten metal to compensate the shrinkage volume during solidification. Therefore, it is desirable to better understand the feeding behaviors of molten metal under high pressure and rapid cooling conditions in the die casting process. In this study, the permeabilities of Al–Si alloys during the solidification process under die-casting conditions were determined by measuring the pressure transmission of the molten metal from the plunger to the mold cavity so as to obtain the feeding resistance coefficients. The formation of shrinkage porosities in die-castings was proven to be predictable by numerical simulation using the obtained feeding resistance coefficients.
This Paper was Originally Published in Japanese in J. JFS 91 (2019) 529–533.
Die casting method, which is capable of manufacturing complex-shaped parts with high efficiency, is applied to producing various kinds of automobile components. However, in this process, melt is injected into a cavity at high speed and solidifies under high pressure, incurring various defects1–9) in die castings. Although the internal defects of die castings are mainly caused by gas entrapment9) during the filling of the melt, shrinkage cavities are also observed in the thick-wall portions. As these internal defects deteriorate the strength of the castings, they need to be avoided.
The gas entrapments have been investigated,6–8) and the technology for reducing these defects, such as vacuum die casting, has been developed. Meanwhile, the shrinkage cavity defects are mainly reduced by supplying melt to the shrinkage cavity through pressurization via plunger or squeeze pins.7) In order to reduce the shrinkage cavity defects effectively by feeding melt, the optimal condition for the pressurization is necessary, thus, the development of an analysis method is desired for predicting the shrinkage cavity under pressurization.
Therefore, clarifying the feeding behavior of melt in the solid-liquid coexistence state under a high pressure of 60 MPa and developing an analysis method considering this behavior are indispensable for predicting the occurrence of the shrinkage cavity in die castings. According to the past studies, the analysis of melt-feeding behavior has mainly been conducted using Darcy’s equation, which describes inter-dendritic liquid flow and is often applied to gravity casting.10,11) Meanwhile, the measurement of the permeability required for Darcy’s analysis has also been attempted.12) However, the melt-feeding behavior during solidification under the high pressure of die casting still remains to be clarified.
In this research, we attempted to obtain the permeability of Al–Si alloy die castings during rapid solidification under high pressure by measuring the pressure transmission of melt and examined the application of this permeability to the melt-feeding simulation.
The die casting used for the measurement is shown in Fig. 1. The configuration of the die casting was designed to transfer the pressure of the plunger to the tip of the thick-wall portion through the thin-wall portion. The die with a cavity of this configuration was attached to a vertical injection casting machine, and melt was poured into the thermally insulated cylindrical-shaped sleeve. The melt was injected into the cavity when the temperature reached the liquidus plus 100 K. The casting pressure and injection speed were set at 60 MPa and 0.4 m/s, respectively, and the plunger was moved upwards from the bottom of the sleeve to inject the melt in the sleeve into the cavity. During casting, diaphragm-type pressure gauges (made by Dynisco) were installed in the die such that the pressure-sensing face was aligned with the inner surface of the die cavity. The melt pressure was measured at two points, i.e., the thin-wall portion in the middle and the thick-wall portion at the top. The internal melt pressure of the die casting was measured by fixing a heat-insulating material (Kaowool sheet) onto the pressure-sensing face of the pressure gauge. The temperature of the internal melt at the thin-wall portion was measured by inserting a φ0.1 mm C.A. thermocouple2) into the center of the cavity, and the solid fraction was calculated with the measured temperature according to Scheil’s equation.13) Al–6–12.6%Si, ADC12 (Al–11%Si–2.34%Cu–0.12%Mg), and AC4C (Al–7%Si–0.3%Mg) alloys were used for this research.
Cavity shape of die-casting mold.
The melt-feeding simulation during solidification was performed by the following method. The permeability of the melt in the solid-liquid coexistence state during solidification was assumed to vary with the increase in the solid fraction in the following order: permeable zone, quasi-permeable zone, and impermeable zone. In the permeable zone, the liquid phase was assumed to flow together with the solid phase, and the viscosity of the melt was adjusted in the flow simulation to express the increase in the solid fraction. In the quasi-permeable zone, the solid was assumed not to flow, while the liquid phase flowed through the gaps of the solid phase. In this zone, the flow resistance of the solid-phase was considered by adding a resistance term (hereafter referred to as flow resistance) to the motion equations (Navier-Stokes equations).14) The melt was assumed not to flow in the impermeable zone. In this research, we used the thermal fluid analysis software, FLOW3D (Flow Science, Inc.), which contains all the functions necessary to perform the analyses mentioned above.
Figure 2 shows the mesh divisions used in the analysis, and Table 1 shows the thermal properties of the die casting. In the simulation, the solid fraction was calculated for each mesh; then, the melt flow between the solid phases was calculated. In addition, considering that the main purpose of this research was not to predict the exact shape but rather the occurrence position of the shrinkage cavity, a mesh size of 1 mm was used, which was larger than the size of the dendrites.
Mesh division used for simulation.
The measured permeability of the melt was classified using the method proposed by Bear.15) In other words, a range of permeability value greater or less than 10−11 m2 was assumed as the permeable and the quasi-permeable zones, respectively. When the permeability value decreased to less than 10−13 m2, the range of permeability was assumed as impermeable zone. In the simulation, the change in the viscosity of the permeable zone with the increase in the solid fraction was considered using the measured viscosity coefficient.16) The flow resistance of the quasi-permeable zone was given by eqs. (1)–(3).
| \begin{equation} \text{Flow resistance in x-direction:}\ K_{b}\cdot \varepsilon \cdot u \end{equation} | (1) |
| \begin{equation} \text{Flow resistance in y-direction:}\ K_{b}\cdot \varepsilon \cdot v \end{equation} | (2) |
| \begin{equation} \text{Flow resistance in z-direction:}\ K_{b}\cdot \varepsilon \cdot w \end{equation} | (3) |
| \begin{equation} \text{Resistance coefficient $K_{b}$} = \mu/(\rho \cdot K) \end{equation} | (4) |
Permeability K was calculated from the measured results mentioned in Section 2.1. In other words, K was calculated by eq. (5) after the mean melt velocity ub was obtained at the thin-wall portion of the cavity from the movement speed of the plunger, using the melt pressure difference |Δp| between the upper and lower portions from the measured values at the two portions and the distance L between the upper and lower portions.
| \begin{equation} K = u_{b}\cdot L\cdot \mu/|\varDelta p| \end{equation} | (5) |
Figure 3 shows the measured cooling curve of the melt, the measured pressure curves at the upper and lower portions, and the pressure difference between the upper and the lower portions of the AC4C alloy die casting. The horizontal axis indicates the time from the start of the mold clamping. The melt pressures measured at both the upper and the lower portions reached peak values at 2.5 s. The peak values of the measured melt pressures at both the upper and the lower portions were equal to the plunger pressure. The melt pressure at the upper portion decreased drastically at 3.7 s, and the pressure difference with the lower portion increased. The melt pressure at the lower portion decreased rapidly at 4 s, decreasing slightly thereafter. The melt pressure difference between the upper and the lower portions was obtained from the above melt pressure curves, and the relationship between the melt pressure difference and the melt cooling behavior was examined. As the melt reached the liquidus temperature, 893 K, primary solidification commenced, and at approximately 823 K, eutectic solidification began.
Pressure transmission and solidification behaviors of molten metal in die-castings.
The upper and lower melt pressures were almost the same at the beginning of the solidification; however, the pressure difference increased as solidification progressed. Subsequently, with the finish of solidification at 4 s, the transmission of the melt pressure from the lower portion to the upper portion halted, and the pressure difference showed a peak, followed by a decrease.
Figure 4 shows the displacement of the plunger, the difference in the upper and the lower melt pressures, and the melt temperature during the above measurement. The plunger started to move from 45 mm, which was the bottom dead center, and its speed was rapidly reduced at 2.5 s at which the melt has almost filled up the cavity. Afterwards, the plunger moved just a little, owing to the feeding of the melt to the solidification shrinkage, and stops at 4 s when the solidification of the melt finished. During the filling procedure, the pressure difference between the lower portion near the plunger and the upper portion increased for a moment. This increase in the pressure difference is considered to originate from the impact of the plunger. Subsequently, the upper and lower pressures became almost identical, and the pressure difference vanished. The pressure difference between the upper and the lower portions increased slightly during solidification but increased rapidly at the end of solidification. The pressure difference reached a peak at 4 s when the melt finished solidification and disappeared at last. In the present die casting experiment, the pressure difference between the upper and lower portions increased with the movement of the plunger and decreased rapidly when the plunger stopped; thus, the variation in the pressure difference corresponded well with the movement of the plunger. The pressure difference between the upper and lower portions is considered to be related to the flowability of the melt, and the melt flow resistance during the crystallization of the solid phase is assumed to be obtainable from the measured pressure difference.
Plunger movement and pressure transmission of molten metal during die-casting.
Figure 5 shows the melt temperature and melt pressure differences between the upper and lower portions during the die casting of Al–6–11% Si alloys. In Fig. 5, the curves are shown by taking the start points of the plunger as the same time. The melt pressure difference between the upper and lower portions increased with the decrease in the melt temperature, slightly at first, and then rapidly for all of the alloys. The onset time of the pressure difference was different depending on the alloys. For Al–6% Si and Al–7.5% Si alloys, the pressure differences started to increase during the primary solidification and showed a peak during the eutectic solidification. However, when the silicon content increased to as much as 9% and 11%, the onset time of the pressure difference tended to delay, especially in the case of Al–11% Si alloy, the melt pressure difference showed only a slight increase just near the end of the eutectic solidification. One of the main reasons for this onset time change in the melt pressure difference is considered due to the change in the solidification mode caused by the increase in silicon content. The solidification of Al–6% Si and Al–7.5% Si alloys belongs to the mushy type, because the solid phase (primary Al phase) begins to crystallize from the melt at the early stage of solidification. Pressure loss occurs when the liquid flows through the gaps of the solid phase, therefore, flow resistance comes into being as soon as the primary phase appears. Meanwhile, for the alloys of the skin-formation-type solidification such as Al–11%Si alloy, the melt can flow through the liquid-phase region in the center part in the thickness direction, thus, the flow resistance does not increase until the end of solidification.
Influence of Si content on pressure transmission of molten metal.
The permeability was determined from the above pressure difference by eq. (5), and the resistance coefficient Kb was calculated by eq. (4). Figure 6 shows the calculated resistance coefficients for Al–6% Si, Al–7.5% Si, and Al–11% Si alloys. In order to examine the accuracy of the calculated resistance coefficients, the resistance coefficients calculated from the permeability by the Kozeny–Carman principle model17,18) are also shown in Fig. 6.
Variations in feeding resistance of Al–Si alloys with solidification.
Here, the characteristic length d (the arm spacing of the primary dendrite) in the Kozeny-Carman equation was measured from the microstructure of the cross section in the Al–6% Si alloy die casting. According to this equation, the resistance coefficient increased to 5.0 × 106 s−1 when the solid fraction increased from 0 to 0.5. For both Al–6% Si and Al–7.5% Si alloys, the fractions of the primary solid are greater than 50%. The flow resistance depends on the distribution of the primary Al phase, because the liquid phase flows through the gaps of the primary Al phase. Therefore, there is nearly no difference in the resistance coefficients of Al–6% Si and Al–7.5% Si alloys at the initial stage of solidification when the solid fraction is 0.5 or less. However, in the case of Al–11% Si alloy, the amount of the primary Al is small, and the network of the primary Al phase is difficult to form. Therefore, the resistance coefficient hardly increases until the solid fraction reaches a high level and shows a rapid increase when the solid fraction becomes as high as 0.8. The measured resistance coefficient was smaller than that calculated by the permeability obtained from the Kozeny-Carman equation at a high solid fraction. Under the high pressure of die casting, the solid phase might flow together with the liquid phase, even at a high solid fraction, thus, the resistance coefficient became smaller than that of gravity casting. Nevertheless, the measured values are in the same order as those obtained by the Kozeny–Carman equation; thus, the accuracy of measured values is recognized.
Figure 7 shows the enlarged view of the region with a solid fraction less than 0.4. The resistance coefficient of Al–11% Si alloy hardly increased at the early stage of solidification. The solid fraction corresponding to the resistance coefficient (broken line in the figure) obtained from a permeability of 10−11 m2, which is the value of the quasi-permeable zone, is as high as 0.2.
Variations in feeding resistance of Al–Si alloy for low solid fraction.
Meanwhile, the resistance coefficients of Al–6% Si and Al–7% Si alloys, which form a network of the primary Al at the early stage of solidification, showed almost identical behavior. For both alloys, the resistance coefficient immediately increased as soon as the solidification began; in addition, the solid fraction where the resistance coefficient entered the quasi-permeable zone reached a value as low as 0.1. For these hypoeutectic alloys, the solid-liquid multiphase flow at the early stage of solidification transfers to the liquid single-phase flow through the gaps of the solid phase at the latter stage of solidification.
In order to clarify the solid fraction at which the permeability in Al–Si binary alloy changed, the threshold permeability for the permeable zone was assumed to be 10−11 m2 and 10−13 m2, and the solid fractions corresponding to the threshold permeability were calculated from the measured permeability. Figure 8 shows the relationship between the silicon content and the solid fraction corresponding to the permeable zone change. In the permeable zone, the liquid phase flows together with the solid phase, while in the quasi-permeable zone, the liquid phase flows through the gaps of the solid phase. Furthermore, in the impermeable zone, the melt stops flowing. In an alloy with a low content of silicon, the amount of the primary Al is large, and a dendrite network of the primary Al forms at the early stage of solidification. Therefore, the permeable zone is narrow, and the permeable zone changes to the quasi-permeable zone at the low solid fraction of 0.1. Meanwhile, when the silicon content of an alloy increases, the influence of the primary Al phase becomes minor, and the solid fraction at which the permeability changes from the permeable zone to the quasi-permeable zone also increases. Furthermore, the solid fraction at which the permeability changes from the quasi-permeable zone to the impermeable zone increases with the increase of the silicon content i.e., approaching the eutectic composition.
Influences of Si content and solid fraction on permeability.
Based on the results of the above sections, the coupled analysis of solidification and melt feeding was performed, and the shrinkage distribution for the test die casting of ADC12 alloy was examined. The melt flow after the start of the solid-phase crystallization was analyzed using the resistance coefficient obtained above, and the melt feeding into the shrinkage cavity was analyzed until the end of the solidification.
Figure 9 shows the calculated and measured values of the melt temperature in the thin-wall portion and the melt pressure difference between the upper and lower portions. From the measured temperature, the solidification started with a super-cooling at 2.5 s immediately after the filling process, then, the melt temperature remained at a constant value of 830 K. Finally, the solidification terminated approximately at 4 s. The simulation also showed the same result as the measurement, i.e., the melt started to solidify at 2.5 s, and the solidification completed approximately at 4 s. Both the measured and melt pressure differences started to increase rapidly during solidification at 3.5 s. Although there was some difference between the absolute values of the measured and calculated values, they showed good agreement with respect to the behavior of the melt pressure transmission. Therefore, it is confirmed that the melt feeding into the shrinkage cavity can be simulated by using the resistance coefficient obtained above.
Measured and simulated temperature and pressure transmission of ADC12 alloy melt.
Figure 10 shows the void distributions (shrinkage cavity) predicted by the simulation and observed by X-ray CT in the die casting. Figure 11 shows the calculated result of the shrinkage cavity in the final solidification part through a solidification simulation using the commercial code TOPCAST (Toyota Systems Co., Ltd.) without taking the melt feeding into consideration. In this simulation, an inverted triangular shape of shrinkage cavity was obtained in the upper thick-wall portion of the die casting. However, in the simulation considering melt feeding, the shrinkage cavity occurred uniformly in the center of the upper thick-wall portion of the die castings. This shrinkage cavity distribution is almost identical to the observed result. Therefore, it is confirmed that the shrinkage cavity distribution can be predicted with high accuracy by considering melt feeding.
X-ray computed tomography image and shrinkage porosities by feeding simulation of die-castings.
Solid fraction distribution and internal voids by solidification analysis.
The flow resistance during the melt-feeding was calculated from the melt pressure transmission measured during solidification in the aluminum alloy die castings, and the following was obtained by investigating the melt-feeding behavior.
