Solidification Simulation of Pure Metal Castings by Considering the Effects of Shrinkage Cavity Formation Process on Heat Transfer Behavior
2019 Volume 60 Issue 1 Pages 25-32
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2019 Volume 60 Issue 1 Pages 25-32
In this study, the solidification simulation of pure metal castings was conducted and the effects of open shrinkage cavity formation process on heat transfer behavior were investigated. The shrinkage cavity predicted by the conventional simulation method was shallower than the experimental results obtained using the proposed method, although an inverted conical shrinkage cavity was formed on top of cylindrical pure metal castings. The change in the heat transfer behavior during solidification was not modeled well using the conventional method, which was associated with the long duration of shrinkage cavity formation process and the resulting deep shrinkage cavity. On the contrary, when we altered the reduction of melt level based on solidification shrinkage and the proper interfacial heat release to the atmosphere, the predicted shape and depth of the shrinkage cavity were very close to the experimental results. Therefore, a comprehensive simulation of the effects of the shrinkage cavity formation process on the heat transfer behavior is important for predicting the shrinkage cavity formed in pure metal castings.
Heatsinks are often used in semiconductor devices, such as an integrated circuit or a light emitting diode, among other power devices, to facilitate the dissipation of heat. Branched sleeves and crimp terminals are used for electrical wire connections in applications, such as electrical transmission, substation equipment, and electric railways. These products require excellent heat or electrical conductivity and are often made from pure aluminum or pure copper. In addition, these products are manufactured via a casting process to achieve near-net-shape production of their complex shapes containing fins or as-cast holes.1,2) However, the generation of casting defects can cause some serious problems in the process, such as porosity and shrinkage cavities. An effective approach to manufacture sound castings is to predict the generation of the defects using a casting simulation. Various techniques have been developed to predict the generation position and/or the volume of shrinkage defects through simulation.3–12) Since casting materials are mainly metal alloys, most techniques including NIYAMA criterion are based on the feeding ability in the dendritic mushy zone.3–10) On the contrary, pure metals exhibit skin formation-type solidification that progresses with almost no mushy zone. Conventional prediction techniques for the shrinkage defects, thus, cannot be used always to create pure metal castings.2,11,13,14) In particular, small temperature gradient and/or low solidification directionality would not always cause shrinkage defects due to the greater feeding ability of pure metal castings than that of common alloys.2,13–15)
Meanwhile, macroscale shrinkage cavities are often formed in pure metal castings instead of microporosity.14,16,17) Although simulation techniques have also been developed for predicting the shapes of shrinkage cavities, they are still not optimal because of the applicability to pure metal castings and/or the practicality such as reasonable calculation time.8,10–12) In addition, when open shrinkage cavities are generated, an initial melt is partially replaced with air.7) For cast steels, the variation in the heat dissipation due to the open shrinkage cavity formation has low effects on shapes and depths of cavities.6,10) On the contrary, both thermal conductivity and solidification shrinkage of pure aluminum or pure copper are greater than cast steels, which may not only affect the heat transfer behavior during solidification but may also affect the resulting shrinkage cavities.7,12,14,18) This implies that heat transfer and solidification simulation while considering the effects of open shrinkage cavity formation process are valuable for high accuracy predictions of cavity shapes in pure metal castings.11,12,14)
In this study, pure metal castings were prepared and then the solidification simulation was conducted under various conditions. By comparing the numerical results with the corresponding experimental results, the effects of the open shrinkage cavity formation process on the heat transfer behavior were investigated.
Table 1 shows the casting conditions employed in this study, including the solidification simulation. Four types of molds (room temperature) were employed. Figure 1 shows the casting design.12) The sand molds were made from silica sand and water glass via CO2 process. The metal molds were coated by boron nitride spray. Pure aluminum (>99.99 mass%), Al–7 mass%Si alloy, and pure tin (>99.99 mass%) were used as casting materials, which were melted using a high-frequency induction furnace and a graphite crucible under atmospheric conditions. The entire melt was poured into the mold. Despite the casting conditions, the pouring time was less than 4 s. In addition, one-dimensional surface shapes, i.e., the height distribution along a line of the melt and/or solid after mold filling were measured in real time using a laser profilometer (Keyence Corporation, LJ-V7200). As shown in Figs. 1(a)–(c), the measured positions of profiles were along the centerline of the top view of mold cavities. The vertical displacement at the center of the mold cavity is defined as the depth of the open shrinkage cavity (D). Approximate solidification (solidus temperature transit) time of the castings was also obtained based on the central temperature measured by a thermocouple, as shown in Figs. 1(a) and 1(b).
Schematic view of the casting design (unit: mm). (a) Rectangular (sand mold), (b) cylindrical sand mold, (c) cylindrical metal mold, and (d) double-decker cylindrical (sand mold) castings.12)
The castings were cut along the center planes. The generation status of the shrinkage defects was observed by visual inspection. The ultimate depth was also estimated based on the cross section and initial melt surface height. The cross sections of pure aluminum and pure tin castings were etched and electropolished, respectively, to observe the macrostructures. The etching was conducted using an aqueous solution of phosphoric acid (85 mass%).19) Electropolishing was conducted using an electrolytic aqueous solution of sulfuric acid (31 mass%) at an applied voltage of 10 V.19)
2.2 Conventional simulationA commercial software, ADSTEFAN (Hitachi Industry & Control Solutions, Ltd.), was used to perform the three-dimensional heat transfer and solidification simulation of cylindrical and double-decker cylindrical pure metal castings. The initial height and curved shapes of the melt surface were reflected using the measured profiles and/or the recorded video, which differed among pure aluminum and pure tin castings. All computational elements were set to be cubic, with each side as 0.5 mm. The casting and mold elements were surrounded by air elements. Table 2 shows the physical properties2,7,10,18,20,21) and initial temperatures of the materials used in the simulation. The air elements were isothermalized by setting the value of thermal conductivity and specific heat sufficiently high. Table 3 shows the interfacial heat resistance among the materials. To fit the experimental conditions, the interfacial heat resistance, initial temperatures, and specific physical properties (i.e., specific heat of pure aluminum, latent heat of pure tin, thermal conductivity of sand mold, thermal conductivity and specific heat of metal mold) were adjusted according to several cooling curves of cylindrical castings. The initial temperature, as listed in Table 2, was consequently lower than the corresponding pouring temperatures due to the decrease in temperature during mold filling.2) Since the pouring time was shorter than the solidification time, the temperature distribution due to mold filling was assumed to have small effects on simulation results.6) The simulation without interfacial heat release (with heat insulation) to the atmosphere was also performed for comparison. Sufficiently great interfacial heat resistance between casting or mold and air elements was set.
The filled ratio (degree of soundness, originally 100%) distribution based on the solidification simulation was calculated as a conventional method.10) The filled ratio of the casting elements decreases in response to the solidification shrinkage amount. The maximum solid fraction that can feed and be fed during the progress of solidification shrinkage (critical solid fraction) was set to 0.9 to simulate the easily feedable skin formation-type solidification of pure metals. This value is greater than that of common alloys.7,10) Melt was completely fed from the highest casting (source) elements of the continuous elements having less than the critical solid fraction.10) Subsequently, the filled ratio of the source elements decreased in response to the feeding amount. The open group of the elements having small filled ratio was determined as the macroscale open shrinkage cavity.10) The solidification shrinkage ratios of casting materials are shown in Table 2. The latent heat and solidification shrinkage ratio were distributed uniformly over the temperature range between liquidus and solidus temperatures. The numerical depth of the shrinkage cavity (D) was also obtained from the simulation results.
2.3 Simulation with element substitutionTwo-dimensional axisymmetric heat transfer and solidification simulation were performed using a finite volume method and cylindrical coordinate system.22) An element substitution calculation was also conducted based on the solidification simulation as an alternative open shrinkage cavity prediction method.8,14) This method substitutes casting elements with air ones based on the progress of solidification shrinkage. The highest source elements under less than the critical solid fraction were substituted in response to the feeding amount.8,10,14) The shrinkage cavity during the formation process, thus, can be reflected to the computational elements, where the open group of the substituted elements was determined as the macroscale open shrinkage cavity. This method is almost the same as the conventional method, except that the elements under the filled ratio of 0% were not substituted with the air elements for the conventional method.8,10,14) For comparison, the simulation without element substitution was conducted. The simulation under the initial flat shape of melt surface was also conducted. The initial height of the melt surface was set to be the same as the highest point of the non-flat shape.
All elements were set to be square with each side as 0.5 mm. Table 3 shows the interfacial heat resistance between the casting and mold for the simulation with the element substitution. The interfacial heat resistance was similarly adjusted according to the several cooling curves of cylindrical castings. The heat resistance was different from that of the conventional simulation, suggesting that the numerical cooling curves were changed due to the element substitution and/or handling of the cylindrical shape. Other conditions were same as those shown in Section 2.2. Meanwhile, the density of the casting element was assumed to be constant with temperature, although casting elements were substituted with air one.8) The consistent density was confirmed to have negligible effects on the ultimate depth and the shapes of the shrinkage cavity.
Figure 2 shows the temporal changes of the experimental depth of the open shrinkage cavity in rectangular castings. Figure 2 also presents the ultimate depth of the castings and the solidification time of the Al–7 mass%Si alloy casting. The shallow shrinkage cavity formation process and ultimate depth after the noise reduction can be measured suitably using the laser profilometer. However, the deep shrinkage cavity formation process of the pure metal castings was noisy and could not be measured. The depth change of Al–7 mass%Si alloy casting was smaller than pure metal castings. The open shrinkage cavity formation process also ended earlier than the solidification time. The shallow open shrinkage cavity and dispersed porosity were observed in the cross section. These results suggest that feeding from the highest position was difficult for the Al–7 mass%Si alloy casting because of the wide semisolid area during solidification.16,17) On the contrary, the duration of shrinkage cavity formation process for pure metal castings was longer than that for the Al–7 mass% Si alloy casting.16,17) Due to a shorter solidification time for pure aluminum than that required for aluminum alloys,15,23) the shrinkage cavity formation process of pure metal castings might continue until solidification ends. In addition, the resulting ultimate depths of both pure aluminum and pure tin castings were greater than that of the Al–7 mass% Si alloy casting, irrespective of the smaller solidification shrinkage ratio of pure tin than that of Al–7 mass%Si alloy.16,17) These results suggest that the feeding form of the highest position was much easier for pure metals because the skin formation-type solidification had much narrower semisolid area than that for the Al–7 mass% Si alloy casting.
Experimental depth changes in open shrinkage cavity in rectangular castings.
Figure 3 shows the cross-sectional macrostructures of the cylindrical pure metal castings and the predicted shapes of open shrinkage cavities under simulations. As shown in Figs. 3(a)–3(d), an inverted conical shrinkage cavity was formed on top of the castings. However, as shown in Figs. 3(e)–3(h), the shrinkage cavity predicted by the conventional simulation method was shallower than the experimental results, as shown in Figs. 3(a)–3(d). Therefore, the conventional method cannot be used to adequately model the change of the heat transfer behavior associated with the long duration of the shrinkage cavity formation process during solidification and the resulting deep shrinkage cavity. On the contrary, as shown in Figs. 3(i)–3(l), the shrinkage cavity predicted by the simulation using the element substitution was deeper than that obtained by the conventional simulation method, as shown in Figs. 3(e)–3(h), respectively. The shapes and depth were very close to the experimental results as shown in Figs. 3(a)–3(d), respectively. In addition, as shown in Figs. 3(m)–3(p), the shrinkage cavity predicted by the simulation without interfacial heat release to the air elements was shallower in comparison with the results obtained by the simulation with the heat release (Figs. 3(i)–3(l)), respectively. For the metal mold castings (Figs. 3(k)–3(p)), the simulation with the heat release had smaller effects on the predicted shapes and depth of the shrinkage cavity than those for the sand mold castings (Figs. 3(m)–3(p)). As shown in Fig. 3(b), coarse crystal grain was observed in the vicinity of the center of the sand mold casting. On the contrary, as shown in Figs. 3(c) and 3(d), fine crystal grains were observed throughout the metal mold castings. The cooling effect of the metal mold was dominant, despite the casting position.
Cross-sectional macrostructures of cylindrical pure metal castings and predicted shapes of open shrinkage cavity under simulations.
Figure 4 shows the temporal changes in the predicted depth of the shrinkage cavity in the cylindrical pure aluminum casting under simulations. Figure 4 also shows the experimental early un-noisy depth change, ultimate depth, and solidification time. Although the simulations or simulation conditions were different, as shown in Figs. 4(a) and 4(b), the depth changes by the simulation with element substitution are close to the experimental results. As shown in Fig. 4(a), by the simulation with element substitution, the end time of the depth change in the sand mold casting were almost the same as the experimental solidification time. Meanwhile, the interfacial heat release to the air elements for the metal mold casting, as shown in Figs. 3(k)–3(p) and 4(b), only had small effects on both the solidification time distribution and the depth changes. Similar tendencies were observed for pure tin castings. The heat release to the metal mold is greater than that by the heat release to the atmosphere.
Predicted depth changes of the shrinkage cavity in cylindrical pure aluminum castings under simulations. (a) Sand mold and (b) metal mold.
Figures 5(a)–5(d) show the predicted shapes of the shrinkage cavities and the solidification time distributions under the simulation without the element substitution. The simulation results with the element substitution are also shown in Figs. 5(e)–5(h). The scale was equalized to the results without the element substitution. It was shown that the solidification time distribution was changed by simulation with element substitution, suggesting that the element substitution is one of the non-negligible numerical factors to reflect the heat transfer behavior due to the shrinkage cavity formation process.14) For pure aluminum castings (Figs. 5(a), 5(c), 5(e), and 5(g)), the difference in the solidification time distribution between the simulation conditions was greater than those for pure tin castings (Figs. 5(b), 5(d), 5(f), and 5(h)). The change in the ratios of the solidification time for the pure aluminum castings (Figs. 3(i), 3(k), 5(a) and 5(c)) were also greater than those for pure tin castings (Figs. 3(j), 3(l), 5(b) and 5(d)). The casting material with great solidification shrinkage ratio had significant effect of the volume reduction due to the element substitution on the heat transfer behavior.
Predicted shapes of the shrinkage cavity under simulation conditions in cylindrical pure metal castings (solidification time distribution, unit: s).
Here, the simulation with element substitution reflected a drop in the melt level due to the solidification shrinkage. The above findings suggest that the volume decreased in the casting elements due to the drop of the melt level. An increase in the interfacial heat release area to the air elements, which was associated with the shape of the top surface, affected the cooling conditions during solidification and the subsequent shrinkage cavity formation. Thus, to predict the shrinkage cavity formed in pure metal castings, it is important to perform a comprehensive simulation of the effects of the shrinkage cavity formation process on the heat transfer behavior. However, as shown in Figs. 4(a) and 4(b), the differences between numerical and experimental depth changes gradually increased. Other influencing factors, such as thermal shrinkage, temperature non-linearity of latent heat and/or solidification shrinkage, the temperature change in the substituted air elements, as well as temporal and/or positional dependence of interfacial heat resistance between casting and air elements, might exist.
3.4 Effect of initial shape of the melt surfaceFigures 5(i)–5(l) show the predicted shapes of the shrinkage cavity and the solidification time distributions under the initial flat shape of the melt surface. The predicted depth of the shrinkage cavity under the initial flat shape of the melt surface was deeper than that under the initial non-flat shape, as shown in Figs. 5(e)–5(h) (Figs. 3(i)–3(l)). This tendency was significant for metal mold castings. The initial non-flat shape for pure tin castings, as shown in Figs. 5(f) (3(j)), 5(h) (3(l)), 5(j), and 5(l), also had non-negligible effect of the slightly round-edged shape. In addition, irrespective of the volume shown in Figs. 5(i)–5(l), the solidification time under the initial flat shape was lesser than that under the initial non-flat shape (Figs. 3(i)–3(l)). The interfacial contact area between casting and mold elements could be a dominant factor to influence the heat transfer behavior, which is important for metal mold castings because of the cooling effect of the mold. Therefore, considering both the initial height and the initial shape of the melt surface is important to predict the shrinkage cavity. The above findings suggest that the balance of the heat release to the mold and to the atmosphere is also critical for evaluating the importance of the interfacial heat release to the air elements, as mentioned in Sections 3.2 and 3.3.
3.5 Effect on double-decker cylindrical castingFigure 6 shows the cross-section of the double-decker cylindrical pure aluminum casting and the predicted shapes of the open shrinkage cavity under simulations. As shown in Fig. 6(a), an undercut-shaped shrinkage cavity was formed along the centerline of the casting, which had a larger depth than that for cylindrical castings. Meanwhile, as shown in Fig. 6(c), the shrinkage cavity predicted by the simulation with element substitution was slightly deeper than the results obtained by the conventional simulation (Fig. 6(b)), where the depth and the upper shape were very close to the experimental results (Fig. 6(a)). The simulation with element substitution is similarly available to predict the undercut-shaped and/or greatly deep shrinkage cavity. As shown in Figs. 6(c) and 6(d), the interfacial heat release from the inner surface of the shrinkage cavity to the air elements had a lower effect on the predicted shape and depth of the shrinkage cavity.
Cross-section of the double-decker cylindrical pure aluminum casting and predicted shapes of open shrinkage cavity under simulations.
Figure 7 shows the temporal changes in the predicted depth of the shrinkage cavity in the double-decker cylindrical pure aluminum casting under simulations as well as the experimental ultimate depth. There were differences in the upper shrinkage cavity formation process between both the simulations. However, the differences between the simulations or the simulation conditions had smaller effects on the subsequent depth changes than those for cylindrical castings (Figs. 4(a) and 4(b)). In particular, the depth change was little affected by the interfacial heat release from the inner surface of the shrinkage cavity to the air elements. A similar tendency was observed for metal mold castings, as shown in Figs. 3(k), 3(l), 3(o), 3(p), and 4(b). In addition, the drop of melt level was much faster than that shown in Figs. 2, 4(a), and 4(b), because the horizontal cross-sectional area is smaller than that for the rectangular and cylindrical castings. Thus, the cooling effect of the sand mold is much greater than that of the heat release from the inner surface of the shrinkage cavity due to the presence of large interfacial contact area with the mold and/or the small effect of the fast drop of melt level on the heat transfer behavior.
Predicted depth changes of the shrinkage cavity in double-decker cylindrical pure aluminum casting under simulations.
The solidification simulation of pure metal castings was conducted and the effects of shrinkage cavity formation process on the heat transfer behavior were investigated. The following conclusions were drawn from the results of this study:
This study was supported by the Hitachi Metals · Materials Science Foundation. A function based on the element substitution has been provided by the commercial software, ADSTEFAN (version 2017, revision 01 or later).
