Prediction of Shrinkage Cavity in Heavy-Section Ductile Cast Iron Using CAE Considering Volume Change during Solidification
2018 Volume 59 Issue 10 Pages 1578-1584
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2018 Volume 59 Issue 10 Pages 1578-1584
A new analysis parameter, which is the volume balance during solidification in heavy section ductile cast irons, was adopted to predict shrinkage cavities by computer simulation. To realize higher precision and quantify the behavior of expansion/contraction during solidification, the temperature and solidification ratio of each reaction stage from the start to completion of solidification were determined by the tangent line method. The expansion/contraction amounts of each reaction were calculated from chemical compositions of carbon and silicon and the initial temperature of the test material. Finally, the expansion/contraction degree was calculated by dividing the amounts of the expansion/contraction at each reaction by the solidification ratio. The quantified value was input into the casting simulation software as the expansion/contraction amounts. The result showed better matching compared to the actual shrinkage phenomenon.
This Paper was Originally Published in Japanese in J. JFS 90 (2018) 175–181.
It is known that sound cast iron can be produced from heavy-section ductile cast iron (large FCD) under riserless conditions owing to the expansion pressure and volume of eutectic graphite.1–4) Large FCD does not have any shrinkage cavities. However, while producing plate-type cast iron, shrinkage cavities may be generated under a riserless condition; thus, the riserless technique cannot be applied to the formation of some shapes. A practical calculation of the riserless safety index, based on the modulus of casting (Mc) and/or the shape factor, is used to determine whether the riserless design is applicable to create a desired shape.5–7) When it is determined that a riser is necessary, the risers are designed by a similar method to that used for designing cast steel. In addition, the use of heat balancers, which would not undergo shrinkage themselves, has been proposed to minimize the size of the riser needed.8,9) However, in heavy-section FCD, the shape of cast iron is more complicated, therefore it is more difficult to predict the portions that will generate shrinkage cavities. If weld repairs are not feasible due to the quality specifications, the part must be produced again (even if it is a few tons of cast iron), which would result in a significant loss. A design with excessive risers is employed to reduce the risk of such losses. However, this can reduce the work efficiency and/or product yield in some cases due to the difficulty in predicting the shrinkage cavities formed in FCD by computer-aided engineering (CAE). Various prediction methods can be used depending on the material and manufacturing method,10) including the Niyama-criterion method, temperature-gradient method, and closed-loop method. The accuracy of these analyses has been established for cast steel and cast aluminum alloy, among others, which are formed in a skin-like solidification process by continuing contraction. However, the mushy-type solidification, accompanied by graphite expansion in cast FCD, can be evaluated using various analysis software,11–15) but the prediction accuracy is inefficient with these approaches.16) To achieve an appropriate prediction accuracy, there is a need for analysis software that takes the FCD-specific solidification process and volumetric changes into consideration.
To predict the volumetric changes upon solidification, the proposed approaches include measuring the expansion and contraction of a cast material in a measurement mold or calculating the expansion and contraction of a material from its chemical composition. However, even when the chemical composition of a material is known, the volumetric balance is theoretically positive owing to the generation of shrinkage cavities. Therefore, it is used only as a referential index to assess the tendency toward the generation of shrinkage cavities after casting.17–20) Such issues may occur because, as mentioned above, the generation of shrinkage cavities varies depending on the size of the cast material and also causes variations in the timing, ratio, and amount of expansion/contraction during the solidification process. However, there have been a few attempts to simulate solidification that involved the quantitative study and characterization of these factors. Accordingly, in this study, we explored a method for predicting the generation of shrinkage cavities, involving the determination of the theoretical volumes of contraction and expansion associated with solidification. Then we conducted calculations by substituting these volumes for the corresponding areas that were divided at the flexion points of a cooling curve during solidification.
To simulate the expansion and/or contraction that occur during the solidification process, a solidification analysis is conducted to predict the formation of shrinkage cavities. This analysis involved the quantitative determination of volumetric changes, which are then used as input values for the simulation software. First, using the experimentally measured cooling curve from the solidification process, as shown in Fig. 1, the flexion points were determined by a tangent-line method and temperature and solidification ratio were determined for each point. We assumed that the change in the solidification ratio takes place when the pouring was completed and that the respective reactions occurred in the following order: (1) liquid contraction → (1) liquid contraction and (2) proeutectic reaction → (1) liquid contraction → (3) eutectic reaction → (4) austenite contraction between eutectic cells at the last stage of solidification. Thereafter, the obtained values for the C and Si contents and pouring completion temperature were substituted into eq. (1) to determine the theoretical volumetric change.5)
| \begin{equation} \mathit{TV}=\mathit{Sl}+\mathit{Epg}\ (\text{or}\ \mathit{Sp}\gamma)+\mathit{Eeg}+\mathit{Se}\gamma \end{equation} | (1) |
Critical points of volumetric change in solidification curve of 300 × 300 × 150 mm sample casting, for example.
In the above equations, Epg was used when the chemical composition was hypereutectic and Spγ was used when the composition was hypoeutectic. These values may be determined by the following equations:
| \begin{equation} \mathit{Sl}=((\mathit{Ti}-1423)/100)\times 1.5 \end{equation} | (2) |
| \begin{equation} \mathit{Epg}=(\mathit{Cx}-\mathit{Ce})/(100-\mathit{Ce})\times 3.4\times 100 \end{equation} | (3) |
| \begin{equation} \mathit{Sp}\gamma=(\mathit{Ce}-\mathit{Cx})/(\mathit{Ce}-\mathit{C}\gamma)\times-3.5 \end{equation} | (4) |
| \begin{align} \mathit{Eeg}&=((1-\mathit{Sl})/100)\times((100-\mathit{Cx})/(100-\mathit{Ce}))\\ &\quad\times((\mathit{Ce}-\mathit{C}\gamma)/(100-\mathit{C}\gamma))\times 3.4\times 100 \end{align} | (5) |
| \begin{align} \mathit{Se}\gamma&=((1-\mathit{Sl})/100)\times((100-\mathit{Cx})/(100-\mathit{Ce})) \\ &\quad\times((100-\mathit{Ce})/(100-\mathit{C}\gamma))\times-3.5 \end{align} | (6) |
| \begin{equation} \mathit{Ce}=4.27+\mathit{Si}/3 \end{equation} | (7) |
| \begin{equation} \mathit{C}\gamma=2.045-0.178\times\mathit{Si} \end{equation} | (8) |
Dividing the expansion and contractions volumes in the reactions by respective solidification ratios, the degrees of expansion and contraction were calculated. The actual calculation results will be reported in Chapter 3.
For the solidification analysis, ADSTEFAN Ver. 2016 from by Hitachi Industry & Control Solutions, Ltd. was used. The solidification analysis was conducted without conducting a fluidity analysis before and assuming that the temperature of the molten metal was consistent in the respective areas of the mold.
The predicted expansion and contraction behavior were entered into the software in the form of numerical values for the solidification shrinkage rates. These rates were used to determine the amount of solidification shrinkage15) by taking the flow of the molten metal into account and multiplying the increase in the solidification ratio by the solidification shrinkage rate. In the analysis, the flow of molten metal was assumed to occur in partially flowable regions, in which the solidification ratio was greater than the critical solid fraction, and it was assumed that the supply of molten metal occurs only from adjacent elements. When the solidification ratio was smaller than the critical solid fraction, the area was assumed to be a free-flow area and was divided such that the supply occurs from the elements within that free-flow area. The analytical predictions regarding the solidification shrinkage were expressed as indices, which are known as “filled ratios”. The physical properties and boundary conditions, used as the initial values, in the solidification analysis were representative of those in practical situations and are shown in Table 1. Moreover, to reproduce the expansion and shrinkage behavior, the flow-critical solid fraction was set to 1.0. The splitting mesh size, in the three-dimensional model, was set to 5 mm.
It is known that there are various factors, other than the solidification characteristics, that lead to the generation of shrinkage cavities. In this study, disregarding the noise factors, the tendency toward cavity generation due to shrinkage, under the manufacturing conditions of the heavy-section FCD, was characterized experimentally in four types of plate test blocks. The shapes and casting designs of the test blocks are shown in Fig. 2. A riserless design with a contraction rule of 8/1000 (220 mm wide, 300 mm deep, and 70 mm in thickness), as shown in Fig. 2(a), was used as the basic shape. For the pad design shown in Fig. 2(b), a pad having dimensions of 220 × 70 × 70 mm (width × depth × thickness) was installed on the top part of the test block at the center in the longitudinal direction. For the chillers design shown in Fig. 2(C), two chillers with dimensions of 50 × 100 × 50 mm (width × depth × thickness) were installed on the top and bottom of the test block. For the riser design shown in Fig. 2(d), a neck-down riser having dimensions of 240 × 240 mm (diameter × height) was installed on the top of the test block. A flow-off of φ = 30 mm was installed in one position at the center of the top surface of each test block. In addition, to minimize the variables in the casting conditions, such as chemical composition and pouring temperature, the casting mold was made by connecting the four types of test blocks via runners within one casting frame. The casting mold was prepared by kneading silica sand, 0.8 mass% furan resin, and 40 mass% (relative to the resin) curing agent, to obtain a mold strength of 4.5 MPa or greater, and prevent movement of the mold wall. Alcoholic MgO-type material was used as a mold-coating material. After drying the mold, by firing, it was further air-dried for 24 hours or more to fully recover the mold strength.
Casting design for plate test blocks. (Unit; mm)
The method of melting and pouring the metal is shown in Fig. 3. A low-frequency induction furnace was used to melt the return materials from production. After melting to a temperature of 1,723 K, the composition was adjusted to the desired ratios. After superheating for 5 minutes at a temperature of 1,770 K or higher, the melt was allowed to cool gradually and the molten metal was tapped. For the spheroidizing treatment and inoculation, 1.2 mass% of an alloy of Fe–45 mass% Si–5.8 mass% Mg, 0.3 mass% of an alloy of Fe–50% Si, and 1.0 mass% of a cover material were put in a ladle sequentially and a sandwich method was employed. The time between the end of the reaction and completion of pouring was five minutes. The chemical composition was analyzed after the spheroidizing treatment using an emission spectrophotometric analyzer. Setting the target chemical composition as hypoeutectic component(s), another identical mold was prepared with a K thermocouple at the center of the thickness of the plate section of each type of test block to measure the cooling curve during solidification.
Temperature and time schedule for melting, liquid treatment and pouring.
Table 2 shows the obtained chemical compositions of the test blocks upon completion of the pouring; the composition was equivalent to that of FCD 450 and yield of Mg was satisfactory.
Figure 4 shows the cooling curves measured during the solidification of the cast test blocks. The eutectic temperature increased, and the solidification completion time increased from the chiller deign to the riserless design to the pad design to the riser design. These findings confirm that the temperature measurements were successfully conducted.
Cooling curves during the solidification of plate test blocks.
Figure 5 shows the relation between the temperature and solidification ratio, in the respective reactions during the solidification process, as determined by the experimentally measured cooling curves. The periods for which the length of the solidification completion time of the test block was correlated with the solidification ratio of the respective reaction. This included only the eutectic reaction period and the inter-cell austenite shrinkage period generated in the last stage of the solidification.
Relationship between temperature and solidification ratio at each reaction of plate test blocks.
In samples with long solidification times, the eutectic reaction period was large and period of inter-cell austenite shrinkage was small. Table 3 shows the theoretical volumetric changes in the different test blocks. Since the initial temperature of the molten metal in the mold upon completion of pouring varies, the cooling curves were measured during solidification and the values were calculated from each curve independently. The data shows that the volumetric balance was net positive by the time the solidification was completed in all samples. This shows that, theoretically, the chemical composition used here does not generate shrinkage cavities, even in the riserless design. Generally, a eutectic composition that results in minimal shrinkage cavities should be used.
However, a hypoeutectic composition may be employed for some heavy-section FCD as a measure to control the generation of chunky graphite, which frequently causes problems.23–25) Figure 6 shows the behavior of expansion and contraction during the solidification process. The degrees of expansion and contraction were calculated by dividing the calculated theoretical volumetric changes for the respective reactions by the solidification ratio. On comparing the degrees of expansion and contraction for the respective reactions in the test blocks having different solidification times, it was found that the degree of contraction of the inter-cell austenite in the last stage of the solidification process decreased as the time required to complete the solidification increased.
Relationship between expansion and contraction at each reaction of plate test blocks.
Figure 7(a) shows the result of a penetrant examination of the center cross-sections of the different test blocks. In the riserless design, there was a positive indication that shrinkage cavities were generated near the center of the thick portion. A similar finding was observed in the pad design near the center of the thick portion. In the chiller design, there was a positive indication that shrinkage cavities were generated near the center of the thick portion on both ends. Moreover, the area of the shrinkage cavities was larger on the gate side. In the riser design, there was no indication on the plate portion, but there was an indication inside the riser that shrinkage cavities were generated. Figure 7(b) shows the analytical results of this study in terms of the filled ratio; the behavior of expansion and contraction was represented as the solidification contraction rates in the software and the amount of solidification contraction was determined. Figure 7(c) shows results obtained by the G/$\sqrt{\text{R}} $ method. The observation points were at the same positions as those on the cross sections where the shrinkage cavities were observed experimentally. The filled ratio is expressed as an index of the amount of solidification contraction and threshold of the shrinkage cavities was set as not greater than 99.9%. This is based on the assumption that a filled ratio of 100% represents the completely filled state and that the smaller shrinkage cavities are generated when the filled ratio is less than 100%. It was observed that the positions where shrinkage cavities were actually generated corresponded closely to the predicted positions of the shrinkage cavities according to the filled ratio measurements. However, the actual positions of the shrinkage cavities were slightly higher than those that predicted by the G/$\sqrt{\text{R}} $ method. In addition, the results show that the final solidification positions were shifted upward from the center of the thick portions in the actual casted metal blocks.
Result of CAE analysis for plate test blocks. a) Shrinkage distribution at cross section of test blocks. (The right side of the photos is the gate) b) Filled ratio 99.9∼0.0%. c) G/$\sqrt{\text{R}} $ 0.7∼0.0.
FCD is known for not generating shrinkage cavities when the Mc is high enough and shape is close to a cube. Figure 8(a) shows the result of the penetrant examination of cross sections from the 600 mm cubic test blocks (hereinafter, Mc = 10 cm) cast with a hypoeutectic composition and cut at the center. Although these samples had hypoeutectic compositions, similar to those of the plate test blocks, there was no indication of shrinkage cavities in the center. However, according to predictions made by the G/$\sqrt{\text{R}} $ method, the portion at the center of the cube, which solidifies last, was always indicated as an at-risk area. Thus, it was considered as impossible to produce cast metal without shrinkage cavities with a riserless design. However, the proposed results reveal that it is actually possible to produce cast metal without shrinkage cavities. This is because, when the solidification time is long, eutectic cells of graphite and austenite grow and fill the shrunk portions during the last stage of the solidification process. Therefore, it is also necessary to predict the absence of shrinkage cavities in addition to the generation positions of shrinkage cavities in order to make accurate predictions for heavy-section FCD. As shown in Fig. 8(b), the solidification analysis conducted on Mc = 10 cm test blocks indicated that no shrinkage cavities would be generated following the final solidification. Figure 9 shows the cooling curves of the plate test blocks and the Mc = 10 cm test blocks during solidification. The solidification time of the Mc = 10 cm test blocks was sufficiently long (9 hours or longer). Figure 10 shows the solid phase ratio and the amount of expansion and shrinkage in the Mc = 10 cm test blocks. The solidification shrinkage area and amount of shrinkage of the eutectic inter-cell austenite were smaller than that of the plate test blocks. Assuming that the mechanism of generating a shrinkage cavity is partially related to the growth of eutectic cells upon solidification, this behavior can be reproduced by the proposed method. Therefore, it can be considered that the tendency of generating shrinkage cavities was lower even in the analytical results.
Cross section of Mc = 10 cm block and analysis result. a) Shrinkage distribution. b) Filled ratio 99.9∼0.0%.
Cooling curves during solidification of plate test blocks.
Relationship between “temperature and solidification ratio” and “expansion and shrinkage” in each reaction of Mc = 10 cm block.
In this study, the expansion and shrinkage of the metal during solidification were considered. In the prepared test blocks, factors influencing the generation of shrinkage cavities, such as gas generation and the movement of the mold wall, were excluded. Therefore, both the test blocks and analytical results can be considered to have simulated the shrinkage cavity generation occurring due to solidification. According to the observed shrinkage cavities in the 70 mm-thick test blocks, although the theoretical volumetric balance was positive in the view of chemical composition, shrinkage cavities were generated in the final solidification positions. Even in the analytical results, the positions of the generated shrinkage cavities were at the same positions and it was possible to set a reasonable and easily understandable threshold stating that shrinkage cavities are generated when the filled ratio is 99.9% or less. Furthermore, the areas of the shrinkage cavities generated on the left and right sides of the test blocks were not equal in the chiller design. This may take place due to the influence of the gate. However, if we assume that the tendency toward shrinkage cavity generation is generally consistent and variations would be negligible for estimating the shrinkage cavities, the precision seems to be improved by quantitatively calculating the expansion and shrinkage and incorporating a solidification simulation compared with the predictions obtained by the theoretical volumetric balance or G/$\sqrt{\text{R}} $ methods.
In this study, the expansion and shrinkage that occur upon solidification were calculated and compared with the values obtained from the pouring tests. From the results, the following conclusions were made:
