In the field of metal casting, the formation of internal defects such as shrinkage porosity remains a significant challenge, particularly for aluminum alloys used in sand casting parts. These defects arise during solidification due to volumetric contraction and hindered liquid metal flow within the mushy zone, leading to reduced density and mechanical properties. Counter-gravity casting, a process where metal is fed under controlled pressure, offers potential for minimizing porosity by enhancing feeding. This study focuses on evaluating the applicability of various porosity criteria for predicting shrinkage formation in Al-4.5%Cu alloy cast under counter-gravity sand casting conditions. The goal is to identify the most suitable criterion for optimizing process parameters and improving the quality of sand casting parts, which are widely used in industries for their versatility and cost-effectiveness.
Casting involves the phase transformation of liquid metal into solid parts, and during this process, shrinkage occurs as the metal contracts. In the mushy zone, dendritic structures impede the flow of liquid metal, preventing adequate feeding of interdendritic spaces and resulting in porosity. Additionally, gas evolution from the melt can form dispersed micro-pores, acting as nuclei for shrinkage. Thus, controlling porosity is crucial for producing high-integrity sand casting parts. Various researchers have developed models based on energy and momentum conservation in porous media flow to predict porosity. Notable among these are the criteria proposed by Niyama, Lee, and Suri, which relate porosity formation to thermal parameters like temperature gradient (G) and cooling rate (R). These criteria are mathematical functions used to assess the likelihood of shrinkage in castings. However, their applicability to aluminum alloys under specific casting conditions, such as counter-gravity sand casting, is not well-established. Aluminum alloys, with their low density, wide freezing range, and susceptibility to gas porosity, present unique challenges. This research aims to compare these criteria by correlating them with experimentally measured porosity rates in Al-4.5%Cu alloy specimens produced via counter-gravity sand casting, thereby providing insights for better process design and defect reduction in sand casting parts.
The experiments were conducted using a self-developed counter-gravity casting setup, where wedge-shaped specimens were cast in clay sand molds. The alloy used was Al-4.5%Cu, with a pouring temperature of 705°C. To minimize the influence of dissolved gases, particularly hydrogen, the melt was degassed under vacuum at -91.2 kPa for 600 seconds after refining. This step is critical for aluminum alloys in sand casting parts to prevent gas-induced porosity. The mold was then filled under counter-gravity conditions with a pressure difference of 50.7 kPa. After filling, the pressure was rapidly increased to a specified feeding pressure and maintained for 120 seconds to promote solidification under stable feeding conditions. Three sets of specimens were cast with feeding pressures of 50.7 kPa, 101.3 kPa, and 151.0 kPa to study the effect of pressure on porosity. This approach helps in understanding how pressure variations influence the internal quality of sand casting parts.
After casting, the specimens were cleaned, and thin sections were extracted from the central region. Each section was divided into smaller samples for metallographic analysis. Using optical microscopy, micrographs were taken at regular intervals and stitched together to form composite images covering the entire sample area. Porosity was quantified using image analysis software to measure the area fraction of pores, referred to as porosity rate (p). The distribution of porosity across the specimens was mapped, showing higher porosity at the thicker sections and lower near the tip. Results indicated that increasing the feeding pressure significantly reduced porosity, highlighting the importance of pressure control in counter-gravity sand casting for producing dense sand casting parts. The absence of noticeable gas pores confirmed the effectiveness of vacuum degassing and pressure-assisted solidification in suppressing hydrogen evolution.
To analyze the solidification behavior, temperature field evolution was simulated using ProCAST software, complemented by experimental measurements. The initial and boundary conditions for simulation are summarized in Table 1. The thermal properties of Al-4.5%Cu alloy were calculated using ProCAST’s built-in database. Temperature-time curves at various locations within the specimen were obtained, corresponding to the points where porosity was measured. From these curves, key thermal parameters—temperature gradient (G) and cooling rate (R)—were derived. For porosity analysis, G was taken at the temperature corresponding to 90% solid fraction, and R was averaged over the solidification range. Specifically, for Al-4.5%Cu, G was evaluated at 558.2°C, and R over 548°C to 652°C. The simulation results showed that near the tip of the wedge, higher G and R led to a narrow mushy zone and better feeding, whereas the thicker sections exhibited lower G and R, resulting in a wider mushy zone and increased porosity susceptibility. This thermal analysis is essential for understanding porosity formation in sand casting parts, as it links process conditions to defect generation.
| Parameter | Value |
|---|---|
| Initial Pouring Temperature | 705°C |
| Initial Mold Temperature | 25°C |
| Heat Transfer Coefficient (Mold-Environment) | 10 W/m²/K |
| Heat Transfer Coefficient (Specimen-Mold) | 1000 W/m²/K |
Four porosity criteria were evaluated in this study, each expressed as a function of G and R. These criteria are derived from Darcy’s law for flow in porous media and incorporate different assumptions about permeability in the mushy zone. The mathematical forms are as follows:
Niyama Criterion: $$ CF = \frac{G}{\sqrt{R}} $$
Lee Criterion: $$ CF = \frac{R^5}{G^6} $$
Suri Criterion for Columnar Dendrites: $$ CF = \frac{R^{1.6}}{G^{1.652}} $$
Suri Criterion for Equiaxed Dendrites: $$ CF = \frac{1}{R^{0.35} G^{0.318}} $$
Here, CF represents the criterion function, with higher values typically indicating a greater tendency for porosity. However, the relationship between CF and actual porosity rate (p) needs to be established empirically. In this study, we used a power-law equation to fit the experimental data: $$ p = A (CF)^B $$ where A and B are fitting constants. The correlation coefficient R² was calculated to assess the goodness of fit, with higher R² indicating better predictive capability. This approach allows for a direct comparison of how well each criterion predicts porosity in sand casting parts produced under counter-gravity conditions.
The experimental porosity rates and calculated CF values for each criterion were fitted using the power-law equation. Table 2 summarizes the fitting results for specimens cast at different feeding pressures. The correlation coefficients (R²) were averaged across pressures to evaluate overall applicability. As shown, the Suri criterion for equiaxed dendrites consistently yielded the highest R² values, indicating superior predictive performance for porosity in these sand casting parts. In contrast, the Niyama criterion showed the lowest correlation, suggesting limited suitability for aluminum alloys under these conditions. The Lee and Suri (columnar) criteria performed moderately but were less accurate than the equiaxed version. This outcome underscores the importance of selecting an appropriate criterion based on the microstructure and casting process, especially for complex sand casting parts where thermal conditions vary significantly.
| Criterion | Feeding Pressure (kPa) | A | B | R² | Average R² |
|---|---|---|---|---|---|
| Niyama: CF = G/√R | 50.7 | 0.0001939 | 7.875 | 0.5102 | 0.4745 |
| 101.3 | 0.0001356 | 5.895 | 0.5455 | ||
| 151.0 | 0.0001161 | 4.918 | 0.3677 | ||
| Lee: CF = R⁵/G⁶ | 50.7 | 0.001216 | -0.4921 | 0.7765 | 0.7558 |
| 101.3 | 0.0005781 | -0.3866 | 0.8005 | ||
| 151.0 | 0.0003767 | -0.3413 | 0.6904 | ||
| Suri (Columnar): CF = R¹·⁶/G¹·⁶⁵² | 50.7 | 0.001496 | -1.393 | 0.7905 | 0.7698 |
| 101.3 | 0.0006180 | -1.015 | 0.8053 | ||
| 151.0 | 0.0004365 | -0.9738 | 0.7136 | ||
| Suri (Equiaxed): CF = 1/(R⁰·³⁵ G⁰·³¹⁸) | 50.7 | 0.003972 | 2.923 | 0.8245 | 0.8137 |
| 101.3 | 0.001247 | 2.111 | 0.8202 | ||
| 151.0 | 0.0008974 | 2.113 | 0.7963 |
The superior performance of the Suri equiaxed criterion can be attributed to the solidification characteristics in sand casting parts under counter-gravity conditions. Clay sand molds have low thermal conductivity and heat capacity, leading to reduced temperature gradients during later stages of solidification. This promotes equiaxed grain formation, as the low G favors nucleation and growth of independent crystals. Additionally, the pressure applied during counter-gravity casting may cause fragmentation of dendritic arms in the chill zone, which are carried into the melt and act as nuclei for equiaxed grains. The Suri equiaxed criterion assumes that permeability in the mushy zone is related to dendrite length in a quadratic manner, which aligns well with the microstructural evolution in these sand casting parts. In contrast, the Niyama criterion, based on linear permeability assumptions, may not capture the complex flow dynamics in aluminum alloys with equiaxed structures. This highlights the need for criterion selection based on actual casting conditions, particularly for sand casting parts where mold properties influence solidification patterns.
Further analysis of the porosity distribution reveals that increasing feeding pressure from 50.7 kPa to 151.0 kPa reduced porosity rates by enhancing liquid metal feeding. This demonstrates the effectiveness of counter-gravity casting in producing high-density sand casting parts. The relationship between pressure and porosity can be described by extending the criteria to include pressure effects, though this was not within the scope of this study. However, it underscores the interplay between process parameters and defect formation. For industrial applications, optimizing feeding pressure based on criterion predictions can lead to significant improvements in the quality of sand casting parts, reducing scrap rates and enhancing mechanical properties. The use of vacuum degassing further minimizes gas porosity, making the process suitable for critical aluminum components.
In terms of mathematical modeling, the power-law fitting provided a straightforward way to correlate CF with porosity rate. The constants A and B vary with feeding pressure, indicating that the criteria may need pressure-dependent adjustments for accurate predictions. For instance, as pressure increases, the exponent B decreases in magnitude, suggesting reduced sensitivity of porosity to thermal parameters. This aligns with the physical understanding that higher pressure mitigates shrinkage by forcing liquid into pores. Future work could involve developing integrated models that combine thermal criteria with pressure terms for a more comprehensive prediction tool. Such models would be invaluable for designing casting processes for complex sand casting parts, where multiple factors influence defect formation.
The experimental methodology employed here—combining counter-gravity casting, metallography, and thermal simulation—offers a robust framework for studying porosity in various alloys and mold types. For sand casting parts, which often have intricate geometries and varying section thicknesses, this approach can be adapted to map porosity risk across different regions. By applying the Suri equiaxed criterion, foundresses can identify areas prone to shrinkage and adjust gating or riser designs accordingly. This proactive defect control is essential for meeting the stringent quality standards required in industries such as automotive and aerospace, where sand casting parts are commonly used for engine blocks, housings, and structural components.
In conclusion, this study demonstrates that the Suri criterion for equiaxed dendrites is the most applicable for predicting porosity in Al-4.5%Cu alloy cast under counter-gravity sand casting conditions. The high correlation coefficients across different feeding pressures confirm its reliability for sand casting parts. The Niyama criterion, while useful for ferrous alloys, showed poor performance, emphasizing the need for alloy-specific criteria. The findings highlight the importance of considering microstructural morphology—equiaxed versus columnar—when selecting porosity criteria. For practical applications in sand casting parts, using the Suri equiaxed criterion can aid in process optimization, leading to reduced porosity and improved product integrity. Future research should explore its applicability to other aluminum alloys and casting methods, as well as incorporate pressure effects for enhanced predictive capability. By advancing our understanding of porosity formation, we can contribute to the production of higher-quality sand casting parts, driving innovation in the casting industry.
To summarize key points: Porosity in sand casting parts arises from solidification shrinkage and hindered feeding, and its prediction relies on thermal parameters G and R. Among four evaluated criteria, the Suri equiaxed criterion best fits experimental data for Al-4.5%Cu alloy in counter-gravity sand casting. This criterion accounts for equiaxed grain formation, common in sand molds due to low thermal gradients. Increasing feeding pressure reduces porosity, showcasing the benefits of counter-gravity techniques. These insights can guide foundries in improving the quality and reliability of sand casting parts, ultimately enhancing performance in end-use applications. As casting technologies evolve, such comparative studies will remain vital for defect minimization and process advancement.