In my extensive research on casting processes, I have focused on the pervasive issue of porosity defects, particularly in aluminum alloys produced through sand casting. Sand casting, due to its low thermal conductivity and high versatility, is widely used in industry, but it often leads to shrinkage porosity because of the extended solidification range and poor feeding characteristics. This study delves into the application of counter-gravity casting combined with sand molds to mitigate these defects, and I systematically compare various porosity criteria to predict shrinkage formation in A-l4.5%Cu alloys. The goal is to identify the most suitable criterion for optimizing sand casting processes, thereby enhancing casting density and mechanical properties.
Casting is a transformative process where liquid metal undergoes phase change to form components, but it is invariably accompanied by volumetric shrinkage. During solidification, the formation of dendritic structures hinders liquid metal flow, leading to unfilled interdendritic spaces and porosity. In some cases, gas evolution from the melt, such as hydrogen in aluminum alloys, can form dispersed micro-pores that act as nuclei for shrinkage. Therefore, castings, especially those made via sand casting, are prone to internal defects like shrinkage cavities and porosity, compromising their integrity. To control these defects, researchers have developed models based on energy and momentum conservation in porous media flow, resulting in several porosity criteria functions. The most prominent ones include those proposed by Niyama, Lee, and Suri, each with distinct mathematical formulations derived from Darcy’s law and assumptions about permeability in the mushy zone.
In my investigation, I consider these criteria to evaluate their applicability in counter-gravity sand casting. The Niyama criterion, for instance, assumes a linear relationship between permeability and liquid fraction, expressed as:
$$CF_{Niyama} = \frac{G}{\sqrt{R}}$$
where \(G\) is the temperature gradient and \(R\) is the cooling rate. This criterion was originally developed for ferrous alloys but has been extended to others. The Lee criterion modifies this by assuming a quadratic relationship, leading to:
$$CF_{Lee} = \frac{R^5}{G^6}$$
Suri’s approach further differentiates between columnar and equiaxed grain structures. For columnar dendrites, the permeability is related to secondary dendrite arm spacing, yielding:
$$CF_{Suri-col} = \frac{R^{1.6}}{G^{1.652}}$$
For equiaxed dendrites, it relates permeability to dendrite length, resulting in:
$$CF_{Suri-eq} = \frac{1}{R^{0.35} G^{0.318}}$$
These criteria are pivotal for predicting porosity in sand casting, where thermal conditions vary significantly due to the mold’s insulating properties. My study aims to test these functions empirically in a controlled sand casting environment.
To conduct this research, I designed an experiment using a self-developed counter-gravity casting setup. The alloy chosen was A-l4.5%Cu, known for its wide freezing range and susceptibility to porosity in sand casting. The mold was a traditional clay sand mold, typical in industrial sand casting applications, to replicate real-world conditions. The pouring temperature was set at 705°C, and to minimize gas content—a common issue in aluminum sand casting—the melt was subjected to vacuum degassing at -91.2 kPa for 600 seconds after refining. This step is crucial in sand casting to reduce hydrogen solubility and prevent gas-induced porosity.
The casting process involved counter-gravity filling with a pressure difference of 50.7 kPa, followed by rapid pressurization to enhance feeding during solidification. I varied the feeding pressure to 101.3 kPa and 151.0 kPa in additional trials to assess the effect on porosity reduction. After casting, the specimens were extracted and sectioned into thin plates for metallographic analysis. Using optical microscopy, I captured multiple micrographs per sample and employed image analysis software to quantify porosity area ratio, ensuring accurate measurement of shrinkage distribution. The results showed that porosity was more prevalent in regions with lower temperature gradients, as expected in sand casting due to slower cooling.
The temperature field during solidification was critical for evaluating the criteria. I combined experimental measurements with ProCAST simulations to obtain \(G\) and \(R\) values at various locations. For A-l4.5%Cu, I defined \(G\) at the temperature \(T = T_S + 0.1(T_L – T_S)\), which is 558.2°C, and \(R\) as the average cooling rate between 548°C and 652°C. The simulation parameters, based on sand casting conditions, are summarized in Table 1.
| Parameter | Value |
|---|---|
| Initial Pouring Temperature | 705°C |
| Initial Mold Temperature | 25°C |
| Heat Transfer Coefficient (Mold-Environment) | 10 W/m²K |
| Heat Transfer Coefficient (Cast-Mold) | 1000 W/m²K |
Table 1: Simulation conditions for the sand casting process, reflecting typical sand casting thermal properties. The low mold temperature and heat transfer coefficients are characteristic of sand casting, leading to gradual solidification.
The porosity distribution, as measured from the samples, indicated that higher feeding pressures significantly reduced porosity, underscoring the importance of pressure-assisted feeding in sand casting. For instance, at 50.7 kPa, the porosity ratio was higher, especially in thicker sections, while at 151.0 kPa, it decreased markedly. This aligns with the principles of counter-gravity sand casting, where applied pressure compensates for shrinkage. The data were then fitted to the porosity criteria using a power-law equation:
$$p = A (CF)^B$$
where \(p\) is the porosity ratio, \(CF\) is the criterion function value, and \(A\) and \(B\) are constants. The correlation coefficient \(R^2\) was calculated to assess the fit quality. My analysis involved comparing the four criteria across different pressure conditions, as shown in Table 2.
| Criterion | Pressure (kPa) | A | B | R² | Average R² |
|---|---|---|---|---|---|
| Niyama: \(CF = G/\sqrt{R}\) | 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: \(CF = R^5/G^6\) | 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): \(CF = R^{1.6}/G^{1.652}\) | 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): \(CF = 1/(R^{0.35} G^{0.318})\) | 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 |
Table 2: Fitting results for porosity criteria under different feeding pressures in sand casting. The Suri (equiaxed) criterion consistently shows the highest correlation, making it most suitable for porosity prediction in this sand casting context.
From these results, I observed that the Suri criterion for equiaxed grains yielded the highest average \(R^2\) value of 0.8137, indicating the best fit to the experimental data. In contrast, the Niyama criterion had the lowest average \(R^2\) of 0.4745, suggesting poor applicability for aluminum alloys in sand casting. This outcome can be explained by the inherent characteristics of sand casting. The clay sand mold has low thermal conductivity, which promotes a gradual temperature drop and low temperature gradients during solidification, favoring equiaxed grain formation. Additionally, in counter-gravity sand casting, the applied pressure during the feeding stage may cause dendrite fragmentation in the chill zone, providing nuclei for equiaxed growth. Therefore, Suri’s assumption of permeability being related to dendrite length in equiaxed structures aligns well with the microstructural evolution in sand casting.
To further elucidate, I derived the theoretical basis for these criteria. In general, porosity formation in sand casting is governed by the balance between feeding flow and solidification kinetics. Using Darcy’s law for flow in the mushy zone:
$$v = -\frac{K}{\mu} \nabla P$$
where \(v\) is the velocity, \(K\) is permeability, \(\mu\) is viscosity, and \(\nabla P\) is pressure gradient. For sand casting, the permeability \(K\) is often modeled as a function of liquid fraction \(f_l\) or dendritic geometry. In the Niyama criterion, \(K \propto f_l\), while Lee assumes \(K \propto f_l^2\). Suri’s approach for equiaxed grains considers \(K \propto L_d^2\), where \(L_d\) is dendrite length, which correlates with cooling conditions. In sand casting, the slow cooling leads to coarse dendrites, making Suri’s model more representative.
My experimental data also highlighted the effectiveness of vacuum degassing and pressure application in reducing gas porosity. This is particularly relevant for aluminum sand casting, where hydrogen pickup is common. The process I employed—vacuum degassing followed by counter-gravity feeding—minimized pore formation, allowing a clearer analysis of shrinkage-driven porosity. The porosity distribution maps showed that defects were concentrated in regions with low \(G\) and \(R\), consistent with theoretical predictions for sand casting.
In discussing the implications, I emphasize that the choice of porosity criterion is critical for process optimization in sand casting. For instance, using the Suri (equiaxed) criterion, foundries can predict porosity hotspots and adjust feeding systems or pressure parameters accordingly. This is especially valuable in sand casting of complex geometries, where traditional methods may fail. Moreover, the integration of simulation tools like ProCAST with these criteria enables virtual prototyping, reducing trial-and-error in sand casting production.
To extend this research, I propose several future directions. First, investigating other aluminum alloys, such as A356 or 7075, in sand casting could validate the generality of the Suri criterion. Second, exploring the effect of mold materials—like resin-bonded sand versus green sand—on porosity formation would provide insights into sand casting variants. Third, incorporating real-time monitoring of temperature gradients during sand casting could refine the criteria further. The mathematical framework can be expanded by including additional factors, such as alloy composition effects on solidification paths. For example, the relationship between porosity and criterion functions can be expressed as a generalized equation:
$$p = \alpha \cdot (CF)^\beta + \gamma \cdot f(G, R, \text{alloy params})$$
where \(\alpha\), \(\beta\), and \(\gamma\) are constants derived from sand casting experiments.
In conclusion, my study demonstrates that in counter-gravity sand casting of A-l4.5%Cu alloys, the Suri criterion for equiaxed grains is the most reliable predictor of shrinkage porosity, outperforming the Niyama, Lee, and Suri columnar criteria. This finding underscores the importance of considering grain structure when modeling porosity in sand casting processes. The combination of vacuum degassing and pressure feeding effectively minimizes defects, highlighting practical strategies for improving sand casting outcomes. As sand casting continues to evolve with advancements in counter-gravity techniques, this research provides a foundational framework for enhancing casting quality through scientifically grounded porosity prediction.