Sand casting parts are among the most widely manufactured metallic components, yet their solidification behavior largely controls the final microstructure, mechanical properties, and defect content. Traditional sand molds are dense, which limits the ability to spatially control heat extraction. With the advent of binder jetting three-dimensional (3DP) sand printing, mold geometries can be designed with complex internal cavities, thin shells, and tailored insulation zones. In this work, I developed a multi-layer nested shell sand mold that, when combined with a controlled rising water level, enables directional solidification of aluminum alloy castings. The proposed process significantly enhances the cooling efficiency, increases the vertical temperature gradient, and refines the microstructure of sand casting parts.
1. Process Overview and Heat Transfer Analysis
The multi-layer shell sand mold consists of several concentric thin-walled sand shells separated by air gaps. The innermost shell is in direct contact with the casting, while the outer shells act as radiation shields and structural reinforcement. Figure 1 shows a typical production setup for sand casting parts using such transparent shell structures.
During solidification, the mold is placed in a water tank. The water level rises at a controlled rate, submerging the mold from the bottom upwards. Below the water line, the innermost shell surface is in contact with water; because the shell is thin and initially very hot, nucleate boiling occurs, extracting heat rapidly from the lower part of the casting. The steam generated rises through the air gaps, heating the upper portions of the sand mold and the casting, thereby delaying solidification there. This combined action produces a steep temperature gradient along the height direction, which is the prerequisite for directional solidification. After the water level covers the entire mold and the temperature drops below the boiling point, the heat transfer mode changes to single-phase natural convection of water, providing fast and uniform cooling for the solidified casting, which also helps reduce residual stresses.
For the conduction heat transfer through a single sand shell of thickness \(\delta_m\), the steady-state heat flux is expressed by Fourier’s law:
$$q_{cond} = \lambda_m \frac{T_{a} – T_{b}}{\delta_m}$$
where \(\lambda_m\) is the thermal conductivity of the sand material, \(T_a\) and \(T_b\) are the temperatures of the inner and outer surfaces, respectively. The air gap between two adjacent shells transports heat by free convection and radiation. For the radiation component between two long concentric cylindrical shells with emissivities \(\varepsilon_1\) and \(\varepsilon_2\), the net radiative heat transfer rate is approximated by:
$$Q_{rad} = \frac{\sigma (T_1^4 – T_2^4)}{\frac{1-\varepsilon_1}{\varepsilon_1 A_1} + \frac{1}{A_1 F_{12}} + \frac{1-\varepsilon_2}{\varepsilon_2 A_2}}$$
where \(F_{12}\) is the view factor (close to unity for closely spaced shells), \(\sigma\) is the Stefan-Boltzmann constant, and \(A_1\), \(A_2\) are the surface areas. Because the thermal conductivity of air is approximately two orders of magnitude lower than that of resin-bonded sand, the air layers substantially increase the overall thermal resistance. Thus, the multi-layer shell design greatly improves the thermal insulation of the upper part of the mold during the water-cooling process.
When the cooling water contacts the over-heated innermost shell, the boiling heat flux can be described by empirical correlations. For saturated nucleate boiling on the outside of a vertical cylinder, the heat flux \(q_{boil}\) may be estimated by the Rohsenow correlation:
$$q_{boil} = \mu_l h_{fg} \left[ \frac{g(\rho_l – \rho_v)}{\sigma} \right]^{1/2} \left( \frac{C_{pl} \Delta T_e}{C_{sf} h_{fg} Pr_l^n} \right)^3$$
where \(\mu_l\) is liquid viscosity, \(h_{fg}\) is latent heat of vaporization, \(g\) is gravity, \(\rho_l\) and \(\rho_v\) are liquid and vapor densities, \(\sigma\) is surface tension, \(C_{pl}\) is liquid specific heat, \(\Delta T_e\) is the excess temperature, and \(C_{sf}\), \(n\) are empirical constants. Once boiling subsides, natural convection prevails, and the Nusselt number for the water layer can be obtained from standard correlations, such as:
$$Nu = C \, Ra^n$$
where \(Ra\) is the Rayleigh number, and \(C\), \(n\) depend on geometry and flow regime.
2. Numerical Simulation of Solidification
I performed finite-element simulations using ProCAST to evaluate the thermal response of the multi-layer shell sand mold and to optimize the water-level rising strategy. Three mold configurations were compared: a four-layer nested shell mold, a single-layer shell mold, and a dense sand mold. The casting was a cylindrical bar of diameter 40 mm and height 150 mm, with a conical riser on top. The alloy was AlSi7Mg0.3 (A356). The material properties used in the simulations are summarized in Table 1.
| Property | AlSi7Mg0.3 liquid | AlSi7Mg0.3 solid | Furan resin sand |
|---|---|---|---|
| Density (kg/m³) | 2400 | 2680 | 1520 |
| Thermal conductivity (W/m·K) | 70 | 160 | 0.5 |
| Specific heat (J/kg·K) | 1180 | 900 | 1050 |
| Liquidus temperature (°C) | 613 | – | – |
| Solidus temperature (°C) | 548 | – | – |
For natural cooling, the boundary conditions were set to ambient air at 20 °C with a heat transfer coefficient of 10 W/m²·K. The emissivity of the dense and single-layer molds was 0.6, while the four-layer mold had a reduced emissivity of 0.3 because the outer shell temperature remained lower. The simulations revealed that the four-layer shell mold extended the total solidification time to 1517 s, compared to 827 s for the single-layer and 588 s for the dense mold. Thus, the thermal insulation of the four-layer shell mold is approximately 1.8 times that of the single-layer shell and 2.6 times that of the dense sand mold. The temperature uniformity was also the best among the three designs, with the smallest average vertical temperature gradient and the smallest interfacial sag during solidification.
Subsequently, I modeled the water-cooling directional solidification process. The water level was set to rise from the bottom of the mold at constant rates of 0.1, 0.2, 0.3, 0.4, and 0.5 mm/s. The boundary conditions on the wetted surface were assigned a convective heat transfer coefficient of 5000 W/m²·K with a water temperature of 15 °C. On the unwetted surface, the ambient temperature was set to 100 °C (representing the steam-filled cavities) and the emissivity was 0.3. The results showed that the total solidification time decreased with increasing water-level rising rate, as listed in Table 2.
| Water-level rising rate (mm/s) | Total solidification time (s) |
|---|---|
| 0.1 | 907 |
| 0.2 | 747 |
| 0.3 | 637 |
| 0.4 | 560 |
| 0.5 | 500 |
Higher water-level rising rates produced larger temperature gradients between the bottom and the top of the casting, but also increased the interfacial sag because the solidification front lagged behind the water level. The sag rate \(\delta\) is defined as:
$$\delta = \frac{h}{D}$$
where \(h\) is the vertical distance between the highest and lowest points of the solidification front, and \(D\) is the casting diameter. I found that \(\delta\) increases monotonically with the height difference \(H\) between the solidification front and the water level. When \(H\) is positive (solidification front above water level), the interface becomes flatter and eventually planar. This observation led to the design of a variable-rate control strategy, where the water-level velocity is adjusted so that the height difference \(H\) remains constant while the solidification front advances. Three variable-rate profiles were tested. The optimal profile (referred to as “process 3” in the original thesis) maintained the solidification front slightly above the water level, with a constant positive \(H\) of about 5 mm. In this condition, the sag rate \(\delta\) decreased to zero after a short transient and remained planar for the rest of the solidification. Such an ideal directional solidification state is highly desirable for producing columnar or single-crystal microstructures in sand casting parts.
3. Experimental Setup and Casting Procedure
Based on the simulation findings, I designed and fabricated four-layer nested shell sand molds for cylindrical castings with diameters of 40 mm and 20 mm. The mold shells were 5 mm thick, and the air gaps were 10 mm. The sand was 3D printed using an ExOne S-Max printer with silica sand and furan resin binder. The mold consisted of the main body and a matching insulating cover, both having the same multi-layer geometry. The inner cavity included the cylindrical casting and a conical riser. For each diameter, two molds were produced: one for natural air cooling and one for water-cooling directional solidification.
I built an experimental platform with a PLC-controlled water pump and an ultrasonic level sensor. The water level was raised manually by adjusting the pump speed according to the monitored temperatures. Four K-type thermocouples were embedded at heights of 30, 60, 90, and 120 mm from the bottom of the sand mold. A commercial A356 aluminum alloy was melted in a crucible at 700 °C and degassed with a rotating impeller. The melt was poured into the molds for air-cooling experiments first. Then, the molds for water-cooling were placed one by one into the water tank immediately after pouring. The water level was raised gradually, following the rule that the water level should advance only when the temperature of the adjacent upper thermocouple falls below the solidus temperature (556 °C). This ensures that the solidification front moves ahead of the water level, maintaining a positive height difference as suggested by the simulations. The entire temperature histories were recorded by a multichannel data logger at 5-second intervals. A thermal infrared camera also monitored the outer surface of the molds throughout the process.
The water level rising rates measured during the experiments are shown in Figure 2. Since the control was manual, the rate fluctuated, but the average behavior followed the desired upward trend. The total time for the water level to reach the top of the casting was about 250 s for both diameters.
4. Thermal Results and Temperature Gradients
For the 40 mm diameter castings, the natural cooling casting (referred to as casting 1) required 1650 s to cool to 400 °C, while the water-cooled directional solidification casting (casting 2) required only 285 s. Thus, the cooling efficiency was improved by a factor of 5.8. For the 20 mm diameter castings, the air-cooled casting (casting 3) took 800 s to reach 400 °C, while the water-cooled casting (casting 4) took 300 s, an improvement of 2.7 times. The average temperature gradient along the height direction was calculated from the thermocouple data. The water-cooled process achieved an average gradient of 3.0 °C/mm, whereas the air-cooled process produced gradients below 0.7 °C/mm. These results confirm that the multi-layer shell mold combined with rising water level can impose a strong directional thermal condition, which is essential for directional solidification of sand casting parts.
The thermal images of the molds also revealed the role of the air layers. In the air-cooled mold, the temperature of the solid reinforcing ribs was higher than that of the hollow shell regions, indicating that the air gaps are better insulators than the bulk sand. In the water-cooled experiment, a nearly 100 °C temperature difference was observed between the submerged lower part and the exposed upper part of the mold. The steam generated by boiling filled the cavities and heated the upper shell, further increasing the temperature gradient.
5. Microstructure Characterization
After solidification, samples were sectioned from different heights of each casting, polished, and etched with 0.5% HF. Optical microscopy and scanning electron microscopy (SEM) were used to examine the α-Al dendrites and eutectic silicon. The water-cooled castings exhibited significantly finer and more rounded α-Al grains compared to the air-cooled ones. The secondary dendrite arm spacing (SDAS) was measured at four heights (30, 60, 90, and 120 mm) for each casting. The results are summarized in Table 3.
| Height (mm) | Casting 1 (air, φ40) | Casting 2 (water, φ40) | Casting 3 (air, φ20) | Casting 4 (water, φ20) |
|---|---|---|---|---|
| 30 | 72.1 | 47.4 | 49.7 | 40.8 |
| 60 | 83.1 | 60.0 | 62.2 | 65.4 |
| 90 | 97.2 | 60.0 | 75.0 | 55.2 |
| 120 | 98.6 | 65.4 | 78.3 | 65.0 |
On average, the SDAS of the water-cooled 40 mm casting was 66% of that of the air-cooled casting, while for the 20 mm castings the ratio was 82%. The eutectic silicon in the air-cooled samples appeared as coarse, elongated needles with lengths ranging from 10 to 50 µm. In contrast, the water-cooled samples contained fine, spherical silicon particles with diameters mostly between 2 and 8 µm, about one-fifth of the natural-cooling size. This refinement is attributed to the higher cooling rate and greater undercooling, which restricts dendrite growth and promotes a more isotropic eutectic structure. The improvement is particularly important for sand casting parts, as fine microstructures generally lead to better ductility and toughness.
6. Mechanical Properties
Standard tensile specimens were machined from the castings. The stress-strain curves were obtained and the key mechanical properties (ultimate tensile strength, yield strength, and elongation) are listed in Table 4. Brinell hardness was also measured using a 62.5 kg load (31.2 kg for the soft air-cooled 40 mm casting).
| Casting | Diameter (mm) | Cooling method | Tensile strength (MPa) | Yield strength (MPa) | Elongation (%) | Hardness (HBW) |
|---|---|---|---|---|---|---|
| 1 | 40 | Air cooling | 116 | 67 | 2.6 | 24.3 |
| 2 | 40 | Water directional | 181 | 81 | 7.4 | 39.5 |
| 3 | 20 | Air cooling | 139 | 98 | 2.8 | 34.3 |
| 4 | 20 | Water directional | 164 | 101 | 3.6 | 40.3 |
For the 40 mm castings, the water-cooled directional solidification process increased the ultimate tensile strength by 56%, the yield strength by 20%, the elongation by 185%, and the hardness by 62.6%. The improvements for the 20 mm castings were 18%, 3%, 29%, and 17.5%, respectively. The smaller diameter castings showed less improvement because their lower heat content reduces the effectiveness of the mold insulation and the contrast between natural and forced cooling. Nevertheless, the water-cooling directional solidification process substantially enhances the mechanical performance of sand casting parts, especially for larger and thicker sections.
Fracture surface analysis of casting 2 was performed with X-ray computed tomography. The scans revealed a few large pores near the fracture origin, likely caused by insufficient degassing. These pores acted as crack initiation sites, and micro-cracks were observed around them. This highlights the importance of melt quality in addition to solidification control. With proper degassing, the mechanical properties of the water-cooled directional solidified castings could be further improved.
7. Conclusion
This work demonstrated a new process for producing high-quality sand casting parts by using a multi-layer nested shell sand mold fabricated with 3D printing and applying a controlled rising water level for directional solidification. The key conclusions are:
- The air gaps in the multi-layer shell mold provide excellent thermal insulation, which is 1.8 times better than a single-layer shell and 2.6 times better than a dense sand mold in terms of solidification time extension.
- The water-cooling process creates a steep vertical temperature gradient (about 3.0 °C/mm), while the steam generated during boiling heats the upper mold and delays solidification there, promoting directional solidification.
- The variable-rate control strategy, where the water level pushes the solidification front upward with a small constant height offset, yields a planar and stable solidification interface, which is ideal for directional microstructures.
- Experimental validation on A356 aluminum alloy castings showed that the water-cooling directional solidification process refines the α-Al dendrites, reduces the secondary dendrite arm spacing by 18–34%, and refines the eutectic silicon particles to one-fifth of their natural-cooling size.
- The tensile strength, yield strength, elongation, and hardness of 40 mm diameter castings were improved by 56%, 20%, 185%, and 62.6%, respectively, while the 20 mm castings showed lower but still positive gains.
The proposed method offers a promising route to produce advanced sand casting parts with improved mechanical performance, without the need for expensive directional solidification furnaces. It is particularly attractive for the automotive and heavy-equipment industries, where 3D-printed sand molds are already becoming a standard tool for rapid and flexible production.