In the pursuit of high-performance components for aerospace and advanced equipment, ZL205 aluminum-copper alloy stands out due to its exceptional strength-to-weight ratio. The alloy’s properties are primarily derived from the solid solution and age-hardening effects of its copper content, which is optimally maintained between 4.6 wt.% and 5.3 wt.%. However, this advantageous composition also presents significant challenges within the investment casting process. The alloy exhibits a wide solidification range, inherently poor fluidity, and high sensitivity to section thickness, making it prone to defects such as shrinkage porosity, hot tearing, and oxide inclusions. These challenges are particularly acute when attempting to cast thin-walled or complex geometries. To address these issues and optimize the investment casting process for ZL205 alloy, this study integrates numerical simulation with physical experimentation. A critical step involves the inverse determination of the interfacial heat transfer coefficient (IHTC) to enhance the accuracy of the finite element (FE) model. Subsequently, the validated model is employed to simulate and analyze the flow, solidification behavior, and defect formation under various process conditions, with findings corroborated through practical casting trials.
Numerical simulation of the casting process has become an indispensable tool for predicting solidification patterns, thermal histories, and potential defects, thereby reducing development time and cost. The fidelity of such simulations hinges on the accuracy of the input parameters, among which the boundary condition at the metal-mold interface is paramount. The heat flux, $q$, across this interface is commonly described by Newton’s law of cooling:
$$ q = h (T_m – T_s) $$
where $h$ is the interfacial heat transfer coefficient (IHTC, in W/m²·K), $T_m$ is the metal surface temperature, and $T_s$ is the mold surface temperature. This coefficient is not a material property but a complex function of surface roughness, air gap formation, thermal contact pressure, and the thermophysical properties of both materials. Direct measurement is extremely difficult, making inverse solution techniques a practical necessity for accurate simulation. In this work, we perform temperature measurements during the solidification of ZL205 alloy within a ceramic shell to inversely calculate the IHTC. This refined boundary condition is then applied to simulate a comprehensive test casting under different shell preheating and cooling conditions, aiming to elucidate the alloy’s ultimate castability and defect formation mechanisms.
Materials, Methodology, and Model Development
The study focuses on a high-strength ZL205 Al-Cu alloy. The mold material is a standard mullite-based ceramic shell with a nominal thickness of 10 mm. The key thermophysical properties used for the simulation, derived from material databases and literature, are summarized in Table 1.
| Parameter | ZL205 Alloy | Mullite Shell |
|---|---|---|
| Density (kg/m³) | 2800 (liquid), 2780 (solid) | 2600 |
| Thermal Conductivity (W/m·K) | Variable with temperature | 1.5 |
| Specific Heat (J/kg·K) | Variable with temperature | 1100 |
| Liquidus Temperature (°C) | ~645 | – |
| Solidus Temperature (°C) | ~548 | – |
| Latent Heat of Fusion (kJ/kg) | ~389 | – |
1. Casting Design and Finite Element Modeling
A bottom-gated浇注系统 was designed to promote平稳, non-turbulent filling and directional solidification. The 3D model incorporated test samples of various geometries and dimensions to assess castability across a range of conditions. The test pieces included round bars with diameters of 3 mm, 10 mm, 20 mm, and 40 mm, and flat plates with thicknesses of 3 mm, 6 mm, 12 mm, and 24 mm. All samples were 300 mm in height. The main runner had a cross-section of 40 mm x 40 mm. The model was discretized using a hybrid meshing strategy, applying a finer mesh (Level 2) to the test samples and critical浇道 areas, and a coarser mesh (Level 10) to the bulk shell and less critical runner sections. The final mesh consisted of approximately 4.78 million volume elements, ensuring a balance between computational accuracy and efficiency.
2. Inverse Determination of Interfacial Heat Transfer Coefficient
An inverse problem is formulated where the boundary condition (IHTC) is unknown, but the system response (temperature history at specific points) is measured. The objective is to find the value of $h$ that minimizes the difference between the simulated temperature $T_{sim}(h,t)$ and the experimentally measured temperature $T_{exp}(t)$ at corresponding locations. A common approach is to define an error function $S(h)$:
$$ S(h) = \sum_{i=1}^{N} [T_{sim,i}(h) – T_{exp,i}]^2 $$
where $N$ is the number of data points. The optimal $h$ is found iteratively by updating an initial guess until $S(h)$ is minimized.
Experimentally, K-type thermocouples were embedded at three strategic locations within the investment casting shell assembly (see Figure 3a in the original manuscript). Point P1 was located at the center of a ϕ15.3 mm tensile specimen, while points P2 and P3 were positioned within the upper and lower main runners, respectively. The shell was at ambient temperature. ZL205 alloy was melted, refined, and poured at 725°C. The temperature histories at these three points were recorded throughout the pouring and solidification process (see Figure 4 in the original manuscript). Using the ProCAST software’s inverse solver module, these temperature curves served as the target response. The thermophysical properties of the alloy and shell, along with other initial conditions (pouring temperature, ambient cooling), were input. The solver then iteratively adjusted the IHTC values assigned to the corresponding metal-shell interfaces until the simulated cooling curves matched the experimental ones with acceptable accuracy. The optimally determined IHTC values were 542 W/(m²·K) for the tensile bar location, 911 W/(m²·K) for the lower runner, and 875 W/(m²·K) for the upper runner. These values were subsequently applied as boundary conditions in all subsequent simulations, significantly improving the model’s predictive reliability for the ZL205 investment casting process.
3. Simulation Setup and Process Parameters
The simulations were conducted to investigate the effects of two key process variables: shell preheat temperature and cooling mode. The conditions are outlined in Table 2. The pouring temperature was fixed at 725°C with a pouring time of 10 s, corresponding to a mass flow rate of approximately 1.054 kg/s. Gravity-driven filling was simulated. The IHTCs determined from the inverse analysis were assigned to their respective interface regions. The simulation ran until the entire system cooled to 20°C.
| Simulation Case | Shell Preheat Temp. (°C) | Cooling Condition | Assigned IHTC (W/m²·K) |
|---|---|---|---|
| Case A (Low Temp / Slow Cool) | 200 | Natural Convection (Air) | P1: 542, P2: 911, P3: 875 |
| Case B (High Temp / Slow Cool) | 500 | Natural Convection (Air) | P1: 542, P2: 911, P3: 875 |
| Case C (High Temp / Fast Cool) | 500 | Forced Convection (Fan) | P1: 542, P2: 911, P3: 875 |
Results and Analysis
1. Flow and Filling Behavior
The simulation for Case B (500°C preheat) revealed the characteristic flow sequence of the bottom-gated system. Metal entered the sprue, filled the lower horizontal runner in about 3.5 seconds (38% volume filled), and then began ascending into the vertical test samples. The filling sequence was strongly influenced by geometry. Larger cross-section samples (e.g., 40 mm bar, 24 mm plate) filled rapidly from the bottom up. However, for thinner sections like the 3 mm plate, the flow pattern was less favorable. The metal rising from the lower runner met the metal descending from the upper runner, creating a “counter-current” flow or撞流 in the upper regions of these thin sections. This turbulence increases the risk of oxide entrapment and air entrainment, compromising the internal quality of thin-walled sections in this浇注系统 design.
The total filling time for the entire mold cavity was approximately 8.2 seconds. The last areas to fill were the extremities of the upper horizontal runner, which is beneficial as it allows inclusions to float away from the critical castings.
2. Thermal Field and Solidification Evolution
The thermal history directly dictates the microstructure, stress development, and defect formation. The solid fraction, $f_s$, is a critical output, ranging from 0 (fully liquid) to 1 (fully solid). Its evolution can be described in relation to the local temperature, $T$:
$$ f_s = \begin{cases}
0 & T \geq T_{liq} \\
\frac{T_{liq} – T}{T_{liq} – T_{sol}} & T_{sol} < T < T_{liq} \\
1 & T \leq T_{sol}
\end{cases} $$
where $T_{liq}$ and $T_{sol}$ are the liquidus and solidus temperatures, respectively.
Under the high preheat condition (Case B), solidification was significantly retarded. At 12.3 seconds after the start of pour, the overall solid fraction was only 0.2%. The 3 mm thin-wall section, despite its high surface-area-to-volume ratio, remained mostly above the liquidus temperature. By 20.1 seconds ($f_s$ ~1%), this thin section cooled below the liquidus and began to solidify rapidly, with the solid front progressing from the edges towards the center. The temperature isotherms and solid fraction contours showed a pronounced “peak” shape at the ends of the thin plates, indicating non-uniform cooling and high thermal gradients, which are precursors to hot tearing and distortion. The bulkier sections and the浇道 system remained mostly liquid, acting as feeders. Complete solidification of the entire casting and runner system took over 1900 seconds under natural cooling, highlighting the profound insulating effect of the preheated ceramic shell in the investment casting process.
In contrast, the simulation for Case A (200°C preheat) showed a much more rapid temperature drop and solidification initiation, particularly in the thin sections, which began freezing almost immediately upon filling, severely hindering the feeding capability from the runners.
3. Prediction of Shrinkage Defects
Shrinkage porosity forms due to the volume contraction of the metal during solidification if liquid feed metal is unavailable to compensate. The Niyama criterion, $G/\sqrt{\dot T}$, where $G$ is the temperature gradient and $\dot T$ is the cooling rate, is a widely used indicator for predicting microporosity in alloys with a mushy zone. Low values of this criterion indicate regions prone to shrinkage porosity.
The simulation results for shrinkage (macro- and micro-porosity) are summarized in Table 3. A critical defect-prone area predicted across all cases was the junction between the lower horizontal runner and the large (ϕ40 mm) bar. This corresponds directly to the location where the initial metal stream impacted and splashed during filling (as seen in flow simulation), likely creating localized turbulence and early solidification that blocked feeding paths.
The effect of process parameters was clear:
- Case A (200°C preheat): Predicted severe and extensive shrinkage in the smaller-diameter bars (ϕ3, ϕ10 mm) and thin plates (3 mm). The rapid heat extraction caused these sections to freeze quickly and isolate from the liquid feed metal.
- Case B (500°C preheat, Natural Cool): Showed a dramatic reduction in predicted shrinkage in the thin and small sections. The slower, more controlled solidification allowed for longer feeding. Defects were largely confined to the problematic runner junctions and the thermal centers of the very thick sections.
- Case C (500°C preheat, Forced Cool): While faster cooling might be expected to refine grains, the simulation predicted a return of significant shrinkage in small sections. The accelerated solidification again shortened the feeding time, recreating the isolated hot spots seen in the low-preheat case. This indicates that for ZL205 alloy, rapid cooling alone does not improve internal soundness and can be detrimental.
| Predicted Defect Severity | ϕ3 mm / 3 mm plate | ϕ10 mm bar | ϕ20 mm bar | Runner Junction (Lower) |
|---|---|---|---|---|
| Case A: 200°C + Natural Cool | Severe shrinkage, Likely misrun | Severe centerline shrinkage | Moderate shrinkage at root | Major shrinkage cavity |
| Case B: 500°C + Natural Cool | Minor micro-porosity, Full fill predicted | Localized shrinkage spots | Very minor fiber-like shrinkage | Shrinkage cavity present |
| Case C: 500°C + Forced Cool | Substantial shrinkage | Significant shrinkage | Moderate shrinkage | Major shrinkage cavity |
Discussion and Experimental Validation
The simulation findings point towards a critical process window for the successful investment casting of thin-walled ZL205 components. The primary controlled variable is the shell preheat temperature. A low preheat temperature (200°C) causes premature solidification of thin sections, leading to incomplete filling (misruns) and severe internal shrinkage due to isolated, unfed hot spots. The thermal gradient, $G$, is high, but the feeding time is insufficient. The relationship between solidification time, $t_f$, and thickness, $d$, can be approximated by Chvorinov’s rule:
$$ t_f = B \left( \frac{V}{A} \right)^n = B \cdot d^n $$
where $B$ is the mold constant, $V$ is volume, $A$ is surface area, and for a plate, the modulus $V/A \approx d/2$. For thin sections, $t_f$ is very short unless $B$ is increased.
Preheating the shell to 500°C drastically increases the mold constant $B$. This extends the solidification time $t_f$ for all sections, but its effect is most crucial for thin walls. It allows the thin section to remain feedable from the larger, still-liquid reservoirs (runners and thick sections) for a longer duration. The temperature gradient $G$ is reduced, promoting more directional solidification towards the feeders and minimizing isolated liquid pockets. The simulation predicted that this condition enables the complete filling of a 3 mm thin wall, which represents the approximate limiting castability for ZL205 alloy under gravity investment casting process with natural cooling.
To validate these simulations, physical casting trials were conducted. Shells were preheated to 500°C, and ZL205 alloy was poured at 725°C, followed by natural cooling. The results strongly corroborated the numerical predictions (see Table 4).
| Test Sample Geometry | Experimental Result (500°C Preheat) | Correlation with Simulation (Case B) |
|---|---|---|
| ϕ3 mm Round Bar | Failed to fill (Misrun) | Predicted fill but with severe defects; actual fill limit reached. |
| 3 mm Thick Plate | Filled completely, but with visible surface shrinkage/slag | Predicted full fill with minor micro-porosity. |
| 6 mm Thick Plate | Filled completely, good internal quality | Predicted sound casting. |
| ϕ10 mm Round Bar | Filled, but with significant shrinkage porosity | Predicted localized shrinkage spots. |
| ϕ20 mm Round Bar | Filled, minor fibrous shrinkage at root | Predicted very minor shrinkage. |
| Lower Runner Junction | Visible shrinkage cavity present | Predicted major shrinkage cavity. |
The agreement between the experimental outcomes and the simulation results from the model employing the inversely-calculated IHTCs is remarkably good. It confirms that:
- The inverse method successfully captured the real heat transfer conditions of the ZL205-shell interface.
- The high preheat temperature (500°C) is essential for achieving the complete filling of thin-walled features (down to ~3 mm) in ZL205 alloy.
- The defect locations, particularly the problematic runner junctions, were accurately forecast, providing a clear target for future浇注系统 design optimization (e.g., adding filters, modifying runner geometry to reduce impact).
- Forced cooling, while potentially desirable for grain refinement, reintroduces feeding-related defects and should be avoided unless combined with other mitigation techniques like high-pressure feeding.
Conclusion
This study demonstrates a robust methodology for simulating and optimizing the investment casting process for challenging alloys like ZL205. The key to achieving predictive accuracy lay in the inverse determination of the interfacial heat transfer coefficient through in-situ temperature measurement, which effectively calibrated the finite element model to physical reality. Using this validated model, we systematically analyzed the effects of shell preheat temperature and cooling rate on the filling behavior, solidification progression, and defect formation in multi-scale test castings.
The primary findings are:
- The interfacial heat transfer between ZL205 alloy and a ceramic shell is spatially variable. The inversely solved IHTC values (542-911 W/m²·K) provided a critical and accurate boundary condition for meaningful simulation.
- For a bottom-gated system, thin-walled and small-diameter sections are susceptible to unfavorable flow dynamics (counter-current flow) and are the last to fill, increasing defect risk.
- Shell preheat temperature is the dominant factor controlling the castability of ZL205. A high preheat temperature of 500°C is necessary to sufficiently delay the solidification of thin sections (≥3 mm), enabling adequate liquid feeding from the浇注系统 and preventing catastrophic shrinkage and misruns. Under these conditions, the limiting wall thickness for complete filling in gravity pouring is approximately 3 mm.
- Rapid cooling (forced convection) negates the benefits of shell preheating by shortening the feeding time, leading to increased shrinkage porosity. Process optimization should therefore focus on thermal management to control solidification rate rather than accelerate it.
- The strong correlation between simulated predictions and experimental validation confirms the reliability of the approach. The identified defect-prone areas, especially at flow impact zones, provide clear guidance for浇注系统 redesign.
In summary, the integration of inverse heat transfer analysis with comprehensive process simulation forms a powerful tool for advancing the investment casting process of high-performance aluminum alloys. It enables a science-based approach to defect prevention and工艺 optimization, reducing the reliance on costly and time-consuming trial-and-error methods.