In the advancement of domestic aero-engine manufacturing technology and to meet strategic national development demands, the technical requirements for high-temperature alloy components in aviation are increasingly stringent. Currently, such components are trending towards complex, thin-walled, and precision-oriented structures to enhance overall performance, achieve structural weight reduction, and ensure high reliability. As a critical hot-section component in aero-engines, nickel-based superalloy casing castings often feature intricate geometries, including multi-layered structures or crisscrossing ribs and bosses, posing significant manufacturing challenges. Among various techniques, lost wax casting, also known as investment casting, is predominantly employed in industrial production due to its ability to produce castings with high dimensional accuracy, low surface roughness, and near-net-shape capabilities. Although the lost wax casting process for nickel-based superalloy casings has matured, designing gating systems remains cumbersome, and internal defects such as shrinkage porosity, shrinkage cavities, and slag inclusion are inevitable. In recent years, numerical simulation technologies for investment casting processes have rapidly developed, with commercial software like ProCAST widely applied to streamline process design, validation, and reduce costs and lead times. This study integrates numerical simulation with experimental investigation to predict and analyze defects in the lost wax casting of K4169 superalloy complex thin-walled parts, providing technical insights for high-efficiency, high-quality production.
The K4169 superalloy, a nickel-based alloy, exhibits excellent comprehensive properties at temperatures up to 650°C, meeting requirements for easy filling, repairability, and high load-bearing capacity, making it suitable for integral cast casings and related components in various aero-engines. However, research on defect prediction and comparative studies for K4169 complex thin-walled castings remains limited, necessitating ongoing experimentation and refinement of casting processes. In our work, we employ ProCAST finite element software to simulate the filling and solidification processes during the lost wax casting of a typical K4169 complex thin-walled casting. We analyze temperature fields, predict defect formation, and subsequently produce castings using identical process parameters. The as-cast and heat-treated samples are examined for shrinkage levels, microstructure, and tensile mechanical properties, aiming to establish correlations between process parameters, defect distribution, and performance.
Our numerical simulation begins with the three-dimensional modeling of the casting and gating system using UG software. The casting is a representative complex thin-walled structure with a height of 150 mm, maximum outer diameter of 246 mm, minimum outer diameter of 125 mm, and typical wall thicknesses ranging from 1.5 to 3.5 mm in thin-walled regions. It features internal multi-layered extensions from outer thin walls, numerous cross-sectional abrupt changes, external grooves composed of thin walls, and solid bosses. The model is imported into ProCAST’s Visual-Mesh module for meshing, balancing computational accuracy and efficiency. The gating system is meshed with an element length of 3 mm, while the casting body is refined to 1.2 mm. The ceramic mold shell, with a thickness of 10 mm, is also meshed accordingly. The final mesh comprises 596,822 surface elements and 3,965,256 volume elements. The material for the casting is K4169 superalloy, and the mold shell is made of a mullite-fused silica mixture, with thermophysical parameters sourced from the ProCAST database. The interfacial heat transfer coefficient (IHTC) between the casting and mold shell is defined as temperature-dependent: 1500 W·m-2·K-1 above the liquidus temperature, 400 W·m-2·K-1 below the solidus temperature, and linearly interpolated between. The convective heat transfer coefficient between the mold shell and environment is set to 20 W·m-2·K-1, with an emissivity of 0.8 and ambient temperature of 20°C. Initial process parameters, based on empirical knowledge, include a pouring temperature of 1530°C, mold shell preheat temperature of 1000°C, and pouring time of 5 s.
The governing equations for the simulation involve fluid flow, heat transfer, and solidification. The Navier-Stokes equations describe the fluid flow during filling:
$$
\rho \left( \frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \rho \mathbf{g}
$$
where $\rho$ is density, $\mathbf{v}$ is velocity, $t$ is time, $p$ is pressure, $\mu$ is dynamic viscosity, and $\mathbf{g}$ is gravitational acceleration. The energy equation accounts for heat transfer:
$$
\rho c_p \frac{\partial T}{\partial t} + \rho c_p \mathbf{v} \cdot \nabla T = \nabla \cdot (k \nabla T) + \dot{Q}
$$
where $c_p$ is specific heat capacity, $T$ is temperature, $k$ is thermal conductivity, and $\dot{Q}$ is a source term representing latent heat release during solidification. The latent heat is modeled using the enthalpy method:
$$
H = \int c_p \, dT + f_L L
$$
where $H$ is enthalpy, $f_L$ is liquid fraction, and $L$ is latent heat of fusion. The solidification kinetics are tracked via the volume fraction of solid, with criteria based on temperature thresholds. The Niyama criterion is often used to predict shrinkage porosity, expressed as:
$$
N_y = \frac{G}{\sqrt{\dot{T}}}
$$
where $G$ is temperature gradient and $\dot{T}$ is cooling rate. A lower Niyama value indicates a higher risk of shrinkage porosity.
Table 1 summarizes the chemical composition of the K4169 superalloy used in our study, which aligns with standard specifications.
| Element | Min | Max | Element | Min | Max |
|---|---|---|---|---|---|
| C | 0.02 | 0.08 | Co | – | ≤1.0 |
| Cr | 17.0 | 21.0 | B | – | ≤0.006 |
| Ni | 51.0 | 55.0 | Zr | – | ≤0.05 |
| Mo | 2.85 | 4.40 | Mn | – | ≤0.35 |
| Al | 0.4 | 0.7 | Si | – | ≤0.35 |
| Ti | 0.75 | 1.15 | P | – | ≤0.015 |
| Nb+Ta | 4.4 | 5.5 | S | – | ≤0.015 |
| Fe | Balance | Cu | – | ≤0.30 | |
| Trace elements: Sb ≤0.001, Sn ≤0.002, As ≤0.005, Bi ≤0.001, Pb ≤0.002. | |||||
Simulation results for the filling process reveal a stable metal flow. At 12.6% fill, the molten metal fills the bottom sprue and then distributes into the lower gating system. By 48.4% fill, the metal begins filling the casting, starting with the lower flange at front velocities of 0.28–0.37 m/s. The lower flange completes filling by 58.1% fill, followed by upward flow into inclined thin-walled regions. At 66.6% fill, the metal enters the middle annular runner, converging in the central part of the casting. By 86.5% fill, the metal steadily fills the vertical three-layer thin-walled regions. Finally, the thin-walled regions and upper gating system are fully filled, completing the process in 6.5 s. Throughout filling, the minimum metal temperature remains above the liquidus temperature, indicating good fluidity and appropriate setup of pouring and preheat temperatures. The temperature field evolution shows that the metal front temperature consistently exceeds 1500°C, ensuring no premature solidification during filling.
The solidification process is analyzed through thermal modulus distribution and solid fraction evolution. The thermal modulus, a measure of the casting’s ability to retain heat, is calculated as volume-to-surface area ratio. For our casting, the bottom regions have a thermal modulus of 0.25–0.35 cm, while thin-walled areas exhibit lower values of 0.09–0.19 cm due to smaller wall thicknesses and larger surface areas, leading to faster heat dissipation. Solidification initiates at the top thin walls and progresses downward and inward, following a directional pattern. At 28.1 s, the top two thin layers solidify first; feeders attached to outer thin walls provide some compensation. By 153.1 s, upper and lower thin-walled regions are largely solidified, while the central thick section cools gradually from outside inward. At 340.5 s, the innermost wall connected to the upper main runner solidifies last, marking the final solidification point in the casting body. This sequence aligns with the principle of directional solidification, which is crucial for minimizing defects in lost wax casting.
Defect prediction using ProCAST’s shrinkage module indicates that larger defects are primarily located in the main sprues and annular runners, with several significant defects predicted at mid-section transition regions where thickness variations occur. These areas act as thermal centers, isolated by earlier solidification of surrounding thin walls, leading to inadequate liquid metal feeding. The lower flange, though thick, is well-fed via attached runners, showing minimal macro-shrinkage. The top inner thick region, despite solidifying last, benefits from feeding through the upper runner and exhibits fewer defects. The Niyama criterion values are computed post-solidification; regions with values below a critical threshold (e.g., 1 °C1/2·s1/2/mm) are flagged as prone to shrinkage porosity. Our simulation maps these critical zones, which correspond to predicted defect locations.
To validate the simulation, we conduct actual lost wax casting experiments using the same parameters. The mold shell is fabricated via standard investment casting procedures: wax pattern assembly, slurry coating, stuccoing, drying, and dewaxing. The K4169 alloy is melted in a vacuum induction furnace and poured at 1530°C into a mold shell preheated to 1000°C. After cooling, the casting is removed, and the gating system is cut off. X-ray radiography inspection reveals no apparent cracks or major shrinkage cavities, with only minor shrinkage porosity in localized areas, consistent with simulation predictions. This confirms the accuracy of our numerical model and parameter selection for the lost wax casting process.
We sample eight characteristic locations (Samples 1–8) from the casting body for detailed analysis. Two sets of specimens are taken from each location: one in as-cast state and another after standard heat treatment. The heat treatment follows HB/Z 140-2004 specifications for K4169 alloy: 1095°C/2 h/air cooling + 955°C/1 h/air cooling + 720°C/8 h, furnace cooling at 56°C/h to 620°C/8 h/air cooling. Microstructural examination involves grinding, polishing, and etching with a solution of 4 g CuCl2, 50 mL HCl, 50 mL ethanol, and 45 mL deionized water. Optical microscopy (OM) and scanning electron microscopy (SEM) are used to observe microstructure, measure secondary dendrite arm spacing (SDAS), and quantify micro-shrinkage porosity volume fraction via image analysis software according to HB 20058-2011. SDAS is measured using the intercept method on at least five primary dendrite arms per sample, each containing over 20 secondary arms.
Table 2 presents the statistical results of micro-shrinkage porosity volume fraction for as-cast samples. The values range from 0.11% to 1.01%, with Samples 4 and 5 (transition and thick-walled regions) showing the highest levels, aligning with simulation predictions. Overall, the casting exhibits low shrinkage levels, affirming the effectiveness of the lost wax casting process parameters.
| Sample | Location Description | Average Micro-Shrinkage Volume Fraction (%) | Standard Deviation (%) |
|---|---|---|---|
| 1 | Lower flange region | 0.17 | 0.03 |
| 2 | Mid-thick section | 0.23 | 0.04 |
| 3 | Inclined thin wall | 0.36 | 0.05 |
| 4 | Transition region (thick to thin) | 0.86 | 0.07 |
| 5 | Central thick wall | 1.01 | 0.09 |
| 6 | Upper vertical thin wall | 0.11 | 0.02 |
| 7 | Top thin wall | 0.15 | 0.03 |
| 8 | Inner thick wall | 0.18 | 0.03 |
The as-cast microstructure of all samples reveals dendritic structures typical of nickel-based superalloys solidified via lost wax casting. However, SDAS varies significantly with location due to differences in cooling rates. SDAS is related to local solidification time (tf) and cooling rate (ε) by empirical relationships such as:
$$
\lambda_2 = k \cdot t_f^n \quad \text{or} \quad \lambda_2 = a \cdot \varepsilon^{-b}
$$
where $\lambda_2$ is SDAS, $k$, $n$, $a$, and $b$ are material constants. For K4169 alloy, approximate values are $n \approx 1/3$ and $b \approx 1/2$ based on literature. Table 3 summarizes SDAS measurements. Thin-walled regions (Samples 6 and 7) show the finest dendrites with SDAS as low as 18.4 μm, attributable to high cooling rates. In contrast, thick-walled regions (Samples 2 and 8) exhibit coarser dendrites with SDAS up to 38.8 μm due to slower cooling. This variation impacts mechanical properties, as finer dendrites often enhance strength and ductility.
| Sample | SDAS (μm) | Standard Deviation (μm) | Estimated Cooling Rate (°C/s) |
|---|---|---|---|
| 1 | 34.1 | 2.1 | ~5.2 |
| 2 | 38.7 | 2.5 | ~3.8 |
| 3 | 29.7 | 1.9 | ~7.1 |
| 4 | 31.5 | 2.0 | ~6.3 |
| 5 | 34.6 | 2.2 | ~5.0 |
| 6 | 21.4 | 1.4 | ~15.0 |
| 7 | 18.4 | 1.2 | ~20.0 |
| 8 | 38.8 | 2.5 | ~3.7 |
SEM analysis of as-cast samples reveals precipitates within interdendritic regions. Blocky or island-like Laves phases, along with needle-like δ phase and lens-shaped γ″ phase, are observed, surrounded by random blocky or script-like MC carbides. The Laves phase, rich in Nb and Mo, forms due to microsegregation during solidification and is detrimental to ductility. After standard heat treatment, microstructures show significant evolution: dendrites coarsen, primary arms thicken, and secondary arms become shorter and thicker, with dendritic morphology becoming less distinct within grains. The Laves phases largely dissolve into the matrix, while δ phase precipitation increases, particularly along grain boundaries and around MC carbides. The dissolution of Laves and homogenization of elements improve alloy integrity, but excessive δ phase can create γ″-depleted zones, acting as potential crack initiation sites.
Tensile tests are conducted on specimens from as-cast and heat-treated states, as well as from locations with high (Sample 5) and low (Sample 6) shrinkage levels. The tensile specimens are machined according to GB/T 228-2002, and tests are performed at room temperature using a Zwick Z250 machine, with three replicates per condition. Table 4 summarizes the tensile properties. As-cast K4169 alloy exhibits an average yield strength (YS) of 481.4 MPa, tensile strength (TS) of 673.3 MPa, and elongation (El) of 23.7%. The presence of brittle Laves phases and micro-shrinkage contributes to lower strength but relatively high ductility due to the dendritic structure’s capacity for energy absorption. After heat treatment, average YS increases to 659.7 MPa, TS to 785.0 MPa, but El decreases to 13.9%. This strengthening is attributed to the dissolution of Laves, precipitation of strengthening phases (γ″ and γ’), and homogenization, while reduced ductility stems from δ phase-induced embrittlement.
| Condition | Yield Strength (YS, MPa) | Tensile Strength (TS, MPa) | Elongation (El, %) | Sample Location (if specified) |
|---|---|---|---|---|
| As-cast (average of all samples) | 481.4 ± 15.2 | 673.3 ± 18.5 | 23.7 ± 2.1 | – |
| Heat-treated (average of all samples) | 659.7 ± 12.8 | 785.0 ± 14.3 | 13.9 ± 1.5 | – |
| As-cast, high shrinkage (Sample 5) | 459.8 ± 10.5 | 638.4 ± 12.7 | 22.5 ± 1.8 | Central thick wall |
| As-cast, low shrinkage (Sample 6) | 506.3 ± 11.2 | 711.2 ± 13.4 | 24.1 ± 2.0 | Upper vertical thin wall |
Comparing high vs. low shrinkage locations in the as-cast state, low-shrinkage samples show 10.2% higher YS and 11.4% higher TS, while El remains similar. This indicates that shrinkage porosity significantly affects strength metrics by reducing effective load-bearing area and inducing stress concentration, as described by the stress concentration factor (Kt):
$$
K_t = 1 + 2\sqrt{\frac{A_p}{A_0}}
$$
where $A_p$ is pore area and $A_0$ is nominal cross-sectional area. However, elongation is less sensitive to shrinkage level in this study, possibly due to the small difference in porosity volume (0.9% max) and the distribution characteristics; dispersed pores may have less impact on ductility than clustered ones.
Fracture surface analysis via SEM reveals that as-cast specimens exhibit ductile transgranular fracture with deep, equiaxed dimples and tearing ridges, indicative of good plasticity. Heat-treated specimens show shallower dimples and some flat facets, correlating with reduced ductility due to δ phase involvement. Pores from shrinkage are visible in some dimples, confirming their role as crack initiators.
Our study underscores the efficacy of numerical simulation in optimizing lost wax casting processes for complex thin-walled parts. The ProCAST software accurately predicted filling patterns, solidification sequences, and defect-prone zones, which were validated experimentally. The K4169 alloy casting produced under the simulated parameters exhibited satisfactory quality with low shrinkage levels. Microstructural analysis highlighted the influence of cooling rates on SDAS, which in turn affects mechanical properties. Heat treatment enhanced strength but compromised ductility, a trade-off that must be managed based on component requirements. Furthermore, shrinkage porosity, even at low volumes, notably degrades tensile strength, emphasizing the need for meticulous process control in lost wax casting.
Future work could explore advanced simulation techniques, such as coupling macro-scale simulations with micro-scale models (e.g., CAFE) to predict grain structure and phase formation during lost wax casting. Additionally, investigating the effects of varying pouring temperatures, mold preheat temperatures, and gating designs on defect formation for K4169 alloy could further refine the process. The integration of machine learning for rapid parameter optimization in lost wax casting also holds promise for industrial applications.
In conclusion, through combined numerical simulation and experimental investigation, we have demonstrated a robust methodology for defect prediction and quality assessment in the lost wax casting of K4169 superalloy complex thin-walled parts. The insights gained contribute to the advancement of precision casting technologies for aero-engine components, supporting the ongoing pursuit of lightweight, high-performance designs.