The relentless pursuit of performance and efficiency in aerospace propulsion systems has driven the development and adoption of advanced materials capable of withstanding extreme environments while reducing component weight. Among these, titanium aluminide (TiAl) alloys have emerged as a leading candidate for high-temperature structural applications, particularly within the hot sections of aero-engines. These intermetallic compounds offer a compelling combination of properties, including low density (approximately 3.8–4.0 g/cm³), high specific strength and stiffness, excellent creep resistance, and good oxidation resistance at elevated temperatures (typically up to 750–850°C). These attributes make them ideal for replacing heavier nickel-based superalloys in components such as low-pressure turbine blades, turbocharger wheels, and various structural assemblies within the engine’s hot gas path.
However, the very same ordered crystal structure that grants TiAl alloys their high-temperature strength also imparts significant challenges for manufacturing, particularly in near-net-shape forming processes. TiAl alloys exhibit inherently low room-temperature ductility and fracture toughness, high melting points, limited fluidity in the molten state, and a pronounced tendency for hot tearing and solidification cracking. These characteristics make conventional machining and forging operations difficult, expensive, and material-inefficient. Consequently, the investment casting process, also known as the lost-wax process, has become the primary manufacturing route for producing complex, thin-walled TiAl components. This process enables the creation of intricate geometries with excellent surface finish and dimensional accuracy in a single casting step, minimizing the need for subsequent machining.
Despite its advantages, the investment casting process of TiAl alloys is fraught with technical hurdles. The poor melt fluidity can lead to misruns and cold shuts, especially in thin sections. The substantial solidification shrinkage and thermal contraction, combined with the alloy’s low ductility, create high internal stresses that often manifest as casting cracks. Furthermore, the formation of shrinkage porosity and gas entrapment within the casting can severely compromise its mechanical integrity and fatigue life. These defects are particularly problematic for critical safety components like casings, diffusers, and nozzle guide vanes, which often feature complex ring-and-strut configurations.
This study focuses on the investment casting process optimization for a representative, challenging geometry: a double-ring thin-wall braced plate structure. This component, analogous to compressor casings or exhaust manifolds, consists of an inner ring and an outer ring connected by multiple radial, thin-walled struts (or plates). The combination of large planar surfaces, thin sections (1–3 mm), and abrupt changes in cross-section at the ring-strut junctions creates classic hotspots and presents a formidable challenge for achieving sound, crack-free castings. Traditional trial-and-error methods for gating and riser design are prohibitively costly and time-consuming for such components. Therefore, numerical simulation has become an indispensable tool for virtual prototyping and process optimization.
This research employs ProCAST, a commercial finite element method (FEM)-based software, to simulate and analyze the filling, solidification, and stress development during the investment casting process of this TiAl alloy structure. The primary objectives are threefold: first, to investigate the influence of different gating system designs (specifically, the location of bottom gates) on the melt filling pattern and the risk of filling-related defects; second, to compare the effectiveness of gravity pouring versus centrifugal casting in mitigating these defects and improving casting soundness; and third, to predict the distribution of shrinkage porosity and stress concentrations to assess the risk of hot tearing. The numerical findings are subsequently validated through actual casting trials. The insights gained aim to establish a systematic methodology for designing robust investment casting processes for complex TiAl alloy components.
Numerical Simulation Methodology and Process Design
The foundation of an accurate numerical simulation lies in the precise definition of the physical model, material properties, and boundary conditions. The geometry of the double-ring braced plate structure was modeled in three dimensions. To mitigate the high cracking risk associated with the original four-strut design—due to significant constrained thermal contraction—the design was modified to feature eight equally spaced struts, thereby reducing the unsupported span and associated stresses. Two distinct bottom-gated gating system concepts were designed for investigation, as illustrated schematically below. Both systems feature a central downsprue feeding a horizontal runner, from which eight ingates rise to feed the casting.
- Scheme 1 (Gates Under Struts): The ingates are positioned directly beneath the eight radial struts, connecting to the lower flanges of both the inner and outer rings.
- Scheme 2 (Gates Between Struts): The ingates are positioned midway between the struts, connecting to the lower flanges of the rings at points not directly aligned with the struts.
The 3D models of the casting and gating systems were imported into ProCAST for meshing. A fine tetrahedral mesh was generated, with particular refinement in the thin strut regions and at geometric transitions to ensure solution accuracy for thermal gradients and fluid flow. The critical thermophysical properties of the Ti-47Al-2Cr-2Nb (at.%) alloy and the yttria (Y₂O₃)-based ceramic shell used in the simulation are summarized in Table 1. Yttria shells are preferred for TiAl casting due to their excellent chemical inertness and resistance to metal-mold reaction.
| Material | Density, ρ (kg/m³) | Thermal Conductivity, k (W/m·K) | Specific Heat Capacity, Cp (J/kg·K) | Latent Heat, L (kJ/kg) | Solidus-Liquidus Range (°C) | Dynamic Viscosity, μ (Pa·s) | Interfacial Heat Transfer Coefficient, h (W/m²·K) |
|---|---|---|---|---|---|---|---|
| TiAl Alloy | 3872 | 15 – 28 | 600 – 800 | 400 | 1468 – 1523 | (4.2 – 5.4) × 10⁻³ | 1500 |
| Y₂O₃ Shell | 4200 | 2.1 – 2.4 | 700 – 1000 | — | — | — | — |
The simulation accounted for the transient phenomena of the investment casting process. The initial conditions were set with a superheated melt temperature of 1600°C and a preheated mold temperature of 800°C. Two casting environments were simulated:
- Gravity Casting: Simulating conventional pouring under Earth’s gravity (g = 9.81 m/s²).
- Centrifugal Casting: Simulating a casting process where the mold rotates at a constant speed (300 rpm) about a central axis, generating a centrifugal acceleration field. The acceleration at a radius \(r\) is given by \(a_c = \omega^2 r\), where \(\omega\) is the angular velocity (\(\omega = 2\pi N/60\), with N in rpm).
The filling process was modeled as a transient, non-isothermal, viscous flow. The governing equations for fluid flow and heat transfer during the investment casting process include the continuity, Navier-Stokes, and energy equations, adapted for the presence of a liquid-solid mushy zone. The Volume of Fluid (VOF) method was used to track the melt front. For defect prediction, the Niyama criterion \(G/\sqrt{\dot{T}}\), where \(G\) is the thermal gradient and \(\dot{T}\) is the cooling rate, was employed to identify regions prone to shrinkage porosity. Stress analysis was performed using a thermo-elasto-plastic model to compute residual stresses and identify areas with a high hot tearing propensity, often evaluated using a stress-based or strain rate-based index during the vulnerable solidification temperature range.
Simulation Results: Gating System and Casting Method Analysis
Melt Flow and Filling Behavior
The simulation of the filling stage provides critical insights into the likelihood of surface defects like misruns and cold shuts. The behavior differs markedly between gravity and centrifugal processes.
In gravity casting, the melt fills the mold cavity in a bottom-up fashion. For both gating schemes, the melt first fills the runner and ingates, then begins to fill the lower flanges of the rings. Due to the smaller volume and shorter flow path, the inner ring flange fills faster than the outer ring flange. Subsequently, melt flows from the inner ring into the struts and towards the outer ring, and concurrently from the outer ring flange into the struts towards the inner ring. The final areas to fill are typically the upper edges of the struts and the top of the outer ring.
- Scheme 1 (Gates Under Struts): The melt front in the outer ring is uneven. The melt tends to flow preferentially upward at the strut locations (where gates are present), leaving the mid-span regions between struts lagging. This creates a significant risk of a “missed join” or misrun at the top of the outer ring between two struts, as the converging melt streams may solidify before meeting.
- Scheme 2 (Gates Between Struts): The filling of the outer ring is more uniform because the gates are at the mid-span. The melt rises more evenly around the circumference, converging at the strut locations. This configuration significantly reduces the risk of a misrun at the top of the outer ring.
The flow behavior can be partially characterized by the Reynolds number (\(Re = \frac{\rho u L}{\mu}\)), which indicates flow regime. In thin sections, the characteristic length \(L\) is small, but the velocity \(u\) can be high, potentially leading to turbulent flow that entraps air. The modified Froude number is also relevant for free surface flows in gating systems.
In centrifugal casting, the driving force is the centrifugal pressure head, which is much greater than gravitational pressure, dramatically improving melt fluidity. The filling sequence is “outside-in.” Melt is forced under pressure through the runner to the farthest points of the mold (the outer ring gates) first. The outer ring fills rapidly from its base. The melt then progresses inward through the struts to fill the inner ring. The last areas to fill are the inner ring flange and the top of the inner ring.
- Both Schemes: The centrifugal force ensures complete filling for both gating designs, eliminating the misrun risk predicted in gravity casting for Scheme 1. The pressure forces the melt into all sections of the mold. However, in Scheme 1, the confluence of melt streams from two adjacent gates meeting at the mid-span of the outer ring can still trap air, whereas in Scheme 2, this confluence occurs at the strut location, allowing the air to be pushed through the strut and vented toward the inner ring.
The pressure \(P\) at any point in the rotating mold at a distance \(r\) from the axis is given by:
$$ P(r) = \frac{1}{2} \rho \omega^2 (r^2 – r_0^2) $$
where \(r_0\) is the radius of the melt free surface in the pouring basin. This equation shows the significant pressure boost available for filling thin sections.
Defect Prediction: Shrinkage Porosity and Gas Entrapment
The solidification simulation and subsequent shrinkage analysis reveal the internal soundness of the castings. Table 2 summarizes the predicted defect distribution characteristics for the four simulated scenarios.
| Casting Method | Gating Scheme | Predicted Defect Distribution & Characteristics |
|---|---|---|
| Gravity Casting | 1 (Under Strut) |
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| 2 (Between Struts) |
|
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| Centrifugal Casting | 1 (Under Strut) |
|
| 2 (Between Struts) |
|
The formation of shrinkage porosity is governed by the inability to feed liquid metal to compensate for the volumetric contraction during solidification. The critical pressure drop required to feed through a mushy zone can be described by Darcy’s law and the continuity equation, leading to criteria like the Niyama criterion mentioned earlier. Regions with low thermal gradient \(G\) and high cooling rate \(\dot{T}\) are most susceptible.
Stress Analysis and Hot Tearing Propensity
Thermal stresses arise from non-uniform cooling and the constraint imposed by the rigid ceramic mold. TiAl’s low ductility makes it highly susceptible to hot tearing in the late stages of solidification when a continuous liquid film exists along grain boundaries while tensile stresses build up. The simulated stress distributions for the two schemes under gravity conditions showed distinct patterns:
- Scheme 1: High effective stress concentrations were predicted at the junction of the outer ring and the strut root, as well as at the root of the ingates connecting to the ring flanges. Stress values in these localized regions exceeded 330 MPa.
- Scheme 2: High stress concentrations were predicted at the mid-section of the struts and at the ingate roots, also exceeding 330 MPa.
The hot tearing indicator within ProCAST, which integrates factors like strain rate and fraction solid, highlighted the ingate attachment fillets and the strut-root junctions as the highest risk areas, though the specific location varied with gating. After simulated shell removal, the residual stress in the casting was notably lower for Scheme 1, as the aligned gate provided some stress relief during cooling compared to the more constrained Scheme 2.
The fundamental thermo-mechanical relationship governing stress development is given by the constitutive equation incorporating elastic, plastic, and thermal strain:
$$ \sigma = D_{ep} : (\epsilon_{total} – \epsilon_{th} – \epsilon_{pl}) $$
where \(\sigma\) is the stress tensor, \(D_{ep}\) is the elasto-plastic stiffness matrix, \(\epsilon_{total}\) is the total strain, \(\epsilon_{th}\) is the thermal strain (\(\alpha \Delta T\), with \(\alpha\) as CTE), and \(\epsilon_{pl}\) is the plastic strain. The high coefficient of thermal expansion (CTE) of TiAl and the mold constraint lead to large \(\epsilon_{th}\) and consequently high \(\sigma\).
Experimental Validation and Discussion
To validate the numerical findings, actual casting trials were conducted using the Ti-47Al-2Cr-2Nb alloy and the yttria shell system. The investment casting process parameters mirrored those used in the simulation. Scheme 1 (Gates Under Struts) was selected for physical trials using both gravity and centrifugal casting methods.
1. Casting Integrity and Filling:
- Gravity Casting Trial: The resultant casting exhibited a clear misrun defect on the outer ring, located precisely in the mid-span region between two struts, as predicted by the filling simulation for Scheme 1. The size and location matched the simulation forecast.
- Centrifugal Casting Trial: The casting produced was fully formed, with no visible misruns or cold shuts, confirming the simulation prediction that centrifugal force ensures complete filling regardless of the gating scheme’s inherent filling risks under gravity.
2. Internal Defect Analysis:
Non-destructive evaluation (X-ray radiography) was performed on the castings to inspect internal porosity.
- Gravity Casting: The radiograph revealed a high population of gas porosity (small, spherical voids) throughout the casting, along with pronounced shrinkage cavities at the predicted locations: the strut-outer ring junctions and the ingate-inner ring junctions. The presence of extensive gas porosity, not fully captured by the shrinkage-only simulation, indicates significant air entrainment during the turbulent gravity pour—a common issue in TiAl investment casting process due to the high melt viscosity and density.
- Centrifugal Casting: The radiograph showed a dramatic improvement. Gas porosity was nearly absent due to the pressurized filling forcing out entrapped air. The shrinkage cavities at the hotspots were still present but were significantly smaller in size compared to the gravity casting, aligning perfectly with the simulation’s comparative prediction.
Discussion:
The excellent correlation between the ProCAST simulations and the experimental results validates the model’s predictive capability for the TiAl investment casting process. Key insights include:
- Gating Design is Crucial for Gravity Casting: For gravity-poured TiAl thin-wall structures, gate placement must prioritize uniform filling to avoid misruns. Scheme 2 is superior to Scheme 1 in this regard. However, Scheme 2 exacerbates shrinkage at the strut root, a critical stress area, creating a trade-off.
- Centrifugal Casting is Overwhelmingly Beneficial: It solves the primary filling problems and drastically reduces both gas entrapment and shrinkage porosity. The centrifugal pressure head \( \left( \frac{1}{2} \rho \omega^2 r^2 \right) \) provides a powerful feeding force throughout solidification, compensating for shrinkage more effectively than gravity.
- Defect Location Consistency: The simulation accurately identified the persistent thermal hotspots (gate junctions, strut roots) as the last areas to solidify and the most prone to macro-shrinkage, regardless of the process variant. This information is vital for targeted process improvement, such as local chilling or strategic padding.
- Process Optimization Strategy: For the highest quality, centrifugal casting should be the preferred method. Within centrifugal casting, Scheme 1 appears to offer a better compromise, as it provides direct feeding to the high-stress strut root region, leading to smaller defects there compared to Scheme 2, while still achieving perfect fill.
The governing equation for fluid flow under centrifugal conditions incorporates the centrifugal force term:
$$ \rho \frac{D\vec{u}}{Dt} = -\nabla p + \mu \nabla^2 \vec{u} + \rho \vec{g} + \rho \omega^2 \vec{r} $$
where \(\rho \omega^2 \vec{r}\) is the centrifugal body force per unit volume. This term dominates over \(\rho \vec{g}\), explaining the superior filling and feeding.
Conclusion and Outlook
This integrated numerical and experimental study on the investment casting process of a complex TiAl alloy double-ring structure provides definitive guidelines for process design. The ProCAST software proved to be an effective tool for predicting critical outcomes, including filling completeness, shrinkage defect location and severity, and stress concentration zones.
The primary conclusions are:
- The filling pattern and risk of surface defects like misruns are highly sensitive to gating design in gravity casting. Gates placed between struts (Scheme 2) promote more uniform filling of ring sections compared to gates placed directly under struts (Scheme 1).
- Centrifugal casting fundamentally overcomes the filling limitations of gravity casting for TiAl alloys, ensuring complete mold filling for both gating schemes studied, thereby validating its necessity for reliable production of such thin-wall components.
- Shrinkage porosity is inevitable at geometric hotspots (strut roots, gate attachments), but its magnitude is significantly reduced by centrifugal casting. The simulation accurately predicted these hotspot locations and the relative improvement offered by centrifugal force.
- There is a trade-off in gating design concerning defect distribution: gates between struts improve ring soundness but worsen strut-root shrinkage, and vice versa. For centrifugal casting, aligning gates with struts (Scheme 1) offers a more balanced defect profile by providing better feeding to the critical, high-stress strut-root junction.
- The experimental trials confirmed the simulation predictions for filling behavior and the relative size/location of shrinkage defects. They also highlighted the additional benefit of centrifugal casting in drastically reducing gas porosity, an advantage not fully quantified by the shrinkage-only simulation model.
For future work, the investment casting process optimization can be taken further by exploring hybrid gating systems or applying localized cooling techniques to the identified hotspots. Furthermore, integrating microstructural prediction models (e.g., CAFE) with the current thermo-fluid-stress analysis would enable the prediction of mechanical properties like tensile strength and fatigue life directly from the process parameters, paving the way for full digital qualification of safety-critical TiAl cast components.
The successful application of this methodology demonstrates that a simulation-driven approach is essential for mastering the demanding investment casting process of advanced intermetallic alloys like TiAl, reducing development costs, and ensuring the reliability of next-generation aerospace components.