Numerical Simulation and Analysis of Hot Tearing in a High-Performance Turbine Investment Casting Process

Introduction and Background

The investment casting process, often referred to as the lost-wax process, is the premier manufacturing route for producing complex, near-net-shape components from high-performance alloys, particularly for aerospace and automotive applications. Its capability to replicate fine details and produce excellent surface finish makes it indispensable for parts like gas turbine blades and turbocharger wheels. The process involves creating a wax pattern, building a ceramic shell around it, melting out the wax, and then pouring molten metal into the resulting cavity.

For turbocharger applications, the IN713C alloy is a preferred material due to its excellent balance of high-temperature strength, oxidation resistance, and fatigue life. Its microstructure in the as-cast condition primarily consists of a γ nickel matrix strengthened by a high volume fraction of coherent γ’ precipitates (Ni₃(Al, Ti)), along with minor carbides and borides. Despite its favorable properties, the investment casting process of IN713C is fraught with the risk of hot tearing. Hot tearing is a defect that occurs in the late stages of solidification, when the coherent solid network has limited strength and ductility, and is subjected to tensile stresses induced by constrained thermal contraction. The large difference in section thickness between the thin blade sections (~0.7 mm) and the thick hub (~28 mm) in a turbine creates severe thermal gradients, leading to differential cooling rates and contraction, which in turn generate high levels of residual stress. The regions of stress concentration, often at the blade tips or roots where geometry changes abruptly, are the most likely sites for hot crack initiation. Therefore, a predictive understanding of stress development and hot tearing risk is crucial for designing a robust investment casting process. Numerical simulation has emerged as a powerful tool for this purpose, allowing for virtual experimentation and optimization before costly physical trials.

Theoretical Foundation for Hot Tearing and Numerical Modeling

The numerical prediction of hot tearing requires a coupled analysis of heat transfer, fluid flow during filling, solidification kinetics, and thermo-mechanical stress development. For this study, the stress calculation is based on a thermal elastic-plastic constitutive model. This model realistically represents material behavior during cooling: it behaves elastically until the yield point is reached, after which plastic deformation occurs. The fundamental relationship between stress and strain in the elastic regime is governed by Hooke’s Law:

$$ \{ d\sigma \} = [D^e] \{ d\varepsilon^e \} $$

where $\{ d\sigma \}$ is the incremental stress vector, $[D^e]$ is the elastic stiffness matrix, and $\{ d\varepsilon^e \}$ is the incremental elastic strain vector.

In the more comprehensive thermal elastic-plastic model, the total strain increment $\{ d\varepsilon \}$ is decomposed into its elastic, plastic, and thermal components:

$$ \{ d\varepsilon \} = \{ d\varepsilon^e \} + \{ d\varepsilon^p \} + \{ d\varepsilon^T \} $$

The stress-strain relationship then becomes:

$$ \{ d\sigma \} = [D^{ep}] \left( \{ d\varepsilon \} – \{ d\varepsilon^p \} – \{ d\varepsilon^T \} \right) $$

where $[D^{ep}]$ is the elastic-plastic stiffness matrix. For many metallic alloys, a linear hardening rule is often assumed post-yield:

$$ \sigma = \sigma_0 + H \varepsilon_{pl} $$

where $\sigma_0$ is the initial yield stress, $H$ is the plastic modulus, and $\varepsilon_{pl}$ is the equivalent plastic strain.

To quantitatively assess the risk of hot tearing, a Hot Tearing Indicator (HTI) is employed. This model is based on the accumulated plastic strain rate during the vulnerable “mushy zone” period of solidification, typically when the material has a solid fraction ($f_s$) between approximately 0.9 and 1.0. During this interval, liquid films remain between dendritic grains, offering minimal strength. The HTI is calculated as:

$$ HTI = \int_{t_{coh}}^{t_s} \sqrt{\frac{2}{3} \dot{\boldsymbol{\varepsilon}}^p : \dot{\boldsymbol{\varepsilon}}^p } \, d\tau $$

where $\dot{\boldsymbol{\varepsilon}}^p$ is the plastic strain rate tensor, $t_{coh}$ is the time at which a coherent solid skeleton forms (often associated with $f_s \approx 0.9$), and $t_s$ is the time at which the local temperature reaches the solidus. A higher HTI value indicates a greater susceptibility to hot tearing at that location.

Simulation Setup and Process Parameters

This investigation focuses on a specific automotive turbocharger turbine geometry. The component features ten highly curved blades emanating from a central hub. The overall height is approximately 60 mm, with a maximum base diameter of about 86 mm. A cluster molding approach was simulated, with a gating system comprising one central down-sprue, a pour cup/sprue base, and three ingates, each feeding a single turbine casting. The turbine axis was oriented at 130° relative to the down-sprue centerline to promote smooth filling.

The core of the simulation involves defining accurate material properties for both the IN713C alloy and the ceramic shell. The thermophysical properties of IN713C, including enthalpy, solid fraction vs. temperature, thermal conductivity, and specific heat, were calculated using the Scheil-Gulliver model within the simulation software’s database, based on the nominal composition. Key solidification characteristics are listed below:

The alloy was modeled using a temperature-dependent elastic-plastic material model. The ceramic shell was treated as a rigid body. The interfacial heat transfer coefficient (IHTC) between the metal and the shell was set to 900 W/(m²·K), a typical value for the investment casting process. A full-factorial simulation matrix was designed to study the effects of process parameters:

Results and Analysis of the Investment Casting Process Simulation

Filling and Solidification Sequence

The simulation of the filling stage for the baseline case ($T_{pour}$=1450°C, $T_{mold}$=850°C) confirmed a rapid and complete fill, taking approximately 1 second. This is attributed to the short flow length and generous cross-sectional area of the gating system. Analysis of the temperature field during solidification revealed a distinct pattern. The thin blade sections cooled and began to solidify significantly faster than the massive hub. The solidification front progressed from the blade tips and edges inwards towards the hub center. This created a substantial temperature gradient and a large time gap between the solidification of the blades and the hub, setting the stage for the development of significant thermal stresses.

Stress Distribution and Hot Tearing Prediction

The thermo-mechanical simulation clearly identified regions of high stress concentration. As anticipated, the highest tensile stresses were located at the outer edges (tips) of the turbine blades. These areas experience the most severe constraint: they solidify first and attempt to contract, but are mechanically hindered by the hotter, still-molten or mushy material in the hub and blade roots. The calculated Hot Tearing Indicator (HTI) map showed a perfect correlation with the stress map, with peak HTI values precisely at the blade tips. This simulation prediction was validated against an actual casting from a similar investment casting process, where visible hot cracks were found at the blade tip locations, confirming the accuracy of the model.

Effect of Pouring Temperature

A critical location at the tip of a representative blade (Point A) was selected for detailed parametric analysis. Holding the mold temperature constant at 800°C, the effect of varying the pouring temperature was examined. The results revealed a non-monotonic relationship between pouring temperature and hot tearing risk.

The underlying mechanism is a competition between two factors: thermal stress and the duration of the vulnerable solidification period. At low pouring temperatures (1400°C), the metal enters the mold with less superheat, causing rapid solidification. This leads to high thermal stress but a very short time window ($t_s – t_{coh}$) for plastic strain accumulation. Consequently, the HTI is moderately high. As the pouring temperature increases to 1450°C, the thermal stress decreases due to a more moderate cooling rate, but the vulnerable period lengthens considerably. The extended time for strain accumulation in the weak, mushy state dominates, resulting in the maximum HTI. At even higher pouring temperatures (1500°C and 1550°C), the continued reduction in thermal stress becomes the dominant factor, outweighing the effect of the longer vulnerable period, leading to a decrease in HTI.

Effect of Mold Preheat Temperature

Next, the pouring temperature was fixed at 1500°C while the mold preheat temperature was varied. The influence of this parameter was more straightforward.

A higher mold temperature reduces the thermal gradient between the metal and the mold, significantly slowing down the cooling rate. This directly leads to a reduction in thermally induced contraction stresses. Although the slower cooling also prolongs the vulnerable solidification period, the stress reduction effect is so pronounced that it consistently lowers the HTI. There is no competing peak as seen with pouring temperature; a hotter mold uniformly decreases the hot tearing risk for this geometry.

Synthesis of Process Parameter Effects

The interaction between pouring temperature and mold temperature is vital for process design. The following summary can be formulated:

1. Thermal Stress Reduction: Both increasing $T_{pour}$ and $T_{mold}$ act to reduce the peak thermal stress. The effect is most potent when one parameter is low; raising the other has a significant impact. When both are already high, further increases yield diminishing returns.

2. Hot Tearing Risk (HTI): The hot tearing tendency shows a complex response. $T_{mold}$ has a consistently beneficial effect. $T_{pour}$, however, has an optimum value that minimizes HTI for a given $T_{mold}$. For the conditions studied, a pouring temperature that is too low or too high relative to the mold temperature can be detrimental, with a risk peak observed around 1450°C for cooler molds.

The most effective strategy to minimize hot tearing at the critical blade tips in this investment casting process is to employ a combination of high pouring and high mold temperatures. Based on the simulation matrix, the optimal parameters identified are a pouring temperature of 1500°C and a mold preheat temperature of 900°C. It is noteworthy that at the highest pouring temperature (1550°C), the HTI becomes relatively insensitive to the mold temperature, offering some process flexibility, though excessively high pouring temperatures may promote other defects like coarse grain structure.

Discussion and Practical Implications

The successful correlation between the simulated HTI maps and the actual failure locations in physical castings underscores the reliability of the coupled thermo-mechanical simulation approach for the investment casting process. This virtual tool allows foundry engineers to pre-emptively identify critical defect-prone areas without the need for multiple expensive and time-consuming trial runs. The analysis elucidates the physics behind hot tearing in thin-walled, high-contrast sections: it is not merely high stress, but the interplay of stress and the time-dependent mechanical integrity of the semi-solid material.

The finding that both very high and very low pouring temperatures can mitigate hot tearing, with a dangerous zone in between, is particularly crucial for process design. It moves beyond the conventional wisdom of simply “increasing superheat to reduce stress” and highlights the critical role of the solidification time window. In practice, while a very high pouring temperature (e.g., 1550°C) may reduce hot tearing risk, it must be balanced against other considerations such as increased metal oxidation, reaction with the mold, and energy consumption. Therefore, the recommended optimum of 1500°C/900°C represents a balanced solution.

Furthermore, the strong beneficial effect of a high mold preheat temperature is clear. This reduces thermal shock, minimizes gradients, and promotes more directional solidification, all of which contribute to lower stresses. In an industrial investment casting process, maintaining a consistent and adequately high shell preheat temperature is a key controllable variable for quality assurance.

This study focused on hot tearing. A complete process optimization would also integrate the results with simulations of shrinkage porosity and microstructure prediction to find a global optimum that balances all quality criteria. Future work could also involve validating the simulated stress levels with in-situ measurements or neutron diffraction studies on actual castings.

Conclusion

This comprehensive numerical investigation of the investment casting process for an IN713C turbocharger turbine has yielded significant insights into the genesis and control of hot tearing defects. The primary conclusions are as follows:

1. The thin blade tips are the most vulnerable locations for hot tearing due to extreme thermal gradients and constrained contraction resulting from the stark difference in cooling rates between the blades and the hub.
2. The Hot Tearing Indicator (HTI), derived from accumulated plastic strain in the mushy zone, provides an accurate predictive measure for defect localization, as confirmed by real-world casting results.
3. The influence of pouring temperature on hot tearing risk is non-linear. An intermediate risk peak exists because lower temperatures induce high stress, while higher temperatures excessively prolong the vulnerable solidification period. The lowest risk is achieved at adequately high pouring temperatures.
4. Increasing the mold preheat temperature uniformly reduces thermal stress and, consequently, the hot tearing tendency, demonstrating a consistently beneficial effect.
5. For the specific turbine geometry and alloy studied, an optimized investment casting process to minimize hot tearing is achieved with a pouring temperature of 1500°C and a mold preheat temperature of 900°C.

This work demonstrates the power of simulation-driven engineering in optimizing complex manufacturing processes like investment casting, enabling the production of higher-integrity, high-performance components with greater efficiency and reliability.