In the automotive industry, turbocharging technology is widely adopted to enhance engine power, reduce size, and control CO2 emissions. The turbocharger turbine, a core component, requires lightweight and complex designs to minimize lag and improve efficiency. However, these intricate structures, such as large-curvature blades and significant cross-sectional variations between the shaft and blades, make the turbine prone to hot tearing defects during the lost wax investment casting process. Hot tearing occurs near the solidus temperature when the alloy’s strength and ductility are low, and internal stresses exceed the material’s limit, leading to crack formation. This study focuses on numerical simulation of the lost wax investment casting process for IN713C nickel-based superalloy turbines to predict hot tearing tendencies and analyze the effects of process parameters.
The lost wax investment casting process involves creating a ceramic shell around a wax pattern, which is melted out to form a mold cavity. Molten metal is then poured into the cavity, and upon solidification, the shell is broken away to reveal the cast part. This method is ideal for complex geometries like turbine blades but poses challenges in controlling thermal stresses. We utilized ProCAST software to simulate the process, employing a thermo-elastoplastic model for stress analysis. The model accounts for elastic, plastic, and thermal strain components, with the total strain increment expressed as:
$$\{ d\varepsilon \} = \{ d\varepsilon_e \} + \{ d\varepsilon_p \} + \{ d\varepsilon_T \}$$
where $\{ d\varepsilon_e \}$ is the elastic strain increment, $\{ d\varepsilon_p \}$ is the plastic strain increment, and $\{ d\varepsilon_T \}$ is the thermal strain increment. The stress increment in the thermo-elastoplastic model is given by:
$$\{ d\sigma \} = [ D_{ep} ] ( \{ d\varepsilon \} – \{ d\varepsilon_p \} – \{ d\varepsilon_T \} )$$
Here, $[ D_{ep} ]$ is the elastoplastic modulus matrix. The linear hardening relationship for the material is defined as:
$$\sigma = \sigma_0 + H \varepsilon_{pl}$$
where $\sigma_0$ is the yield stress, $H$ is the plastic modulus, and $\varepsilon_{pl}$ is the total plastic strain. To assess hot tearing, the Hot Tearing Index (HTI) is calculated based on accumulated strain during solidification:
$$HTI = \int_{t_{coh}}^{t_s} \sqrt{\frac{2}{3} \dot{\varepsilon}_p : \dot{\varepsilon}_p} d\tau$$
In this equation, $t_{coh}$ is the time when grains begin to cohere, $t_s$ is the solidus time, and $\dot{\varepsilon}_p$ is the plastic strain rate. This model helps identify regions susceptible to hot tearing by integrating strain over the vulnerable temperature range (90–99% solid fraction).
The turbine geometry consists of a central hub with ten blades, each approximately 0.7 mm thick, connected to a shaft about 28 mm thick. The overall height is 60 mm, with a base diameter of 86 mm. The gating system includes a sprue, pouring cup, and three ingates, arranged at a 130-degree angle to the turbine axis to facilitate filling. IN713C alloy, known for its high-temperature strength, oxidation resistance, and fatigue performance, was used. Its composition includes elements like Ni, Cr, Al, and Mo, with liquidus and solidus temperatures of 1,345°C and 1,196°C, respectively. Thermo-physical properties, such as thermal conductivity and specific heat, were derived from Scheil model calculations, as summarized in Table 1.
| Property | Value |
|---|---|
| Liquidus Temperature | 1,345°C |
| Solidus Temperature | 1,196°C |
| Thermal Conductivity | Varies with temperature (e.g., 25 W/m·K at 1,200°C) |
| Specific Heat | 500 J/kg·K (average) |
| Young’s Modulus | 200 GPa (at room temperature) |
| Poisson’s Ratio | 0.3 |
Simulations were conducted under varying process parameters: pouring temperatures of 1,400°C, 1,450°C, 1,500°C, and 1,550°C, and mold shell preheat temperatures of 800°C, 850°C, and 900°C. The alloy was modeled as elastoplastic, while the shell was treated as rigid, with a heat transfer coefficient of 900 W/(m²·K) at the interface. The filling process, completed in about 1 second due to the short flow path and large gate cross-sections, showed rapid mold filling. Temperature field analysis revealed higher temperatures at the hub compared to the blade tips, with solidification progressing from the blades inward. This differential cooling induced significant thermal stresses, particularly at the blade edges where thickness variations and curvature exacerbated stress concentrations.
Stress distribution and HTI analysis indicated that hot tearing was most likely at the blade margins, where stresses peaked during solidification. For instance, at a pouring temperature of 1,450°C and shell temperature of 850°C, the maximum stress reached 30 MPa at the blade edges, with an HTI of approximately 8.5 × 10⁻⁴. Experimental validation confirmed cracks at these locations, aligning with simulation predictions. The vulnerable period, when the alloy is between 90% and 99% solid, was critical for crack initiation due to the presence of low-strength liquid films.
To quantify the impact of process parameters, we analyzed a specific point (Point A) on the blade edge. As shown in Table 2, varying pouring and shell temperatures influenced thermal stress and HTI. Higher shell temperatures generally reduced thermal stress and HTI, while pouring temperature effects were non-linear.
| Pouring Temperature (°C) | Shell Temperature (°C) | Thermal Stress (MPa) | HTI (×10⁻⁴) |
|---|---|---|---|
| 1,400 | 800 | 47 | 6.2 |
| 1,450 | 800 | 35 | 8.5 |
| 1,500 | 800 | 25 | 7.1 |
| 1,550 | 800 | 24 | 6.3 |
| 1,500 | 850 | 22 | 6.8 |
| 1,500 | 900 | 20 | 6.1 |
Increasing the shell temperature from 800°C to 900°C at a constant pouring temperature of 1,500°C decreased thermal stress from 25 MPa to 20 MPa and HTI from 7.1 × 10⁻⁴ to 6.1 × 10⁻⁴. This reduction is attributed to slower cooling rates, which minimize thermal gradients and stress accumulation. In contrast, raising the pouring temperature from 1,400°C to 1,450°C initially increased HTI due to prolonged vulnerability time, but further increases to 1,550°C reduced HTI as lower thermal stresses dominated. The relationship can be modeled using a quadratic equation for HTI as a function of pouring temperature (T_pour):
$$HTI = a T_{pour}^2 + b T_{pour} + c$$
where $a$, $b$, and $c$ are coefficients derived from regression analysis. For instance, at a shell temperature of 800°C, HTI peaks around 1,450°C. This non-linearity highlights the interplay between stress and solidification time in the lost wax investment casting process.
Optimization studies suggest that a pouring temperature of 1,500°C and shell temperature of 900°C minimize hot tearing risks while avoiding defects like shrinkage porosity. Higher temperatures reduce thermal stresses but must be balanced against potential microstructure coarsening. The lost wax investment casting method, with its ability to produce precise geometries, benefits greatly from such simulations to tailor process parameters. Future work could explore additional factors like cooling rate control and alloy modifications to further enhance hot tearing resistance in complex castings.
In conclusion, numerical simulation of the lost wax investment casting process for IN713C turbines effectively predicts hot tearing tendencies. The thermo-elastoplastic model and HTI analysis provide insights into stress distributions and defect formation, enabling parameter optimization to improve casting quality and reliability in automotive applications.