In the field of precision casting, investment casting plays a critical role in manufacturing complex components such as automotive turbine wheels. These components require high dimensional accuracy and superior mechanical properties, which are achieved through controlled solidification processes. However, hot tearing defects often arise due to thermal stresses during cooling, particularly in thin-walled sections like turbine blades. This study focuses on the numerical simulation of hot tearing in IN713C alloy turbine parts produced via investment casting. Using ProCAST software, we analyze the filling process, temperature distribution, stress evolution, and hot tearing tendency under various process parameters. The goal is to optimize the investment casting process to minimize defects and enhance the reliability of precision casting for automotive applications.
The IN713C nickel-based superalloy is widely used in high-temperature environments due to its excellent creep resistance, oxidation stability, and fatigue strength. Its composition primarily includes gamma prime (γ′) precipitates as strengthening phases, along with carbides and borides. For investment casting, the alloy’s thermophysical properties, such as liquidus and solidus temperatures, are crucial. The liquidus temperature is approximately 1,345°C, while the solidus is 1,196°C. The thermal conductivity, specific heat, and density vary with temperature, influencing the solidification behavior in precision casting. The following equations describe the stress model used in the simulation, based on a thermo-elasto-plastic approach:
$$ \{ d\sigma \} = [ D_e ] \{ d\varepsilon_e \} $$
where \( \{ d\sigma \} \) is the elastic stress increment, \( [ D_e ] \) is the elastic modulus matrix, and \( \{ d\varepsilon_e \} \) is the elastic strain increment. The total strain incorporates elastic, plastic, and thermal components:
$$ \{ d\varepsilon \} = \{ d\varepsilon_e \} + \{ d\varepsilon_p \} + \{ d\varepsilon_T \} $$
In the thermo-elasto-plastic model, the stress-strain relationship is expressed as:
$$ \{ d\sigma \} = [ D_{ep} ] \left( \{ d\varepsilon \} – \{ d\varepsilon_p \} – \{ d\varepsilon_T \} \right) $$
where \( [ D_{ep} ] \) is the elasto-plastic modulus matrix. The linear hardening behavior of the material is given by:
$$ \sigma = \sigma_0 + H \varepsilon_{pl} $$
with \( \sigma_0 \) as the yield stress and \( H \) as the plastic modulus. To assess hot tearing, the Hot Tearing Index (HTI) is computed based on accumulated strain during the vulnerable solidification period:
$$ HTI = \int_{t_{coh}}^{t_s} \sqrt{\frac{2}{3} \dot{\varepsilon}_p : \dot{\varepsilon}_p} d\tau $$
where \( t_{coh} \) is the coherency time when grains contact, and \( t_s \) is the solidus time. This model helps predict defect-prone areas in investment casting processes.
The turbine geometry consists of a central hub and ten curved blades, with a height of 60 mm and a maximum diameter of 86 mm. The blade thickness is approximately 0.7 mm, while the hub section is 28 mm thick, creating significant thermal gradients during solidification. The gating system includes a sprue, a pouring basin, and three ingates, arranged to fill three turbines simultaneously with a 130° angle between the turbine axis and sprue centerline. This design aims to ensure uniform filling in precision casting, but it also introduces challenges in stress distribution. The alloy properties were derived from Scheil model calculations, and key parameters are summarized in the table below:
| Property | Value |
|---|---|
| Liquidus Temperature | 1,345°C |
| Solidus Temperature | 1,196°C |
| Thermal Conductivity | Varies with temperature |
| Specific Heat | Function of temperature |
| Density | Temperature-dependent |
Simulations were conducted with pouring temperatures of 1,400°C, 1,450°C, 1,500°C, and 1,550°C, and mold shell temperatures of 800°C, 850°C, and 900°C. The heat transfer coefficient between the alloy and shell was set to 900 W/(m²·K). The material model assumed elasto-plastic behavior for the alloy and rigid properties for the shell, which is typical in investment casting simulations to capture realistic stress patterns.
During the filling stage, molten metal flows rapidly through the gating system, completing the fill in about 1 second due to the small turbine size and large cross-sectional areas. The temperature field analysis reveals that cooling initiates at the blade tips and progresses toward the hub, creating a steep thermal gradient. This uneven solidification sequence leads to differential contraction, generating thermal stresses that peak in the blade edges. The solid fraction distribution shows that blades solidify earlier than the hub, exacerbating the risk of hot tearing in precision casting. The stress concentration in these areas aligns with the HTI predictions, indicating high susceptibility to defects.
To quantify the effects of process parameters, we examined the stress and HTI at a critical point on the blade edge. The results demonstrate that increasing the mold shell temperature consistently reduces thermal stress and HTI, as higher shell temperatures minimize thermal shocks and promote gradual cooling. For instance, at a pouring temperature of 1,500°C, raising the shell temperature from 800°C to 900°C decreases the maximum stress from 30 MPa to 20 MPa and the HTI from 8×10⁻⁴ to 6×10⁻⁴. This trend underscores the importance of mold preheating in investment casting to mitigate hot tearing. Conversely, pouring temperature variations show a non-linear impact: HTI initially rises with temperature up to 1,450°C due to extended vulnerable solidification times, then declines as higher fluidity reduces stress concentrations. The table below summarizes HTI values under different conditions:
| Pouring Temperature (°C) | Shell Temperature (°C) | Maximum Stress (MPa) | HTI |
|---|---|---|---|
| 1,400 | 800 | 47 | 7.2×10⁻⁴ |
| 1,450 | 800 | 35 | 9.5×10⁻⁴ |
| 1,500 | 800 | 25 | 8.0×10⁻⁴ |
| 1,550 | 800 | 22 | 6.1×10⁻⁴ |
| 1,500 | 850 | 23 | 7.0×10⁻⁴ |
| 1,500 | 900 | 20 | 6.1×10⁻⁴ |
The interplay between pouring and shell temperatures highlights that lower values of one parameter amplify the effect of the other. For example, at a shell temperature of 800°C, increasing the pouring temperature from 1,400°C to 1,500°C reduces stress by nearly 50%, but the HTI peaks at 1,450°C. This complexity necessitates balanced optimization in investment casting processes. Based on the simulations, the optimal parameters for minimizing hot tearing are a pouring temperature of 1,500°C and a shell temperature of 900°C, which yield low HTI without inducing other defects like shrinkage porosity. These findings align with practical observations in precision casting, where controlled cooling rates are essential for integrity.
In conclusion, numerical simulation provides valuable insights into hot tearing mechanisms in investment casting of IN713C alloy turbines. The blade edges are most prone to defects due to high thermal stresses from uneven solidification. By adjusting process parameters, such as increasing mold shell temperature and selecting an intermediate pouring temperature, the hot tearing tendency can be significantly reduced. This study demonstrates the efficacy of precision casting simulations in enhancing product quality and reliability for automotive components. Future work could explore additional factors like alloy modifications or alternative gating designs to further improve the investment casting process.