In precision investment casting, the thermal behavior of ceramic shells during sintering directly impacts dimensional accuracy and surface quality of final titanium castings. This study establishes a comprehensive numerical model to analyze temperature evolution in complex thin-walled shell structures through reverse solidification theory and advanced material characterization.
The thermal transport properties of Y2O3-ZrO2-SiO2 composite shells were systematically measured using Hot Disk TPS 2500S and LFA457 instruments. Three-dimensional heat transfer governing equations were formulated as:
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (\lambda \nabla T) + Q $$
where $ \rho $ represents density (kg/m³), $ c_p $ specific heat capacity (J/kg·K), $ \lambda $ thermal conductivity (W/m·K), and $ Q $ internal heat source. Boundary conditions incorporate convective and radiative heat transfer:
$$ q_{\text{conv}} = h(T_{\text{fluid}} – T_{\text{surface}}) $$
$$ q_{\text{rad}} = \epsilon \sigma (T_{\text{surroundings}}^4 – T_{\text{surface}}^4) $$
Material properties for unsintered and sintered shells reveal significant phase transformation effects:
| Temperature (°C) | Thermal Conductivity (W/m·K) | Density (kg/m³) | Specific Heat (J/kg·K) |
|---|---|---|---|
| 25 | 0.68 | 2,150 | 850 |
| 200 | 0.72 | 2,130 | 910 |
| 400 | 0.81 | 2,100 | 980 |
| 600 | 0.92 | 2,080 | 1,050 |
| 800 | 1.05 | 2,050 | 1,120 |
| 1,000 | 1.18 | 2,030 | 1,180 |
| Temperature (°C) | Thermal Conductivity (W/m·K) | Density (kg/m³) | Specific Heat (J/kg·K) |
|---|---|---|---|
| 25 | 1.25 | 2,450 | 720 |
| 200 | 1.32 | 2,430 | 760 |
| 400 | 1.44 | 2,410 | 820 |
| 600 | 1.58 | 2,390 | 880 |
| 800 | 1.73 | 2,370 | 930 |
| 1,000 | 1.89 | 2,350 | 980 |
The developed reverse solidification algorithm successfully predicted temperature lag phenomena in precision investment casting shells. For a ZTA15 titanium alloy component with 4mm wall thickness, thermal analysis revealed:
$$ \Delta T_{\text{max}} = 127^\circ \text{C} \quad \text{at 2,400s heating phase} $$
$$ \frac{dT}{dt}_{\text{peak}} = 0.85^\circ \text{C/s} \quad \text{at sharp corners} $$
Key findings demonstrate that precision investment casting shells exhibit 18-22% faster heat transfer at geometric discontinuities compared to bulk regions. The automated shell generation algorithm achieved 97.3% geometric fidelity with actual castings, significantly improving thermal simulation accuracy.
Thermal gradient evolution during sintering follows the modified Fourier relationship:
$$ \nabla T = \frac{q”}{\lambda_{\text{eff}}} \left[ 1 + \beta (T – T_0) \right] $$
where $ \beta $ represents the thermal expansion compensation factor (0.0045 K⁻¹ for sintered shells). This model effectively captures the 9.8% temperature hysteresis between furnace setpoints and shell surface measurements.
Optimization strategies for precision investment casting processes should prioritize corner radius design (R ≥ 3mm) and implement graded sintering schedules:
$$ t_{\text{hold}} = \frac{\delta^2}{4\alpha} \ln\left(\frac{T_{\infty} – T_0}{T_{\infty} – T_c}\right) $$
where $ \delta $ is shell thickness (mm), $ \alpha $ thermal diffusivity (m²/s), and $ T_c $ critical stress temperature. Implementation reduces thermal shock defects by 63% in production trials.
This comprehensive approach advances precision investment casting technology through physics-based modeling and empirical validation, enabling first-pass success in complex titanium aerospace components.