This study investigates the solidification behavior of 16Cr20Ni14Si2 austenitic heat-resistant steel during precision investment casting through a coupled Cellular Automaton-Finite Element (CAFE) approach. The methodology enables multiscale analysis of grain evolution while addressing critical process parameters affecting microstructure formation.
Thermophysical Modeling Framework
The heat transfer governing equations for precision investment casting include three modes:
- Heat conduction: Fourier’s law
$$ \vec{q} = -\lambda \cdot \text{grad}T = -\lambda \frac{\partial T}{\partial n} \cdot \vec{n} $$ - Thermal convection: Newton’s cooling law
$$ q = h(T_w – T) $$ - Radiation: Stefan-Boltzmann law
$$ q = \varepsilon \sigma_{\text{SB}}(T_w^4 – T^4) $$
| Parameter | Value |
|---|---|
| Liquidus temperature | 1441°C |
| Solidus temperature | 1353°C |
| Gibbs-Thomson coefficient | 2×10⁻⁷ m·K |
Nucleation and Growth Kinetics
The continuous nucleation model for precision investment casting follows Gaussian distribution:
$$ n(\Delta T) = \int_0^{\Delta T} \frac{dn}{d(\Delta T’)}d(\Delta T’) $$
$$ \frac{dn}{d(\Delta T)} = \frac{n_{\text{max}}}{\sqrt{2\pi}\Delta T_\sigma} \exp\left(-\frac{(\Delta T – \Delta T_{\text{max}})^2}{2\Delta T_\sigma^2}\right) $$
Dendrite tip growth velocity is expressed as:
$$ v = a_2\Delta T^2 + a_3\Delta T^3 $$
with coefficients derived from KGT model extensions:
$$ a_2 = 6.63 \times 10^{-8} \, \text{m/s·K}^2 $$
$$ a_3 = 1.18 \times 10^{-6} \, \text{m/s·K}^3 $$
Process Parameter Optimization
Orthogonal experiments revealed critical factors affecting grain refinement in precision investment casting:
| Factor | Optimal Range | Effect on Grain Count |
|---|---|---|
| Shell thickness | 7-9 mm | +18% grains at 7mm |
| Shell preheat | 1143-1203 K | +23% grains at 1143K |
| Pouring speed | 3.5 kg/s | Minimum orientation deviation (31.99°) |
The optimal parameter combination for maximum equiaxed grains (94.7% fraction) was:
- Shell thickness: 7 mm
- Preheat temperature: 1173 K
- Pouring temperature: 1923 K
- Water cooling (h=5000 W/m²·K)
Industrial Validation
For complex thin-wall engine housing components (216×180×240 mm), precision investment casting simulations predicted:
$$ \text{Shrinkage porosity risk} < 0.5\% $$
$$ \text{Filling completeness} > 99.8\% $$
Experimental results showed excellent agreement with CAFE predictions:
| Metric | Simulation | Experiment |
|---|---|---|
| Average grain size | 11.91 μm | 12.80 μm |
| Equiaxed fraction | 94.7% | 92.3% |
Technical Advancements
Key innovations in precision investment casting process design include:
- Multi-scale coupling of macro transport phenomena with microstructural evolution
- Quantitative prediction of columnar-to-equiaxed transition (CET)
- Inverse determination of nucleation parameters through experimental calibration
The CAFE methodology demonstrates strong applicability for precision investment casting of high-temperature alloys, enabling virtual process optimization with 0.07% grain size prediction error. This approach significantly reduces trial costs while improving mechanical consistency in critical aerospace components.