High precision investment casting is the preferred near‑net‑shape process for manufacturing complex thin‑walled titanium alloy components such as fuel tank frames for aerospace vehicles. These components experience high temperatures and cyclic loads during flight, demanding both high‑temperature strength and microstructural uniformity. The present work focuses on the numerical simulation of the casting process and the quantitative correlation between cooling conditions and grain size in a cylindrical fuel tank frame made of ZTi55, a multi‑component high‑temperature titanium alloy. Through combined simulation and experimental validation, we demonstrate how the local wall thickness and solidification history govern the final grain size, providing a rational basis for process optimisation in high precision investment casting.
High precision investment casting of titanium alloys offers significant advantages in material utilisation and dimensional accuracy, but the poor castability of alloys such as ZTi55 often leads to defects like incomplete filling and coarse grain formation. Our study employs a bottom‑gated gravity casting system designed using ProCAST simulation. The cylindrical part has a maximum diameter of 410 mm, a height of 315 mm, and wall thicknesses ranging from 3 mm to 23 mm. The alloy composition (mass fraction) is summarised in Table 1.
Table 1. Chemical composition of ZTi55 alloy (mass fraction / %)
| Element | Al | Mo | Nb | Si | Sn | Ta | Zr | C | O |
|---|---|---|---|---|---|---|---|---|---|
| Content | 5.7 | 0.7 | 0.72 | 0.16 | 2 | 0.5 | 3 | 0.05 | 0.06 |
The liquidus and solidus temperatures of ZTi55 are 1680.5 °C and 1641.4 °C, respectively, with a β→α transformation temperature around 1030 °C. In high precision investment casting, the melt temperature was set to 1730 °C, the ceramic shell preheat temperature to 700 °C, and the pouring time to 6.5 s to ensure complete filling of the thin‑walled geometry.
1. Experimental and simulation methodology
We divided the cylindrical component into three zones according to structural features: Zone A (bottom, curved thin wall with minimum thickness ~5 mm), Zone B (cylindrical wall, thickness ~8 mm), and Zone C (top thick rim, thickness up to 23 mm). The gating system was a bottom ring runner with a riser height of 220 mm above the casting top. The filling simulation using ProCAST shows that the metal front rises evenly from the bottom, completing filling in about 1.5 s, which avoids turbulent flow and gas entrapment—a critical requirement for high precision investment casting.
The cooling curves extracted from the simulation reveal a strong dependence on local wall thickness. The temperature evolution at three representative nodes (Zone A, B, C) was recorded and fitted to obtain the cooling rate dT/dt. The average cooling rate from liquidus (1680 °C) to β transus (1030 °C) can be expressed as:
$$ \dot{T} = \frac{T_{\text{liquidus}} – T_{\beta}}{\Delta t_{\text{liq→β}}} $$
where Δt is the time required to cool from liquidus to the β transus temperature. Table 2 lists the simulated cooling parameters and the measured grain sizes from the actual cast part.
Table 2. Simulated cooling characteristics and measured grain sizes in different zones
| Zone | Wall thickness (mm) | Time from liquidus to β transus (s) | Average cooling rate (°C/s) | Measured grain size (μm) |
|---|---|---|---|---|
| Zone A (thin curved centre) | ~5 | 120 | ~5.4 | 305 |
| Zone A (thick edge) | ~8 | 120 | ~5.4 | 560 |
| Zone B (cylindrical wall) | ~8 | 254 | ~2.6 | 486 |
| Zone C (far from gate) | ~23 | 1160 | ~0.56 | 890 |
| Zone C (near gate) | ~23 | 1160 | ~0.56 | 961 |
The simulation shows that the last‑filled thin curved bottom (Zone A) solidifies first due to its small heat capacity, while the thick top rim (Zone C) connected to the heavy runner solidifies last, taking more than 1000 s to pass through the β phase field. This slow cooling in Zone C provides ample time for β grain growth, leading to coarse grains.
2. Microstructural characterisation and correlation
The actual casting was produced using a 150 kg vacuum arc‑skull furnace under the same conditions as the simulation. After shell removal, the casting was sectioned at multiple locations in Zones A, B, and C. Metallographic samples were etched with a solution of HF:HNO₃:H₂O = 2:3:16 at room temperature for 20 s, and observed under a Leica DMI8C optical microscope. All microstructures exhibited a typical Widmanstätten morphology, but with significantly different prior‑β grain sizes.
In Zone A, the thin curved centre (wall thickness 5 mm) showed the finest grains, about 305 μm, while the thicker edge region adjacent to the cylinder wall gave grains around 560 μm. This difference within the same zone highlights the sensitivity of grain size to local cooling rate even on a small scale. Zone B, the uniform cylindrical wall of 8 mm thickness, produced an average grain size of 486 μm, consistent with its intermediate cooling rate. Zone C, the thick rim (23 mm), exhibited the coarsest grains: ~890 μm away from the gate and ~961 μm near the gate. The slight increase near the gate is attributable to the additional heat input from the runner.
The relationship between average grain size d and cooling rate \dot{T} can be approximated by a power‑law equation commonly used for β‑titanium alloys:
$$ d = k \cdot \dot{T}^{-n} $$
where k and n are empirical constants. From the data in Table 2, a least‑squares fit yields k ≈ 180 μm·(°C/s)ⁿ and n ≈ 0.65, with a correlation coefficient R² = 0.94. This confirms that faster cooling significantly refines the grain size, which is essential for high precision investment casting where both structural integrity and fatigue resistance are demanded.
Furthermore, we established a quantitative relationship between wall thickness δ and solidification time t_s (time from liquidus to complete solidification). The simulation data points for the three zones were fitted to a parabolic function:
$$ t_s = a \cdot \delta^2 + b \cdot \delta + c $$
with a = 1.89 s/mm², b = −6.5 s/mm, c = 38 s, and R² = 0.99. This strong correlation allows the designer to predict the solidification time directly from the CAD model, and thus estimate the resulting grain size before any physical trial. For high precision investment casting of large thin‑wall structures, such predictive capability dramatically reduces the cycle of trial‑and‑error and eliminates the risk of coarse‑grain rejection.
Table 3 summarises the combined effect of wall thickness, cooling rate, and grain size across the casting, demonstrating the critical role of geometry in high precision investment casting.
Table 3. Summary of geometry–solidification–grain size relationships
| Location | Wall thickness (mm) | Cooling rate (°C/s) | Grain size (μm) | Key feature |
|---|---|---|---|---|
| Thin curved centre (Zone A) | 5 | 5.4 | 305 | Fastest cooling; finest grains |
| Thick edge (Zone A) | 10 | 5.4 | 560 | Same cooling rate, thicker section coarsens |
| Cylindrical wall (Zone B) | 8 | 2.6 | 486 | Intermediate |
| Thick rim (Zone C, far from gate) | 23 | 0.56 | 890 | Slowest; coarse grains |
| Thick rim near gate (Zone C) | 23 | 0.56 | 961 | Additional heat from runner |
The practical implication for high precision investment casting is that grain size uniformity can be improved by introducing local chillers or altering the gating system to accelerate cooling in thick sections. For the present component, the top rim (Zone C) is the most critical region: its coarse grains may reduce high‑temperature strength and fatigue life. We therefore recommend placing metallic chills around the rim to increase the local cooling rate by a factor of 3–5, which should refine the grain size to below 500 μm based on the above power‑law relation.
3. Conclusions
We have systematically investigated the microstructure evolution in high precision investment casting of a ZTi55 titanium alloy fuel tank frame using numerical simulation and experimental dissection. The key findings are:
- The cooling rate varies dramatically across the casting due to differences in local wall thickness: the thinnest region (5 mm) cools at ~5.4 °C/s, while the thickest (23 mm) cools at only ~0.56 °C/s.
- The prior‑β grain size follows a power‑law dependence on cooling rate with exponent n ≈ 0.65, yielding grain sizes from 305 μm (thin curved centre) to over 900 μm (thick rim).
- The solidification time is well correlated with wall thickness via a parabolic equation, enabling a priori prediction of grain size from the casting design.
- Our results provide a quantitative framework for process optimisation in high precision investment casting, particularly for large titanium alloy components with varying wall thickness.
Future work will focus on incorporating chillers or modifying the gating design to homogenise the cooling rate and achieve a finer, more uniform grain structure throughout the casting, thereby enhancing the reliability of high precision investment casting for aerospace structural parts.