Thin-walled connecting shells are used in high-power engines to combine structural connection, fluid passage, and sealing functions. Their geometry usually includes a massive flange, a curved thin-wall tube, and abrupt section transitions. Investment casting is well suited to such parts because a ceramic shell can reproduce complex external and internal contours with limited machining. The same features, however, create a narrow process window: the thin sections must fill before the melt freezes, while the thick flange must remain feedable long enough to avoid shrinkage porosity. Hot tearing adds a second constraint because the flange-to-wall transition accumulates thermal strain during the final stage of solidification.
Why thin-walled investment castings fail in two different modes
Shrinkage porosity and hot tearing originate at different stages of the casting cycle, and a process change that suppresses one can aggravate the other. Shrinkage porosity forms when a region solidifies without sufficient liquid feeding. In a thin-wall shell, the thin section often solidifies first because its surface-to-volume ratio is high. If that solidification front isolates a thicker flange or a junction, the remaining liquid in the hot spot cannot be replenished. The Niyama criterion captures this feeding difficulty through the temperature gradient \(G\) and cooling rate \(R\):
$$N=\frac{G}{\sqrt{R}}$$
Low \(N\) values indicate a weak thermal gradient relative to the local cooling rate, and therefore a higher risk of shrinkage porosity. The criterion is useful for locating likely porosity zones, but it does not by itself describe mechanical cracking.
Hot tearing occurs later, when the alloy is in a semi-solid or coherent mushy state. Solidification shrinkage is constrained by the shell and by cooler, already rigid sections. If the accumulated plastic strain in the vulnerable interval exceeds the tolerance of the material, a crack initiates. A common simulation index integrates the plastic strain rate \(\dot{\varepsilon}_{p}\) over the time between coherency and solidification:
$$\mathrm{HTI}=\int_{t_{\mathrm{coh}}}^{t_{\mathrm{sol}}}\dot{\varepsilon}_{p}\,\mathrm{d}t$$
A higher hot tearing indicator, HTI, means a greater accumulated cracking risk. The practical implication is that process optimization cannot rely on a single defect index. Pouring temperature, filling rate, and shell preheat alter the temperature field, the feeding path, and the mechanical constraint at the same time.
Case geometry: thin walls, thick flange, and a constrained transition
A representative 16Cr20Ni14Si2 connecting shell has an overall envelope of 249.5 mm × 180 mm × 142 mm and a casting mass of about 8.5 kg. The flange is approximately 180 mm in outer diameter, 120 mm in inner diameter, and 20 mm thick. The straight tube has a 142 mm outer diameter and a 5 mm wall, while the large-diameter thin section has a 137 mm outer diameter and a 3.5 mm wall. The flange includes internal threads and four through-holes, which are more accurately produced by machining after casting. The rest of the shell is designed as a near-net-shape investment casting.
| Region | Geometric feature | Dominant risk | Mechanism |
|---|---|---|---|
| Thin-wall section | 3.5 mm wall, long flow path | Misrun, cold shut, dispersed porosity | Rapid heat loss and viscosity rise reduce flowability and feeding |
| Flange | 20 mm thick, large thermal mass | Shrinkage porosity, hot spot | Late solidification and insufficient liquid supply |
| Flange-to-wall transition | Abrupt section change | Hot tearing | Uneven contraction and stress concentration under shell constraint |
| Curved channel | Changing flow direction | Gas entrapment, flow instability | Local velocity change and stagnation during filling |
The alloy composition used for the material database is given in Table 2. The carbon content is relatively low, while chromium and nickel provide oxidation and corrosion resistance. Silicon increases high-temperature strength and scale resistance but also affects fluidity and solidification behavior.
| Element | C | Cr | Ni | Si | Mn | P | S | Fe |
|---|---|---|---|---|---|---|---|---|
| Composition (wt.%) | 0.158 | 20.18 | 14.12 | 1.98 | 0.62 | 0.012 | 0.009 | Balance |
The liquidus temperature is about 1440 °C and the solidus temperature about 1268 °C, giving a freezing interval of approximately 172 °C. This wide interval produces a persistent mushy zone, while the viscosity rises sharply near the end of solidification. Both effects make the thin-wall shell sensitive to feeding interruption. At the same time, the high-alloy melt requires sufficient superheat to fill the 3.5 mm sections before the flow front arrests.
Gating and thermal design for a thin-wall shell
A top-pouring system was selected because the thin-wall sections require a short filling path and a low risk of cold shut. A bottom-pouring arrangement would produce a more quiescent fill, but the longer vertical path would increase heat loss before the melt reaches the upper thin sections. The top-pouring design uses a central sprue, an annular runner, and two symmetric side gates connected to the flange hot spots. The two adjacent hot spots, with characteristic dimensions of 9.5 mm and 12.2 mm, were treated as a single feeding zone; the equivalent hot-spot diameter was estimated as about 28 mm and corrected to 27.16 mm using a weight factor of 0.97.
Each gate has an equivalent section of 60 mm × 22.5 mm, or 1350 mm², giving a total gate area of 2700 mm². The runner area is 3375 mm², approximately 1.25 times the total gate area. The pouring cup has a maximum diameter of 115 mm, a throat diameter of 35 mm, and a height of 77 mm. The ceramic shell was modeled with an 8 mm thickness. A finite-element mesh with a 2 mm surface edge length on the casting and a 3 mm edge length on the gating system produced about 1.40 million tetrahedral volume elements including the shell.
The baseline simulation used a pouring temperature of 1550 °C, a mass flow rate of 2.0 kg/s, and a shell preheat temperature of 750 °C. The 1550 °C value corresponds to about 110 °C superheat above the liquidus. The flow rate was chosen at the lower end of the estimated 1.7–2.8 kg/s window for an 8.5 kg casting filled in 3–5 s, so that the baseline case would expose filling limitations rather than conceal them. The shell preheat temperature reflects a deliberate compromise: high-alloy steel practice often suggests 700–800 °C, while a heavier 8.5 kg casting would normally favor a lower preheat to limit grain coarsening. Because the 3.5 mm sections are vulnerable to chilling, the thin-wall requirement was given priority. The metal–shell heat transfer coefficient was set to 900 W/(m²·K), with air cooling at 20 °C and gravity acting in the negative vertical direction. The stress calculation used an elastic–plastic material model.
Baseline result: stable filling does not guarantee sound feeding
The baseline filling simulation was completed in about 5.6 s. The melt entered the runner, divided into the two side gates, and filled the shell without a visible misrun or large-scale recirculation. At approximately 75% fill, the thin-wall region began to cool faster than the flange, which is consistent with its higher surface-to-volume ratio. Complete filling was nevertheless achieved, so the gating system satisfied its primary purpose.
The solidification result revealed the limitation of the design. Solidification proceeded generally from the casting toward the gating system, and the gating system remained liquid until late in the cycle. The total solidification time was about 2570 s. However, the bottom thin-wall region had already formed a solid layer while the flange and gate region were still feeding. The result was a shrinkage porosity volume of 1.153 cm³, concentrated at the thin-wall bottom. The maximum HTI in the flange-to-wall transition, defined as region A, reached 0.0120. The hot-tearing risk was localized near the gate and the flange-to-wall junction, where the last liquid remained and the shell constraint was strongest. Thus, the baseline process filled completely but did not provide a robust feeding path.
Single-factor response: temperature, flow rate, and shell preheat
Pouring temperature had a strong effect on shrinkage porosity, but its effect on hot tearing was not monotonic. With the flow rate fixed at 2.0 kg/s and the shell preheat at 750 °C, increasing the pouring temperature from 1550 °C to 1650 °C reduced the shrinkage volume from 1.153 cm³ to 0.334 cm³. A local rebound occurred at 1610 °C, where the volume rose to 0.784 cm³ from 0.721 cm³ at 1590 °C, indicating a change in local solidification order rather than a simple thermal trend. The HTI fell from 0.0120 at 1550 °C to 0.0026 at 1610 °C, then varied between 0.0030 and 0.0040 at higher temperatures. The lowest HTI was therefore not obtained at the highest pouring temperature.
| Pouring temperature (°C) | Shrinkage porosity (cm³) | Maximum HTI in region A |
|---|---|---|
| 1550 | 1.153 | 0.0120 |
| 1570 | 0.983 | 0.0043 |
| 1590 | 0.721 | 0.0048 |
| 1610 | 0.784 | 0.0026 |
| 1630 | 0.514 | 0.0038 |
| 1650 | 0.334 | 0.0032 |
Flow rate showed a clear non-monotonic response. The minimum shrinkage volume, 0.272 cm³, occurred at 2.5 kg/s. Increasing the rate to 3.0 kg/s raised the volume to 0.440 cm³, and further changes produced values between 0.411 cm³ and 0.594 cm³. The HTI remained low between 2.5 kg/s and 3.5 kg/s, at 0.0023–0.0027, but rose to 0.0042 at 4.0 kg/s and 0.0084 at 4.5 kg/s. A very low flow rate allows the thin sections to cool before filling is complete, while an excessively high rate disturbs the temperature field and reduces filling stability. For this geometry, the practical flow-rate window is therefore approximately 2.5–3.5 kg/s, not the highest rate that the pump or pouring system can deliver.
Shell preheat produced the most consistent trend. Raising the preheat from 750 °C to 1000 °C reduced the shrinkage volume from 1.153 cm³ to 0.102 cm³ and lowered the region-A HTI from 0.0120 to approximately 0.0015–0.0020. About 76% of the total shrinkage reduction between 750 °C and 1000 °C occurred in the first step from 750 °C to 800 °C, where the volume fell from 1.153 cm³ to 0.356 cm³. Above 850 °C, the improvement became more gradual. A high shell temperature reduces the thermal shock at the melt front and keeps the feeding channel open, but it also increases energy consumption and can reduce shell strength or promote grain coarsening. The optimum is therefore an engineering balance rather than the highest achievable preheat.
| Factor | Setting | Shrinkage porosity (cm³) | Maximum HTI in region A |
|---|---|---|---|
| Flow rate (kg/s) | 2.0 | 1.153 | 0.0120 |
| Flow rate (kg/s) | 2.5 | 0.272 | 0.0025 |
| Flow rate (kg/s) | 3.0 | 0.440 | 0.0023 |
| Flow rate (kg/s) | 3.5 | 0.491 | 0.0027 |
| Flow rate (kg/s) | 4.0 | 0.411 | 0.0042 |
| Flow rate (kg/s) | 4.5 | 0.594 | 0.0084 |
| Shell preheat (°C) | 750 | 1.153 | 0.0120 |
| Shell preheat (°C) | 800 | 0.356 | 0.0023 |
| Shell preheat (°C) | 850 | 0.292 | 0.0019 |
| Shell preheat (°C) | 900 | 0.242 | 0.0020 |
| Shell preheat (°C) | 950 | 0.193 | 0.0015 |
| Shell preheat (°C) | 1000 | 0.102 | 0.0017 |
Multi-parameter optimization with an L9 orthogonal design
The single-factor results cannot be combined directly because the three parameters interact. An L9(3³) orthogonal array was therefore used with three levels for each factor: pouring temperature at 1550, 1610, and 1650 °C; flow rate at 2.5, 3.0, and 3.5 kg/s; and shell preheat at 850, 950, and 1000 °C. The shell preheat range starts at 850 °C because lower values produced excessive porosity in the single-factor trials, while 850 °C remains near the upper limit of the recommended range for high-alloy steel shells. The nine runs produced shrinkage volumes from 0.053 cm³ to 0.773 cm³ and HTI values from 0.0029 to 0.0061. The best combination was 1650 °C, 3.0 kg/s, and 850 °C, with 0.053 cm³ shrinkage porosity and an HTI of 0.0029.
Range analysis ranked the factors as pouring temperature > flow rate > shell preheat for both responses. The analysis of variance supported this ranking. For shrinkage porosity, pouring temperature was highly significant at \(P=0.0043\), and flow rate was significant at \(P=0.0484\). Shell preheat was not statistically significant in the 850–1000 °C range, with \(P=0.5100\). For HTI, pouring temperature and flow rate were both significant, at \(P=0.0179\) and \(P=0.0449\), respectively, while shell preheat was not significant at \(P=0.1879\).
| Response | Factor | P value | Statistical interpretation |
|---|---|---|---|
| Shrinkage porosity | Pouring temperature | 0.0043 | Highly significant |
| Shrinkage porosity | Flow rate | 0.0484 | Significant |
| Shrinkage porosity | Shell preheat | 0.5100 | Not significant |
| HTI | Pouring temperature | 0.0179 | Significant |
| HTI | Flow rate | 0.0449 | Significant |
| HTI | Shell preheat | 0.1879 | Not significant |
The selection of 850 °C rather than 1000 °C illustrates the difference between a numerical minimum and a manufacturing optimum. A 1000 °C shell preheat gave the lowest single-factor shrinkage volume, but the orthogonal range from 850 °C to 1000 °C showed no statistically significant effect. Raising the shell preheat to 1000 °C would increase energy use and expose the shell to greater high-temperature softening and grain-coarsening risk. At 850 °C, the shell still provides enough thermal buffering for the 3.5 mm sections, while the process remains easier to control in production. The selected window is therefore 1650 °C pouring temperature, 3.0 kg/s flow rate, and 850 °C shell preheat.
The optimized simulation reduced shrinkage porosity from 1.153 cm³ to 0.053 cm³, a decrease of about 95.4%, and reduced the region-A HTI from 0.0120 to 0.0029, a decrease of about 75.8%. The improvement is not simply a consequence of a hotter melt. The combination of higher superheat, a moderate flow rate, and a moderately preheated shell keeps the thin sections liquid long enough to fill, while maintaining a feed path from the gate to the flange hot spot. The flange and the thin wall then cool with a smaller temperature difference, which lowers the tensile strain accumulated at the transition.
| Process condition | Pouring temperature (°C) | Flow rate (kg/s) | Shell preheat (°C) | Shrinkage porosity (cm³) | Region-A HTI | Shrinkage reduction | HTI reduction |
|---|---|---|---|---|---|---|---|
| Baseline | 1550 | 2.0 | 750 | 1.153 | 0.0120 | — | — |
| Optimized | 1650 | 3.0 | 850 | 0.053 | 0.0029 | 95.4% | 75.8% |
Production trial and inspection
The optimized parameters were transferred to a conventional investment casting route: wax injection, shell building with a silica sol binder and zircon/mullite stucco, steam dewaxing, shell firing and preheat, induction melting, pouring, shell removal, gate cutting, and shot blasting. The wax pattern was injected at 57–58 °C with a 25 s injection time, 15–25 kg/cm² injection pressure, and 60 s holding time. The shell was built as a four-and-a-half-layer ceramic mold and dewaxed at 160 ± 10 °C under 0.7–0.8 MPa steam. The shell was then fired and brought to the selected preheat before pouring.
For each process condition, 25 castings were trial produced. The optimized condition produced 24 acceptable castings, a qualified yield of 96%. The baseline condition produced 17 acceptable castings, a qualified yield of 68%. X-ray inspection focused on the flange root and the 3.5 mm wall junction, which were the high-risk zones in the simulation. In the optimized castings, the inspected zones showed no visible indications of porosity or cracking. In the baseline castings, clustered dark indications consistent with shrinkage porosity appeared at the flange root and wall junction, matching the predicted high-risk region.
| Inspection item | Drawing requirement | Measured value | Result |
|---|---|---|---|
| Flange outer diameter | Φ180 ± 1.0 mm | 179.62 mm | Within tolerance |
| Flange inner diameter | Φ120 ± 1.0 mm | 120.25 mm | Within tolerance |
| Flange thickness | 20 ± 0.5 mm | 19.85 mm | Within tolerance |
| Large thin-section outer diameter | Φ137 ± 1.0 mm | 136.92 mm | Within tolerance |
| Thin-wall thickness | 3.5 ± 0.5 mm | 3.47 mm | Within tolerance |
| Straight-tube outer diameter | Φ142 ± 1.0 mm | 142.08 mm | Within tolerance |
| Straight-tube wall thickness | 5 ± 0.5 mm | 5.06 mm | Within tolerance |
The dimensional results showed no systematic bias in the thin-wall or flange-transition regions. The measured thin-wall thickness of 3.47 mm and the flange thickness of 19.85 mm were close to nominal, consistent with a filling and contraction pattern that remained stable after the process change. The trial was limited to 25 castings per condition and one production lot, so the 96% yield should be treated as a demonstration of capability rather than a universal guarantee. Within that scope, the X-ray indications, dimensional measurements, and simulated defect locations were mutually consistent.
Engineering implications for investment casting process control
The case shows that filling quality and internal soundness must be assessed separately. A casting can fill completely in 5.6 s and still contain 1.153 cm³ of shrinkage porosity because the thin wall solidifies before the flange hot spot is fed. Gating designs for thin-wall shells should therefore place the gate near the feeding-limited hot spot, even when this requires a top-pouring arrangement that is less quiescent than bottom pouring. Flow control then becomes the means of limiting turbulence and gas entrapment, not the sole solution to feeding.
Shell preheat is a powerful thermal variable because it changes the heat-transfer boundary along the entire casting. In this case, raising the preheat from 750 °C to 800 °C removed most of the shrinkage volume reduction available up to 1000 °C, but the higher temperatures also increased energy demand and shell-risk exposure. A statistically insignificant improvement at 1000 °C was therefore not adopted as a production target. This distinction is important when simulation results are transferred to manufacturing: the lowest predicted defect volume is not necessarily the most stable or economical process point.
The optimization also illustrates why single-parameter tuning is insufficient. Pouring temperature was the dominant factor for both shrinkage and hot tearing, but its HTI response was non-monotonic. Flow rate had a clear low-defect window but degraded filling stability at high values. Shell preheat improved both responses yet had limited statistical leverage once the range was restricted to 850–1000 °C. The selected 1650 °C / 3.0 kg/s / 850 °C combination is a compromise within those coupled constraints, not a universal recipe for thin-walled 16Cr20Ni14Si2 shells. Other geometries, shell systems, and melting practices would require recalibration of the heat-transfer coefficients, alloy properties, and defect criteria before the same window could be applied.