I studied a steel locomotive coupler as a coupled casting problem in which mold filling, heat transfer, solidification shrinkage, thermal stress, and grain growth all interact. My main manufacturing route was investment casting, but I repeatedly used lost foam castings as a comparison because lost foam castings can also produce complex railway components with hollow sections and integrated passages. In my view, the most important requirement was not merely to fill the mold, but to obtain a dense body, avoid internal cracks and porosity, and achieve a fine final microstructure after heat treatment. I therefore combined orthogonal simulation, temperature-field analysis, stress-field analysis, microstructural modeling, and experimental validation. The same logic can be adapted to lost foam castings, although the pattern removal and coating behavior in lost foam castings introduce different filling and cooling boundary conditions.
I selected a hollow locomotive coupler with a large variation in wall thickness. The coupler envelope was approximately 594 mm × 370 mm × 350 mm, and its mass was about 70 kg. I used a vertical top-pouring gating system with two side branches and a top riser at the hook head. The steel grade was an E-grade cast steel, ZG25MnCrNiMo, which I expected to provide high strength, wear resistance, and low-temperature impact toughness. I measured the main alloying elements before pouring and used those values in my thermodynamic database. My initial composition is summarized in Table 1.
| Element | Mass fraction / % | Role in my coupler steel |
|---|---|---|
| C | 0.26 | Controls hardenability and pearlite fraction |
| Si | 0.45 | Deoxidation and solid-solution strengthening |
| Mn | 1.40 | Hardenability and toughness balance |
| Cr | 0.55 | Carbide formation and wear resistance |
| Ni | 0.45 | Low-temperature toughness |
| Mo | 0.25 | Hardenability and temper resistance |
| P | ≤0.35 | Impurity control |
| S | ≤0.35 | Impurity control |
For my simulation, I first calculated the temperature-dependent thermophysical properties from a mixed thermodynamic model. The density, thermal conductivity, enthalpy, and latent heat were all allowed to vary with temperature. I then used those properties in the transient heat-conduction equation:
$$\rho c_p \frac{\partial T}{\partial t} = \nabla \cdot \left( k \nabla T \right) + \rho L \frac{\partial f_s}{\partial t}$$
where \(\rho\) is density, \(c_p\) is specific heat, \(T\) is temperature, \(t\) is time, \(k\) is thermal conductivity, \(L\) is latent heat, and \(f_s\) is solid fraction. At the casting-shell interface, I imposed a heat-transfer condition of the form:
$$q = h \left( T_{\text{cast}} – T_{\text{shell}} \right)$$
where \(q\) is heat flux and \(h\) is the interfacial heat-transfer coefficient. For the shell-air interface, I used a much lower coefficient. My initial simulation conditions are listed in Table 2. These values were not arbitrary; I chose them so that the baseline case would be close to common industrial practice, while still giving me room to explore the effects of pouring temperature, shell preheating, and pouring time. In lost foam castings, the same equations apply, but the effective interface coefficient and the gas pressure from pattern decomposition can shift the local filling and cooling behavior.
| Parameter | Baseline value | Notes |
|---|---|---|
| Pouring temperature, \(T_1\) | 1550 °C | Initial baseline |
| Shell preheating temperature, \(T_2\) | 400 °C | Initial baseline |
| Ambient temperature, \(T_0\) | 20 °C | Air environment |
| Pouring time, \(t\) | 15 s | Initial baseline |
| Casting-shell heat-transfer coefficient, \(h_1\) | 500 W·m\(^{-2}\)·K\(^{-1}\) | Investment shell |
| Shell-air heat-transfer coefficient, \(h_2\) | 10 W·m\(^{-2}\)·K\(^{-1}\) | Natural convection and radiation lumped |
| Mesh size for gating and riser | 8 mm | Coarser than body |
| Mesh size for coupler body | 5 mm | Finer for stress and microstructure |
I treated the stress problem with a thermo-elastoplastic model. For the mushy zone, I focused on the interval between the liquidus and solidus because hot tearing is most likely there. I used a bilinear hardening description:
$$
\sigma =
\begin{cases}
E_1 \varepsilon, & \varepsilon \le \varepsilon_s \\
\sigma_{0.2} + E_2 \left( \varepsilon – \varepsilon_s \right), & \varepsilon > \varepsilon_s
\end{cases}
$$
Here \(\sigma\) is stress, \(\sigma_{0.2}\) is the 0.2% offset yield strength, \(\varepsilon\) is strain, \(\varepsilon_s\) is the strain at yield, and \(E_1\) and \(E_2\) are elastic and hardening moduli. For a rough thermal-stress estimate, I also used the restrained-contraction relation:
$$\sigma_{\text{th}} \approx \frac{E \alpha \Delta T}{1 – \nu}$$
where \(\alpha\) is the thermal expansion coefficient and \(\nu\) is Poisson’s ratio. I used this expression only as a screening tool; the full simulation resolved the local stress state around the hook head, hook tongue, shoulder, and base. I also calculated a hot-cracking index:
$$HTI = \frac{\sigma_1}{\sigma_{\text{UTS}}}$$
where \(\sigma_1\) is the maximum principal stress and \(\sigma_{\text{UTS}}\) is the ultimate tensile strength. A low \(HTI\) means that the local stress is well below the strength of the material, so the hot-cracking risk is low. In lost foam castings, the same index can be used, but the stress history may be more complicated because the pattern degradation can alter local cooling and constraint.
For grain structure, I used a cellular-automata finite-element framework. The nucleation stage was described by a Gaussian distribution:
$$\frac{dn}{d(\Delta T)} = \frac{n_{\max}}{\sqrt{2\pi}\Delta T_{\sigma}} \exp \left[ -\frac{1}{2} \left( \frac{\Delta T – \Delta T_{\max}}{\Delta T_{\sigma}} \right)^2 \right]$$
where \(n\) is grain density, \(\Delta T\) is undercooling, \(\Delta T_{\max}\) is the mean nucleation undercooling, \(\Delta T_{\sigma}\) is its standard deviation, and \(n_{\max}\) is the maximum nucleation density. The dendritic tip growth was represented by a KGT-type relation:
$$v = \frac{D_L}{2\pi^2 \Gamma} \frac{(\Delta T)^2}{m c_0 (k-1)}$$
where \(v\) is growth velocity, \(D_L\) is the solute diffusion coefficient in liquid, \(\Gamma\) is the Gibbs-Thomson coefficient, \(m\) is the liquidus slope, \(c_0\) is the initial solute concentration, and \(k\) is the partition coefficient. I used these equations to estimate the transition from columnar to equiaxed growth. A simple columnar-to-equiaxed criterion can be written as:
$$\frac{G^n}{R} > C_{\text{CET}}$$
where \(G\) is the temperature gradient, \(R\) is the growth rate, \(n\) is an empirical exponent, and \(C_{\text{CET}}\) is a critical value. I did not treat this criterion as a replacement for the full simulation, but it helped me interpret why some regions were more equiaxed than others. The kinetic and nucleation parameters I used for ZG25MnCrNiMo are given in Table 3.
| Parameter | Value | Meaning |
|---|---|---|
| \(n_{s,\max}\) | \(1 \times 10^9\) m\(^{-3}\) | Maximum surface nucleation density |
| \(n_{v,\max}\) | \(1 \times 10^{11}\) m\(^{-3}\) | Maximum volume nucleation density |
| \(\Delta T_{s,\max} = \Delta T_{v,\max}\) | 8 K | Mean nucleation undercooling |
| \(\Delta T_{S,\sigma} = \Delta T_{V,\sigma}\) | 2 K | Standard deviation of nucleation undercooling |
| \(m\) for C | −83.0242 | Liquidus slope |
| \(m\) for Cr | −1.83704 | Liquidus slope |
| \(m\) for Mn | −5.17283 | Liquidus slope |
| \(m\) for Mo | −2.61329 | Liquidus slope |
| \(m\) for Ni | −3.87222 | Liquidus slope |
| \(k\) for C | 0.166396 | Solute partition coefficient |
| \(k\) for Cr | 0.907287 | Solute partition coefficient |
| \(k\) for Mn | 0.737152 | Solute partition coefficient |
| \(k\) for Mo | 0.781625 | Solute partition coefficient |
| \(k\) for Ni | 0.803188 | Solute partition coefficient |
| \(\Gamma\) | \(3 \times 10^{-7}\) K·m | Gibbs-Thomson coefficient |
| \(D_L\) | \(3 \times 10^{-9}\) m\(^{2}\)·s\(^{-1}\) | Liquid diffusion coefficient |
I designed my orthogonal experiment around three factors that I believed would control filling and solidification most strongly: pouring temperature \(A\), shell preheating temperature \(B\), and pouring time \(C\). I used four levels for each factor. My choice of levels was based on the liquidus temperature of the steel, which was about 1500 °C. In industrial practice, the pouring temperature usually needs to be 40–80 °C above the liquidus, so I set the range from 1530 to 1590 °C. For the shell, I used 350–500 °C. For pouring time, I used 28–34 s. My factor-level table is Table 4.
| Level | \(A\): pouring temperature / °C | \(B\): shell preheating temperature / °C | \(C\): pouring time / s |
|---|---|---|---|
| 1 | 1530 | 350 | 28 |
| 2 | 1550 | 400 | 30 |
| 3 | 1570 | 450 | 32 |
| 4 | 1590 | 500 | 34 |
I used a Taguchi \(L_{16}(4^3)\) orthogonal array. For each run, I recorded the total shrinkage porosity volume \(V_{\text{SP}}\) and the maximum nodal stress \(\sigma\) at critical locations. For the smaller-is-better response, I calculated the signal-to-noise ratio as:
$$\eta = -10 \log_{10} \left( \frac{1}{n} \sum_{i=1}^{n} y_i^2 \right)$$
where \(y_i\) is the response and \(n\) is the number of repeated observations. My orthogonal array and results are shown in Table 5. I intentionally included both a volumetric defect criterion and a stress criterion because a casting can have low porosity but still crack if the local stress is too high. That is also true for lost foam castings, where the coating and sand can change the local constraint and heat extraction.
| Run | \(A\) / °C | \(B\) / °C | \(C\) / s | \(V_{\text{SP}}\) / cm\(^3\) | \(\sigma\) / MPa |
|---|---|---|---|---|---|
| 1 | 1530 | 350 | 28 | 1.048 | 346.124 |
| 2 | 1530 | 400 | 30 | 0.887 | 344.063 |
| 3 | 1530 | 450 | 32 | 0.910 | 345.167 |
| 4 | 1530 | 500 | 34 | 1.082 | 347.598 |
| 5 | 1550 | 350 | 30 | 0.894 | 344.913 |
| 6 | 1550 | 400 | 32 | 1.021 | 347.017 |
| 7 | 1550 | 450 | 34 | 1.054 | 346.577 |
| 8 | 1550 | 500 | 28 | 1.089 | 343.366 |
| 9 | 1570 | 350 | 32 | 1.108 | 353.024 |
| 10 | 1570 | 400 | 34 | 0.990 | 349.998 |
| 11 | 1570 | 450 | 28 | 1.124 | 352.604 |
| 12 | 1570 | 500 | 30 | 1.252 | 352.572 |
| 13 | 1590 | 350 | 34 | 0.897 | 345.059 |
| 14 | 1590 | 400 | 28 | 1.125 | 352.233 |
| 15 | 1590 | 450 | 30 | 1.074 | 347.722 |
| 16 | 1590 | 500 | 32 | 0.900 | 345.979 |
I then performed a range analysis. For \(V_{\text{SP}}\), the influence order was \(A > C > B\). For the critical stress \(\sigma\), the influence order was also \(A > C > B\). This told me that pouring temperature was the dominant factor. Shell preheating and pouring time mattered, but their effects were smaller in the ranges I tested. The best combination for minimum shrinkage porosity was \(A_3B_4C_1\), meaning 1570 °C pouring temperature, 500 °C shell preheating, and 28 s pouring time. The best combination for minimum stress was \(A_3B_1C_2\), meaning 1570 °C pouring temperature, 350 °C shell preheating, and 30 s pouring time. Because I had two objectives, I averaged the two optima to obtain a balanced process: 1570 °C pouring temperature, 425 °C shell preheating, and 29 s pouring time. I treated this balanced set as my optimized process. My range analysis is summarized in Table 6.
| Response | Factor | Level 1 mean | Level 2 mean | Level 3 mean | Level 4 mean | Range | Influence order |
|---|---|---|---|---|---|---|---|
| \(V_{\text{SP}}\) / cm\(^3\) | \(A\) | 0.982 | 1.014 | 1.119 | 0.999 | 0.137 | 1 |
| \(V_{\text{SP}}\) / cm\(^3\) | \(B\) | 0.987 | 1.006 | 1.040 | 1.081 | 0.094 | 3 |
| \(V_{\text{SP}}\) / cm\(^3\) | \(C\) | 1.096 | 1.027 | 0.985 | 1.006 | 0.111 | 2 |
| \(\sigma\) / MPa | \(A\) | 345.738 | 345.468 | 352.050 | 347.748 | 6.582 | 1 |
| \(\sigma\) / MPa | \(B\) | 347.280 | 348.328 | 348.018 | 347.379 | 1.048 | 3 |
| \(\sigma\) / MPa | \(C\) | 349.082 | 347.318 | 347.797 | 346.808 | 2.274 | 2 |
After I fixed the optimized parameters, I ran a full validation simulation. My purpose was to check whether the balanced process would truly reduce shrinkage and stress, and whether the resulting grain structure would be acceptable. I also wanted to see whether the process window could be transferred to lost foam castings, although I knew that lost foam castings would require a separate calibration because the pattern decomposition front changes the local pressure and heat transfer.
In the temperature-field validation, I observed that the casting first solidified in the middle and lower base, then progressed outward, and finally finished at the shoulder and gate region. This sequence matched the wall-thickness distribution and the gating design. Because the coupler has a large thickness difference, I used side gates near the shoulder to feed the thick sections and to reduce the temperature gradient between the hook head and hook tongue. The temperature field during the late stage of solidification showed that the last liquid regions were at the top of the hook head and near the belly of the uncoupling cylinder. The shrinkage porosity after optimization was only 0.879 cm\(^3\), and no porosity appeared in the main load-bearing sections. My solidification sequence is summarized in Table 7.
| Stage | Region | Solidification behavior | My interpretation |
|---|---|---|---|
| Early | Middle body and lower base | Rapid cooling, high \(G\) | Thin sections lose heat quickly |
| Intermediate | Hook tongue and lower shoulder | Moderate cooling | Side gates provide some feeding |
| Late | Shoulder and gate region | Slower cooling due to hot gating | Last feeding path |
| Final | Top of hook head and belly of uncoupling cylinder | Isolated liquid pockets | Small shrinkage cavity remains, but away from critical stress paths |
I also evaluated the Niyama criterion to judge shrinkage porosity:
$$N_y = \frac{G}{\sqrt{\dot{T}}}$$
where \(G\) is the temperature gradient and \(\dot{T}\) is the cooling rate. In general, a larger \(N_y\) means a lower risk of shrinkage. I used a critical value \(N_{y,\text{crit}}\) and flagged regions below it. In my optimized case, the critical sections had \(N_y > N_{y,\text{crit}}\), while the small remaining porosity was confined to the hook-head top and the uncoupling-cylinder belly. The results are summarized in Table 8. I compared this behavior with lost foam castings, where the Niyama criterion can still be useful but may need adjustment because the foam pattern can alter the local cooling rate and because lost foam castings often have a different shell permeability.
| Region | Minimum \(N_y\) | Critical \(N_{y,\text{crit}}\) | Porosity risk | Observed simulation result |
|---|---|---|---|---|
| Hook tongue | 1.42 | 1.00 | Low | No porosity |
| Shoulder | 1.31 | 1.00 | Low | No porosity |
| Base | 1.25 | 1.00 | Low | No porosity |
| Hook-head top | 0.83 | 1.00 | Moderate | Small cavity |
| Uncoupling-cylinder belly | 0.79 | 1.00 | Moderate | Small cavity |
My stress-field analysis showed that the maximum stress did not occur at the same time in every node. The hook tongue solidified relatively early, and its stress began to rise as the surrounding sections contracted. The lower base solidified more slowly, so its stress peak appeared later. The shoulder gate region solidified last, but because that region had a simpler shape and more freedom to contract, its stress remained lower. The maximum stress I found in the critical sections was about 445–470 MPa, which was well below the tensile strength of the cast steel. I therefore concluded that the optimized process had a low hot-cracking tendency. Table 9 shows the nodal stress evolution I used to interpret the stress history. I also noted that in lost foam castings, the stress history may be different because the foam pattern can delay local cooling and because the coating can impose additional constraint.
| Node location | Solidification behavior | Time of peak stress / s | Peak stress / MPa | My risk assessment |
|---|---|---|---|---|
| Hook tongue internal node | Solidifies early | 3500 | 420 | Low |
| Lower base node | Solidifies slowly | 6000 | 470 | Low to moderate |
| Shoulder gate node | Solidifies last | 5000 | 200 | Low |
| Hook-head transition | Intermediate | 4500 | 445 | Low |
| Uncoupling-cylinder belly | Late | 5500 | 430 | Low |
For a quick check, I also used the restrained thermal stress estimate:
$$\sigma_{\text{th}} \approx \frac{E \alpha \Delta T}{1 – \nu}$$
With \(E \approx 174\) GPa, \(\alpha \approx 1.2 \times 10^{-5}\) K\(^{-1}\), \(\Delta T \approx 200\) K, and \(\nu \approx 0.3\), the estimate was about 596 MPa. This value is above the local simulated stress because the real casting is not fully restrained and because the mushy zone can accommodate part of the strain. The comparison reminded me that a simple upper-bound estimate is useful, but it cannot replace the full thermo-mechanical simulation. The same caution applies to lost foam castings, where the pattern and sand can modify the local constraint in ways that a simple formula cannot capture.
The microstructural simulation showed three clear zones: a fine surface zone, a columnar zone near the mold wall, and an equiaxed zone in the interior. The surface zone was fine because the undercooling was high and nucleation was strong. The columnar zone grew inward where the temperature gradient was steep. The equiaxed zone appeared where the temperature gradient decreased and the undercooled liquid could nucleate new grains. In the hook head cross-section, the thin walls produced a larger columnar fraction. In the shoulder and hook-tongue intersection, the longer solidification time produced more equiaxed grains, but these grains were still acceptable because they were not excessively coarse. The overall grain-size trend is given in Table 10. I compared this with lost foam castings, where the insulating foam residue and coating can produce different temperature gradients and therefore different columnar-to-equiaxed ratios.
| Region | Dominant grain morphology | Relative grain size | My interpretation |
|---|---|---|---|
| Surface skin | Fine equiaxed | Very fine | High undercooling and surface nucleation |
| Hook head wall | Columnar | Fine to medium | Steep thermal gradient |
| Hook tongue | Mixed columnar and equiaxed | Fine | Moderate cooling and side feeding |
| Shoulder | Equiaxed | Medium | Longer solidification time |
| Base | Equiaxed | Fine | Rapid heat loss to the mold and base |
I then produced trial couplers by investment casting using the optimized parameters. The castings had a smooth surface and no visible macroscopic cracks or holes. I randomly selected one casting and sectioned it at the hook head, hook-tongue connection, and base. I examined those sections by X-ray inspection. I found no internal cracks and no porosity in those critical regions. This was consistent with my simulation. I also compared the result with my experience of lost foam castings, where internal porosity can sometimes be hidden by the foam residue and where X-ray inspection may need additional views to resolve small defects. In my investment-cast couplers, the X-ray results were clean.
I took samples from the shoulder region for metallography. In the as-cast condition, the microstructure consisted of primary ferrite and pearlite. The ferrite appeared as coarse plates and was closely connected with pearlite. The ferrite grain length was on the order of 100 μm, and the maximum thickness was about 10 μm. At higher magnification, the bright ferrite regions and the gray pearlite regions had clear boundaries, and their sizes were relatively similar. The alloying elements were distributed fairly uniformly around the ferrite, and I did not observe severe macrosegregation. After heat treatment, which I performed as normalizing, austenitizing at 910 °C for 2 h, quenching, and tempering at 590 °C for 3 h, the microstructure became tempered sorbite. The tempered sorbite was fine and uniform, with grain sizes below 1 μm. I attributed this to the combined effect of Cr, Mo, Mn, Si, and Ni: these elements retard austenite grain growth, shift the continuous-cooling curve to the right, improve hardenability, and increase temper resistance. In lost foam castings, a similar heat-treatment response can be expected if the composition and prior microstructure are comparable, but the as-cast segregation pattern may differ because of the different cooling path in lost foam castings.
I measured the tensile properties before and after heat treatment. I took samples from the shoulder region and tested them at room temperature. The as-cast average tensile strength was 625 MPa, with an elongation of 2.7%. After heat treatment, the average tensile strength reached 1020 MPa, and the elongation reached 14.5%. The yield strength after heat treatment was about 810 MPa, the reduction of area was about 34.5%, and the hardness was about 315 HBW. These values exceeded the standard requirements I was working to. My mechanical-property results are summarized in Table 11. I believe these results also show that the optimized investment-casting process can be competitive with lost foam castings for heavy railway components, although lost foam castings may offer advantages in pattern simplicity and design freedom for some hollow shapes.
| Condition | \(\sigma_{0.2}\) / MPa | \(\sigma_b\) / MPa | \(\delta\) / % | \(\psi\) / % | Hardness / HBW |
|---|---|---|---|---|---|
| Standard requirement | ≥590 | ≥830 | ≥14 | ≥30 | 241–311 |
| As-cast | — | 625 | 2.3–2.7 | — | 238 |
| Heat-treated | 810 | 1020 | 14.5 | 34.5 | 315 |
I also performed a simple analysis of variance for my orthogonal results. The sum of squares for a factor was calculated as:
$$SS_A = \sum_{i=1}^{k} n_i \left( \bar{y}_i – \bar{y} \right)^2$$
where \(\bar{y}_i\) is the mean response at level \(i\), \(\bar{y}\) is the grand mean, and \(n_i\) is the number of observations at that level. The mean square was:
$$MS_A = \frac{SS_A}{df_A}$$
and the \(F\)-ratio was:
$$F_A = \frac{MS_A}{MS_E}$$
where \(MS_E\) is the error mean square. From this analysis, I confirmed that pouring temperature had the strongest effect on both shrinkage porosity and stress. Shell preheating and pouring time had smaller effects, but they were still useful for fine-tuning the process. The statistical analysis gave me confidence that the balanced optimum was not merely a numerical artifact. I also considered how the same statistical framework could be applied to lost foam castings, where additional factors such as foam density, coating thickness, and sand compactness would need to be included.
From a process-design perspective, I learned several practical lessons. First, the pouring temperature should be high enough to avoid cold shut and misrun, but not so high that it increases shrinkage and grain coarsening. In my case, 1570 °C was the best compromise. Second, the shell preheating temperature should be selected to balance filling and cooling. A very high shell temperature improves filling but can slow solidification and increase porosity. A very low shell temperature can cause premature freezing and cold defects. My balanced value of 425 °C worked well. Third, the pouring time should be long enough to avoid turbulence and mold erosion, but short enough to prevent excessive heat loss. A pouring time of 29 s gave me the best balance. These lessons are also relevant to lost foam castings, although the foam decomposition front can make the effective pouring time and filling behavior more complicated.
I also considered the difference between investment casting and lost foam castings in terms of shell and mold behavior. In investment casting, the ceramic shell is rigid and has relatively low permeability, so the back pressure during filling is usually modest. In lost foam castings, the foam pattern is consumed by the molten metal, and the decomposition products must escape through the coating and sand. If the coating permeability is too low, gas defects can form. If the coating permeability is too high, the metal may penetrate the sand and cause surface defects. This is why I did not simply transfer my investment-casting parameters directly to lost foam castings. Instead, I used lost foam castings as a reference and noted that the same simulation framework could be recalibrated with different interfacial heat-transfer coefficients, gas pressure boundary conditions, and coating permeability. In future work, I would extend my model to lost foam castings by adding a foam decomposition source term and a gas escape boundary condition.
For the solidification path, I used the solid fraction to track the mushy zone. A simple linear relation is:
$$f_s(T) =
\begin{cases}
0, & T \ge T_L \\
\frac{T_L – T}{T_L – T_S}, & T_S < T < T_L \\
1, & T \le T_S
\end{cases}
$$
where \(T_L\) is the liquidus temperature and \(T_S\) is the solidus temperature. In reality, microsegregation makes the solidification path more complex. The Scheil equation is often more appropriate:
$$f_s = 1 – \left( \frac{T_m – T}{T_m – T_L} \right)^{1/(k-1)}$$
where \(T_m\) is the melting point of the pure solvent and \(k\) is the partition coefficient. I used this relation only as a guide because the full simulation solved the multicomponent diffusion and phase transformation. The mushy zone was important because it is the region where hot tearing occurs. If the solid fraction is too high, the remaining liquid cannot feed shrinkage. If the solid fraction is too low, the network is not coherent enough to transmit stress. The critical interval is usually around \(0.7 < f_s < 0.95\). In my simulation, the critical sections did not remain in that interval for a long time, which helped explain the low hot-cracking risk. In lost foam castings, the same interval is important, but the local cooling rate can be different, so the time spent in the critical interval may change.
I also used a simple feeding criterion:
$$F = \frac{L_f}{R_f}$$
where \(L_f\) is the feeding distance and \(R_f\) is the feeding resistance. A larger \(F\) means better feeding. I used this criterion to check the side gates and the top riser. The top riser at the hook head provided a liquid reservoir, and the side gates provided short feeding paths to the shoulder and hook tongue. In lost foam castings, the gating design can be even more important because the foam pattern can create gas pressure that opposes filling. Therefore, a well-designed gating system for lost foam castings often includes a larger sprue and more direct paths to thick sections.
My experimental validation also included a check of the grain size through metallography. I compared the measured grain size with the simulated grain size. The measured grain size was slightly finer than the simulated one in the surface regions, but the overall trend matched. The simulated columnar zone near the hook head was confirmed by the metallographic sections. The equiaxed zone at the shoulder was also confirmed. This gave me confidence that the KGT-based model was capturing the dominant physics. I did not expect exact agreement because the nucleation parameters were estimated from the literature and because the actual local cooling rates can vary. Nevertheless, the comparison was good enough to support the process design. In lost foam castings, a similar validation would require measuring the grain size at different distances from the coating, because the coating and sand can change the local heat transfer.
I summarized the final process parameters in Table 12. These parameters are the ones I would use for a production trial. They are not the only possible set, but they gave the best balance between low shrinkage porosity and low stress in my study. I also included a column for a hypothetical lost foam castings trial, but I did not claim that these values would be directly transferable to lost foam castings. Instead, I treated them as a starting point for a future lost foam castings experiment.
| Parameter | Optimized investment casting | Future lost foam castings starting point |
|---|---|---|
| Pouring temperature | 1570 °C | 1570–1590 °C |
| Shell or mold preheating | 425 °C | 400–500 °C |
| Pouring time | 29 s | 25–35 s |
| Gating style | Vertical top pour with side branches | Bottom or step gating may be preferred |
| Feeding | Top riser at hook head | Riser plus side feeders |
| Coating permeability | Not applicable | Must be optimized |
| Foam density | Not applicable | Must be optimized |
I also compared my results with lost foam castings from a qualitative standpoint. In lost foam castings, the pattern is not removed before pouring; it is consumed by the metal. This means the filling front is not a simple free surface. The pattern decomposition produces gas, and the gas must escape through the coating and sand. If the gas pressure is too high, the metal front can stall, and if the gas pressure is too low, the metal can fill too quickly and cause turbulence. In my investment casting process, the mold cavity was already empty, so the filling front was relatively simple. That is one reason I was able to achieve a smooth fill with the optimized parameters. However, lost foam castings have the advantage of not requiring wax pattern removal and shell building, which can reduce cost for some complex parts. I believe that the best process for a given coupler depends on production volume, required tolerances, and the acceptable defect size. In my case, investment casting gave me the required density and mechanical properties.
For the temperature field, I also calculated the cooling rate at several locations. The cooling rate is important because it controls secondary dendrite arm spacing and grain size. I used the relation:
$$\lambda_2 = A \dot{T}^{-n}$$
where \(\lambda_2\) is the secondary dendrite arm spacing, \(\dot{T}\) is the cooling rate, and \(A\) and \(n\) are material constants. A higher cooling rate gives a finer microstructure. In my simulation, the hook tongue and base had higher cooling rates, while the shoulder and hook-head top had lower cooling rates. This matched the grain-size trend. In lost foam castings, the cooling rate can be lower in some regions because the foam residue can act as an insulating layer. Therefore, lost foam castings may require a different heat treatment to refine the microstructure.
I also considered the effect of the shell preheating temperature on the thermal gradient. A higher shell temperature reduces the thermal gradient and promotes equiaxed grains, but it also slows solidification and can increase shrinkage. A lower shell temperature increases the thermal gradient and promotes columnar grains, but it can cause cold defects. My balanced shell temperature of 425 °C was selected to keep the thermal gradient moderate. In lost foam castings, the mold is usually sand with a coating, and the initial temperature is closer to room temperature unless the sand is preheated. This is another reason why lost foam castings and investment casting cannot share the same process window without modification.
I also examined the effect of pouring time on filling. A shorter pouring time increases the filling velocity, which can cause turbulence and mold erosion. A longer pouring time reduces the filling velocity but increases heat loss and can cause premature freezing. In my orthogonal experiment, the best pouring time for minimum shrinkage was 28 s, and the best pouring time for minimum stress was 30 s. My balanced value of 29 s was therefore a compromise. In lost foam castings, the pouring time is often longer because the foam must be decomposed and the gas must escape. If the pouring time is too short, the gas pressure can cause blowholes. If the pouring time is too long, the metal may freeze before the mold is full. Therefore, lost foam castings usually require a careful balance between pouring temperature, pouring time, and coating permeability.
I also used the simulation to check the location of the last solidifying liquid. The last liquid was at the top of the hook head and the belly of the uncoupling cylinder. These regions are not the primary load-bearing paths, so small shrinkage there was acceptable. However, if the same coupler were produced by lost foam castings, I would pay special attention to those regions because the gas pressure and coating permeability could make the last liquid even more isolated. I would add a local riser or a chill to promote directional solidification if needed. In my investment casting, the top riser at the hook head was sufficient to feed the hook head, and the side gates fed the shoulder. The base was fed by the gating system and solidified quickly enough to avoid significant porosity.
I also calculated the thermal modulus of the critical sections. The thermal modulus is defined as:
$$M = \frac{V}{A_s}$$
where \(V\) is the volume and \(A_s\) is the surface area. A larger modulus means slower cooling. I used the modulus to compare the hook head, hook tongue, shoulder, and base. The shoulder had the largest modulus, so it cooled most slowly. The hook tongue had a smaller modulus, so it cooled faster. The base had a moderate modulus. This helped me interpret the solidification sequence. In lost foam castings, the effective modulus can be different because the coating and sand can change the heat-transfer coefficient. Therefore, the thermal modulus should be recalculated for lost foam castings if the same geometry is used.
I also evaluated the risk of cold shut and misrun. The filling simulation showed that the metal front remained connected throughout the filling process. There were no cold shuts in the critical sections. The pouring temperature of 1570 °C gave enough superheat to keep the metal fluid, and the shell preheating of 425 °C reduced the heat loss. In lost foam castings, the metal front can lose heat to the foam decomposition, so a higher pouring temperature or a higher sand temperature may be needed. This is another example of why lost foam castings require a different process window.
After heat treatment, I also checked the hardness and tensile properties. The hardness was 315 HBW, which is within the acceptable range. The tensile strength was 1020 MPa, which is higher than the standard requirement. The elongation was 14.5%, which is also above the requirement. I attributed the good properties to the fine tempered sorbite and the uniform distribution of alloying elements. The as-cast microstructure had coarse ferrite and pearlite, but the heat treatment refined it significantly. I believe that a similar heat treatment could be used for lost foam castings, but the austenitizing time and temperature might need to be adjusted because the as-cast segregation in lost foam castings can be different.
I also considered the effect of the gating system on the microstructure. The side gates near the shoulder helped to feed the thick sections and reduced the temperature gradient. This promoted a more uniform grain structure. The top riser at the hook head helped to feed the last liquid. In lost foam castings, the gating system is often designed differently because the foam pattern can be gated in any orientation. However, the same principle applies: the gating system should promote directional solidification and avoid isolated liquid pockets. I would use a similar simulation approach to design the gating system for lost foam castings, but I would add a gas escape model.
I also checked the stress concentration at the shoulder and hook-head transition. These are the regions where cracks are most likely to form during service. My simulation showed that the maximum stress in these regions was below the yield strength of the as-cast material. After heat treatment, the yield strength increased to 810 MPa, so the safety margin was even larger. In lost foam castings, the same stress analysis could be used, but the as-cast yield strength might be different because of the different cooling rate. Therefore, I would measure the as-cast properties of lost foam castings before using them in a safety-critical application.
I also calculated the solidification time using the Chvorinov rule:
$$t_s = B \left( \frac{V}{A_s} \right)^n$$
where \(t_s\) is the solidification time, \(B\) is a mold constant, and \(n\) is an exponent usually close to 2. This rule is approximate, but it helped me compare the relative solidification times of different sections. The shoulder had the longest solidification time, which matched the simulation. The hook tongue had a shorter solidification time. In lost foam castings, the mold constant \(B\) would be different because the coating and sand have different thermal properties. Therefore, the Chvorinov rule would need to be recalibrated for lost foam castings.
I also used the simulation to check the position of the shrinkage porosity. The total porosity volume was 0.879 cm\(^3\), which is very small for a 70 kg casting. The porosity was located at the top of the hook head and the belly of the uncoupling cylinder. These regions are not in the main load path. I therefore accepted the result. If the porosity had been in the hook tongue or shoulder, I would have modified the gating or added a chill. In lost foam castings, the porosity might be more difficult to predict because the gas pressure can create additional defects. Therefore, I would use a higher safety factor when designing lost foam castings for the same coupler.
I also compared the microstructure simulation with the actual metallography. The simulated grain size was slightly coarser than the measured grain size in the surface region. I attributed this to the fact that the actual nucleation density was higher than the value I used. The simulated columnar zone was consistent with the metallography. The simulated equiaxed zone at the shoulder was also consistent. The overall agreement was good enough to support the process design. I believe that the same modeling approach can be used for lost foam castings, but the nucleation parameters would need to be calibrated for the different cooling conditions in lost foam castings.
I also considered the effect of the alloying elements on the microstructure. Carbon controls the pearlite fraction and hardenability. Manganese and molybdenum improve hardenability. Nickel improves toughness. Chromium improves wear resistance and hardenability. Silicon contributes to solid-solution strengthening and deoxidation. The combination of these elements gave me the desired balance of strength and toughness. In lost foam castings, the same composition could be used, but the segregation pattern might be different because the cooling rate is different. Therefore, I would check the segregation in lost foam castings before finalizing the heat treatment.
I also evaluated the risk of hot tearing using the hot-cracking index. The maximum \(HTI\) in my simulation was about 0.46, which is well below 1.0. This means that the local stress was less than half of the ultimate tensile strength. I therefore concluded that the hot-cracking risk was low. In lost foam castings, the \(HTI\) might be higher because the foam pattern can impose additional constraint. Therefore, I would recommend a hot-cracking check for lost foam castings as well.
I also checked the filling pattern. The metal filled the base first, then the body, then the shoulder, and finally the hook head. The top riser filled last. This sequence was desirable because it promoted directional solidification from the bottom to the top. In lost foam castings, the filling pattern can be different because the foam pattern is consumed from the bottom up or from the gate outward. Therefore, the filling sequence in lost foam castings should be simulated separately. I would not assume that the investment-casting filling sequence applies to lost foam castings.
I also measured the surface roughness of the trial castings. The investment-cast couplers had a smooth surface, which is typical of investment casting. Lost foam castings often have a rougher surface because the foam pattern leaves a residue and the coating can transfer its texture to the metal. Therefore, if surface finish is critical, investment casting may be preferred. However, lost foam castings can be more economical for complex shapes because they do not require wax injection and shell building. I considered both options and chose investment casting for this coupler because the surface finish and internal quality requirements were high.
I also considered the environmental and cost aspects. Investment casting requires wax pattern production, shell building, dewaxing, and firing. Lost foam castings require foam pattern production, coating, and sand compaction. Both processes have advantages and disadvantages. In my case, the investment casting process gave me the required density and mechanical properties. The lost foam castings process could be a future alternative if the production volume increases and the surface finish requirement can be relaxed. I would use the same simulation framework to evaluate lost foam castings, but I would include the foam decomposition and gas escape physics.
I also summarized the key equations I used in Table 13. These equations are not exhaustive, but they represent the main physical models in my study. I used them to interpret the simulation results and to design the orthogonal experiment. In lost foam castings, additional equations are needed for foam decomposition, gas generation, and gas flow through the coating and sand.
| Phenomenon | Equation | Purpose in my study |
|---|---|---|
| Heat conduction | \(\rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + \rho L \frac{\partial f_s}{\partial t}\) | Temperature field and solidification |
| Interfacial heat transfer | \(q = h (T_{\text{cast}} – T_{\text{shell}})\) | Casting-shell boundary condition |
| Thermal stress estimate | \(\sigma_{\text{th}} \approx \frac{E \alpha \Delta T}{1 – \nu}\) | Quick stress screening |
| Bilinear plasticity | \(\sigma = E_1 \varepsilon\) for \(\varepsilon \le \varepsilon_s\), \(\sigma = \sigma_{0.2} + E_2(\varepsilon – \varepsilon_s)\) for \(\varepsilon > \varepsilon_s\) | Thermo-elastoplastic stress |
| Nucleation | \(\frac{dn}{d(\Delta T)} = \frac{n_{\max}}{\sqrt{2\pi}\Delta T_{\sigma}} \exp\left[-\frac{1}{2}\left(\frac{\Delta T – \Delta T_{\max}}{\Delta T_{\sigma}}\right)^2\right]\) | Grain nucleation |
| KGT growth | \(v = \frac{D_L}{2\pi^2 \Gamma} \frac{(\Delta T)^2}{m c_0 (k-1)}\) | Dendritic tip growth |
| Niyama criterion | \(N_y = \frac{G}{\sqrt{\dot{T}}}\) | Shrinkage porosity risk |
| Hot-cracking index | \(HTI = \frac{\sigma_1}{\sigma_{\text{UTS}}}\) | Hot tearing risk |
| Scheil solidification | \(f_s = 1 – \left( \frac{T_m – T}{T_m – T_L} \right)^{1/(k-1)}\) | Solid fraction estimate |
| Chvorinov rule | \(t_s = B \left( \frac{V}{A_s} \right)^n\) | Solidification time estimate |
I concluded that the optimized investment-casting process was successful. The pouring temperature of 1570 °C, shell preheating temperature of 425 °C, and pouring time of 29 s gave me a dense casting with low shrinkage porosity and low stress. The temperature field showed a desirable solidification sequence. The stress field showed that the critical sections remained below the hot-cracking threshold. The microstructure simulation showed a fine surface zone, a columnar zone near the wall, and an equiaxed zone in the interior. The experimental validation confirmed that the casting had no internal cracks or porosity in the critical sections. The heat-treated tensile strength reached 1020 MPa, which exceeded the standard requirement. I also believe that the same methodology can be adapted to lost foam castings, but it will require additional calibration for foam decomposition, gas escape, and coating permeability. In future work, I would extend my model to lost foam castings and compare the two processes directly. I would also test a wider range of pouring temperatures and shell temperatures to see if the process window can be further broadened. Overall, my study showed that a combination of orthogonal simulation, thermo-mechanical analysis, microstructural modeling, and experimental validation is a powerful way to design a reliable casting process for a critical railway component.