Casting is a fundamental process in the manufacturing industry, and the vast majority of components in a horizontal split pump are produced by casting. The pump body is a typical complex casting that must withstand harsh service environments, including corrosive media, high pressure, and significant temperature variations. The duplex stainless steel grade 00Cr25Ni6Mo2N was selected for this pump body due to its excellent combination of mechanical strength and corrosion resistance. However, this material presents considerable challenges in sand casting because of its wide solidification range, strong tendency to form shrinkage defects, and sensitivity to brittle phase precipitation. The present study focuses on developing and optimizing a robust sand casting process for this difficult component, using advanced numerical modeling and statistical design methods.
The work is organized in several stages. First, the structural and metallurgical characteristics of the pump body are analyzed. Second, two initial sand casting layout alternatives are designed and evaluated through filling and solidification simulations. Third, the chemical composition is optimized using D-optimal mixture design to simultaneously enhance yield strength and pitting corrosion resistance. Fourth, the selected casting layout is refined by adding risers, chills, and modifying the gating system. Fifth, pouring parameters are optimized via orthogonal experiments. Finally, a simple phase ratio analysis method is developed for quality control. Throughout the investigation, emphasis is placed on producing high-quality sand casting parts with minimal shrinkage porosity and good internal integrity.
1. Introduction
Duplex stainless steels have evolved through four generations since their invention in France about 80 years ago. They exhibit a two-phase microstructure consisting of austenite and ferrite, usually with ferrite content between 30% and 50%. The combination of high chromium, low nickel, and nitrogen alloying provides excellent resistance to chloride stress corrosion cracking and pitting, as well as yield strengths roughly twice those of conventional austenitic stainless steels. These properties make duplex stainless steels particularly attractive for pumps, valves, and other equipment used in the petrochemical, marine, and nuclear industries.
In modern petroleum processing plants, horizontal split pumps are widely employed as transmission equipment. The pump body is a pressure-containing component that also converts kinetic energy into static pressure. Defects such as shrinkage porosity, gas holes, and inclusions not only lower the yield rate but also reduce the service life of the entire pump assembly. The specific pump body investigated here is a large sand casting part with overall dimensions of 1660 mm × 1100 mm × 850 mm and a finished weight of about 1400 kg. Its geometry is complex, with two volute chambers, multiple flanges, and integral support legs. Wall thicknesses vary from only 16 mm to as much as 89 mm, creating significant thermal nodes and a high risk of shrinkage defects. The specified material is grade 00Cr25Ni6Mo2N, whose nominal composition ranges are given in Table 1.
| Element | C | Si | Mn | P | S | Cr | Ni | Mo | N |
|---|---|---|---|---|---|---|---|---|---|
| Min | — | — | — | — | — | 25.0 | 4.5 | 1.2 | 0.08 |
| Max | 0.05 | 1.00 | 2.00 | 0.035 | 0.030 | 28.0 | 6.5 | 2.0 | 0.20 |
The as-cast material requirement for the pump body includes a tensile strength of 800–880 MPa, a yield strength of at least 550 MPa, and an elongation of 20% or higher. In addition, the component must be water-tight under hydrostatic testing. Attaining such demanding properties is impossible without controlling solidification shrinkage, micro-porosity, and phase balance. These objectives motivated the research described in the following sections.
2. Casting Process Design and Numerical Simulation
2.1 Numerical simulation framework
Cast filling and solidification encompass complex transport phenomena. The governing equations for mass, momentum, and energy conservation are solved numerically by the commercial software AnyCasting. The continuity equation, the Navier–Stokes equations, and the energy equation are expressed as follows:
$$
\frac{\partial \rho}{\partial t} + \frac{\partial (\rho u)}{\partial x} + \frac{\partial (\rho v)}{\partial y} + \frac{\partial (\rho w)}{\partial z} = 0
\tag{1}
$$
$$
\rho \left( \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + w \frac{\partial u}{\partial z} \right) = -\frac{\partial p}{\partial x} + \rho g_x + \mu \nabla^2 u
\tag{2}
$$
$$
\rho C_p \frac{\partial T}{\partial t} = k \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + Q
\tag{3}
$$
where \(u, v, w\) are velocity components, \(\rho\) is density, \(p\) is pressure, \(\mu\) is dynamic viscosity, \(C_p\) is specific heat, \(k\) is thermal conductivity, and \(Q\) is the heat generation term associated with phase change. Solidification shrinkage is predicted using the Niyama criterion and the residual melt modulus (RMM) method. The Niyama parameter is defined as
$$
N = \frac{G}{\sqrt{R}}
\tag{4}
$$
where \(G\) is the temperature gradient and \(R\) is the cooling rate. A value of \(N\) below a certain threshold indicates a high probability of micro-shrinkage porosity. The residual melt modulus is given by
$$
M_r = \frac{V_r}{A_r}
\tag{5}
$$
where \(V_r\) is the volume of isolated molten metal and \(A_r\) is its surface area. Larger \(M_r\) suggests a greater tendency to form macro-shrinkage cavities.
The three-dimensional model of the pump body was created using UG NX. Two alternative sand casting layouts were designed, each consisting of a horizontal split line through the center of the pump body, with the split face vertical to allow natural placement of cores. The mold was made of furan resin-bonded self-hardening sand, while chromium ore sand was used for the flow path cores to improve dimensional accuracy. The pouring system was constructed from ceramic tubes to withstand the high pouring temperature of duplex stainless steel.
Scheme 1 employed a sprue located at the parting line with a middle side-gating arrangement. Scheme 2 used a step gating system located at the inlet and outlet flanges. The risers were designed according to corporate standards. Scheme 1 included seven runner-type blind risers and four pads. Scheme 2 initially omitted the risers on the flanges, relying on the gating system for feeding. Both schemes were meshed with 1.5 million finite difference cells, and the same material properties and boundary conditions were applied. The pouring temperature was set to 1560°C, and the mold initial temperature was 25°C. The heat transfer coefficient between the alloy and sand was defined as a function of temperature, as shown in the simulation setup.
The simulation produced detailed results for the filling pattern, final temperature field, and solidification sequence. Figure below depicts a representative sand casting part requiring careful gating design.
2.2 Filling behavior comparison
The total filling time was 28 s for Scheme 1 and 27 s for Scheme 2. In Scheme 1, because the gate was placed in the middle, the early filling stage showed a strong turbulent jet that impacted the core surfaces, increasing the risk of sand erosion and oxide entrapment. In Scheme 2, although the step gating was intended to feed sequentially from bottom to top, the simulation revealed a noticeable “mixing” phenomenon in the initial stage, meaning that the upper ingate began to deliver metal before the melt level reached that height. This was caused by the insufficient height difference between the two ingates, resulting in an upper-layer static pressure that was too high. Nevertheless, the overall filling in Scheme 2 was smoother, with less turbulence and better distribution of temperature. The final temperature field of Scheme 2 exhibited a more uniform gradient, with the upper part slightly hotter than the lower part, which is favorable for directional solidification.
2.3 Solidification and shrinkage defect prediction
Both schemes showed a solidification sequence starting from the thin walls and the gating system, with the heavy sections and the top of the casting solidifying last. However, in Scheme 2, the flanges had no dedicated risers, and the ingates solidified quickly, so the gating system could not compensate for the solidification shrinkage of the flanges. This resulted in a high probability of shrinkage porosity in those areas. Based on the Niyama criterion and the RMM method, the quantitative defect analysis was performed by counting the number of volume elements whose defect parameter exceeded 0.9. The results are summarized in Table 2.
| Defect indicator | Scheme 1 | Scheme 2 |
|---|---|---|
| Total elements considered | 95,700 | 99,753 |
| Elements with Niyama parameter > 0.9 | 262 | 267 |
| Percentage based on Niyama | 0.2738% | 0.2677% |
| Elements with RMM > 0.9 | 279 | 247 |
| Percentage based on RMM | 0.2915% | 0.2476% |
Although the difference was not large, Scheme 2 showed a lower risk of macro-shrinkage and also demonstrated better filling performance. Therefore, Scheme 2 was chosen as the baseline for further improvement.
3. Chemical Composition Optimization Using D-Optimal Mixture Design
The mechanical and corrosion properties of duplex stainless steel strongly depend on the precise balance of alloying elements. A systematic optimization of the chemical composition was carried out using D-optimal mixture design, which is particularly suitable when the sum of all components must equal 100% and each component has upper and lower limits. The nine minor elements—C, Si, Mn, P, S, Cr, Ni, Mo, and N—were treated as mixture variables, while iron was the remainder. The response variables were yield strength (\(\sigma_{0.2}\)) and pitting resistance equivalent number (PREN), defined as
$$
\mathrm{PREN} = \mathrm{Cr} + 3.3\mathrm{Mo} + 16\mathrm{N}
\tag{6}
$$
The constrained ranges were exactly those listed in Table 1. A quadratic Scheffe polynomial model was assumed, and 55 experimental points were generated by the D-optimal algorithm in Design-Expert software. To obtain the responses without consuming expensive foundry heats, the JMatPro material property simulation package was used. For each composition, the PREN value was computed directly, and the yield strength was extracted from the simulated Stress–Grain Size curve at a grain size of 2 µm after 950°C solution treatment, a condition representative of the actual casting. The full experimental plan and the calculated responses are given in Table 3 (a subset of the 55 runs is displayed for brevity).
| Run | C (%) | Si (%) | Mn (%) | P (%) | S (%) | Cr (%) | Ni (%) | Mo (%) | N (%) | PREN | \(\sigma_{0.2}\) (MPa) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.03 | 1.000 | 0.000 | 0.035 | 0.000 | 28.0 | 6.178 | 1.678 | 0.080 | 34.79 | 735 |
| 2 | 0.05 | 1.000 | 0.958 | 0.035 | 0.000 | 28.0 | 5.458 | 1.300 | 0.200 | 35.49 | 718 |
| 3 | 0.05 | 1.000 | 2.000 | 0.035 | 0.000 | 28.0 | 4.500 | 1.335 | 0.080 | 33.69 | 776 |
| 4 | 0.04 | 0.225 | 0.000 | 0.035 | 0.000 | 28.0 | 6.500 | 2.000 | 0.200 | 37.80 | 701 |
| 5 | 0.05 | 0.000 | 2.000 | 0.035 | 0.015 | 26.2 | 6.500 | 2.000 | 0.200 | 36.00 | 660 |
| 6 | 0.03 | 0.343 | 0.000 | 0.018 | 0.030 | 28.0 | 6.500 | 2.000 | 0.080 | 35.88 | 715 |
| 7 | 0.05 | 1.000 | 2.000 | 0.035 | 0.000 | 25.335 | 6.500 | 2.000 | 0.080 | 33.22 | 649 |
| 8 | 0.03 | 1.000 | 1.953 | 0.035 | 0.030 | 27.953 | 4.500 | 1.300 | 0.200 | 35.44 | 762 |
| 9 | 0.05 | 1.000 | 1.250 | 0.000 | 0.000 | 28.0 | 4.500 | 2.000 | 0.200 | 37.80 | 794 |
| 10 | 0.05 | 0.000 | 0.600 | 0.000 | 0.000 | 28.0 | 6.500 | 1.650 | 0.200 | 36.65 | 698 |
| 11 | 0.05 | 1.000 | 2.000 | 0.035 | 0.000 | 25.335 | 6.500 | 2.000 | 0.080 | 33.22 | 649 |
| 12 | 0.03 | 0.000 | 2.000 | 0.035 | 0.030 | 26.905 | 6.500 | 1.300 | 0.200 | 34.40 | 659 |
| 13 | 0.05 | 0.000 | 0.335 | 0.035 | 0.000 | 28.0 | 6.500 | 2.000 | 0.080 | 35.88 | 700 |
| 14 | 0.05 | 1.000 | 2.000 | 0.000 | 0.000 | 25.250 | 6.500 | 2.000 | 0.200 | 35.05 | 624 |
| 15 | 0.03 | 1.000 | 1.000 | 0.035 | 0.000 | 26.935 | 6.500 | 1.300 | 0.200 | 34.42 | 654 |
| 16 | 0.05 | 1.000 | 2.000 | 0.035 | 0.030 | 27.185 | 4.500 | 2.000 | 0.200 | 36.99 | 767 |
| 17 | 0.05 | 0.355 | 2.000 | 0.000 | 0.015 | 28.0 | 4.500 | 2.000 | 0.080 | 35.88 | 778 |
| 18 | 0.03 | 1.000 | 0.000 | 0.000 | 0.030 | 28.0 | 6.090 | 1.650 | 0.200 | 36.65 | 723 |
| 19 | 0.05 | 0.000 | 2.000 | 0.000 | 0.030 | 28.0 | 4.720 | 2.000 | 0.200 | 37.80 | 759 |
| 20 | 0.03 | 1.000 | 2.000 | 0.000 | 0.030 | 27.300 | 4.500 | 2.000 | 0.140 | 36.14 | 787 |
| 21 | 0.05 | 0.000 | 2.000 | 0.000 | 0.000 | 27.070 | 6.500 | 1.300 | 0.080 | 32.64 | 644 |
| 22 | 0.05 | 1.000 | 2.000 | 0.018 | 0.030 | 28.0 | 4.523 | 1.300 | 0.080 | 33.57 | 775 |
| 23 | 0.04 | 1.000 | 0.000 | 0.000 | 0.000 | 28.0 | 6.500 | 1.380 | 0.080 | 33.83 | 707 |
| 24 | 0.03 | 1.000 | 1.000 | 0.000 | 0.030 | 26.360 | 6.500 | 2.000 | 0.080 | 34.24 | 691 |
| 25 | 0.05 | 1.000 | 2.000 | 0.035 | 0.030 | 25.885 | 6.500 | 1.300 | 0.200 | 33.38 | 614 |
The regression models for PREN and yield strength were fitted using the Design-Expert software. Both models were highly significant, with \(p < 0.0001\). The coefficient of determination \(R^2\) was 1.000 for PREN and 0.980 (adjusted) for yield strength. The resulting quadratic Scheffe polynomial equations are given below (in terms of actual component proportions):
$$
\begin{aligned}
\mathrm{PREN} = &\; -503.39\,C + 37.81\,Si + 37.80\,Mn + 22.23\,P + 36.84\,S + 34.99\,Cr \\
& + 37.81\,Ni + 28.73\,Mo + 0.93\,N + 545.92\,C\cdot Si + 543.45\,C\cdot Mn \\
& + 671.36\,C\cdot P + 488.05\,C\cdot S + 545.12\,C\cdot Cr + 544.21\,C\cdot Ni \\
& + 545.02\,C\cdot Mo + 536.92\,C\cdot N + 16.48\,Si\cdot P + 1.73\,Si\cdot S \\
& – 0.050\,Si\cdot Cr – 0.036\,Si\cdot Ni – 0.26\,Si\cdot Mo – 8.69\,Si\cdot N \\
& + 16.26\,Mn\cdot P – 0.27\,Mn\cdot Mo – 8.67\,Mn\cdot N + 15.38\,P\cdot Cr \\
& + 15.41\,P\cdot Ni + 16.24\,P\cdot Mo + 1.23\,S\cdot Cr + 1.23\,S\cdot Ni \\
& – 0.28\,Cr\cdot Mo – 8.64\,Cr\cdot N – 0.30\,Ni\cdot Mo – 8.44\,Ni\cdot N \\
& – 9.20\,Mo\cdot N
\end{aligned}
\tag{7}
$$
The yield strength equation is:
$$
\begin{aligned}
\sigma_{0.2} = &\; -15253.67\,C + 761.36\,Si + 674.20\,Mn + 4647.83\,P – 341900\,S \\
& + 599.4\,Cr + 788.42\,Ni + 866.44\,Mo + 2112.17\,N + 21287.68\,C\cdot Mn \\
& + 508100\,C\cdot S + 20529.46\,C\cdot Cr + 19547.44\,C\cdot Ni + 8130.54\,C\cdot Mo \\
& – 8653.40\,Si\cdot P + 339500\,Si\cdot S – 1085.07\,Si\cdot N + 348900\,Mn\cdot S \\
& – 53.84\,Mn\cdot Cr – 374.99\,Mn\cdot Mo – 742.12\,Mn\cdot N + 491300\,P\cdot S \\
& – 4405.36\,P\cdot Cr – 4088.34\,P\cdot Ni – 14847.71\,P\cdot Mo – 36421.50\,P\cdot N \\
& + 347100\,S\cdot Cr + 347200\,S\cdot Ni + 343300\,S\cdot Mo + 295900\,S\cdot N \\
& + 112.08\,Cr\cdot Ni – 259.81\,Cr\cdot Mo – 236.84\,Ni\cdot Mo – 690.90\,Ni\cdot N
\end{aligned}
\tag{8}
$$
Analysis of the coefficients revealed that carbon content had the strongest single-element influence on PREN, while sulfur, carbon, and phosphorus were the most important variables affecting yield strength. Sulfur was particularly detrimental to mechanical properties, so it was kept as low as possible. To balance the two competing objectives, the optimization criterion was set to maximize PREN while maintaining yield strength above 700 MPa. Additionally, since P and S cannot be completely eliminated in industrial melting, their lower bounds were constrained to 0.01%. The optimized composition is listed in Table 4.
| Element | C | Si | Mn | P | S | Cr | Ni | Mo | N |
|---|---|---|---|---|---|---|---|---|---|
| Mass fraction (%) | 0.040 | 1.00 | 1.00 | 0.010 | 0.025 | 28.00 | 4.70 | 2.00 | 0.20 |
With this composition, the simulated PREN was 37.8 and the yield strength was 790 MPa, comfortably exceeding the specification limit of 550 MPa.
Using this optimized composition, the melting and charging calculation was performed by solving a set of linear mass balance equations. The charge consisted of return scrap, pure iron, low-carbon stainless steel scrap, and various ferroalloys. The equation system can be written in matrix form as:
$$
\mathbf{A} \mathbf{x} = \mathbf{b}
\tag{9}
$$
where \(\mathbf{A}\) is the matrix of element concentrations in each charge material, \(\mathbf{x}\) is the vector of unknown weights of each charge component, and \(\mathbf{b}\) is the vector representing the desired total amount of each element plus the total batch weight. The computation was carried out in a spreadsheet environment using iterative calculation. For a 500 kg batch, the actual charge weights were determined, and the resulting sulfur and phosphorus contents were verified to be within acceptable limits.
4. Process Improvement and Simulation Verification
4.1 Riser and pad modifications
The selected Scheme 2 still had several weaknesses that needed correction. First, the inlet and outlet flanges lacked dedicated risers, leading to predicted shrinkage porosity in those thick sections. To remedy this, two additional waisted risers were added on the flanges. Their dimensions were 400 × 100 × 300 mm and 320 × 100 × 300 mm with a radius of 50 mm. Second, the original top risers were not sufficiently effective for the heavy central part of the casting, especially around the shaft bore and the upper flange. Therefore, the three upper risers were replaced with ceramic fiber insulating riser sleeves. The insulating material reduced the rate of heat loss from the riser, prolonging the liquid state of the molten metal and improving feeding efficiency. The cavity dimensions remained unchanged, and the sleeve thickness was 40 mm.
4.2 Chill placement
Several T-shaped and cross-shaped thermal nodes existed in the lower middle portion of the casting, far from the risers. These locations were identified as zones with a high residual melt modulus, making them prone to shrinkage porosity and hot tears. To accelerate local solidification and reduce the local thermal peak, a total of 24 chills were placed at these hot spots. The chills were made of a steel material and were applied directly against the cavity in the mold with a thin layer of coating. Their shapes and sizes were individually matched to the local geometry, including several conformal chills that followed curved surfaces. Table 5 summarizes the dimensions of the chills, and the locations were selected based on the simulation results.
| Chill number | Dimensions (mm) | Remarks |
|---|---|---|
| 1 | 80 × 60 × 20 | Rectangular plate |
| 2–4 | 100 × 50 × 20 | Rectangular plate |
| 5–7 | 120 × 40 × 20 | Rectangular plate |
| 8–14 | 80 × 40 × 20 | Rectangular plate |
| 15–16 | 60 × 60 × 15 | Rectangular plate |
| 17 | R50 circular arc, thickness 20 | Conformal chill |
| 18–19 | 100 × 50 × 15 | Rectangular plate |
| 20–23 | Conformal shapes | For curved joint regions |
4.3 Gating system modification
The original step gating showed an undesirable initial surge through the upper ingate. To solve this problem, the upper ingate was moved to a higher position near the two added risers, thereby increasing the vertical distance between the lower and upper ingates to 700 mm. At the same time, the upper ingate cross-section was enlarged to Φ45 mm to reduce the velocity of the molten metal. The gating layout was also changed to a “reverse sprue” design: the molten metal first passed through a primary sprue of Φ50 mm, then entered a wider reverse sprue of Φ65 mm. Because the reverse sprue was not completely filled, the flow was forced to enter the cavity through the lower ingate first, and then, as the metal level rose, the upper ingate took over. This provided the desirable characteristics of step gating while preventing premature delivery. The effective pouring head was 1400 mm.
4.4 Numerical verification of the improved process
Because the optimized composition changed the thermophysical properties of the alloy, the material data used in the simulation were updated accordingly. The liquidus temperature increased to 1474°C and the solidus temperature decreased to 1333°C. Density, thermal conductivity, and specific heat were defined as temperature-dependent curves based on JMatPro outputs. The updated material data table is presented in Table 6.
| Temperature (°C) | Density (g/cm³) | Thermal conductivity (W/(m·K)) | Specific heat (J/(g·K)) |
|---|---|---|---|
| 200 | 7.62 | 40.83 | 0.58 |
| 400 | 7.56 | 25.75 | — |
| 480 | — | — | 0.97 |
| 600 | 7.54 | 20.65 | 0.92 |
| 800 | 7.48 | 21.88 | 0.66 |
| 1000 | 7.32 | 29.33 | 0.72 |
| 1200 | 7.23 | 31.76 | 0.77 |
| 1300 | — | — | 0.85 |
| 1400 | 7.13 | 33.92 | — |
| 1600 | 6.86 | 32.46 | 0.83 |
The improved process was simulated again. The filling analysis confirmed that the “mixing” phenomenon was eliminated. During the initial 15% and 30% filling stages, the flow was smooth and free of turbulent jets. The final temperature field exhibited a favorable gradient, with the highest temperatures located near the top risers. The solidification sequence followed the intended pattern: thin sections solidified first, heavy sections later, and the risers remained liquid for a sufficiently long time to feed the casting. The residual melt modulus defect percentage decreased from 0.2476% in the original Scheme 2 to 0.2386% in the improved process. The maximum residual melt modulus was found inside the riser rather than in the casting body, confirming that shrinkage porosity had been shifted to the risers. The casting yield was 60.8%, which is acceptable for a medium-size stainless steel casting.
5. Optimization of Pouring Parameters
Pouring temperature, pouring time, and mold initial temperature are important process variables that affect the filling and solidification behavior. To determine the optimal combination of these parameters, an orthogonal experimental design was adopted. A \(L_{16}(4^5)\) orthogonal array was chosen, with three factors: pouring temperature (A), pouring time (B), and mold temperature (C). The fourth and fifth columns were left empty as dummy factors to estimate random error. Each factor was tested at four levels, as shown in Table 7.
| Level | A: Pouring temperature (°C) | B: Pouring time (s) | C: Mold temperature (°C) |
|---|---|---|---|
| 1 | 1520 | 20 | 15 |
| 2 | 1540 | 35 | 25 |
| 3 | 1560 | 50 | 35 |
| 4 | 1580 | 65 | 45 |
Sixteen numerical simulation runs were carried out according to the orthogonal array. The response variable was the maximum residual melt modulus (\(M_r\)) in the casting body. A smaller \(M_r\) signifies less shrinkage tendency. The results are provided in Table 8.
| Run | A | B | C | Dummy 1 | Dummy 2 | \(M_r\) (mm) |
|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 44.921 |
| 2 | 1 | 2 | 2 | 2 | 2 | 44.520 |
| 3 | 1 | 3 | 3 | 3 | 3 | 44.232 |
| 4 | 1 | 4 | 4 | 4 | 4 | 44.122 |
| 5 | 2 | 1 | 2 | 3 | 4 | 45.334 |
| 6 | 2 | 2 | 1 | 4 | 3 | 44.931 |
| 7 | 2 | 3 | 4 | 1 | 2 | 44.767 |
| 8 | 2 | 4 | 3 | 2 | 1 | 44.800 |
| 9 | 3 | 1 | 3 | 4 | 2 | 45.906 |
| 10 | 3 | 2 | 4 | 3 | 1 | 45.480 |
| 11 | 3 | 3 | 1 | 2 | 4 | 45.085 |
| 12 | 3 | 4 | 2 | 1 | 3 | 45.232 |
| 13 | 4 | 1 | 4 | 2 | 3 | 45.503 |
| 14 | 4 | 2 | 3 | 1 | 4 | 44.643 |
| 15 | 4 | 3 | 2 | 4 | 1 | 45.625 |
| 16 | 4 | 4 | 1 | 3 | 2 | 45.453 |
Analysis of variance was performed to evaluate the significance of each factor. The sums of squares and mean squares were calculated according to standard orthogonal design formulas. The results are shown in Table 9.
| Source | Degrees of freedom | Sum of squares | Mean square | F ratio |
|---|---|---|---|---|
| Pouring temperature (A) | 3 | 2.303 | 0.767 | 2.970 |
| Pouring time (B) | 3 | 0.778 | 0.259 | 1.003 |
| Mold temperature (C) | 3 | 0.193 | 0.064 | 0.249 |
| Error | 15 | 3.880 | 0.259 | — |
The F ratio for pouring temperature was the largest, indicating that it had the most significant effect on shrinkage formation. Pouring time was secondary, while mold temperature had almost no significant influence. The range analysis in Table 10 shows the same ranking: \(R_A > R_B > R_C\). The optimal level for each factor was A1, B4, and C3, i.e., a pouring temperature of 1520°C, a pouring time of 65 s, and a mold temperature of 35°C. The analysis of the influence trend showed that as pouring temperature increased, \(M_r\) first increased then decreased slightly; as pouring time increased, \(M_r\) generally decreased; and as mold temperature increased, \(M_r\) initially increased and then decreased, but the effect was negligible.
| Statistic | A | B | C | Dummy 1 | Dummy 2 |
|---|---|---|---|---|---|
| \(\bar{k}_1\) | 44.449 | 45.416 | 45.098 | 44.891 | 45.206 |
| \(\bar{k}_2\) | 44.958 | 44.893 | 45.178 | 44.977 | 45.162 |
| \(\bar{k}_3\) | 45.426 | 44.927 | 44.895 | 45.125 | 44.974 |
| \(\bar{k}_4\) | 45.306 | 44.902 | 44.968 | 45.167 | 44.796 |
| Range \(R\) | 0.977 | 0.523 | 0.283 | 0.255 | 0.041 |
A verification simulation using the optimal combination A1B4C3 produced a maximum residual melt modulus of 44.122 mm, equal to the best result among the orthogonal runs. The shrinkage porosity was confined to the riser, and the casting body remained sound. Therefore, the final recommended pouring parameters for the pump body are: pouring temperature 1515–1525°C, pouring time 63–67 s, and mold temperature around 35°C.
6. A Simple Phase Ratio Analysis Method for Duplex Stainless Steel
Quality control of duplex stainless steel castings requires monitoring the ferrite/austenite phase balance. Traditional manual point counting methods are slow, laborious, and subject to human error. Industrial image analyzers are accurate but expensive. To offer a low-cost, efficient alternative, a MATLAB-based image processing method was developed. The approach is analogous to automatic point counting on a digital micrograph, but the “grid” consists of the pixel array. By converting the original grayscale image into a black-and-white binary image, every pixel is classified as either austenite (dark) or ferrite (light). The phase fraction is then calculated as the ratio of the number of pixels of the phase of interest to the total pixel count.
The key step is choosing an appropriate threshold for binarization. The Otsu method, also called the maximum inter-class variance method, was used to determine the threshold adaptively. The method maximizes the variance between the two classes of pixels. Let \(w_0\) and \(w_1\) be the proportions of dark and bright pixels, and \(\mu_0\) and \(\mu_1\) their mean gray levels. The overall mean gray level is
$$
u = w_0 \mu_0 + w_1 \mu_1
\tag{10}
$$
and the between-class variance is
$$
g = w_0 (\mu_0 – u)^2 + w_1 (\mu_1 – u)^2
\tag{11}
$$
The threshold that maximizes \(g\) gives the best separation between the two phases. In practice, because of uneven illumination or staining, the Otsu threshold may need slight manual adjustment, but it provides a reliable starting point. The MATLAB script reads the image, converts it to grayscale if necessary, computes the Otsu threshold, performs binarization, and then calculates the phase fraction.
To validate the method, a metallographic specimen was taken from a runner bar of the same duplex stainless steel material. The specimen was ground, polished, and etched with a solution containing 5 g FeCl₃, 45 mL HCl, and 100 mL H₂O. A photomicrograph was captured using a standard metallurgical microscope. The MATLAB calculation gave an austenite content of 39.23% and a ferrite content of 60.77%. A commercial image analysis software package reported about 38% austenite for the same image, showing excellent agreement. The difference of about 1 percentage point is well within acceptable engineering accuracy. This simple method provides the foundry with a practical tool for daily production control without requiring dedicated expensive hardware.
7. Conclusion
This research has successfully developed a reliable sand casting process for a duplex stainless steel horizontal split pump body. The main findings and achievements are as follows:
(1) Two initial sand casting layouts were designed and evaluated using numerical simulation. The step gating layout with a horizontal split line proved superior because it provided smoother filling, less oxide entrapment, and lower shrinkage porosity risk according to both the Niyama criterion and residual melt modulus method.
(2) The chemical composition was optimized via D-optimal mixture design. The regression models for PREN and yield strength were highly significant. The optimized composition, with approximately 0.04% C, 1% Si, 1% Mn, 0.010% P, 0.025% S, 28% Cr, 4.70% Ni, 2% Mo, and 0.20% N, delivered a PREN of 37.8 and a yield strength of 790 MPa.
(3) The improved casting layout incorporated additional risers on the flanges, insulating sleeves on the upper risers, and 24 strategically placed chills. The gating system was redesigned as a reverse-sprue step gating system, which eliminated the initial “mixing” phenomenon. The final simulation confirmed that the defect percentage decreased to 0.2386%, and the casting yield reached 60.8%.
(4) The pouring parameter optimization by orthogonal experimental design determined that pouring temperature is the most influential factor, followed by pouring time and mold temperature. The optimal combination was a pouring temperature of 1520°C, pouring time of 65 s, and mold temperature of 35°C.
(5) A MATLAB-based phase ratio analysis method was developed as a low-cost and accurate alternative to manual and dedicated image analysis techniques. The method achieved results within 1 percentage point of commercial software, demonstrating its viability for routine quality control of sand casting parts made from duplex stainless steel.
The combination of CAD/CAE simulation, statistical design of experiments, and practical process knowledge proved to be a powerful approach for tackling the difficult production of duplex stainless steel castings. The methodologies presented here can be easily adapted to other complex castings, offering significant improvements in quality and efficiency for foundry operations.