In the field of modern industrial manufacturing, ductile iron casting stands out as a critical material due to its superior mechanical properties, including high strength, toughness, forgeability, and wear resistance. Compared to conventional cast iron, ductile iron casting finds extensive applications in automotive components, machinery, construction materials, and pipeline systems, driving advancements in various sectors. However, the production of ductile iron casting is often plagued by defects such as shrinkage porosity, shrinkage cavities, and poor nodularization, leading to high rejection rates. While international research has extensively explored the solidification characteristics and defect formation in ductile iron casting, domestic studies remain limited, often focusing on single or dual factors without a comprehensive multi-factor analysis. In this study, we aim to address this gap by investigating the influence of different nodularizers and inoculants on the thermal analysis curve characteristics of ductile iron casting, and establishing mathematical models to predict shrinkage tendency and nodularization effectiveness. Our work leverages thermal analysis technology, which provides real-time insights into the solidification process by recording temperature changes during cooling, enabling proactive quality control in ductile iron casting.
The core of our approach involves univariate experiments to systematically examine how variations in nodularizers and inoculants affect key thermal analysis curve eigenvalues, which in turn govern the shrinkage behavior and graphite morphology in ductile iron casting. Thermal analysis curves, derived from thermocouple measurements during solidification, encapsulate the dynamic thermal events of ductile iron casting, such as the precipitation of primary austenite and eutectic reactions. By analyzing these curves, we can extract eigenvalues like the eutectic recalescence temperature (ΔT), eutectic minimum temperature (TEU), and time ratios for different solidification stages (G1/G, G2/G, G3/G), which are pivotal for understanding the performance of ductile iron casting. Our methodology integrates traditional foundry practices with advanced data analysis tools, including SPSS regression software and Python-based image processing for metallographic evaluation, to develop robust predictive models. This holistic strategy not only enhances the reliability of ductile iron casting but also paves the way for intelligent manufacturing systems where thermal analysis serves as a real-time diagnostic tool.
To ensure consistency and accuracy in our study, we meticulously controlled all experimental parameters, starting with the preparation of ductile iron casting specimens. The base composition was designed to align with standard QT400-18 specifications, with target chemical ranges as summarized in Table 1. This formulation provides a balanced carbon equivalent, essential for achieving the desired graphite spheroidization and mechanical properties in ductile iron casting.
| Element | Raw Iron Melt (wt.%) | Final Iron Melt (wt.%) |
|---|---|---|
| C | 3.7–3.9 | 3.6–3.8 |
| Si | 1.6–1.8 | 2.6–2.8 |
| Mn | <0.3 | <0.3 |
| Mg | – | 0.035–0.055 |
| RE | – | 0.007–0.012 |
| P | <0.04 | <0.04 |
| S | <0.02 | <0.01 |
For the nodularization and inoculation treatments, we selected five novel nodularizers (labeled Q1 to Q5) and seven inoculants (labeled Y1 to Y7), each with distinct chemical compositions to modulate the microstructure of ductile iron casting. The compositions of these additives are detailed in Table 2, highlighting variations in elements like Si, Mg, RE (rare earth), and trace additives such as Ba, Al, Bi, and Sr, which influence graphite nucleation and growth in ductile iron casting.
| Additive | Si (wt.%) | Mg (wt.%) | RE (wt.%) | Other Elements (wt.%) |
|---|---|---|---|---|
| Q1 | 46 | 7.0 | 1.5 (La65Ce35) | Ca: 2.5 |
| Q2 | 46 | 7.0 | 1.5 (La35Ce65) | Ca: 2.5 |
| Q3 | 46 | 7.0 | 1.5 (La65Y35) | Ca: 2.5 |
| Q4 | 46 | 7.0 | 1.5 (La35Y65) | Ca: 2.5 |
| Q5 | 46 | 7.0 | 1.5 (La100) | Ca: 2.5 |
| Y1 | 70 | – | 1.0 (La100) | Ba: 1.0 |
| Y2 | 76 | – | 1.0 (Ce100) | Ba: 1.0 |
| Y3 | 73 | – | 1.0 (Ce100) | Al: 1.0 |
| Y4 | 70 | – | – | Ba: 3.0 |
| Y5 | 64 | – | – | Sr: 1.0 |
| Y6 | 73 | – | – | Mn: 3.0 |
| Y7 | 70 | – | – | S+O: 1.0 |
The experimental procedure involved melting 20 kg batches of ductile iron casting in a controlled environment, with pouring temperatures maintained at 1520°C using infrared thermometry. Nodularization was performed via the sandwich method, where nodularizers and inoculants were placed in a preheated ladle well, covered with insulating materials to minimize oxidation. After treatment, slag was removed using perlite, and the melt was poured into thermal analysis samples and shrinkage test specimens. For thermal analysis, we recorded cooling curves using embedded thermocouples, from which eigenvalues were extracted as defined in Table 3. These eigenvalues are crucial for interpreting the solidification dynamics of ductile iron casting, such as the onset of eutectic reaction and graphite expansion phases.
| Eigenvalue | Symbol | Description |
|---|---|---|
| Liquidus Temperature | Tliq | Temperature at start of solidification, corresponding to the first maximum in the second derivative. |
| Eutectic Minimum Temperature | TEU | Lowest temperature before recalescence, where the first derivative equals zero. |
| Eutectic Recalescence Temperature | ΔT | Difference between eutectic maximum and minimum temperatures: ΔT = TER – TEU. |
| Eutectic End Temperature | TES | Temperature at completion of solidification, indicated by a minimum in the first derivative. |
| Early Shrinkage Time Ratio | G1/G | Ratio of time from Tliq to TEU to total solidification time. |
| Graphite Expansion Time Ratio | G2/G | Ratio of time from TEU to TER to total solidification time. |
| Late Shrinkage Time Ratio | G3/G | Ratio of time from TER to TES to total solidification time. |
Metallographic analysis was conducted to evaluate the nodularization effectiveness in ductile iron casting. We employed Python-based image processing algorithms to quantify nodularity rate and graphite count from micrographs. The nodularity rate (pnod) was calculated using both count-based and area-based methods, as expressed in the formulas below. These approaches minimize human bias and provide objective metrics for assessing the quality of ductile iron casting.
For count-based nodularity:
$$ p_{\text{nod}} = \frac{N_{\text{VI}} + N_{\text{V}}}{N_{\text{all}}} $$
where \( N_{\text{VI}} \) and \( N_{\text{V}} \) are the counts of type VI and V graphite particles (with roundness ≥0.6), and \( N_{\text{all}} \) is the total graphite count.
For area-based nodularity:
$$ p_{\text{nod}} = \frac{A_{\text{VI}} + A_{\text{V}}}{A_{\text{all}}} $$
where \( A_{\text{VI}} \), \( A_{\text{V}} \), and \( A_{\text{all}} \) are the respective areas.
Our experimental data, summarized in Table 4, reveal the relationships between thermal analysis eigenvalues and the performance of ductile iron casting. This dataset forms the foundation for our regression analysis, aiming to predict shrinkage tendency and nodularity rate in ductile iron casting.
| Sample | TEU (°C) | ΔT (°C) | G1/G | G2/G | G3/G | Shrinkage Rate (%) | Nodularity Rate (%) | Graphite Count |
|---|---|---|---|---|---|---|---|---|
| Y1 | 1136.43 | 10.43 | 0.00 | 0.36 | 0.64 | 3.34 | 68.51 | 426.2 |
| Y2 | 1137.39 | 6.27 | 0.14 | 0.24 | 0.62 | 2.74 | 73.85 | 525.6 |
| Y3 | 1133.33 | 5.93 | 0.13 | 0.23 | 0.63 | 2.50 | 72.02 | 489.0 |
| Y4 | 1134.52 | 8.72 | 0.17 | 0.29 | 0.54 | 3.19 | 71.31 | 391.0 |
| Y5 | 1131.72 | 6.81 | 0.20 | 0.25 | 0.56 | 3.05 | 70.40 | 436.2 |
| Y6 | 1130.52 | 11.67 | 0.22 | 0.28 | 0.50 | 3.39 | 63.94 | 391.2 |
| Y7 | 1138.66 | 1.31 | 0.21 | 0.29 | 0.50 | 3.54 | 76.99 | 546.2 |
| Q1 | 1138.46 | 3.55 | 0.22 | 0.25 | 0.53 | 3.38 | 70.27 | 547.4 |
| Q2 | 1135.45 | 6.41 | 0.23 | 0.27 | 0.51 | 3.42 | 68.88 | 531.4 |
| Q3 | 1138.79 | 2.85 | 0.14 | 0.23 | 0.64 | 3.06 | 71.12 | 555.2 |
| Q4 | 1131.32 | 7.11 | 0.25 | 0.29 | 0.48 | 3.60 | 65.92 | 474.0 |
| Q5 | 1127.81 | 7.66 | 0.17 | 0.24 | 0.59 | 3.12 | 64.65 | 490.2 |
The analysis of thermal analysis curve eigenvalues provides profound insights into the nodularization effectiveness of ductile iron casting. We observed that the eutectic recalescence temperature ΔT plays a pivotal role in determining graphite morphology. As ΔT increases, the eutectic reaction accelerates, leading to a reduction in average graphite count and deterioration in nodularity grade. This is mathematically represented by the inverse correlation between ΔT and nodularity rate, as shown in our data. For instance, in ductile iron casting samples with higher ΔT values, graphite particles tend to be more irregular, compromising the mechanical integrity. Conversely, the eutectic minimum temperature TEU exhibits a positive correlation with nodularity rate. A higher TEU indicates reduced undercooling, promoting graphite formation over carbide phases, thereby enhancing spheroidization in ductile iron casting. This relationship underscores the importance of controlling solidification kinetics to optimize the microstructure of ductile iron casting.
Regarding shrinkage tendency in ductile iron casting, the time ratios derived from thermal analysis curves are critical indicators. The early shrinkage time ratio G1/G, which corresponds to the period from liquidus to eutectic minimum temperature, directly influences shrinkage cavity formation. A longer G1/G duration allows more time for liquid metal flow to compensate for contraction, but if excessive, it can lead to pronounced shrinkage porosity in ductile iron casting. Our results demonstrate that as G1/G increases, the shrinkage rate rises, highlighting the need for precise cooling control during the initial solidification stage of ductile iron casting. The graphite expansion time ratio G2/G, spanning from TEU to TER, governs dispersed shrinkage. During this phase, graphite precipitation generates expansion that can offset contraction, but prolonged G2/G may result in isolated shrinkage voids in ductile iron casting. Thus, optimizing G2/G is essential for minimizing defects in ductile iron casting. Lastly, the late shrinkage time ratio G3/G, from TER to TES, relates to final solidification and feeding efficiency. A shorter G3/G implies inadequate feeding, exacerbating shrinkage in ductile iron casting, whereas a longer G3/G facilitates better compensation.
To quantify these relationships, we employed SPSS regression analysis to develop predictive models for ductile iron casting. The correlation analysis, summarized in Table 5, reveals the interdependencies among eigenvalues and their influence on shrinkage tendency and nodularity in ductile iron casting.
| Variable | G1/G | G2/G | G3/G | Shrinkage Rate | TEU | ΔT | Nodularity Rate |
|---|---|---|---|---|---|---|---|
| G1/G | 1.000 | -0.389 | -0.834 | 0.596 | 0.112 | 0.205 | -0.254 |
| G2/G | -0.389 | 1.000 | -0.177 | 0.577 | 0.089 | -0.102 | 0.187 |
| G3/G | -0.834 | -0.177 | 1.000 | -0.743 | -0.156 | -0.088 | 0.045 |
| Shrinkage Rate | 0.596 | 0.577 | -0.743 | 1.000 | -0.211 | 0.304 | -0.332 |
| TEU | 0.112 | 0.089 | -0.156 | -0.211 | 1.000 | -0.610 | 0.744 |
| ΔT | 0.205 | -0.102 | -0.088 | 0.304 | -0.610 | 1.000 | -0.693 |
| Nodularity Rate | -0.254 | 0.187 | 0.045 | -0.332 | 0.744 | -0.693 | 1.000 |
Based on curve estimation, we selected appropriate function forms for the eigenvalues. For shrinkage tendency prediction in ductile iron casting, G1/G was modeled using a cubic function, while G2/G and G3/G were fitted with quadratic functions, ensuring high accuracy. The resulting mathematical model for shrinkage tendency (K) in ductile iron casting is expressed as:
$$ K = 28.51 \times G1 + 30.15 \times G2_{1} – 210.7 \times G3_{1} – 175.63 \times G2 + 354.23 \times G2^{2} – 13.94 \times G3 + 20.54 \times G3^{2} + 21.17 $$
where \( G1 \), \( G2 \), and \( G3 \) represent the time ratios G1/G, G2/G, and G3/G, respectively. This model for ductile iron casting achieves a coefficient of determination \( R^{2} = 0.922 \), indicating excellent predictive capability. The validation, as shown in Table 6, confirms that the predicted shrinkage rates for ductile iron casting align closely with experimental values, with relative errors below 5%, underscoring the model’s reliability for industrial applications in ductile iron casting.
| Sample | Actual Shrinkage Rate (%) | Predicted Shrinkage Rate (%) | Relative Error (%) |
|---|---|---|---|
| Y1 | 3.34 | 3.343 | 0.09 |
| Y2 | 2.74 | 2.679 | 2.21 |
| Y3 | 2.50 | 2.620 | 4.80 |
| Y4 | 3.19 | 3.173 | 0.53 |
| Y5 | 3.05 | 3.150 | 3.28 |
| Y6 | 3.39 | 3.418 | 0.83 |
| Y7 | 3.54 | 3.558 | 0.51 |
| Q1 | 3.38 | 3.271 | 3.22 |
| Q2 | 3.42 | 3.395 | 0.73 |
| Q3 | 3.06 | 3.010 | 1.63 |
| Q4 | 3.60 | 3.620 | 0.56 |
| Q5 | 3.12 | 3.030 | 2.88 |
For nodularity rate prediction in ductile iron casting, we developed a linear regression model using TEU and ΔT as predictors, based on their strong correlations. The model is given by:
$$ SG = 0.532 \times T_{\text{EU}} – 0.481 \times \Delta T – 530.937 $$
where SG denotes the nodularity rate. This simple yet effective equation for ductile iron casting captures the combined effect of eutectic undercooling and recalescence on graphite spheroidization. As validated in Table 7, the predicted nodularity rates for ductile iron casting exhibit relative errors within 4%, demonstrating the model’s accuracy for quality assessment in ductile iron casting.
| Sample | Actual Nodularity Rate (%) | Predicted Nodularity Rate (%) | Relative Error (%) |
|---|---|---|---|
| Y1 | 68.51 | 68.63 | 0.18 |
| Y2 | 73.85 | 71.14 | 3.67 |
| Y3 | 72.02 | 69.14 | 3.92 |
| Y4 | 71.31 | 69.43 | 2.03 |
| Y5 | 70.40 | 68.86 | 2.18 |
| Y6 | 63.94 | 64.89 | 1.49 |
| Y7 | 76.99 | 74.21 | 3.61 |
| Q1 | 70.27 | 73.01 | 3.89 |
| Q2 | 68.88 | 70.04 | 1.68 |
| Q3 | 71.12 | 73.53 | 3.38 |
| Q4 | 65.92 | 67.51 | 2.41 |
| Q5 | 64.65 | 62.18 | 3.82 |
In conclusion, our study underscores the efficacy of thermal analysis technology for predicting the microstructure and properties of ductile iron casting. We found that eigenvalues such as ΔT and TEU are reliable indicators of nodularization effectiveness, while time ratios G1/G, G2/G, and G3/G govern shrinkage tendency in ductile iron casting. The established mathematical models enable accurate real-time prediction of nodularity rate and shrinkage propensity, facilitating proactive adjustments in foundry processes for ductile iron casting. These insights not only enhance the quality control of ductile iron casting but also contribute to sustainable manufacturing by reducing defect rates. Future work could expand this approach to multi-variable optimization, integrating machine learning for even more robust predictions in ductile iron casting. Overall, thermal analysis emerges as a powerful tool for advancing the reliability and performance of ductile iron casting in industrial applications.