A method for predicting the composition and properties of nodular cast iron

Abstract

The application discloses a kind of based on nodular cast iron's component and performance prediction method, comprising the following steps: with multiple different components nodular cast iron material as sample, measure the chemical component data of each sample, quantitative metallographic structure feature data and mechanical property data, obtain initial data set;Then the continuous variable in initial data set is standardized, and according to statistical diagnosis method, abnormal sample in initial data set is removed, to obtain clean data set;Again, the model is trained based on clean data set, to obtain prediction model;Finally, the mechanical properties or chemical composition of nodular cast iron is forward predicted or inversely designed by prediction model.The application can introduce and quantify the interaction between specific trace elements, improve the prediction accuracy of nodular cast iron.

Description

Technical Field

[0001] This invention relates to the field of ductile iron, and in particular to a method for predicting the composition and properties of ductile iron. Background Technology

[0002] As an important engineering structural material, the mechanical properties of ductile iron are a decisive indicator for product design and quality control. These mechanical properties are jointly controlled by the material's chemical composition (such as C, Si, Mn, and key trace elements Sn and Sb) and the resulting metallographic structure (such as graphite morphology and matrix composition). Based on this, traditional methods for composition design and performance control of ductile iron heavily rely on engineers' practical experience, employing a trial-and-error cycle of "formulation development - sample production - performance testing - formulation adjustment," repeatedly experimenting to adjust the ductile iron formulation. However, this method not only has a long development cycle and consumes significant material and human resources costs, but also struggles to systematically approximate the optimal relationship between composition and performance, thus limiting the efficiency of material development and the stability of product performance.

[0003] With the development of materials technology, utilizing historical experimental data and constructing predictive models through statistical or machine learning methods has become a new approach to replace traditional trial-and-error methods in the research and development of ductile iron. For example, patent 202411399043.1, "A Method for Evaluating and Controlling the Wear Resistance of Ductile Iron Based on Electronic Work Function," analyzes the correlation between the material properties and wear resistance of ductile iron through a mathematical model, enabling the model to predict the wear resistance of ductile iron based on material composition and proportions. However, the drawback of this predictive method is that, on the one hand, existing models only consider the influence of the proportion of a single element on the mechanical properties of ductile iron during training, treating the content of each element as an independent variable. This makes it impossible for the model to take into account the interactions between multiple elements during training, and the prediction results will deviate from the actual data of real ductile iron. On the other hand, because carbon and silicon constitute a relatively high proportion in ductile iron, they have a significant impact on its mechanical properties, while trace elements such as Sn and Sb have extremely low contents, and their impact on the mechanical properties of ductile iron is relatively weak after adjustment. This leads existing prediction models to prioritize learning the data characteristics of major elements such as carbon and silicon during training, amplifying the dominant role of major elements in the properties of ductile iron, while ignoring the interactions between key trace elements. This simplification results in insufficient prediction accuracy when dealing with complex multi-element formulations, failing to truly reflect the intrinsic mechanisms of the material, especially prone to inaccuracies at compositional boundaries or high-alloy sections.

[0004] Furthermore, current predictive models often rely purely on data-driven statistical correlations during construction, failing to validate and constrain known fundamental physical laws, such as Si promoting graphitization while inhibiting pearlite formation, and Mn, Sn, and Sb promoting pearlite formation. This leads to the model generating spurious correlations that violate metallurgical common sense based on a fixed training set during training, resulting in fluctuations in predictions for ductile iron under different production batches or process conditions, weak generalization ability, and difficulty in directly guiding actual production.

[0005] Therefore, existing methods for predicting the properties of ductile iron suffer from insufficient prediction accuracy. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the composition and properties of ductile iron. This method can introduce and quantify the interactions between specific trace elements, thereby improving the accuracy of predictions for ductile iron.

[0007] The technical solution of this invention: a method for predicting the composition and properties of ductile iron, comprising the following steps:

[0008] A. Using multiple ductile iron materials with different compositions as samples, the chemical composition data, quantitative metallographic structure characteristics data, and mechanical property data of each sample were measured to obtain an initial dataset;

[0009] B. Standardize the continuous variables in the initial dataset and remove outlier samples from the initial dataset using statistical diagnostic methods to obtain a clean dataset;

[0010] C. Train the model using a clean dataset to obtain a prediction model;

[0011] D. The mechanical properties or chemical composition of ductile iron are predicted or designed in reverse using a predictive model. Forward prediction involves the predictive model predicting the mechanical properties of ductile iron based on chemical composition data, while reverse design involves the predictive model predicting the optimal range of chemical composition of ductile iron based on the target mechanical properties and main component constraints.

[0012] In the aforementioned method for predicting the composition and properties of ductile iron, step B specifically includes the following steps:

[0013] B1. The continuous variables in the initial dataset are standardized using the Z-score standardization method;

[0014] B2. Based on the standardized data, establish a preliminary linear model, and then calculate the Cook distance of each sample to the preliminary linear model;

[0015] B3. Identify and remove samples with a Cook distance greater than 4 / (n-2), where n is the total number of samples, to obtain a clean dataset.

[0016] In the aforementioned method for predicting the composition and properties of ductile iron, step C specifically includes the following steps:

[0017] C1. Using stepwise regression analysis, with statistical significance level as the criterion, key variables that significantly affect the target performance were screened from the candidate chemical composition and quantitative metallographic structure characteristics variables.

[0018] C2. The product term Sn×Sb, which characterizes the interaction between trace elements Sn and Sb, is introduced as an independent variable, and the candidate variable set is forcibly introduced.

[0019] C3. Based on the final variable set containing the interaction term Sn×Sb, three types of quantitative relationship mathematical models are constructed using the multiple linear regression method. The first type of quantitative relationship mathematical model is the correlation model between chemical composition and quantitative metallographic characteristics. The second type of quantitative relationship mathematical model is the correlation model between quantitative metallographic characteristics and mechanical properties. The third type of quantitative relationship mathematical model is the correlation model between chemical composition and mechanical properties, thus obtaining the prediction model.

[0020] C4. Set physical constraints for the prediction model based on metallurgical principles, and verify the consistency of the coefficient signs of the prediction model through physical constraints.

[0021] In the aforementioned method for predicting the composition and properties of ductile iron, the significance level threshold for the stepwise regression analysis method in step C1 is set to a p-value less than 0.05, and the exclusion threshold is set to a p-value greater than 0.10.

[0022] In the aforementioned method for predicting the composition and properties of ductile iron, the physical constraints in step C4 include the following:

[0023] In the mathematical model for the quantitative relationship between pearlite content, tensile strength, or hardness, the regression coefficient of Si is negative, while the regression coefficients of Mn, Sn, and Sb are positive.

[0024] In the quantitative mathematical model for predicting elongation, the regression coefficient of Si is positive, while the regression coefficients of Mn, Sn, and Sb are negative.

[0025] In the aforementioned method for predicting the composition and properties of ductile iron, the relationship between chemical composition and quantitative metallographic structure characteristics in step C3 is: Quantitative metallographic structure characteristics P = a + k1C + k2Si + k3Mn + k4Sn + k5Sb + k6 (Sn × Sb), where a is the regression constant term, and k1, k2, k3, k4, k5 and k6 correspond to the regression coefficients of each variable, respectively.

[0026] The relationship between quantitative metallographic structure characteristics and mechanical properties is given by the formula: Mechanical property Y = a + k1 spheroidization rate + k2 pearlite area ratio + k3 graphite area ratio + k4 number of graphite particles per unit area + k5 average graphite diameter, where a is the regression constant term, and k1, k2, k3, k4 and k5 are the regression coefficients of each variable.

[0027] The relationship between chemical composition and mechanical properties is given by the formula: Mechanical property Y = a + k1C + k2Si + k3Mn + k4Sn + k5Sb + k6 (Sn × Sb), where a is the regression constant term, and k1, k2, k3, k4, k5 and k6 are the regression coefficients of each variable, respectively.

[0028] The absolute value of the regression coefficient k reflects the degree of influence of the element, and the sign ± indicates the direction of the influence. + indicates promotion and - indicates inhibition. The Sn×Sb coefficient reveals the influence of the interaction between elements Sn and Sb.

[0029] In the aforementioned method for predicting the composition and properties of ductile iron, the chemical composition data in step A includes the mass percentages of C, Si, Mn, Sn, and Sb elements; the quantitative metallographic structure characteristics data include pearlite area ratio, graphite spheroidization rate, and average graphite diameter; and the mechanical property data include tensile strength, elongation, and Brinell hardness.

[0030] In the aforementioned method for predicting the composition and properties of ductile iron, the reverse design in step D involves the prediction model using a numerical optimization algorithm to reversely solve for the chemical composition optimization range that satisfies the target based on the target mechanical properties and main component constraints of ductile iron. The chemical composition optimization range includes the synergistic ratio range of Sn and Sb.

[0031] In the aforementioned method for predicting the composition and properties of ductile iron, the numerical optimization algorithm is a grid search method, and the chemical composition optimization interval ensures that the contribution of the interaction term Sn×Sb to the prediction result conforms to the physical constraints of step C4 during the solution process.

[0032] In the aforementioned method for predicting the composition and properties of ductile iron, after the prediction model in step C is established, empirical conversion formulas between key mechanical property indicators such as tensile strength, Brinell hardness, and elongation are derived based on the prediction model.

[0033] Compared with the prior art, the present invention has the following characteristics:

[0034] (1) This invention introduces the Sn×Sb interaction term during model construction, enabling the model to explore the influence of the interaction between Sn and Sb on the metallographic structure and mechanical properties of ductile iron during training. This makes up for the training defects of existing prediction models that only consider a single element, and allows the model to more realistically reflect the complex internal mechanism of the material. Experiments show that the introduction of this interaction term can increase the determination coefficient R² of the tensile strength prediction model by 2.7%, proving that the introduction of Sn×Sb has a positive effect on the prediction accuracy of the model.

[0035] (2) By removing abnormal samples from the initial dataset and embedding physical constraints, the erroneous associations formed by data noise during the training process of the model can be effectively reduced, thereby reducing the prediction bias caused by the limitation of sample data, improving the generalization ability of the prediction model and the prediction stability of ductile iron under different production and process conditions.

[0036] (3) Through the combination of forward prediction and reverse design, the prediction model of the present invention can also realize a complete digital design closed loop when used. It can predict the mechanical properties of ductile iron based on its chemical composition, and can directly solve its composition scheme according to the target performance of ductile iron, thereby transforming the existing lengthy trial and error process into efficient numerical calculation, which greatly improves the design efficiency of manufacturers.

[0037] Therefore, this invention can introduce and quantify the interaction between specific trace elements, thereby improving the accuracy of prediction for ductile iron. Attached Figure Description

[0038] Figure 1 This is a scatter plot showing the correlation between tensile strength and hardness for the 35 groups of samples in the experimental example.

[0039] Figure 2 This is a scatter plot showing the correlation between tensile strength and elongation of the 35 samples in the experimental example.

[0040] Figure 3 This is a scatter plot showing the correlation between hardness and elongation of 35 samples in the experimental example. Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0042] Example. A method for predicting the composition and properties of ductile iron, comprising the following steps:

[0043] A. Using multiple ductile iron materials with different compositions as samples, the chemical composition data, quantitative metallographic structure characteristics data, and mechanical property data of each sample were measured to obtain an initial dataset;

[0044] B. Standardize the continuous variables in the initial dataset and remove outlier samples from the initial dataset using statistical diagnostic methods to obtain a clean dataset;

[0045] C. Train the model using a clean dataset to obtain a prediction model;

[0046] D. The mechanical properties or chemical composition of ductile iron are predicted or designed in reverse using a predictive model. Forward prediction involves the predictive model predicting the mechanical properties of ductile iron based on chemical composition data, while reverse design involves the predictive model predicting the optimal range of chemical composition of ductile iron based on the target mechanical properties and main component constraints.

[0047] Step B specifically includes the following steps:

[0048] B1. The continuous variables in the initial dataset are standardized using the Z-score standardization method;

[0049] B2. Based on the standardized data, establish a preliminary linear model, and then calculate the Cook distance of each sample to the preliminary linear model;

[0050] B3. Identify and remove samples with a Cook distance greater than 4 / (n-2), where n is the total number of samples, to obtain a clean dataset.

[0051] Step C specifically includes the following steps:

[0052] C1. Using stepwise regression analysis, with statistical significance level as the criterion, key variables that significantly affect the target performance were screened from the candidate chemical composition and quantitative metallographic structure characteristics variables.

[0053] C2. The product term Sn×Sb, which characterizes the interaction between trace elements Sn and Sb, is introduced as an independent variable, and the candidate variable set is forcibly introduced.

[0054] C3. Based on the final variable set containing the interaction term Sn×Sb, three types of quantitative relationship mathematical models are constructed using the multiple linear regression method. The first type of quantitative relationship mathematical model is the correlation model between chemical composition and quantitative metallographic characteristics. The second type of quantitative relationship mathematical model is the correlation model between quantitative metallographic characteristics and mechanical properties. The third type of quantitative relationship mathematical model is the correlation model between chemical composition and mechanical properties, thus obtaining the prediction model.

[0055] The model output includes the t-test results for the regression coefficients of each independent variable. With a significance level of α = 0.05, if the p-value corresponding to the coefficient of the "Sn×Sb" term is less than 0.05, the null hypothesis that "the coefficient of this interaction term is zero" is rejected, statistically confirming that the interaction term has a significant effect on the dependent variable.

[0056] C4. Set physical constraints for the prediction model based on metallurgical principles, and verify the consistency of the coefficient signs of the prediction model through physical constraints.

[0057] In step C1, the significance level of the stepwise regression analysis method is set to an admission threshold of p-value less than 0.05 and an exclusion threshold of p-value greater than 0.10.

[0058] The physical constraints in step C4 include the following:

[0059] In the mathematical model for the quantitative relationship between pearlite content, tensile strength, or hardness, the regression coefficient of Si is negative, while the regression coefficients of Mn, Sn, and Sb are positive.

[0060] In the quantitative mathematical model for predicting elongation, the regression coefficient of Si is positive, while the regression coefficients of Mn, Sn, and Sb are negative.

[0061] The relationship between chemical composition and quantitative metallographic structure characteristics in step C3 is: Quantitative metallographic structure characteristics P = a + k1C + k2Si + k3Mn + k4Sn + k5Sb + k6 (Sn × Sb), where a is the regression constant term, and k1, k2, k3, k4, k5 and k6 correspond to the regression coefficients of each variable, respectively.

[0062] The relationship between quantitative metallographic structure characteristics and mechanical properties is given by the formula: Mechanical property Y = a + k1 spheroidization rate + k2 pearlite area ratio + k3 graphite area ratio + k4 number of graphite particles per unit area + k5 average graphite diameter, where a is the regression constant term, and k1, k2, k3, k4 and k5 are the regression coefficients of each variable.

[0063] The relationship between chemical composition and mechanical properties is given by the formula: Mechanical property Y = a + k1C + k2Si + k3Mn + k4Sn + k5Sb + k6 (Sn × Sb), where a is the regression constant term, and k1, k2, k3, k4, k5 and k6 are the regression coefficients of each variable.

[0064] After the prediction model in step C is generated, its prediction accuracy and generalization ability can be evaluated using the criterion of determination (R²) and mean relative error (MAPE). The formula for calculating the criterion of determination (R²) is as follows: The formula for calculating the mean relative error (MAPE) is as follows: In the formula This represents the model's predicted value. This represents the true value; if the prediction accuracy and generalization ability of the prediction model meet the set requirements, proceed to the next step.

[0065] The coefficient of determination R² represents the portion of the variation in the dependent variable that can be explained by the variation in the independent variable. A higher goodness of fit indicates a greater degree of explanation by the independent variable for the dependent variable, a higher percentage of the total variation attributable to the independent variable, and a denser concentration of observations near the regression line. R² can be used to predict the dependent variable value for new data; a higher R² value generally indicates a more reliable and accurate prediction. For multivariate regression relationships, the adjusted multiple coefficient of determination (Ra²) is used to assess accuracy.

[0066] The chemical composition data in step A includes the mass percentage of C, Si, Mn, Sn, and Sb elements; the quantitative metallographic structure data includes pearlite area ratio, graphite spheroidization rate, and average graphite diameter; and the mechanical property data includes tensile strength, elongation, and Brinell hardness.

[0067] The reverse design in step D involves the prediction model using a numerical optimization algorithm to reverse-solve the chemical composition optimization range that satisfies the target based on the target mechanical properties and main component constraints of ductile iron. The chemical composition optimization range includes the synergistic ratio range of Sn and Sb.

[0068] The numerical optimization algorithm is a grid search method. When solving the chemical composition optimization interval, it is ensured that the contribution of the interaction term Sn×Sb to the prediction result meets the physical constraints of step C4.

[0069] After the prediction model in step C is established, empirical conversion formulas between key mechanical performance indicators such as tensile strength, Brinell hardness and elongation are derived based on the prediction model.

[0070] Both Sn and Sb are surface-active elements in ductile iron, readily segregating at grain boundaries or phase interfaces. Their coexistence alters the diffusion kinetics of carbon atoms, the stability of the graphite / austenite interface, and the growth rate of pearlite clusters. Based on this, this embodiment introduces the Sn×Sb interaction term, which indirectly reflects the coupled effect of this synergistic effect on the microstructure formation kinetics, and explores the nonlinear correlation between this coupled effect and the mechanical properties of ductile iron.

[0071] When the interaction term Sn×Sb is introduced, the prediction model in this embodiment can explain and predict the "composition window" effect that cannot be described by the single-element model. That is, ductile iron can only obtain the optimal comprehensive performance when the Sn and Sb contents are within a specific ratio range. This provides a direct basis for the composition range design of ductile iron.

[0072] Experimental Example: With the goal of developing QT700 grade ductile iron with a tensile strength ≥700MPa and elongation ≥2%, the predictive method of the example was used to design the composition and predict the performance of this ductile iron. The specific steps include:

[0073] A. First, the main variation ranges of each element in ductile iron were set as 3.4–3.8% C, 1.8–2.5% Si, 0.1–0.7% Mn, 0.005–0.06% Sn, and 0.001–0.06% Sb, with P, S, and Mg strictly controlled at low levels. Based on this, an orthogonal experimental design method was used to prepare and melt 38 groups of ductile iron samples with different compositions as samples.

[0074] Then, the chemical composition of 38 samples was determined using a direct-reading spectrometer, and the chemical composition data of each sample was obtained.

[0075] The pearlite area ratio, graphite spheroidization rate and average graphite diameter of 38 samples were quantitatively determined using image analysis software, and quantitative metallographic structure characteristics data of each sample were obtained.

[0076] The samples were processed into standard tensile specimens, and then the tensile strength Rm, elongation after fracture A and Brinell hardness HB of the specimens were measured to obtain the mechanical property data of each specimen.

[0077] Then, the chemical composition data, quantitative metallographic structure data, and mechanical property data of 38 sets of samples were entered to form the initial dataset.

[0078] B1. For continuous independent variables such as chemical composition and quantitative metallographic structure characteristics in the initial dataset, the Z-score standardization method is used to standardize them so that the mean is 0 and the standard deviation is 1.

[0079] B2. Based on the standardized data, a preliminary linear model is established, and then the Cook distance of each sample to the preliminary linear model is calculated, with a threshold of 4 / (38-2)≈0.111.

[0080] B3. Identify and remove 3 groups of highly influential abnormal samples whose Cook distance is greater than the threshold, and retain 35 samples as a clean dataset.

[0081] C1. Using tensile strength Rm as the target variable, stepwise regression analysis was performed using statistical software. The significance level for the variable entering the model was set at 0.05, and the removal level was set at 0.10.

[0082] C2. Sn×Sb is taken as a candidate independent variable, and together with C, Si, Mn and other elements related to ductile iron, it is taken as a set of candidate variables;

[0083] C3. The significant variables finally selected by the stepwise regression algorithm include Si, Mn, Sn, Sb and the interaction term Sn×Sb. Then, the first type of quantitative relationship mathematical model, the second type of quantitative relationship mathematical model and the third type of quantitative relationship mathematical model are constructed by multiple linear regression method to obtain the prediction model.

[0084] The mathematical model for the first type of quantitative relationship between chemical composition and pearlite area ratio is: Pearlite area ratio (%) = -69.786 - 35.373Si + 19.382Mn + 2283.877Sn + 2658.439Sb - 63282.907Sn×Sb. The adjusted complex coefficient of determination (Adj.R²) of the model is 0.952. Further testing of the model coefficients using physical constraint embedding revealed that the Si coefficient is negative, consistent with its role in graphitization and reducing pearlite content; the Mn, Sn, and Sb coefficients are positive, consistent with their role in promoting pearlite formation; and the Sn×Sb interaction term has a negative coefficient, consistent with metallurgical experience. The model passed the physical consistency verification.

[0085] The second type of quantitative mathematical model based on quantitative metallographic microstructure characteristics data and tensile strength is: tensile strength = -23.958 + 4.418 spheroidization rate (%) + 3.841 pearlite area ratio (%). The adjusted complex coefficient of determination Adj.R² of the model is 0.980. The model coefficients are then checked by physical constraint embedding. The spheroidization rate coefficient and the pearlite area ratio coefficient are both positive, which is consistent with the experience of ductile iron. The model passes the physical consistency verification.

[0086] The second type of quantitative mathematical model based on quantitative metallographic microstructure characteristics data and hardness is: Hardness (HB) = 89.375 + 0.789 spheroidization rate (%) + 1.206 pearlite area ratio (%) - 0.951 average diameter of graphite spheres (μm). The adjusted complex coefficient of determination Adj.R² of the model is 0.969. The model coefficients were then checked by physical constraint embedding. The measured spheroidization rate coefficient was positive, the pearlite area ratio coefficient was positive, and the average diameter of graphite spheres coefficient was negative, which is consistent with the experience of ductile iron. The model passed the physical consistency verification.

[0087] The second type of quantitative mathematical model based on quantitative metallographic microstructure characteristics data and elongation is elongation (%) = 13.209 + 0.12 spheroidization (%) - 0.191 pearlite area ratio (%). The adjusted complex coefficient of determination Adj.R² of the model is 0.935. The model coefficients are then checked by physical constraint embedding. The measured spheroidization coefficient is positive and the pearlite area ratio coefficient is negative, which is consistent with the experience of ductile iron. The model passes the physical consistency verification.

[0088] The third type of quantitative mathematical model based on chemical composition and tensile strength is: Tensile strength (MPa) = 435.234 - 59.715Si + 69.476Mn + 9896.994Sn + 14643.762Sb - 361956.407Sn×Sb. After model adjustment, the complex coefficient of determination (Adj.R²) is 0.961. Further physical constraint embedding was used to check the model coefficients. The measured Si coefficient is negative, consistent with its role in graphitization and reducing pearlite content. The Mn, Sn, and Sb coefficients are positive, consistent with their role in promoting pearlite formation and increasing strength. The Sn×Sb interaction term has a negative coefficient, indicating that in the high Sn and high Sb regions, there may be side effects due to oversaturation, which is consistent with metallurgical experience. The model passed the physical consistency verification.

[0089] The mathematical model for the third type of quantitative relationship between chemical composition and hardness is: Hardness (HB) = 158.937 - 20.589Si + 25.172Mn + 3097.097Sn + 3300.358Sb - 75515.406Sn×Sb. The adjusted complex coefficient of determination (Adj.R²) of the model is 0.954. Further testing of the model coefficients using physical constraint embedding revealed that the Si coefficient is negative, while the Mn, Sn, and Sb coefficients are positive, and the interaction term Sn×Sb has a negative coefficient. Therefore, the model passed the physical consistency check.

[0090] The third type of quantitative mathematical model based on chemical composition and elongation is elongation (%) = 50.731 - 11.059C + 7.395Si - 6.925Mn - 452.476Sn - 470.95Sb + 11403.714Sn×Sb. The adjusted complex coefficient of determination (Adj.R²) of the model is 0.909. After checking the model coefficients through physical constraint embedding, the measured coefficient of Si is positive, while the coefficients of C, Mn, Sn, and Sb are negative. The coefficient of the interaction term Sn×Sb is positive, which is opposite to the influence on tensile strength and hardness, and is consistent with metallurgical experience. The model passes the physical consistency verification.

[0091] As can be seen from the above quantitative mathematical model, under this chemical composition system, the trace addition of Sn and Sb has a significantly greater multiplier effect on the improvement of strength and hardness than conventional elements (see specific coefficients k4 and k5). While Si strengthens through solid solution, it also exhibits a complex negative correlation with pearlite content and elongation due to its strong graphitization effect. This reveals the synergistic and antagonistic effects of Sn and Sb on various performance parameters of ductile iron after their interaction, providing a direct basis for the forward prediction and reverse design of this invention.

[0092] The multiple correlation coefficient and adjusted coefficient of determination of the interaction term Sn×Sb before and after its introduction into the quantitative modeling relationship are shown in Table 1:

[0093] Table 1. Correlation coefficients and adjusted complex determination coefficients of the quantitative relationships before and after the introduction of the Sn×Sb interaction term.

[0094]

[0095] As shown in Table 1, after the introduction of the interaction term Sn×Sb, the adjusted complex coefficients of determination of the relationships between tensile strength, hardness, and elongation and chemical composition increased from 0.934, 0.944, and 0.898 to 0.961, 0.954, and 0.909, respectively. This means that the prediction accuracy improved by 2.7%, 1.0%, and 1.1%, respectively, indicating that the introduction of the interaction term Sn×Sb can improve the prediction accuracy of the model.

[0096] Nine sets of data not used in the modeling were reserved as a test set. The prediction model predicted the tensile strength based on the chemical composition of these nine sets of data. The prediction results of the prediction model before and after introducing the interaction term Sn×Sb are shown in Table 2.

[0097] Table 2 Comparison of tensile strength prediction results and actual values ​​of the prediction model before and after the introduction of the Sn×Sb interaction term.

[0098]

[0099] As shown in Table 2, the average relative error (MAPE) of the prediction model before introducing the interaction term Sn×Sb was 2.31%, and the average relative error (MAPE) after introducing the interaction term Sn×Sb decreased to 1.78%, indicating that the introduction of the interaction term Sn×Sb can improve the prediction accuracy of the prediction model for the tensile strength of ductile iron.

[0100] The hardness was predicted by the prediction model based on the chemical composition of these 9 sets of data. The prediction results of the prediction model before and after introducing the interaction term Sn×Sb are shown in Table 3:

[0101] Table 3 Comparison of hardness prediction results and actual values ​​of the prediction model before and after the introduction of the Sn×Sb interaction term.

[0102]

[0103] As shown in Table 3, the average relative error (MAPE) of the prediction model before introducing the interaction term Sn×Sb was 3.82%, and the average relative error (MAPE) after introducing the interaction term Sn×Sb decreased to 2.60%, indicating that the introduction of the interaction term Sn×Sb can improve the prediction accuracy of the prediction model for the hardness of ductile iron.

[0104] The elongation rate was predicted by the prediction model based on the chemical composition of these 9 sets of data. The prediction results of the prediction model before and after introducing the interaction term Sn×Sb are shown in Table 4:

[0105] Table 4 Comparison of elongation prediction results and actual values ​​of the prediction model before and after the introduction of the Sn×Sb interaction term.

[0106]

[0107] As shown in Table 4, the average relative error (MAPE) of the prediction model before introducing the interaction term Sn×Sb was 4.13%, and the average relative error (MAPE) after introducing the interaction term Sn×Sb decreased to 2.44%, indicating that the introduction of the interaction term Sn×Sb can improve the prediction accuracy of the prediction model for the elongation of ductile iron.

[0108] D. The chemical composition of ductile iron is reverse-engineered using a predictive model. The target mechanical properties of the ductile iron are set as tensile strength ≥700MPa and elongation ≥2%. The median values ​​of C, Si, and Mn are fixed within the controllable process range: C=3.65%, Si=2.2%, and Mn=0.3%.

[0109] Then, the target tensile strength and elongation values, along with the fixed values ​​of C, Si, and Mn, are substituted into the third type of quantitative mathematical model. A grid search method is used to traverse and calculate in the two-dimensional space of Sn (0.005-0.06%) and Sb (0.001-0.06%) with a step size of 0.001%, to find all (Sn,Sb) point sets that simultaneously satisfy tensile strength ≥700MPa and elongation ≥2%. The projection of this point set on the two-dimensional plane is the recommended safety window for Sn and Sb to be added together, such as Sn=0.023-0.034% and Sb=0.023-0.034%.

[0110] Next, a formula was selected from the component window recommended by the reverse design for trial production, such as Sn=0.0318% and Sb=0.0338%. The trial sample was then tested, and the measured tensile strength was 732.0 MPa and the elongation was 8.4%. The test results were then compared with the predicted values ​​of the prediction model, and the comparison data is shown in Table 5.

[0111] Table 5. Comparison of predicted values ​​and actual values ​​from the prediction model.

[0112]

[0113] As shown in Table 5, the predicted tensile strength of the prototype sample (737.2 MPa) differs from the measured tensile strength (732.0 MPa) by 5.2 MPa, with a relative error of 0.71%. The predicted elongation of the prototype sample (8.02%) differs from the measured elongation (8.4%) by 0.38%, with a relative error of 4.7%. Furthermore, the measured values ​​fall entirely within the performance range predicted by the model, verifying the effectiveness of the reverse design.

[0114] Based on the above prediction method, the scatter plot of the correlation between tensile strength and hardness of 35 groups of samples is shown below. Figure 1 As shown in the figure, the scatter plot of the correlation between tensile strength and elongation for 35 groups of samples is as follows. Figure 2 As shown in the figure, the scatter plot of the correlation between hardness and elongation for 35 groups of samples is as follows. Figure 3 As shown; therefore, a rapid conversion formula applicable to this series of materials can be derived as follows:

[0115] Tensile strength (MPa) = -27.058 + 3.0153 hardness (HB);

[0116] Tensile strength (MPa) = 860.89 - 21.321 Elongation (%)

[0117] Hardness (HB) = 293.13 - 6.9809 Elongation (%)

[0118] Based on this rapid conversion formula, operators can infer other mechanical properties from any mechanical property of ductile iron, such as inferring tensile strength and elongation from hardness, thereby achieving rapid estimation of the mechanical properties of ductile iron.

[0119] In ductile iron, both Sn and Sb are trace elements that promote pearlite formation. When they coexist, they have a nonlinear effect on the phase transformation process of austenite decomposing into pearlite. Based on this, this embodiment introduces the interaction term Sn×Sb to quantify the direction and intensity of this combined effect. The experiments show that the coefficient of the Sn×Sb interaction term is negative in the mathematical models based on the quantitative relationship between chemical composition and tensile strength and chemical composition and hardness. This indicates that in the high Sn and high Sb regions, the two may produce a certain antagonistic effect due to supersaturation or the formation of complex segregation; that is, their effect on improving strength and hardness is lower than the simple superposition of their individual effects, and may even be weakened. Conversely, in the mathematical model based on the quantitative relationship between chemical composition and elongation, the coefficient of the Sn×Sb interaction term is positive, indicating that under certain conditions, their influence on plasticity exhibits a synergistic protective effect.

Claims

1. A method for predicting the composition and properties of ductile iron, characterized in that, Includes the following steps: A. Using multiple ductile iron materials with different compositions as samples, the chemical composition data, quantitative metallographic structure characteristics data, and mechanical property data of each sample were measured to obtain an initial dataset; B. Standardize the continuous variables in the initial dataset and remove outlier samples from the initial dataset using statistical diagnostic methods to obtain a clean dataset; C. Train the model using a clean dataset to obtain a prediction model; D. The mechanical properties or chemical composition of ductile iron are predicted or designed in reverse using a predictive model. Forward prediction involves the predictive model predicting the mechanical properties of ductile iron based on chemical composition data, while reverse design involves the predictive model predicting the optimal range of chemical composition of ductile iron based on the target mechanical properties and main component constraints.

2. The method for predicting the composition and properties of ductile iron according to claim 1, characterized in that, Step B specifically includes the following steps: B1. The continuous variables in the initial dataset are standardized using the Z-score standardization method; B2. Based on the standardized data, establish a preliminary linear model, and then calculate the Cook distance of each sample to the preliminary linear model; B3. Identify and remove samples with a Cook distance greater than 4 / (n-2), where n is the total number of samples, to obtain a clean dataset.

3. The method for predicting the composition and properties of ductile iron according to claim 1, characterized in that, Step C specifically includes the following steps: C1. Using stepwise regression analysis, with statistical significance level as the criterion, key variables that significantly affect the target performance were screened from the candidate chemical composition and quantitative metallographic structure characteristics variables. C2. The product term Sn×Sb, which characterizes the interaction between trace elements Sn and Sb, is introduced as an independent variable, and the candidate variable set is forcibly introduced. C3. Based on the final variable set containing the interaction term Sn×Sb, three types of quantitative relationship mathematical models are constructed using the multiple linear regression method. The first type of quantitative relationship mathematical model is the correlation model between chemical composition and quantitative metallographic characteristics. The second type of quantitative relationship mathematical model is the correlation model between quantitative metallographic characteristics and mechanical properties. The third type of quantitative relationship mathematical model is the correlation model between chemical composition and mechanical properties, thus obtaining the prediction model. C4. Set physical constraints for the prediction model based on metallurgical principles, and verify the consistency of the coefficient signs of the prediction model through physical constraints.

4. The method for predicting the composition and properties of ductile iron according to claim 3, characterized in that: In step C1, the significance level of the stepwise regression analysis method is set to an admission threshold of p-value less than 0.05 and an exclusion threshold of p-value greater than 0.

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5. The method for predicting the composition and properties of ductile iron according to claim 3, characterized in that, The physical constraints in step C4 include the following: In the mathematical model for the quantitative relationship between pearlite content, tensile strength, or hardness, the regression coefficient of Si is negative, while the regression coefficients of Mn, Sn, and Sb are positive. In the quantitative mathematical model for predicting elongation, the regression coefficient of Si is positive, while the regression coefficients of Mn, Sn, and Sb are negative.

6. The method for predicting the composition and properties of ductile iron according to claim 3, characterized in that, The relationship between chemical composition and quantitative metallographic structure characteristics in step C3 is: Quantitative metallographic structure characteristics P = a + k1C + k2Si + k3Mn + k4Sn + k5Sb + k6 (Sn × Sb), where a is the regression constant term, and k1, k2, k3, k4, k5 and k6 correspond to the regression coefficients of each variable, respectively. The relationship between quantitative metallographic structure characteristics and mechanical properties is given by the formula: Mechanical property Y = a + k1 spheroidization rate + k2 pearlite area ratio + k3 graphite area ratio + k4 number of graphite particles per unit area + k5 average graphite diameter, where a is the regression constant term, and k1, k2, k3, k4 and k5 are the regression coefficients of each variable. The relationship between chemical composition and mechanical properties is given by the formula: Mechanical property Y = a + k1C + k2Si + k3Mn + k4Sn + k5Sb + k6 (Sn × Sb), where a is the regression constant term, and k1, k2, k3, k4, k5 and k6 are the regression coefficients of each variable.

7. The method for predicting the composition and properties of ductile iron according to claim 1, characterized in that: The chemical composition data in step A includes the mass percentage of C, Si, Mn, Sn, and Sb elements; the quantitative metallographic structure data includes pearlite area ratio, graphite spheroidization rate, and average graphite diameter; and the mechanical property data includes tensile strength, elongation, and Brinell hardness.

8. The method for predicting the composition and properties of ductile iron according to claim 3, characterized in that: The reverse design in step D involves the prediction model using a numerical optimization algorithm to reverse-solve the chemical composition optimization range that satisfies the target based on the target mechanical properties and main component constraints of ductile iron. The chemical composition optimization range includes the synergistic ratio range of Sn and Sb.

9. The method for predicting the composition and properties of ductile iron according to claim 8, characterized in that: The numerical optimization algorithm is a grid search method. When solving the chemical composition optimization interval, it is ensured that the contribution of the interaction term Sn×Sb to the prediction result meets the physical constraints of step C4.

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