A method for searching and screening of nb-si alloy based on characteristic contribution degree guided super-high-temperature alloy fracture toughness optimization

Abstract

A kind of superalloy fracture toughness optimization method based on feature contribution degree guidance and screened Nb-Si alloy, the present application is to solve the problem of slow convergence, low fracture toughness of existing alloy design method based on machine learning.The superalloy fracture toughness optimization method: I, collect the composition and fracture toughness data of Nb-Si base alloy;II, build a simplified feature set;III, train the fracture toughness relationship model, the fracture toughness relationship model adopts Gaussian process regression model;IV, the fracture toughness prediction value, uncertainty estimation and contribution degree guidance output by the fracture toughness relationship model are combined to generate sampling score according to fusion rule;V, select candidate components for preparation and measurement according to sampling score, retrain the model after data backfilling and closed loop iteration, and determine the composition of Nb-Si alloy.The Nb-Si alloy fracture toughness closed loop optimization method of the present application has fast convergence speed, and the fracture toughness of the screened Nb-Si alloy is excellent.

Description

Technical Field

[0001] This invention belongs to the field of alloy material design, specifically relating to a method for optimizing the fracture toughness of ultra-high temperature alloys based on characteristic contribution degree and the screening of Nb-Si alloys. In particular, it relates to a method for rapidly optimizing the fracture toughness and screening the composition of Nb-Si alloys by using a regression model with uncertainty output capability and a sampling score guided by characteristic contribution degree through closed-loop experimental iteration. Background Technology

[0002] Nb-Si based alloys are important ultra-high temperature structural materials, characterized by high melting points (Nb5Si3 melting point can reach about 1920℃) and low densities (about 6.6 g / cm³). 3 With its superior high-temperature mechanical properties, Nb-Si alloys have broad application prospects in high-temperature structures such as aerospace, engines, and gas turbines. Compared to Ni-based superalloys, Nb-Si alloys can operate at temperatures approximately 200°C higher and have a density about 15% lower, potentially improving turbine efficiency and reducing aviation emissions. However, the room-temperature fracture toughness of most cast Nb-Si alloys is between 7 and 15 MPa·m. 1 / 2 The range is far lower than the approximately 18 MPa·m typically required for reliable structural fabrication. 1 / 2 The high room temperature brittleness and low fracture toughness severely limit its engineering applications.

[0003] The compositional space of multi-component ultra-high temperature alloy systems is enormous. Taking multi-component systems such as Nb-Si-Ti-Al-Cr-Hf-Zr-V as an example, even small adjustments to the element content can produce a vast number of compositional combinations. Using traditional trial-and-error methods for alloy design requires extensive experimental verification, resulting in long development cycles, high costs, and difficulty in systematically exploring the composition-performance relationship, as well as in quickly screening out alloy compositions with optimal fracture toughness.

[0004] In recent years, machine learning methods have shown great potential in the field of materials design, enabling the learning of complex relationships between material composition, structure, and properties from existing experimental data, the establishment of predictive models, and the rapid screening and prediction of the properties of new materials. However, existing machine learning methods have three shortcomings when applied to optimizing the fracture toughness of Nb-Si alloys: First, most sampling strategies rely solely on the predicted mean and prediction uncertainty, indiscriminately giving equal exploration priority to all high-uncertainty regions, failing to utilize the physical correlation between features and target properties. This results in sampling points being scattered in spatially limited areas, leading to slow convergence and wasted experiments. Second, the interpretability of surrogate models fluctuates significantly in the small sample stage. Existing methods lack adaptive control mechanisms for the reliability of guiding signals. If sampling is heavily reliant on feature importance signals from the outset, the search is easily locked into unreliable directions. Third, most studies train models once on static datasets, failing to form a closed loop of "prediction-experiment-backfill-retraining," preventing the model from being continuously corrected as measured data accumulates.

[0005] Therefore, it is necessary to develop a machine learning-based closed-loop optimization method for fracture toughness of Nb-Si alloy systems. This method can guide sampling by utilizing the physical correlation between features and fracture toughness, enabling rapid, low-cost, and high-precision alloy design. Furthermore, closed-loop experiments can be used to verify that the actual performance of the optimized alloy meets application requirements. Summary of the Invention

[0006] The purpose of this invention is to address the problems of slow convergence, high experimental costs, and difficulty in breaking through the fracture toughness bottleneck of cast Nb-Si alloys within a limited experimental budget in existing machine learning-based alloy design methods. Instead, this invention provides a method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution and a screened Nb-Si alloy.

[0007] The present invention provides a method for optimizing the fracture toughness of ultra-high temperature alloys based on characteristic contribution, which is implemented according to the following steps:

[0008] Step 1: Collect composition and fracture toughness data of Nb-Si based alloys and construct a dataset;

[0009] Step 2: Using the mean thermal conductivity, thermodynamic stability parameter Ω, average electronegativity, mixing entropy contribution ΔSmix, and mean electron affinity of Nb-Si based alloys as key features, a simplified feature set is formed, thus obtaining a simplified feature-fracture toughness dataset.

[0010] Step 3: Train the fracture toughness relationship model using a simplified feature-fracture toughness dataset. The fracture toughness relationship model adopts a Gaussian process regression model with uncertainty output capability to obtain the trained fracture toughness relationship model.

[0011] Step 4: Generate a candidate set within the preset Nb-Si based alloy composition constraint boundary. Based on the trained fracture toughness relationship model, perform feature contribution decomposition on each candidate component in the candidate set to obtain the contribution decomposition value of each key feature to the fracture toughness prediction at the candidate component. And combine the global normalized importance of each key feature on the simplified feature-fracture toughness dataset. The contribution guidance amount is calculated using the following formula: , Key features In candidate components The contribution decomposition value of the position to the prediction of fracture toughness. Key features Globally normalized importance on the feature descriptor-fracture toughness dataset. This is a normalization constant;

[0012] Then, the fracture toughness prediction, uncertainty estimate, and contribution guidance output by the fracture toughness relationship model are combined according to the preset fusion rules to generate a sampling score;

[0013] Step 5: Select multiple candidate components in descending order of sampling scores. Perform alloy preparation and fracture toughness measurement on the selected candidate components. Calculate the corresponding key features based on the composition data of the selected candidate components. Backfill the calculated key features and fracture toughness measurement data into the simplified feature-fracture toughness dataset. Retrain the fracture toughness relationship model and repeat steps 4 and 5 for iteration until the preset stopping criterion is met. Screen and determine the Nb-Si alloy composition and atomic percentage of each element that meet the fracture toughness requirements from the iteration process, thus completing the ultra-high temperature alloy fracture toughness optimization method based on feature contribution degree.

[0014] In step three, the covariance kernel of the fracture toughness relationship model is a combination of the radial basis function kernel (RBF kernel) and the white noise kernel, and the kernel function is: ,in and As candidate components, For signal variance, For length scale, For noise variance, This refers to the Kronecker delta function.

[0015] The Nb-Si alloy selected in this invention is composed of the following elements in atomic percentage: Nb 43.40%, Si 10.12%, Ti 23.86%, Al 2.11%, V 16.77%, and Zr 3.74%.

[0016] The Nb-Si alloy obtained by screening in this invention has a room temperature fracture toughness of 20.88 MPa·m. 1 / 2 .

[0017] This invention provides a method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution and a selected Nb-Si alloy. The method improves feature quality and model accuracy through feature simplification strategy, uses a Gaussian process regression model with uncertainty output capability to predict fracture toughness, and combines feature contribution-guided sampling scoring and closed-loop experimental iteration to achieve rapid optimization of fracture toughness. The method also ensures the reliability and practicality of the optimization results through a complete experimental verification process.

[0018] Compared with existing technologies, the closed-loop optimization method for fracture toughness of Nb-Si alloys in this invention has the following advantages:

[0019] 1. A two-stage feature simplification strategy was adopted to select 5 physically interpretable key features from 205 candidate descriptors, which significantly reduced model complexity and improved prediction accuracy and generalization ability. The coefficient of determination R² on the test set reached 0.907, and the root mean square error was controlled at 0.978 MPa·m. 1 / 2 .

[0020] 2. By aggregating the feature contribution decomposition results with the global importance of features into a contribution guide and embedding it into the sampling score, the sampling no longer treats high uncertainty regions equally, but rather tilts towards physically desirable component intervals. In the demonstration experiment, a fracture toughness of 20.88 MPa·m was obtained in only 3 optimization rounds. 1 / 2 The alloy has a fast convergence speed.

[0021] 3. The fusion weight of the contribution guidance quantity increases monotonically with the optimization round. When the variance of the early guidance signal is large, its influence is reduced to avoid misleading the direction. In the later stage, the influence is increased after the guidance signal shrinks to the advantageous area, so as to achieve a smooth transition from exploration to development, without the need for manual intervention.

[0022] 4. By establishing a quantitative correlation between simplified features and microstructure parameters such as phase fraction and grain size, the optimization process becomes interpretable and the results are reproducible. Compared with the traditional trial-and-error method, this invention significantly shortens the R&D cycle and reduces experimental costs, providing a new approach for the rapid design of Nb-Si alloys and other alloy systems with composition as the main design variable. Attached Figure Description

[0023] Figure 1 The above is an overall flowchart of the feature contribution-guided method for optimizing the fracture toughness of ultra-high temperature alloys in an embodiment.

[0024] Figure 2 This is a diagram illustrating the two-stage feature simplification process in the embodiment;

[0025] Figure 3 The example shows the convergence graph of contribution-guided sampling as the optimization rounds progress;

[0026] Figure 4 This is a microstructure diagram of the optimal Nb-Si alloy in the examples. Detailed Implementation

[0027] Specific Implementation Method 1: This implementation method, based on the feature contribution-guided method for optimizing the fracture toughness of ultra-high temperature alloys, is carried out according to the following steps:

[0028] Step 1: Collect composition and fracture toughness data of Nb-Si based alloys and construct a dataset;

[0029] Step 2: Using the mean thermal conductivity, thermodynamic stability parameter Ω, average electronegativity, mixing entropy contribution ΔSmix, and mean electron affinity of Nb-Si based alloys as key features, a simplified feature set is formed, thus obtaining a simplified feature-fracture toughness dataset.

[0030] Step 3: Train the fracture toughness relationship model using a simplified feature-fracture toughness dataset. The fracture toughness relationship model adopts a Gaussian process regression model with uncertainty output capability to obtain the trained fracture toughness relationship model.

[0031] Step 4: Generate a candidate set within the preset Nb-Si based alloy composition constraint boundary. Based on the trained fracture toughness relationship model, perform feature contribution decomposition on each candidate component in the candidate set to obtain the contribution decomposition value of each key feature to the fracture toughness prediction at the candidate component. And combine the global normalized importance of each key feature on the simplified feature-fracture toughness dataset. The contribution guidance amount is calculated using the following formula: , Key features In candidate components The contribution decomposition value of the position to the prediction of fracture toughness. Key features Globally normalized importance on the feature descriptor-fracture toughness dataset. This is a normalization constant;

[0032] Then, the fracture toughness prediction, uncertainty estimate, and contribution guidance output by the fracture toughness relationship model are combined according to the preset fusion rules to generate a sampling score;

[0033] Step 5: Select multiple candidate components in descending order of sampling scores. Perform alloy preparation and fracture toughness measurement on the selected candidate components. Calculate the corresponding key features based on the composition data of the selected candidate components. Backfill the calculated key features and fracture toughness measurement data into the simplified feature-fracture toughness dataset. Retrain the fracture toughness relationship model and repeat steps 4 and 5 for iteration until the preset stopping criterion is met. Screen and determine the Nb-Si alloy composition and atomic percentage of each element that meet the fracture toughness requirements from the iteration process, thus completing the ultra-high temperature alloy fracture toughness optimization method based on feature contribution degree.

[0034] In step three, the covariance kernel of the fracture toughness relationship model is a combination of the radial basis function kernel (RBF kernel) and the white noise kernel, and the kernel function is: ,in and As candidate components, For signal variance, For length scale, For noise variance, This refers to the Kronecker delta function.

[0035] The five key features in step two of this embodiment are obtained based on the composition calculation of Nb-Si based alloys.

[0036] In step two of this implementation method, when simplifying features, firstly, constant descriptors with a uniqueness rate of less than 0.1 are removed. Then, among descriptor pairs with a pairwise correlation coefficient absolute value greater than 0.95, one descriptor with a low correlation to fracture toughness is removed. Then, the remaining descriptors are relevance scored using a combination of Pearson correlation coefficient absolute value, mutual information, and conditional variance discrimination score with weights of 35%, 35%, and 30%, respectively. A greedy selection algorithm with minimum redundancy and maximum relevance is performed using normalized mutual information as the redundancy measure, retaining 50 descriptors. Then, within the Gaussian process model family, the top 15 descriptors are selected according to a weighted importance index that is adapted to the statistical characteristics of the Gaussian process model family. A combination search is performed with the minimum error of leave-one-out cross-validation as the criterion to determine a simplified feature set containing 5 descriptors.

[0037] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the Nb-Si based alloy in step one contains 4 to 11 kinds of metallic elements.

[0038] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that the fracture toughness data in step 1 is the room temperature fracture toughness value of the cast Nb-Si based alloy.

[0039] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the average thermal conductivity in step two is... According to the formula Calculation, where For elements atomic fraction, Let i be the thermal conductivity of element i. This indicates the summation of all elements in the alloy.

[0040] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One through Four in that the thermodynamic stability parameter Ω in step two is calculated using the formula... Calculation, where The component-weighted average melting point of the Nb-Si based alloy is given. Contributes to mixed entropy It is a mixed enthalpy.

[0041] This implementation method , Let be the melting point of element i.

[0042] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that the average electronegativity in step two is... According to the formula Calculation, where For elements The atomic fraction (i.e., the percentage of atoms divided by 100). For elements Pauling's electronegativity, This indicates the summation of all elements in the alloy.

[0043] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the contribution of mixed entropy in step two is... According to the formula Calculation, where For elements The atomic fraction, where R is the gas constant. This indicates the summation of all elements in the alloy.

[0044] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that the average electron affinity in step two is... According to the formula Calculation, where For elements The atomic fraction (i.e., the percentage of atoms divided by 100). For elements electron affinity, This indicates the summation of all elements in the alloy.

[0045] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that step four... Features In candidate components The contribution decomposition value (Shapley value) to the fracture toughness prediction is calculated according to the formula. Calculation, where To reduce the number of key features in the feature set, It is a set consisting of all key features. For those without key features Feature subset, For feature subset The number of key features in the middle, For only known feature subsets Fracture toughness relationship model for candidate components when the feature values ​​are taken The predicted value of fracture toughness; Key features The global normalized importance on the simplified feature-fracture toughness dataset is calculated using the formula... Calculation, where To streamline the features—fracture toughness dataset, the first... Each training sample represents a key feature. The sum of absolute SHAP values ​​across all training samples, with the denominator being the sum of absolute SHAP values ​​of all key features across all training samples.

[0046] Specific Implementation Method 10: This implementation method differs from Specific Implementation Methods 1 to 9 in that the hyperparameters of the fracture toughness relationship model in step 3 aim to maximize the logarithmic marginal likelihood, and the L-BFGS-B (quasi-Newton method) is used as the optimizer.

[0047] Specific Implementation Method Eleven: This implementation method differs from Specific Implementation Methods One through Ten in that the calculation formula for the sampling score in step four is as follows:

[0048]

[0049] in , For the desired improvement value, The fusion weight of contribution-guided quantity The value range is [0.2, 0.5]; , , and This provides the fracture toughness prediction and uncertainty estimate output by the trained fracture toughness relationship model. This is the currently measured optimal fracture toughness value. To preset exploration parameters, and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively.

[0050] Specific Implementation Method Twelve: This implementation method differs from Specific Implementation Methods One to Eleven in that the preset Nb-Si based alloy composition constraint boundaries in step four are: Nb content 35-55 atomic percentage, Si content 8-18 atomic percentage, Ti content 15-35 atomic percentage, Al content 0-10 atomic percentage, Cr content 0-10 atomic percentage, Hf content 0-10 atomic percentage, V content 0-20 atomic percentage, Zr content 0-10 atomic percentage, Mo content 0-5 atomic percentage, Ta content 0-5 atomic percentage, Sn content 0-5 atomic percentage, and W content 0-5 atomic percentage.

[0051] Specific Implementation Method Thirteen: The Nb-Si alloy selected in this implementation method is composed of the following elements in terms of atomic percentage: Nb is 43.40%, Si is 10.12%, Ti is 23.86%, Al is 2.11%, V is 16.77%, and Zr is 3.74%.

[0052] Example 1: The construction and simplification of feature descriptors in this example are carried out according to the following steps:

[0053] Step 1: Collect composition and fracture toughness data of Nb-Si based alloys prepared by as-cast and electric arc melting processes from literature databases. Inclusion criteria: fracture toughness tests were completed at room temperature and K values ​​were reported. Q Value; the alloy is as-cast and has not undergone post-cast heat treatment; the elements appearing in the composition appear at least 10 times in the database, and a dataset containing 202 samples is established according to the above conditions;

[0054] Step 2: Calculate alloy-grade feature descriptors based on the alloy composition, constructing a total of 205 candidate descriptors. Elemental properties include atomic radius, covalent radius, Pauling electronegativity, electron affinity, ionization energy, melting point, boiling point, thermal conductivity, electrical conductivity, elastic modulus, Mohs hardness, density, specific heat capacity, coefficient of thermal expansion, cohesive energy, magnetic susceptibility, sound velocity, valence electron concentration, Miedema enthalpy of mixing parameter, and Hume-Rothery stability parameter. For each elemental property, perform four statistical transformations: combined weighted average, combined weighted variance, normalized deviation, and normalized deviation extreme difference, to obtain the alloy-grade descriptor. The combined weighted average reflects the average level of the property in the alloy; the combined weighted variance reflects the dispersion of the property in the alloy; the normalized deviation reflects the degree to which the contribution of each element deviates from the mean; and the normalized deviation extreme difference reflects the range of the contribution of each element.

[0055] Step 3: Employ a two-stage feature simplification strategy. First, eliminate constant descriptors with a uniqueness rate below 0.1. The uniqueness rate refers to the ratio of the number of distinct values ​​for a descriptor in the dataset to the total number of samples, used to identify constant or near-constant descriptors whose values ​​are almost unchanged. Next, eliminate the descriptor pair with the lowest absolute correlation to fracture toughness among pairs of descriptors with a Pearson correlation coefficient absolute value greater than 0.95. The remaining descriptors are then weighted and scored using a combination of Pearson correlation coefficient absolute value (35% weight), mutual information (35% weight), and conditional variance discriminant score (30% weight). Distance correlation is introduced as an auxiliary signal when available. A greedy selection process with minimum redundancy and maximum correlation is performed using normalized mutual information as the redundancy measure, retaining 50 descriptors.

[0056] The second stage: Within the Gaussian process model family, the top 15 descriptors are selected according to the weighted importance index for model adaptation. Then, a combined search is performed using the leave-one-out cross-validation root mean square error as the criterion. The error curve plateaus at the number of features (5), determining a simplified feature set containing 5 descriptors. These 5 simplified features are denoted as F1 (mean thermal conductivity), F2 (thermodynamic stability parameter Ω), F3 (average electronegativity), F4 (mixing entropy contribution ΔSmix), and F5 (mean electron affinity). F1 is calculated using the formula... Calculate F2 according to the formula Calculate F3 according to the formula Calculate, F4 according to formula Calculate, F5 according to the formula calculate, For elements The atomic fraction (i.e., the percentage of atoms divided by 100). , and elements respectively Thermal conductivity, average electronegativity (Pauling electronegativity), and electron affinity. The component-weighted average melting point of the Nb-Si based alloy is given. Let R be the enthalpy of mixture and R be the gas constant.

[0057] The process of this embodiment employing a two-stage feature simplification strategy is as follows: Figure 2 As shown.

[0058] Example 2: The process of establishing and verifying the fracture toughness relationship model in this example is as follows:

[0059] The fracture toughness relationship model is trained based on a simplified feature set. The model employs a Gaussian process regression model with uncertainty output capability. The covariance kernel of the fracture toughness relationship model is a combination of a radial basis function kernel (RBF kernel) and a white noise kernel. The RBF kernel provides a smooth and continuous performance response surface, while the white noise term characterizes experimental observation noise, meeting the smoothness requirements of alloy performance modeling. The kernel function is... ,in and As candidate components, For signal variance, For length scale, For noise variance, The Kronecker delta function is used; the hyperparameters of the fracture toughness relationship model are optimized by maximizing the logarithmic marginal likelihood, using L-BFGS-B as the optimizer and initializing with 30 sets of random starting points to obtain the trained fracture toughness relationship model.

[0060] The evaluation index of the fracture toughness relationship model in this embodiment includes the coefficient of determination R. 2 The root mean square error (RMSE) and the mean absolute error (MAE) are, among which , , , Let be the measured value of the i-th sample. Let be the predicted value for the i-th sample, and n be the total number of samples. The dataset is divided into an 80% training set and a 20% test set, evaluated using 10-fold cross-validation, with the test set reserved for the final performance report. After training, the model's RMSE on the test set is 0.978 MPa·m. 1 / 2 Test set R 2 The value is 0.907, indicating that the model has good prediction accuracy and generalization ability (e.g., Figure 2 (As shown in the figure); in addition to prediction accuracy, this fracture toughness relationship model provides analytical expressions for the predicted fracture toughness value and uncertainty for any candidate component, which is a necessary prerequisite for sampling score calculation.

[0061] Example 3: This example uses feature contribution-guided sampling scoring for closed-loop optimization:

[0062] Latin hypercube sampling is used to generate 100,000 candidate compositions within the compositional constraint boundaries. In this embodiment, the preset compositional constraint boundaries for the Nb-Si based alloy are: Nb content 35-55 atomic percentage, Si content 8-18 atomic percentage, Ti content 15-35 atomic percentage, Al content 0-10 atomic percentage, Cr content 0-10 atomic percentage, Hf content 0-10 atomic percentage, V content 0-20 atomic percentage, Zr content 0-10 atomic percentage, Mo content 0-5 atomic percentage, Ta content 0-5 atomic percentage, Sn content 0-5 atomic percentage, and W content 0-5 atomic percentage.

[0063] For each candidate component, a contribution decomposition based on cooperative game theory is performed according to the current fracture toughness relationship model to obtain the contribution decomposition values ​​of each key feature (i.e., F1 to F5) to the fracture toughness prediction. According to the formula: Calculate (M=5 in this embodiment); then compare with the global normalized importance of the features. Aggregation as contribution guide ,in According to the formula: Calculate Z, where Z is the normalization constant.

[0064] Sampling and scoring Calculation, where , , , and For the predicted fracture toughness and uncertainty estimates of the model output, This is the currently measured optimal fracture toughness value. The preset exploration parameters are (0.01 in this embodiment). and Let these be the cumulative distribution function and probability density function of the standard normal distribution. The fusion weights are set to [0.2, 0.5]. The logarithmic transformation avoids optimization stagnation caused by gradient vanishing in distant regions without altering the candidate ranking.

[0065] Fusion weights A fixed scheduling method is adopted, with values ​​of 0.2, 0.2, 0.3, 0.3, 0.4, and 0.5 respectively for rounds 1 to 6, which monotonically increase with the number of optimization rounds.

[0066] This embodiment employs contribution-guided sampling to conduct a six-round closed-loop experiment. The preset stopping criterion is reaching the maximum optimization round of 6. In each round, three candidate components are selected in descending order of sampling scores for preparation and testing. After the measured data is backfilled, the model is retrained. The convergence trajectory with each optimization round is as follows: Figure 3 As shown in Table 1, the optimal fracture toughness measured in each round is as follows.

[0067] Table 1. Contribution-guided sampling: Six rounds of measured optimal fracture toughness.

[0068]

[0069] Note: Three candidate components were measured in each round, and the table shows the highest measured value in each round.

[0070] The peak loads of the load-displacement curves measured in the three rounds using the contribution-guided sampling strategy were 194.9 N, 204.3 N, and 233.0 N, respectively, corresponding to fracture toughnesses of 16.95, 18.77, and 20.88 MPa·m. 1 / 2 The fracture toughness of the three candidate components in the third round increased monotonically with each round; the measured fracture toughness of the three candidate components in the third round were 20.88, 19.06, and 19.27 MPa·m. 1 / 2 The overall values ​​are in the high range, indicating that the sampling is concentrated in the dominant component region. The optimal composition is Nb 43.40 atomic percentage, Si 10.12 atomic percentage, Ti 23.86 atomic percentage, Al 2.11 atomic percentage, V 16.77 atomic percentage, and Zr 3.74 atomic percentage, with a measured fracture toughness of 20.88 MPa·m. 1 / 2 This is the highest value for cast-state arc-melted Nb-Si alloys in the demonstration database, and it is higher than the reported values ​​for most similar alloys prepared by heat treatment or additive manufacturing routes.

[0071] Example 4: Preparation and Verification of the Optimal Nb-Si Alloy:

[0072] Step 1) Raw material preparation. Weigh Nb, Si, Ti, Al, V and Zr raw materials with a purity greater than 99.9% according to the atomic percentage obtained in Example 3.

[0073] Step 2) Vacuum arc melting. Place the raw material into a water-cooled copper crucible in a vacuum arc melting furnace, evacuate the furnace, and then fill it with high-purity argon gas (purity greater than 99.999%). Perform arc melting on the raw material, repeating the melting process at least 7 times and turning it over each time to ensure uniform composition. After cooling, obtain an Nb-Si alloy ingot.

[0074] Step 3) Specimen preparation and performance testing. Three-point bending specimens (2 mm × 4 mm × 20 mm) were obtained from alloy ingots via wire electrical discharge machining. A pre-existing crack of approximately 2 mm was introduced through fatigue loading. Fracture toughness was tested at room temperature at a loading rate of 0.05 mm / min according to ASTM E399 standard. The measured fracture toughness was 20.88 MPa·m. 1 / 2 .

[0075] Table 2. Composition and fracture toughness of the optimal Nb-Si alloy

[0076]

[0077] Microstructure characterization of the optimal Nb-Si alloy (e.g.) Figure 4 As shown): X-ray diffraction confirmed that the alloy consists of a body-centered cubic Nb solid solution phase and a γ-Nb5Si3 phase; scanning electron microscopy showed a two-phase structure consisting of primary Nb solid solution dendrites and γ-Nb5Si3 distributed between the dendrites; electron backscatter diffraction showed that the Nb solid solution is the matrix phase and the two phases are evenly distributed.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the fracture toughness of ultra-high temperature alloys based on characteristic contribution, characterized in that... The method for optimizing the fracture toughness of ultra-high temperature alloys is implemented according to the following steps: Step 1: Collect composition and fracture toughness data of Nb-Si based alloys and construct a dataset; Step 2: Using the mean thermal conductivity, thermodynamic stability parameter Ω, average electronegativity, mixing entropy contribution ΔSmix, and mean electron affinity of Nb-Si based alloys as key features, a simplified feature set is formed, thus obtaining a simplified feature-fracture toughness dataset. Step 3: Train the fracture toughness relationship model using a simplified feature-fracture toughness dataset. The fracture toughness relationship model adopts a Gaussian process regression model with uncertainty output capability to obtain the trained fracture toughness relationship model. Step 4: Generate a candidate set within the preset Nb-Si based alloy composition constraint boundary. Based on the trained fracture toughness relationship model, perform feature contribution decomposition on each candidate component in the candidate set to obtain the contribution decomposition value of each key feature to the fracture toughness prediction at the candidate component. And combine the global normalized importance of each key feature on the simplified feature-fracture toughness dataset. The contribution guidance amount is calculated using the following formula: , Key features In candidate components The contribution decomposition value of the position to the prediction of fracture toughness. Key features Globally normalized importance on the feature descriptor-fracture toughness dataset This is the normalization constant; Then, the fracture toughness prediction, uncertainty estimate, and contribution guidance output by the fracture toughness relationship model are combined according to the preset fusion rules to generate a sampling score; Step 5: Select multiple candidate components in descending order of sampling scores. Perform alloy preparation and fracture toughness measurement on the selected candidate components. Calculate the corresponding key features based on the composition data of the selected candidate components. Backfill the calculated key features and fracture toughness measurement data into the simplified feature-fracture toughness dataset. Retrain the fracture toughness relationship model and repeat steps 4 and 5 for iteration until the preset stopping criterion is met. Screen and determine the Nb-Si alloy composition and atomic percentage of each element that meet the fracture toughness requirements from the iteration process, thus completing the ultra-high temperature alloy fracture toughness optimization method based on feature contribution degree. In step three, the covariance kernel of the fracture toughness relationship model is a combination of a radial basis function kernel and a white noise kernel, and the kernel function is: ,in and As candidate components, For signal variance, For length scale, For noise variance, This refers to the Kronecker delta function.

2. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... In step one, the Nb-Si based alloy contains 4 to 11 kinds of metallic elements.

3. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... Average thermal conductivity in step two According to the formula Calculation, where For elements atomic fraction, Let i be the thermal conductivity of element i. This indicates the summation of all elements in the alloy.

4. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... In step two, the thermodynamic stability parameter Ω is calculated using the formula... Calculation, where The component-weighted average melting point of the Nb-Si based alloy is given. Contributes to mixed entropy It is a mixed enthalpy.

5. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... Average electronegativity in step two According to the formula Calculation, where For elements atomic fraction, For elements Pauling's electronegativity, This indicates the summation of all elements in the alloy.

6. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... Step 2 contribution of mixed entropy According to the formula Calculation, where For elements The atomic fraction, where R is the gas constant. This indicates the summation of all elements in the alloy.

7. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... Mean electron affinity in step two According to the formula Calculation, where For elements atomic fraction, For elements electron affinity, This indicates the summation of all elements in the alloy.

8. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... In step three, the hyperparameters of the fracture toughness relationship model are optimized by maximizing the logarithmic marginal likelihood, using L-BFGS-B as the optimizer.

9. The method for optimizing the fracture toughness of ultra-high temperature alloys based on feature contribution as described in claim 1, characterized in that... The formula for calculating the sampling score in step four is as follows: in , For the desired improvement value, The fusion weight of contribution-guided quantity The value range is [0.2, 0.5]; , , and This provides the fracture toughness prediction and uncertainty estimate output by the trained fracture toughness relationship model. This is the currently measured optimal fracture toughness value. To preset exploration parameters, and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively.

10. The Nb-Si alloy screened based on the feature contribution-guided method for optimizing the fracture toughness of ultra-high temperature alloys as described in claim 1, characterized in that... The selected Nb-Si alloys were composed of the following elements in atomic percentage: Nb 43.40%, Si 10.12%, Ti 23.86%, Al 2.11%, V 16.77%, and Zr 3.74%.

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