A design method for refractory high-entropy alloys

Abstract

This invention discloses a design method for refractory high-entropy alloys, belonging to the technical field of compositional design of refractory high-entropy alloys. The design method includes the following steps: for refractory high-entropy alloys in the Nb-Ta-Hf-Zr-Mo-Ti-W system, establishing a compositional design method containing 10... ‑3 s ‑1 up to the 2000s ‑1 This invention presents a composition-performance dataset covering a strain rate range. Core physical features are extracted, and the dataset is expanded using Monte Carlo sampling after data cleaning. A random forest model is employed, with alloy composition and physical features as inputs and dynamic strength and fracture strain as outputs. The optimal model is selected through cross-validation, and the MeanUds' regulatory mechanism on performance is analyzed using SHAP value analysis. Target alloy compositions are then selected based on compositional design constraints. This invention achieves a synergistic improvement in the strength and quasi-static ductility of refractory high-entropy alloys.

Description

Technical Field

[0001] This invention relates to the field of composition design technology for refractory high entropy alloys (RHEAs), and specifically to a design method for refractory high entropy alloys. Background Technology

[0002] With the increasing demands on structural material performance in extreme environments such as aerospace and nuclear industries, high-entropy alloys (HEAs), thanks to the freedom of multi-principal component design, have shown superior potential compared to traditional alloys in terms of high-temperature strength and radiation resistance, providing a new path for the development of materials for refractory environments. However, the compositional space of refractory high-entropy alloys (RHEAs, such as the W-Nb-Ta-V-Hf-Zr system) is complex, and traditional empirical trial-and-error methods struggle to overcome the bottleneck of "strength-ductility inversion under wide strain rates"—dynamic loading (strain rate ≥ 10). 3 s -1 Strength increases but plasticity drops sharply under quasi-static loading (strain rate ≤ 10). 3 s -1 While its plasticity is improved, its strength is insufficient, limiting its application in extreme variable load scenarios.

[0003] In recent years, machine learning technology has been gradually applied to the design of high-entropy alloys (such as CN113870957A and CN114678086A), accelerating composition screening through data-driven approaches. However, it has key drawbacks: Limited performance optimization dimensions: Most patents focus on single properties (such as eutectic formation, low activation, and hardness, CN112216356A and WO2024 / 098522), failing to address the coordinated design of strength and ductility under wide strain rates, making it difficult to meet complex load requirements; Insufficient composition space coverage: Existing methods are mostly targeted at specific systems (such as Fe-Cr-VW-Mn, CN114678086A), with limited ability to mine the complex composition space of multi-principal elements (≥5 refractory metals) in refractory high-entropy alloys; Lack of model interpretability: For example, WO2024 / 098522 relies on Pareto front clustering to screen compositions, failing to combine physical mechanisms (such as electronic structure) to analyze performance regulation laws, resulting in a blind design process that is prone to getting trapped in local optima.

[0004] Existing technologies for refractory high-entropy alloys further highlight their limitations: Limitations in dynamic performance optimization: CN115061435A only predicts hardness and does not address the strength-plasticity correlation across a wide strain rate; A lack of static-dynamic synergy: Existing patents do not reveal the regulatory mechanism of electronic structure (such as d-electron filling state) on performance across a wide strain rate, failing to explain "why certain components perform excellently under both dynamic and static loading"; Low data efficiency: Models trained with small sample data (≤300 sets) have poor generalization ability, making it difficult to support high-dimensional compositional searches for refractory high-entropy alloys.

[0005] In summary, the synergistic optimization of the properties of refractory high-entropy alloys across wide strain rates faces four major challenges: complex compositional space, conflicting coupling of multiple properties, unclear physical mechanisms, and scarce data. Existing machine learning methods, lacking guidance from physical features and adaptation to wide strain rate scenarios, cannot overcome these bottlenecks. Therefore, it is urgent to construct a closed-loop design method based on "physical mechanisms + data-driven" approaches. By quantifying the correlation between electronic structure and properties across wide strain rates, this method can achieve efficient and interpretable design of refractory high-entropy alloys. Summary of the Invention

[0006] The purpose of this invention is to overcome the above-mentioned technical deficiencies and provide a design method for refractory high-entropy alloys, solving the technical problem of how to achieve synergistic improvement of the strength and quasi-static ductility of refractory high-entropy alloys in the prior art.

[0007] To achieve the above-mentioned technical objectives, the present invention provides a design method for refractory high-entropy alloys, comprising the following steps:

[0008] S1. For refractory high-entropy alloys in the Nb-Ta-Hf-Zr-Mo-Ti-W system, establish a system containing 10 -3 s -1 up to the 2000s -1 A composition-property dataset for strain rate ranges, the dataset including alloy chemical composition, dynamic compressive yield strength and quasi-static fracture strain;

[0009] S2. Extract core physical features and expand the dataset based on Monte Carlo sampling after data cleaning; the core physical features include the average number of unoccupied d electrons and the valence electron concentration.

[0010] S3. A random forest model is adopted, with alloy composition and physical characteristics as inputs and dynamic strength and fracture strain as outputs. The optimal model is selected through cross-validation, and the performance regulation mechanism of the average unoccupied d electrons (i.e., MeanUds) is analyzed through SHAP value analysis.

[0011] S4. Using the average number of unoccupied d electrons of 5.5 to 7.0 as the core range, target alloy compositions are screened in combination with composition design constraints.

[0012] In any embodiment, in step S1, the alloy chemical composition contains 3 to 6 refractory metals, by atomic percentage; the test condition for the dynamic compressive yield strength is a strain rate ≥ 10. 3 s -1 Typical value is 2000s -1 The test condition for the quasi-static fracture strain is a strain rate ≤ 10. 3 s -1 The typical value is 0.001s. -1 .

[0013] In any implementation, in step S2, the average number of unoccupied d electrons is calculated by weighted summation of the number of unfilled d orbitals of each component; the data cleaning includes deleting outliers and missing values, and averaging duplicate data with a relative error of <10%.

[0014] In any implementation, in step S3, the prediction formula of the random forest model is:

[0015]

[0016] in, Here, f represents the model's predicted value, K is the number of decision trees, and f is the value predicted by the model. k (x) is the prediction result of the k-th decision tree for the input feature x; and / or, in step S3, the SHAP value analysis determines that MeanUds is the primary influencing factor of dynamic intensity and the second influencing factor of fracture strain, with a linear correlation coefficient |r|>0.7 with VEC.

[0017] In any implementation, in step S3, the dynamic intensity prediction R of the optimal model 2 ≥0.75, fracture strain prediction R 2 ≥0.76.

[0018] In any embodiment, in step S4, the composition design constraints are: W+Nb content is 0-30 at.%, Hf+Zr+Ti content is 5-40 at.%, and Ta+V content is 40-70 at.%; the target alloy composition satisfies a dynamic strength of 1.8-2.5 GPa and a quasi-static fracture strain of 11-47%.

[0019] In any embodiment, after step S4, step S5 further includes preparing the alloy by vacuum arc melting and testing its mechanical properties under a wide strain rate.

[0020] In any embodiment, in step S5, the raw materials for vacuum arc melting have a purity of ≥99.9%, are placed in order of melting point from low to high, and are repeatedly melted 5 to 8 times under argon protection; then the quasi-static and dynamic properties are tested respectively.

[0021] In any implementation, in step S5, if the dynamic strength of the test performance is <1.4 GPa and / or the fracture strain is <10%, the data is fed back to the initial dataset, and steps S2 to S5 are repeated.

[0022] In any embodiment, in step S4, the selected alloys include W5Hf5Ta. 35 V 35 Nb 20 W 20 Ta 35 V35 Ti 10 Or W 30 Zr5Ta 20 V 35 Ti 10 .

[0023] Compared with existing technologies, the beneficial effects of this invention include: This invention uses the average unoccupied d-electrons (MeanUds) as the core physical characteristic, combined with interpretable machine learning and data augmentation, to achieve a synergistic improvement in the strength and quasi-static ductility of refractory high-entropy alloys, revealing its effect on 10... -3 ~2000s -1 A dual-effect regulation mechanism for the strength and ductility of refractory high-entropy alloys under wide strain rates breaks through the traditional "performance inversion" bottleneck, enabling efficient design and performance leap under extreme variable load conditions. Attached Figure Description

[0024] Figure 1 This is a schematic diagram illustrating the principle of the design method for refractory high-entropy alloys proposed in this invention.

[0025] Figure 2 This is a model performance evaluation diagram for predicting the alloy strength performance of Embodiment 1 of the present invention.

[0026] Figure 3 This is a performance evaluation diagram of the predicted plasticity properties of the alloy in Example 1 of the present invention.

[0027] Figure 4 This is a comparison chart of the alloy multi-property synergistic optimization of the feature design implemented in Embodiment 1 of the present invention and the properties of existing alloys.

[0028] Figure 5 This is a test curve of the compressive mechanical properties of the alloy designed in Example 1 of the present invention under a wide strain rate range at room temperature.

[0029] Figure 6 This is the XRD pattern of the alloy designed in Embodiment 1 of the present invention. Detailed Implementation

[0030] The "range" disclosed in this application is defined by a lower limit and an upper limit. A given range is defined by selecting a lower limit and an upper limit, which define the boundaries of a particular range. Ranges defined in this way can include or exclude endpoints and can be arbitrarily combined; that is, any lower limit can be combined with any upper limit to form a range. For example, if ranges of 60–120 and 80–110 are listed for a specific parameter, it is understood that ranges of 60–110 and 80–120 are also expected. Furthermore, if minimum range values ​​of 1 and 2 are listed, and if maximum range values ​​of 3, 4, and 5 are listed, then the following ranges are all expected: 1–3, 1–4, 1–5, 2–3, 2–4, and 2–5. In this application, unless otherwise stated, the numerical range "a–b" represents a shortened representation of any combination of real numbers between a and b, where a and b are real numbers. For example, the numerical range "0~5" indicates that all real numbers between "0~5" have been listed in this article; "0~5" is simply a shortened representation of these numerical combinations. Furthermore, when a parameter is stated as an integer ≥2, it is equivalent to disclosing that the parameter is, for example, an integer such as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, etc.

[0031] Unless otherwise specified, the terms "comprising" and "including" as used in this application can be open-ended or closed-ended. For example, "comprising" and "including" can mean that other components not listed may also be included, or that only the listed components may be included.

[0032] Unless otherwise specified, the term "or" is inclusive in this application. For example, the phrase "A or B" means "A, B, or both A and B". More specifically, the condition "A or B" is satisfied by any of the following conditions: A is true (or exists) and B is false (or does not exist); A is false (or does not exist) and B is true (or exists); or both A and B are true (or exist).

[0033] This specific embodiment provides a design method for refractory high-entropy alloys, including the following steps:

[0034] S1. For refractory high-entropy alloys in the Nb-Ta-Hf-Zr-Mo-Ti-W system, establish a system containing 10 -3 s -1 up to the 2000s -1 A composition-property dataset for a strain rate range, comprising alloy chemical composition, dynamic compressive yield strength, and quasi-static fracture strain; the alloy chemical composition contains 3 to 6 refractory metals, expressed as atomic percentages; the dynamic compressive yield strength is tested under strain rate ≥10. 3 s -1 Typical value is 2000s-1 The test condition for the quasi-static fracture strain is a strain rate ≤ 10. 3 s -1 The typical value is 0.001s. -1 .

[0035] S2. Extract core physical features and expand the dataset using Monte Carlo Sampling (MCS) after data cleaning (based on the law of large numbers) to address the scarcity of RHEAs data and improve the sufficiency of model training. The core physical features include the average number of unoccupied d electrons and the valence electron concentration. The average number of unoccupied d electrons is calculated by weighted summation of the number of unfilled electrons in the d orbitals of each component. Data cleaning includes removing outliers and missing values, and averaging duplicate data with a relative error of <10%.

[0036] S3. A random forest model is adopted, with alloy composition and physical characteristics as inputs and dynamic strength and fracture strain as outputs. The optimal model is selected through cross-validation, and the MeanUds regulation mechanism on performance is analyzed through SHAP value analysis. The prediction formula of the random forest model is:

[0037]

[0038] in, Here, f represents the model's predicted value, K is the number of decision trees, and f is the value predicted by the model. k (x) represents the prediction result of the k-th decision tree for the input feature x; the dynamic strength prediction R of the optimal model. 2 ≥0.75, fracture strain prediction R 2 ≥0.76;

[0039] SHAP analysis revealed that MeanUds is the primary influencing factor of dynamic strength and the second influencing factor of fracture strain, showing a strong correlation with VEC (linear correlation coefficient |r|>0.7), validating the rationality of MeanUds as the core physical characteristic for strength-ductility synergistic optimization. The characteristic-performance correlation law was further clarified through linear fitting and SHAP analysis, showing that MeanUds is positively correlated with both dynamic strength and fracture strain in the range of 5.5–7.0 (fitting slope k>0).

[0040] S4. Using the average number of unoccupied d electrons of 5.5–7.0 as the core range, target alloy compositions are screened based on compositional design constraints. The compositional design constraints are: W+Nb content of 0–30 at.%, Hf+Zr+Ti content of 5–40 at.%, and Ta+V content of 40–70 at.%. The target alloy compositions satisfy dynamic strength of 1.8–2.5 GPa and quasi-static fracture strain of 11–47%.

[0041] In some embodiments, after step S4, step S5 further includes preparing an alloy by vacuum arc melting and testing its mechanical properties under a wide strain rate. In step S5, the purity of the raw materials for vacuum arc melting is ≥99.9%, and they are placed in order of melting point from low to high, and repeatedly melted 5 to 8 times under argon protection. Then, quasi-static and dynamic properties are tested respectively. If the dynamic strength of the tested properties is <1.4GPa and / or the fracture strain is <10%, the data is fed back to the initial dataset, and steps S2 to S5 are repeated.

[0042] In some embodiments, in step S4, the selected alloys include W5Hf5Ta. 35 V 35 Nb 20 W 20 Ta 35 V 35 Ti 10 Or W 30 Zr5Ta 20 V 35 Ti 10 .

[0043] This invention is the first to use the average unoccupied d electron number (MeanUds) as the core physical characteristic, and combines interpretable machine learning and data augmentation to reveal its effect on 10 -3 ~2000s -1 A dual-effect regulation mechanism for the strength and ductility of refractory high-entropy alloys under wide strain rates breaks through the traditional "performance inversion" bottleneck, enabling efficient design and performance leap under extreme variable load conditions.

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0045] In this invention, the terms "some embodiments," "this embodiment," and examples are used to describe a subset of all possible embodiments. However, it is understood that "some embodiments" can be the same subset or different subsets of all possible embodiments and can be combined with each other without conflict.

[0046] If the application documents contain similar descriptions such as "first / second", the following explanation shall be added: In the following description, the terms "first / second / third" are used only to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first / second / third" may be interchanged in a specific order or sequence where permitted, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein.

[0047] In this embodiment, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, object A and / or object B can represent three situations: object A exists alone, object A and object B exist simultaneously, and object B exists alone.

[0048] The following describes embodiments of this application. The embodiments described below are exemplary and are only used to explain this application, and should not be construed as limiting this application. Where specific techniques or conditions are not specified in the embodiments, they are performed according to the techniques or conditions described in the literature in this field or according to the product instructions. Reagents or instruments used, unless otherwise specified, are all conventional products that can be obtained commercially.

[0049] Example 1

[0050] Combination Figure 1 This embodiment focuses on refractory high entropy alloys (RHEAs) in the Nb-Ta-Hf-Zr-Mo-Ti-W system, aiming to design alloys with high entropy in 10... -3 ~2000s -1 The alloy composition that possesses both high dynamic strength (≥1.4 GPa) and high quasi-static ductility (≥10%) over a wide strain rate range is determined through the following steps:

[0051] S1: Through literature review, we collected composition and performance data of 120 sets of Nb-Ta-Hf-Zr-Mo-Ti-W system RHEAs, covering the following:

[0052] Alloy composition: Contains 3 to 6 refractory elements, with each element having an atomic percentage between 5% and 35%.

[0053] Mechanical properties: Dynamic compressive yield strength (at 2000s) -1 Under strain rate, a split Hopkinson bar test was used) and quasi-static fracture strain (at 0.001 s⁻¹) was employed. -1 (Tested using an electronic universal testing machine at strain rate).

[0054] Physical characteristic parameters: Calculate the average number of unoccupied d electrons (MeanUds), valence electron concentration (VEC), shear modulus, electronegativity, etc. for each component. MeanUds is calculated by weighting the number of unfilled d orbitals in each component; for example, W has 4 unfilled d electrons, while Ti has 2.

[0055] The data were organized into an initial dataset according to the format of "composition-physical characteristics-dynamic strength-quasi-static fracture strain".

[0056] S2: Delete outliers such as dynamic strength > 3000 MPa and fracture strain < 0, as well as missing values; for repeated data of the same composition, if the relative error is < 10%, take the average value. For example, if the dynamic strength of a certain alloy is reported three times as 1800, 1850 and 1900 MPa, take the average value of 1850 MPa; if the error is > 10%, delete it.

[0057] The dataset was augmented using Monte Carlo sampling (MCS). Based on the statistical distribution of the original data, such as the mean of MeanUds being 6.5 and the standard deviation being 0.5, 1000 virtual samples were generated to ensure that the virtual data had the same feature distribution as the original data.

[0058] S3: A random forest model (implemented via the Python sklearn library) is used, with "alloy composition and physical characteristics" (such as W, Ta content, MeanUds, VEC, etc.) as input and dynamic strength and quasi-static fracture strain as output; the prediction formula of the random forest model is:

[0059]

[0060] in, Here, f represents the model's predicted value, K is the number of decision trees, and f is the value predicted by the model. k (x) represents the prediction result of the k-th decision tree for the input feature x.

[0061] Model parameters are set as follows: 100 decision trees, maximum depth 10, and 10-fold cross-validation (the dataset is divided into 10 groups, with 9 groups used for training and 1 group for validation in rotation). Figure 2-3 The final dynamic intensity prediction R 2 =0.75, fracture strain prediction R 2 =0.76.

[0062] Key features were screened by SHAP value analysis. The results showed that MeanUds had an importance weight of 0.32 for dynamic intensity (ranked 1st) and an importance weight of 0.28 for fracture strain (ranked 2nd). The correlation coefficient r with VEC was 0.72, which verified its rationality as a core descriptor.

[0063] S4: Component design based on MeanUds: combining SHAP analysis and linear fitting, and... Figure 4 It was found that when MeanUds is in the range of 5.5 to 7.0, it is positively correlated with dynamic strength and fracture strain (the fitting slopes are 150 MPa / unit MeanUds and 5% / unit MeanUds, respectively). Therefore, this range is taken as the optimization interval.

[0064] In the Nb-Ta-Hf-Zr-Mo-Ti-W composition space (3-6 elements, content 5%-35%), alloys with MeanUds = 5.5-7.0 were screened out. Combined with pseudo-ternary phase diagram constraints (W+Nb 0-30%, Hf+Zr+Ti 5-40%, Ta+V 40-70%), three candidate compositions were obtained: Alloy 1: W5Hf5Ta 35 V 35 Nb 20 (MeanUds = 6.8, i.e., W5) Alloy 2: W 20 Ta 35 V 35 Ti 10 (MeanUds = 6.9, i.e., W20) Alloy 3: W 30 Zr5Ta 20 V 35 Ti 10 (MeanUds = 6.85, i.e. W30).

[0065] S5: Select W, Nb, Ta, V, Hf, Zr, and Ti metal blocks with a purity ≥99.9%. After grinding to remove the oxide scale, ultrasonically clean for 15 minutes. Weigh according to the composition ratio, place the raw materials in a non-consumable vacuum arc furnace, and melt them sequentially in order of melting point from low to high (Ti→V→Zr→Nb→Hf→Ta→W) under argon protection (vacuum degree 5×10-3Pa, argon pressure 0.05MPa). Repeat the melting process 6 times to obtain a Φ20mm×10mm ingot.

[0066] Combination Figure 6 XRD analysis showed that all three alloys had a single BCC structure (diffraction peaks were located near 40°, 60°, and 80°, corresponding to the (110)(200)(211) crystal planes).

[0067] Performance testing:

[0068] Combination Figure 5 Quasi-static compression (0.001s) -1 Alloy 1 has a yield strength of 1282.7 MPa and a fracture strain of 47.3%; Alloy 2 has a yield strength of 1856.2 MPa and a fracture strain of 11.7%; Alloy 3 has a yield strength of 1190.3 MPa and a fracture strain of 12.7%.

[0069] Dynamic compression (2000s) -1 Alloy 1 has a dynamic strength of 1814.7 MPa and no macroscopic fracture; Alloy 2 has a dynamic strength of 1402.5 MPa and a fracture strain of 10.1%; Alloy 3 has a yield strength of 1765.9 MPa and a fracture strain of 13.6%.

[0070] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A design method for refractory high-entropy alloys, characterized in that, Includes the following steps: S1. For refractory high-entropy alloys in the Nb-Ta-Hf-Zr-Mo-Ti-W system, establish a system containing 10 -3 s -1 up to the 2000s -1 S1. A composition-performance dataset for the strain rate range, comprising alloy chemical composition, dynamic compressive yield strength, and quasi-static fracture strain; S2. Extracting core physical features and expanding the dataset after data cleaning using Monte Carlo sampling; the core physical features include the average number of unoccupied d electrons and valence electron concentration; S3. Employing a random forest model with alloy composition and physical features as inputs and dynamic strength and fracture strain as outputs, selecting the optimal model through cross-validation, and analyzing the regulation mechanism of the average number of unoccupied d electrons on performance through SHAP value analysis; S4. Selecting target alloy compositions with an average number of unoccupied d electrons of 5.5–7.0 as the core range, combined with composition design constraints.

2. The design method for refractory high-entropy alloys according to claim 1, characterized in that, In step S1, the alloy chemical composition contains 3 to 6 refractory metals, by atomic percentage; the test condition for the dynamic compressive yield strength is a strain rate ≥ 10. 3 s -1 Typical value is 2000s -1 The test condition for the quasi-static fracture strain is a strain rate ≤ 10. 3 s -1 The typical value is 0.001s. -1 .

3. The design method for refractory high-entropy alloys according to claim 1, characterized in that, In step S2, the average number of unoccupied d electrons is calculated by weighted summation of the number of unfilled d orbitals in each component; the data cleaning includes deleting outliers and missing values, and averaging duplicate data with a relative error of <10%.

4. The design method for refractory high-entropy alloys according to claim 1, characterized in that, In step S3, the prediction formula of the random forest model is: in, Here, K represents the predicted value from the model, and K is the number of decision trees. This represents the prediction result of the k-th decision tree for the input feature x. And / or, in step S3, the SHAP value analysis determines that the average number of unoccupied d electrons is the primary influencing factor of dynamic intensity and the second influencing factor of fracture strain, with a linear correlation coefficient |r|>0.7 with VEC.

5. The design method for refractory high-entropy alloys according to claim 4, characterized in that, In step S3, the dynamic intensity prediction R of the optimal model is... 2 ≥0.75, fracture strain prediction R 2 ≥0.

76.

6. The design method for refractory high-entropy alloys according to claim 1, characterized in that, In step S4, the composition design constraints are: W+Nb content is 0~30 at.%, Hf+Zr+Ti content is 5~40 at.%, and Ta+V content is 40~70 at.%; the target alloy composition satisfies a dynamic strength of 1.8~2.5 GPa and a quasi-static fracture strain of 11~47%.

7. The design method for refractory high-entropy alloys according to claim 1, characterized in that, After step S4, step S5 further includes preparing the alloy using vacuum arc melting and testing its mechanical properties under a wide strain rate.

8. The design method for refractory high-entropy alloys according to claim 7, characterized in that, In step S5, the raw materials for vacuum arc melting have a purity of ≥99.9%, are placed in order of melting point from low to high, and are repeatedly melted 5 to 8 times under argon protection; then the quasi-static and dynamic properties are tested respectively.

9. The design method for refractory high-entropy alloys according to claim 8, characterized in that, In step S5, if the dynamic strength of the test performance is <1.4 GPa and / or the fracture strain is <10%, the data is fed back to the initial dataset, and steps S2 to S5 are repeated.

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