Design method of refractory high-entropy alloy

Abstract

The invention discloses a design method of a refractory high-entropy alloy, and belongs to the technical field of component design of refractory high-entropy alloys. The design method of the refractory high-entropy alloy comprises the following steps: aiming at the Nb-Ta-Hf-Zr-Mo-Ti-W system refractory high-entropy alloy, establishing a component-performance data set containing a strain rate range of 10 <-3 > s <-1 > to 2000 s <-1 >; extracting core physical characteristics, and expanding a data set based on Monte Carlo sampling after data cleaning; a random forest model is adopted, alloy components and physical characteristics serve as input, dynamic strength and fracture strain serve as output, an optimal model is screened through cross validation, a regulation and control mechanism of MeanUds on performance is analyzed through SHAP value analysis, and target alloy components are screened in combination with component design constraints. According to the method, the strength and the quasi-static ductility of the refractory high-entropy alloy are synergistically improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of component design of refractory high-entropy alloys (RHEAs), and in particular to a design method of refractory high-entropy alloys. BACKGROUND

[0002] With the upgrading of performance requirements of structural materials in extreme environments such as aerospace and nuclear industry, high-entropy alloys (HEAs) have shown potential superior to traditional alloys in high-temperature strength and radiation resistance due to the freedom of multi-principal component design, providing a new path for the research and development of materials for refractory environments. However, the composition space of refractory high-entropy alloys (RHEAs, such as W-Nb-Ta-V-Hf-Zr system) is complex, and the traditional empirical trial-and-error method is difficult to break through the "inversion of strength-ductility at wide strain rate" bottleneck - the strength is improved but the plasticity is sharply reduced at dynamic loading (strain rate ≥ 10 3 s -1 ), and the plasticity is improved but the strength is insufficient at quasi-static loading (strain rate ≤ 10 3 s -1 ), which limits its application in extreme variable load scenarios.

[0003] In recent years, machine learning technology has been gradually applied to high-entropy alloy design (such as CN113870957A, CN114678086A), accelerating the composition screening through data-driven methods, but there are key defects: single performance optimization dimension: most patents focus on a single performance (such as eutectic formation, low activation, hardness, CN112216356A, WO2024 / 098522), and do not design for strength-ductility synergy at wide strain rate, which is difficult to meet the complex load demand; insufficient composition space coverage: existing methods are mostly targeted at specific systems (such as Fe-Cr-V-W-Mn, CN114678086A), and have limited ability to explore the complex composition space of multi-principal components (≥5 refractory metals) of refractory high-entropy alloys; lack of model interpretability: such as WO2024 / 098522 relies on Pareto frontier clustering to screen components, and does not combine physical mechanisms (such as electronic structure) to analyze performance regulation rules, which makes the design process blind and prone to local optimization.

[0004] The existing technology for refractory high-entropy alloys further highlights the limitations: dynamic performance optimization limitation: CN115061435A only predicts hardness and does not involve the correlation between strength and plasticity at wide strain rate; static-dynamic synergy blank: existing patents do not reveal the regulation mechanism of electronic structure (such as d electron filling state) on wide strain rate performance, which cannot explain "why some components perform well under dynamic and static loading"; low data efficiency: the model trained by small sample data (≤300 groups) has poor generalization ability, which is difficult to support high-dimensional composition search of refractory high-entropy alloys.

[0005] In summary, the wide strain rate performance of refractory high-entropy alloys is synergistically optimized, and faces four challenges: complex composition space, multiple performance coupling conflicts, unknown physical mechanism, and data scarcity. Existing machine learning methods cannot break through the bottleneck due to the lack of physical feature guidance and wide strain rate scene adaptation. Therefore, it is urgent to build a closed-loop design method of "physical mechanism + data-driven", to realize the efficient and interpretable design of refractory high-entropy alloys by quantifying the correlation between electronic structure and wide strain rate performance. SUMMARY

[0006] The purpose of the present application is to overcome the above technical deficiencies, and provide a design method of refractory high-entropy alloy, which solves the technical problem of how to realize the synergistic improvement of strength and quasi-static ductility of refractory high-entropy alloy in the prior art.

[0007] To achieve the above technical purpose, the technical scheme of the present application provides a design method of refractory high-entropy alloy, comprising the following steps:

[0008] S1, for the Nb-Ta-Hf-Zr-Mo-Ti-W system refractory high-entropy alloy, a composition-performance data set containing 10 -3 s -1 to 2000s -1 strain rate range is established, and the data set includes alloy chemical composition, dynamic compression yield strength and quasi-static fracture strain;

[0009] S2, after data cleaning, the core physical features are extracted and the data set is expanded based on Monte Carlo sampling; the core physical features include average unoccupied d electron number and valence electron concentration;

[0010] S3, a random forest model is adopted, the alloy composition and physical features are taken as inputs, the dynamic strength and fracture strain are taken as outputs, the optimal model is selected through cross-validation, and the regulation mechanism of the average unoccupied d electron number (i.e. MeanUds) on the performance is analyzed through SHAP value analysis;

[0011] S4, taking the average unoccupied d electron number 5.5-7.0 as the core interval, the target alloy composition is selected in combination with the composition design constraint.

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

[0013] In any embodiment, in step S2, the average unoccupied d-electron number is calculated by weighted summation of the unoccupied electron number of each group d-orbital; the data cleaning includes deleting outliers, missing values, and averaging repeated data with relative error <10%.

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

[0015]

[0016] wherein, is the predicted value of the model, K is the number of decision trees, f k (x) is the prediction result of the kth decision tree on the input feature x; and / or, in step S3, the SHAP value analysis determines that MeanUd is the primary influencing factor of dynamic strength, and is the second influencing factor of fracture strain, with a linear correlation coefficient |r|>0.7 with VEC.

[0017] In any embodiment, in step S3, the dynamic strength prediction R 2 of the optimal model is ≥0.75, and the fracture strain prediction R 2 is ≥0.76.

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

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

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

[0021] In any embodiment, in step S5, if the tested dynamic strength <1.4 GPa and / or fracture strain <10%, the data is fed back to the initial data set, and steps S2-S5 are repeated.

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

[0023] Compared with the prior art, the beneficial effects of the present application include: the present application takes the mean unoccupied d electron number (Mean Uds) as the core physical feature, combines interpretable machine learning and data enhancement, realizes the synergistic improvement of the strength and quasi-static ductility of refractory high-entropy alloys, and reveals its effect on 10 -3 ~2000s -1 The dual-effect regulation mechanism of the strength-ductility of refractory high-entropy alloys under wide strain rate, breaks through the traditional "performance inversion" bottleneck, and realizes the efficient design and performance leap under extreme variable load environment. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 is the principle diagram of the design method of the refractory high-entropy alloy proposed by the present application.

[0025] Figure 2 is the model performance evaluation diagram of the alloy strength performance prediction of embodiment 1 of the present application.

[0026] Figure 3 is the model performance evaluation diagram of the alloy plasticity performance prediction of embodiment 1 of the present application.

[0027] Figure 4 is the comparison diagram of the multi-performance synergistic optimization of the alloy of the embodiment feature design of embodiment 1 of the present application and the performance of the existing alloy.

[0028] Figure 5 is the compression mechanical property test curve diagram of the alloy designed in embodiment 1 of the present application under wide strain rate at room temperature.

[0029] Figure 6 is the XRD diagram of the alloy designed in embodiment 1 of the present application. DETAILED DESCRIPTION

[0030] "ranges" recited in the specification are inclusive of the endpoints and are presented as shorthand for describing a group of values that includes the endpoints. A range of values includes the endpoint values unless specifically excluded. For example, a range of "60% to 120%" is intended to include 60% and 120% and not the exclusion of 60 and 120 individually. Similarly, a range of "60% to 120%" is intended to include 60% to 120% and not the exclusion of 60 and 120 individually. In addition, a range of values written as "a to b" is intended to include any and all values and / or sub-ranges encompassed therein. For example, a range of "0 to 5" is intended to include any and all sub-ranges between (and including) the minimum value of zero and the maximum value of five, that is, any value that falls between the minimum of zero and the maximum of five, as well as any and all sub-ranges within that range (for example, 1 to 2.5).

[0031] The terms "comprise" (and any grammatical variations thereof, such as "comprises" and "comprising"), "contain" (and any grammatical variations thereof, such as "contains" and "containing"), "include" (and any grammatical variations thereof, such as "includes" and "including") and "have" (and any grammatical variations thereof, such as "has" and "having") are open-ended, both in the dictionaries and the patent law, and specify the presence of the stated

[0032] The term "or" as used in the application is inclusive, unless otherwise indicated. For example, the phrase "A or B" means "A, B, or both A and B." More specifically, any of the following are satisfied: A is true (or present) and B is false (or not present); A is false (or not present) and B is true (or present); or both A and B are true (or present).

[0033] The detailed description provides a design method of refractory high-entropy alloys, comprising the following steps:

[0034] S1, for a Nb-Ta-Hf-Zr-Mo-Ti-W system refractory high-entropy alloy, a composition-property data set containing 10 -3 s -1 to 2000s -1 strain rate range, the data set comprising alloy chemical composition, dynamic compression yield strength and quasi-static fracture strain; the alloy chemical composition comprises 3-6 refractory metals in atomic percentage; the test condition of the dynamic compression yield strength is a strain rate ≥ 10 3 s -1 , and a 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] The term "and / or" in the present embodiment only describes the association relationship of the associated objects, and means that there can be three relationships, for example, object A and / or object B, which can represent three cases of the existence of object A alone, the existence of object A and object B, and the existence of object B alone.

[0048] Hereinafter, the embodiments of the present application will be described. The embodiments described below are exemplary and are for the purpose of explaining the present application only and are not to be understood as limiting the present application. In the embodiments, the specific techniques or conditions not mentioned are performed in accordance with the techniques or conditions described in the literature in the art or in accordance with the product manual. The reagents or instruments not mentioned by the manufacturer are all conventional products that can be obtained commercially.

[0049] Embodiment 1

[0050] In combination Figure 1 , the present embodiment takes Nb-Ta-Hf-Zr-Mo-Ti-W system refractory high-entropy alloys (RHEAs) as the research object, aiming to design an alloy composition with high dynamic strength (≥1.4 GPa) and high quasi-static ductility (≥10%) in a wide strain rate range of 10 -3 ~2000s -1 , the specific steps are as follows:

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

[0052] Alloy composition: containing 3-6 refractory elements, the atomic percentage of each single element is between 5% and 35%.

[0053] Mechanical properties: dynamic compression yield strength (at 2000s -1 strain rate, tested by split Hopkinson pressure bar) and quasi-static fracture strain (at 0.001s -1 strain rate, tested by electronic universal testing machine).

[0054] Physical characteristic parameters: the average unoccupied d electron number (MeanUds) of each component, the valence electron concentration (VEC), the shear modulus, the electronegativity, etc. are calculated. Among them, MeanUds is calculated by weighting the number of d orbital unoccupied electrons of each component, for example, the d electron unoccupied number of W is 4 and that of Ti is 2.

[0055] These data are arranged in the format of "composition-physical characteristics-dynamic strength-quasi-static fracture strain" to form an initial data set.

[0056] S2: Delete abnormal values with dynamic strength > 3000 MPa, fracture strain < 0, and missing values; for repeated data of the same composition, if the relative error is < 10%, take the average value, for example, the dynamic strength of an alloy is reported 3 times as 1800, 1850, and 1900 MPa, take the average value 1850 MPa; if the error is > 10%, delete it.

[0057] Based on Monte Carlo sampling (MCS), the data set is expanded. According to the statistical distribution of the original data, such as the mean value of MeanUds is 6.5, the standard deviation is 0.5, 1000 groups of virtual samples are generated to ensure that the virtual data is consistent with the feature distribution of the original data.

[0058] S3: Adopt random forest model (implemented through Python sklearn library), take "alloy composition and physical characteristics" (such as W, Ta content and 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] wherein, is the predicted value of the model, K is the number of decision trees, f k (x) is the prediction result of the kth decision tree for input feature x.

[0061] The model parameters are set as follows: the number of decision trees is 100, the maximum depth is 10, 10-fold cross-validation (the data set is divided into 10 groups, and 9 groups are used for training and 1 group is used for validation) is adopted, combined with Figures 2-3 , the final dynamic strength prediction R 2 = 0.75, and the fracture strain prediction R 2 = 0.76.

[0062] The key features are screened through SHAP value analysis, the results show that the importance weight of MeanUds to dynamic strength is 0.32 (ranking first), and the importance weight of MeanUds to fracture strain is 0.28 (ranking second), and the correlation coefficient r with VEC is 0.72, which verifies the rationality of it as the core descriptor.

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

[0064] In the Nb-Ta-Hf-Zr-Mo-Ti-W component space (3-6 kinds of elements, 5%-35% content), the alloys with MeanUds = 5.5-7.0 are screened out, and combined with the pseudo-ternary phase diagram constraints (W+Nb 0-30%, Hf+Zr+Ti 5-40%, Ta+V 40-70%), 3 groups of candidate components are 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, Ti metal blocks with purity ≥ 99.9%, ultrasonic clean for 15 minutes after polishing to remove oxide skin. After weighing according to the component ratio, the raw materials are placed in a non-consumable vacuum arc furnace under argon protection (vacuum degree 5x10-3Pa, argon pressure 0.05MPa), and are sequentially melted in the order of low to high melting point (Ti→V→Zr→Nb→Hf→Ta→W), and are repeatedly flipped and melted 6 times to obtain Φ20mmx10mm ingots.

[0066] Combined Figure 6 , XRD analysis shows that the three alloys are single BCC structure (diffraction peaks are located near 40°, 60°, 80°, corresponding to (110) (200) (211) crystal planes).

[0067] Performance test:

[0068] Combined Figure 5 , quasi-static compression (0.001s -1 ): the yield strength of alloy 1 is 1282.7MPa, and the fracture strain is 47.3%; the yield strength of alloy 2 is 1856.2MPa, and the fracture strain is 11.7%; the yield strength of alloy 3 is 1190.3MPa, and the fracture strain is 12.7%.

[0069] Dynamic compression (2000s -1 ): the dynamic strength of alloy 1 is 1814.7MPa, and there is no macroscopic fracture; the dynamic strength of alloy 2 is 1402.5MPa, and the fracture strain is 10.1%; the yield strength of alloy 3 is 1765.9MPa, and the fracture strain is 13.6%.

[0070] The above description of the specific embodiments of the present application is not intended to limit the scope of the present application. Any other corresponding changes and modifications made according to the technical concept of the present application should be included in the scope of protection of the claims of the present application.

Claims

1. A method of designing a refractory high-entropy alloy, characterized by, The method comprises the following steps: S1, for Nb-Ta-Hf-Zr-Mo-Ti-W system refractory high-entropy alloys, establish a composition-property dataset containing 10 -3 s -1 to 2000s -1 strain rate range, the dataset including alloy chemical composition, dynamic compression yield strength, and quasi-static fracture strain; S2, extracting core physical characteristics, and expanding the data set based on Monte Carlo sampling after data cleaning; the core physical characteristics include average unoccupied d electron number and valence electron concentration; S3, using a random forest model, taking alloy composition and physical characteristics as input, dynamic strength and fracture strain as output, selecting the optimal model through cross-validation, and analyzing the regulation mechanism of average unoccupied d electron number on performance through SHAP value analysis; S4, taking 5.5-7.0 as the core interval of average unoccupied d electron number, and screening target alloy composition in combination with composition design constraints.

2. The method of designing refractory high-entropy alloys according to claim 1, wherein, 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 method of designing refractory high-entropy alloys of claim 1, wherein, In step S2, the average unoccupied d electron number is calculated by weighted summation of d orbital unoccupied electron numbers of each group element; the data cleaning includes deleting outliers, missing values, and averaging repeated data with relative error <10%.

4. The method of designing refractory high-entropy alloys of claim 1, wherein, In step S3, the prediction formula of the random forest model is: wherein, is the predicted value of the model, K is the number of decision trees, f k (x) is the prediction result of the kth decision tree for the input feature x; And / or, in step S3, the SHAP value analysis determines that the average unoccupied d electron number is the primary influencing factor of dynamic strength and the second influencing factor of fracture strain, and the linear correlation coefficient |r| of VEC is >0.

7.

5. The method of designing refractory high-entropy alloys according to claim 4, wherein, In step S3, the dynamic strength prediction R of the optimum model 2 ≥ 0.75, the fracture strain prediction R 2 ≥ 0.

76.

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

7. The method of designing refractory high-entropy alloys of claim 1, wherein, After step S4, step S5: further comprising using vacuum arc melting to prepare alloys, and testing mechanical properties under wide strain rate.

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

9. The design method of a refractory high-entropy alloy according to claim 8, wherein, In step S5, if the tested performance dynamic strength <1.4 GPa and / or fracture strain <10%, the data is fed back to the initial data set, and steps S2-S5 are repeated.

10. The method of designing refractory high-entropy alloys of claim 1, wherein, In step S4, the screened 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 .

Images