Calculation-driven high-temperature high-specific-strength refractory high-entropy alloy component design method
By constructing machine learning models and molecular dynamics calculations, screening important features, and combining SHAP analysis and Bayesian optimization, the problem of the inversion between high-temperature mechanical properties and density in the composition design of refractory high-entropy alloys was solved, and high-specific-strength material optimization with high efficiency and low cost was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XIAN UNIV OF TECH
- Filing Date
- 2026-02-11
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies exhibit an inverse relationship between high-temperature mechanical properties and density in the composition design of refractory high-entropy alloys, which limits the development of high-specific-strength materials. Furthermore, the reliance of machine learning models on experimental data leads to high optimization costs, making it difficult to quickly and cost-effectively improve high-temperature high-specific-strength materials.
By constructing a machine learning model, screening important features, combining SHAP analysis and Bayesian optimization theory, and using molecular dynamics calculations to replace experimental markers, the composition of refractory high-entropy alloys is optimized, achieving efficient and low-cost high-temperature high-specific-strength design.
In complex compositional spaces, high-temperature, high-specific-strength, refractory, high-entropy alloys can be designed rapidly and accurately, achieving a synergistic balance between high-temperature mechanical properties and density, and a synergistic improvement of multiple properties.
Smart Images
Figure CN122024933A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of refractory high-entropy alloy composition design technology, specifically involving a computation-driven method for designing the composition of high-temperature, high-specific-strength refractory high-entropy alloys. Background Technology
[0002] The higher the operating temperature of the high-temperature section of an aero-engine, the higher its operating efficiency. Historically, breakthroughs in engine performance have been based on the continuous development of high-strength structural materials. These materials not only need to possess high-temperature stability and excellent mechanical properties, but also need to meet the core requirement of low density to achieve a comprehensive goal of high reliability, long lifespan, and lightweight design. Refractory high-entropy alloys (RHEAs) are high-entropy alloys with IV-VI group refractory metals as the main components. They possess excellent high-temperature mechanical properties and stability, making them a promising high-strength material system for high-temperature and high-load conditions, following traditional high-temperature alloys. However, empirically, improvements in high-temperature performance depend on the large-scale addition of high-density components such as W, Nb, and Ta. Therefore, the high-temperature mechanical properties of RHEAs have an inverse relationship with density, which restricts the development of high-strength RHEAs.
[0003] Generally speaking, adding different elements and adjusting their proportions can significantly modify the properties of refractories (RHEA), including mechanical properties and density. However, RHEA has a complex composition, a vast compositional space, and lacks accurate models and criteria to guide its rational design. Therefore, optimizing its performance through the traditional method of expensive experimental testing-feedback-redesign is severely hampered. Although machine learning methods have achieved a series of successes in rapidly optimizing the composition of high-entropy alloys in recent years, establishing accurate machine learning models requires a large amount of expensive alloy composition-performance data, and the high-temperature testing conditions further increase the difficulty of obtaining this data. Even selectively labeling properties through active learning requires significant time and economic costs. These resource requirements limit the ability to quickly and cost-effectively improve the high-temperature specific strength of RHEA through experimentally assisted active learning. Therefore, effectively alleviating the dependence of machine learning on experimental data, thereby optimizing the composition of refractory high-entropy alloys faster and at a lower cost, is of great significance for developing refractory high-entropy alloys with high high-temperature specific strength. Summary of the Invention
[0004] The purpose of this invention is to provide a computation-driven method for designing the composition of high-temperature, high-specific-strength, refractory high-entropy alloys, which can effectively alleviate the dependence of machine learning on experimental data, thereby optimizing the composition of refractory high-entropy alloys faster and at a lower cost.
[0005] The technical solution adopted in this invention is a computation-driven method for designing the composition of high-temperature, high-specific-strength, refractory, high-entropy alloys, specifically as follows:
[0006] Step 1: Collect sample data of refractory high-entropy alloys; Step 2: Consult the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; Step 3: Construct the features required for the machine learning model; Step 4: Select the best-performing machine learning model and parameters to form a strength and phase composition prediction model; Step 5: Obtain a body-centered cubic single-phase alloy sample; Step 6: Obtain the points to be marked; Step 7: Update the dataset and the specific intensity prediction model; Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy sample in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition.
[0007] The invention is further characterized in that: In step 1, the refractory high-entropy alloy sample data package contains the specific composition of the alloy, the corresponding mechanical properties, and the phase structure composition; the metallic elements in the refractory alloy in the sample data include Ti, V, Zr, Nb, Mo, Hf, Ta, W, Al, and Cr; In step 1, the alloy samples collected for refractory high-entropy alloys were all prepared by arc melting, and the strengths were all the alloy yield strength at 1000℃. The phase composition of the alloys was obtained based on X-ray diffraction.
[0008] In step 2, the physicochemical properties of the refractory high-entropy alloying elements include: Pauling electronegativity, Allerozoic electronegativity, valence electron concentration, free electron concentration, electron work function, first ionization energy, second ionization energy / electron volts, number of filled valence orbitals, number of unfilled valence orbitals, number of filled s valence orbitals, number of filled d valence orbitals, number of unfilled d valence orbitals, electron density at the Wigner-Seitz cell surface, atomic number, group, period, bulk modulus, shear modulus, Young's modulus, relative atomic mass, molar volume, density, Poisson's ratio, specific heat capacity, Brinell hardness, thermal conductivity, electrical conductivity, shear modulus at 0 K, viscosity of liquid metal, metal radius, covalent radius, atomic radius, atomic volume, body-centered cubic lattice constant, melting temperature, boiling point, heat of vaporization, heat of fusion, enthalpy of atomization, cohesive energy, vacancy migration energy, and vacancy formation energy.
[0009] In step 3, the features are used as the input to the machine learning model, and the mechanical properties and phase structure composition of the alloy in step 1 are used as the mapping end. In step 3, the features are constructed using the following formula:
[0010]
[0011] in For the weighted summation characteristic, This is a weighted characteristic curve based on the squared deviation, where n is the number of physicochemical properties of the elements. Percentage of atoms of an element This represents the value of the i-th physicochemical quantity in the j-th element. It represents the weighted average of the physicochemical characteristics of an element.
[0012] Step 4 specifically involves: ranking and filtering the features from Step 3 based on their importance, evaluating the parameters of multiple machine learning models, traversing the hyperparameter space of the five algorithm models, and selecting the best-performing machine learning model and its parameters to form a prediction model based on the strength and phase composition for different mapping evaluation metrics in Step 3. In step 4, the selected machine learning models include five models: extreme boosting tree, decision tree, random forest, gradient boosting tree, and Gaussian regression. The parameters adjusted include the hyperparameters of various machine learning models. In step 4, the process of ranking and filtering the features in step 3 based on their importance is carried out as follows: (1) Calculate the Person correlation coefficient between each feature and delete features with an average correlation coefficient greater than 0.8; (2) Conduct feature importance analysis on the feature set that has not been deleted and retain the top 15 features in terms of importance; (3) Perform an exhaustive analysis on these 15 features to obtain the best-performing feature combination, which includes seven features: squared deviation of Young's modulus E-2, weighted melting point Tm-1, weighted relative atomic mass Ar-1, weighted specific heat capacity C-1, squared deviation of Allerois electronegativity χar-2, squared deviation of atomic volume Vat-2, and weighted atomic radius rat-1.
[0013] In step 4, the evaluation index for the intensity and phase composition prediction model is the classification accuracy of the model on the test set, and the evaluation index for the intensity and phase composition prediction model is the coefficient of determination between the predicted value and the true value on the test set.
[0014] Step 5 specifically involves: using SHAP (SHapley Additive exPlanations) analysis in game theory to interpret and analyze the importance of alloying elements based on the features screened in Step 4, identifying high-entropy alloy systems with potential high temperature and high specific strength based on the elements with the highest importance, designing alloy samples by setting element concentration range constraints, and using the phase composition prediction model in Step 4 to screen the designed alloy samples for body-centered cubic single-phase alloy samples. In step 5, the process of determining the high-entropy alloy system with potential high-temperature and high specific strength through SHAP analysis includes: (1) SHAP analysis gives the relationship between machine learning model features and performance indicators (direct or inverse); (2) analysis gives the relationship between the best-performing feature combination in step 4 and the SHAP value (direct or inverse); (3) based on the analysis conclusions of (1) and (2), determine the relationship between the best-performing feature combination in step 4 and the alloy-related properties (direct or inverse), and determine the types of elements based on the above relationship, that is, select the types of elements that are beneficial to the high-temperature and high specific strength of the alloy according to the physicochemical characteristics of the elements.
[0015] Step 6 specifically involves: using Bayesian optimization theory to generate the next round of target component points for the body-centered cubic single-phase alloy samples selected in Step 5, in order to obtain samples with high potential values from the function calculation as target points.
[0016] In step 6, the body-centered cubic single-phase alloy sample is a set of components obtained by screening the corresponding composition space through the strength and phase composition prediction model after the alloy system to be optimized has been determined. In step 6, Bayesian optimization theory uses a machine learning intensity prediction model as a surrogate model and Expected Improvement (EI) as the acquisition function. The formula for calculating the function is as follows:
[0017] Where EI represents the expected improvement value of the alloy sample. The deviation between the predicted mean specific strength and the optimal specific strength. This is the corrected standard deviation of the specific strength prediction. For standardization bias, The cumulative distribution function of the standard normal distribution. The probability density is based on a standard normal distribution. During the implementation process, eight component points to be evaluated are selected each time.
[0018] Step 7 specifically involves: using a molecular dynamics-based alloy strength prediction method to provide the specific strength values of the component points to be marked in Step 6, and updating the dataset and specific strength prediction model; In step 7, the predicted strength of the alloy is obtained based on molecular dynamics calculations. The molecular dynamics calculation method is to calculate the critical slip stress of edge dislocations and screw dislocations on different slip surfaces, thereby determining the critical shear stress of the alloy with the corresponding composition. Then, the macroscopic yield stress of the polycrystalline material is obtained by using the Taylor factor (which is 3 based on the BCC single-phase alloy). In step 7, updating the dataset means adding the calculated intensity-performance data to the dataset of the machine learning model; updating the intensity prediction model means retraining the machine learning model based on the updated dataset.
[0019] Step 8 specifically involves repeating steps 6 and 7 until the specific strength improvement of the marked alloy samples in the potentially high-temperature, high-specific-strength alloy system from step 5 meets the convergence condition, at which point the process ends. In step 8, the alloy specific strength improvement satisfies the convergence condition when the EI values of the two optimal samples in two adjacent optimization rounds reach convergence.
[0020] The beneficial effects of this invention are: This invention's method, through feature construction and comparative optimization with multiple machine learning models, eliminates redundant features and selects the optimal model and parameter combination, reducing the risk of bias caused by predictions from a single feature or model. In the vast compositional space of refractory high-entropy alloys, it combines SHAP analysis to screen and determine alloy systems with potentially high high-temperature specific strength. Furthermore, based on Bayesian optimization theory and the uncertainty of model predictions, it adopts the expected performance improvement method, combined with high-precision molecular dynamics calculations to replace experimental markers. This enables efficient and low-cost compositional design of high-temperature, high-specific-strength refractory high-entropy alloys in complex compositional spaces. Through closed-loop iterative optimization, it ultimately obtains the target refractory high-entropy alloy composition that achieves a synergistic balance between high-temperature mechanical properties and density, and a synergistic improvement in multiple properties quickly and accurately. Attached Figure Description
[0021] Figure 1 This is a flowchart of the method of the present invention; Figure 2(a) shows the performance of the yield strength prediction model in the embodiment of the present invention; Figure 2(b) shows the performance of the phase composition prediction model in the embodiment of the present invention; Figure 3 This is a body-centered cubic single-phase composition distribution diagram of the Mo-Ti-Nb-Ta-Zr alloy system obtained after screening in an embodiment of the present invention. Figure 4 This is a comparison chart between the molecular dynamics calculation values and the alloy strength experimental values in the embodiments of the present invention; Figure 5(a) shows the high-temperature specific strength variation process of the alloy in the three-round optimized Mo-Ti-Nb-Ta-Zr system in the embodiment of the present invention.
[0022] Figure 5(b) shows the change process of high-temperature yield strength of the alloy in the three-round optimized Mo-Ti-Nb-Ta-Zr system in the embodiment of the present invention. Detailed Implementation
[0023] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0024] This invention provides a computationally driven method for designing the composition of high-temperature, high-specific-strength, refractory, high-entropy alloys. It consists of two parts: alloy system design and Bayesian optimization of the composition, such as... Figure 1 As shown, the complete process of data collection, modeling, and optimization is illustrated below: Step 1: Collect sample data of refractory high-entropy alloys from relevant reported literature and materials from 2004 to 2025; In step 1, the refractory high-entropy alloy sample data package contains the specific composition of the alloy, the corresponding mechanical properties, and the phase structure composition; the metallic elements in the refractory alloy in the sample data include Ti, V, Zr, Nb, Mo, Hf, Ta, W, Al, and Cr; In step 1, the alloy samples collected for refractory high-entropy alloys were all prepared by arc melting, and the strengths were all the alloy yield strength at 1000℃. The phase composition of the alloys was obtained based on X-ray diffraction.
[0025] Step 2: Consult authoritative theoretical manuals for the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; In step 2, the physicochemical properties of the refractory high-entropy alloying elements include: Pauling electronegativity, Allerozoic electronegativity, valence electron concentration, free electron concentration, electron work function, first ionization energy, second ionization energy / electron volts, number of filled valence orbitals, number of unfilled valence orbitals, number of filled s valence orbitals, number of filled d valence orbitals, number of unfilled d valence orbitals, electron density at the Wigner-Seitz cell surface, atomic number, group, period, bulk modulus, shear modulus, Young's modulus, relative atomic mass, molar volume, density, Poisson's ratio, specific heat capacity, Brinell hardness, thermal conductivity, electrical conductivity, shear modulus at 0 K, viscosity of liquid metal, metal radius, covalent radius, atomic radius, atomic volume, body-centered cubic lattice constant, melting temperature, boiling point, heat of vaporization, heat of fusion, enthalpy of atomization, cohesive energy, vacancy migration energy, and vacancy formation energy.
[0026] Step 3: Construct the features required for the machine learning model using the alloy composition ratio in Step 1 and the physicochemical properties in Step 2. Use the features as the input of the machine learning model and the mechanical properties and phase structure composition of the alloy in Step 1 as the mapping end. In step 3, the features are constructed using the following formula:
[0027]
[0028] in For the weighted summation characteristic, This is a weighted characteristic curve based on the squared deviation, where n is the number of physicochemical properties of the elements. Percentage of atoms of an element This represents the value of the i-th physicochemical quantity in the j-th element. Represents the weighted average of the physicochemical characteristics of an element; Step 4: Rank and filter the features in Step 3 according to their importance, evaluate the parameters of multiple machine learning models, traverse the hyperparameter space of five algorithm models, and select the best-performing machine learning model and parameters to form a prediction model for different mapping evaluation metrics in Step 3. In step 4, the selected machine learning models include five models: extreme boosting tree, decision tree, random forest, gradient boosting tree, and Gaussian regression. The parameters adjusted include the hyperparameters of various machine learning models. In step 4, the process of ranking and filtering the features in step 3 based on their importance is carried out as follows: (1) Calculate the Person correlation coefficient between each feature and delete features with an average correlation coefficient greater than 0.8; (2) Conduct feature importance analysis on the feature set that has not been deleted and retain the top 15 features in terms of importance; (3) Perform an exhaustive analysis on these 15 features to obtain the best-performing feature combination, which includes seven features: E-2 (squared deviation of Young's modulus), Tm-1 (weighted melting point), Ar-1 (weighted relative atomic mass), C-1 (weighted specific heat capacity), χar-2 (squared deviation of Allerois electronegativity), Vat-2 (squared deviation of atomic volume), and rat-1 (weighted atomic radius).
[0029] In step 4, the evaluation index for the intensity and phase composition prediction model is the classification accuracy of the model on the test set, and the evaluation index for the intensity and phase composition prediction model is the coefficient of determination between the predicted value and the true value on the test set.
[0030] Step 5: Based on SHAP (SHapley Additive exPlanations) analysis in game theory, the importance of alloying elements is ranked according to the features screened in Step 4. Based on the elements with the highest importance, high-entropy alloy systems with potential high temperature and high specific strength are identified. Alloy samples are designed by setting element concentration range constraints. The phase composition prediction model in Step 4 is used to screen the designed alloy samples for body-centered cubic single phase to obtain body-centered cubic single phase alloy samples. In step 5, the process of determining the high-entropy alloy system with potential high-temperature and high specific strength through SHAP analysis includes: (1) SHAP analysis gives the relationship between machine learning model features and performance indicators (direct or inverse); (2) analysis gives the relationship between the best-performing feature combination in step 4 and the SHAP value (direct or inverse); (3) based on the analysis conclusions of (1) and (2), determine the relationship between the best-performing feature combination in step 4 and the alloy-related properties (direct or inverse), and determine the types of elements based on the above relationship, that is, select the types of elements that are beneficial to the high-temperature and high specific strength of the alloy according to the physicochemical characteristics of the elements. Step 6: Based on Bayesian optimization theory, the body-centered cubic single-phase alloy samples selected in Step 5 are used to generate the next round of target component points for active learning optimization, so as to obtain samples with high potential values in function calculation as target points.
[0031] In step 6, the body-centered cubic single-phase alloy sample is a set of components obtained by screening the corresponding composition space through the strength and phase composition prediction model after the alloy system to be optimized has been determined. In step 6, Bayesian optimization theory uses a machine learning intensity prediction model as a surrogate model and Expected Improvement (EI) as the acquisition function. The calculation formula is as follows:
[0032] Where EI represents the expected improvement value of the alloy sample. The deviation between the predicted mean specific strength and the optimal specific strength. This is the corrected standard deviation of the specific strength prediction. For standardization bias, The cumulative distribution function of the standard normal distribution. The probability density is based on a standard normal distribution. During the implementation process, eight component points to be evaluated are selected each time. Step 7: Use the alloy strength prediction method based on molecular dynamics calculations to give the specific strength value of the component points to be marked in Step 6, and update the dataset and strength prediction model; In step 7, the predicted strength of the alloy is obtained based on molecular dynamics calculations. The molecular dynamics calculation method is to calculate the critical slip stress of edge dislocations and screw dislocations on different slip surfaces, thereby determining the critical shear stress of the alloy with the corresponding composition. Then, the macroscopic yield stress of the polycrystalline material is obtained by using the Taylor factor (which is 3 for BCC single-phase alloys).
[0033] In step 7, updating the dataset means adding the calculated intensity-performance data to the dataset of the machine learning model; updating the intensity prediction model means retraining the machine learning model based on the updated dataset.
[0034] Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy samples in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition, and the process ends. In step 8, the alloy specific strength improvement satisfies the convergence condition when the EI values of the two optimal samples in two adjacent optimization rounds reach convergence.
[0035] Example 1 This embodiment includes the following steps: 1) Compressive yield strength data of refractory high-entropy alloys with different compositions at 1000℃ were collected from relevant literature from 2014 to 2025, totaling 101 data points. At the same time, phase composition data of alloys with different compositions were also collected, totaling 232 data points.
[0036] 2) Forty-three elemental physicochemical properties related to yield strength and alloy phase composition were extracted from authoritative theoretical manuals.
[0037] 3) By using the weighted summation of the specific element atomic ratios in step 1 and the physicochemical quantities in step 2, as well as the weighted calculation of the squared deviation, we can construct machine learning model features and obtain 86 initial machine learning model features, covering the synergistic relationship between element composition ratios and element physicochemical quantities.
[0038] 4) The 86 machine learning model features in step 3 are used as the model input, and the compressive yield strength and alloy phase composition at 1000℃ are used as the mapping end. The training set and test set are divided in a ratio of 85:15. Five mainstream machine learning models are selected: extreme boosting tree, gradient boosting number, decision tree, random forest and Gaussian regression. The parameter space is formed by the hyperparameter values selected by each of these models. All parameter combinations of the five models are traversed. Finally, the gradient boosting number regressor is determined to be the best performing algorithm model for the current strength and phase composition prediction task. The following steps are to sort the importance of the 86 features in step 3: (1) Calculate the person correlation coefficient between each feature and delete features with an average correlation coefficient greater than 0.8; (2) Conduct feature importance analysis on the feature set that has not been deleted and retain the top 15 features in terms of feature importance; (3) Perform an exhaustive analysis on these 15 features to obtain the best performing feature combination. The above process is performed separately for the strength and phase composition prediction tasks. Figure 2(a) shows the performance of the yield strength prediction model, and Figure 2(b) shows the performance of the phase composition prediction model. The coefficient of determination and classification accuracy reached 0.9622 and 0.98, respectively.
[0039] 5) Combine SHAP analysis to calculate the contribution of elements to high temperature and high specific strength: (1) SHAP analysis gives the relationship between machine learning model features and performance indicators (direct or inverse); (2) Analysis gives the relationship between the best-performing feature combination in step 4 and the SHAP value (direct or inverse); (3) Based on the above analysis, determine the relationship between the best-performing feature combination in step 4 and alloy-related properties (direct or inverse), and select the element types that are beneficial to the high temperature and high specific strength of the alloy based on the above relationship and the physicochemical characteristics of the elements. The results show that the top five contributing elements are Nb, Ta, Ti, Mo, and Zr, so the Mo-Ti-Nb-Ta-Zr system is determined as the system to be optimized in this embodiment. Next, based on the empirical ranges of elemental concentrations in similar systems studied in the literature collected in Step 1, concentration constraints were set for each of the five elements: Nb concentration range 12%~44%, Ta concentration range 5%~44%, Mo concentration range 8%~35%, Ti concentration range 6%~38%, and Zr concentration range 5%~30%, with the total atomic percentage of each element being 100%. A 2% interval was used for the generation, resulting in 33,329 candidate alloy compositions. The phase composition prediction model from Step 4 was used to screen the body-centered cubic single-phase alloy samples among the candidate compositions, yielding 500 body-centered cubic single-phase alloy samples. For example... Figure 3 The image shows a body-centered cubic single-phase alloy sample of the Mo-Ti-Nb-Ta-Zr alloy system obtained after screening.
[0040] 6) Bayesian theory is used to improve the high-temperature specific strength of the alloy. The surrogate model is the yield strength prediction model in step 4, the acquisition function is EI expectation improvement, and the density of the alloy is calculated based on the density of the elements using the mixing rule. The mean and variance at the candidate composition points are estimated by the following means: (1) Ten different gradient boosting regression models are set using the same parameters as the optimized model but different random initialization parameters; (2) These 10 different models are used to predict the same composition point, and the mean and variance of the predicted values of different models are used as the mean and variance of the model at that point. Then, using the calculated mean and variance data, the current specific strength threshold is set to 50 MPa·cm3 / g, and the expected improvement value of the high-temperature specific strength of the alloy at that point is finally calculated. The top 8 samples are used as the points to be labeled.
[0041] 7) Perform strength calculations on the eight components from step 6. Use molecular dynamics to calculate the dislocation motion on the 110, 112, and 123 crystal planes of the alloy at 1000℃ to obtain the critical slip shear stress of the current alloy. Use the Taylor factor (based on a BCC single-phase value of 3) to obtain the yield stress on the polycrystalline material. Figure 4The figure shows a comparison between molecular dynamics calculations and experimental values of alloy strength. It can be seen that molecular dynamics calculations can predict the yield strength of the alloy at 1000℃ very well, and the error between the calculated and experimental values is controlled within 15%.
[0042] 8) Add the yield strength calculation data of the 8 component points obtained in step 7 to the training set of the current machine learning model, and repeat steps (6) and (7) until the EI value of the two optimal samples in the two adjacent optimization processes of the alloy at 1000℃ decreases to 0, and then stop the process. Figure 5(a) and Figure 5(b) show the high-temperature specific strength and strength change process of the alloy in the Mo-Ti-Nb-Ta-Zr system after three rounds of optimization. It can be seen that the specific strength of the alloy gradually increases as the Bayesian theory optimization proceeds. After three rounds of optimization, the EI value converges. Compared with the initial dataset Mo-Ti-Nb-Ta-Zr system, the designed high-temperature high specific strength optimized alloy composition Mo 0.34 Ti 0.34 Nb 0.18 Ta 0.09 Zr 0.05 Its yield strength at 1000℃, calculated by molecular dynamics, is 510 MPa, its density is 8.39 g / cm³, and its specific strength reaches 60.75 MPa. cm³ / g, mean specific intensity of samples after three iterations (41.28 MPa) (cm³ / g) compared to the initial data, the average specific strength of the same system (26.52 MPa) The concentration of 1000 mg / cm³ increased by 55.65%.
[0043] Figures 5(a) and 5(b) compare the high-temperature specific strength and high-temperature yield strength of the alloy designed in Example 1 with the reported Mo-Ti-Nb-Ta-Zr alloy system, showing the effective results of the implementation of the present invention, namely, the specific strength of the designed alloy is significantly improved at the corresponding temperature. The invention achieves low-cost and high-efficiency design of refractory high-entropy alloy composition with high specific strength at high temperature.
[0044] Example 2 A computationally driven compositional design method for high-temperature, high-specific-strength, refractory, high-entropy alloys is as follows: Step 1: Collect sample data of refractory high-entropy alloys; Step 2: Consult the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; Step 3: Construct the features required for the machine learning model; Step 4: Select the best-performing machine learning model and parameters to form a strength and phase composition prediction model; Step 5: Obtain a body-centered cubic single-phase alloy sample; Step 6: Obtain the points to be marked; Step 7: Update the dataset and the specific intensity prediction model; Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy sample in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition.
[0045] Example 3 A computationally driven compositional design method for high-temperature, high-specific-strength, refractory, high-entropy alloys is as follows: Step 1: Collect sample data of refractory high-entropy alloys; In step 1, the refractory high-entropy alloy sample data package contains the specific composition of the alloy, the corresponding mechanical properties, and the phase structure composition; the metallic elements in the refractory alloy in the sample data include Ti, V, Zr, Nb, Mo, Hf, Ta, W, Al, and Cr; Step 2: Consult the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; Step 3: Construct the features required for the machine learning model; Step 4: Select the best-performing machine learning model and parameters to form a strength and phase composition prediction model; Step 5: Obtain a body-centered cubic single-phase alloy sample; Step 6: Obtain the points to be marked; Step 7: Update the dataset and the specific intensity prediction model; Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy sample in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition.
[0046] Example 4 A computationally driven compositional design method for high-temperature, high-specific-strength, refractory, high-entropy alloys is as follows: Step 1: Collect sample data of refractory high-entropy alloys; In step 1, the refractory high-entropy alloy sample data package contains the specific composition of the alloy, the corresponding mechanical properties, and the phase structure composition; the metallic elements in the refractory alloy in the sample data include Ti, V, Zr, Nb, Mo, Hf, Ta, W, Al, and Cr; In step 1, the alloy samples collected for refractory high-entropy alloys were all prepared by arc melting, and the strengths were all the alloy yield strength at 1000℃. The phase composition of the alloys was obtained based on X-ray diffraction.
[0047] Step 2: Consult the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; Step 3: Construct the features required for the machine learning model; Step 4: Select the best-performing machine learning model and parameters to form a strength and phase composition prediction model; Step 5: Obtain a body-centered cubic single-phase alloy sample; Step 6: Obtain the points to be marked; Step 7: Update the dataset and the specific intensity prediction model; Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy sample in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition.
[0048] Example 5 A computationally driven compositional design method for high-temperature, high-specific-strength, refractory, high-entropy alloys is as follows: Step 1: Collect sample data of refractory high-entropy alloys; In step 1, the refractory high-entropy alloy sample data package contains the specific composition of the alloy, the corresponding mechanical properties, and the phase structure composition; the metallic elements in the refractory alloy in the sample data include Ti, V, Zr, Nb, Mo, Hf, Ta, W, Al, and Cr; In step 1, the alloy samples collected for refractory high-entropy alloys were all prepared by arc melting, and the strengths were all the alloy yield strength at 1000℃. The phase composition of the alloys was obtained based on X-ray diffraction.
[0049] Step 2: Consult the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; In step 2, the physicochemical properties of the refractory high-entropy alloying elements include: Pauling electronegativity, Allerozoic electronegativity, valence electron concentration, free electron concentration, electron work function, first ionization energy, second ionization energy / electron volts, number of filled valence orbitals, number of unfilled valence orbitals, number of filled s valence orbitals, number of filled d valence orbitals, number of unfilled d valence orbitals, electron density at the Wigner-Seitz cell surface, atomic number, group, period, bulk modulus, shear modulus, Young's modulus, relative atomic mass, molar volume, density, Poisson's ratio, specific heat capacity, Brinell hardness, thermal conductivity, electrical conductivity, shear modulus at 0 K, viscosity of liquid metal, metal radius, covalent radius, atomic radius, atomic volume, body-centered cubic lattice constant, melting temperature, boiling point, heat of vaporization, heat of fusion, enthalpy of atomization, cohesive energy, vacancy migration energy, and vacancy formation energy.
[0050] Step 3: Construct the features required for the machine learning model; Step 4: Select the best-performing machine learning model and parameters to form a strength and phase composition prediction model; Step 5: Obtain a body-centered cubic single-phase alloy sample; Step 6: Obtain the points to be marked; Step 7: Update the dataset and the specific intensity prediction model; Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy sample in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition.
[0051] Example 6 A computationally driven compositional design method for high-temperature, high-specific-strength, refractory, high-entropy alloys is as follows: Step 1: Collect sample data of refractory high-entropy alloys; In step 1, the refractory high-entropy alloy sample data package contains the specific composition of the alloy, the corresponding mechanical properties, and the phase structure composition; the metallic elements in the refractory alloy in the sample data include Ti, V, Zr, Nb, Mo, Hf, Ta, W, Al, and Cr; In step 1, the alloy samples collected for refractory high-entropy alloys were all prepared by arc melting, and the strengths were all the alloy yield strength at 1000℃. The phase composition of the alloys was obtained based on X-ray diffraction.
[0052] Step 2: Consult the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; In step 2, the physicochemical properties of the refractory high-entropy alloying elements include: Pauling electronegativity, Allerozoic electronegativity, valence electron concentration, free electron concentration, electron work function, first ionization energy, second ionization energy / electron volts, number of filled valence orbitals, number of unfilled valence orbitals, number of filled s valence orbitals, number of filled d valence orbitals, number of unfilled d valence orbitals, electron density at the Wigner-Seitz cell surface, atomic number, group, period, bulk modulus, shear modulus, Young's modulus, relative atomic mass, molar volume, density, Poisson's ratio, specific heat capacity, Brinell hardness, thermal conductivity, electrical conductivity, shear modulus at 0 K, viscosity of liquid metal, metal radius, covalent radius, atomic radius, atomic volume, body-centered cubic lattice constant, melting temperature, boiling point, heat of vaporization, heat of fusion, enthalpy of atomization, cohesive energy, vacancy migration energy, and vacancy formation energy.
[0053] Step 3: Construct the features required for the machine learning model; In step 3, the features are used as the input to the machine learning model, and the mechanical properties and phase structure composition of the alloy in step 1 are used as the mapping end. Step 4: Select the best-performing machine learning model and parameters to form a strength and phase composition prediction model; Step 5: Obtain a body-centered cubic single-phase alloy sample; Step 6: Obtain the points to be marked; Step 7: Update the dataset and the specific intensity prediction model; Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy sample in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition.
Claims
1. A computationally driven method for designing the composition of high-temperature, high-specific-strength, refractory, high-entropy alloys, characterized in that: Specifically: Step 1: Collect sample data of refractory high-entropy alloys; Step 2: Consult the physicochemical properties of elements related to yield strength and phase composition in refractory high-entropy alloys; Step 3: Construct the features required for the machine learning model; Step 4: Select the best-performing machine learning model and parameters to form a strength and phase composition prediction model; Step 5: Obtain a body-centered cubic single-phase alloy sample; Step 6: Obtain the points to be marked; Step 7: Update the dataset and the specific intensity prediction model; Step 8: Repeat steps 6 and 7 until the specific strength improvement of the marked alloy sample in the potentially high-temperature high-specific-strength alloy system in step 5 meets the convergence condition.
2. The computationally driven high-temperature, high-specific-strength, refractory, high-entropy alloy composition design method according to claim 1, characterized in that, In step 1, the refractory high-entropy alloy sample data package contains the specific composition of the alloy, the corresponding mechanical properties, and the phase structure composition; the metallic elements in the refractory alloy in the sample data include Ti, V, Zr, Nb, Mo, Hf, Ta, W, Al, and Cr; In step 1, the alloy samples collected for refractory high-entropy alloys were all prepared by arc melting, and the strengths were all the alloy yield strength at 1000℃. The phase composition of the alloys was obtained based on X-ray diffraction.
3. The computationally driven high-temperature, high-specific-strength, refractory high-entropy alloy composition design method according to claim 2, characterized in that, In step 2, the physicochemical properties of the refractory high-entropy alloying elements include: Pauling electronegativity, Allerozoic electronegativity, valence electron concentration, free electron concentration, electron work function, first ionization energy, second ionization energy / electron volts, number of filled valence orbitals, number of unfilled valence orbitals, number of filled s valence orbitals, number of filled d valence orbitals, number of unfilled d valence orbitals, electron density at the Wigner-Seitz cell surface, atomic number, group, period, bulk modulus, shear modulus, Young's modulus, relative atomic mass, molar volume, density, Poisson's ratio, specific heat capacity, Brinell hardness, thermal conductivity, electrical conductivity, shear modulus at 0 K, viscosity of liquid metal, metal radius, covalent radius, atomic radius, atomic volume, body-centered cubic lattice constant, melting temperature, boiling point, heat of vaporization, heat of fusion, enthalpy of atomization, cohesive energy, vacancy migration energy, and vacancy formation energy.
4. The computationally driven high-temperature, high-specific-strength, refractory, high-entropy alloy composition design method according to claim 3, characterized in that, In step 3, the features are used as the input to the machine learning model, and the mechanical properties and phase structure composition of the alloy in step 1 are used as the mapping end. In step 3, the features are constructed using the following formula: in For the weighted summation characteristic, This is a weighted characteristic curve based on the squared deviation, where n is the number of physicochemical properties of the elements. Percentage of atoms of an element This represents the value of the i-th physicochemical quantity in the j-th element. It represents the weighted average of the physicochemical characteristics of an element.
5. The computationally driven high-temperature, high-specific-strength, refractory, high-entropy alloy composition design method according to claim 4, characterized in that, Step 4 specifically involves: ranking and filtering the features from Step 3 based on their importance, evaluating the parameters of multiple machine learning models, traversing the hyperparameter space of the five algorithm models, and selecting the best-performing machine learning model and its parameters to form a prediction model based on the strength and phase composition for different mapping evaluation metrics in Step 3. In step 4, the selected machine learning models include five models: extreme boosting tree, decision tree, random forest, gradient boosting tree, and Gaussian regression. The parameters adjusted include the hyperparameters of various machine learning models. In step 4, the process of ranking and filtering the features in step 3 based on their importance is carried out as follows: (1) Calculate the Person correlation coefficient between each feature and delete features with an average correlation coefficient greater than 0.8; (2) Conduct feature importance analysis on the feature set that has not been deleted and retain the top 15 features in terms of importance; (3) Perform an exhaustive analysis on these 15 features to obtain the best-performing feature combination, which includes seven features: squared deviation of Young's modulus E-2, weighted melting point Tm-1, weighted relative atomic mass Ar-1, weighted specific heat capacity C-1, squared deviation of Allerois electronegativity χar-2, squared deviation of atomic volume Vat-2, and weighted atomic radius rat-1. In step 4, the evaluation index for the intensity and phase composition prediction model is the classification accuracy of the model on the test set, and the evaluation index for the intensity and phase composition prediction model is the coefficient of determination between the predicted value and the true value on the test set.
6. The computationally driven high-temperature, high-specific-strength, refractory, high-entropy alloy composition design method according to claim 5, characterized in that, Step 5 specifically involves: using SHAP analysis in game theory to interpret and analyze the importance of alloy elements based on the features screened in Step 4, identifying high-entropy alloy systems with potential high temperature and high specific strength based on the elements with the highest importance, designing alloy samples by setting element concentration range constraints, and using the phase composition prediction model in Step 4 to screen the designed alloy samples for body-centered cubic single-phase alloy samples. In step 5, the process of determining the high-entropy alloy system with potential high temperature and high specific strength through SHAP analysis includes: (1) SHAP analysis gives the relationship between machine learning model features and performance indicators; (2) Analyze the relationship between the best-performing feature combination in step 4 and the SHAP value; (3) Determine the relationship between the best-performing feature combination in step 4 and the alloy-related properties based on the analysis conclusions of (1) and (2), and determine the types of elements based on the above relationship, that is, select the types of elements that are beneficial to the high temperature and high specific strength of the alloy according to the physicochemical characteristics of the elements.
7. The computationally driven high-temperature, high-specific-strength, refractory, high-entropy alloy composition design method according to claim 6, characterized in that, Step 6 specifically involves: using Bayesian optimization theory to generate the next round of target component points for the body-centered cubic single-phase alloy samples selected in Step 5, so as to obtain samples with high potential values in function calculation as target points; In step 6, the body-centered cubic single-phase alloy sample is a set of components obtained by screening the corresponding composition space through the strength and phase composition prediction model after the alloy system to be optimized has been determined. In step 6, the formula for calculating the function is as follows: Where EI represents the expected improvement value of the alloy sample. The deviation between the predicted mean specific strength and the optimal specific strength. This is the corrected standard deviation of the specific strength prediction. For standardization bias, The cumulative distribution function of the standard normal distribution. The probability density is based on a standard normal distribution. During the implementation process, eight component points to be evaluated are selected each time.
8. The computationally driven high-temperature, high-specific-strength, refractory, high-entropy alloy composition design method according to claim 7, characterized in that, Step 7 specifically involves: using a molecular dynamics-based alloy strength prediction method to provide the specific strength values of the component points to be marked in Step 6, and updating the dataset and specific strength prediction model; In step 7, the predicted strength of the alloy is obtained based on molecular dynamics calculations. The molecular dynamics calculation method is to calculate the critical slip stress of edge dislocations and screw dislocations on different slip surfaces, thereby determining the critical shear stress of the alloy with the corresponding composition. Then, the macroscopic yield stress of the polycrystalline material is obtained through the Taylor factor. In step 7, updating the dataset means adding the calculated intensity-performance data to the dataset of the machine learning model; updating the intensity prediction model means retraining the machine learning model based on the updated dataset.
9. The computationally driven high-temperature, high-specific-strength, refractory, high-entropy alloy composition design method according to claim 8, characterized in that, Step 8 specifically involves repeating steps 6 and 7 until the specific strength improvement of the marked alloy samples in the potentially high-temperature, high-specific-strength alloy system from step 5 meets the convergence condition, at which point the process ends. In step 8, the alloy specific strength improvement satisfies the convergence condition when the EI values of the two optimal samples in two adjacent optimization rounds reach convergence.