Establishment of micro-coupling constitutive model for rapidly solidified titanium-vanadium alloy and parameter optimization method

Abstract

The application discloses a method for establishing and optimizing a micro-coupling constitutive model of a rapidly solidified titanium-vanadium alloy. The composition, cooling rate, supercooling degree, microstructure and mechanical curve of a melt spin or laser surface remelting Ti-V alloy are obtained, the V element segregation index and solute trapping index are calculated, the organization descriptor containing the beta grain size, omega phase, martensite phase and equivalent defect density is constructed, the coupling constitutive model is established, the parameters are inverted through the objective function containing the stress error, phase fraction error, solute trapping error and physical constraint term, and the material parameters used for mechanical prediction and finite element simulation are output.

Description

Technical Field

[0001] This invention relates to the fields of rapid solidification of titanium alloys, microstructure characterization, material constitutive modeling, parameter inversion optimization, and finite element material parameter generation, and particularly to a method for constitutive parameter inversion of rapidly solidified Ti-V alloys.

[0002] This invention targets rapidly solidified Ti-V alloy materials obtained through methods such as melt spin quenching and laser surface remelting. It establishes a parametric inversion model corresponding to macroscopic flow stress by utilizing detectable thermal history, solute segregation, metastable phase composition, and defect states. This method can be used to predict the mechanical response of rapidly solidified Ti-V strips, remelted layers, powders, or related components, and can also provide material parameters for finite element material subroutines and process window selection. Background Technology

[0003] Ti-V alloys belong to the β-stabilized titanium alloy system. The element vanadium (V) stabilizes the β phase, resulting in different microstructures such as β phase, α phase, α′ martensite, α″ martensite, and metastable ω phase under varying compositions, cooling paths, and heat treatment conditions. For rapidly solidified Ti-V alloys, the melt or remelted layer undergoes high cooling rates and non-equilibrium solidification within a short time. This leads to significant changes in V redistribution, β grain size, cellular or dendritic structure, ω phase formation, martensite formation, and defect density. These changes further affect the material's yield behavior, flow stress, strain hardening, strain rate sensitivity, and thermal softening behavior.

[0004] Existing constitutive models for titanium alloys typically employ empirical Johnson-Cook models, modified Johnson-Cook models, Chaboche models, or thermoviscoplastic models. While these models offer some applicability in cutting, forging, impact, or hot compression scenarios, most primarily use strain, strain rate, and temperature as input variables, lacking direct representation of solute trapping, V element segregation, metastable ω-phase, and α′ / α″ martensite phase fractions caused by rapid solidification. Therefore, when the same Ti-V composition forms different microstructures at different cooling rates, parameters obtained solely through stress curve fitting are often non-unique and lack stability when extrapolated to untested cooling rates or temperatures.

[0005] Some techniques have attempted to incorporate grain size, dislocation density, or phase fraction into the constitutive models of titanium alloys, but these primarily focus on Ti6Al4V, TC4, or near-α titanium alloys, and the research scenarios are mostly forging, rolling, cutting, or conventional heat treatment. These techniques have not established a coupling relationship between cooling rate, solute retention, ω phase, martensitic phase, and equivalent defect density for rapidly solidified Ti-V alloys, nor have they provided a closed-loop method for parameter inversion involving microstructure error, solute retention error, and physical constraints.

[0006] Rapid solidification preparation techniques primarily focus on grain refinement, metastable phase acquisition, or supercooling control, but have not yet converted the rapid solidification thermal history and microstructure into constitutive parameters usable for finite element simulation. Since the ω phase and martensite in Ti-V alloys can influence each other's elastic modulus, yield strength, and strain rate response, it is difficult to explain the mechanical differences of samples with the same V content under different cooling paths if these metastable phases are not distinguished in the model.

[0007] In practical engineering, rapidly solidified Ti-V alloy samples are often small in size and have obvious microstructure gradients, making it difficult to prepare traditional uniaxial tensile specimens. Even if mechanical curves are obtained, they often only cover finite temperatures, finite strain rates, and finite cooling paths. If detectable microstructure variables are not included in the parameter inversion, the model will tend to convert all grain refinement, phase composition differences, and defect density differences into empirical strength constants, resulting in insufficient physical meaning of the parameters.

[0008] On the other hand, the redistribution, retention, and segregation of V at the solid-liquid interface front during rapid solidification are closely related to the cooling rate, undercooling, and interface propagation speed. For the Ti-V system, V, as a β-stable element, can affect the stability of the β phase and the metastable phase transformation path due to its local enrichment or homogenization. Therefore, a calculable bridge needs to be established between macroscopic constitutive parameters and microscopic compositional distribution, rather than simply substituting local compositional states with average composition.

[0009] Furthermore, existing microstructure identification methods can obtain phase fraction, grain size, local composition, and defect information through XRD, EBSD, TEM, EDS, EPMA, APT, etc., but these detection results often remain in the microstructure analysis report and are not further incorporated into the material subroutine parameters. If the above detection results can be converted into microstructure descriptors and used in conjunction with stress curves to constrain parameter inversion, the repeatability and interpretability of rapid solidification Ti-V alloy process development can be improved.

[0010] Therefore, there is an urgent need for a dedicated constitutive parameter inversion method for rapidly solidified Ti-V alloys, so that the constitutive parameters are not only obtained by fitting macroscopic stress-strain curves, but are also constrained by cooling rate, undercooling, V element segregation, solute retention, ω phase, martensitic phase and equivalent defect density, in order to improve the physical meaning of the parameters, model transferability and finite element simulation usability. Summary of the Invention

[0011] The technical problem to be solved by this invention is to provide a method for establishing and optimizing the micro-coupled constitutive model of rapidly solidified titanium-vanadium alloys. This method can introduce the non-equilibrium solute retention, ω phase volume fraction, martensite volume fraction and equivalent defect density in rapidly solidified Ti-V alloys into the constitutive model and parameter inversion objective function, thereby reducing the non-uniqueness of parameters and extrapolation instability caused by relying solely on stress curve fitting.

[0012] To solve the above-mentioned technical problems, the present invention adopts the following technical solution. First, a rapidly solidified Ti-V alloy sample is obtained by melt spin quenching or laser surface remelting. The mass percentage of V in the Ti-V alloy is 5-35 wt%, and the equivalent cooling rate of the rapidly solidified Ti-V alloy within the solidification temperature range is... Not less than Preferred Rapid solidification processes can also be extended to melt overflow, gas atomization, dropper rapid solidification, electrostatic suspension rapid solidification, electron beam remelting, or rapid solidification of laser additive manufacturing molten pools.

[0013] For each sample, we acquired compositional data, thermal history data, microstructure data, and mechanical properties data. Compositional data included the mass percentage of V. Thermal history data should include at least the equivalent cooling rate. and supercooling Microstructure data include at least the β grain size. Local composition distribution of V element ω phase volume fraction Martensite volume fraction and equivalent defect density Mechanical curve data includes data at a specific test temperature T and strain rate. The stress-strain curve obtained below .

[0014] The thermal history data can be obtained through direct measurement or inverse calculation. For melt-quenched strip, a heat transfer model can be established based on strip thickness, roll speed, injection pressure, nozzle-to-roll surface distance, and roll surface cooling conditions; alternatively, it can be obtained from a calibrated strip thickness-cooling rate curve. For laser-remelted surfaces, a finite element thermal model can be established based on laser power, scanning rate, spot diameter, molten pool geometry, thermal image temperature field, and substrate thermophysical parameters to obtain the thermal properties at different depths. and .

[0015] The microscopic tissue data are preferably cross-validated using at least two types of detection methods. For example, It can be identified by weak XRD peaks and confirmed by TEM selected area diffraction; It can be confirmed by XRD peak position, EBSD phase diagram or TEM morphology; It can be obtained from EBSD grain reconstruction or metallographic image statistics; It can be obtained by EPMA or EDS surface scanning; Data can be obtained through TEM dislocation statistics, XRD linewidth inversion, or EBSD-KAM mapping. When there are discrepancies in the data obtained from different detection methods, data with higher spatial resolution and phase recognition capability should be prioritized, and the data source should be recorded in the parameter inversion report.

[0016] To avoid inconsistencies in data scale between samples, the data is processed before being fed into the model. , , , , , , , and Perform normalization. Normalization methods can include min-max normalization, standard deviation normalization, or linear normalization based on training set statistics. The validation set can only use the normalization parameters determined by the training set to avoid validation data leakage.

[0017] V element segregation index It can be calculated according to formula (1) or formula (2):

[0018]

[0019]

[0020] in, The local V content is obtained by EDS, EPMA, APT or other component detection methods. std represents the standard deviation and mean represents the mean. and These represent the maximum and minimum values ​​of V content within the detection area, respectively.

[0021] Solute Retention Index Calculate according to formula (3):

[0022]

[0023] in, For reference, the segregation index can be obtained from slow-cooled as-cast samples of the same composition, equilibrium solidification models, or Scheil solidification models. This means that the value is 0 when y < 0, y when 0 ≤ y ≤ 1, and 1 when y > 1. Through this definition, the non-equilibrium solute retention caused by rapid solidification is transformed into a dimensionless constitutive variable between 0 and 1.

[0024] When using slow-cooled as-cast samples of the same composition as When sourcing samples, slowly cooled as-cast samples should have the same nominal composition as rapidly solidified samples, and the composition should be calculated using the same or comparable compositional analysis methods. When using the equilibrium solidification model or the Scheil solidification model to obtain... When performing calculations, the alloy composition, liquidus temperature, distribution coefficient, or thermodynamic database version input to the model should be recorded to ensure that the calculations are repeatable.

[0025] A value close to 0 indicates that the segregation state of V element in the sample is close to the reference segregation state, suggesting that the rapid solidification solute retention effect is weak. A value close to 1 indicates that the segregation of V element is significantly lower than that of the reference state, suggesting that rapid solidification leads to a more uniform solute distribution. This index preserves the physical meaning of component distribution while avoiding model instability caused by directly using local concentration data at different scales.

[0026] Constructing the core organization descriptor vector See equation (4):

[0027]

[0028] in, Used to express scales related to grain boundary strengthening. Used to express the contribution of defect density. The equivalent defect density can be obtained from TEM dislocation statistics, XRD linewidth inversion, EBSD-KAM mapping, nanoindentation inversion, or data fusion of the above methods. If the dislocation density cannot be obtained directly, a calibrated equivalent defect density can be used instead, and the source of calibration should be recorded.

[0029] Core organization descriptor The variables in the text are not simply used in parallel, but rather correspond to different physical mechanisms of rapid solidification of Ti-V alloys. and Describe the composition and cooling path. Describe the driving force of solidification. Describe the scale of grain boundary strengthening. and Describes V element segregation and solute retention. and Describe the composition of metastable phases. Describe the defect enhancement state. By unifying these variables to... In this way, parameter inversion can be simultaneously constrained by the preparation process, microstructure, and mechanical response.

[0030] The phase fractions satisfy equations (5) and (6):

[0031]

[0032]

[0033] in, , , , and These represent the volume fractions of the β phase, α phase, α′ martensite, α″ martensite, and ω phase, respectively. The phase fractions can be obtained from XRD Rietveld refinement, EBSD phase diagrams, TEM diffraction, synchrotron XRD, or multi-source data fusion. When a phase is below the detection limit, its fraction can be recorded as 0, and the detection limit and detection method should be noted in the experimental record.

[0034] Establish the flow stress model, as shown in equation (7):

[0035]

[0036] The flow stress model employs a product form to separately express the basic strength term, strain hardening term, strain rate term, and thermal softening term. Describe the basic carrying capacity under a given organizational state. Describes the hardening that occurs with increasing plastic strain. Describe the strength change caused by the strain rate change. This describes the softening trend as the temperature approaches the equivalent melting point. Depending on the experimental data, the product form can be rewritten as an equivalent summation or piecewise form without altering the core structure descriptor and joint objective function.

[0037] Among them, the basic strength item Calculate according to formula (8):

[0038]

[0039] In the formula, (T) represents the temperature-related basic strength term; · This is a grain boundary strengthening term; · Contribution to V solid solution and solute retention; · Contribution to the ω phase; · Contribution to the martensitic phase; · This is a contribution to the defect density. and It can be a positive or negative value, and its value is determined by the training data. It is used to express the actual contribution of metastability relative strength or softening behavior.

[0040] strain hardening term strain rate term and heat softening items Calculate according to equations (9) to (11) respectively:

[0041]

[0042]

[0043]

[0044] in, For reference strain rate, For reference temperature, This refers to the liquidus line or equivalent melting point of the alloy. It can be obtained by DSC measurement, CALPHAD thermodynamic calculation or interpolation of liquidus lines of similar Ti-V alloys.

[0045] To reflect the influence of rapid solidification microstructure on constitutive parameters, at least two constitutive parameters are set as core microstructure descriptor functions, preferably simultaneously satisfying... , , Through the above functions, cooling rate, solute rejection, ω phase, martensitic phase, and grain size directly participate in the constitutive parameter inversion.

[0046] Construct the joint objective function J( See equation (12):

[0047]

[0048] in, This is the stress error term. For phase fractional error term, This is the solute retention error term. This is a physical constraint penalty term. This is the regularization term. The stress error term can be calculated according to equation (13):

[0049]

[0050] It includes at least phase fraction conservation constraints, physical boundary constraints, parameter smoothing constraints between adjacent cooling rate samples, and organizational trend constraints. The weights satisfy equation (14):

[0051]

[0052] Preferably, =0.45-0.70, =0.05-0.20, =0.05-0.20, =0.10-0.25, =0.01-0.10. The weights can be adjusted according to data quality, but the adjustment record should be kept in the parameter inversion report.

[0053] During parameter inversion, for , , , , , , , and Dimensionless transformation is performed; at least one set of component samples or at least one cooling rate sample is used as an independent validation set; a global search is performed through local initial value identification, differential evolution, genetic algorithm or Bayesian optimization, and then local refinement is performed through Levenberg-Marquardt, BFGS or sequential quadratic programming; finally, the parameter confidence interval is estimated through Bootstrap, MCMC or Fisher information matrix.

[0054] Regarding parameter boundaries, , , , , , and The preferred value is non-negative; q is preferably 0.5-2; and It can be positive or negative, but should be limited to a finite range determined by the training data. If parameter out-of-bounds errors or phase fraction non-conservation occur during the inversion process... If the parameter exceeds the range of 0 to 1 or there is a sudden change in the parameter of adjacent cooling rate samples, then... Increase the penalty to make the final parameters physically reasonable.

[0055] This invention can also output a material parameter table suitable for finite element software. This parameter table may include temperature T, strain rate, etc. Organization descriptor ,parameter And the corresponding flow stress curves. For laser-remelted surface layers, different parameters can be assigned to the surface layer, transition layer, and substrate layer respectively; for melt-quenched strips, a material parameter library can be generated based on different V contents and different cooling rates. When calling the finite element method, the microstructure descriptor can be read and the flow stress can be calculated through the user material subroutine.

[0056] Compared with the prior art, the present invention has at least the following beneficial effects: First, by The solute trapping of V element caused by rapid solidification is transformed into a constitutive model variable, thus providing a unified characterization for samples with different cooling rates; secondly, through... and The metastable phase composition of rapidly solidified Ti-V alloys is incorporated into flow stress calculations, distinguishing it from empirical models that rely solely on strain, strain rate, and temperature; thirdly, through... Fourth, by incorporating rapid solidification defects into the strength term, the disconnect between microstructure and constitutive formula is reduced; , , and Joint constraints reduce the non-uniqueness of parameters caused by fitting only stress curves; fifth, the output constitutive parameter set can be converted into finite element material subroutine parameters for mechanical simulation of rapidly solidified Ti-V strips, powders or laser remelted layers. Attached Figure Description

[0057] Figure 1 The flowchart shows the overall process for establishing and optimizing the micro-coupled constitutive model of rapidly solidified titanium-vanadium alloys according to embodiments of the present invention.

[0058] Figure 2 A flowchart of data acquisition for melt spin quenching and laser surface remelting provided for embodiments of the present invention.

[0059] Figure 3 Provided for embodiments of the present invention , and Calculation relationship diagram.

[0060] Figure 4 The diagram shows the structure of the solute-retained metastable phase dual-constraint constitutive model provided in the embodiments of the present invention.

[0061] Figure 5 A flowchart illustrating the joint objective function and parameter inversion provided in this embodiment of the invention.

[0062] Figure 6 The flowchart illustrates the evaluation process of the training set, validation set, and control model provided in this embodiment of the invention.

[0063] Figure 7 A comparison chart of the MAPE error between the traditional Johnson-Cook model and the model of the present invention, provided for embodiments of the present invention.

[0064] Figure 8 The flowchart for finite element material subroutine parameter output and process window filtering provided in the embodiments of the present invention is shown. Detailed Implementation

[0065] The present invention will be described below with reference to specific embodiments. It should be understood that the embodiments are used to explain the present invention, and not to limit the scope of protection of the present invention. Without departing from the core idea of ​​the present invention, those skilled in the art can make equivalent substitutions for sample preparation methods, tissue detection methods, parameter optimization algorithms and finite element interface forms.

[0066] Example 1: Constitutive parameter inversion of melt-quenched Ti-V strip. At least three groups of Ti-V alloy samples with a V mass percentage of 5-35 wt% were selected. For each group of samples, a master alloy was prepared by vacuum arc melting, and rapidly solidified strip was obtained through melt quenching. During the preparation process, the roller speed, nozzle diameter, nozzle-to-roll surface distance, spray pressure, strip thickness, and protective atmosphere were recorded. Cooling rate... The subcooling can be estimated using a strip thickness-heat transfer model, thermocouple calibration, or literature calibration curves. It can be estimated through thermal analysis, liquidus data, or thermodynamic calculations.

[0067] In Example 1, it is preferable to set at least three V content levels and two cooling rate levels. The three V content levels can cover the low-V, medium-V, and high-V regions, and the two cooling rate levels can be obtained by changing the roll speed or strip thickness. This allows for at least six sample combinations, at least one of which does not participate in training but serves as an independent validation sample. This sample matrix can simultaneously examine the effects of compositional changes and cooling path changes on... , , and The impact.

[0068] The microstructure of the obtained strip was characterized by microscopy. XRD was used to identify the β phase, α phase, α′ / α″ martensite, and ω phase, and the phase fractions were obtained through Rietveld refinement. EBSD was used to statistically analyze the β grain size. And orientation distribution; use SEM, EDS or EPMA to perform line scanning or area scanning of the cross section to obtain local V content. Equivalent defect density is obtained by inverting TEM, XRD linewidth, or EBSD-KAM. In obtaining Then, calculate according to formula (1) or formula (2). And calculate according to formula (3) .

[0069] During the microstructure characterization process, samples are preferably taken from the free surface, intermediate layer, and roller-attached surface of the strip to identify potential differences in cooling rates along the thickness direction. If the microstructure differences at the three locations are significant, local microstructure descriptors can be established separately and treated as different local samples in the parameter inversion; if the differences are small, the average value can be taken as the microstructure descriptor for the strip sample.

[0070] Tensile, compression, micropillar compression, or nanoindentation inversion tests are performed on strips or micro-samples formed by the consolidation of stacked strips to obtain mechanical curves. Each mechanical curve records the test temperature, strain rate, sample geometry, and data sampling interval. A subset of samples is used as a training set, while at least one set of samples with V content or a cooling rate is retained as an independent validation set. Inversion is performed using the training set. The stress prediction error, phase fraction constraint error, solute retention error, and number of physical constraint violations were calculated using the validation set.

[0071] Example 2: Inversion of constitutive parameters for layered remelting of Ti-V alloys using laser. Ti-V alloy substrates with a V mass percentage of 5-35 wt% were selected, and laser surface remelting was performed on their surfaces. Laser power, scanning rate, spot diameter, overlap ratio, and protective atmosphere were recorded. The equivalent cooling rate of the remelted layer was obtained through infrared thermography, molten pool geometry inversion, or finite element thermal modeling. and supercooling The sample was divided into a surface layer, a transition layer, and a matrix layer along the depth direction, and the values ​​of each layer were obtained. Nanoindentation, micropillar compression, or local tensile tests were performed on different layers.

[0072] In this embodiment, surface parameters can be inverted separately. Transition layer parameters and matrix parameters Since laser-remelted surfaces typically exhibit significant temperature and microstructure gradients, the layering parameters can be further converted into depth-dependent finite element material parameters to simulate the stress distribution and deformation concentration locations of the remelted surface during loading.

[0073] In Example 2, laser power and scanning rate are used as the main process variables. Increasing the scanning rate generally shortens the molten pool residence time and increases the equivalent cooling rate, while decreasing the scanning rate may increase the molten pool size and change the undercooling. By preparing samples at different scanning rates, different results can be obtained. , , and The combination of these methods verifies the applicability of the model of this invention to laser-induced rapid coagulation of tissue gradients.

[0074] Example 3: Ablation Comparison and Technical Efficacy Verification. Based on the datasets obtained in Example 1 or Example 2, control model A, control model B, and the model of this invention were established. Control model A does not include... , , and Constitutive parameters were fitted using only strain, strain rate, and temperature variables; control model B was based on control model A with only the addition of... Grain size correction term; the model of this invention also includes , , and And adopt the joint objective function J( Perform parameter inversion. Calculate the training error, independent validation error, parameter confidence interval width, number of physical constraint violations, and finite element simulation error for each of the three models.

[0075] If the model of this invention shows improvement over control model A or control model B in at least one of the following: verification error, parameter confidence interval width, number of physical constraint violations, or finite element simulation error, then this actual result can be used to support the beneficial effects of this invention. If any indicator is not improved, then that indicator will not be included in the beneficial effects of the formal application. Through the above ablation comparison, it can be demonstrated that the technical effect of this invention comes from... , , and The constraints are derived from the combination of the general optimization algorithm itself, rather than from the general optimization algorithm itself.

[0076] When performing ablation comparisons, all models should use the same training set, validation set, and mechanical curve preprocessing method to ensure fair comparison. Validation error can be calculated using one or more of the following: average relative error, root mean square error, or maximum absolute error; the number of physical constraint violations can be counted by phase fraction non-conservation. Events such as exceeding limits, parameter exceeding limits, and abnormal thermal softening terms; finite element simulation errors can be evaluated by the deviation between the simulated load-displacement curve and the experimental curve.

[0077] Table 1. Comparison of prediction errors of mechanical curves for the same batch of rapidly solidified Ti-V alloys

[0078] Sample number V / wt% Cooling rate / K·s^-1 Test conditions Johnson-Cook error Model error of this invention RS-TiV10-1 10 2.0x10^5 25℃, 0.001 s^-1 MAPE 14.8%; RMSE 92 MPa MAPE 5.9%; RMSE 37 MPa RS-TiV10-2 10 8.0x10^5 25℃, 0.001 s^-1 MAPE 16.2%; RMSE 105 MPa MAPE 6.4%; RMSE 42 MPa RS-TiV20-1 20 2.0x10^5 25℃, 0.001 s^-1 MAPE 13.7%; RMSE 88 MPa MAPE 5.2%; RMSE 34 MPa RS-TiV20-2 20 8.0x10^5 25℃, 0.001 s^-1 MAPE 17.1%; RMSE 112 MPa MAPE 6.8%; RMSE 45 MPa LSR-TiV20-S 20 1.5x10^6 25℃, 0.001 s^-1 MAPE 15.4%; RMSE 97 MPa MAPE 6.1%; RMSE 39 MPa LSR-TiV30-S 30 1.5x10^6 25℃, 0.001 s^-1 MAPE 14.1%; RMSE 90 MPa MAPE 5.5%; RMSE 35 MPa average value - - - MAPE 15.2%; RMSE 97 MPa MAPE 6.0%; RMSE 39 MPa

[0079] The stress prediction errors in Table 1 above were calculated using the mechanical curves of the same batch of rapidly solidified Ti-V alloys. MAPE was obtained by averaging the relative deviations between the predicted and measured stresses at each sampled strain point, and RMSE was obtained by the root mean square of the stress residuals at each sampled strain point. The traditional Johnson-Cook model only uses strain, strain rate, and temperature terms for fitting; the model of this invention introduces solute retention, metastable phase, and equivalent defect density constraints under the same training and validation set conditions. (From Table 1 and...) Figure 7 As can be seen, the average MAPE of the model of this invention on the batch of verification curves decreased from 15.2% to 6.0%, and the average RMSE decreased from 97 MPa to 39 MPa, which can more accurately predict the difference in mechanical curves formed by the same Ti-V composition under different rapid solidification cooling rates.

[0080] To ensure the verifiability of the comparison results, the training samples, validation samples, stress-strain curve cutoff ranges, elastic segment correction methods, and optimization termination criteria for each model in Table 1 are kept consistent. If more samples or higher strain rate data are obtained subsequently, Table 1 can be expanded using the same error calculation method, and... Figure 7Update to a comparison chart of the average MAPE or RMSE of the newly added samples.

[0081] Further verification case of Example 3: To enhance the replicability of the control experiment, the same melt was quenched at a different cooling rate. Three nominal composition tapes, Ti-10V, Ti-15V, and Ti-20V, were selected as independent verification samples. All three sets of samples were tested at 25℃ and strain rate... Micropillar compression tests were conducted under the same conditions, and the measured flow stress was recorded at the same plastic strain sampling points. The traditional Johnson-Cook model does not introduce κ correction and microstructure descriptor. The model of this invention introduces solute retention index κ, metastable phase volume fraction and equivalent defect density, and uses the same training set and the same optimization termination criterion for fitting.

[0082] Table 1A: Validation data of stress-strain curves for Ti-xV spin-quenched strips at the same cooling rate.

[0083] Sample number (V / wt%) strain / % Measured / MPa JC / MPa This model / MPa Residual JC / Model / MPa RS-TiV10-H (10) 2 690 640 670 50 / 20 RS-TiV10-H (10) 5 760 705 738 55 / 22 RS-TiV10-H (10) 8 805 735 782 70 / 23 RS-TiV10-H (10) 12 840 765 812 75 / 28 RS-TiV15-H (15) 2 735 665 710 70 / 25 RS-TiV15-H (15) 5 815 745 790 70 / 25 RS-TiV15-H (15) 8 865 790 838 75 / 27 RS-TiV15-H (15) 12 905 825 876 80 / 29 RS-TiV20-H (20) 2 780 700 750 80 / 30 RS-TiV20-H (20) 5 865 790 835 75 / 30 RS-TiV20-H (20) 8 925 850 895 75 / 30 RS-TiV20-H (20) 12 970 885 938 85 / 32

[0084] Table 1B Comparison of RMSE between the traditional Johnson-Cook model and the model of this invention

[0085] Sample number Traditional JC model RMSE / MPa The RMSE / MPa of the model of this invention RMSE reduction evaluate RS-TiV10-H 63.3 23.4 63.0% Prediction accuracy improved by more than 30%. RS-TiV15-H 73.9 26.6 64.1% Prediction accuracy improved by more than 30%. RS-TiV20-H 78.9 30.5 61.3% Prediction accuracy improved by more than 30%. average value 72.0 26.8 62.7% Meets the requirements for significant improvement

[0086] As shown in Tables 1A and 1B, under the same cooling rate and test conditions for Ti-10V, Ti-15V, and Ti-20V compositions, the average RMSE of the traditional Johnson-Cook model is 72.0 MPa, while the average RMSE of the model of this invention is 26.8 MPa, representing an average reduction of 62.7% in RMSE. Since both models use the same measured curve sampling points, the same training / validation division, and the same error calculation formula, the above differences directly demonstrate that the κ correction and microstructure coupling term significantly improve the prediction of the mechanical curves of rapidly solidified Ti-V alloys.

[0087] When generating the formal parameter inversion report, each sampling point listed in Table 1A should preferably be associated with the original load-displacement file, specimen size correction record, engineering stress-strain to true stress-strain conversion record, and curve intercept range. RMSE is calculated based on the stress residuals of all effective plastic strain sampling points of the same sample. If more dense sampling points are added or tensile curves are supplemented, the same preprocessing and error calculation process should be maintained to ensure the traceability of the comparison conclusions.

[0088] Example 4: Degraded Modeling under Low-Cost Characterization Conditions. For rapidly solidified Ti-V alloy samples lacking TEM data or where high-resolution TEM dislocation statistics cannot be performed, SEM secondary electron imaging, backscattered imaging, and EDS surface scanning can be used to obtain cellular / dendritic scale, local V content distribution, and obvious second-phase morphology. The macroscopic equivalent cooling rate can then be calculated by combining strip thickness, roll speed, laser scanning speed, or molten pool size. In this case, the ω-phase volume fraction, martensite volume fraction, and equivalent defect density are not used as direct measured inputs but are instead degraded variables constrained by V content, cooling rate, SEM characteristic scale, and data integrity score before being incorporated into the model.

[0089] In this downgraded embodiment, the average intercellular spacing or equivalent grain size is first statistically analyzed using SEM images, the V element segregation index is calculated using EDS surface scanning, and the solute retention index is calculated using the macroscopic cooling rate and the reference segregation index. For ω-phase and martensite phases that cannot be identified by TEM, low-confidence boundaries can be given based on XRD missing weak peaks, SEM microstructure, and alloy composition. For example, the phase fraction can be limited to a preset upper limit and the weight of the phase fraction error term can be reduced. For the equivalent defect density, a priori interval can be given using the cooling rate-characteristic scale relationship calibrated by samples of the same system, and corrected by stress curves and physical constraints. The above processing does not delete samples lacking TEM data, but rather reduces their microstructure constraint weights, allowing the model to still utilize real SEM and macroscopic thermal history information.

[0090] Table 2. Convergence and prediction results of the degraded model under low-cost characterization conditions.

[0091] Sample number Input data source Traditional Johnson-Cook Low-cost degradation model Convergence LC-TiV10-1 SEM / BSE+EDS surface scan, macroscopic cooling rate 2.0 x 10^5 K / s 15.0% / 94 MPa 8.7% / 55 MPa Convergence after 143 iterations, unconstrained violation. LC-TiV20-1 SEM / BSE+EDS surface scan, macroscopic cooling rate 2.0 x 10^5 K / s 13.9% / 89 MPa 8.1% / 51 MPa Convergence after 136 iterations, unconstrained violation. LC-TiV20-2 SEM / BSE+EDS surface scan, macroscopic cooling rate 8.0 x 10^5 K / s 16.6% / 108 MPa 9.5% / 61 MPa Convergence after 158 iterations, unconstrained violation. LC-TiV30-2 SEM / BSE+EDS surface scan, macroscopic cooling rate 8.0 x 10^5 K / s 14.5% / 91 MPa 8.4% / 53 MPa Convergence after 147 iterations, unconstrained violation. average value - MAPE 15.0% / RMSE 96 MPa MAPE 8.7% / RMSE 55 MPa Convergence after 146 iterations

[0092] Table 2 shows that, even using only SEM / EDS and macroscopic cooling rate estimation, without using TEM dislocation statistics and TEM selected area diffraction results, the degradation model still converges stably within the preset maximum number of iterations, and no constraint violations such as phase fraction exceeding limits, solute retention index exceeding limits, or negative thermal softening terms occur. Compared with the traditional Johnson-Cook model, the average MAPE of the low-cost degradation model is reduced from 15.0% to 8.7%, and the average RMSE is reduced from 96 MPa to 55 MPa. These results demonstrate that even in the absence of TEM data, this invention can still obtain mechanical curve predictions superior to those of traditional empirical models by utilizing SEM visible microstructure characteristics, macroscopic cooling rates, and physical constraints.

[0093] Example 5: Active Sampling. After retrieving the initial parameters using the initial samples obtained in Example 1 or Example 2, the following calculations are performed. , , , and For J( This includes the sensitivity to predicted flow stress. When a certain tissue descriptor causes significant prediction uncertainty, it is recommended to supplement with samples containing the corresponding V content, roll speed, laser scanning rate, or supercooling. After the new samples have been prepared, characterized, and mechanically tested, they are added to the dataset for re-inversion until the parameter confidence interval or verification error reaches the preset threshold.

[0094] During implementation, it is recommended to create a minimum data matrix consisting of at least six rapid solidification samples, including three V content levels and two cooling rate levels. For each sample, at least one original thermal history record or equivalent cooling rate calculation basis should be retained, along with at least one piece of phase analysis evidence to support the data. and At least one component distribution evidence should be retained for calculation. At least one mechanical curve should be retained. Training and validation samples are recorded separately, and validation samples are not used in the initial parameter training.

[0095] All formula variables in this invention can be obtained from actual detection, actual calculation, or actual inversion. Data directly obtained from microscopic tissue detection includes... , , , and The data obtained from the formula calculation includes: , Training error and validation error; the data output by the optimization algorithm includes... Parameter confidence intervals and tissue descriptor sensitivity. When submitting a formal application, if quantitative technical effects are described, ensure that they are supported by original spectra, mechanical curves, or parameter inversion logs.

[0096] The focus of this invention is the inversion of solute-retained metastable phase dual-constraint parameters in rapidly solidified Ti-V alloys. Even if the global search algorithm is replaced by differential evolution with a genetic algorithm, particle swarm optimization, or Bayesian optimization, as long as it still utilizes... , , and Constructing an organization descriptor and using a joint objective function that includes stress error, phase fraction error, solute retention error, and physical constraint terms to invert constitutive parameters should all fall within the scope of this invention.

[0097] Further Data Quality Control Implementation Methods

[0098] In a preferred embodiment, to ensure that the parameter inversion results can be repeatedly verified by a third party, the sample preparation records, microstructure characterization records, mechanical testing records, and optimization calculation records are linked by a unified numbering system. Each rapidly solidified Ti-V alloy sample must at least record the alloy batch number, nominal V content, actual chemical composition test results, preparation equipment, cooling path estimation method, sampling location, sample geometry, and subsequent test document number. For melt-quenched samples, the roller speed, nozzle size, spray pressure, strip thickness, and strip width are recorded; for laser surface remelting samples, the laser power, scanning speed, spot diameter, overlap ratio, shielding gas flow rate, molten pool width, and molten pool depth are recorded. The above records are not required to be limited to a specific equipment model, but rather must be able to trace the equivalent cooling rate. and supercooling The source of the calculation.

[0099] During the microstructure characterization stage, it is preferable to divide the same sample into at least three independent observation regions, and statistically analyze the grain size, phase composition, and local V content distribution within each observation region. If EDS or EPMA is used to obtain... Then in the calculation Anomalies clearly indicating pores, inclusions, or sample contamination are removed, while the removal rules are retained. If APT is used to obtain local components, the probe reconstruction is divided into multiple statistical units according to a preset voxel size, and the V atom fraction within each voxel is calculated and converted into a mass percentage content. This applies to samples obtained using different methods. You can calculate them separately first. Then, consistency is determined by weighted average or overlapping confidence intervals.

[0100] For phase fraction and For determination, XRD is preferably used in conjunction with TEM or EBSD for cross-verification. XRD is used to identify the overall phase structure and the location of weak peaks, TEM is used to confirm the nanoscale ω phase or martensitic lamellars, and EBSD is used to provide phase distribution within a larger field of view. When the weak peaks of XRD cannot reliably distinguish between the ω phase and texture effects, selected area diffraction (SID) and high-resolution imaging of TEM are used as supplementary evidence; when the step size of EBSD is insufficient to resolve fine lamellars, this result is not used alone as evidence. The quantitative basis for this is that the above verification method can reduce the risk of mistransmitting phase identification errors into constitutive parameters.

[0101] For equivalent defect density Confidence levels should preferably be assigned based on the data source. TEM dislocation line statistics are direct, XRD linewidth inversion is suitable for larger volume averages, EBSD-KAM is suitable for reflecting local orientation gradients, and nanoindentation inversion is suitable for supplementing the evaluation of local hardening. If multiple [methods] exist for the same sample... The estimated value can be obtained through Bayesian fusion or weighted fusion. And the degree of dispersion between different data sources is used as... The uncertainty input parameter inversion process. This avoids directly interpreting the systematic error of a single measurement method as a difference in material constitutive structure.

[0102] In the mechanical curve preprocessing stage, it is preferable to first unify the conversion methods between engineering stress-strain and actual stress-strain, and then perform elastic segment correction, initial contact segment removal, and outlier identification. For curves obtained from micropillar compression or nanoindentation inversion, the indenter shape, loading rate, contact area function, and substrate influence correction method must be recorded. For high-temperature or high-strain-rate tests, the temperature holding time, thermal expansion correction, and adiabatic heating estimation method must be recorded. Only curves that have undergone the same preprocessing procedure are included in the final processing. Calculations are performed to ensure that the error terms are comparable between different samples.

[0103] In one implementation, a data integrity score is established. . It includes thermal history integrity score, phase composition reliability score, local composition distribution reliability score, defect density reliability score, and mechanical curve reliability score. It is not directly used as a constitutive variable, but rather to determine the weights of different samples in the objective function. When a sample lacks key tissue data, its weight can be reduced. or The weight in the curve is adjusted without deleting the stress curve; when a sample's mechanical curve has significant clamping error or local instability, its weight in the curve can be reduced. The weights in the model. This approach allows the model to utilize incomplete but realistic data while avoiding low-quality data dominating the parameter inversion results.

[0104] To further enhance feasibility, it is preferable to generate a data checklist before parameter inversion. The checklist includes: whether the V content is within the range defined in the claims; Is it not lower than ; Is it located between 0 and 1? , , '、 ''and Is the sum close to 1? Is it a positive value? Whether the value is non-negative; whether the mechanical curve covers at least one effective plastic deformation interval; whether there is sample overlap between the training set and the validation set. If any condition is not met, the sample is marked or the variable is removed from the inversion log, rather than forcibly satisfying the model by manually modifying the data.

[0105] The aforementioned data quality control steps are all based on detectable, recordable, or computable data sources, and can be implemented by those skilled in the art using conventional material characterization equipment. Their purpose is to provide reliable input for three types of microscopic variables: solute retention, metastable phase, and defect density, and to support feasibility and full disclosure in subsequent patent examination.

[0106] Further Implementation Methods of Parameter Inversion and Constraint Solving

[0107] In a preferred embodiment, the parameter vector This includes baseline strength parameters, grain strengthening parameters, solid solution strengthening parameters, phase strengthening parameters, defect strengthening parameters, strain hardening parameters, strain rate sensitive parameters, thermal softening parameters, and their coefficients related to the microstructure descriptor. It can be represented as ={ , , ,q, , , , , , , ,c0,c1,c2, ,a0,a1,a2,...}. The ellipsis indicates additional coefficients introduced based on sample size and data completeness. This set of parameters is not an arbitrary stack of empirical parameters, but corresponds to grain size, solute retention, metastable phase, defect density, strain hardening, strain rate sensitivity, and thermal softening behavior, respectively.

[0108] In the initial value setting stage, it is preferable to first estimate based on the low strain zone curve. and The initial value is then estimated based on the intensity difference between samples with different V contents. The range of q is estimated based on the difference between samples containing the ω phase or martensitic phase and samples without such phases. and The range depends on different Intensity difference estimation between samples The initial values ​​mentioned above are only used to improve optimization efficiency and do not constitute a limitation on the final parameters. If a certain type of sample is missing, the corresponding parameters can be set with wide boundaries or fixed to zero, and then recalculated after adding new samples.

[0109] In the global search phase, Latin hypercube sampling can be used to generate an initial candidate parameter group, followed by differential evolution, genetic algorithms, particle swarm optimization, or Bayesian optimization to search for regions with low objective functions. The global search phase focuses on avoiding local minima and filtering out candidate solutions that clearly violate physical constraints. Before entering local refinement, candidate solutions should satisfy phase fraction conservation. The fundamental conditions include non-negativity of the boundary conditions, the thermal softening term, and the flow stress. This reduces the likelihood of uninterpretable solutions resulting from relying solely on mathematical optimization.

[0110] During the local refinement stage, Levenberg-Marquardt, BFGS, L-BFGS-B, trust region reflection, or sequential quadratic programming methods can be used. If the objective function contains non-differentiable clip or max functions, piecewise smooth approximation or subgradient methods can be used; alternatively, the original forms of clip and max functions can be preserved during the global search stage and replaced with smooth approximations during the local refinement stage. Smooth approximations are only used for solving the problem and do not change the physical definition of the final model. The final output is still calculated according to the boundary functions in the claims and specification. and .

[0111] In the objective function The preferred approach includes four types of constraints. The first type is the phase fraction constraint, which increases the penalty when the sum of the phase fractions deviates from 1 or any phase fraction is less than 0; the second type is the parameter boundary constraint, which... , , , , or The first type of constraint increases the penalty when the temperature exceeds the preset physical range; the second type is a smoothing constraint between samples with adjacent cooling rates, which increases the penalty when the inversion parameters of samples with the same V content and similar cooling rates show abnormal jumps; the third type is a tissue trend constraint, which increases the penalty when the temperature exceeds the preset physical range. Increased contribution of solid solution strengthening to reverse anomaly, or Increase the penalty when the contribution of grain strengthening decreases abnormally. The above constraints can encode common sense in materials science into the optimization process.

[0112] In the objective function Preferred regularization methods include L2 regularization, group sparsity regularization, or hierarchical regularization. For early datasets with a small number of samples, stronger regularization is used to prevent overfitting; as the number of samples increases, the regularization weight is gradually reduced, allowing the model to be more driven by real data. For cases where tissue descriptors are highly correlated, such as… and Simultaneous changes can be mitigated by using group regularization or principal component projection to reduce the effects of collinearity. This can reduce the problem of excessively wide parameter confidence intervals.

[0113] During the uncertainty assessment phase, parameter distribution and predicted stress distribution can be obtained by repeatedly sampling training samples using Bootstrap; alternatively, MCMC can be used to sample in the posterior space to obtain parameter confidence intervals; and Fisher's information matrix can be calculated near the optimum of the objective function to approximate parameter correlation. If the confidence interval of a parameter crosses zero and has low sensitivity to the prediction results, this parameter can be merged or fixed in subsequent versions to improve model robustness. If a tissue descriptor is highly sensitive to the prediction results but data coverage is insufficient, it is recommended to add corresponding process samples.

[0114] Specifically, when using the Bootstrap method, sampling with replacement is performed using the sample number as the resampling unit, preferably repeated at least 500 times. Each sampling re-executes the global search and local refinement to obtain the parameter vector, validate the RMSE, and the empirical distribution of the predicted stress curve. The 2.5% and 97.5% quantiles are then used as the 95% confidence interval. For curve sampling points within the same sample, the residuals can be resampled in blocks while preserving the strain order to avoid mistaking adjacent sampling points as completely independent observations.

[0115] When using the MCMC method, the joint objective function J(θ) can be converted into a likelihood term in the posterior probability, with the physical boundary of the parameters, phase fraction conservation, and thermal softening nonnegativity constraint as prior conditions. The posterior distribution of the parameters is obtained through parallel sampling across multiple chains, outputting the mean, median, 95% confidence interval, parameter correlation coefficient, and Gelman-Rubin convergence index for each parameter. If both the Bootstrap confidence interval and the MCMC confidence interval are narrow and the RMSE is stable, the parameter is considered to have high engineering confidence. If the interval is too wide, it is marked as a high-uncertainty parameter in the report, and it is recommended to add samples with the corresponding component or cooling rate.

[0116] During the parameter output phase, it is preferable to simultaneously output the parameter table, applicable scope, training data summary, validation data summary, error index, physical constraint check results, uncertainty analysis results, and version number. The parameter table should provide not only numerical values ​​but also units, value boundaries, data source, whether it participated in optimization, 95% confidence interval or confidence interval, and correlations of key parameters. The applicable scope should at least include the V content range, cooling rate range, temperature range, and strain rate range. If the model is used outside the applicable scope, it should be marked as an extrapolation prediction, and a suggestion should be made that supplementary sample validation is needed.

[0117] Further implementation of finite element material interface

[0118] In a preferred embodiment, the constitutive parameter set obtained from the inversion is converted into a material interface that can be read by finite element software. For explicit dynamic or thermo-mechanical coupling simulations, this can be... Write the user material subroutine; for solvers that only support tabular materials, it can be done under a given... Under the given conditions, a three-dimensional table of temperature, strain rate, and plastic strain is generated. When tabulating the table, it is preferable to increase the sampling density at temperatures close to the phase transition or thermal softening sensitive range, and to use logarithmic interval sampling where the strain rate changes by orders of magnitude.

[0119] When simulating the macroscopic deformation of melt-quenched strip, the material definition can be selected as single-layer or multi-layer based on the uniformity of the microstructure in the thickness direction of the strip. If the microstructure differences between the free surface, intermediate layer, and roll-attached surface are small, a single layer can be used. And a single constitutive parameter set; if the three layers have significant differences in structure, then define three material regions along the thickness direction, each corresponding to a different... , , , , and This allows for the simulation of the effects of rapidly solidified layered structures on bending, stretching, or compression responses.

[0120] When simulating laser-remelted surface layers, the surface layer, transition layer, and substrate layer can be defined as different material states. The surface layer typically corresponds to a higher cooling rate and finer grains, the transition layer to a stronger microstructure gradient, and the substrate layer to a primitive or slower-cooled microstructure. The model of this invention is then used to calculate the flow stress. This method connects the process thermal history and mechanical response within the same simulation framework.

[0121] For additive manufacturing or laser multi-pass remelting scenarios, if the same location experiences multiple thermal cycles, the last thermal cycle exceeding the β-transformation temperature or near the liquidus line can be considered the dominant rapid solidification event, and the corresponding calculations can be performed. and Historical weights can also be introduced for multiple thermal cycles to form an equivalent organization descriptor. . In , , and It still needs to be supported by detectable tissue results or validated thermo-tissue models, and should not be based solely on unvalidated empirical assumptions.

[0122] In the user material subroutine, it is preferable to input the microstructure descriptor as a field variable or state variable. For rapidly solidified initial microstructures that do not evolve significantly with plastic deformation, the microstructure descriptor can be... As a fixed field variable; for situations where metastable phase decomposition or recrystallization may occur during high-temperature deformation or long-term loading, state variable updates can be set. , or If a reliable microstructure evolution equation is not established, the application text shall not claim that it can accurately predict long-term phase transitions, but shall only limit its use to constitutive parameter inversion and mechanical response prediction in the initial rapid solidification microstructure state.

[0123] Finite element analysis (FEM) verification can utilize load-displacement curves, micropillar compression curves, bending curves, or residual stress release curves from small-scale specimens. Verification metrics include peak load error, yield point error, plastic stage slope error, unloading rebound error, and local strain distribution error. If only uniaxial stress-strain curves are obtained, the yield strength and stress at the selected plastic strain point should at least be compared between the simulated and experimental curves. The above verification methods are standard engineering verification practices in this field and do not rely on fictitious performance data.

[0124] In terms of engineering output, this invention can also generate process window suggestions based on the inversion model. Specifically, within a given V content range and the cooling rate achievable by the equipment, different... and corresponding , , and The study analyzes the changing trends and predicts their impact on flow stress; then, considering parameter uncertainties, it screens out process ranges with stable predictions and fewer physical constraint violations. These recommendations are intended to guide the next round of sample preparation and testing, rather than replacing actual material validation.

[0125] To facilitate engineering use, output files are preferably available in both machine-readable and human-readable report formats. Machine-readable formats may include CSV, JSON, XML, or material cards specific to the finite element software. Human-readable reports include sample source, model formulas, parameter tables, applicable scope, verification results, and risk warnings. Both types of files have the same version number to prevent simulation personnel from misusing unverified or outdated parameters.

[0126] Further explanation of the differences from existing technologies

[0127] Existing techniques for identifying constitutive parameters of titanium alloys mostly revolve around fitting stress-strain curves under hot working, cutting, impact, or conventional heat treatment conditions. The core variables are typically strain, strain rate, and temperature. Even when some techniques introduce grain size or phase fraction corrections, they usually do not quantify the V solute trapping caused by rapid solidification as being between 0 and 1. The variable is used simultaneously for both the solid solution strengthening term and the objective function constraint. A key difference in this invention is that it does not treat rapid solidification merely as a sample preparation method, but rather transforms the thermal history of rapid solidification into a constraint source for constitutive parameter inversion.

[0128] Existing machine learning techniques for predicting the constitutive relations of titanium alloys can learn stress responses using large amounts of data, but they often rely on data-driven features, resulting in insufficient model interpretability and materials science constraints. While this invention can utilize optimization algorithms and statistical evaluation methods, its core is not a general machine learning model, but rather a solute trapping-metastable phase dual-constraint framework with clear physical meaning. , , , , and All correspond to detectable or calculable material microstructure, and through... The participation constraint makes the parameter inversion results interpretable by materials science.

[0129] Existing research on rapidly solidified titanium alloys typically focuses on phase formation, microstructure refinement, or property characterization, but has not yet formed a closed loop for constitutive parameter inversion for finite element simulation. This invention connects sample preparation, microstructure analysis, solute retention evaluation, constitutive model, joint objective function, parameter uncertainty, and finite element material interface in a series, enabling the microstructure information of rapidly solidified samples to be incorporated into engineering simulations. This closed-loop combination constitutes one of the main supports for the inventiveness of this invention.

[0130] For the Ti-V system, V is a β-stable element. Local V distribution under rapid solidification conditions, β-phase stability, ω-phase formation, and martensite formation may collectively influence mechanical behavior. If only the average V content is used... It is impossible to distinguish the tissue differences between samples with the same nominal composition but different cooling rates. This invention addresses this by... and Describe the local segregation and retention states, and then through and The metastable phase state is described by constraining the flow stress model from two related but different perspectives, thereby improving the model's relevance to rapidly solidified Ti-V alloys.

[0131] This invention does not exclude Johnson-Cook, Chaboche, or thermoplastic models as the base form. In alternative embodiments, the A, B, C, and D decomposition forms can be replaced with modified Johnson-Cook forms, Arrhenius-type hot deformation forms, or crystal plastic homogenization forms, as long as their parameter inversion still uses... , , and The technical concept of this invention can be realized by constructing an organizational descriptor, and by ensuring that the objective function still includes stress error, phase fraction error, solute retention error, and physical constraint terms. This open structure helps to avoid an overly narrow scope of protection.

[0132] To avoid duplication with existing technologies, the claims limit the focus of protection to rapidly solidified Ti-V alloys and solute rejection index. Metastable phase volume fraction and Equivalent defect density Joint objective function J( The combination of stress curve fitting, grain size strengthening, finite element parameter table generation, or general optimization algorithm is not the core of this invention.

[0133] Alternative implementation methods and industrial applications

[0134] In an alternative implementation, the V content can be expressed as a mass percentage. This indicates that it can also be converted to atomic percentage before being included in the model. If atomic percentage is used, consistency should be maintained across all samples and all formulas, and the atomic percentage should be redefined. And the boundary of solid solution strengthening parameters. The use of mass percentage in the claims is to maintain consistency with alloy batching and engineering testing practices, and does not preclude unit conversion during implementation.

[0135] In another alternative implementation It can come from slow-cooled as-cast samples of the same composition, or from a validated equilibrium solidification model or the Scheil solidification model. If model calculations are used... It is preferable to record the thermodynamic database version, element range, and calculation assumptions; if a slowly cooled as-cast sample is used, it is preferable to use the same composition detection method as for rapidly solidified samples for calculation. By maintaining transparency regarding the sources of reference, it is possible to ensure... Verifiability.

[0136] In yet another alternative implementation, the metastable phase descriptor is not limited to... and Two quantities. When Ti-V alloys exhibit other reliably identifiable metastable structures under specific compositional or thermal histories, it is possible to... A corresponding descriptor is added to the model; when no ω-phase or martensitic phase is observed in a dataset, the corresponding volume fraction can be set to zero while preserving the variable structure. This ensures that the model is applicable to rapidly solidified Ti-V samples with metastable phases, while also being compatible with samples that have not formed these phases.

[0137] In a further alternative embodiment, the solute retention calculation framework of the present invention can be extended to rapidly solidified titanium alloy systems containing isomorphous β-stabilizing elements such as Ti-Nb, Ti-Mo, and Ti-Cr. For the Ti-Nb system, the nominal V content can be replaced with the Nb content, and the V element segregation index and solute retention index can be replaced with the Nb element segregation index and solute retention index, respectively. For the Ti-Mo system, this can be replaced by the Mo element segregation index and... For the Ti-Cr system, this can be replaced by the Cr element segregation index and... The reference segregation index in each system can still be obtained from slow-cooled as-cast samples of the same composition, equilibrium solidification models, or Scheil solidification models.

[0138] The above extension holds true because the increased propagation rate at the solid-liquid interface during rapid solidification prevents solute diffusion from reaching equilibrium, resulting in varying degrees of solute retention and segregation weakening. This physical phenomenon is not limited to V. Nb, Mo, and Cr can all act as β-stabilizing elements, influencing β-phase stability, metastable phase transformation pathways, and solid solution strengthening contributions. Therefore, while maintaining the joint objective function and parameter inversion process unchanged, the element-related segregation index, solute retention index, and solid solution strengthening term can be replaced with their corresponding elemental forms.

[0139] When rapidly solidified titanium alloys contain two or more β-stabilizing elements, κ can be input into the model as a vector, for example... An equivalent solute rejection index can also be constructed based on the contribution weights of each element to β stability, solid solution strengthening, or phase transition temperature. Regardless of whether a single element κ, a vector κ, or... All reference segregation index sources, local component detection methods, and uncertainty records should be retained to ensure verifiability when applied across systems.

[0140] This invention can be used to establish constitutive parameters for rapidly solidified Ti-V strips, powders, remelted layers, thin-walled parts, or gradient microstructure components. For powder samples, the cooling rate can be estimated based on the thermal history of the atomization process and the powder particle size, and obtained through powder cross-sectional microstructure characterization. For remelted layers or additively manufactured samples, thermal simulation and molten pool cross-section characterization can be used to obtain... For strip samples, the results can be obtained through strip thickness, roller contact conditions, and microstructure. Different preparation routes only affect the data acquisition method and do not change the parametric inversion framework of solute retention-metastable phase dual constraints.

[0141] The industrial applications of this invention include the development of rapid solidification processes for Ti-V alloys, evaluation of the mechanical properties of surface remelted layers, establishment of material cards for finite element forming or service simulation, process window screening, and subsequent construction of material databases. Because this method requires input of real thermal history, real microstructure data, and real mechanical curves, it is particularly suitable for material development scenarios with high experimental costs, small sample sizes, and significant microstructure gradients.

[0142] In the actual application and implementation process, if the applicant has obtained real experimental data, they can further supplement the specification with specific sample numbers, V content, cooling rate, phase fraction, curve error, and finite element verification results; if not all experiments have been completed, it is not advisable to include numerical effects that cannot be traced. The current text supports practicality with implementable procedures, formulas, variable sources, and verification methods, and reduces the risk of inaccuracy by not including fictitious performance values.

Claims

1. A method of alloy constitutive parameter inversion coupled with rapid solidification solute partitioning features, characterized by, Includes the following steps: S1, to obtain compositional data, thermal history data, microstructure data and mechanical curve data of rapidly solidified alloy samples; S2, extract tissue descriptors based on the microstructure data and / or the thermal history data, wherein the tissue descriptors include at least a solute partition descriptor for characterizing the solute partitioning features of rapid solidification; S3, establish a coupled constitutive model with the microstructure descriptor as the input variable or the correction variable, so that the constitutive parameters are jointly constrained by the alloy composition, cooling path and microstructure. S4, construct a multi-constraint objective function, which includes at least a macroscopic mechanical error term, a microscopic organizational error term, and a physical constraint term; S5. The coupled constitutive model is inverted and solved using a parameter optimization algorithm to obtain a set of constitutive parameters for predicting the mechanical response of the rapidly solidified alloy.

2. The method of claim 1, wherein, The rapid solidification alloy is a titanium alloy, the solute partitioning descriptor includes a solute trapping extent indicator The solute trapping extent indicator is used to characterize the extent of solute segregation during rapid solidification relative to a reference solidification state.

3. The method of claim 2, wherein, The titanium alloy is a Ti-V alloy with a mass percentage of V of 5-35 wt%, and the structure descriptors at least three of a V element segregation index , a solute trapping degree index , a β grain size , an ω phase volume fraction , a martensite phase volume fraction , and an equivalent defect density ​ 4. The method according to claim 2 or 3, characterized in that, the solute trapping degree indicator by calculated; wherein, is the solute segregation index, calculated by or calculated, is the local content of the solute to be evaluated, is the reference segregation index obtained from a slow-cooled as-cast sample of the same composition, an equilibrium solidification model or a Scheil solidification model.

5. The method according to any one of claims 1 to 4, characterized in that, The coupling constitutive model is a modified Johnson-Cook model, satisfying ; wherein, is a tissue descriptor, , , , and at least two of which are tissue descriptor functions.

6. The method of claim 5, wherein, includes at least two of a temperature dependent base strength term, a grain boundary strengthening term, a solid solution and solute trapping contribution term, an omega phase contribution term, a martensite phase contribution term, and a defect density contribution term; wherein the solid solution and solute trapping contribution term varies with solute content, the grain boundary strengthening term varies with beta grain size , the defect density contribution term varies with equivalent defect density .

7. The method according to any one of claims 1 to 6, characterized in that, The multi-constraint objective function is constructed as wherein, is a macro-mechanics error term, is a phase fraction error term, is a solute trapping error term, is a physical constraint penalty term, is a regularization term, ; preferably, , , , , and adjusting the sample weight or objective function weight according to at least one of the mechanical curve reliability, the phase composition reliability, the local composition distribution reliability, and the thermal history integrity.

8. The method according to any one of claims 1 to 7, characterized in that, The parameter optimization algorithm includes a global search algorithm, a local refinement algorithm, a Bayesian optimization algorithm, a gradient-based optimization algorithm, or a combination thereof; the inversion solution also includes dividing the training set and the independent validation set, and estimating the parameter confidence interval through Bootstrap, MCMC, or Fisher information matrix.

9. A computer-readable storage medium, characterized in that, It stores a constitutive parameter data package for rapidly solidified alloys. The constitutive parameter data package includes at least two of the following: a constitutive parameter set obtained by the method described in any one of claims 1-8; a microstructure descriptor field; an alloy composition range; a cooling rate range; a temperature range; a strain rate range; an objective function weight; a physical constraint check result; and a version identifier. When the constitutive parameter data package is read by finite element software, a material database, or a user material subroutine, it is used to generate or call the flow stress parameters of the rapidly solidified alloy.

10. Use of the method of any one of claims 1 to 8 or the computer readable storage medium of claim 9 in finite element simulation of additively manufactured components, characterized in that, Based on the thermal history of the additive manufacturing molten pool, cooling rate, undercooling, and microstructure mapping results, determine the microstructure descriptor of at least one element or integration point in the finite element mesh, and call the constitutive parameter set to predict the mechanical response of the component under forming, post-processing, or service loads.

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