Monocrystal plastic constitutive parameter prediction method and system based on nanoindentation data driving

Abstract

The invention discloses a method and a system for predicting crystal plasticity constitutive parameters of a single crystal based on nanoindentation data driving, and belongs to the technical field of crossing of material computational mechanics and artificial intelligence. The method comprises the following steps: generating a nanoindentation simulation data set and a uniaxial tension simulation data set by using a crystal plasticity finite element, and constructing a hierarchical mapping relation of nanoindentation curve-stress-strain curve-crystal plasticity constitutive parameter by using a multilayer sensor. According to the method, a staged hierarchical neural network prediction framework based on single crystal nanoindentation data driving is constructed, and efficient and accurate prediction of crystal plasticity constitutive parameters is realized.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of materials computational mechanics and artificial intelligence, and in particular relates to a method and system for predicting the plastic constitutive parameters of single crystals based on nanoindentation data. Background Technology

[0002] Crystal plasticity (CP) modeling methods have demonstrated unique advantages in micro- and nano-scale mechanics research due to their ability to accurately characterize the anisotropic plastic deformation behavior of crystalline materials. However, the strong nonlinear coupling characteristics between different crystal plasticity constitutive parameters make the efficient and accurate identification of these parameters a key bottleneck restricting the application of CP.

[0003] Constitutive parameters (CP) essentially describe the deformation behavior of single crystals, while the CP constitutive parameters of polycrystalline materials can be calibrated through uniaxial tensile or compressive tests. This calibration process is typically based on representative volume elements (RVEs) simulations of the polycrystalline material's microstructure, ensuring that the RVEs are consistent with the crystallographic texture of the polycrystalline material. The core idea is to use the homogenization assumption to make the macroscopic mechanical response of the RVEs match the experimental results. However, for materials with significantly non-homogeneous structures, such as welded metal joints, it is difficult to obtain local mechanical responses because standard tensile / compression specimens cannot be prepared.

[0004] The rise of multi-scale micromechanical testing methods has provided a new approach, with microscopic testing methods such as micropillar compression and nanoindentation being used to obtain the elastoplastic properties of materials. Among these, nanoindentation technology, with its advantages of high resolution, near non-destructive nature, low sample requirements, and high throughput testing, has become an ideal solution to address the lack of macroscopic experimental data for multiphase materials. However, the complexity of micropillar compression tests and the time-consuming nature of a single nanoindentation simulation limit the number of samples that can be collected.

[0005] Therefore, there is an urgent need for an efficient and universal parameter prediction framework to realize the mapping from easily available nanoindentation data to complex constitutive parameters. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method and system for predicting the plastic constitutive parameters of a single crystal based on nanoindentation data. This method is based on a two-step machine learning data-driven framework. The core of this method is to generate a simulation dataset using the crystal plasticity finite element method and to map the nanoindentation curve to the stress-strain curve and then to the constitutive parameters through a multilayer perceptron (MLP) neural network.

[0007] The first aspect of this invention proposes a method for predicting the plastic constitutive parameters of a single crystal based on nanoindentation data, characterized in that the method includes:

[0008] Step S1: Determine multiple crystal samples and use crystal plasticity finite element method to generate nanoindentation simulation dataset and uniaxial tensile simulation dataset for each crystal sample;

[0009] Step S2: Establish a nanoindentation curve based on the nanoindentation simulation dataset, extract multiple first feature values ​​from the nanoindentation curve to form a first feature vector, and form a first feature sample set from the first feature vectors of multiple crystal samples.

[0010] Step S3: Establish a stress-strain curve based on the uniaxial tensile simulation dataset, extract multiple second feature values ​​from the stress-strain curve to form a second feature vector, and form a second feature sample set from the second feature vectors of multiple crystal samples.

[0011] Step S4: Extract multiple third eigenvalues ​​from the known crystal plastic constitutive model to form a third eigenvector for each crystal sample; the third eigenvectors of multiple crystal samples form a third eigensample set.

[0012] Step S5: Establish a first mapping relationship model and a second mapping relationship model using a multilayer perceptron; the input values ​​of the first mapping relationship model are the first feature value, Poisson's ratio and anisotropy coefficient, and the output value is the second feature value; the input values ​​of the second mapping relationship model are the second feature value, Poisson's ratio and anisotropy coefficient, and the output value is the third feature value.

[0013] Step S6: Train, validate, and test the first mapping relationship model and the second mapping relationship model based on the first feature sample set, the second feature sample set, and the third feature sample set to obtain the final first mapping relationship model and the second mapping relationship model.

[0014] Step S7: Obtain nanoindentation data of the crystal to be tested, and use the final first mapping relationship model and second mapping relationship model to predict the crystal plastic constitutive parameters of the crystal to be tested.

[0015] According to the method of the first aspect of the present invention, in step S2, the first feature value includes: load values ​​at different depths, slope of the loading segment curve at different depths, initial unloading stiffness, and plastic work ratio.

[0016] According to the method of the first aspect of the present invention, in step S3, the second characteristic value includes: elastic modulus, yield stress, and rheological stress at different plastic strains.

[0017] According to the method of the first aspect of the present invention, in step S4, the third characteristic value includes: elastic stiffness along the x-axis of the lattice, elastic stiffness along the diagonal direction, shear stiffness along the y-axis of the lattice, initial slip hardening modulus, initial critical shear stress, saturated flow stress, and saturated hardening modulus.

[0018] According to the method of the first aspect of the present invention, the method further includes: before step S5, normalizing the first feature value, the second feature value and the third feature value respectively.

[0019] According to the method of the first aspect of the present invention, the method further includes: between step S5 and step S6, performing Bayesian hyperparameter optimization on the first mapping relationship model and the second mapping relationship model respectively.

[0020] According to the method of the first aspect of the present invention, in step S6, the first mapping relationship model and the second mapping relationship model are trained by dynamically adjusting the learning rate.

[0021] According to the method of the first aspect of the present invention, in step S1, when generating the nanoindentation simulation dataset of each crystal sample using the crystal plastic finite element method, an explicit dynamic solution algorithm combined with a semi-automatic mass scaling method is used to perform nanoindentation simulation of each crystal sample.

[0022] When generating a uniaxial tensile simulation dataset for each crystal sample using the crystal plastic finite element method, the uniaxial tensile process of a single crystal is simplified to the uniaxial tensile process of a single element. The solution-related state variables of the single element are directly solved and the stress state is updated.

[0023] A second aspect of this invention discloses a single-crystal plastic constitutive parameter prediction system based on nanoindentation data, the system comprising:

[0024] The data generation module is used to identify multiple crystal samples and generate a nanoindentation simulation dataset and a uniaxial tensile simulation dataset for each crystal sample using the crystal plasticity finite element method.

[0025] The first extraction module is used to establish a nanoindentation curve based on the nanoindentation simulation dataset, extract multiple first feature values ​​from the nanoindentation curve to form a first feature vector, and the first feature vectors of multiple crystal samples form a first feature sample set.

[0026] The second extraction module is used to establish a stress-strain curve based on the uniaxial tensile simulation dataset, extract multiple second feature values ​​from the stress-strain curve to form a second feature vector, and the second feature vectors of multiple crystal samples form a second feature sample set.

[0027] The third extraction module is used to extract multiple third eigenvalues ​​of each crystal sample from the known crystal plastic constitutive model to form a third eigenvector, and the third eigenvectors of multiple crystal samples form a third eigensample set;

[0028] The model building module is used to establish a first mapping relationship model and a second mapping relationship model using a multilayer perceptron; the input values ​​of the first mapping relationship model are a first feature value, Poisson's ratio and anisotropy coefficient, and the output value is a second feature value; the input values ​​of the second mapping relationship model are a second feature value, Poisson's ratio and anisotropy coefficient, and the output value is a third feature value.

[0029] The model training module is used to train, validate, and test the first mapping relationship model and the second mapping relationship model based on the first feature sample set, the second feature sample set, and the third feature sample set, so as to obtain the final first mapping relationship model and the second mapping relationship model.

[0030] The prediction module is used to acquire nanoindentation data of the crystal under test and to predict the crystal plastic constitutive parameters of the crystal under test using the final first mapping relationship model and the second mapping relationship model.

[0031] According to the system of the second aspect of the present invention, the first characteristic value includes: load values ​​at different depths, slope of the loading segment curve at different depths, initial unloading stiffness, and plastic work ratio;

[0032] The second characteristic value includes: elastic modulus, yield stress, and rheological stress at different plastic strains;

[0033] The third characteristic value includes: elastic stiffness along the x-axis of the lattice, elastic stiffness along the diagonal, shear stiffness along the y-axis of the lattice, initial slip hardening modulus, initial critical shear stress, saturated flow stress, and saturated hardening modulus.

[0034] The solution proposed in this invention has the following technical effects:

[0035] This invention constructs a staged hierarchical neural network prediction framework driven by single-crystal nanoindentation data, which realizes efficient and accurate prediction of crystal plastic constitutive parameters. Specifically, it uses crystal plasticity finite element method to generate simulation dataset, and uses multilayer perceptron (MLP) neural network to realize hierarchical mapping of nanoindentation curve → stress-strain curve → constitutive parameters.

[0036] Furthermore, the mapping model between the nanoindentation curve and the stress-strain curve constructed in this invention, namely the first mapping relationship model, predicts the coefficient of determination R of the stress-strain curve. 2 >0.97, the mean absolute percentage error (MAPE) of the rheological stress in the plastic segment is only 4.80%; when inverting constitutive parameters using the mapping model of stress-strain curve → constitutive parameters, i.e., the second mapping relationship model, the initial critical shear stress τ0 and saturated flow stress τ s Prediction of key parameters R 2 The value >0.99 verifies the high precision of the two mapping relationship models.

[0037] Furthermore, the first mapping relationship model constructed in this invention is not limited by the mathematical form of the constitutive model. When the form of the crystal plastic constitutive model changes, the degree of agreement between the stress-strain curve predicted by the first mapping relationship model and the set value curve remains at R. 2 >0.95, which solves the problem of traditional methods' dependence on specific models.

[0038] Furthermore, this invention combines explicit dynamic crystal plasticity finite element (CPFE) simulation with a simplified uniaxial tensile model, significantly reducing the simulation time for a single nanoindentation from 10 hours using an implicit algorithm to 30 minutes. The trained neural network predicts the entire process in just 5 seconds, which is significantly more efficient than traditional optimization methods and provides an engineering solution for high-throughput constitutive parameter identification of multiphase materials.

[0039] Furthermore, the indentation curve reconstructed from constitutive parameters derived from experimental nanoindentation data in this invention, and the R value of the measured value, are compared with those of the actual curve. 2 The method can still guarantee prediction reliability when the value reaches above 0.99 and the assumed value of the elastic parameter is within ±30% error range, which confirms the practical value of the method in the local mechanical characterization of non-homogeneous materials such as welded joints. Attached Figure Description

[0040] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram illustrating the extraction of input features from a nanoindentation curve in one embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram of extracting input features from a stress-strain curve in one embodiment of the present invention.

[0043] Figure 3 This is an embodiment of the present invention that uses nanoindentation curves and stress-strain curves to extract the input and output features of a neural network.

[0044] Figure 4 This is a summary of the test set prediction results of the first mapping relationship model in one embodiment of the present invention, based on five cross-validations.

[0045] Figure 5 This is a comparison of the predicted and actual values ​​of rheological stress in a cross-validation result in one embodiment of the present invention (solid line represents the actual value, and dots represent the predicted value).

[0046] Figure 6 This is the predicted result of the elastic constant of the test set in one embodiment of the present invention.

[0047] Figure 7 This is a test result predicting the parameters of the plastic component in one embodiment of the present invention.

[0048] Figure 8 This is a comparison of two predicted values ​​with the actual values ​​in one embodiment of the present invention.

[0049] Figure 9 This is a comparison between the set value and the predicted value of the sample stress-strain curve under a given combination of parameters in one embodiment of the present invention.

[0050] Figure 10 This is a comparison between the predicted stress-strain curve and the actual value in one embodiment of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] The first aspect of this embodiment proposes a method for predicting the plastic constitutive parameters of a single crystal based on nanoindentation data, the method comprising:

[0053] Step S1: Determine multiple crystal samples and use crystal plasticity finite element method to generate a nanoindentation simulation dataset and a uniaxial tensile simulation dataset for each crystal sample.

[0054] Step S2: Establish a nanoindentation curve based on the nanoindentation simulation dataset, extract multiple first feature values ​​from the nanoindentation curve to form a first feature vector, and form a first feature sample set from the first feature vectors of multiple crystal samples.

[0055] Step S3: Establish a stress-strain curve based on the uniaxial tensile simulation dataset, extract multiple second feature values ​​from the stress-strain curve to form a second feature vector, and form a second feature sample set from the second feature vectors of multiple crystal samples.

[0056] Step S4: Extract multiple third eigenvalues ​​from the known crystal plastic constitutive model to form a third eigenvector for each crystal sample, and form a third eigensample set from the third eigenvectors of multiple crystal samples.

[0057] Step S5: Establish a first mapping relationship model and a second mapping relationship model using a multilayer perceptron; the input values ​​of the first mapping relationship model are the first feature value, Poisson's ratio and anisotropy coefficient, and the output value is the second feature value; the input values ​​of the second mapping relationship model are the second feature value, Poisson's ratio and anisotropy coefficient, and the output value is the third feature value.

[0058] Step S6: Train, validate, and test the first mapping relationship model and the second mapping relationship model based on the first feature sample set, the second feature sample set, and the third feature sample set to obtain the final first mapping relationship model and the second mapping relationship model.

[0059] Step S7: Obtain nanoindentation data of the crystal to be tested, and use the final first mapping relationship model and second mapping relationship model to predict the crystal plastic constitutive parameters of the crystal to be tested.

[0060] The design inspiration for this invention comes from the hierarchical mapping characteristics of nanoindentation curves and stress-strain curves: the former reflects local deformation behavior, while the latter characterizes macroscopic flow properties. By performing stepwise predictions, the complexity of directly constructing high-dimensional nonlinear mappings can be avoided, effectively improving the model's generalization ability. This invention generates nanoindentation and uniaxial tensile simulation datasets using CPFE, and establishes the mapping relationship between nanoindentation curves and macroscopic stress-strain curves through machine learning, thereby achieving direct prediction of constitutive parameters.

[0061] In step S1, multiple crystal samples are determined, and a nanoindentation simulation dataset and a uniaxial tensile simulation dataset for each crystal sample are generated using the crystal plasticity finite element method.

[0062] In some embodiments, in step S1, when generating the nanoindentation simulation dataset for each crystal sample using the crystal plastic finite element method, an explicit dynamic solution algorithm combined with a semi-automatic mass scaling method is used to perform nanoindentation simulation for each crystal sample.

[0063] When generating a uniaxial tensile simulation dataset for each crystal sample using the crystal plastic finite element method, the uniaxial tensile process of a single crystal is simplified to the uniaxial tensile process of a single element. The solution-related state variables of the single element are directly solved and the stress state is updated.

[0064] Specifically, this embodiment uses explicit kinetics instead of implicit kinetics, primarily because the computational cost of implicit kinetics (10 hours per sample) far exceeds that of explicit kinetics (only 30 minutes per sample). Although explicit kinetics significantly reduces computational cost, its accuracy depends on the setting of the mass scaling parameters. To alleviate the critical time step limitation caused by tiny units in the explicit algorithm, this embodiment employs a semi-automatic mass scaling method. After irrelevance analysis, the preset target time step threshold is 0.005 s. Furthermore, considering the anisotropic deformation behavior of the single crystal during nanoindentation, this embodiment uses a three-dimensional model for numerical simulation. The Berkovich indenter is set as an analytical rigid body, with the indenter tip as the reference point; the sample size is set to 20 × 20 × 10 μm. 3 The deformable cube, composed of 37,020 C3D8 elements, was locally meshed in the contact area with the indenter and along the indentation direction, with a minimum element size of 50 nm. The height of the cube is more than 10 times the maximum indentation depth (600 nm), and the upper and lower surface areas are much larger than the indentation size. Displacement in all directions on the bottom surface of the specimen is constrained, and the reference point at the tip of the indenter restricts displacement in all directions except the indentation direction (Z) to prevent the indenter from tilting or rotating during indentation. Other surfaces are free surfaces. The indentation load is achieved by applying displacement constraints to the reference point at the tip of the indenter. A displacement of 600 nm in the positive and negative directions along the Z direction is applied in two analysis steps with a duration of 30 s, respectively. This indentation depth exceeds the critical depth for most face-centered cubic single crystals affected by the indentation size effect and is set as a fixed value in all samples. The contact surface between the indenter and the specimen is set to 'Hard' contact, and the coefficient of friction is set to 0.1.

[0065] Specifically, this embodiment simplifies the uniaxial stretching process of a single crystal into a uniaxial stretching process of a single unit. It directly solves the solution-related state variables of a single unit and updates the stress state without calling ABAQUS, which can greatly improve computational efficiency and provide a large number of simulation samples of stress-strain curves corresponding to crystal plastic constitutive parameters for the neural network in a short time.

[0066] In step S2, a nanoindentation curve is established based on the nanoindentation simulation dataset. Multiple first feature values ​​are extracted from the nanoindentation curve to form a first feature vector, and the first feature vectors of multiple crystal samples form a first feature sample set.

[0067] In some embodiments, in step S2, the first feature value includes: load values ​​at different depths, slope of the loading segment curve at different depths, initial unloading stiffness, and plastic work ratio.

[0068] Specifically, in existing technologies, a common method for processing continuous nanoindentation curves into inputs that can be received by neural networks is to fit the loading and unloading segments separately using the following formula:

[0069]

[0070] Among them, h r It is the residual depth after complete unloading, and k,a,m,b are the fitting parameters.

[0071] This reduces a complete nanoindentation curve to five parameters, but it also loses a significant amount of information, such as the slope of the loaded section curve as a function of depth. This variation cannot be simply determined using only k and m. Therefore, this embodiment extracts the following features from the load-depth curve:

[0072]

[0073] Among them, h i From h1 to h m Equally spaced depth values ​​(i = 1, 2, 3, ..., 15), h m This represents the maximum depth. The maximum displacement of the indenter tip during nanoindentation simulation is a fixed value, therefore h... i It is exactly the same in every sample. P(h) i ) for h i The load value at depth, S(h) i ) represents the curve of the loading segment at h i Slope at depth, S unload The initial unloading stiffness, i.e., the unloading segment curve at the maximum depth h. m The slope at Coeff W The plastic work W done during the pressing process of the indenter p With total power W p +W e The ratio, i.e., the proportion of plastic work, is shown in the calculation method of each parameter in the load-depth curve. Figure 1 .

[0074] In step S3, a stress-strain curve is established based on the uniaxial tensile simulation dataset. Multiple second feature values ​​are extracted from the stress-strain curve to form a second feature vector. The second feature vectors of multiple crystal samples form a second feature sample set.

[0075] In some embodiments, in step S3, the second characteristic value includes: elastic modulus, yield stress, and rheological stress at different plastic strains.

[0076] Specifically, this embodiment extracts the following features from the stress-strain curve: in, For Young's modulus, For yield stress, Plastic strain values ​​at equal intervals from 0.01% to 26% ( ), for Rheological stress at plastic strain. Given... The complete plastic segment of the stress-strain curve can be reconstructed using interpolation methods. The calculation methods for each parameter in the stress-strain curve are illustrated below. Figure 2 .

[0079] In step S4, multiple third eigenvalues ​​of each crystal sample are extracted from the known crystal plastic constitutive model to form a third eigenvector, and the third eigenvectors of multiple crystal samples form a third eigensample set.

[0080] In some embodiments, in step S4, the third characteristic value includes: elastic stiffness along the x-axis direction of the lattice (i.e., the

[100] direction), elastic stiffness along the diagonal direction (i.e., the

[110] direction), shear stiffness along the y-axis direction of the lattice (i.e., the

[001] direction), initial slip hardening modulus, initial critical shear stress, saturated flow stress, and saturated hardening modulus.

[0081] Specifically, the crystal plasticity model is a microscopic mechanism model describing the plastic deformation of crystalline materials under macroscopic loads. This model primarily attributes the plastic deformation behavior of crystals to dislocation movement along specific slip systems within the crystal. When the slip system is activated, the slip surfaces slide relative to each other under the drive of the decomposed shear stress along the slip direction. This deformation can be defined as the plastic deformation gradient F. p Furthermore, assuming that all inelastic deformations of the crystal are caused by slip, the total deformation gradient F of the crystal can be decomposed into the elastic deformation gradient Fc. e and plastic deformation gradient F p :

[0082] F = F e ·F p

[0083] Plastic velocity gradient L p Slip strain rate of slip system α Related:

[0084]

[0085] FCC crystals have 12 slip systems, of which N slip Represents the total number of slip systems that can be activated. Vector and These are the slip direction vector and the normal vector of the slip surface in the intermediate configuration, respectively. The main driving force of slip behavior lies in the decomposed shear stress along the slip direction:

[0086]

[0087] Wherein, vector s α and m α These are the slip direction vector and the normal vector of the slip surface, respectively. The slip system will be activated when the decomposed shear stress exceeds the critical decomposed shear stress. The viscoplastic deformation related to the rate of the crystalline material is expressed using a simple power-law function as follows:

[0088]

[0089] in, To take into account the critical shear stress of current strain hardening, Here, n is the reference strain rate and n is the rate sensitivity index. This embodiment does not study the rate-dependent properties of the material; therefore, the rate sensitivity index n and the reference strain rate are used in numerical simulations. The values ​​are set to constants of 40 and 0.006, respectively. The strain hardening effect is described by the incremental relationship of slip strain:

[0090]

[0091] Among them, h αα and h αβ (α≠β) represent the self-hardening modulus and the latent hardening modulus, respectively. Based on the Voce hardening model, the self-hardening modulus h... αα With cumulative slip plastic strain The evolutionary expression is as follows:

[0092]

[0093] Where h0 is the initial slip hardening modulus, τ0 is the initial critical shear stress, and τ s For saturated flow stress, h s This is the saturated hardening modulus. The latent hardening modulus is determined by the slip system interaction coefficient q. αβ Sure:

[0094] h αβ =q αβ h αα

[0095] Define equivalent slip plastic strain Sum of the cumulative slip shear strain for all slip systems:

[0096]

[0097] This embodiment uses a crystal plastic constitutive model defined by the above eight formulas to generate simulation samples for extracting the third feature sample set. The variable parameters include h0, h s ,τ0,τ s .

[0098] In addition to the four crystal plastic constitutive parameters mentioned above, the third eigenvector of this embodiment also includes three elasticity-related parameters c of the FCC crystal. 11 ,c 12 ,c 44 (C11: elastic stiffness along the

[100] direction, C12: elastic stiffness along the

[110] direction, C44: shear stiffness along the

[001] direction), which can be represented by three constants E, ν, A stretched along the crystal axis direction, and satisfy the following relationship.

[0099]

[0100] Where E is Young's modulus, ν is Poisson's ratio, and A is the anisotropy coefficient.

[0101] In step S5, a first mapping relationship model and a second mapping relationship model are established using a multilayer perceptron; the input values ​​of the first mapping relationship model are a first feature value, Poisson's ratio, and anisotropy coefficient, and the output value is a second feature value; the input values ​​of the second mapping relationship model are a second feature value, Poisson's ratio, and anisotropy coefficient, and the output value is a third feature value.

[0102] Specifically, from c 11 ,c 12 ,c 44 As can be seen from the relationship, besides Young's modulus, which can be directly obtained from the elastic part of the stress-strain curve, Poisson's ratio and anisotropy coefficient are also useful for solving c. 11 ,c 12 ,c 44 Because these are key parameters, Poisson's ratio and anisotropy coefficient are also used as input values ​​for the first and second mapping relationship models in this embodiment. It should be noted that when training, validating, and testing the network model, the Poisson's ratio and anisotropy coefficient are the accurate values ​​for the corresponding crystal samples. However, when predicting the stress-strain curves and crystal plastic constitutive parameters of unknown materials using nanoindentation curves, assumed Poisson's ratio and anisotropy system need to be given.

[0103] In summary, the first mapping model (MLP1) in this embodiment takes the reduced-order nanoindentation curve (i.e., the first eigenvalue) and the additional input ν,A as input, and outputs the reduced-order stress-strain curve (i.e., the second eigenvalue). The second mapping model (MLP2) takes the reduced-order stress-strain curve (i.e., the second eigenvalue) and the additional input ν,A as input, and outputs a 7-dimensional vector composed of the plastic constitutive parameters of the sample crystal (i.e., the third eigenvalue). The prediction process of the neural network is illustrated below. Figure 3 As shown.

[0104] The number and spacing of feature points are determined based on sensitivity analysis: the spacing between nanoindentation depth points corresponds to the key area of ​​strain gradient change during the indentation process; the plastic strain points cover 0.01%-26%, covering the typical hardening stage (from the initial yielding stage to the saturation zone), ensuring a balance between curve reconstruction accuracy and economy.

[0105] In some embodiments, the method further includes: before step S5, normalizing the first feature value, the second feature value, and the third feature value respectively, to prevent the neural network from focusing on features with large absolute values ​​during training.

[0106]

[0107] in, The normalized value, x (i) For the original data points, μ i σ is the mean of the corresponding feature. i This represents the standard deviation of the corresponding feature.

[0108] In some embodiments, the method further includes: between steps S5 and S6, setting the number of hidden layers in the first mapping model and the second mapping model, as well as the number of neurons in each hidden layer, as variables; using Bayesian optimization with a Gaussian process to find the optimal combination of hyperparameters; setting the search space to have 1 to 5 hidden layers and 5 to 500 neurons; setting the maximum number of iterations to 2000; and defining the loss function of the Bayesian optimization process as the normalized mean square error (NMSE) to balance all output dimensions.

[0109]

[0110] Where k is the output dimension, n is the number of samples, and y ij Let be the j-th dimension feature value in the i-th sample. For the predicted value, y j Let be the vector formed by the j-th dimension feature values ​​of all samples.

[0111] The optimal hyperparameter combinations obtained after Bayesian hyperparameter optimization of the first and second mapping relationship models are shown in Table 1.

[0112] Table 1 Optimal Hyperparameter Combinations

[0113] First mapping relationship model Second mapping relationship model Optimal number of hidden layers 3 3 Optimal number of neurons [147,335,94] [101,299,74] Optimal NMSE 0.21248 0.01589

[0114] In step S6, the first mapping relationship model and the second mapping relationship model are trained, validated, and tested based on the first feature sample set, the second feature sample set, and the third feature sample set to obtain the final first mapping relationship model and the second mapping relationship model.

[0115] In some embodiments, in step S6, a method of dynamically adjusting the learning rate is used to train the first mapping relationship model and the second mapping relationship model. In the early stage, a larger learning rate is used to quickly approach the optimal solution region, and in the later stage, the learning rate is reduced to allow the model to converge more finely.

[0116]

[0117] Where, η t η is the learning rate for the current step, η0 is the initial learning rate (set to 0.01), α is the decay factor (set to 0.9), and T is the decay period (set to 500). This is the floor function.

[0118] Specifically, the first, second, and third feature sample sets are randomly divided into training, validation, and test sets in an 8:1:1 ratio. Using the hyperparameter combinations in Table 1, the training set is used to train the first and second mapping relationship models; the validation set is used to detect the generalization ability of the neural network and adjust individual hyperparameters in the Adam optimizer; and the test set is used to detect the final prediction effect. In evaluating the final prediction effect, this embodiment does not use the NMSE defined in the above formula because NMSE is calculated using normalized values. While this is beneficial for optimizing the neural network to find the optimal hyperparameters, it is not intuitive enough for reflecting the deviation between the true and predicted values ​​in actual dimensions. Therefore, this embodiment uses the mean absolute percentage error (MAPE) and the coefficient of determination (R²) of the inversely normalized true and predicted values ​​(initial dimensions). 2 Evaluate the final prediction results:

[0119]

[0120] Where N is the total number of samples, y i Let i be the true value vector of the i-th sample. Let be the predicted value vector for the i-th sample. It is a vector consisting of the average of the true values ​​of the corresponding elements of all samples.

[0121] In this embodiment, the Latin hypercube sampling method was used to extract 400 and 20,000 samples from the sample set to train the first and second mapping relationship models, respectively. The difference in sample set size stems from the cost of data generation: nanoindentation simulation is computationally expensive, so the sample size is smaller (400), focusing on covering the diversity of parameter space; uniaxial tensile simulation is highly efficient, so the sample size is larger (20,000), ensuring that the neural network can fully learn the complex mapping between constitutive parameters and stress-strain curves.

[0122] For the first mapping relationship model, to avoid the randomness of sample partitioning leading to insufficient representativeness of the results of a single cross-validation, the results of five cross-validations are combined and then applied to E,σ. y Calculate R 2 The result is as follows Figure 4 As shown, the R values ​​of both 2 All are above 0.97, indicating that MLP1 is effective for E,σ y All of them have good prediction accuracy.

[0123] The rheological stress values ​​at 10 specific plastic strain points for each cross-validation The results of the MAPE calculation are shown in Table 2:

[0124] Table 2. MAPE results of rheological stress in 5 cross-validations

[0125] Number of calculations 1 2 3 4 5 average value MAPE 5.37％ 4.23％ 4.74％ 5.23％ 4.42％ 4.80％

[0126] Five predicted stress-strain curves were randomly selected from the results of a cross-validation study and compared with their corresponding actual curves to determine the rheological stress. The deviation, the result is as follows Figure 5 As shown, the predicted and actual values ​​of rheological stress in the plastic segment have relatively small errors, indicating that the established neural network first mapping model can extract material information from the nanoindentation curve and predict the corresponding stress-strain curve. The first mapping model, in addition to considering Young's modulus E and yield stress σ, also supports these parameters. y It has high prediction accuracy and can also capture the rheological stress in the plastic segment of the material. The trend of change is observed, and the mean absolute percentage error (MAPE) within the finite strain does not exceed 5%. Even so, it can be observed that the deviation between the predicted and true values ​​of the latter half of the black curve sample is significantly greater than that of other samples. This may be because the samples in the range of values ​​near the crystal plastic constitutive parameter combination corresponding to the stress-strain curve of this sample are relatively sparse. The Latin hypercube sampling method used does not result in a completely uniform distribution of samples under constrained conditions. The first mapping relationship model does not fully capture the correspondence between the nanoindentation curve and the stress-strain curve of this type of sample. This error can be reduced by increasing the number of samples. Since the input of the second mapping relationship model is a reduced-order curve feature (such as E, σ), y ), while such features have lower errors (R). 2 With a value greater than 0.97, the prediction error will not be significantly amplified to the constitutive parameter prediction, thus ensuring the overall reliability of the model.

[0127] For the second mapping model, the number of samples is already large enough to eliminate the difference in sample representativeness caused by the randomness of cross-validation; therefore, only the results of a single cross-validation are shown. The elasticity constant R is calculated. 2 The results are as follows Figure 6 As shown, three elastic constants c can be observed. 11 ,c 12 ,c 44 R 2 The similar levels, all above 0.99, indicate that MLP2 has high prediction accuracy for the elastic component, which is expected, because a set of elastic constants c can be uniquely determined from the accurate input values ​​of ν and A, as well as the Young's modulus E of the stress-strain curve. 11 ,c 12 ,c 44 This mapping relationship can be easily captured by neural networks.

[0128] Calculate R for the remaining crystal plastic constitutive parameters 2 like Figure 7 As shown, τ0,τ s R 2 All are above 0.99, greater than h0 and h s The prediction accuracy, h s With the lowest R 2 The value is 0.8714.

[0129] In step S7, nanoindentation data of the crystal to be tested is obtained, and the crystal plastic constitutive parameters of the crystal to be tested are predicted using the final first mapping relationship model and the second mapping relationship model.

[0130] Specifically, this embodiment uses the nanoindentation curves of an unknown material (the crystal under test) to predict the crystal's plastic constitutive parameters. This involves chaining together the aforementioned single-step prediction process, using the output of the first mapping model as the input of the second mapping model. Five sample nanoindentation curves are randomly selected from the sample set. After two-step neural network prediction, the predicted crystal plastic constitutive parameters are input into the nanoindentation simulation and compared with the original curves. Boundary conditions and other settings remain unchanged. The results are as follows. Figure 8 As shown, the predicted values ​​closely match the actual values, indicating that the cumulative error of the two-step prediction neural network established in this embodiment is small, and the corresponding crystal plasticity constitutive parameters can be predicted from the nanoindentation curve of the unknown material.

[0131] For unknown materials, it is impossible to know the exact values ​​of ν and A in advance. To quantitatively analyze the impact of the deviation between the assumed ν and A values ​​and the actual values ​​on the final inverted nanoindentation curve, a nanoindentation curve was selected from the sample set for prediction. Different levels of perturbation were applied to the accurate values ​​of ν and A as input, and the prediction was repeated. The curve that caused the largest prediction error among each level of perturbation was selected, thereby determining the error range of the nanoindentation curve corresponding to the inverted parameters. The results were plotted on [the graph]. Figure 9 The results show that applying error perturbations of 10% and 30% to ν and A, respectively, has a relatively small impact on the prediction accuracy, falling within an acceptable range. For the material to be predicted, empirical assumptions generally allow the values ​​of ν and A to be within a reasonable range, thus obtaining a set of relatively reasonable crystal plasticity constitutive parameters through two-step prediction.

[0132] Furthermore, this embodiment verifies the universality of the established first mapping relationship model neural network, specifically verifying whether the mapping relationship between the nanoindentation curve and the stress-strain curve remains unchanged when different crystal plastic constitutive models are used to characterize the deformation behavior of the same material. For this purpose, a self-hardening modulus h of the Peirce-Asaro constitutive model is adopted. αα The simplest form:

[0133]

[0134] At this point, the plastic constitutive parameters become h0,τ0,τ s That is, it reduced h s .

[0135] Next, a suitable set of parameters was selected (see Table 3) to ensure that the shape range of the stress-strain curve of the material it describes is within the training sample set. Nanoindentation curves and stress-strain curves were generated through simulation. The nanoindentation curves were then input into the first mapping model, and the predicted stress-strain curves were compared with the actual stress-strain curves. The results are as follows: Figure 10As shown, it can be observed that even if the form of the crystal plastic constitutive model changes, the mapping relationship between its nanoindentation curve and stress-strain curve still satisfies the mapping relationship of the first mapping relationship model. That is to say, for the same material, the mapping relationship between the curves generated by the nanoindentation process and the uniaxial tensile process is determined by their respective deformation behaviors. As a medium for characterizing crystal deformation, the crystal plastic constitutive model does not affect this mapping relationship when the deformation behaviors (such as slip systems and rate-dependent properties) are consistent, even if the form of the crystal plastic constitutive model is different. Cross-model validation shows that the prediction accuracy of the Peirce-Asaro constitutive model is comparable to that of the Voce model, confirming the universality of the mapping from nanoindentation curve to stress-strain curve and supporting the application of the framework in various structural scenarios.

[0136] Table 3 New combinations of crystal plastic constitutive parameters

[0137] <![CDATA[h0]]> <![CDATA[τ0]]> <![CDATA[τ s ]]> 600MPa 350MPa 300MPa

[0138] The second aspect of this embodiment proposes a single-crystal plastic constitutive parameter prediction system based on nanoindentation data, characterized in that the system comprises:

[0139] The data generation module is used to identify multiple crystal samples and generate a nanoindentation simulation dataset and a uniaxial tensile simulation dataset for each crystal sample using the crystal plasticity finite element method.

[0140] The first extraction module is used to establish a nanoindentation curve based on the nanoindentation simulation dataset, extract multiple first feature values ​​from the nanoindentation curve to form a first feature vector, and the first feature vectors of multiple crystal samples form a first feature sample set.

[0141] The second extraction module is used to establish a stress-strain curve based on the uniaxial tensile simulation dataset, extract multiple second feature values ​​from the stress-strain curve to form a second feature vector, and the second feature vectors of multiple crystal samples form a second feature sample set.

[0142] The third extraction module is used to extract multiple third eigenvalues ​​of each crystal sample from the known crystal plastic constitutive model to form a third eigenvector, and the third eigenvectors of multiple crystal samples form a third eigensample set;

[0143] The model building module is used to establish a first mapping relationship model and a second mapping relationship model using a multilayer perceptron; the input values ​​of the first mapping relationship model are a first feature value, Poisson's ratio and anisotropy coefficient, and the output value is a second feature value; the input values ​​of the second mapping relationship model are a second feature value, Poisson's ratio and anisotropy coefficient, and the output value is a third feature value.

[0144] The model training module is used to train, validate, and test the first mapping relationship model and the second mapping relationship model based on the first feature sample set, the second feature sample set, and the third feature sample set, so as to obtain the final first mapping relationship model and the second mapping relationship model.

[0145] The prediction module is used to acquire nanoindentation data of the crystal under test and to predict the crystal plastic constitutive parameters of the crystal under test using the final first mapping relationship model and the second mapping relationship model.

[0146] In some embodiments, the first feature value includes: load values ​​at different depths, the slope of the loading segment curve at different depths, the initial unloading stiffness, and the proportion of plastic work.

[0147] The second characteristic value includes: elastic modulus, yield stress, and rheological stress at different plastic strains;

[0148] The third characteristic value includes: elastic stiffness along the x-axis direction of the lattice (i.e., the

[100] direction), elastic stiffness along the diagonal direction (i.e., the

[110] direction), shear stiffness along the y-axis direction of the lattice (i.e., the

[001] direction), initial slip hardening modulus, initial critical shear stress, saturated flow stress, and saturated hardening modulus.

[0149] In summary, the solution proposed in this invention has the following technical effects:

[0150] This invention constructs a staged hierarchical neural network prediction framework driven by single-crystal nanoindentation data, which realizes efficient and accurate prediction of crystal plastic constitutive parameters. Specifically, it uses crystal plasticity finite element method to generate simulation dataset, and uses multilayer perceptron (MLP) neural network to realize hierarchical mapping of nanoindentation curve → stress-strain curve → constitutive parameters.

[0151] Furthermore, the mapping model between the nanoindentation curve and the stress-strain curve constructed in this invention, namely the first mapping relationship model, predicts the coefficient of determination R of the stress-strain curve. 2 >0.97, the mean absolute percentage error (MAPE) of the rheological stress in the plastic segment is only 4.80%; when inverting constitutive parameters using the mapping model of stress-strain curve → constitutive parameters, i.e., the second mapping relationship model, the initial critical shear stress τ0 and saturated flow stress τ s Prediction of key parameters R 2 The value >0.99 verifies the high precision of the two mapping relationship models.

[0152] Furthermore, the first mapping relationship model constructed in this invention is not limited by the mathematical form of the constitutive model. When the form of the crystal plastic constitutive model changes, the degree of agreement between the stress-strain curve predicted by the first mapping relationship model and the set value curve remains at R. 2>0.95, which solves the problem of traditional methods' dependence on specific models.

[0153] Furthermore, this invention combines explicit dynamic crystal plasticity finite element (CPFE) simulation with a simplified uniaxial tensile model, significantly reducing the simulation time for a single nanoindentation from 10 hours using an implicit algorithm to 30 minutes. The trained neural network predicts the entire process in just 5 seconds, which is significantly more efficient than traditional optimization methods and provides an engineering solution for high-throughput constitutive parameter identification of multiphase materials.

[0154] Furthermore, the indentation curve reconstructed from constitutive parameters derived from experimental nanoindentation data in this invention, and the R value of the measured value, are compared with those of the actual curve. 2 The method can still guarantee prediction reliability when the value reaches above 0.99 and the assumed value of the elastic parameter is within ±30% error range, which confirms the practical value of the method in the local mechanical characterization of non-homogeneous materials such as welded joints.

[0155] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for predicting the plastic constitutive parameters of a single crystal based on nanoindentation data, characterized in that, The method includes: Step S1: Determine multiple crystal samples and use crystal plasticity finite element method to generate nanoindentation simulation dataset and uniaxial tensile simulation dataset for each crystal sample; Step S2: Establish a nanoindentation curve based on the nanoindentation simulation dataset, extract multiple first feature values ​​from the nanoindentation curve to form a first feature vector, and form a first feature sample set from the first feature vectors of multiple crystal samples. Step S3: Establish a stress-strain curve based on the uniaxial tensile simulation dataset, extract multiple second feature values ​​from the stress-strain curve to form a second feature vector, and form a second feature sample set from the second feature vectors of multiple crystal samples. Step S4: Extract multiple third eigenvalues ​​from the known crystal plastic constitutive model to form a third eigenvector for each crystal sample; the third eigenvectors of multiple crystal samples form a third eigensample set. Step S5: Establish a first mapping relationship model and a second mapping relationship model using a multilayer perceptron; the input values ​​of the first mapping relationship model are the first feature value, Poisson's ratio and anisotropy coefficient, and the output value is the second feature value; the input values ​​of the second mapping relationship model are the second feature value, Poisson's ratio and anisotropy coefficient, and the output value is the third feature value. Step S6: Train, validate, and test the first mapping relationship model and the second mapping relationship model based on the first feature sample set, the second feature sample set, and the third feature sample set to obtain the final first mapping relationship model and the second mapping relationship model. Step S7: Obtain nanoindentation data of the crystal to be tested, and use the final first mapping relationship model and second mapping relationship model to predict the crystal plastic constitutive parameters of the crystal to be tested.

2. The method according to claim 1, characterized in that, In step S2, the first feature value includes: load values ​​at different depths, slope of the loading segment curve at different depths, initial unloading stiffness, and plastic work ratio.

3. The method according to claim 1, characterized in that, In step S3, the second characteristic value includes: elastic modulus, yield stress, and rheological stress at different plastic strains.

4. The method according to claim 1, characterized in that, In step S4, the third characteristic value includes: elastic stiffness along the x-axis of the lattice, elastic stiffness along the diagonal direction, shear stiffness along the y-axis of the lattice, initial slip hardening modulus, initial critical shear stress, saturated flow stress, and saturated hardening modulus.

5. The method according to claim 1, characterized in that, The method further includes: before step S5, normalizing the first feature value, the second feature value, and the third feature value respectively.

6. The method according to claim 1, characterized in that, The method further includes: between steps S5 and S6, performing Bayesian hyperparameter optimization on the first mapping relationship model and the second mapping relationship model respectively.

7. The method according to claim 1, characterized in that, In step S6, the first mapping relationship model and the second mapping relationship model are trained by dynamically adjusting the learning rate.

8. The method according to claim 1, characterized in that, In step S1, when generating the nanoindentation simulation dataset for each crystal sample using the crystal plastic finite element method, an explicit dynamic solution algorithm combined with a semi-automatic mass scaling method is used to perform nanoindentation simulation for each crystal sample. When generating a uniaxial tensile simulation dataset for each crystal sample using the crystal plastic finite element method, the uniaxial tensile process of a single crystal is simplified to the uniaxial tensile process of a single element. The solution-related state variables of the single element are directly solved and the stress state is updated.

9. A single-crystal plastic constitutive parameter prediction system based on nanoindentation data, characterized in that, The system includes: The data generation module is used to identify multiple crystal samples and generate a nanoindentation simulation dataset and a uniaxial tensile simulation dataset for each crystal sample using the crystal plasticity finite element method. The first extraction module is used to establish a nanoindentation curve based on the nanoindentation simulation dataset, extract multiple first feature values ​​from the nanoindentation curve to form a first feature vector, and the first feature vectors of multiple crystal samples form a first feature sample set. The second extraction module is used to establish a stress-strain curve based on the uniaxial tensile simulation dataset, extract multiple second feature values ​​from the stress-strain curve to form a second feature vector, and the second feature vectors of multiple crystal samples form a second feature sample set. The third extraction module is used to extract multiple third eigenvalues ​​of each crystal sample from the known crystal plastic constitutive model to form a third eigenvector, and the third eigenvectors of multiple crystal samples form a third eigensample set; The model building module is used to establish a first mapping relationship model and a second mapping relationship model using a multilayer perceptron; the input values ​​of the first mapping relationship model are a first feature value, Poisson's ratio and anisotropy coefficient, and the output value is a second feature value; the input values ​​of the second mapping relationship model are a second feature value, Poisson's ratio and anisotropy coefficient, and the output value is a third feature value. The model training module is used to train, validate, and test the first mapping relationship model and the second mapping relationship model based on the first feature sample set, the second feature sample set, and the third feature sample set, so as to obtain the final first mapping relationship model and the second mapping relationship model. The prediction module is used to acquire nanoindentation data of the crystal under test and to predict the crystal plastic constitutive parameters of the crystal under test using the final first mapping relationship model and the second mapping relationship model.

10. The system according to claim 9, characterized in that, The first characteristic value includes: load values ​​at different depths, slope of the loading segment curve at different depths, initial unloading stiffness, and plastic work ratio; The second characteristic value includes: elastic modulus, yield stress, and rheological stress at different plastic strains; The third characteristic value includes: elastic stiffness along the x-axis of the lattice, elastic stiffness along the diagonal, shear stiffness along the y-axis of the lattice, initial slip hardening modulus, initial critical shear stress, saturated flow stress, and saturated hardening modulus.

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