Methods, systems, devices, media, and program product for inversion of material constitutive parameters

Abstract

The application provides a material constitutive parameter inversion method, which can be applied to the field of artificial intelligence technology. The material constitutive parameter inversion method comprises the following steps: obtaining the elastic modulus and the measured load-depth curve of the material to be measured in a single nanoindentation test; performing extrapolation translation preprocessing on the measured load-depth curve to obtain an equivalent ideal curve; performing characteristic processing on the equivalent ideal curve to extract input characteristic parameters, wherein the input characteristic parameters comprise indentation stiffness, unloading stiffness and plastic work ratio; and inputting the indentation stiffness, unloading stiffness, plastic work ratio and elastic modulus into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material to be measured, wherein the indentation constitutive mapping model is a fully connected back propagation neural network pre-trained by a finite element virtual test sample. The application also provides a material constitutive parameter inversion system, device, storage medium and program product.

Description

Technical Field

[0001] This application relates to the field of artificial intelligence technology, specifically to the field of material mechanical property characterization technology, and more specifically to a method, system, device, medium, and program product for inverting material constitutive parameters. Background Technology

[0002] Nanoindentation can obtain the elastic modulus and hardness of a material in a single measurement at the micrometer scale, but it cannot directly provide the yield strength and hardening index. In related technologies, the inversion methods for plastic constitutive parameters from nanoindentation testing typically require multiple indenters, multiple tests, or finite element-optimized iterations. Dual-indenter testing or multiple-test inversion processes are complex and time-consuming, and cannot handle cases where samples are not repeatable. Inversion calculations rely on iterative finite element simulations, which are inefficient for testing requirements. Single-test inversion accuracy is low, and non-ideal test curves can have unpredictable impacts on accuracy. Therefore, a new method is urgently needed that can rapidly and accurately extract power-law constitutive parameters using only a single nanoindentation measurement. Summary of the Invention

[0003] In view of the above problems, this application provides a method, system, device, medium and program product for inverting material constitutive parameters.

[0004] According to a first aspect of this application, a method for inverting material constitutive parameters is provided, comprising: acquiring the elastic modulus and measured load depth curve of the material under test in a single nanoindentation test; performing extrapolation and translation preprocessing on the measured load depth curve to obtain an equivalent ideal curve; performing feature processing on the equivalent ideal curve to extract input feature parameters, the input feature parameters including indentation stiffness, unloading stiffness, and plastic work ratio; inputting the indentation stiffness, the unloading stiffness, the plastic work ratio, and the elastic modulus into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material under test, wherein the indentation constitutive mapping model is a fully connected backpropagation neural network pre-trained with finite element virtual test samples.

[0005] According to an embodiment of this application, the preprocessing of extrapolating and translating the measured load depth curve to obtain an equivalent ideal curve includes: selecting data points in the range of 50% to 100% of the maximum load in the measured load depth curve, performing quadratic polynomial fitting to obtain the indentation segment fitting function; extending the indentation segment fitting function to the measured maximum depth and reading the corresponding load value as the extrapolated maximum load; and translating the unloading segment curve upward along the load axis so that the load value at the unloading starting point is equal to the extrapolated maximum load, thereby constructing an equivalent ideal curve, wherein the translation amount is the difference between the extrapolated maximum load and the measured maximum load.

[0006] According to an embodiment of this application, the step of characterizing the equivalent ideal curve to extract input feature parameters includes: extracting the quadratic coefficient of the fitting function of the indentation segment as the indentation stiffness; fitting a power function to the unloading segment of the equivalent ideal curve, and using the derivative of the power function at the maximum depth as the unloading stiffness; integrating the fitting function of the indentation segment from the initial depth to the maximum depth to obtain the total work, integrating the fitting function of the unloading segment from the residual depth of the unloading segment to the maximum depth to obtain the rebound work, and dividing the difference between the total work and the rebound work by the total work, with the resulting quotient being used as the proportion of plastic work.

[0007] According to an embodiment of this application, the pre-training of the indentation constitutive mapping model includes: establishing a diamond Glasst indenter nanoindentation simulation model in finite element software, with the material constitutive model selected as power-law hardening; obtaining a finite element virtual test training sample set; and training a fully connected backpropagation neural network based on the finite element virtual test training sample set to obtain the indentation constitutive mapping model.

[0008] According to an embodiment of this application, obtaining the finite element virtual test training sample set includes: equidistantly sampling levels within the respective value ranges of four factors—elastic modulus, yield strength, strain hardening exponent, and maximum indentation depth—to complete the full combination of the four factors and form multiple sets of virtual test conditions; simulating each set of virtual test conditions to extract indentation stiffness, unloading stiffness, and plastic work ratio; and using the indentation stiffness, unloading stiffness, plastic work ratio, and elastic modulus as input samples, and using the corresponding yield strength and hardening exponent as output labels to generate the finite element virtual test training sample set.

[0009] According to an embodiment of this application, training a fully connected backpropagation neural network based on the finite element virtual test training sample set to obtain an indentation constitutive mapping model includes: inputting the finite element virtual test training sample set into the neural network to obtain power-law constitutive prediction parameters, the power-law constitutive prediction parameters including a predicted yield strength value and a predicted strain hardening exponent value; determining a target loss based on the predicted yield strength value, the predicted strain hardening exponent value, and the output label; and training a fully connected backpropagation network based on the target loss to obtain the indentation constitutive mapping model.

[0010] A second aspect of this application provides an inversion system for material constitutive parameters, comprising: an acquisition module for acquiring the elastic modulus and measured load-depth curve of the material under test in a single nanoindentation test; a preprocessing module for performing extrapolation and translation preprocessing on the measured load-depth curve to obtain an equivalent ideal curve; a parameter extraction module for performing feature processing on the equivalent ideal curve to extract input feature parameters, the input feature parameters including indentation stiffness, unloading stiffness, and plastic work ratio; and a prediction module for inputting the indentation stiffness, the unloading stiffness, the plastic work ratio, and the elastic modulus into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material under test, wherein the indentation constitutive mapping model is a fully connected backpropagation neural network pre-trained with finite element virtual test samples.

[0011] A third aspect of this application provides an electronic device comprising: one or more processors; and a memory for storing one or more computer programs, wherein the one or more processors execute the one or more computer programs to implement the steps of the method described above.

[0012] A fourth aspect of this application also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0013] The fifth aspect of this application also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the steps of the above-described method. Attached Figure Description

[0014] The above-mentioned contents, other objects, features and advantages of this application will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0015] Figure 1 A flowchart illustrating a method for inverting material constitutive parameters according to an embodiment of this application is shown;

[0016] Figure 2 A flowchart of a method for training an indentation constitutive mapping model according to an embodiment of this application is shown;

[0017] Figure 3 A schematic diagram of a fully connected backpropagation neural network according to an embodiment of this application is shown;

[0018] Figure 4 A schematic diagram of a virtual test load depth curve according to an embodiment of this application is shown;

[0019] Figure 5 A schematic diagram illustrating the prediction bias of the validation dataset according to an embodiment of this application is shown;

[0020] Figure 6 A flowchart of a method for characterizing the equivalent ideal curve to extract input feature parameters according to an embodiment of this application is shown;

[0021] Figure 7A A schematic diagram illustrating the extraction of parameters for indentation stiffness according to an embodiment of this application is shown;

[0022] Figure 7B A schematic diagram illustrating parameter extraction of unloading stiffness according to an embodiment of this application is shown;

[0023] Figure 7C A schematic diagram illustrating the extraction of parameters for the plastic work ratio according to an embodiment of this application is shown;

[0024] Figure 8 A structural block diagram of an inversion system for material constitutive parameters according to an embodiment of this application is shown;

[0025] Figure 9 A block diagram of an electronic device suitable for implementing a method for inverting material constitutive parameters according to an embodiment of this application is shown. Detailed Implementation

[0026] The embodiments of this application will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this application. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of this application for ease of explanation. However, it will be apparent that one or more embodiments may be implemented without these specific details. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0027] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0028] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0029] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0030] In related technologies, the shortcomings of the plastic constitutive parameter inversion method for nanoindentation testing mainly include: the inversion process of dual-indenter testing or multiple tests is complex and time-consuming, and it cannot handle the situation where the sample is not repeatable; the inversion calculation relies on finite element simulation iterative calculation, and the efficiency cannot meet the testing requirements; the inversion accuracy of a single test is low, and non-ideal test curves have an unpredictable impact on the test accuracy.

[0031] Based on the above-mentioned technical problems, embodiments of this application provide a method for inverting material constitutive parameters. The method includes: acquiring the elastic modulus and measured load depth curve of the material under test in a single nanoindentation test; performing extrapolation and translation preprocessing on the measured load depth curve to obtain an equivalent ideal curve; performing feature processing on the equivalent ideal curve to extract input feature parameters, the input feature parameters including indentation stiffness, unloading stiffness, and plastic work ratio; inputting the indentation stiffness, the unloading stiffness, the plastic work ratio, and the elastic modulus into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material under test, wherein the indentation constitutive mapping model is a fully connected backpropagation neural network pre-trained with finite element virtual test samples.

[0032] Figure 1 A flowchart is shown for a method of inverting material constitutive parameters according to an embodiment of this application.

[0033] like Figure 1 As shown, the inversion method for material constitutive parameters in this embodiment includes operations S110 to S140, which can be executed by a server or other computing device.

[0034] In operation S110, the elastic modulus and measured load depth curve of the material under test in a single nanoindentation test are obtained.

[0035] In operation S120, the measured load depth curve is preprocessed by extrapolation and translation to obtain an equivalent ideal curve.

[0036] According to an embodiment of this application, the extrapolation and translation preprocessing of the measured load depth curve to obtain an equivalent ideal curve includes: selecting data points in the range of 50% to 100% of the maximum load in the measured load depth curve, performing quadratic polynomial fitting to obtain the indentation segment fitting function; extending the indentation segment fitting function to the measured maximum depth and reading the corresponding load value as the extrapolated maximum load; and translating the unloading segment curve upward along the load axis so that the load value at the unloading starting point is equal to the extrapolated maximum load, thereby constructing an equivalent ideal curve, wherein the translation amount is the difference between the extrapolated maximum load and the measured maximum load.

[0037] In one example, a constant maximum indentation force is used. A quasi-static loading method was used to perform nanoindentation tests on the test material, obtaining the elastic modulus E of the material and recording the measured load-depth curve (Ph curve). The indentation depth at which the maximum indentation force is reached in the measured load-depth curve is [value missing]. At the end of the maximum indentation force holding time, material creep causes the indentation depth to increase further. Set an appropriate size during the test. This makes the measured Ph curve and In virtual experiment Within the specified range, the diamond indenter used in the test was identical in size and material to the simulation model of the nanoindentation virtual experiment using the Finite Element Method (FEM). Because the measured load-depth curve experiences a slight dip during the maximum load holding phase after a single indentation due to material creep, and the blunt indenter tip causes nonlinearity in the initial loading stage, to eliminate the non-ideal deviations introduced by the blunt indenter tip, material creep, and surface roughness, data points in the 50%~100% range of the maximum load were selected and subjected to quadratic polynomial fitting to obtain the fitting function for the indentation segment. This function was extended to the measured maximum depth, and the corresponding load was read as the extrapolated maximum load. The entire unloading segment was shifted upwards along the load axis so that the unloading starting point coincided with the extrapolated maximum load; the shift amount was the difference between the extrapolated value and the measured value. After these three steps, the distortion at the head of the original curve and the creep dip were eliminated, forming an equivalent ideal curve for subsequent feature extraction. The entire preprocessing was completed automatically within the testing software, requiring no additional hardware.

[0038] In operation S130, the equivalent ideal curve is characterized to extract input feature parameters.

[0039] According to embodiments of this application, the input characteristic parameters include indentation stiffness, unloading stiffness, and plastic work ratio.

[0040] In operation S140, the indentation stiffness, the unloading stiffness, the plastic work ratio, and the elastic modulus are input into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material under test.

[0041] According to an embodiment of this application, the indentation constitutive mapping model is a fully connected backpropagation neural network pre-trained with finite element virtual test samples.

[0042] In one example, a constant maximum load is applied to the test area, and the instrument simultaneously records the load-depth curve and directly provides the elastic modulus of the test point. Data within the 50%–100% range of the maximum load in the curve are selected, and a quadratic polynomial fitting is performed to extrapolate the maximum load corresponding to the maximum depth. Then, the unloading section is shifted upwards along the load axis so that the unloading starting point coincides with the extrapolated value, thereby eliminating non-ideal deviations caused by the blunt rounding of the indenter tip, material creep, and surface roughness, and constructing an equivalent ideal curve. Three physical features are extracted from the equivalent ideal curve: the quadratic coefficient of the fitting function of the indentation section is used as the indentation stiffness; the derivative of the power function of the unloading section at the maximum depth is used as the unloading stiffness; and the percentage of the difference between the total energy consumption of the indentation section and the rebound energy consumption of the unloading section is used as the plastic work percentage. These three features, along with the elastic modulus, are input into a pre-trained fully connected backpropagation neural network, which instantly outputs the yield strength and strain hardening index of the test point. The entire process, from loading to obtaining constitutive parameters, takes only a few seconds, without the need for additional indenters or repeated sampling, achieving second-level inversion of single indentation, and meeting the online inspection needs of microelectronic production lines.

[0043] Through a chain of steps—"single nanoindentation → extrapolation and translation preprocessing → three physical feature extraction → neural network mapping"—non-ideal deviations caused by blunt indenter tip, material creep, and surface roughness are eliminated in one step. The measured curve is transformed into a reusable equivalent ideal curve, exhibiting high tolerance for "non-ideal" test data caused by factors such as material surface roughness and material creep, resulting in good consistency of inversion results. Furthermore, the elastoplastic behavior of the material is fully characterized by three physical quantities: indentation stiffness, unloading stiffness, and the proportion of plastic work. Inputting these quantities into a fully connected backpropagation network trained with wide-domain virtual samples directly outputs the yield strength and strain hardening exponent. This achieves "one-time indentation, second-level inversion, and engineering accuracy," eliminating the need for multiple indenters or finite element iterations, significantly improving testing efficiency and result consistency.

[0044] The following is through Figures 2-5 The training process of the indentation constitutive mapping model in the embodiments of this application is described.

[0045] Figure 2 A flowchart of a method for training an indentation constitutive mapping model according to an embodiment of this application is shown; Figure 3A schematic diagram of a fully connected backpropagation neural network according to an embodiment of this application is shown; Figure 4 A schematic diagram of a virtual test load depth curve according to an embodiment of this application is shown; Figure 5 A schematic diagram illustrating the prediction bias of the validation dataset according to an embodiment of this application is shown.

[0046] like Figure 2 As shown, this includes operations S210 to S230.

[0047] In the S210 operation, a simulation model of diamond Glass indenter nanoindentation was established in the finite element software, and the material constitutive model was selected as power-law hardening.

[0048] During operation of S220, a finite element virtual experiment training sample set is obtained.

[0049] According to an embodiment of this application, obtaining a finite element virtual test training sample set includes: equidistantly sampling levels within the respective value ranges of four factors—elastic modulus, yield strength, strain hardening exponent, and maximum indentation depth—to complete a full combination of the four factors and form multiple sets of virtual test conditions; simulating each set of virtual test conditions to extract indentation stiffness, unloading stiffness, and plastic work ratio; and using the indentation stiffness, unloading stiffness, plastic work ratio, and elastic modulus as input samples, and using the corresponding yield strength and hardening exponent as output labels to generate a finite element virtual test training sample set.

[0050] In one example, a numerical mapping model architecture for nanoindentation feature parameters and material constitutive parameters is constructed. The artificial neural network uses a fully connected backpropagation neural network, such as... Figure 3 As shown, the input layer contains characteristic parameters of the nanoindentation test load-depth curve. The output layer includes the elastic modulus E of the tested material, and the yield strength of the tested material. The hardening exponent n. The fully connected backpropagation network in this embodiment contains 3 hidden layers, each containing 10 neurons. The neurons in each layer are connected in the form of... The activation function is connected. Parameter C is the nanometer test indentation stiffness, defined as the fitting function of the indentation segment of the Ph curve. The parameters are: P is the indentation force, h is the indentation depth; and S is the unloading stiffness, defined as the fitting function of the unloading segment of the Ph curve. At maximum indentation depth slope at ,in The residual depth of the ideal curve represents the remaining indentation depth of the indentation surface relative to the initial surface after the indenter is completely unloaded. Coefficients related to material properties are used to characterize the stiffness characteristics of a material during unloading. The material hardening index describes the relationship between load and depth during material unloading and is an indicator of the plastic deformation characteristics of materials. The proportion of plastic work is defined as the compressive work. in The total work done is equal to the area under the indentation segment of the Ph curve. The unloading work is equal to the area under the unloading segment of the Ph curve.

[0051] In one example, a virtual nanoindentation test was conducted using finite element method simulation to obtain a large amount of high-precision data for training a fully connected backpropagation network and to submit the model for training. Specifically, a simulation model of the nanoindentation test process was established using finite element method simulation software. The indenter in the simulation model is a diamond tetrahedral Bollard indenter, the shape of which is consistent with the test equipment. In this embodiment, the angle between the cone surface and the axis of the cone is 65.3°. A 2D axisymmetric indenter model with the same projected area (cone angle 70.32°) is used instead to speed up the simulation. The material under test in the simulation model is set as a power-law hardening constitutive model. The stress-strain equation of this constitutive model is formula (1):

[0052] (1)

[0053] in These represent strain and the plastic portion of strain, respectively.

[0054] Finite element method simulation virtual experiment includes Four experimental variable factors, among which As a variable factor for the experiment, 5 to 15 uniformly distributed levels are determined based on the possible value range of the material being tested; For the virtual experiment's variable factors, 5 to 15 levels are determined based on the possible indentation depth range of actual nanoindentation tests. This embodiment addresses the testing needs of common metals such as gold, silver, copper, aluminum, and iron, setting the levels of each variable factor as follows:

[0055] Elastic modulus E (unit GPa, 9 levels): 60, 80, 100, 120, 140, 160, 180, 200, 220.

[0056] Yield strength (Unit: MPa, 10 levels): 40, 60, 80, 100, 120, 140, 160, 180, 200, 220.

[0057] Strain hardening index n (7 levels): 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6.

[0058] Maximum indentation depth (Unit: nm, 5 levels): 300, 400, 500, 600, 700.

[0059] The total number of combinations of the above four variable factor levels is 9×10×7×5=3150.

[0060] Nanoindentation virtual experiments were conducted using each of the 3150 variable factor level combinations mentioned above, and load-depth curves were extracted from the virtual experiment simulation results, such as... Figure 4 As shown in (a), the curve of the indentation force P as a function of the indentation depth h is shown during the indentation and unloading process of the material under test in nanoindentation testing.

[0061] In one example, since the load depth curve obtained by simulation is in good agreement with the theoretical value and is close to the "ideal" curve, function fitting is performed on the pressing section and the unloading section respectively, and the fitting function is shown in formula (2).

[0062] (2)

[0063] The parameter C of the fitting function for the indentation section represents the nanometer-scale indentation stiffness; the unloading section is at the maximum indentation depth. slope at The obtained S is the unloading stiffness.

[0064] Further calculation of the proportion of plastic work . The total indentation work is equal to the area under the indentation section of the load depth curve, from which... Figure 4 As shown in (b), for and The sum of the areas of the two regions; The unloading work is equal to the area under the unloading segment of the load depth curve, i.e. Figure 4 Area in (b) .calculate The plastic work ratio was obtained; a set of characteristic parameters of the nanoindentation test curves were obtained from each load depth curve. Finally, 3150 sets of variable factors were obtained. The corresponding 3150 sets of feature parameters .

[0065] In operation S230, a fully connected backpropagation neural network is trained based on the finite element virtual test training sample set to obtain the indentation constitutive mapping model.

[0066] According to an embodiment of this application, the finite element virtual test training sample set is input into a neural network to obtain power-law constitutive prediction parameters, the power-law constitutive prediction parameters including predicted yield strength and predicted strain hardening exponent; a target loss is determined based on the predicted yield strength, the predicted strain hardening exponent, and the output label; and a fully connected backpropagation network is trained based on the target loss to obtain the indentation constitutive mapping model.

[0067] In one example, the 3150 sets of data obtained above are used. The constructed artificial neural network regression model was trained to obtain a numerical mapping model between nanoindentation feature parameters and material constitutive parameters. It should be noted that... These are not input / output parameters of the model and therefore are not included in the model's training. By adjusting the model's hyperparameters and performing iterative updates over approximately 3000 epochs, the average loss on the validation set stabilized below 0.001, achieving good convergence. Figure 5 As shown in (a) and (b), the trained model has been validated on the test set and has captured the nonlinear relationship between the input and output parameters well, and has good prediction accuracy. The relative error is less than ±5%, and the absolute error of n is less than ±0.02.

[0068] The following is combined Figure 6 , Figures 7A-7C The feature processing of the preprocessed actual test data is described in detail. Figure 6 A flowchart is shown of a method for characterizing the equivalent ideal curve to extract input feature parameters according to an embodiment of this application. Figure 7A A schematic diagram of parameter extraction for indentation stiffness according to an embodiment of this application is shown. Figure 7B A schematic diagram of parameter extraction for unloading stiffness according to an embodiment of this application is shown. Figure 7C A schematic diagram illustrating the extraction of parameters for the plastic work ratio according to an embodiment of this application is shown.

[0069] like Figure 6 As shown, this includes operations S310 to S330.

[0070] In operation S310, the quadratic coefficients of the fitting function of the indentation segment are extracted as the indentation stiffness.

[0071] In one example, this embodiment demonstrates a single nanoindentation test on electroplated copper material. The diamond indenter used in the test is identical in size and material to the virtual nanoindentation test FEM simulation model, specifically a diamond tetrahedral Beaucher indenter with a cone-shaped angle of 65.3° between the cone surface and the axis of the cone. A constant maximum indentation force is employed. The quasi-static loading method was used to perform nanoindentation testing on the test material. The instrument directly provided the elastic modulus of the test material (electroplated copper) as E=122.8GPa, and simultaneously recorded the measured load-depth curve as shown in the figure. Figure 7A As shown in (a).

[0072] In one example, the least squares method is used to press the upper half of the Ph curve. Curve fitting yields function (3), where C, The fitting parameters are C, which are the extracted measured feature parameters C.

[0073] (3)

[0074] like Figure 7A As shown in the attached figure, reference numeral 501 represents the upper half of the measured Ph curve indentation segment; reference numeral 502 represents the Ph curve segment with the maximum indentation force held for the duration of the maximum indentation force; and reference numeral 503 represents the fitted curve of the measured indentation segment. The least squares method was used to analyze the upper half of the Ph curve indentation segment. The function obtained by fitting curve 501 ,Right now Figure 7A Curve 503 in (b) therefore the measured characteristic parameters .

[0075] In operation S320, a power function is fitted to the unloading segment of the equivalent ideal curve, and the derivative of the power function at the maximum depth is used as the unloading stiffness.

[0076] In one example, the extrapolated maximum indentation force is calculated based on function (3). The initial part of the unloading segment of the measured Ph curve. The entire object is translated along the positive direction of the P-axis by a distance. Then, starting from the initial part of the unloading segment of the measured Ph curve after translation, the least squares method is used to fit the function (4), where For the fitting parameters. Calculate function (4) in Derivative of a point The derivative S is the extracted measured feature parameter S.

[0077] (4)

[0078] Figure 7B In the attached figure, reference numeral 601 represents the initial portion of the unloading segment of the measured Ph curve; reference numeral 602 represents the distance 601 is translated along the positive P-axis. The subsequent curves; Figure 603 shows the fitted curve for the measured unloading section. Based on the function... The extrapolated maximum indentation force was calculated. Then, the initial part of the unloading segment of the measured Ph curve was... ,Right now Figure 7B (As shown by reference numeral 601 in the attached diagram), the entire structure is translated a distance along the positive direction of the P-axis. ,See Figure 7B (b). Then, from the initial part of the unloading segment of the translated measured Ph curve (shown as reference numeral 602 in the attached figure), the function is obtained by least squares fitting. (As shown by reference numeral 603 in the attached diagram). For example... Figure 7B (d) This function is in Derivative of a point Therefore, the measured characteristic parameter S = 173.5.

[0079] During operation S330, the total work is obtained by integrating the fitting function of the indentation section from the initial depth to the maximum depth, and the springback work is obtained by integrating the fitting function of the unloading section from the residual depth of the unloading section to the maximum depth. The difference between the total work and the springback work is divided by the total work, and the quotient is used as the proportion of plastic work.

[0080] In one example, the fitted function (3) above is in Integrating over the interval yields the total work done. ; for the above fitting function (4) in Integrating over the interval yields the unloading work. Then, the measured characteristic parameters are calculated. .

[0081] In one example, the fitted function obtained in operation S310 exist Integrating over the interval (5.223, 416.2) yields the total work done. That is Figure 7C middle and The sum of the areas of the two regions; the fitted function obtained in operation S320. exist Integrating over the interval (361.2, 416.2) yields the unloading power. , Right now Figure 7C area Then, the measured characteristic parameters are calculated. .

[0082] Switch the trained artificial neural network regression model obtained from the above operations to prediction mode, and input the acquired test data. Model output That is, the plastic constitutive parameter of the material under test, yield strength. ) and hardening index (n). Through the above operations, the accurate plastic constitutive parameters of the material at the test point can be obtained by inversion using only a single nanoindentation test. By simply repeating the feature parameter extraction and prediction steps, the material plastic constitutive parameters of multiple test points can be tested quickly.

[0083] Based on the aforementioned method for inverting material constitutive parameters, this application also provides a system for inverting material constitutive parameters. The following will combine... Figure 8 The system is described in detail.

[0084] Figure 8 A structural block diagram of a material constitutive parameter inversion system according to an embodiment of this application is shown.

[0085] like Figure 8 As shown, the material constitutive parameter inversion system 800 of this embodiment includes an acquisition module 810, a preprocessing module 820, a parameter extraction module 830, and a prediction module 840.

[0086] The acquisition module 810 is used to acquire the elastic modulus and measured load-depth curve of the material under test in a single nanoindentation test. In one embodiment, the acquisition module 810 can be used to perform the operation S110 described above, which will not be repeated here.

[0087] The preprocessing module 820 is used to perform extrapolation and translation preprocessing on the measured load depth curve to obtain an equivalent ideal curve. In one embodiment, the preprocessing module 820 can be used to perform the operation S120 described above, which will not be repeated here.

[0088] The parameter extraction module 830 is used to perform feature processing on the equivalent ideal curve to extract input feature parameters, including indentation stiffness, unloading stiffness, and plastic work ratio. In one embodiment, the parameter extraction module 830 can be used to perform the operation S130 described above, which will not be repeated here.

[0089] The prediction module 840 is used to input the indentation stiffness, the unloading stiffness, the plastic work ratio, and the elastic modulus into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material under test. The indentation constitutive mapping model is a fully connected backpropagation neural network pre-trained with finite element virtual test samples. In one embodiment, the prediction module 840 can be used to perform the operation S140 described above, which will not be repeated here.

[0090] According to embodiments of this application, any multiple modules among the acquisition module 810, preprocessing module 820, parameter extraction module 830, and prediction module 840 can be combined into one module, or any one of these modules can be split into multiple modules. Alternatively, at least part of the functionality of one or more of these modules can be combined with at least part of the functionality of other modules and implemented in one module. According to embodiments of this application, at least one of the acquisition module 810, preprocessing module 820, parameter extraction module 830, and prediction module 840 can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging the circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, at least one of the acquisition module 810, preprocessing module 820, parameter extraction module 830, and prediction module 840 may be implemented at least partially as a computer program module, which can perform corresponding functions when the computer program module is run.

[0091] Figure 9 A block diagram of an electronic device suitable for implementing a method for inverting material constitutive parameters according to an embodiment of this application is shown.

[0092] like Figure 9 As shown, an electronic device 900 according to an embodiment of this application includes a processor 901, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 902 or a program loaded from a storage portion 908 into a random access memory (RAM) 903. The processor 901 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor, such as an application-specific integrated circuit (ASIC), etc. The processor 901 may also include onboard memory for caching purposes. The processor 901 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of this application.

[0093] RAM 903 stores various programs and data required for the operation of electronic device 900. Processor 901, ROM 902, and RAM 903 are interconnected via bus 904. Processor 901 executes various operations of the method flow according to embodiments of this application by executing programs in ROM 902 and / or RAM 903. It should be noted that the programs may also be stored in one or more memories other than ROM 902 and RAM 903. Processor 901 may also execute various operations of the method flow according to embodiments of this application by executing programs stored in said one or more memories.

[0094] According to embodiments of this application, the electronic device 900 may further include an input / output (I / O) interface 905, which is also connected to a bus 904. The electronic device 900 may also include one or more of the following components connected to the input / output (I / O) interface 905: an input section 906 including a keyboard, mouse, etc.; an output section 907 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 908 including a hard disk, etc.; and a communication section 909 including a network interface card such as a LAN card, modem, etc. The communication section 909 performs communication processing via a network such as the Internet. A drive 910 is also connected to the input / output (I / O) interface 905 as needed. A removable medium 911, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 910 as needed so that computer programs read from it can be installed into the storage section 908 as needed.

[0095] This application also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0096] According to embodiments of this application, the computer-readable storage medium can be a non-volatile computer-readable storage medium, such as including but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of this application, the computer-readable storage medium may include ROM 902 and / or RAM 903 and / or one or more memories other than ROM 902 and RAM 903 described above.

[0097] Embodiments of this application also include a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. When the computer program product is run on a computer system, the program code is used to enable the computer system to implement the material constitutive parameter inversion method provided in the embodiments of this application.

[0098] When the computer program is executed by the processor 901, it performs the functions defined in the system / apparatus of this application embodiment. According to the embodiments of this application, the systems, modules, units, etc., described above can be implemented by computer program modules.

[0099] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and downloaded and installed via the communication section 909, and / or installed from a removable medium 911. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0100] In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 909, and / or installed from the removable medium 911. When the computer program is executed by the processor 901, it performs the functions defined in the system of this application embodiment. According to the embodiments of this application, the systems, devices, modules, units, etc., described above can be implemented by computer program modules.

[0101] According to embodiments of this application, program code for executing the computer programs provided in the embodiments of this application can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0102] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0103] Those skilled in the art will understand that the features described in the various embodiments of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application.

Claims

1. A method for inverting material constitutive parameters, characterized in that, The method includes: Obtain the elastic modulus and measured load-depth curve of the material under test in a single nanoindentation test; The measured load depth curve is preprocessed by extrapolation and translation to obtain an equivalent ideal curve; The equivalent ideal curve is characterized to extract input feature parameters, which include indentation stiffness, unloading stiffness, and plastic work ratio. The indentation stiffness, the unloading stiffness, the plastic work ratio, and the elastic modulus are input into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material under test. The indentation constitutive mapping model is a fully connected backpropagation neural network pre-trained with finite element virtual test samples. The step of extrapolating and translating the measured load depth curve to obtain an equivalent ideal curve includes: Data points in the range of 50% to 100% of the maximum load in the measured load-depth curve are selected, and a quadratic polynomial fitting is performed to obtain the fitting function for the indentation segment. The fitting function for the indentation segment is extended to the measured maximum depth, and the corresponding load value is read as the extrapolated maximum load; and The unloading section curve is shifted upward along the load axis so that the load value at the unloading starting point is equal to the extrapolated maximum load, thereby constructing an equivalent ideal curve. The shift amount is the difference between the extrapolated maximum load and the measured maximum load. The step of performing feature processing on the equivalent ideal curve to extract input feature parameters includes: The coefficients of the quadratic term of the fitting function of the indentation segment are extracted as the indentation stiffness; A power function is fitted to the unloading segment of the equivalent ideal curve, and the derivative of the power function at the maximum depth is taken as the unloading stiffness; and The total work is obtained by integrating the fitting function of the indentation section from the initial depth to the maximum depth, and the rebound work is obtained by integrating the fitting function of the unloading section from the residual depth of the unloading section to the maximum depth. The difference between the total work and the rebound work is divided by the total work, and the quotient is used as the proportion of plastic work.

2. The method according to claim 1, characterized in that, The pre-trained indentation constitutive mapping models include: A simulation model of nanoindentation of a diamond Glass indenter was established in finite element software, and the material constitutive model was selected as power-law hardening. Obtain the training sample set for finite element virtual experiments; and A fully connected backpropagation neural network is trained based on the finite element virtual test training sample set to obtain the indentation constitutive mapping model.

3. The method according to claim 2, characterized in that, The acquisition of the finite element virtual experiment training sample set includes: By sampling levels at equal intervals within the respective value ranges of the four factors—elastic modulus, yield strength, strain hardening exponent, and maximum indentation depth—a full combination of the four factors is completed to form multiple sets of virtual test conditions. Simulations were performed for each set of virtual test conditions to extract the compression stiffness, unloading stiffness, and the proportion of plastic work; and The input sample is composed of the indentation stiffness, the unloading stiffness, the plastic work ratio, and the elastic modulus, and the corresponding yield strength and hardening index are used as output labels to generate a finite element virtual test training sample set.

4. The method according to claim 2, characterized in that, The step of training a fully connected backpropagation neural network based on the finite element virtual test training sample set to obtain the indentation constitutive mapping model includes: The finite element virtual test training sample set is input into the neural network to obtain power-law constitutive prediction parameters, which include predicted yield strength and predicted strain hardening index. The target loss is determined based on the predicted yield strength, the predicted strain hardening index, and the output label. as well as The indentation constitutive mapping model is obtained by training a fully connected backpropagation network based on the target loss.

5. A system for inverting material constitutive parameters, characterized in that, The system includes: The acquisition module is used to acquire the elastic modulus and measured load depth curve of the material under test in a single nanoindentation test; The preprocessing module is used to perform extrapolation and translation preprocessing on the measured load depth curve to obtain an equivalent ideal curve; The parameter extraction module is used to perform feature processing on the equivalent ideal curve to extract input feature parameters, which include indentation stiffness, unloading stiffness, and plastic work ratio. The prediction module is used to input the indentation stiffness, the unloading stiffness, the plastic work ratio and the elastic modulus into a pre-trained indentation constitutive mapping model to predict the yield strength and strain hardening index of the material under test, wherein the indentation constitutive mapping model is a fully connected backpropagation neural network pre-trained with finite element virtual test samples. The preprocessing module is also used to select data points in the range of 50% to 100% of the maximum load in the measured load-depth curve, perform quadratic polynomial fitting to obtain the indentation segment fitting function; extend the indentation segment fitting function to the measured maximum depth, read the corresponding load value as the extrapolated maximum load; and shift the unloading segment curve upward along the load axis so that the load value at the unloading starting point is equal to the extrapolated maximum load to construct an equivalent ideal curve, wherein the shift amount is the difference between the extrapolated maximum load and the measured maximum load; The parameter extraction module is also used to extract the quadratic coefficients of the fitting function of the indentation segment as the indentation stiffness; to perform power function fitting on the unloading segment of the equivalent ideal curve, and to use the derivative of the power function at the maximum depth as the unloading stiffness; to integrate the fitting function of the indentation segment from the initial depth to the maximum depth to obtain the total work, and to integrate the fitting function of the unloading segment from the residual depth of the unloading segment to the maximum depth to obtain the rebound work, and to divide the difference between the total work and the rebound work by the total work, and use the quotient as the plastic work ratio.

6. An electronic device, comprising: One or more processors; Memory, used to store one or more computer programs. The characteristic feature is that the one or more processors execute the one or more computer programs to implement the steps of the method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 4.

8. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 4.

Images