A method for predicting material tensile properties based on nanoindentation and machine learning

Abstract

The present application relates to the technical field of material tensile property prediction, in particular to a material tensile property prediction method based on nanoindentation and machine learning.The method comprises the following steps: S1, using a metallographic microscope to take a microstructure metallographic photo, and preprocessing the metallographic photo; S2, carrying out organization-based finite element simulation on the preprocessed metallographic photo to obtain stress-strain data; S3, constructing a microstructure-stress-strain field database based on the metallographic photo and the stress-strain data; S4, based on the microstructure-stress-strain field database, adjusting and optimizing a U-Net deep learning framework to predict material tensile property, and providing stress-strain cloud maps and curves.The present application designs a U-Net deep learning model which is trained, can make a highly automated prediction result on the structure-activity relationship of the material, and provides the prediction curve and cloud map in a very short time, greatly reducing the labor cost and time cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material tensile property prediction, in particular to a material tensile property prediction method based on nanoindentation and machine learning. BACKGROUND

[0002] The traditional constitutive model fails to consider the stress-strain cloud distribution corresponding to the stress-strain curve while predicting the stress-strain curve, the prediction result is single and cannot effectively reflect the stress-strain distribution and change process inside the material, the existing metal material consumes materials and takes time to obtain the stress-strain curve and serialized cloud map; Traditional material mechanical property testing, such as tensile test, usually requires preparation of a large number of samples, and each test can only obtain limited data points. This not only consumes a lot of time and resources, but also is particularly expensive for materials testing under new development or special application scenarios; The macroscopic mechanical properties of materials are closely related to their microstructure (such as grain size, phase distribution, defects, etc.). However, it is difficult for traditional methods to directly link microstructure features to macroscopic mechanical properties, making the understanding of material behavior not deep enough; Therefore, a material tensile property prediction method based on nanoindentation and machine learning is provided. SUMMARY

[0003] The purpose of the present application is to provide a material tensile property prediction method based on nanoindentation and machine learning to solve the problems of single prediction result of traditional constitutive model and time-consuming material consumption of existing metal material to obtain stress-strain curve and serialized cloud map.

[0004] To achieve the above purpose, the present application provides a material tensile property prediction method based on nanoindentation and machine learning, comprising the following steps:

[0005] S1, taking microstructure metallographic photos using a metallographic microscope and preprocessing the metallographic photos;

[0006] S2, performing organization-based finite element simulation on the preprocessed metallographic photos to obtain stress-strain data;

[0007] S3, constructing a microstructure-stress-strain field database based on the metallographic photos and the stress-strain data;

[0008] S4, based on the microstructure-stress-strain field database, adjusting and optimizing the architecture of the U-Net deep learning framework to predict the material tensile property and provide stress-strain cloud map and curve.

[0009] As a further improvement of the present technical solution, in S2, the preprocessed metallographic photos are subjected to organization-based finite element simulation to obtain stress-strain data, comprising the following steps:

[0010] S2.1, select multiple positions from the pretreated metallographic photos, apply a series of known loads using a nanoindenter, and record the corresponding displacement response;

[0011] S2.2, import the pretreated metallographic photos into the finite element software, divide the image into fine grids according to the microstructure features in the metallographic photos, and each grid element corresponds to a pixel point in the metallographic photo;

[0012] S2.3, apply periodic boundary conditions to the finite element model;

[0013] S2.4, according to the results of nanoindentation, specify the material properties of different regions in the finite element model;

[0014] S2.5, set the simulation conditions, start the finite element analysis software to perform simulation calculation according to the set conditions, and output the data according to the equal strain interval during the calculation process;

[0015] S2.6, after the simulation calculation is completed, the stress-strain data corresponding to the microstructure image at each time is extracted frame by frame, and the stress-strain value of each grid element is extracted in turn for each frame;

[0016] S2.7, use the extracted stress-strain value data to draw the stress-strain cloud chart, and calculate the average value of the stress-strain value of all grid elements as the stress-strain curve data of the whole material.

[0017] As a further improvement of the technical solution, in S3, a microstructure-stress strain field database is constructed based on the metallographic photos and stress strain data, including the following steps:

[0018] S3.1, obtain all pretreated metallographic photos and corresponding stress strain data as samples from steps S1 and S2;

[0019] S3.2, according to the time and space position, each metallographic photo and its corresponding stress strain data are one-to-one corresponding through the spatiotemporal registration algorithm;

[0020] S3.3, convert the metallographic photos into tensor format used by machine learning, and also convert the stress strain data into tensor format;

[0021] S3.4, divide the processed tensor data into training set and test set according to the required proportion;

[0022] S3.5, select a relational database management system, define the table structure, and import the converted image tensor and stress strain data tensor into the database to form a microstructure-stress strain field database.

[0023] As a further improvement of the technical solution, in S3.2, each metallographic photo is corresponded to its corresponding stress-strain data by a spatio-temporal registration algorithm, including the following steps:

[0024] S3.21, verify whether the timestamps of each metallographic photo and corresponding stress-strain data are accurately recorded and synchronized with each other;

[0025] S3.22, based on the experimental setup, preliminarily estimate the spatial positional relationship between the metallographic photo and the stress-strain nephogram;

[0026] S3.23, use the feature detection algorithm SIFT to extract stable feature points from the metallographic photo;

[0027] S3.24, match the two sets of feature points to find the best corresponding relationship;

[0028] S3.25, calculate the geometric transformation model according to the matched feature points;

[0029] S3.26, apply the calculated transformation to the stress-strain nephogram data to align it with the metallographic photo in space;

[0030] S3.27, use mutual information as a measure, adjust the transformation parameters through an optimization algorithm until the best match is achieved.

[0031] As a further improvement of the technical solution, in S3.27, the mutual information is:

[0032] ;

[0033] where, represents the pixel value distribution in the metallographic photo; represents the stress value distribution in the stress-strain nephogram; represents the probability of a certain pixel value appearing in the metallographic photo; represents the probability of a certain stress value appearing in the stress-strain nephogram; represents the probability of the pixel value and stress value in the metallographic photo and stress-strain nephogram at the same position appearing together; represents all possible pixel values in the metallographic photo; represents all possible stress values in the stress-strain nephogram; represents a specific pixel value in the metallographic photo; represents a specific stress value in the stress-strain nephogram.

[0034] As a further improvement of the technical solution, in S4, based on the microstructure-stress strain field database, the U-Net deep learning framework is adjusted and optimized to predict the material tensile performance, and the stress strain cloud picture and curve are provided, including the following steps:

[0035] S4.1, load the training set and test set from the constructed microstructure-stress strain field database;

[0036] S4.2, select U-Net architecture composed of encoder and decoder as the starting point, and connect the two ends of the encoder and decoder through jump connection;

[0037] S4.3, adjust the encoder and decoder;

[0038] S4.4, define error function to measure the difference between predicted stress strain value and true value;

[0039] S4.5, determine the model hyperparameters, and train the model based on the training set, monitor the change trend of training loss, save the parameters after training;

[0040] S4.6, evaluate the model based on the test set in the database constructed in step S3;

[0041] S4.7, use the trained model to predict new metallographic photos, output the corresponding predicted stress strain cloud picture, and draw the stress strain curve according to the predicted stress strain value.

[0042] As a further improvement of the technical solution, in S4.3, the adjustment of the encoder and the decoder includes the following steps:

[0043] S4.31, adjust the encoder to use 3x3 convolution kernel in each layer of convolution layer, step length is 1, use the same padding method to fill each layer of weight is initialized to normal distribution random value with mean value of 0 and standard deviation of 0.02;

[0044] S4.32, use ReLU as the activation function in the encoder, and use the maximum pooling method to gradually reduce the spatial dimension of the input;

[0045] S4.33, adjust the decoder to use 2x2 convolution kernel in each layer of deconvolution layer, step length is 2;

[0046] S4.34, splice the feature map in the encoder with the corresponding hierarchical feature map in the decoder, if the size after deconvolution does not match, adjust to appropriate size by using bilinear interpolation.

[0047] As a further improvement of the technical solution, in S4.32, the spatial dimension of the input is gradually reduced using the max-pooling method, including the following steps:

[0048] S4.321, image segmentation is performed on the preprocessed metallographic photo;

[0049] S4.322, the size of the pooling window is selected ;

[0050] S4.323, the distance of each movement of the pooling window is determined ;

[0051] S4.324, for each channel traverse the entire input image, for position calculate the maximum value by the max-pooling formula, and optimize the max-pooling formula for the directional features of the grain boundaries in the metallographic photo;

[0052] S4.325, place the maximum value in the corresponding position of the new output activation map to form the down-sampled image;

[0053] S4.326, after max-pooling, a new feature map is obtained, and the spatial dimension of the new feature map is smaller than the original input.

[0054] As a further improvement of the technical solution, in S4.324, the max-pooling formula is:

[0055] ;

[0056] wherein, represents the value of the output feature map of the pooling operation in a certain layer of the U-Net model at position and channel ; represents the height of the pooling window; represents the width of the pooling window; represents the step of the pooling window; represents the channel index; represents the row offset within the pooling window; represents the column offset within the pooling window;

[0057] The max-pooling formula is optimized for the directional features of the grain boundaries in the metallographic photo:

[0058] ;

[0059] ;

[0060] wherein, ​represents the value of the optimized output feature map at position and channel ; represents the direction-sensitive weight of the grain boundary; represents the adjustment coefficient of the direction weight; represents the gradient direction of the th pixel in the pooling window; represents the principal direction angle; represents the weight adjustment coefficient of the gradient amplitude; represents the gradient value of the pixel point in the metallographic photo in the direction; represents the gradient value of the pixel point in the metallographic photo in the direction.

[0061] As a further improvement of the technical solution, in S4.4, the error function is:

[0062] ;

[0063] wherein, represents the average mean square error of all samples; represents the total number of samples; represents the number of frames of each sample; represents the true stress-strain value of the th sample in the th frame; represents the predicted stress-strain value of the th sample in the th frame; represents the sample index; represents the frame number index.

[0064] Compared with the prior art, the beneficial effects of the present application are:

[0065] 1. In the material tensile property prediction method based on nanoindentation and machine learning, the U-Net deep learning model trained can make highly automated prediction results for the structure-activity relationship of the material. Compared with the test and finite element simulation method, the U-Net deep learning model can give the prediction curve and cloud chart in a very short time, greatly reducing the labor cost and time cost. The model after training can achieve a prediction accuracy of more than 95%, and can maintain stable prediction for different test images.

[0066] 2、The method for predicting material tensile properties based on nanoindentation and machine learning, the frame data of the material stress strain field is output through the U-Net deep learning model, so that the stress strain nephogram can be drawn based on the output data, and the internal stress state of the material under stress can be analyzed according to the stress strain nephogram at different stages, the stress and strain physical field is predicted through the material microstructure geometry, which bridges the gap between the microstructure and physical properties of the material, and provides scalability by predicting complex material behavior regardless of component shape, boundary conditions and geometric hierarchy. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 The overall method flowchart of the present application is shown in the figure;

[0068] Figure 2 A network model schematic diagram provided by the present application is shown in the figure;

[0069] Figure 3 A comparison between the predicted stress field nephogram and the target nephogram of the present application is shown in the figure;

[0070] Figure 4 A comparison between the predicted strain field nephogram and the target nephogram of the present application is shown in the figure;

[0071] Figure 5 A comparison between the predicted stress strain curve and the target curve of the present application is shown in the figure. DETAILED DESCRIPTION

[0072] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0073] Embodiment: please refer to Figure 1 The embodiment provides a method for predicting material tensile properties based on nanoindentation and machine learning, which comprises the following steps:

[0074] S1, a metallographic microscope is used to take a microstructure metallographic photo, and the metallographic photo is pretreated;

[0075] In the embodiment, a sample is cut from a material, the surface of the sample is first ground flat using sandpaper of different grits, then polished and etched, and then a plurality of metallographic photos are taken by a metallographic microscope. Then the aforementioned metallographic photos are pretreated to have uniform size, color and consistent length and width.

[0076] S2, the pretreated metallographic photo is subjected to organization-based finite element simulation to obtain stress strain data;

[0077] In this embodiment, the microstructure-based finite element simulation can directly link the microstructure features of materials (such as grain size, shape, orientation, phase distribution, etc.) with macroscopic mechanical properties, thereby providing a deeper understanding of the relationship between the two. This helps to develop new high-performance materials and optimize existing materials. Finite element simulation is a numerical method that does not require physical destruction of the actual material, and the same set of data can be used repeatedly for multiple simulation experiments, saving materials and costs. Compared with traditional experimental methods, finite element simulation can complete a large number of simulations under different conditions in a short time, reducing the time and resource investment required for physical experiments. By combining microstructure information, finite element simulation can span different scales from micro to macro, providing more comprehensive and accurate mechanical behavior prediction, and supporting the demand for multi-scale modeling.

[0078] The stress-strain data obtained by the microstructure-based finite element simulation of the pretreated metallographic photos includes the following steps:

[0079] S2.1. Select multiple positions from the pretreated metallographic photos and use a nanoindenter to apply a series of known loads, and record the corresponding displacement response. Each test point should correspond to a pixel area in the metallographic photo as much as possible to ensure that the measured hardness, elastic modulus, and other parameters can reflect the true characteristics of different microstructures (such as grains, phase boundaries, precipitates, etc.) of the material.

[0080] S2.2. Import the pretreated metallographic photos into the finite element software, and divide the image into fine grids according to the microstructure features in the metallographic photos, with each grid element corresponding to a pixel point in the metallographic photo.

[0081] S2.3. Apply periodic boundary conditions to the finite element model to simulate the behavior of an infinite material body and reduce the influence of edge effects.

[0082] S2.4. According to the results of nanoindentation, specify the material properties of different regions in the finite element model, for example, different grains or phases can be assigned different elastic moduli and Poisson's ratios.

[0083] S2.5. Set the simulation conditions, including the loading mode (determine the loading mode during simulation, such as uniaxial tension, biaxial tension, etc., to match the actual experimental conditions) and set the step size (determine the total strain during simulation and the step size of each output data. In general, data is output at equal strain intervals to obtain continuous stress-strain curves). Start the finite element analysis software to perform simulation calculation according to the set conditions. During the calculation process, the output data is output at equal strain intervals, that is, the stress-strain data is output once every fixed step from the initial state under the condition of fixed total strain.

[0084] S2.6, After the simulation calculation is completed, the stress and strain data corresponding to the microstructure image at each time point are extracted frame by frame, and the stress and strain values of each grid element are extracted in turn for each frame;

[0085] S2.7, The stress and strain cloud chart is drawn by using the extracted stress and strain value data, the stress distribution in the material is displayed, and the average value of the stress and strain values of all grid elements is calculated as the stress and strain curve data of the whole material.

[0086] S3, Constructing microstructure-stress strain field database based on metallographic photos and stress strain data;

[0087] In this embodiment, by combining the microstructure characteristics of the material (such as grain size, shape, distribution, etc.) with the corresponding stress and strain data, the relationship between the two can be better understood. This association helps to reveal how the internal structure of the material affects its macroscopic mechanical behavior; The well-constructed database can be reused in multiple research projects, reducing the need for repeated experiments, saving time and resources. At the same time, it provides valuable historical data support for subsequent research;

[0088] Based on the metallographic photos and stress strain data, a microstructure-stress strain field database is constructed, including the following steps:

[0089] S3.1, All pre-processed metallographic photos and corresponding stress and strain data obtained from steps S1 and S2 are taken as samples, and the formats of all images and data files are ensured to be consistent, such as converting the metallographic photos to a uniform resolution and color mode, and saving the stress and strain data in a standardized table or array format;

[0090] S3.2, According to the time and spatial position, each metallographic photo and its corresponding stress and strain data are matched one by one through a time and space registration algorithm, which means that each frame of stress and strain cloud chart data must accurately reflect the stress distribution in the material at that time, and match the metallographic photo taken at the same time point;

[0091] Among them, the spatio-temporal registration algorithm is a technology for synchronizing and aligning data from different sources or time points, ensuring that they accurately correspond in time and space, ensuring that each metallographic photo and the corresponding stress-strain data are accurately matched in time and space, which is crucial for establishing the relationship between microstructure characteristics and macroscopic mechanical properties. Precise registration can improve the accuracy of model predictions; spatio-temporal registration helps reduce measurement errors caused by changes in material internal structure or external loading conditions. By adjusting the transformation parameters through optimization algorithms to achieve the best match, the consistency and reliability of the data can be ensured, and the internal relationship between the microstructure of the material (such as grains, phase boundaries, etc.) and the mechanical response (such as stress-strain) can be more clearly revealed, which helps to deeply understand the behavior mechanism of the material and provides theoretical support for material design;

[0092] Through the spatio-temporal registration algorithm, each metallographic photo and its corresponding stress-strain data are corresponded one by one, including the following steps:

[0093] S3.21, verify whether the timestamps of each metallographic photo and corresponding stress-strain data are accurately recorded and synchronized with each other;

[0094] S3.22, based on experimental settings (such as sample fixation method, loading direction, etc.), preliminarily estimate the spatial positional relationship of metallographic photos and stress-strain cloud maps;

[0095] S3.23, use the feature detection algorithm SIFT to extract stable feature points from the metallographic photo;

[0096] S3.24, match the two sets of feature points to find the best corresponding relationship;

[0097] S3.25, calculate the geometric transformation model according to the matched feature points: , where is the original point coordinate, is the transformed point coordinate, is the transformation matrix;

[0098] S3.26, apply the calculated transformation to the stress-strain cloud map data to align it with the metallographic photo in space;

[0099] S3.27, use mutual information as a measure, adjust the transformation parameters through optimization algorithms until the best match is achieved;

[0100] Further, mutual information is a statistical measure of the degree of interdependence between two variables, representing how much information one variable can obtain through the other; mutual information can capture the non-linear relationship between variables, not just linear correlation. This is particularly important for handling complex datasets, especially when there are complex interactions between variables. Mutual information is invariant to monotonic transformations, which means that even if two variables undergo different monotonic transformations (such as logarithmic or exponential transformation), their mutual information values remain unchanged. This makes mutual information more stable when comparing data at different scales or distributions; mutual information can reflect all forms of correlation, not just the first and second order statistical characteristics based on mean and variance. It takes into account the complete probability distribution of the data, so it can more comprehensively measure the dependence between two random variables;

[0101] Mutual information is:

[0102] ;

[0103] Where, represents the distribution of pixel values in the metallographic photo; represents the distribution of stress values in the stress-strain cloud map; represents the probability of a certain pixel value appearing in the metallographic photo; represents the probability of a certain stress value appearing in the stress-strain cloud map; represents the probability of the pixel value and stress value at the same position in the metallographic photo and stress-strain cloud map appearing together; represents all possible pixel values in the metallographic photo; represents all possible stress values in the stress-strain cloud map; represents a specific pixel value in the metallographic photo; represents a specific stress value in the stress-strain cloud map;

[0104] S3.3, convert the metallographic photo into a tensor format used by machine learning, each image can be represented as a three-dimensional tensor (width x height x channel number), where the channel number is usually 3 (RGB image) or 1 (gray image), and also convert the stress-strain data into a tensor format, which involves rearranging the stress-strain values into a form compatible with the image tensor, such as creating a two-dimensional tensor with the same size as the image, where each element represents the stress-strain value of the corresponding pixel;

[0105] S3.4, divide the processed tensor data into training set and test set (10:1) according to the required proportion;

[0106] S3.5, select a relational database management system, define the table structure, ensure that the image tensor and its corresponding stress-strain data tensor can be efficiently stored and retrieved, and enter the converted image tensor and stress-strain data tensor into the database to form a microstructure-stress-strain field database, and ensure that each record contains a unique identifier for easy tracking and association.

[0107] S4, based on the microstructure-stress-strain field database, adjust and optimize the U-Net deep learning framework to predict material tensile properties and provide stress-strain cloud maps and curves;

[0108] In this embodiment, by using detailed microstructure information and stress-strain data as input, U-Net can learn the complex relationship between the internal structure of the material and the mechanical properties, thereby achieving high-precision tensile property prediction. The stress-strain cloud map generated can intuitively show the internal stress distribution of the material, helping researchers better understand the behavior of the material under different loading conditions. In addition, the stress-strain curve provides the basis for quantitative analysis, facilitating the evaluation of key characteristics such as the strength and ductility of the material; traditional material testing methods are time-consuming and costly. This method can complete a large number of simulation experiments in a short time, quickly screen out potential new materials or optimize the design of existing materials, greatly shortening the research and development cycle of new materials; using a deep learning model for virtual testing can significantly reduce the number of actual physical experiments, saving resources while reducing development costs;

[0109] Based on the microstructure-stress-strain field database, adjust and optimize the U-Net deep learning framework to predict material tensile properties and provide stress-strain cloud maps and curves, including the following steps:

[0110] S4.1, load the training set and test set from the constructed microstructure-stress-strain field database, ensuring that the image tensor and stress-strain data tensor are correctly paired;

[0111] S4.2, select the U-Net architecture composed of an encoder (shrinkage path) and a decoder (expansion path) as the starting point, and connect the encoder and decoder through a jump connection (as shown in Figure 2 ), where the encoder gradually reduces the spatial dimensions of the input tensor with convolution, and the decoder gradually restores the spatial dimensions of the image with deconvolution, reducing the number of feature channels;

[0112] S4.3, adjust the encoder and decoder;

[0113] Wherein, the adjustment of the encoder and the decoder includes the following steps:

[0114] S4.31, adjust the encoder to use a 3x3 convolution kernel at each layer of the convolutional layer, with a step size of 1, and use the same padding method to fill in order to keep the spatial dimensions unchanged, the weights of each layer are initialized to normal distribution random values with a mean of 0 and a standard deviation of 0.02;

[0115] S4.32, use ReLU as the activation function in the encoder, and use the max pooling method to gradually reduce the spatial dimensions of the input, using ReLU as the activation function in the encoder introduces nonlinearity, allowing the network to learn complex features, while max pooling gradually reduces the spatial dimensions of the input by selecting the maximum value in the local region, while retaining the most critical information;

[0116] The advantage of using the max pooling method to gradually reduce the spatial dimensions of the input is that it can retain the most significant feature information, while reducing the amount of calculation and model parameters, helping to prevent overfitting and improve the generalization ability of the model. In addition, max pooling can also provide a certain degree of translation invariance, making the model less sensitive to small movements of the input data;

[0117] Using the max pooling method to gradually reduce the spatial dimensions of the input includes the following steps:

[0118] S4.321, image segmentation is performed on the preprocessed metallographic photo to convert it into a format suitable for input into the neural network;

[0119] S4.322, select the size of the pooling window ;

[0120] S4.323, determine the distance that the pooling window moves each time ;

[0121] S4.324, for each channel traverse the entire input image, for position calculate the maximum value through the max pooling formula, and optimize the max pooling formula for the directional feature of the grain boundary in the metallographic photo;

[0122] Further, the max pooling formula is:

[0123] ;

[0124] where, represents the value of the output feature map of the pooling operation in the U-Net model at position and channel , which is the maximum value in the region covered by the pooling window, retaining the most significant feature information in the region; represents the height of the pooling window, indicating the number of pixels covered by the pooling window in the vertical direction (row) in the metallographic image or stress-strain field tensor; represents the width of the pooling window, indicating the number of pixels covered by the pooling window in the horizontal direction (column); represents the step size of the pooling window, defining the distance of each sliding of the pooling window, which controls the resolution of the feature map after the pooling operation of the metallographic image or stress-strain field tensor; represents the channel index, indicating different types of feature channels in the metallographic image or stress-strain field (e.g., RGB image channels or stress and strain components); represents the row offset within the pooling window; represents the column offset within the pooling window;

[0125] Grain boundary directionality is one of the important factors affecting the tensile properties of materials, especially in predicting stress-strain distribution and material failure behavior. The optimized pooling method can more sensitively capture the directional features of grain boundaries by introducing directional weights, thereby providing more rich feature information for deep learning models. The traditional maximum pooling method only extracts the maximum value within the window, which easily ignores the complexity of grain boundary directionality. By optimizing the pooling method, different pixel points are given importance weights based on direction and gradient, which can effectively preserve grain boundary features and reduce information loss. In the conversion process from metallographic image to finite element simulation, microstructure features directly affect grid partitioning and regional attribute assignment. After optimizing the pooling method, the extracted direction-sensitive features can more accurately guide finite element modeling, improving the resolution and accuracy of simulation, and thus obtaining more realistic stress-strain data. The optimized pooling method generates high-quality feature maps in metallographic image preprocessing, making it more suitable for inputting into deep learning models. In the training process, these direction-sensitive features can help U-Net learn local patterns in grain and boundary regions more effectively, thereby improving prediction performance.

[0126] The maximum pooling formula is optimized for the directional features of grain boundaries in metallographic images:

[0127] ;

[0128] ;

[0129] wherein, represents the value of the output feature map after optimization at position and channel ; represents the direction-sensitive weight of the grain boundary; represents the adjustment coefficient of the direction weight; represents the first The gradient direction of each pixel is calculated from the gradient information of the metallographic image and is used to describe the direction of the grain boundary. The principal direction angle (in radians) represents the statistical principal direction of grain distribution in a metallographic photograph of a material. This represents the weight adjustment coefficient for the gradient magnitude; Represents pixels in metallographic photographs Dot at Gradient value in the direction; Represents pixels in metallographic photographs Dot at Gradient value in the direction;

[0130] S4.325, Place the maximum value into the new output activation graph. At the corresponding positions in the image, a downsampled image is formed;

[0131] S4.326. After max pooling, a new feature map is obtained. The spatial dimension of the new feature map is smaller than that of the original input. This new feature map retains the most important information in the original input while reducing the amount of computation and the number of parameters.

[0132] S4.33. Adjust the decoder to use a 2×2 convolution kernel with a stride of 2 in each deconvolution layer to restore the spatial dimension;

[0133] S4.34. Concatenate the feature maps in the encoder with the corresponding layer feature maps in the decoder to retain more detailed information. If there is a size mismatch after deconvolution, use bilinear interpolation to adjust it to a suitable size (bilinear interpolation estimates the pixel value at the new position by calculating the weighted average of four adjacent pixels, thereby smoothly adjusting the image to the required size). Select hyperparameters such as model rounds, batch size, and buffer size.

[0134] S4.4 Define an error function to measure the difference between the predicted stress and strain values ​​and the actual values;

[0135] Furthermore, the error function is:

[0136] ;

[0137] in, The mean squared error of all samples is used as the final loss function. Indicates the total number of samples; This indicates the number of frames for each sample; Indicates the first The sample at the th The actual stress and strain values ​​of the frame; Indicates the first The sample at the th The predicted stress and strain values ​​of the frame; represents a sample index; represents a frame number index;

[0138] S4.5, model training based on the training set, monitoring the change trend of training loss, and timely discovering overfitting or underfitting phenomenon, the training process is carried out by model parameters, after the training is completed, the model parameters are saved down, which is convenient for subsequent deployment and use;

[0139] S4.6, model evaluation based on the test set in the database constructed in step S3, to ensure that the model can also perform well on unseen data, if the accuracy meets the requirements, then the model training is completed, if it does not meet the requirements, modify the model hyperparameters and then perform new training, continue to evaluate until the model prediction accuracy meets the requirements;

[0140] S4.7, using the trained model to predict new metallographic photos, output the corresponding predicted stress strain cloud map (as shown in Figure 3 , Figure 4 indicated), which intuitively displays the internal stress distribution of the material, and according to the predicted stress strain value, a stress strain curve (as shown in Figure 5 indicated) is drawn to reflect the mechanical response of the material at different strain levels;

[0141] Stress strain cloud map is a commonly used visualization tool in material mechanics analysis, which represents the distribution of internal stress or strain of the material through color change. Its main functions are as follows: intuitively display the stress strain distribution inside the material, including stress concentration area and low stress area. Through the change of color, the high and low stress can be quickly identified; evaluate the uniformity of stress distribution. By observing the color distribution in the stress strain cloud map, the stress uniformity of the material can be understood, and when the color distribution is relatively uniform, it indicates that the stress distribution of the material is relatively uniform, and if the color appears obvious unevenness, it indicates that the stress is concentrated; assist in design optimization. The cloud map provides an intuitive way to observe and analyze the internal stress state of the material under stress, which is of great significance for optimizing design, improving material utilization efficiency and structural reliability. There are mainly two methods to obtain the stress strain curve of the material, namely preparing tensile specimens for physical test or establishing finite element model for numerical simulation; and drawing stress strain cloud map mainly through finite element model numerical simulation, in addition, it can also be completed through digital image correlation (DIC) test.

[0142] The above shows and describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above-mentioned embodiments, and the above-mentioned embodiments and descriptions in the specification are only preferred examples of the present application and are not intended to limit the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application.

Claims

1. A method for predicting material tensile properties based on nanoindentation and machine learning, characterized by, The method comprises the following steps: S1, using metallographic microscope to take microstructure metallographic photo, and pretreating the metallographic photo; S2, carrying out tissue-based finite element simulation on the pretreated metallographic photo to obtain stress-strain data; S3, constructing microstructure-stress strain field database based on the metallographic photo and the stress-strain data; S4, based on the microstructure-stress strain field database, adjusting and optimizing the U-Net deep learning framework to predict the material tensile performance, and providing stress-strain cloud picture and curve.

2. The nanoindentation and machine learning based material tensile property prediction method of claim 1, wherein: In the S2, the stress-strain data is obtained by carrying out tissue-based finite element simulation on the pretreated metallographic photo, comprising the following steps: S2.1, selecting multiple positions from the pretreated metallographic photo, using nanoindenter to apply a series of known load, and recording the corresponding displacement response; S2.2, importing the pretreated metallographic photo into the finite element software, dividing the image into fine grid according to the microstructure characteristics in the metallographic photo, and each grid unit corresponds to a pixel point in the metallographic photo; S2.3, applying periodic boundary conditions to the finite element model; S2.4, according to the results of nanoindentation, specifying the material properties of different regions in the finite element model; S2.5, setting simulation conditions, starting the finite element analysis software to execute simulation calculation according to the set conditions, and outputting the data according to the equal strain interval during the calculation process; S2.6, after the simulation calculation is completed, the stress-strain data corresponding to the microstructure image at each time is extracted frame by frame, and the stress-strain value of each grid unit is extracted in turn for each frame; S2.7, using the extracted stress-strain value data to draw stress-strain cloud picture, and calculating the average value of all grid unit stress-strain values as the stress-strain curve data of the whole material.

3. The nanoindentation and machine learning based material tensile property prediction method of claim 2, wherein: In the S3, the microstructure-stress strain field database is constructed based on the metallographic photo and the stress-strain data, comprising the following steps: S3.1, obtaining all pretreated metallographic photos and corresponding stress-strain data as samples from steps S1 and S2; S3.2, according to time and space position, each metallographic photo and its corresponding stress-strain data are corresponded by time and space registration algorithm; S3.3, converting the metallographic photo into tensor format used by machine learning, and converting the stress-strain data into tensor format; S3.4, dividing the processed tensor data into training set and test set according to the required proportion; S3.5, selecting a relational database management system, defining table structure, and importing the converted image tensor and stress-strain data tensor into the database to form the microstructure-stress strain field database.

4. The nanoindentation and machine learning based material tensile property prediction method of claim 3, wherein: In the S3.2, each metallographic photo and its corresponding stress-strain data are corresponded by time and space registration algorithm, comprising the following steps: S3.21, verifying whether the time stamps of each metallographic photo and corresponding stress-strain data are accurately recorded and synchronized with each other; S3.22, based on the experimental setting, preliminarily estimating the spatial position relationship of the metallographic photo and the stress-strain cloud picture; S3.23, using feature detection algorithm SIFT to extract stable feature points from the metallographic photo; S3.24, match the two sets of feature points to find the best correspondence; S3.25, calculate the geometric transformation model according to the matched feature points; S3.26, apply the calculated transformation to the stress-strain cloud data to align it with the metallographic photo in space; S3.27, use mutual information as a metric to adjust the transformation parameters through an optimization algorithm until the best match is achieved.

5. The nanoindentation and machine learning based material tensile property prediction method of claim 4, wherein: In S3.27, the mutual information is: ； wherein, represents a distribution of pixel values in a metallographic image; represents a distribution of stress values in a stress-strain map; represents a probability of a certain pixel value occurring in a metallographic image; represents a probability of a certain stress value occurring in a stress-strain map; represents a probability of a certain pixel value and stress value occurring together at the same location in a metallographic image and a stress-strain map; represents all possible pixel values in a metallographic image; represents all possible stress values in a stress-strain map; represents a specific pixel value in a metallographic image; represents a specific stress value in a stress-strain map.

6. The nanoindentation and machine learning based material tensile property prediction method of claim 5, wherein: In S4, based on the microstructure-stress-strain field database, the U-Net deep learning framework is adjusted and optimized to predict the material tensile performance and provide stress-strain cloud and curve, including the following steps: S4.1, load the training set and test set from the constructed microstructure-stress-strain field database; S4.2, select the U-Net architecture composed of encoder and decoder as the starting point, and connect the two ends of the encoder and decoder through jump connection; S4.3, adjust the encoder and decoder; S4.4, define an error function to measure the difference between the predicted stress-strain value and the true value; S4.5, determine the model hyperparameters and train the model based on the training set, monitor the trend of training loss, and save the parameters after training; S4.6, evaluate the model based on the test set in the database constructed in step S3; S4.7, use the trained model to predict new metallographic photos, output the corresponding predicted stress-strain cloud, and draw the stress-strain curve according to the predicted stress-strain value.

7. The nanoindentation and machine learning based material tensile property prediction method of claim 6, wherein: In S4.3, the adjustment of the encoder and decoder includes the following steps: S4.31, adjust the encoder to use a 3x3 convolution kernel at each layer of the convolution layer with a step size of 1, and use the same padding method to fill each layer's weight is initialized to a normal distribution random value with a mean of 0 and a standard deviation of 0.02; S4.32, use ReLU as the activation function in the encoder, and use the maximum pooling method to gradually reduce the spatial dimension of the input; S4.33, adjust the decoder to use a 2x2 convolution kernel at each layer of the deconvolution layer with a step size of 2; S4.34, concatenate the feature maps in the encoder with the corresponding hierarchical feature maps in the decoder, and if the size after deconvolution does not match, adjust to the appropriate size using bilinear interpolation.

8. The nanoindentation and machine learning based material tensile property prediction method of claim 7, wherein: In S4.32, the maximum pooling method is used to gradually reduce the spatial dimension of the input, including the following steps: S4.321, perform image segmentation on the preprocessed metallographic photo; S4.322、select the pooling window size ; S4.323, determining the distance the pooling window moves each time ; S4.324, For each channel Iterate through the entire input image, for each position The maximum value is calculated using the max pooling formula, and the max pooling formula is optimized to take into account the directional characteristics of grain boundaries in metallographic images. S4.325, place the maximum value to the new output activation map In the corresponding positions of the down-sampled image is formed. S4.326, after maximum pooling, a new feature map is obtained, and the spatial dimension of the new feature map is smaller than the original input.

9. The nanoindentation and machine learning based material tensile property prediction method of claim 8, wherein: In S4.324, the maximum pooling formula is: ； wherein, denotes the value of the output feature map of a certain layer of the U-Net model in position and channel ; denotes the height of the pooling window; denotes the width of the pooling window; denotes the step size of the pooling window; denotes the channel index; denotes the row offset within the pooling window; denotes the column offset within the pooling window; For the directional features of the grain boundaries in the metallographic photo, the maximum pooling formula is optimized: ； ； wherein, represents the value of the optimized output feature map at position and channel ; represents the direction-sensitive weight of the grain boundary; represents the adjustment coefficient of the direction weight; represents the gradient direction of the th pixel in the pooling window; represents the principal direction angle; represents the weight adjustment coefficient of the gradient amplitude; represents the gradient value of the pixel point in the direction in the metallographic photo; represents the gradient value of the pixel point in the direction in the metallographic photo.

10. The nanoindentation and machine learning based material tensile property prediction method of claim 9, wherein: In S4.4, the error function is: ； in, This represents the average mean squared error of all samples; Indicates the total number of samples; This indicates the number of frames for each sample; Indicates the first The sample at the th The actual stress and strain values ​​of the frame; Indicates the first The sample at the th The predicted stress and strain values ​​of the frame; Indicates the sample index; Indicates the frame number index.

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