Recycled concrete compression plasticity stage discriminating device based on acoustic emission and stress-strain analysis

By designing a compressed plasticity stage discrimination device for regenerated concrete based on acoustic emission and stress-strain analysis, the problem of difficulty in real-time monitoring and analyzing the acoustic emission signals and stress-strain changes of materials in the compressed plasticity stage in the prior art is solved, and intuitive display and accurate judgment of the performance of regenerated concrete materials is achieved.

CN120213624AActive Publication Date: 2025-06-27HUAZHONG UNIV OF SCI & TECH

Patent Information

Application Number
CN202510399903.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-01
Publication Date
2025-06-27
Estimated Expiration
2045-04-01

AI Technical Summary

Technical Problem

The prior art is difficult to monitor and analyze the acoustic emission signals and stress-strain changes of recycled concrete materials in real time during the compression plasticization stage, resulting in the inconvenient judgment of material performance.

Method used

A compression plasticity phase discrimination device for regenerated concrete based on acoustic emission and stress-strain analysis is designed, including data acquisition, preprocessing, storage, graphical user interface, data processing, analysis and result output modules. The graphical user interface is constructed through MATLAB to realize real-time processing and intuitive display of data.

Benefits of technology

Real-time monitoring and analysis of acoustic emission signals and stress-strain changes of recycled concrete materials in the compressive plasticization stage is realized, providing an intuitive display of material performance, simplifying data processing and computing interfaces, and improving the accuracy of material performance judgment.

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Abstract

The invention discloses a recycled concrete compression plasticity stage discriminating device based on acoustic emission and stress-strain analysis, which comprises the following steps: applying axial pressure load to recycled concrete test pieces under different working conditions, and synchronously measuring acoustic emission signals and material compression stress-strain curves of the recycled concrete test pieces; and outputting a time and accumulated acoustic emission energy value, an acoustic emission b value, stress and strain Excel table. Constructing a GUI interface through MATLAB, and creating an execution button, an input box and a result and graph display area; callback functions for file selection and operation monitoring are respectively defined based on a GUI interface; extracting data of acoustic emission, b value, stress and strain from a specified Excel worksheet, and performing interpolation processing; calling a function to detect the yield strength and the time and strain of complete damage, and outputting a result. According to the method, the plasticity stage of the material can be rapidly detected by processing the acoustic emission data and the stress-strain data, so that data processing and result display are more intuitive.
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Description

Technical Field

[0001] The present invention belongs to the technical field of acoustic emission detection, and particularly relates to a discriminant device for the plastic stage of recycled concrete under compression based on acoustic emission and stress-strain analysis. Background Art

[0002] With the continuous development of building materials, recycled concrete, as a new type of environmentally friendly material, has received increasing attention. Traditional testing methods mainly rely on physical experiments to evaluate the mechanical properties of recycled concrete. However, these methods are usually time-consuming and difficult to provide real-time feedback on the performance changes of the material. Especially in the plastic stage of the material, traditional methods are difficult to capture the key acoustic emission signals and stress-strain changes, thus affecting the judgment of the material performance.

[0003] Currently, although relevant studies have attempted to use acoustic emission monitoring technology to evaluate material performance, existing technologies often lack efficient data processing and visualization means, resulting in an unintuitive result display and an inability to effectively achieve real-time monitoring and analysis of data. Therefore, it is necessary to develop a new type of graphical user interface application device that can quickly process acoustic emission data and stress-strain data and intuitively display the plastic stage of recycled concrete materials under compression. Summary of the Invention

[0004] The present invention proposes a discriminant device for the plastic stage of recycled concrete under compression based on acoustic emission and stress-strain analysis to solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above object, the present invention provides a discriminant device for the plastic stage of recycled concrete under compression based on acoustic emission and stress-strain analysis, including:

[0006] A data acquisition module, configured to apply an axial compressive load to recycled concrete specimens under different working conditions at different confining pressures and synchronously acquire acoustic emission signal and stress-strain curve data;

[0007] A data preprocessing module, configured to preprocess the acquired acoustic emission signals, obtain time, acoustic emission cumulative energy data, amplitude, and rise time data, and eliminate invalid data;

[0008] A data storage module, configured to store acoustic emission b values, processed acoustic emission signals, stress, and strain data;

[0009] A graphical user interface module, configured for data input, processing start, result display, and graphical display;

[0010] A data processing module, configured to extract the stored data and unify different data sources onto the stress-strain time axis through interpolation processing to obtain unified data;

[0011] An analysis module for testing unified data, obtaining the yield strength, complete failure time and strain of recycled concrete, and determining the start and end of the plastic phase;

[0012] The result output module is used to output the analysis results to the result display area of ​​the graphical user interface module for display.

[0013] Preferably, the data acquisition module comprises:

[0014] Axial compression load equipment, used to apply axial pressure to recycled concrete specimens under different confining pressures and simultaneously collect stress and strain data;

[0015] The acoustic emission monitoring unit is used to record the occurrence time, acoustic emission energy, rise time and amplitude information of each acoustic emission signal during the loading process of recycled concrete under different confining pressures.

[0016] Preferably, the data preprocessing module includes:

[0017] A data screening unit is used to remove the time point data where the acoustic emission energy and rise time are 0;

[0018] The data calculation unit is used to calculate the b-value of acoustic emission.

[0019] Preferably, the data calculation unit calculates the acoustic emission b-value including:

[0020] Divide the acoustic emission signal into time periods according to the set time step;

[0021] Calculate the magnitude information in each time period;

[0022] The logarithmic function curve of magnitude and frequency was linearly fitted using the Gutenberg-Richter relationship to calculate the b value.

[0023] Preferably, the graphical user interface module is constructed by MATLAB, including:

[0024] Execute button to start data processing;

[0025] Input box, used to enter the Excel file path and worksheet name;

[0026] Result display area, used to display analysis results;

[0027] Graphical display area for visualizing stress-strain curves and acoustic emission signals versus time.

[0028] Preferably, the data processing module includes:

[0029] A file reading unit for extracting acoustic emission cumulative energy, b-value, stress, and strain data from a specified Excel file through the readtable function of MATLAB;

[0030] An interpolation processing unit for unifying different data sources onto the stress-strain time axis through linear interpolation.

[0031] Preferably, the analysis module includes:

[0032] A yield strength detection unit for calculating the yield strength, complete failure time, and strain of the material;

[0033] A plastic stage determination unit for determining the starting and ending points of the plastic stage through a sharp increase in acoustic emission cumulative energy and a significant decrease in the b-value.

[0034] Preferably, the determination method of the plastic stage determination unit includes:

[0035] When the increment of the acoustic emission cumulative energy exceeds 50% of the historical maximum increment, it is determined that the acoustic emission cumulative energy has increased significantly;

[0036] When the b-value drops by more than 0.2, it is determined that there is a significant decrease in the b-value;

[0037] The first event of a sharp increase in acoustic emission cumulative energy or a decrease in the b-value is determined as the starting point of the plastic stage;

[0038] The last event of a sharp increase in acoustic emission cumulative energy or a decrease in the b-value is determined as the ending point of the plastic stage.

[0039] Compared with the prior art, the present invention has the following advantages and technical effects:

[0040] The present invention utilizes the corresponding relationship between acoustic emission signals and stress-strain curves, defines the sharp increase in acoustic emission cumulative energy and the significant decrease interval of the b-value during the compression process of recycled concrete under different confining pressures to define the key points of the transition from elastic to plastic. And through the GUI application device, the non-destructive testing results are visualized more intuitively and the results are fed back. Using this device, the corresponding relationship between the acoustic emission signal results and the stress-strain curve is expressed more simply and intuitively, and different functions in MATLAB are called to directly calculate the test results, providing a more convenient and concise operation interface and method, and being able to intuitively display the plastic stage of the material. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0042] Figure 1It is the flowchart of the device operation in the embodiment of the present invention;

[0043] Figure 2 It is the cumulative energy curve diagram of acoustic emission of the recycled concrete specimen in the embodiment of the present invention;

[0044] Figure 3 It is the result diagram of b-value calculation of the recycled concrete specimen in the embodiment of the present invention;

[0045] Figure 4 It is the complete curve diagram of compressive stress-strain of the recycled concrete in the embodiment of the present invention;

[0046] Figure 5 It is the overall layout schematic diagram of the graphical user interface in the embodiment of the present invention;

[0047] Figure 6 It is the schematic diagram of the GUI interface for determining the result of the compressive plastic stage of recycled concrete in the embodiment of the present invention

[0048] Figure 7 It is the device implementation step diagram in the embodiment of the present invention. Detailed implementation manners

[0049] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will describe this application in detail with reference to the drawings and in combination with the embodiments.

[0050] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0051] Embodiment 1

[0052] As Figure 1 shown, in this embodiment, a discriminant device for the compressive plastic stage of recycled concrete based on acoustic emission and stress-strain analysis is provided, including:

[0053] A data acquisition module, which is used to apply an axial compressive load to recycled concrete specimens under different working conditions, and synchronously acquire acoustic emission signals and stress-strain curve data;

[0054] A data preprocessing module, which is used to preprocess the acquired acoustic emission signals, obtain time, acoustic emission energy, amplitude and rise time data, and eliminate invalid data;

[0055] A data storage module, which is used to store the acoustic emission b-value, the processed acoustic emission signals, stress and strain data;

[0056] Graphical user interface module for data entry, process initiation, result display and graphical presentation;

[0057] The data processing module is used to extract the stored data and unify different data sources onto the stress-strain time axis through interpolation processing to obtain unified data;

[0058] An analysis module for testing unified data, obtaining the yield strength, complete failure time and strain of recycled concrete, and determining the start and end of the plastic phase;

[0059] The result output module is used to output the analysis results to the result display area of ​​the graphical user interface module for display.

[0060] Furthermore, the data acquisition module includes:

[0061] Axial compression load equipment, used to apply axial pressure to recycled concrete specimens and simultaneously collect stress and strain data;

[0062] The acoustic emission monitoring unit is used to record the occurrence time, acoustic emission energy, rise time and amplitude information of each acoustic emission signal during the loading process of recycled concrete under different confining pressures.

[0063] Furthermore, the data preprocessing module includes:

[0064] A data screening unit is used to remove the time point data where the acoustic emission energy and rise time are 0;

[0065] The data calculation unit is used to calculate the b-value of acoustic emission.

[0066] Further, the data calculation unit calculates the acoustic emission b value including:

[0067] Divide the acoustic emission signal into time periods according to the set time step;

[0068] Calculate the magnitude information in each time period;

[0069] The logarithmic function curve of magnitude and frequency was linearly fitted using the Gutenberg-Richter relationship to calculate the b value.

[0070] Furthermore, the graphical user interface module is constructed by MATLAB, including:

[0071] Execute button to start data processing;

[0072] Input box, used to enter the Excel file path and worksheet name;

[0073] Result display area, used to display analysis results;

[0074] A graphical display area for visualizing the stress-strain curve and the relationship between acoustic emission signals and time.

[0075] Furthermore, the data processing module includes:

[0076] A file reading unit for extracting acoustic emission cumulative energy, b-value, stress, and strain data from a specified Excel file through the readtable function in MATLAB;

[0077] An interpolation processing unit for unifying different data sources onto the stress-strain time axis through linear interpolation.

[0078] Furthermore, the analysis module includes:

[0079] A yield strength detection unit for calculating the yield strength, complete failure time, and strain of the material;

[0080] A plastic stage determination unit for determining the start and end points of the plastic stage through a sharp increase in acoustic emission cumulative energy and a significant decrease in the b-value.

[0081] Furthermore, the determination method of the plastic stage determination unit includes:

[0082] When the increment of the acoustic emission cumulative energy exceeds 50% of the historical maximum increment, it is determined that the acoustic emission cumulative energy has a significant sharp increase;

[0083] When the b-value drops by more than 0.2, it is determined that there is a significant drop in the b-value;

[0084] The first event of a sharp increase in acoustic emission cumulative energy or a drop in the b-value is determined as the start point of the plastic stage;

[0085] The last event of a sharp increase in acoustic emission cumulative energy or a drop in the b-value is determined as the end point of the plastic stage.

[0086] As Figure 7 shown, the operation of the device in this embodiment includes the following steps:

[0087] Apply an axial compressive load to the recycled concrete specimens under different working conditions, and simultaneously measure their acoustic emission signals and the compressive stress-strain curve of the material;

[0088] Output an Excel table of the measured time, cumulative acoustic emission energy value, acoustic emission b-value, stress, and strain.

[0089] The calculation steps of the acoustic emission b-value are as follows:

[0090] Use an acoustic emission monitoring system to record the occurrence time t and amplitude information A of each acoustic emission signal during the monotonic loading process of recycled concrete dB .

[0091] Set the time step \(T\), and divide the entire loading process into multiple consecutive time periods. Take the acoustic emission events in each time period of length \(T\) as a set of data, and calculate and statistically analyze their magnitude information \(M\) according to the following formula.

[0092] \(M = A\) dB / 20;

[0093] For each time period, set the magnitude gradient \(\Delta M\), divide the magnitude into \((M_{max}-M_{min}) / \Delta M\) magnitude intervals, calculate the acoustic emission frequency \(N\) in each magnitude interval. In Example 1, the maximum value of \(A\) dB is 100, so \(M\) is equal to 5, and the sampling frequency is 100. Perform a linear fit on the logarithmic function curve of magnitude and frequency according to the Gutenberg - Richter relationship and calculate the \(b\) value.

[0094] \(\lg N=m - n\times M\);

[0095] In the formula, \(m\) and \(n\) are constants obtained by linear fitting.

[0096] Use the least - squares method to calculate the \(b\) value for each time period according to the steps and obtain its evolution relationship with the loading time.

[0097] Build a graphical user interface through MATLAB, including: an execution button for starting data processing; an input box for inputting the worksheet name; a result display area for displaying the detection results; and a graphical display area for visualizing the stress - strain curve and acoustic emission signal.

[0098] Based on the graphical user interface, define the callback functions for file selection respectively. The callback functions for file selection, selectFilePathAE (cumulative acoustic emission energy data), selectFilePathb (acoustic emission \(b\) value), and selectFilePathStress (stress - strain data) will use the uigetfile function to open the file selection dialog box and display the path of the selected file on the corresponding button.

[0099] Define the callback function for running the detection. The file selection callback function runDetection is used to read the Excel data file paths and worksheet names of the acoustic emission cumulative energy data, \(b\) value data, and stress - strain data input by the user, and display their paths on the GUI interface, ensuring that all inputs are valid, otherwise pop up an error dialog box.

[0100] The detected_yield_strength detection function called is used to calculate the yield strength, complete failure time and strain of the material, and output the results to the result display area. The calculation process includes: calculating the surge value of the cumulative acoustic emission energy; calculating the decrease of the b value; finding the index of the first cumulative acoustic emission energy surge or b value decrease and selecting the earliest event, defining it as the starting point of the plastic stage; outputting the detection result of the starting point of the plastic stage; then finding the index of the last cumulative acoustic emission energy surge or b value decrease and selecting the latest event, defining it as the end point of the plastic stage; outputting the detection result of the end point of the plastic stage.

[0101] The specific steps are as follows:

[0102] Step 1: Specimen preparation and data collection. Select recycled concrete specimens with different working conditions and apply axial compressive loads to the specimens on the MTS equipment. During the loading process, use an acoustic emission sensor to collect acoustic emission signals in real time and record stress and strain values. These data will be stored in Excel format for subsequent processing and analysis. Among them, the acoustic emission signal acquisition data is preprocessed to eliminate signals with an energy value of 0 in the acoustic emission acquisition signal. Figure 2 and Figure 3 The acoustic emission monitoring system is used to record the occurrence time t and amplitude information A of each acoustic emission signal during the monotonic loading process of recycled concrete. dB .

[0103] The time step T is set, and the entire loading process is divided into multiple continuous time periods. The acoustic emission events in each time period of length T are taken as a set of data, and its magnitude information M is calculated and counted according to formula (1).

[0104] M=A dB / 20;

[0105] For each time period, a magnitude gradient ΔM is set, the magnitude is divided into (Mmax-Mmin) / ΔM magnitude intervals, and the acoustic emission frequency N in each magnitude interval is calculated. In this embodiment, A dB The maximum value is 100, so M is equal to 5 and the sampling frequency is 100. The logarithmic function curve of magnitude and frequency is linearly fitted by the Gutenberg-Richter relationship and the b value is calculated.

[0106] lgN=mn*M;

[0107] Where m and n are constants obtained by linear fitting.

[0108] The b value of each time period is calculated step by step using the least squares method, and its evolution relationship with the loading time is obtained.

[0109] Step 2: Graphical User Interface Development. Use MATLAB to build a Graphical User Interface (GUI). The interface design includes execution buttons, input boxes, result display areas, and graphical display areas, as Figure 4 shown. The user selects a data file through the input box and clicks the execution button to start data processing.

[0110] Step 3: Data Processing and Analysis. After the user selects a data file, the program calls the readtable function through a callback function to extract data on acoustic emission signals, b-values, stress, and strain from the specified Excel file and worksheet. The data at different time points are unified onto the stress-strain time axis through interpolation processing to ensure data comparability. Use readtable to read Excel data and unify the time axis through linear interpolation:

[0111] ae_energy_interp = interp1(ae_time_unique, ae_energy_unique, stress_strain_time, 'linear', 'extrap');

[0112] b_value_interp = interp1(b_time_unique, b_value_unique, stress_strain_time, 'linear', 'extrap');

[0113] Step 4: Define callback functions for file selection based on the graphical user interface respectively. The callback functions for file selection, selectFilePathAE (cumulative acoustic emission energy), selectFilePathb (acoustic emission b-value), and selectFilePathStress (stress-strain data), will use the uigetfile function to open a file selection dialog box and display the path of the selected file on the corresponding button.

[0114] Formula for calculating the incremental value of cumulative acoustic emission energy;

[0115] energy_diff = diff(ae_energy(i + 1) - ae_energy(i)); ae_energy(i + 1) is the cumulative acoustic emission energy at the (i + 1)-th moment; ae_energy(i) is the cumulative acoustic emission energy at the i-th moment; energy_diff is the growth value (first-order difference value) of the cumulative acoustic emission energy from the i-th moment to the (i + 1)-th moment. Code operations are performed based on the differences between different moments. When the increase in cumulative acoustic emission energy is greater than 1.0 times energy_diff, it is a significant surge point of cumulative acoustic emission energy. Define the threshold multiple for the acoustic emission energy surge as the parameter energy_threshold = 0.5, that is, assume that when the energy increment at a certain moment exceeds 50% of the historical maximum increment, it is regarded as a surge. The specific formula is:

[0116] energy_diff[i] > max(energy_diff) * energy_threshold

[0117] max(energy_diff) is the historical maximum increment of cumulative acoustic emission energy.

[0118] Step 5: Define the callback function for running the detection in the said file. Select the callback function runDetection to read the Excel data file path and worksheet name of the cumulative acoustic emission energy data, b-value data, and stress-strain data input by the user, and display its path on the GUI interface to ensure that all inputs are valid, otherwise pop up an error dialog box.

[0119] Step 6: Yield strength and failure detection. Call a specific detection function to calculate the yield strength, time to complete failure, and strain of the material, and output these results to the result display area. At the same time, the program can generate graphs of stress-strain curves and acoustic emission signals for the user to intuitively understand the mechanical properties of the material. The called detect_yield_strength detection function is used to calculate the yield strength, time to complete failure, and strain of the material, and output the results to the said result display area. The calculation process includes: calculating the increment value of cumulative acoustic emission energy; calculating the decrease in b-value; finding the index of the first cumulative acoustic emission energy surge or b-value decrease and selecting the earliest-occurring event, defining it as the starting point of the plastic stage; outputting the detection result of the starting point of the plastic stage; then finding the index of the last cumulative acoustic emission energy surge or b-value decrease and selecting the earliest-occurring event, defining it as the ending point of the plastic stage; outputting the detection result of the ending point of the plastic stage;

[0120] Calculating the decrease in b-value; b_diff = diff(b_value(i + 1) - b_value(i))

[0121] b_value(i + 1) is the b value at the (i + 1)-th moment; b_value(i) is the b value at the i-th moment, and b_diff is the change value of the b value from the i-th moment to the (i + 1)-th moment (first-order difference value). When the b_value drops by more than 0.2 at a certain point, a significant b value drop is considered to have occurred. Since the drop in the b value is usually associated with a larger fracture event and may correspond to the yield point. The determination logic is to find the index of the first cumulative acoustic emission energy surge or significant b value drop and select the earliest occurring event, which is defined as the starting point of the plastic stage.

[0122] Step 7: Result output and display. The processed results are exported in the form of an Excel table, and users can view and analyze the data at any time. In addition, the graphic area will be updated in real time to display the stress-strain curve and the acoustic emission signal graph, enhancing the user experience.

[0123] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A device for distinguishing the compressive plastic stage of recycled concrete based on acoustic emission and stress-strain analysis, characterized in that: include: The data acquisition module is used to apply axial compressive loads to recycled concrete specimens under different working conditions under different confining pressures, and synchronously collect acoustic emission signals and stress-strain curve data; The data preprocessing module is used to preprocess the collected acoustic emission signals, obtain the time, acoustic emission cumulative energy data, amplitude and rise time data, and eliminate invalid data; A data storage module, used for storing acoustic emission b-values, processed acoustic emission signals, stress and strain data; Graphical user interface module for data entry, process initiation, result display and graphical presentation; The data processing module is used to extract the stored data and unify different data sources onto the stress-strain time axis through interpolation processing to obtain unified data; An analysis module for testing unified data, obtaining the yield strength, complete failure time and strain of recycled concrete, and determining the start and end of the plastic phase; The result output module is used to output the analysis results to the result display area of ​​the graphical user interface module for display.

2. The device according to claim 1, characterized in that The data acquisition module comprises: Axial compression load equipment, used to apply axial pressure to recycled concrete specimens under different confining pressures and simultaneously collect stress and strain data; The acoustic emission monitoring unit is used to record the occurrence time, acoustic emission energy, rise time and amplitude information of each acoustic emission signal during the loading process of recycled concrete under different confining pressures.

3. The device according to claim 1, characterized in that The data preprocessing module comprises: A data screening unit is used to remove the time point data where the acoustic emission energy and rise time are 0; The data calculation unit is used to calculate the b value of acoustic emission.

4. The device according to claim 3, characterized in that The data calculation unit calculates the acoustic emission b value including: Divide the acoustic emission signal into time periods according to the set time step; Calculate the magnitude information in each time period; The logarithmic function curve of magnitude and frequency was linearly fitted using the Gutenberg-Richter relationship to calculate the b value.

5. The device according to claim 1, characterized in that The graphical user interface module is constructed by MATLAB and includes: Execute button to start data processing; Input box, used to enter the Excel file path and worksheet name; Result display area, used to display analysis results; Graphical display area for visualizing stress-strain curves and acoustic emission signals versus time.

6. The device according to claim 1, characterized in that The data processing module comprises: The file reading unit is used to extract the acoustic emission cumulative energy, b value, stress and strain data from the specified Excel file through the readtable function of MATLAB; The interpolation processing unit is used to unify different data sources onto the stress-strain time axis through linear interpolation.

7. The device according to claim 1, characterized in that The analysis module comprises: Yield strength detection unit, used to calculate the yield strength, complete failure time and strain of the material; The plastic stage determination unit is used to determine the start and end of the plastic stage by the surge in the accumulated energy of acoustic emission and the significant decrease in the b value.

8. The device according to claim 7, characterized in that The determination method of the plastic stage determination unit includes: When the increment of the accumulated energy of acoustic emission exceeds 50% of the historical maximum increment, it is judged that the accumulated energy of acoustic emission has increased significantly; When the b value drops by more than 0.2, it is judged as a significant b value drop; The first event of a surge in the accumulated energy of acoustic emission or a decrease in the b-value was determined as the starting point of the plastic stage; The last event of a surge in the accumulated energy of acoustic emission or a decrease in the b-value was determined as the end point of the plastic stage.

Citation Information

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