Nonlinear calibration method for high temperature mechanical property testing

Abstract

The application discloses a nonlinear calibration method for high-temperature mechanical property testing, and relates to the technical field of mechanical property testing of key components of high-temperature equipment. The method comprises the following steps: obtaining information data of a target material under different working conditions; the information data comprises half-life cycle load-displacement data; pre-processing the information data; based on the pre-processed information data, performing data conversion based on a polynomial function model to determine strain data; the strain data is used to realize cross-working-condition unified representation of data; the polynomial function model is a relationship model used to represent the strain-displacement calibration relationship, which is constructed based on experimental data by using a least square method; the experimental data is strain-displacement data obtained after a set number of fatigue and creep-fatigue tests are performed based on multiple loading conditions. The application aims to realize displacement and strain conversion and improve conversion accuracy.

Description

Technical Field

[0001] This application relates to the field of mechanical performance testing technology for key components of high-temperature equipment, and in particular to a nonlinear calibration method for high-temperature mechanical performance testing. Background Technology

[0002] Many critical materials in equipment such as automobile engines, high-pressure steam boilers, and steam turbines require stable operation at high temperatures for extended periods or for a certain time. During operation, these devices not only withstand static loads but also frequent dynamic loads, such as the frequent switching during equipment startup and shutdown, and large-scale temperature fluctuations. These complex operating conditions often lead to low-cycle fatigue failure of the materials, severely impacting the service life and safety performance of the equipment. High-temperature low-cycle fatigue performance testing is typically performed using a constant-amplitude strain-controlled testing machine, with real-time strain monitoring achieved using a high-temperature ceramic extensometer. However, the ceramic extensometer's gauge length limitation imposes strict requirements on the dimensions of the test material, which to some extent restricts its application range.

[0003] Strain, as an important indicator reflecting the degree of material deformation, directly reflects the material's behavior under complex loads. However, in actual testing, displacement, being a more readily obtainable physical quantity, is often measured first. However, due to the significant nonlinearity exhibited by materials under high temperature and complex load conditions, the relationship between strain and displacement is not a simple linear mapping. Especially under complex service conditions (such as high-temperature fatigue, creep fatigue, and their interactions), the strain-displacement relationship is significantly affected by various factors such as temperature, strain amplitude, and holding time. Existing research has not fully resolved the nonlinear calibration problem between displacement and strain data, particularly under complex load conditions such as multimodal superimposed vibration or creep-fatigue interactions. Achieving high-precision displacement-strain conversion remains a technical challenge. Summary of the Invention

[0004] The purpose of this application is to provide a nonlinear calibration method for high-temperature mechanical property testing, which can realize displacement-strain conversion and improve conversion accuracy.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] This application provides a nonlinear calibration method for high-temperature mechanical property testing, including:

[0007] Acquire information data of the target material under different working conditions; the information data includes: half-life cycle load-displacement data;

[0008] The information data is preprocessed;

[0009] Based on the preprocessed information data, data transformation is performed using a polynomial function model to determine strain data; the strain data is used to achieve a unified representation of data across working conditions; the polynomial function model is a relational model constructed based on experimental data using the least squares method to characterize the strain-displacement calibration relationship; the experimental data is strain-displacement data obtained after conducting a set number of fatigue and creep fatigue tests under various loading conditions.

[0010] Optionally, the information data is preprocessed, specifically including:

[0011] The information data is denoised to obtain denoised data;

[0012] The denoised data is normalized to obtain normalized information data;

[0013] Outlier removal is performed on the normalized information data to obtain preprocessed information data.

[0014] Optionally, the method for determining the polynomial function model specifically includes:

[0015] Obtain experimental data;

[0016] The design matrix and observation data matrix are determined based on the experimental data; the design matrix includes multiple loading conditions and higher-order combinations of the loading conditions; the observation data matrix includes observed values ​​of strain-displacement data.

[0017] Determine the material strain-displacement relationship diagram based on the experimental data;

[0018] Construct a polynomial function based on the material strain-displacement relationship diagram;

[0019] The least squares method is used to fit the polynomial coefficients of the polynomial function based on the design matrix and the observation data matrix to obtain the optimal coefficient matrix;

[0020] The polynomial function model is determined based on the optimal coefficient matrix and the polynomial function.

[0021] Optionally, the expression for the polynomial function model is:

[0022]

[0023] Where y(x; T, Δε, dt) is a polynomial function model; T is temperature; Δε is strain amplitude; dt is holding time; c n，ijk Let c be the series expansion of the Nth-order coefficients of the polynomial. n，ijkis a constant; x is displacement; n is the order number; I is the highest order of the series expansion at temperature T; J is the highest order of the series expansion at strain amplitude Δε; K is the highest order of the series expansion at holding time dt; T i Let be the temperature of the i-th order in the series expansion; (Δε) j Let dt be the strain amplitude of the j-th order in the series expansion. k x is the load time for the k-th order of the series expansion; n This represents the nth shift in the series expansion.

[0024] Optionally, the nonlinear calibration method for the high-temperature mechanical property test further includes:

[0025] The accuracy of the data transformation is evaluated using an error function or a goodness-of-fit score.

[0026] The expression for the error function is:

[0027]

[0028] The expression for the goodness of fit is:

[0029]

[0030] Where E is the mean square error; M is the total number of experimental data; m is the sequence number; ε m This corresponds to the actual data in the experimental data; This is the output data of the polynomial function model; R is the average of the corresponding observations in the experimental data; 2 The goodness of fit is denoted as .

[0031] Optionally, the loading conditions include: temperature, strain amplitude, and holding time.

[0032] According to the specific embodiments provided in this application, this application has the following technical effects:

[0033] This application provides a nonlinear calibration method for high-temperature mechanical property testing, acquiring information data of the target material under different working conditions. The information data includes: half-life cycle load-displacement data. The information data is preprocessed; based on the preprocessed information data, data transformation is performed using a polynomial function model to determine strain data. The strain data is used to achieve a unified characterization of the data across working conditions. The polynomial function model is a relational model constructed based on experimental data using the least squares method to characterize the strain-displacement calibration relationship. The experimental data is strain-displacement data obtained after conducting a set number of fatigue and creep fatigue tests under various loading conditions. By constructing a relational model to characterize the strain-displacement calibration relationship, i.e., a polynomial function model, and integrating multiple variables such as different temperatures, strain amplitudes, and holding times, a high-precision nonlinear calibration relationship is determined. Furthermore, the use of the least squares method for fitting significantly improves the accuracy and standardization level of high-temperature mechanical property testing. Thus, displacement-strain conversion can be achieved, and the conversion accuracy can be improved. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a flowchart of the nonlinear calibration method for high-temperature mechanical property testing in this application;

[0036] Figure 2 This is a strain-displacement diagram of the material.

[0037] Figure 3 This is a schematic diagram illustrating the operational steps of the nonlinear calibration method in practical applications;

[0038] Figure 4 A schematic diagram showing the experimental data analysis results of high-temperature creep fatigue tests on MarM 248 nickel-based superalloy at 900℃ with a total strain range of 0.2%.

[0039] Figure 5 A schematic diagram showing the experimental data analysis results of high-temperature creep fatigue tests on MarM 248 nickel-based superalloy at 900℃ with a total strain range of 0.4%.

[0040] Figure 6 A schematic diagram showing the experimental data analysis results of high-temperature creep fatigue tests on MarM 248 nickel-based superalloy at 900℃ with a total strain range set to 0.6%.

[0041] Figure 7 A schematic diagram showing the experimental data analysis results of high-temperature creep fatigue tests on MarM 248 nickel-based superalloy at 900℃ with a total strain range set to 0.8%.

[0042] Figure 8 A schematic diagram showing the experimental data analysis results of high-temperature creep fatigue tests on MarM 248 nickel-based superalloy at 900℃ with the total strain range set to 1.0%.

[0043] Figure 9 A schematic diagram showing the experimental data analysis results of high-temperature creep fatigue tests on MarM 248 nickel-based superalloy at 900℃ with a total strain range of 0.2% to 1.0%.

[0044] Figure 10 This is a graph showing the relationship between equation coefficients and strain amplitude.

[0045] Figure 11 This is a comparison chart of calibration results. Detailed Implementation

[0046] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0047] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] In one exemplary embodiment, such as Figure 1 As shown, a nonlinear calibration method for high-temperature mechanical property testing is provided, including the following steps.

[0049] Step 100: Obtain information data of the target material under different working conditions. The information data includes: half-life cycle load-displacement data.

[0050] Step 200: Preprocess the information data.

[0051] Step 300: Based on the preprocessed information data, perform data transformation using a polynomial function model to determine the strain data. The strain data is used to achieve a unified representation of the data across different working conditions; the polynomial function model is a relational model constructed based on experimental data using the least squares method to characterize the strain-displacement calibration relationship; the experimental data is strain-displacement data obtained after conducting a set number of fatigue and creep fatigue tests under various loading conditions.

[0052] In one embodiment, the information data is preprocessed, specifically including:

[0053] The information data is denoised to obtain denoised data; the denoised data is normalized to obtain normalized information data; and the normalized information data is subjected to outlier removal to obtain preprocessed information data.

[0054] In one embodiment, the method for determining the polynomial function model specifically includes:

[0055] Acquire experimental data; determine the design matrix and observation data matrix based on the experimental data; the design matrix includes various loading conditions and higher-order combinations of various loading conditions; the observation data matrix includes observed values ​​of strain-displacement data. Loading conditions include temperature, strain amplitude, and holding time.

[0056] The strain-displacement relationship diagram of the material is determined based on the experimental data; a polynomial function is constructed based on the strain-displacement relationship diagram; the polynomial coefficients of the polynomial function are fitted using the least squares method based on the design matrix and the observation data matrix to obtain the optimal coefficient matrix; the polynomial function model is determined based on the optimal coefficient matrix and the polynomial function.

[0057] The expression for the polynomial function model is:

[0058]

[0059] Where y(x; T, Δε, dt) is a polynomial function model; T is temperature; Δε is strain amplitude; dt is holding time; c n，ijk Let c be the series expansion of the Nth-order coefficients of the polynomial. n，ijk is a constant; x is displacement; n is the order number; I is the highest order of the series expansion at temperature T; J is the highest order of the series expansion at strain amplitude Δε; K is the highest order of the series expansion at holding time dt; T i Let be the temperature of the i-th order in the series expansion; (Δε) j Let dt be the strain amplitude of the j-th order in the series expansion. k x is the load time for the k-th order of the series expansion; n This represents the nth shift in the series expansion.

[0060] As an optional implementation method, the nonlinear calibration method for high-temperature mechanical property testing also includes:

[0061] The accuracy of the data transformation is evaluated using an error function or a goodness-of-fit score; the expression for the error function is:

[0062]

[0063] The expression for goodness of fit is:

[0064]

[0065] Where E is the mean square error; M is the total number of experimental data; m is the sequence number; ε m This corresponds to the actual data in the experimental data; This is the output data of the polynomial function model; R is the average of the corresponding observations in the experimental data; 2 The goodness of fit is denoted as .

[0066] This application provides a nonlinear calibration method for strain-displacement relationship in high-temperature mechanical property testing, which can significantly improve the accuracy and standardization of high-temperature mechanical property testing, and has the advantages of being intuitive, highly applicable, and highly accurate.

[0067] In practical applications, such as Figure 3 The steps shown are as follows.

[0068] S1: Obtain strain s-displacement x data of the same material under various loading conditions (including different temperatures T, different strain amplitudes Δε, and different holding times dt) through a certain number of fatigue and creep fatigue tests, which is the experimental data.

[0069] For the same material, under the condition of maintaining a consistent loading rate, the following test conditions were conducted:

[0070] a. Multiple strain amplitudes (from low-cycle fatigue to high-cycle fatigue range).

[0071] b. Multiple temperature ranges (covering the high-temperature service range).

[0072] c. Multiple hold times (from short-time cycles to long-time creep endurance conditions).

[0073] During this process, different experimental equipment (such as servo hydraulic fatigue testing machines, electric creep testing machines, or other temperature-controlled loading devices) are permitted to ensure the comprehensiveness and representativeness of the experimental data.

[0074] S2: Based on experimental data, a polynomial function model is established to characterize the strain-displacement calibration relationship of the material under different temperatures, strain amplitudes, and holding times.

[0075] S21: Based on the experimental data, plot the material strain-displacement relationship diagram, such as... Figure 2 As shown. Due to the non-linear nature of this relationship, the data is divided into an upper curve and a lower curve for independent processing.

[0076] S22: A polynomial function model is selected to represent the strain-displacement relationship, and a model is constructed to represent the relationship between the polynomial coefficients and the temperature T, the strain amplitude Δε, and the holding time dt.

[0077] S23: Form the design matrix X and the observation data matrix Y, where X contains all input variables: temperature T, strain amplitude Δε and holding time dt and their higher-order combinations, and Y contains the observed values ​​in the strain-displacement relationship.

[0078] S24: Use the least squares method to fit the polynomial coefficients and solve for the optimal coefficient matrix A that minimizes the fitting error.

[0079] The relationship between the coefficients of the polynomial function and temperature T, strain amplitude Δε, and holding time dt is expressed as follows:

[0080]

[0081] Among them, a n (T, Δε, dt) are the Nth-order coefficients of the polynomial, which are functions of T, Δε, and dt, and their expansion is as follows:

[0082]

[0083] Among them, c n，ijk Let c be the series expansion of the Nth-order coefficients of the polynomial. n，ijk I is a constant. I is the highest order of the series expansion at temperature T; J is the highest order of the series expansion at strain amplitude Δε; K is the highest order of the series expansion at holding time dt; T i Let be the temperature of the i-th order in the series expansion; (Δε) j Let dt be the strain amplitude of the j-th order in the series expansion. k x is the load time for the k-th order of the series expansion; n Let a be the nth order shift in the series expansion. n Substituting the series expansion of (T, Δε, dt) into the polynomial function, it can be expressed as:

[0084]

[0085] Design matrix X (i.e., Xijk The observed data matrix Y is:

[0086]

[0087] in, Let be the temperature of the i-th order in the series expansion of the m-th experimental data; Let J be the strain amplitude of the jth order in the series expansion of the m-th experimental data. Let be the load time of the kth order in the series expansion of the m-th experimental data; s represents the nth order displacement in the series expansion of the m-th experimental data; M Let Y be the strain in the m-th experimental data. Y = [s1, s2, ..., sm]. M In the diagram, the ' in the upper right corner represents the transpose of the observed data matrix Y.

[0088] The optimal coefficient matrix A is:

[0089]

[0090] Where X′ represents the transpose of the design matrix X.

[0091] S3: Using the established polynomial function model, the displacement or strain data of materials under different equipment and loading conditions are converted to achieve unified calibration and comparison of test data.

[0092] S31: Extract half-life cycle load-displacement data of the same material under different working conditions, and preprocess the extracted data.

[0093] S32: Based on the polynomial function model fitted in step S2, the displacement data under different working conditions are converted into corresponding strain data to achieve a unified representation of the data across working conditions.

[0094] The accuracy of the conversion can be evaluated using the following error function:

[0095]

[0096] The accuracy of the transformation can also be evaluated using goodness of fit:

[0097]

[0098] In this embodiment, the sample material used is MarM 248 nickel-based superalloy, a typical high-temperature structural material widely used in components such as turbine blades for aero-engines. Test parameters were selected based on the actual application environment. The specific high-temperature creep fatigue tests were conducted at four temperature points: 750℃, 800℃, 850℃, and 900℃. The testing equipment used was an Instron testing machine, and the verification tests were conducted using MTS equipment. The sample was a round bar with a diameter of 6mm and an effective gauge length of 25mm. The loading method was strain control, with a strain ratio of **-1** (symmetrical cyclic loading). The total strain range was set to 0.2%–1.0%, and the holding time was set to four conditions: 0s, 10s, 30s, and 60s, to comprehensively characterize the stress relaxation and creep-fatigue behavior of the material.

[0099] The calibration method described in this application is not limited to the experimental parameters and operating conditions mentioned above. For fatigue tests or creep fatigue tests under other temperature conditions and strain control, parameters such as the total strain range, loading rate, and holding time can be adjusted according to actual needs. Furthermore, the test data comes from different equipment (Instron and MTS), which can verify the universality of this method under cross-equipment conditions.

[0100] The nonlinear calibration method for strain-displacement relationship in high-temperature mechanical property testing proposed in this application requires first determining the nonlinear relationship described in step S2. The experimental data analysis results are as follows: Figures 4-9 As shown. Under various temperature and strain amplitude conditions, the strain-displacement relationship conforms to a quadratic parabola. The goodness of fit R between the upper curve (loading stage) and the lower curve (unloading stage) is... 2 All values ​​exceeded 0.99, demonstrating high accuracy and consistency. Furthermore, the results indicate that the larger the strain amplitude, the more pronounced the nonlinearity of the strain-displacement relationship, reflecting the gradual enhancement of plastic deformation and nonlinear behavior of the material under high-temperature conditions.

[0101] To ensure the comparability of data exported from different experimental devices, data preprocessing is required, including steps such as noise reduction, normalization, and outlier removal, to guarantee the accuracy and rationality of the data.

[0102] Based on the experimental data, the strain-displacement relationship is expressed using a quadratic polynomial function in this embodiment, specifically in the form: s = a·x 2 +b·x+c. a, b, and c are all coefficients. The relationship between the function coefficients and the strain amplitude is calculated using the least squares method for fitting. Figure 10 As shown, the results indicate that the function coefficients exhibit a certain regularity with changes in strain amplitude and temperature, verifying the effectiveness of this method in describing nonlinear characteristics.

[0103] To verify the accuracy of the established strain-displacement nonlinear calibration relationship, the established relationship was used to compare and analyze the verification data obtained from MTS equipment. The results are as follows: Figure 11 As shown, the error between the predicted displacement and the actual test data is within ±3%, indicating that the calibration method has high accuracy and can meet the needs of practical engineering applications.

[0104] This application aims to address the technical challenges of strain measurement and flexible conversion of strain data with displacement data during plastic deformation of metallic materials under high-temperature environments. Firstly, experimental research revealed that under the same temperature conditions, the larger the strain amplitude, the more significant the nonlinear relationship between the frame displacement and the extensometer strain reading. This phenomenon has broad applicability across different equipment. Based on this, this application constructs a unified displacement-strain relationship mapping model at the model level, establishing a high-precision nonlinear calibration relationship by integrating multiple variables such as different temperatures, strain amplitudes, and holding times. Next, at the algorithm level, advanced multi-parameter optimization algorithms and nonlinear correction techniques are introduced to generate a universally applicable displacement-strain conversion matrix, significantly improving the accuracy and standardization of high-temperature mechanical property testing. Finally, this application provides crucial technical support for the quantitative characterization, model prediction, and engineering applications of metallic material properties under complex loading conditions.

[0105] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A nonlinear calibration method for high-temperature mechanical property testing, characterized in that, The nonlinear calibration method for the high-temperature mechanical property test includes: Acquire information data of the target material under different working conditions; the information data includes: half-life cycle load-displacement data; The information data is preprocessed; Based on the preprocessed information data, data transformation is performed using a polynomial function model to determine strain data; the strain data is used to achieve a unified representation of data across working conditions; the polynomial function model is a relational model constructed based on experimental data using the least squares method to characterize the strain-displacement calibration relationship; the experimental data is strain-displacement data obtained after conducting a set number of fatigue and creep fatigue tests under various loading conditions. The expression for the polynomial function model is: Where y(x; T, Δε, dt) is a polynomial function model; T is temperature; Δε is strain amplitude; dt is holding time; c n，ijk Let c be the series expansion of the Nth-order coefficients of the polynomial. n，ijk is a constant; x is displacement; n is the order number; I is the highest order of the series expansion at temperature T; J is the highest order of the series expansion at strain amplitude Δε; K is the highest order of the series expansion at holding time dt; T i Let be the temperature of the i-th order in the series expansion; (Δε) j Let dt be the strain amplitude of the j-th order in the series expansion. k x is the load time for the k-th order of the series expansion; n This represents the nth shift in the series expansion.

2. The nonlinear calibration method for high-temperature mechanical property testing according to claim 1, characterized in that, Preprocessing the information data specifically includes: The information data is denoised to obtain denoised data; The denoised data is normalized to obtain normalized information data; Outlier removal is performed on the normalized information data to obtain preprocessed information data.

3. The nonlinear calibration method for high-temperature mechanical property testing according to claim 1, characterized in that, The method for determining the polynomial function model specifically includes: Obtain experimental data; The design matrix and observation data matrix are determined based on the experimental data; the design matrix includes multiple loading conditions and higher-order combinations of the loading conditions; the observation data matrix includes observed values ​​of strain-displacement data. Determine the material strain-displacement relationship diagram based on the experimental data; Construct a polynomial function based on the material strain-displacement relationship diagram; The least squares method is used to fit the polynomial coefficients of the polynomial function based on the design matrix and the observation data matrix to obtain the optimal coefficient matrix; The polynomial function model is determined based on the optimal coefficient matrix and the polynomial function.

4. The nonlinear calibration method for high-temperature mechanical property testing according to claim 1, characterized in that, The nonlinear calibration method for high-temperature mechanical property testing also includes: The accuracy of the data transformation is evaluated using an error function or a goodness-of-fit score. The expression for the error function is: The expression for the goodness of fit is: Where E is the mean square error; M is the total number of experimental data; m is the sequence number; ε m This corresponds to the actual data in the experimental data; This is the output data of the polynomial function model; R is the average of the corresponding observations in the experimental data; 2 The goodness of fit is denoted as .

5. The nonlinear calibration method for high-temperature mechanical property testing according to claim 1, characterized in that, The loading conditions include: temperature, strain amplitude, and holding time.

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