Nonlinear calibration method for high-temperature mechanical property test

Abstract

The invention 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: acquiring information data of a target material under different working conditions; the information data comprises half-life cycle load-displacement data; preprocessing the information data; performing data conversion based on a polynomial function model according to the preprocessed information data, and determining strain data; the strain data is used for realizing cross-working-condition unified representation of the data; the polynomial function model is a relation model which is constructed based on experimental data by adopting a least square method and is used for representing a strain-displacement calibration relation; the experimental data is strain-displacement data obtained after a set number of fatigue and creep fatigue tests are performed on the basis of various loading conditions. The invention aims to realize displacement and strain conversion and improve the conversion precision.

Description

Technical Field

[0001] The present application relates to the technical field of mechanical property testing of key components of high-temperature equipment, and in particular to a nonlinear calibration method for high-temperature mechanical property testing. Background Art

[0002] Many key materials in equipment such as automobile engines, high-pressure steam boilers, and steam turbines need to operate stably for a long time or for a certain period of time in a high-temperature environment. In addition to bearing static loads, these devices also need to deal with frequent dynamic loads during operation, such as frequent switching when the equipment is started and stopped, and temperature fluctuations over a large range. These complex working conditions usually cause low-cycle fatigue damage to the material, seriously affecting the service life and safety performance of the equipment. High-temperature low-cycle fatigue performance testing is usually completed using a constant-amplitude strain control testing machine, and the strain is monitored in real time with the help of a high-temperature ceramic extensometer. However, due to the limitation of its own gauge length, the ceramic extensometer has strict requirements on the size of the test material, which to a certain extent limits its scope of application.

[0003] Strain, as an important indicator reflecting the degree of material deformation, can directly reflect the behavioral characteristics of the material under complex loads. However, in actual testing, displacement is often measured first as a physical quantity that is easier to obtain. However, since the material exhibits significant nonlinearity 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 will be significantly affected by multiple factors such as temperature, strain amplitude, and load holding time. Existing research has not fully solved the problem of nonlinear calibration between displacement data and strain data, especially under complex load conditions such as multi-modal superimposed vibration or creep-fatigue interaction. How to achieve high-precision displacement and strain conversion still faces technical difficulties. Summary of the invention

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

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

[0006] The present application provides a nonlinear calibration method for high temperature mechanical properties testing, including:

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

[0008] Preprocessing the information data;

[0009] According to the preprocessed information data, data conversion is performed based on a polynomial function model to determine strain data; the strain data is used to achieve unified characterization 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 a set number of fatigue and creep fatigue tests are performed based on multiple loading conditions.

[0010] Optionally, preprocessing the information data specifically includes:

[0011] Performing denoising processing on the information data to obtain denoised data;

[0012] Normalizing the denoised data to obtain normalized information data;

[0013] The normalized information data is processed by removing outliers to obtain preprocessed information data.

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

[0015] Obtain experimental data;

[0016] Determine a design matrix and an observation data matrix according to the experimental data; the design matrix includes multiple loading conditions and multiple high-order combinations of the loading conditions; the observation data matrix includes: observation values ​​of strain-displacement data;

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

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

[0019] Using the least square method, the polynomial coefficients of the polynomial function are fitted based on the design matrix and the observation data matrix to obtain an optimal coefficient matrix;

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

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

[0022]

[0023] Among them, y(x; T, Δε, dt) is a polynomial function model; T is temperature; Δε is strain amplitude; dt is holding time; c n，ijk is the series expansion of the Nth-order coefficients of the polynomial, c n，ijkis a constant; x is displacement; n is the order number; I is the highest order of series expansion for temperature T; J is the highest order of series expansion for strain amplitude Δε; K is the highest order of series expansion for holding time dt; T i is the temperature of the i-th order of series expansion; (Δε) j is the strain amplitude of the jth order of series expansion; (dt) k is the dwell time of the kth order of series expansion; x n is the nth-order shift for the series expansion.

[0024] Optionally, the nonlinear calibration method for high temperature mechanical properties testing further includes:

[0025] Evaluating the accuracy of the data conversion using an error function or goodness of fit;

[0026] The expression of the error function is:

[0027]

[0028] The expression of 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 is the real data corresponding to the experimental data; is the output data of the polynomial function model; is the average value of the corresponding observation value in the experimental data; R 2 is the goodness of fit.

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

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

[0033] The present application provides a nonlinear calibration method for high-temperature mechanical properties testing, which obtains information data of target materials under different working conditions; the information data includes: half-life cycle load-displacement data; the information data is preprocessed; according to the preprocessed information data, data conversion is performed based on a polynomial function model to determine strain data; the strain data is used to achieve unified characterization of data across working conditions; the polynomial function model is a relationship model constructed based on experimental data using the least squares method to characterize the strain-displacement calibration relationship; the experimental data is based on a variety of loading conditions, and the strain-displacement data is obtained after a set number of fatigue and creep fatigue tests. By constructing a relationship model for characterizing the strain-displacement calibration relationship, that is, a polynomial function model, a high-precision nonlinear calibration relationship is determined by integrating multivariate conditions such as different temperatures, strain amplitudes, and holding times. And the least squares method is used for fitting, which can significantly improve the accuracy and standardization level of high-temperature mechanical properties testing. As a result, displacement and strain conversion can be achieved, and the conversion accuracy can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 A flow chart of the nonlinear calibration method for high temperature mechanical properties testing for this application;

[0036] Figure 2 is the material strain-displacement relationship diagram;

[0037] Figure 3 It is a schematic diagram of the operation steps of the nonlinear calibration method in practical application;

[0038] Figure 4 Schematic diagram of experimental data analysis results of high temperature creep fatigue test of MarM 248 nickel-based superalloy at 900℃ and total strain range set to 0.2%;

[0039] Figure 5 Schematic diagram of experimental data analysis results of high temperature creep fatigue test of MarM 248 nickel-based superalloy at 900℃ and total strain range set to 0.4%;

[0040] Figure 6 Schematic diagram of the experimental data analysis results of the high temperature creep fatigue test of MarM 248 nickel-based superalloy at 900℃ and the total strain range set to 0.6%;

[0041] Figure 7 Schematic diagram of experimental data analysis results of high temperature creep fatigue test of MarM 248 nickel-based superalloy at 900℃ and total strain range set to 0.8%;

[0042] Figure 8 Schematic diagram of experimental data analysis results of high temperature creep fatigue test of MarM 248 nickel-based superalloy at 900℃ and total strain range set to 1.0%;

[0043] Fig. 9 Schematic diagram of experimental data analysis results of high temperature creep fatigue test of MarM 248 nickel-based superalloy at 900℃ and total strain range set to 0.2% to 1.0%;

[0044] Fig.10 is the relationship diagram between equation coefficient and strain amplitude;

[0045] Fig.11 This is a comparison chart of the calibration results. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0047] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0048] In an exemplary embodiment, Figure 1 As shown, a nonlinear calibration method for high temperature mechanical properties testing is provided, comprising 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: According to the preprocessed information data, data conversion is performed based on the polynomial function model to determine the strain data. The strain data is used to achieve unified characterization of data across working conditions; the polynomial function model is a relationship model constructed based on experimental data using the least squares method to characterize the strain-displacement calibration relationship; the experimental data is based on multiple loading conditions, and is obtained by performing a set number of fatigue and creep fatigue tests. Strain data is used to achieve uniform characterization of data across working conditions; the polynomial function model is a relationship model constructed based on experimental data using the least squares method to characterize the strain-displacement calibration relationship; the experimental data is based on multiple loading conditions, and is obtained by performing a set number of fatigue and creep fatigue tests. Strain-displacement data.

[0052] In one embodiment, preprocessing the information data specifically includes:

[0053] The information data is denoised to obtain denoised data; the denoised data is normalized to obtain normalized information data; the normalized information data is subjected to outlier elimination 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 multiple loading conditions and high-order combinations of multiple loading conditions; the observation data matrix includes: observed values ​​of strain-displacement data. Loading conditions include: temperature, strain amplitude, and holding time.

[0056] Determine the material strain-displacement relationship diagram according to the experimental data; construct a polynomial function according to the material strain-displacement relationship diagram; use the least squares method 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; determine the polynomial function model based on the optimal coefficient matrix and the polynomial function.

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

[0058]

[0059] Among them, y(x; T, Δε, dt) is a polynomial function model; T is temperature; Δε is strain amplitude; dt is holding time; c n，ijk is the series expansion of the Nth-order coefficients of the polynomial, c n，ijk is a constant; x is displacement; n is the order number; I is the highest order of series expansion for temperature T; J is the highest order of series expansion for strain amplitude Δε; K is the highest order of series expansion for holding time dt; T i is the temperature of the i-th order of series expansion; (Δε) j is the strain amplitude of the jth order of series expansion; (dt) k is the dwell time of the kth order of series expansion; x n is the nth-order shift for the series expansion.

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

[0061] The accuracy of the data conversion is evaluated using an error function or goodness of fit; the expression of the error function is:

[0062]

[0063] The expression of 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 is the real data corresponding to the experimental data; is the output data of the polynomial function model; is the average value of the corresponding observation value in the experimental data; R 2 is the goodness of fit.

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

[0067] In practical applications, such as Figure 3 The steps shown include the following steps.

[0068] S1: Through a certain number of fatigue and creep fatigue tests, the 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) are obtained, that is, experimental data.

[0069] For the same material, the following tests are conducted while keeping the loading rate consistent:

[0070] a. Various strain amplitudes (ranging from low cycle fatigue to high cycle fatigue).

[0071] b. Multiple temperatures (covering high temperature service range).

[0072] c. Various load holding times (from short-term cycling to long-term creep endurance conditions).

[0073] During this process, different experimental equipment (such as servo-hydraulic fatigue testing machine, electric creep testing machine or other temperature-controlled loading devices) are allowed to be used 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 at different temperatures, strain amplitudes and holding times.

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

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

[0077] S23: Form a design matrix X and an observation data matrix Y, where X contains all input variables: temperature T, strain amplitude Δε, and holding time dt and their high-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 the optimal coefficient matrix A that minimizes the fitting error.

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

[0080]

[0081] Among them, a n (T, Δε, dt) is the Nth-order coefficient of the polynomial, which is a function of T, Δε, dt, and its expanded form is:

[0082]

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

[0084]

[0085] Design matrix X (i.e. Xijk ) and the observation data matrix Y is:

[0086]

[0087] in, is the temperature of the i-th order in the series expansion of the m-th experimental data; is the strain amplitude of the jth order in the series expansion of the mth experimental data; is the k-th order holding time of the series expansion in the m-th experimental data; is the nth order displacement in the mth experimental data for series expansion; s M is the strain in the mth experimental data. 1 ,s 2 ,…,s M ]′, the ' in the upper right corner is the transposition transformation of the observation data matrix Y.

[0088] The optimal coefficient matrix A is:

[0089]

[0090] Wherein, X′ is the transposition transformation of the design matrix X.

[0091] S3: Use the established polynomial function model to convert the displacement data or strain data of materials under different equipment and loading conditions 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 perform preprocessing based on the extracted data.

[0093] S32: According to the polynomial function model fitted in step S2, the displacement data under different working conditions are converted into corresponding strain data to achieve unified representation of 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 assessed using the goodness of fit:

[0097]

[0098] In the embodiment of the present application, the sample material used is MarM 248 nickel-based high-temperature alloy, which is a typical high-temperature structural material and is widely used in components such as aircraft engine turbine blades. The test parameters are selected according to the actual application environment. The high-temperature creep fatigue test is carried out at four temperature points of 750℃, 800℃, 850℃ and 900℃. The test equipment uses an Instron tester, and the verification test uses MTS equipment. The sample is in the shape of a round rod with a diameter of 6mm and an effective gauge length of 25mm. The loading method is strain control, the strain ratio is **-1** (symmetrical cyclic loading), the total strain range is set to 0.2%~1.0%, and the holding time is 0, 10s, 30s and 60s. Four conditions to fully characterize the stress relaxation and creep-fatigue behavior of the material.

[0099] The calibration method of this application is not limited to the above experimental parameters and working conditions. For other temperature conditions, strain-controlled fatigue tests or creep fatigue tests, the total strain range, loading rate, and holding time can also be adjusted according to actual needs. In addition, 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 of the strain-displacement relationship in the high-temperature mechanical properties test proposed in this application needs to first determine the nonlinear relationship described in step S2. The experimental data analysis results are shown in Figure 4-Figure 9 As shown. Under various temperature and strain amplitude conditions, the strain-displacement relationship conforms to the quadratic parabola relationship, and the goodness of fit R between the upper curve (loading stage) and the lower curve (unloading stage) is 2 All of them are over 0.99, showing high accuracy and consistency. At the same time, the results show that the larger the strain amplitude, the more obvious the nonlinearity of the strain-displacement relationship, reflecting the gradual enhancement of the plastic deformation and nonlinear behavior of the material under high temperature conditions.

[0101] In order to ensure the comparability of data exported by different experimental equipment, data preprocessing is required, including denoising, normalization, and outlier removal to ensure the accuracy and rationality of the data.

[0102] According to the test data, in this embodiment, the strain-displacement relationship is expressed by a quadratic polynomial function, and the specific form is: s = a·x 2 +b·x+c. a, b and c are all coefficients. The relationship between the function coefficient and the strain amplitude is shown in the figure below. Fig.10 As shown in the figure, the results show that the function coefficients show a certain regularity with the variation of strain amplitude and temperature, which verifies the effective description of nonlinear characteristics by this method.

[0103] In order to verify the accuracy of the strain-displacement nonlinear calibration relationship established, the established relationship was used to compare and analyze the verification data obtained by MTS equipment. The results are as follows: Fig.11 As shown in the figure, 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 solve the technical problems of strain measurement and flexible conversion of displacement data during the plastic deformation of metal materials under high temperature environment. First, it was found at the experimental research level 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, and this phenomenon has wide applicability across devices. Based on this, this application constructs a unified displacement-strain relationship mapping model at the model level, and establishes a high-precision nonlinear calibration relationship by integrating multivariate conditions such as different temperatures, strain amplitudes and holding times. Then, at the algorithm level, advanced multi-parameter optimization algorithms and nonlinear correction techniques are introduced to generate a universal displacement-strain conversion matrix, which significantly improves the accuracy and standardization level of high-temperature mechanical properties testing. Finally, this application provides important technical support for the quantitative characterization, model prediction and engineering application of metal material properties under complex load conditions.

[0105] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, 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 article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A nonlinear calibration method for high temperature mechanical properties testing, characterized in that: The nonlinear calibration method for high temperature mechanical properties testing includes: Obtain information data of the target material under different working conditions; the information data includes: half-life cycle load-displacement data; Preprocessing the information data; According to the preprocessed information data, data conversion is performed based on a polynomial function model to determine strain data; the strain data is used to achieve unified characterization 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 a set number of fatigue and creep fatigue tests are performed based on multiple loading conditions.

2. The nonlinear calibration method for high temperature mechanical properties testing according to claim 1, characterized in that: Preprocessing the information data specifically includes: Performing denoising processing on the information data to obtain denoised data; Normalizing the denoised data to obtain normalized information data; The normalized information data is processed by removing outliers to obtain preprocessed information data.

3. The nonlinear calibration method for high temperature mechanical properties testing according to claim 1, characterized in that: The method for determining the polynomial function model specifically includes: Obtain experimental data; Determine a design matrix and an observation data matrix according to the experimental data; the design matrix includes multiple loading conditions and multiple high-order combinations of the loading conditions; the observation data matrix includes: observation values ​​of strain-displacement data; Determine a material strain-displacement relationship diagram based on the experimental data; Constructing a polynomial function based on the material strain-displacement relationship diagram; Using the least square method, the polynomial coefficients of the polynomial function are fitted based on the design matrix and the observation data matrix to obtain an 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 properties testing according to claim 1, characterized in that: The expression of the polynomial function model is: Among them, y(x; T, Δε, dt) is a polynomial function model; T is temperature; Δε is strain amplitude; dt is holding time; c n，ijk is the series expansion of the Nth-order coefficients of the polynomial, c n，ijk is a constant; x is displacement; n is the order number; I is the highest order of series expansion for temperature T; J is the highest order of series expansion for strain amplitude Δε; K is the highest order of series expansion for holding time dt; T i is the temperature of the i-th order of series expansion; (Δε) j is the strain amplitude of the jth order of series expansion; (dt) k is the dwell time of the kth order of series expansion; x n is the nth-order shift for the series expansion.

5. The nonlinear calibration method for high temperature mechanical properties testing according to claim 1, characterized in that: The nonlinear calibration method for high temperature mechanical properties testing also includes: Evaluating the accuracy of the data conversion using an error function or goodness of fit; The expression of the error function is: The expression of 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 is the real data corresponding to the experimental data; is the output data of the polynomial function model; is the average value of the corresponding observation value in the experimental data; R 2 is the goodness of fit.

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

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