SN curve determination method based on test data probability statistics

Abstract

The invention provides an SN curve determination method based on test data probability statistics, and belongs to the field of material data processing, and the method comprises the steps: obtaining fatigue test data, and supposing that the fatigue test data accords with normal distribution; grouping the fatigue test data according to the stress level to obtain a plurality of fatigue test data groups of which the single-stage stress level corresponds to a plurality of fatigue cycle lives, and converting the stress and the fatigue cycle lives in the fatigue test data into a logarithmic value form; calculating a mean value and a standard deviation of the log values of the fatigue cycle life under each stage of stress level according to the log values of the fatigue cycle life; according to the mean value, the standard deviation and the standard normal deviation value of the fatigue cycle life logarithm values, calculating the probability fatigue cycle life of each stage of stress level under the given survival rate; and constructing a relational expression between the stress level under the given survival rate and the corresponding probability fatigue cycle life according to the linear relationship of the SN curve under the double logarithmic coordinates, and fitting the relational expression so as to determine the SN curve.

Description

Technical Field

[0001] The present application belongs to the field of material data processing, and in particular relates to a method for determining an SN curve based on probability statistics of test data. Background Art

[0002] Fatigue failure has become one of the important and common forms of structural failure. The load that causes fatigue failure is usually small, and the structural parts do not have obvious deformation before fatigue failure, which is not easy to detect. However, fatigue failure often causes more serious accidents. There are two main methods to determine the fatigue life of structures: test method and analysis method. The test method has reliable results but high cost, and is only applicable to important structural parts. The analysis method can estimate the fatigue life based on the estimation formula and material fatigue performance parameters combined with the correction factor. It has the advantages of low cost and short cycle. At the same time, the process is simple and the calculation accuracy meets the requirements of engineering use. The analysis results have certain guiding significance for structural design, so it is widely used in engineering.

[0003] The SN curve is the basis and premise for fatigue life analysis and prediction of structures, so the formulation of the SN curve is particularly important. The SN curve of a material is generally determined through experiments, and the SN curve is drawn by processing the fatigue test data of the specimen under symmetrical cyclic uniaxial tensile load. The conventional method uses the group method to test the finite fatigue life area, and the lifting method to test the infinite fatigue life area, and finally performs data fitting. However, since fatigue test data generally have a large dispersion, fatigue life and stress level are not one-to-one corresponding. The existing fatigue test data fitting method will cause the SN curve to be distorted and the accuracy is low. Summary of the invention

[0004] The purpose of the present application is to provide a method for determining an SN curve based on probability statistics of experimental data to solve or alleviate at least one problem in the background technology.

[0005] The technical solution of the present application is: a method for determining an SN curve based on probability statistics of test data, comprising: Fatigue test data are obtained, and assuming that the fatigue test data conforms to a normal distribution, the fatigue test data are grouped according to stress levels to obtain multiple fatigue test data groups corresponding to a single-level stress level and a number of fatigue cycle lives, and at the same time, the stress and fatigue cycle life in the fatigue test data are converted into logarithmic form; According to the logarithmic value of fatigue cycle life in fatigue test data, the mean and standard deviation of the logarithmic value of fatigue cycle life at each stress level are calculated; According to the mean, standard deviation and standard normal deviation of the logarithmic value of fatigue cycle life, the probability fatigue cycle life of each stress level under a given survival rate is calculated; According to the linear relationship of the SN curve in double logarithmic coordinates, a relationship expression between the stress level and its corresponding probabilistic fatigue cycle life under a given survival rate is constructed, and the SN curve is determined by fitting the relationship expression.

[0006] Preferably, the mean value of the logarithmic value of the fatigue cycle life satisfies: ; The standard deviation of the logarithmic value of the fatigue cycle life satisfies: ; In the formula, n i For the i Number of fatigue cycle life samples under graded stress level; For the i The first stress level j The logarithmic value of fatigue cycle life; For the i The mean value of the logarithmic value of fatigue cycle life under the graded stress level; For the i Standard deviation of the logarithm of fatigue cycle life at the same stress level.

[0007] Preferably, given the survival rate P The probability of fatigue cycle life meeting: ; In the formula, lg N i ( P ) is a given survival rate P Next i Logarithmic value of probabilistic fatigue cycle life at graded stress level; u is the standard normal deviation value; P ( u ) is a given survival rate that satisfies the standard normal deviation; e is a natural constant.

[0008] Preferably, the relational expression is fitted by a least squares method.

[0009] Preferably, the relational expression is: ; In the formula, A ( P )and B ( P ) is the coefficient, lg S is the logarithmic value of stress, lgN is the logarithmic value of fatigue cycle life.

[0010] Preferably, the coefficient A ( P ) and coefficients B ( P )satisfy: ; In the formula, For a given survival rate P The logarithmic mean of the probabilistic fatigue cycle life for all stress levels under is the logarithmic mean of all stress levels.

[0011] The SN curve determination method based on test data probability statistics of the present application regards the fatigue test data as a group of random variables, and uses probability statistics method to process the fatigue test data, so that the obtained SN curve is more in line with reality. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0013] Figure 1 This is a schematic diagram of the SN curve determination method based on probability statistics of experimental data in this application.

[0014] Figure 2 It is a scatter plot of fatigue test data in the embodiment of this application.

[0015] Figure 3 It is the standard normal deviation table in the embodiment of this application.

[0016] Figure 4 It is an SN curve generated based on probability statistics of experimental data in the embodiment of the present application. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application.

[0018] The present application provides a method for determining an SN curve based on probability statistics of test data. The method takes fatigue test data as the object, firstly obtains the basic parameters of the fatigue test data by using statistical methods and calculates the fatigue life of the structure under a given survival rate, and finally obtains an SN curve based on probability statistics of the test data by performing data fitting based on the least squares method. The method of the present application can be applied to the material fatigue characteristic parameter database of fatigue analysis software, thereby improving the accuracy and reliability of fatigue life prediction.

[0019] like Figure 1 As shown, the SN curve determination method based on test data probability statistics provided by the present application includes the following steps: S10, obtaining fatigue test data, ignoring the validity verification process of the fatigue test data, assuming that the fatigue test data conforms to the normal distribution and the sample size is large enough, grouping the fatigue test data according to the stress level to obtain multiple fatigue test data groups corresponding to a single-level stress level and a number of fatigue cycle lives, and at the same time converting the stress and fatigue cycle life in the fatigue test data into logarithmic form.

[0020] As shown in Table 1, the group method fatigue test data in this embodiment of the present application has been verified for data validity, and the stress (S) and fatigue cycle life (N) in the fatigue test data are converted into logarithmic form.

[0021] Table 1 Fatigue test data

[0022] like Figure 2 As shown, by plotting the above fatigue test data on an SN curve composed of discrete data points in a double logarithmic coordinate system, it can be seen that the SN curve is approximately linear.

[0023] As shown in Table 2, the above fatigue test data can be divided into multiple fatigue test data groups according to stress levels.

[0024] Table 2 Fatigue test data set under multiple stress levels

[0025] S20, calculate the mean value of the logarithmic value of fatigue cycle life at each stress level based on the logarithmic value of fatigue test data μ and standard deviation σ , the calculation method is: ; In the formula, n i For the i The number of fatigue cycle life samples under the first stress level, For the i The first stress level j The logarithmic value of fatigue cycle life, For the i The mean value of the logarithmic value of fatigue cycle life under the stress level, For the i Standard deviation of the logarithmic value of fatigue cycle life at the primary stress level; Table 3 shows the mean and standard deviation of the logarithmic values ​​of fatigue cycle life at 5 levels of stress in this embodiment of the present application.

[0026] Table 3 Mean and standard deviation of logarithmic values ​​of fatigue cycle life at various stress levels

[0027] S30, based on the mean, standard deviation and standard normal deviation of the logarithmic value of fatigue cycle life, calculate the survival rate of each stress level at a given P Probability of fatigue cycle life under: ; In the formula, lg N i ( P ) is a given survival rate P The logarithmic value of the probabilistic fatigue cycle life at the next i-th stress level; u is the standard normal deviation value, which can be obtained by querying in the standard normal deviation table; P ( u ) is a given survival rate that satisfies the standard normal deviation; e is a natural constant.

[0028] As shown in Table 4, the given survival rate in this embodiment of the present application is ( P =99.9%, P =90.0% and P =50.0%).

[0029] Table 4 Survival rate at various stress levels P Probabilistic fatigue cycle life under

[0030] S40, based on the linear relationship between the SN curves in double logarithmic coordinates, a given survival rate is constructed P The relationship between the stress level and its corresponding probabilistic fatigue cycle life is expressed as , according to the data in step S30, the least squares method is used to fit the relationship expression at a given survival rate P The corresponding coefficient A ( P ) and coefficients B ( P ), so that the SN curve can be determined. Among them, the coefficient A ( P ) and coefficients B ( P ) can be determined according to the following formula: ; In the formula, For a given survival rate P The logarithmic mean of the probabilistic fatigue cycle life for all stress levels under is the logarithmic mean of all stress levels.

[0031] Table 5 shows the coefficients corresponding to the given survival rates calculated in this embodiment. A ( P ) and coefficients B ( P ).

[0032] Table 5 Coefficients obtained by least squares fitting A ( P ) and coefficients B ( P )

[0033] like Figure 4 Shown is a schematic diagram of the fatigue test data and three SN curves based on the probability statistics of the test data obtained by the SN curve determination method of the present application in this embodiment of the present application being plotted in the same coordinate system. The SN curve determination method of the present application, on the basis of making full use of the test data and combining the SN curve obtained with a given survival rate, has a higher use value in fatigue analysis.

[0034] Fatigue life analysis generally requires the fatigue strength coefficient S and fatigue strength index b In this application, based on the above relationship expression and its coefficients, the coefficients A(P) and coefficient B(P) Further calculation to obtain the fatigue strength coefficient S f and fatigue strength index b , where the fatigue strength coefficient S f =10 A ( P ), fatigue strength index b = B ( P ), the final material fatigue properties can be expressed by the relation S=S f •N b Given.

[0035] The SN curve determination method based on test data probability statistics of the present application regards the fatigue test data as a group of random variables, and uses probability statistics method to process the fatigue test data, so that the obtained SN curve is more in line with reality.

[0036] The above is only a specific implementation 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 a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for determining SN curve based on probability statistics of experimental data, characterized in that: include: Fatigue test data are obtained, and assuming that the fatigue test data conforms to a normal distribution, the fatigue test data are grouped according to stress levels to obtain multiple fatigue test data groups corresponding to a single-level stress level and a number of fatigue cycle lives, and at the same time, the stress and fatigue cycle life in the fatigue test data are converted into logarithmic form; According to the logarithmic value of fatigue cycle life in fatigue test data, the mean and standard deviation of the logarithmic value of fatigue cycle life at each stress level are calculated; According to the mean, standard deviation and standard normal deviation of the logarithmic value of fatigue cycle life, the probability fatigue cycle life of each stress level under a given survival rate is calculated; According to the linear relationship of the SN curve in double logarithmic coordinates, a relationship expression between the stress level and its corresponding probabilistic fatigue cycle life under a given survival rate is constructed, and the SN curve is determined by fitting the relationship expression.

2. The SN curve determination method based on test data probability statistics according to claim 1, characterized in that: The mean value of the logarithmic value of the fatigue cycle life satisfies: ； The standard deviation of the logarithmic value of the fatigue cycle life satisfies: ； In the formula, n i For the i Number of fatigue cycle life samples under graded stress level; For the i The first stress level j The logarithmic value of fatigue cycle life; For the i The mean value of the logarithmic value of fatigue cycle life under the graded stress level; For the i Standard deviation of the logarithm of fatigue cycle life at the same stress level.

3. The SN curve determination method based on test data probability statistics according to claim 2, characterized in that: Given survival rate P The probability of fatigue cycle life meeting: ； In the formula, lg N i ( P ) is a given survival rate P Next i Logarithmic value of probabilistic fatigue cycle life at graded stress level; u is the standard normal deviation value; P ( u ) is a given survival rate that satisfies the standard normal deviation; e is a natural constant.

4. The SN curve determination method based on test data probability statistics according to claim 3, characterized in that: The relational expression is fitted by the least square method.

5. The SN curve determination method based on test data probability statistics according to claim 4, characterized in that: The relational expression is: ; In the formula, A ( P )and B ( P ) is the coefficient, lg S is the logarithmic value of stress, lg N is the logarithmic value of fatigue cycle life.

6. The SN curve determination method based on test data probability statistics according to claim 5, characterized in that: The coefficient A ( P ) and coefficients B ( P )satisfy: ； In the formula, For a given survival rate P The logarithmic mean of the probabilistic fatigue cycle life for all stress levels under is the logarithmic mean of all stress levels.

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