High-cycle fatigue life cycle psn curve evaluation method based on small sample data

Abstract

The application discloses a high-cycle fatigue full-life-cycle PSN curve evaluation method based on small sample data, and specifically relates to the following steps: in the limited life zone, the relationship between the fatigue life standard deviation and stress under each stress level is utilized, and the maximum likelihood method is fused to obtain a relatively accurate life standard deviation, and the PSN curve of the limited life zone is fitted; in the infinite life zone, the fatigue sample pairing number is determined by using the ascending and descending method, the relationship between the fatigue limit and the cycle number is combined, the maximum likelihood method is utilized to obtain the probability distribution of the fatigue limit; the PSN curve of the high-cycle fatigue full-life-cycle is obtained by combining the PSN curve of the limited life zone and the fatigue limit under the corresponding survival rate. Meanwhile, the VBA development software is used to realize the automatic calculation, the PSN curve fitting, and the visual display of the calculation and fitting results. The application can simultaneously cover the dispersion in the limited life zone and the infinite life zone, and the calculation method is simple and clear, and is suitable for engineering application.

Description

Technical Field

[0001] This invention pertains to high-cycle fatigue damage assessment technology, and particularly relates to a method for evaluating the full life cycle PSN curve of high-cycle fatigue based on small sample data. Background Technology

[0002] Key components of transportation vehicles such as high-speed trains and aircraft engines are often damaged by defects caused by external impacts, leading to high-cycle fatigue damage. Taking external impact damage as an example, it is affected by multiple factors such as impact velocity, impact angle, and impactor size, further exacerbating the dispersion of fatigue performance in critical structures. To ensure the safety, reliability, and economy of critical components in service, life assessment is typically conducted in engineering based on probabilistic fatigue life (PSN) curves.

[0003] Fitting the Probability of Non-Stress (PSN) curve for high-cycle fatigue typically faces two unavoidable challenges: handling small sample data and improving the accuracy of the probability of non-stress (SN) curve. Traditional methods require high-cycle fatigue tests at four stress levels, with at least 15 usable data points per stress level. This results in time-consuming and costly fatigue tests, failing to meet engineering application requirements. Therefore, in engineering practice, researchers often combine small sample data for fatigue characteristic assessment. Based on this small sample data, researchers introduce data methods such as heteroscedasticity regression, prior distribution, and sample information aggregation principles to further improve the fitting accuracy of the SN curve. This involves further exploring the potential distribution characteristics of the data to improve the accuracy of reliability analysis. However, in current technology assessments, PSN curve fitting generally focuses on solving the standard deviation within the finite life region, neglecting the dispersion effect in the infinite life region of high-cycle fatigue. For high-cycle fatigue performance evaluation, researchers typically distinguish between the finite life region and the infinite life region as two independent parts. Within the finite lifespan region, data analysis methods are used to obtain lifespan dispersion under different stresses and fit data under different survival rates to obtain probability subtraction number (SN) curves within the finite lifespan region. Finally, the relevant curves are extended to the infinite lifespan region to form the probability subtraction number (PSN) curves under the influence of partial dispersion. However, in the infinite lifespan region, researchers mainly focus on the dispersion of fatigue limit, lacking joint analysis with the dispersion in the finite lifespan region.

[0004] In summary, the dual bottlenecks of small sample data and insufficient fit of PSN curves based solely on the dispersion of the finite lifespan limit the fatigue performance evaluation of key components in engineering applications. Summary of the Invention

[0005] To address the above problems, this invention provides a method for evaluating the high-cycle fatigue full-life-cycle PSN curve based on small sample data.

[0006] The present invention provides a method for evaluating the high-cycle fatigue full-life-cycle PSN curve based on small sample data, comprising the following steps:

[0007] Step 1: Analysis of distributed parameters within the finite lifetime region.

[0008] Step 1.1: Within the finite life region, using the Basquin phenomenological model, the relationship between the number of cycles and the stress level of the failed specimen is characterized as follows:

[0009] (1)

[0010] In the formula: parameters m and C are material constants.

[0011] To facilitate linear fitting, the logarithm of the above equation is taken, and the linear relationship between stress and life is as follows:

[0012] (2)

[0013] In the formula: parameters A and B are material constants.

[0014] By combining the failure fatigue data under various stress levels and using the least squares method to fit the equation (2), parameters A and B with a survival rate of 50% are obtained, namely the median SN curve.

[0015] Step 1.2: Within the finite life region, assuming the logarithmic lifetime under each stress level follows a normal distribution, the probability density function f(lgN) is... ij The calculation formula is as follows:

[0016] (3)

[0017] Where: N ij For i-th order stress S i The number of cycles that caused the j-th sample to fail, parameter σ i For and μ i These represent the standard deviation and mean life under that stress level, respectively.

[0018] Step 1.3: The logarithmic life standard deviation σ of metallic materials satisfies a linear relationship with the stress level S, where S is the stress level i. i The corresponding expression for calculating the standard deviation is:

[0019] (4)

[0020] In the formula: parameter K is a material constant, the k-th stress is regarded as the reference stress, and the standard deviation σ k S serves as the benchmark for solving other standard deviations. k These represent the reference stress.

[0021] Step 1.4: When the stresses corresponding to the test data are arranged in ascending order and the minimum stress level is taken as stress level 1, the parameters K and σ1 retrieval formula are obtained based on the log-life normal distribution and the maximum likelihood method:

[0022] (5)

[0023] In the formula: k1…k n These represent the number of test data corresponding to stress levels 1 through n, respectively.

[0024] Step 1.5: Combining the search formulas for K and σ1 above, the search range for the two parameters is defined as follows:

[0025] The upper limit for searching σ1 for steel is 0.2, and the upper limit for searching K is 0.2 / (S). n -S1).

[0026] The initial value for parameter K is 10. -5 The parameter σ1 is initially retrieved with a value ≥ 10. -5 ×(S2-S1)

[0027] Considering that the number of iterations corresponding to the SN curve is ≥10 4 , record 10 4 The corresponding stress level and cycle life standard deviation are S s and σ s When σ is required s ≮10 -3 When the constraint function expression in the main function retrieval process is σ1-(S1-S), then the constraint function expression is σ1-(S1-S). s -10 -3 ≥0.

[0028] Step 1.6: Combining steps 1.1-1.5, obtain the global optimal solution for parameters K and σ1. Then, combining the linear relationship between standard deviation and stress level, obtain the standard deviation for each stress level. Finally, using the following formula, calculate the number of cycles lgN corresponding to stress level i under different survival rates P. (i,P) The calculation formula is as follows:

[0029] (6)

[0030] In the formula: λ P This represents the skewness of the standard normal distribution corresponding to the survival rate P.

[0031] Step 1.7: Combine the fatigue life corresponding to each stress level under different survival rates to obtain the corresponding probability-stress-life curve, that is, obtain the PSN curve fitting in the finite life region.

[0032] Step 2: Analysis of distributed parameters in the infinite lifetime region.

[0033] Step 2.1: When the cyclic load is small, the test specimen may fail or reach the fatigue limit without fracturing after a certain number of cycles. Using the rise-fall method, the stress levels and test life composition data of adjacent fractured and unfractured specimens are compared, i.e., (S... Fi N Fi ) and (S Si N L ) represent the stress and cycle number of the failed and non-failed samples in the i-th pair, respectively.

[0034] Step 2.2: For the i-th pair of paired specimens, the fatigue life N L The corresponding fatigue limit Sa i The solution formula is as follows:

[0035] (7)

[0036] Step 2.3: Combining the Basquin phenomenological model, the retrieval range of parameter m for each data set is as follows:

[0037] (8)

[0038] Where: m i The search range for parameter m corresponding to group i data.

[0039] When there are n sets of experimental data, take the maximum value of the lower limit of the retrieval range of parameter m for each set. xmax and the minimum value of the upper limit m smin The comprehensive search range of the component parameter m (m xmax m smin ).

[0040] Step 2.4: Within the infinite life region, assuming the fatigue limit strength follows a three-parameter Weibull distribution, then the probability density function f(Sa) is... i The calculation formula is as follows:

[0041] (9)

[0042] In the formula: Sa i Let i be the fatigue limit of the data set, b be the shape parameter, and S be the shape parameter. a S0 is the scale parameter, S0 is the position parameter, and the values ​​of the three parameters are within the range Sa. i > S0, Sa> S0, b>0, S0>0.

[0043] Step 2.5: Based on the Weibull distribution of the three parameters of the fatigue limit and the maximum likelihood method, obtain the retrieval formula for the three parameters:

[0044] (10)

[0045] Step 2.6: Combine b and S a The probability distribution function obtained from the three parameters S0 is as follows:

[0046] (11)

[0047] Using the same survival rate as in step 1.6, we can obtain the fatigue limit under different survival rates by combining equation (11).

[0048] Step 3: Software development based on VBA.

[0049] Step 3.1: Call the "Application.GetOpenFilename" function in VBA to manually open the target data file and select the corresponding worksheet.

[0050] Step 3.2: Calculate the life standard deviation under different stresses using professional data analysis software based on VBA.

[0051] Step 3.2.1: Solve for the parameters of the median SN curve.

[0052] (1) Combining the life and stress data in the high-cycle fatigue test data, call the “Application.Worksheet Function.slope” and “Application.WorksheetFunction.intercept” functions in VBA to solve for the slope and intercept of the median SN curve.

[0053] (2) Combining the slope and intercept of the median SN curve, the median lifetime vector and cycle number 10 corresponding to each stress are obtained. 4 The corresponding stress value.

[0054] Step 3.2.2: Analyze the calling and running of the analysis software.

[0055] (1) Call the “optimoptions” and “fmincon” of the analysis software and write a program to solve for the standard deviation and parameter K under minimum stress.

[0056] (2) Call the VBA function “Application.GetOpenFilename” to manually select the script file of the analysis software.

[0057] (3) Call the VBA “batContent” function to create a batch file and convert the VBA vectors into the analysis software for calculation.

[0058] (4) Call the VBA functions “shell” and “Workbooks.Open” respectively to run the analysis software and return the solution results.

[0059] Step 3.2.3: Based on the linear relationship between standard deviation and stress level, obtain the standard deviation corresponding to each stress level.

[0060] Step 3.3: Calculate the probability distribution of fatigue limit using professional data analysis software based on VBA.

[0061] Step 3.3.1: In the test data table, call the “targetSheet.Cells” function in VBA to import the fatigue limit test data into VBA.

[0062] Step 3.3.2: Analyze the calling and running of the software.

[0063] (1) Call the “optimoptions” and “fmincon” functions in the analysis software to solve for shape parameters, scale parameters, SN curve exponent and position parameters.

[0064] (2) Call the “Application.GetOpenFilename” function in VBA to manually select the script file of the analysis software.

[0065] (3) Call the “batContent” function in VBA to create a batch file and convert the VBA vectors into the analysis software for calculation.

[0066] (4) Call the VBA functions “shell” and “Workbooks.Open” respectively to run the analysis software and return the solution results.

[0067] Step 3.4: Analyze the SN curves at each survival rate.

[0068] (1) Call “ExcelBasedNormSInv” in VBA to calculate the deviation corresponding to the survival rate and the life corresponding to each stress.

[0069] (2) Call the “Application.WorksheetFunction.slope” and “Application.Worksheet Function.intercept” functions in VBA to obtain the slope and intercept of the SN curve under different survival rates.

[0070] Step 3.5: Exporting data processing results: including the standard deviation of life under each stress, the slope and intercept under different survival rates, the life corresponding to each stress, the number of cycles corresponding to the fatigue limit, and the fatigue limit.

[0071] Step 3.6: Plot the PSN curve.

[0072] Step 3.6.1: Match a suitable coordinate system range.

[0073] (1) Combining the maximum stress, minimum stress, maximum number of cycles and minimum number of cycles in the test data, call the “Select Case” function in VBA to solve the maximum and minimum values ​​of the X and Y coordinates in stages.

[0074] (2) Call the VBA functions “targetSheet.ChartObjects.Add”, “MinimumScale” and “MaximumScale” to create the chart and assign the maximum and minimum values ​​of the X and Y axes respectively.

[0075] Step 3.6.2: Plot the PSN curves under different survival rates.

[0076] (1) Call the “chartObj.chart.SeriesCollection.NewSeries” and “xlXYScatter SmoothNoMarkers” functions in VBA to generate SN curves for each survival rate, including finite lifetime region and infinite lifetime region.

[0077] (2) Call the “Int(Rnd * 256)” and “Format.Line.ForeColor.RGB” functions in VBA to set different line colors and assign them to curves with different survival rates to distinguish SN curves with different survival rates.

[0078] The beneficial technical effects of this invention compared to the prior art are as follows:

[0079] 1. This invention combines the normal distribution of fatigue life under different stress levels in the finite life region and the three-parameter Weibull distribution of fatigue limit in the infinite life region to obtain PSN curves covering both the finite and infinite life regions. This can fully reflect the dispersion of fatigue life in different regions and also provide a basis for probability assessment in different regions.

[0080] 2. In the finite life region and the infinite life region, this invention combines the relationship between life standard deviation and stress and the relationship between fatigue limit and number of cycles, respectively, selects a more reasonable distribution model and integrates the maximum likelihood method to obtain the globally optimal distribution parameter retrieval, ensuring the uniqueness of parameter solution, avoiding the limitations of local optimal solutions, and improving the accuracy of reliability assessment.

[0081] 3. This invention uses the maximum likelihood method to solve the standard deviation in different regions and gives a clear search range, which is suitable for the processing requirements of small sample data and reduces the demand for experimental data and experimental costs.

[0082] 4. This invention is based on the VBA development environment to complete the software development of the automated calculation process, which avoids tedious manual calculations and realizes the integration of experimental data processing, curve fitting and result display, which significantly improves the engineering application value of this invention. Attached Figure Description

[0083] Figure 1 This is a flowchart of the high-cycle fatigue full-life-cycle PSN curve evaluation method based on small sample data according to the present invention.

[0084] Figure 2 This refers to the human-computer interaction page of the software.

[0085] Figure 3 This is a secondary processing of data for fatigue limit reliability analysis.

[0086] Figure 4 This is a human-computer interaction page for the solution results based on data.

[0087] Figure 5 These are the parameters of the median SN curve obtained using VBA software.

[0088] Figure 6 These are the parameters of the SN curve under the required survival rate, obtained using VBA software.

[0089] Figure 7 The results show the comparison between the MLA method and the traditional TGM method.

[0090] Figure 8 The results show the comparison between the MLA method and the traditional BSIM method. Detailed Implementation

[0091] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0092] This invention proposes a method for evaluating the full lifecycle PSN curve based on small sample data, and combines it with VBA to develop dedicated software to automate the data analysis and curve fitting process. This method can simultaneously cover the dispersion in both finite and infinite lifecycle regions, and the calculation method is simple and clear, making it suitable for engineering applications.

[0093] The flowchart of the high-cycle fatigue full-life-cycle PSN curve evaluation method based on small sample data of the present invention is as follows: Figure 1 As shown, the specific steps include:

[0094] Step 1: Analysis of distributed parameters within the finite lifetime region.

[0095] Step 1.1: Within the finite life region, using the Basquin phenomenological model, the relationship between the number of cycles and the stress level of the failed specimen is characterized as follows:

[0096] (1)

[0097] In the formula: parameters m and C are material constants.

[0098] To facilitate linear fitting, the logarithm of the above equation is taken, and the linear relationship between stress and life is as follows:

[0099] (2)

[0100] In the formula: parameters A and B are material constants.

[0101] By combining the failure fatigue data under various stress levels and using the least squares method to fit the equation (2), parameters A and B with a survival rate of 50% are obtained, namely the median SN curve.

[0102] Step 1.2: Within the finite life region, assuming the logarithmic lifetime under each stress level follows a normal distribution, the probability density function f(lgN) is... ij The calculation formula is as follows:

[0103] (3)

[0104] Where: N ij For i-th order stress S i The number of cycles that caused the j-th sample to fail, parameter σ i For and μ i These represent the standard deviation and mean life under that stress level, respectively.

[0105] Step 1.3: The logarithmic life standard deviation σ of metallic materials satisfies a linear relationship with the stress level S, where S is the stress level i. i The corresponding expression for calculating the standard deviation is:

[0106] (4)

[0107] In the formula: parameter K is a material constant, the k-th stress is regarded as the reference stress, and the standard deviation σ k S serves as the benchmark for solving other standard deviations. k These represent the reference stress.

[0108] Step 1.4: When the stresses corresponding to the test data are arranged in ascending order and the minimum stress level is taken as stress level 1, the parameters K and σ1 retrieval formula are obtained based on the log-life normal distribution and the maximum likelihood method:

[0109] (5)

[0110] In the formula: k1…k n These represent the number of test data corresponding to stress levels 1 through n, respectively.

[0111] Step 1.5: Combining the search formulas for K and σ1 above, the search range for the two parameters is defined as follows:

[0112] The upper limit for searching σ1 for steel is 0.2, and the upper limit for searching K is 0.2 / (S). n -S1).

[0113] The initial value for parameter K is 10. -5 The parameter σ1 is initially retrieved with a value ≥ 10. -5 ×(S2-S1)

[0114] Considering that the number of iterations corresponding to the SN curve is ≥10 4 , record 10 4 The corresponding stress level and cycle life standard deviation are S s and σ s When σ is required s ≮10 -3 When the constraint function expression in the main function retrieval process is σ1-(S1-S), then the constraint function expression is σ1-(S1-S). s -10 -3 ≥0.

[0115] Step 1.6: Combining steps 1.1-1.5, obtain the global optimal solution for parameters K and σ1. Then, combining the linear relationship between standard deviation and stress level, obtain the standard deviation for each stress level. Finally, using the following formula, calculate the number of cycles lgN corresponding to stress level i under different survival rates P. (i,P) The calculation formula is as follows:

[0116] (6)

[0117] In the formula: λ P This represents the skewness of the standard normal distribution corresponding to the survival rate P.

[0118] Step 1.7: Combine the fatigue life corresponding to each stress level under different survival rates to obtain the corresponding probability-stress-life curve, that is, obtain the PSN curve fitting in the finite life region.

[0119] Step 2: Analysis of distributed parameters in the infinite lifetime region.

[0120] Step 2.1: When the cyclic load is small, the test specimen may fail or reach the fatigue limit without fracturing after a certain number of cycles. Using the rise-fall method, the stress levels and test life composition data of adjacent fractured and unfractured specimens are compared, i.e., (S... Fi N Fi ) and (S Si N L ) represent the stress and cycle number of the failed and non-failed samples in the i-th pair, respectively.

[0121] Step 2.2: For the i-th pair of paired specimens, the fatigue life N L The corresponding fatigue limit Sa i The solution formula is as follows:

[0122] (7)

[0123] Step 2.3: Combining the Basquin phenomenological model, the retrieval range of parameter m for each data set is as follows:

[0124] (8)

[0125] Where: m i The search range for parameter m corresponding to group i data.

[0126] When there are n sets of experimental data, take the maximum value of the lower limit of the retrieval range of parameter m for each set. xmax and the minimum value of the upper limit m smin The comprehensive search range of the component parameter m (m xmax m smin ).

[0127] Step 2.4: Within the infinite life region, assuming the fatigue limit strength follows a three-parameter Weibull distribution, then the probability density function f(Sa) is... i The calculation formula is as follows:

[0128] (9)

[0129] In the formula: Sa i Let i be the fatigue limit of the data set, b be the shape parameter, and S be the shape parameter. a S0 is the scale parameter, S0 is the position parameter, and the values ​​of the three parameters are within the range Sa. i > S0, Sa> S0, b>0, S0>0.

[0130] Step 2.5: Based on the Weibull distribution of the three parameters of the fatigue limit and the maximum likelihood method, obtain the retrieval formula for the three parameters:

[0131] (10)

[0132] Step 2.6: Combine b and S a The probability distribution function obtained from the three parameters S0 is as follows:

[0133] (11)

[0134] Using the same survival rate as in step 1.6, we can obtain the fatigue limit under different survival rates by combining equation (11).

[0135] Step 3: Software development based on VBA.

[0136] Step 3.1: Call the "Application.GetOpenFilename" function in VBA to manually open the target data file and select the corresponding worksheet.

[0137] Step 3.2: Calculate the life standard deviation under different stresses using professional data analysis software based on VBA.

[0138] Step 3.2.1: Solve for the parameters of the median SN curve.

[0139] By combining the life and stress data from high-cycle fatigue tests, the VBA functions "Application.Worksheet Function.slope" and "Application.WorksheetFunction.intercept" are called to solve for the slope and intercept of the median SN curve.

[0140] By combining the slope and intercept of the median SN curve, the median lifetime vector corresponding to each stress and the stress value corresponding to the cycle number 104 are obtained.

[0141] Step 3.2.2: Analyze the calling and running of the analysis software.

[0142] (1) Call the “optimoptions” and “fmincon” of the analysis software and write a program to solve for the standard deviation and parameter K under minimum stress.

[0143] (2) Call the VBA function “Application.GetOpenFilename” to manually select the script file of the analysis software.

[0144] (3) Call the VBA “batContent” function to create a batch file and convert the VBA vectors into the analysis software for calculation.

[0145] (4) Call the VBA functions “shell” and “Workbooks.Open” respectively to run the analysis software and return the solution results.

[0146] Step 3.2.3: Based on the linear relationship between standard deviation and stress level, obtain the standard deviation corresponding to each stress level.

[0147] Step 3.3: Calculate the probability distribution of fatigue limit using professional data analysis software based on VBA.

[0148] Step 3.3.1: In the test data table, call the “targetSheet.Cells” function in VBA to import the fatigue limit test data into VBA.

[0149] Step 3.3.2: Analyze the calling and running of the software.

[0150] (1) Call the “optimoptions” and “fmincon” functions in the analysis software to solve for shape parameters, scale parameters, SN curve exponent and position parameters.

[0151] (2) Call the “Application.GetOpenFilename” function in VBA to manually select the script file of the analysis software.

[0152] (3) Call the “batContent” function in VBA to create a batch file and convert the VBA vectors into the analysis software for calculation.

[0153] (4) Call the VBA functions “shell” and “Workbooks.Open” respectively to run the analysis software and return the solution results.

[0154] Step 3.4: Analyze the SN curves at each survival rate.

[0155] (1) Call “ExcelBasedNormSInv” in VBA to calculate the deviation corresponding to the survival rate and the life corresponding to each stress.

[0156] (2) Call the “Application.WorksheetFunction.slope” and “Application.Worksheet Function.intercept” functions in VBA to obtain the slope and intercept of the SN curve under different survival rates.

[0157] Step 3.5: Exporting data processing results: including the standard deviation of life under each stress, the slope and intercept under different survival rates, the life corresponding to each stress, the number of cycles corresponding to the fatigue limit, and the fatigue limit.

[0158] Step 3.6: Plot the PSN curve.

[0159] Step 3.6.1: Match a suitable coordinate system range.

[0160] (1) Combining the maximum stress, minimum stress, maximum number of cycles and minimum number of cycles in the test data, call the “Select Case” function in VBA to solve the maximum and minimum values ​​of the X and Y coordinates in stages.

[0161] (2) Call the VBA functions “targetSheet.ChartObjects.Add”, “MinimumScale” and “MaximumScale” to create the chart and assign the maximum and minimum values ​​of the X and Y axes respectively.

[0162] Step 3.6.2: Plot the PSN curves under different survival rates.

[0163] (1) Call the “chartObj.chart.SeriesCollection.NewSeries” and “xlXYScatter SmoothNoMarkers” functions in VBA to generate SN curves for each survival rate, including finite lifetime region and infinite lifetime region.

[0164] (2) Call the “Int(Rnd * 256)” and “Format.Line.ForeColor.RGB” functions in VBA to set different line colors and assign them to curves with different survival rates to distinguish SN curves with different survival rates.

[0165] Based on the above program development, the following were completed: extraction of experimental data, writing and calling programs to solve the standard deviation of each stress in the data analysis software, writing and calling programs to solve the fatigue limit probability distribution in the data analysis software, exporting data processing results, and fitting PSN curves for two lifetime intervals under each survival rate.

[0166] Furthermore, considering the software usage requirements and result retrieval needs, the human-computer interaction interface design based on VBA software will be as follows: Figure 2 As shown in the figure, the human-computer interaction page in the software mainly includes the input of the required survival rate, the solution of the standard deviation and the display of the fatigue limit reliability solution results, and the save path of the data processing results. The interaction page is simple and clear, avoiding cumbersome operations and path viewing, and improving the engineering application value of the software.

[0167] Step 4: Solve for the probability curve of the entire life cycle.

[0168] Step 4.1: When the survival rate is constant, combine the solution process in Step 1 to obtain the SN curve of the finite life region under that survival rate; combine the solution process in Step 2 to obtain the fatigue limit in the infinite life under that survival rate.

[0169] Step 4.2: Based on the SN curve within the finite life and the fatigue limit within the infinite life region, extend the SN curve towards the low stress region until the fatigue limit stress level is reached. Then, keep the stress value of the SN curve unchanged and continuously increase the life value, i.e., extend it horizontally to obtain the PSN curve in the entire domain.

[0170] Example:

[0171] Taking the fatigue test of EA4T axle steel specimen (with impact defects) as an example, the PSN curve fitting method (MLA) for the whole life region is used for data processing, and the fitting results are compared with those of the traditional group method (TGM) and sample information aggregation principle (BSIM).

[0172] The experimental data obtained based on the experimental process are shown in Table 1.

[0173] Table 1 Experimental Data

[0174]

[0175] Based on the experimental data in Table 1, secondary data processing was performed using the elevation and stabilization method, as follows: Figure 3 As shown, this is to further solve for the fatigue limit dispersion.

[0176] Combination Figure 3 The data pairings for fatigue limit calculation are shown in Table 2.

[0177] Table 2 Data pairing table for fatigue limit solution

[0178]

[0179] Based on the above data, the processed software human-computer interaction page is obtained as follows: Figure 4 As shown. By Figure 4 It can be seen that the analytical values ​​of the life standard deviation σ1 and parameter K corresponding to the minimum stress level are 0.1605 and 5.3 × 10, respectively. -4 .

[0180] Combining the calculation process of traditional methods (such as TGM, BSIM), manually recalculate the median and standard deviation of the lifetime corresponding to each stress and compare them with... Figure 4 The results of the MLA method are shown in Table 3.

[0181] Table 3 Distribution parameters obtained by different calculation methods

[0182]

[0183] Depend on Figure 4It can be seen that the fatigue limit probability distribution parameters, shape parameter b, and scale parameter S, are obtained. a The position parameters S0 are 46.9, 377, and 25.9 respectively, such as... Figure 4 As shown, the probability distribution function of the fatigue limit is as follows:

[0184] (12)

[0185] Depend on Figure 4 It can be seen that, in addition to the median SN curve, it is also necessary to solve for the SN curves corresponding to survival rates of 2.5% and 97.5%, respectively. The experimental data points and the relevant PSN curves should be plotted on the human-computer interaction page, as shown below. Figure 4 The diagram shows the inflection points (fatigue limits), slopes, and intercepts of three SN curves, as follows: Figure 5 and Figure 6 As shown. Combining the TGM and BSIM calculation results, the SN curves corresponding to survival rates of 2.5% and 97.5% are obtained and compared with the MLA calculation method as follows:

[0186] a) TGM method

[0187] (13)

[0188] b) BSIM method

[0189] (14)

[0190] c) MLA method

[0191] (15)

[0192] To further compare the fitting results of the method of this invention with those of two traditional methods, the relevant PSN curves are plotted as follows: Figure 7 and Figure 8 As shown.

[0193] Figure 7 and Figure 8 It includes experimental data, the calculation method of this invention, and the PSN curve predicted by traditional calculation methods. Figure 7 and Figure 8It is known that in traditional methods, TGM (Total Generalized Metrics) cannot reflect the trend of life dispersion gradually increasing with decreasing stress within the finite life region, nor can it reflect the influence of fatigue limit dispersion on the PSN curve. While BSIM (Browser-Signaled Simulation) reflects the trend of life dispersion within the finite life region to some extent, its dispersion band cannot cover experimental data with large dispersion, meaning it does not perform a global dispersion coefficient search. Therefore, its optimal solution carries the risk of finding a local optimum, and it also fails to reflect the influence of fatigue limit dispersion on the PSN curve. In contrast, this patented calculation method uses the maximum likelihood method to perform a global search of dispersion coefficients in both the finite and infinite life regions, combining the dispersion in both regions to obtain a comprehensive solution for the PSN curve covering the entire life region. This not only reflects the relationship between dispersion and stress magnitude in the finite life region and achieves global coverage of experimental data through the dispersion band through global search, but also integrates the influence of fatigue life within the finite life region and fatigue limit dispersion within the infinite life region, improving the accuracy of PSN curve fitting. Furthermore, considering the small sample size of the experimental data, this patent evaluation method can still guarantee the accuracy of the PSN curve and avoid repeated equivalence of experimental data, indicating that the calculation method can reduce the need for small sample data and the complexity of the calculation process. In addition, combined with VBA software development, the calculation of this patent evaluation method can be automated, avoiding repeated manual iterations and tedious calculation processes, further enhancing the engineering application value of this method.

Claims

1. A method for evaluating the high-cycle fatigue full-life-cycle PSN curve based on small sample data, characterized in that, Includes the following steps: Step 1: Analysis of distributed parameters within the finite lifetime region; Step 1.1: Within the finite life region, using the Basquin phenomenological model, the relationship between the number of cycles and the stress level of the failed specimen is characterized as follows: （1） In the formula: parameters m and C are material constants; To facilitate linear fitting, the logarithm of the above equation is taken, and the linear relationship between stress and life is as follows: （2） In the formula: parameters A and B are material constants; By combining the failure fatigue data under various stress levels and using the least squares method to fit the equation (2), parameters A and B with a survival rate of 50% are obtained, namely the median SN curve. Step 1.2: Within the finite life region, assuming the logarithmic lifetime under each stress level follows a normal distribution, the probability density function f(lgN) is... ij The calculation formula is as follows: （3） Where: N ij For i-th order stress S i The number of cycles that caused the j-th sample to fail, parameter σ i For and μ i These are the standard deviation and mean life under this stress level, respectively. Step 1.3: The logarithmic life standard deviation σ of metallic materials satisfies a linear relationship with the stress level S, where S is the stress level i. i The corresponding expression for calculating the standard deviation is: （4） In the formula: parameter K is a material constant, the k-th stress is regarded as the reference stress, and the standard deviation σ k S serves as the benchmark for solving other standard deviations. k These represent the reference stresses; Step 1.4: When the stresses corresponding to the test data are arranged in ascending order and the minimum stress level is taken as stress level 1, the parameters K and σ1 retrieval formula are obtained based on the log-life normal distribution and the maximum likelihood method: （5） In the formula: k1…k n These represent the number of test data corresponding to stress levels 1 through n, respectively. Step 1.5: Combining the search formulas for K and σ1 above, the search range for the two parameters is defined as follows: The upper limit for searching σ1 for steel is 0.2, and the upper limit for searching K is 0.2 / (S). n -S1); The initial value for parameter K is 10. -5 The parameter σ1 is initially retrieved with a value ≥ 10. -5 ×(S2-S1) Considering that the number of iterations corresponding to the SN curve is ≥10 4 , record 10 4 The corresponding stress level and cycle life standard deviation are S s and σ s When σ is required s ≮10 -3 When the constraint function expression in the main function retrieval process is σ1-(S1-S), then the constraint function expression is σ1-(S1-S). s -10 -3 ≥0; Step 1.6: Combining steps 1.1-1.5, obtain the global optimal solution for parameters K and σ1. Then, combining the linear relationship between standard deviation and stress level, obtain the standard deviation for each stress level. Finally, using the following formula, calculate the number of cycles lgN corresponding to stress level i under different survival rates P. (i,P) The calculation formula is as follows: （6） In the formula: λ P The skewness of the standard normal distribution corresponding to the survival rate P; Step 1.7: Combine the fatigue life corresponding to each stress level under different survival rates to obtain the corresponding probability-stress-life curve, that is, obtain the PSN curve fitting in the finite life region. Step 2: Analysis of distributed parameters within the infinite lifetime region; Step 2.1: When the cyclic load is small, the test specimen may fail or reach the fatigue limit without fracturing after a certain number of cycles. Using the rise-fall method, the stress levels and test life composition data of adjacent fractured and unfractured specimens are compared, i.e., (S... Fi N Fi ) and (S Si N L () represents the stress and cycle number of the failed and non-failed samples in the i-th pair, respectively; Step 2.2: For the i-th pair of paired specimens, the fatigue life N L The corresponding fatigue limit Sa i The solution formula is as follows: （7） Step 2.3: Combining the Basquin phenomenological model, the retrieval range of parameter m for each data set is as follows: （8） Where: m i The search range for parameter m corresponding to group i data; When there are n sets of experimental data, take the maximum value of the lower limit of the retrieval range of parameter m for each set. xmax and the minimum value of the upper limit m smin The comprehensive search range of the component parameter m (m xmax m smin ); Step 2.4: Within the infinite life region, assuming the fatigue limit strength follows a three-parameter Weibull distribution, then the probability density function f(Sa) is... i The calculation formula is as follows: （9） In the formula: Sa i Let i be the fatigue limit of the data set, b be the shape parameter, and S be the shape parameter. a S0 is the scale parameter, S0 is the position parameter, and the values ​​of the three parameters are within the range Sa. i > S0, Sa> S0, b>0, S0>0; Step 2.5: Based on the Weibull distribution of the three parameters of the fatigue limit and the maximum likelihood method, obtain the retrieval formula for the three parameters: （10） Step 2.6: Combine b and S a The probability distribution function obtained from the three parameters S0 is as follows: （11） Using the same survival rate as in step 1.6, and combining it with equation (11), we can obtain the fatigue limit under different survival rates; Step 3: Software development based on VBA; Step 3.1: Call the "Application.GetOpenFilename" function in VBA to manually open the target data file and select the corresponding worksheet; Step 3.2: Calculate the life standard deviation under different stresses using professional data analysis software based on VBA; Step 3.2.1: Solving for the parameters of the median SN curve; (1) Combining the life and stress data in the high-cycle fatigue test data, call the "Application.WorksheetFunction.slope" and "Application.WorksheetFunction.intercept" functions in VBA to solve for the slope and intercept of the median SN curve; (2) Combining the slope and intercept of the median SN curve, the median lifetime vector and cycle number 10 corresponding to each stress are obtained. 4 The corresponding stress value; Step 3.2.2: Analyze the software's calls and execution; (1) Call the "optimoptions" and "fmincon" functions of the analysis software and write a program to solve for the standard deviation and parameter K under minimum stress; (2) Call the VBA function "Application.GetOpenFilename" to manually select the script file of the analysis software; (3) Call the VBA "batContent" function to create a batch file and convert the VBA vectors into the analysis software for calculation; (4) Call the VBA functions "shell" and "Workbooks.Open" respectively to run the analysis software and return the solution results; Step 3.2.3: Based on the linear relationship between standard deviation and stress level, obtain the standard deviation corresponding to each stress level; Step 3.3: Calculate the probability distribution of fatigue limit using professional data analysis software based on VBA; Step 3.3.1: In the test data table, call the "targetSheet.Cells" function in VBA to import the fatigue limit test data into VBA; Step 3.3.2: Analyze the software's calls and execution; (1) Call the "optimoptions" and "fmincon" functions in the analysis software to solve for shape parameters, scale parameters, SN curve exponent and position parameters; (2) Call the "Application.GetOpenFilename" function in VBA to manually select the script file of the analysis software; (3) Call the "batContent" function in VBA to create a batch file and convert the VBA vectors into the analysis software for calculation; (4) Call the VBA functions "shell" and "Workbooks.Open" respectively to run the analysis software and return the solution results; Step 3.4: Analyze the SN curves at different survival rates; (1) Call "ExcelBasedNormSInv" in VBA to calculate the deviation corresponding to the survival rate and the life corresponding to each stress; (2) Call the "Application.WorksheetFunction.slope" and "Application.Worksheet Function.intercept" functions in VBA to obtain the slope and intercept of the SN curve under different survival rates; Step 3.5: Export of data processing results: including life standard deviation under each stress, slope and intercept under different survival rates, life corresponding to each stress, fatigue limit corresponding to the number of cycles and fatigue limit; Step 3.6: Plot the PSN curve; Step 3.6.1: Match a suitable coordinate system range; (1) Combining the maximum stress, minimum stress, maximum number of cycles and minimum number of cycles in the test data, call the "Select Case" function in VBA to solve the maximum and minimum values ​​of the X and Y coordinates in stages; (2) Call the VBA functions "targetSheet.ChartObjects.Add", "MinimumScale" and "MaximumScale" to create the chart and assign the maximum and minimum values ​​of the X and Y axes respectively; Step 3.6.2: Plot the PSN curves under different survival rates; (1) Call the "chartObj.chart.SeriesCollection.NewSeries" and "xlXYScatterSmoothNoMarkers" functions in VBA to generate SN curves for each survival rate, including finite lifetime region and infinite lifetime region; (2) Call the "Int(Rnd * 256)" and "Format.Line.ForeColor.RGB" functions in VBA to set different line colors and assign them to curves with different survival rates to distinguish SN curves with different survival rates.

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