A method of fatigue strength testing

Abstract

The application discloses a fatigue strength test method, comprising the following steps: firstly, fatigue experiments are carried out on single samples under multiple stress levels initially estimated as fatigue strength, until the following situation occurs under the three adjacent stress levels: the sample under the highest stress level is damaged within a given cycle, and the samples under the other two stress levels are not damaged within the given cycle; the highest stress level is marked as S1, and the adjacent two stress levels are marked as S2 and S3; then, fatigue experiments are carried out under the S3 stress level, if n p samples tested under the stress level are not damaged, the experiment is stopped; otherwise, the next stress level is continued until n p samples tested under the stress level are not damaged. The fatigue strength test method provided by the application is independent of the test order of the samples under each stress level, and multiple samples can be tested simultaneously, thereby improving the test efficiency.

Description

Technical Field

[0001] This invention belongs to the field of materials and parts testing technology, and specifically relates to a fatigue strength testing method. Background Technology

[0002] Fatigue is a major failure mode of mechanical parts, and fatigue performance evaluation is an important indicator for the safe and reliable service of materials and parts.

[0003] Currently, fatigue strength testing is generally based on the step-down method. The step-down method involves randomly selecting a first specimen and testing it at the estimated average fatigue strength as the first stress level. If the specimen fails within a given number of cycles, a second specimen is randomly selected, and the stress level is lowered by one stress step. If the first specimen does not fail within the given number of cycles, the stress level is increased by one stress step for the selected second specimen. This process continues; if a previous specimen fails within a given number of cycles, the stress level is lowered by one stress step; if a previous specimen does not fail, the stress level is increased by one stress step, until all specimens to be tested have been tested in this manner. The stress step selected during the test should be close to the standard deviation of the fatigue strength of the material being tested. If the standard deviation cannot be obtained, 5% of the estimated average fatigue strength is used as the stress step.

[0004] In this method, the test stress of the subsequent specimen needs to be determined based on the test results of the previous specimen, which often requires a long testing time, especially for ultra-long life fatigue strength evaluation, such as testing 10 at 100Hz. 9 The cycle takes 116 days. If 16 samples are tested effectively, at least 6 of them must achieve a score of 10. 9 If the cycle is repeated, it would take at least 696 days (approximately 1.9 years). Therefore, using the rise-fall method for fatigue strength testing has the problem of a long testing cycle, and is especially unsuitable for fatigue performance testing of materials and components used in ultra-long service life. Summary of the Invention

[0005] This invention provides a fatigue strength testing method in which the testing of specimens at each stress level is independent of the order, which can improve testing efficiency. Moreover, multiple specimens can be tested simultaneously, further improving testing efficiency. This invention is particularly suitable for fatigue strength testing of materials and components in service under ultra-long service life.

[0006] The present invention provides a fatigue strength testing method, comprising the following steps:

[0007] (1) Under multiple stress levels initially set for estimated fatigue strength, fatigue tests are conducted on individual specimens until the test specimens under three consecutive stress levels show the following condition: among the three adjacent stress levels, the specimen under the highest stress level fails within a given number of cycles, while the specimens under the other two stress levels do not fail within a given number of cycles. The highest stress level is marked as S1, and the two adjacent stress levels are marked as S2 and S3.

[0008] (2) Select stress level S3 for fatigue testing. If the measured n under this stress level... p If none of the samples fail, the experiment is stopped; otherwise, the experiment continues to the next stress level until n samples are tested at that stress level. p None of the samples were damaged.

[0009] Furthermore, fatigue tests on multiple specimens can be conducted simultaneously at the same stress level.

[0010] Furthermore, fatigue tests on specimens can be conducted simultaneously under different stress levels.

[0011] Furthermore, if fatigue tests on a single specimen are conducted simultaneously at different stress levels in step (1);

[0012] After testing, if a specimen fails at a certain stress level but does not fail at more than two adjacent lower stress levels, the data from the first three stress levels are used. The stress level where failure occurs is marked as S1, and the two adjacent lower stress levels are marked as S2 and S3 from highest to lowest.

[0013] Furthermore, after the fatigue test, the experimental data are used to estimate the sample parameters and calculate the survival rate. Then, the fatigue strength S under any survival rate 1-p0 is obtained by formula (14). 1-p0 Formula (14) is:

[0014]

[0015] In the formula, S1 is the first stress level, d is the stress step, and α, k, and r are dimensionless parameters. μ and σ are the mean and standard deviation of fatigue strength, respectively.

[0016] Furthermore, after the fatigue test, sample parameter estimation and one-sided error limit analysis were performed on the experimental data. Then, the lower limit of fatigue strength S under a given confidence level 1-β, failure probability p, and degree of freedom v was obtained using formula (18). (p,1-β,v) Formula (18) is:

[0017]

[0018] In the formula, S1 is the first stress level. and These are the estimated values ​​of the mean and standard deviation of fatigue strength, respectively, α, and For dimensionless parameters, d represents the stress step, and the parameter is... Where z p For upper quantiles, For degrees of freedom v⁻¹, the non-central parameter is The distribution function of the non-central t-distribution.

[0019] Furthermore, after the fatigue test is completed, based on the test data of the test sample and the assumed fatigue strength follows a normal distribution, the sample parameters are estimated using the likelihood function to obtain the estimated values ​​of the mean and standard deviation.

[0020] Furthermore, in the fatigue test, the stress step d between two adjacent stress levels is the same.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] 1. This invention, based on probability and statistics theory, establishes a fatigue strength testing method independent of the testing sequence, namely the continuous method. In this invention, fatigue tests are first conducted on individual specimens at the estimated fatigue strength and multiple nearby stress levels. The testing sequence for each stress level is independent, improving testing efficiency. Furthermore, multiple specimens can be tested simultaneously, further enhancing efficiency. This method is particularly suitable for fatigue strength testing of materials and components serving ultra-long service lives.

[0023] 2. According to the method provided by this invention, if n is tested at a certain stress level... p (The number of samples and reliability requirements are determined based on the provided sample count.) If none of the samples fail within a given number of cycles (i.e., fatigue life), the experiment is stopped. Then, through statistical analysis, the fatigue strength or lower limit of the material or component at a given confidence level and failure probability under that fatigue life is obtained. This method can test multiple samples simultaneously, thus greatly improving testing efficiency. Furthermore, this invention can also evaluate fatigue strength under a third-level stress condition, eliminating situations where fatigue strength cannot be evaluated using the test results. Attached Figure Description

[0024] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0025] Figure 1 This is a flowchart illustrating the fatigue strength testing method in an embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of the continuous method in an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the three-level stress level test in an embodiment of the present invention;

[0028] Figure 4 This is a schematic diagram of the four-level stress level test in an embodiment of the present invention;

[0029] Figure 5 Figure a is a schematic diagram of the third-level stress and its converted fourth-level stress in an embodiment of the present invention, and Figure b is a schematic diagram of the third-level stress and the converted fourth-level stress.

[0030] Figure 6 This is a schematic diagram of the five-level stress level test in an embodiment of the present invention;

[0031] Figure 7 This is a schematic diagram of the continuous test results of G20Mn5QT steel in Embodiment 1 of the present invention;

[0032] Figure 8 This is a schematic diagram comparing the dimensionless test time of the continuous method and the rising and falling method in Embodiment 1 of the present invention (the dimensionless test time in the figure is the ratio of the total test time to the test time corresponding to the fatigue life under study). Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] like Figure 1 As shown, the present invention provides a fatigue strength testing method, comprising the following steps:

[0035] (1) Under multiple stress levels initially set for estimated fatigue strength, fatigue tests are conducted on individual specimens until the test specimens under three consecutive stress levels show the following condition: among the three adjacent stress levels, the specimen under the highest stress level fails within a given number of cycles, while the specimens under the other two stress levels do not fail within a given number of cycles. The highest stress level is marked as S1, and the two adjacent stress levels are marked as S2 and S3.

[0036] (2) Select stress level S3 for fatigue testing. If the measured n under this stress level... p (The number of samples provided, reliability requirements, etc.) If none of the samples fail, the experiment is stopped; otherwise, the experiment continues to the next stress level until n samples are tested at that stress level. p None of the samples were damaged.

[0037] This invention, based on probability and statistics theory, establishes a fatigue strength testing method independent of the testing sequence, namely the continuous method. According to this method, based on step (1), if the n values ​​tested at a certain stress level... p (The number of samples provided, reliability requirements, etc.) If none of the samples fail within a given number of cycles (i.e., fatigue life), the experiment is stopped. Then, through statistical analysis, the fatigue strength or lower limit of the material or component at a given confidence level and failure probability under that fatigue life can be obtained. In this method, the testing of samples at each stress level is independent of the order, unlike the step-up method where the test stress of the subsequent sample needs to be determined based on the test results of the previous sample. This invention improves testing efficiency.

[0038] Furthermore, this invention can also evaluate fatigue strength even when the test result is at a stress level of level three, and there is no situation where fatigue strength cannot be evaluated using the test results.

[0039] In this invention, the specific operation process of the continuous method is as follows:

[0040] First, select several samples from the samples that need to be subjected to fatigue testing as test specimens.

[0041] Secondly, the average fatigue strength and standard deviation under a given fatigue life are estimated. Fatigue tests are then conducted on the specimens at the estimated fatigue strength and stress levels near the estimated fatigue strength. One specimen is selected for fatigue testing at each stress level until the test specimens show fatigue at three consecutive stress levels. Figure 2 The cases marked with an asterisk (*) indicate that under three adjacent stress levels, the specimen fails within a given number of cycles at the highest stress level, while it does not fail within the same number of cycles at the other two stress levels. In this case, the highest stress level is labeled S1, and the two adjacent lower stress levels are labeled S2 and S3 from highest to lowest. During testing, the stress step d between adjacent stress levels is the same. The choice of d should be close to the standard deviation. If the standard deviation cannot be obtained, the stress step d can be selected as 5% of the estimated average fatigue strength.

[0042] Then, select Figure 2 The test is conducted at stress level S3. If the n measured at this stress level... p- One specimen did not fail within the given number of cycles (since one specimen had already passed the S3 stress level test in the first step, only n tests are needed in the second step). p If 1 sample is tested, the experiment is stopped; otherwise, the experiment continues to the next stress level until n samples are tested at that stress level. p None of the samples were damaged within the given number of cycles.

[0043] The testing method provided by this invention can simultaneously perform fatigue tests on multiple specimens at the same stress level. Unlike the rise and fall method, where the test stress of the subsequent specimen needs to be determined based on the test results of the previous specimen, this method can further improve testing efficiency.

[0044] In this invention, fatigue tests on specimens can be conducted simultaneously under different stress levels, or fatigue tests on multiple specimens under the same stress level can be conducted simultaneously under different stress levels, thereby shortening the testing time.

[0045] For example, if conditions permit, simultaneously test n under stress level S3. p -1 specimen; if any specimen fails before reaching the given fatigue life under S3 stress, n can also be tested simultaneously under S4 stress. p One sample, until n samples are tested at a certain stress level. p None of the samples were damaged within the given number of cycles.

[0046] Alternatively, a single specimen can be tested simultaneously at the estimated fatigue strength and at different stress levels near the estimated fatigue strength to obtain... Figure 2 In the case of the asterisk (*), n was then simultaneously tested under S3 level stress. p -1 specimen and n under S4 level stress p By testing multiple samples simultaneously at different stress levels, data from multiple samples at different stress levels can be obtained within the same testing time, thereby improving experimental efficiency.

[0047] It should be noted that if, after fatigue tests of individual specimens are conducted simultaneously at different stress levels in step (1), a specimen at a certain stress level fails within a given number of cycles, but specimens at more than two adjacent low stress levels do not fail within the given number of cycles, then the data from the first three stress levels shall be used. The stress level at which no failure occurs shall be marked as S1, and the two adjacent low stress levels shall be marked as S2 and S3 from high to low, respectively.

[0048] If a single specimen is tested simultaneously at stress levels S1 through S4, and the specimen fails under stress level S1 while none of the specimens fail under stress levels S2 through S4, then stress levels S1 through S3 are used as the standard. Figure 2 The case marked with an asterisk (*). In step (2), if n is tested simultaneously at stress level S3.p -1 specimen and n under S4 level stress p One sample, and n under stress level S3 p -1 specimen and n under S4 level stress p If none of the specimens were damaged, the fatigue strength was evaluated using data from stress levels S1 to S3.

[0049] After the fatigue test, the experimental data were used to estimate the sample parameters and calculate the survival rate. Then, the fatigue strength at any survival rate 1-p0 was obtained using formula (14). The specific calculation process is as follows:

[0050] After the fatigue test is completed, the sample parameters are estimated based on the test data and the assumed fatigue strength follows a normal distribution, combined with the likelihood function, to obtain the estimated values ​​of the mean and standard deviation.

[0051] Assuming the fatigue strength S under a given fatigue life follows a normal distribution with a mean and standard deviation of μ and σ respectively, the fatigue strength n measured under the i-th stress level... i +m i n samples i Each sample was damaged, m i The probability P(n) of a sample not being damaged i ,m i |S i )for

[0052]

[0053] In the formula Let be the number of permutations and combinations.

[0054] Where p i and q i S i The probability of specimen failure and non-failure under stress level, i.e.

[0055]

[0056] q i =P(S≥S) i )=1-p i (3)

[0057] In the formula, t is a variable.

[0058] For equation (1), the estimated values ​​of μ and σ are obtained using the likelihood function. The steps are as follows:

[0059] From equation (1), the likelihood function is obtained as follows:

[0060]

[0061] In the formula, L is a function of the mean μ and the standard deviation σ. I represents the total number of stress levels. If K > 1, it means that the likelihood function corresponds to multiple possible test sequences.

[0062] If equation (4) has a maximum value, take its natural logarithm and take the partial derivatives with respect to μ and σ respectively, and we get the following system of equations:

[0063]

[0064] As can be seen from equation (5), for a given stress level, μ and σ are only related to the cumulative number of failures / non-failures, and are not related to the order in which the failures / non-failures appear.

[0065] For convenience and simplicity, an error function is introduced. but

[0066]

[0067] Substituting equation (6) into equation (5) and rearranging, we get:

[0068]

[0069] Equation (7) is a system of two nonlinear equations in μ and σ, and its solution is... It is related not only to the test sequence and the damaged / undamaged state of each sample point, but also to the values ​​of stress level S1 and stress step d.

[0070] If we introduce three dimensionless parameters α, k, and r, then...

[0071]

[0072] This simplifies the nonlinear relationship between the mean μ and the standard deviation σ, and the simplification process is as follows:

[0073] Substituting equation (8) into equation (7), we obtain a system of equations concerning k and r.

[0074]

[0075] The solution (k,r) of equation (9) depends only on the test sequence and the failure / non-failure state of each sample point, and is independent of the values ​​of stress level S1 and stress step d. The estimated value is obtained from equation (7) or (9). and

[0076] If equation (4) does not have a maximum value, then it is necessary to analyze based on the range of values ​​of k and r, and perform a maximum likelihood estimation of equation (4) within its range, and then obtain the result. and It cannot be calculated directly based on equations (7) or (9).

[0077] Referring to national and industry standards, the distribution of fatigue strength is described using a normal distribution. Therefore, this invention adopts the assumption that the fatigue strength S follows a normal distribution under a given fatigue life.

[0078] Based on the normal distribution of fatigue strength, if a certain survival rate 1-p0 is known, assume the stress (i.e., fatigue strength) at that survival rate is... make

[0079]

[0080] In the formula, S1 is the first-order stress. This represents the number of stress steps that differ between the stress at survival rate 1-p0 and S1.

[0081] Based on the relationship between stress and first-level stress at a certain survival rate, and combining the mean μ and standard deviation σ, the relationship between stress and mean μ and standard deviation σ at that survival rate is obtained.

[0082] From equation (8), we get

[0083]

[0084] The survival rate 1-p0 can then be expressed as

[0085]

[0086] From equation (12), we get

[0087]

[0088] That is, the stress at survival rate 1-p0 It can be represented as

[0089]

[0090] or

[0091]

[0092] Equation (14) or (15) gives the relationship between survival rate and fatigue strength, that is, fatigue strength at any survival rate.

[0093] In one embodiment, after the fatigue test, sample parameter estimation and one-sided error limit analysis are performed on the experimental data. Then, the lower limit of fatigue strength S under a given confidence level 1-β, failure probability p, and degree of freedom v is obtained by formula (18). (p,1-β,v) To meet different needs.

[0094] When verifying whether the fatigue strength of any single specimen meets the requirements, the uncertainty of the test results for a single specimen needs to be characterized by the one-sided error limit and the confidence level. The confidence level is the probability that the true value falls within a certain range. From equation (8), the estimated value of the mean is obtained. The estimated values ​​of the standard deviation The formula is as follows:

[0095]

[0096] or

[0097]

[0098] Therefore, given a confidence level of 1-β, a failure probability of p, and degrees of freedom v, the lower limit of fatigue strength S (p,1-β,v) for

[0099]

[0100] Where the parameter k ( ′ p,1-β,v) Determined by the following formula

[0101]

[0102] Where z p For upper quantiles, For degrees of freedom v⁻¹, the non-central parameter is The distribution function of the non-central t-distribution.

[0103] The present invention provides a detailed analysis of several typical cases in fatigue strength testing experiments as follows.

[0104] The following sections respectively address... Figure 2 Further analysis is conducted on the stress levels of levels three, four, and five shown, and the analysis is tailored to n. p The specific calculation results are given for the case where =7. This applies to stress levels greater than level five and n. p The cases with other values ​​can be analyzed similarly.

[0105] a. Third-order stress case. If Figure 2 n tested under S3 stress level p None of the specimens failed within the given number of cycles, resulting in a three-level stress level test scenario. The following is a summary of... Figure 3 The analysis considers three stress levels, where the "?" sign indicates either hypothetical or actual testing at that stress level, where the specimen either fails after exceeding a given number of cycles or fails before reaching the given number of cycles. In other words, it considers stress level S2 with n... pThe possible test results at each experimental point increase the number of samples available for analysis. Of course, if conditions permit, further testing at stress level S2 could be conducted. p -1 sample, specific results can be obtained based on the following analysis.

[0106] According to the principle of maximum likelihood method, σ approaches 0 from equation (4). This contradicts the fact that the fatigue strength of materials or components often has a certain degree of dispersion. That is to say, the standard deviation σ of the fatigue strength (approximately) following a normal distribution under a given fatigue life is a definite value greater than 0. Therefore, it is necessary to reasonably restrict the value of σ, otherwise the maximum likelihood method cannot be used to estimate μ and σ. When the range of σ is unclear, the third-level stress case can be approximated by using the fourth-level stress case.

[0107] Therefore, it can be seen that the fatigue strength testing method provided by the present invention can also evaluate fatigue strength when the test result is a level 3 stress condition, while the rise and fall method cannot evaluate fatigue strength based on the test result in some cases when the test result is a level 3 stress condition.

[0108] b. Fourth-order stress case. If Figure 2 M(1) tested under S3 stress level <M≤n p () Of the samples tested, one failed before reaching the given number of cycles. n samples were tested at stress level S4. p None of the specimens failed within the given number of cycles, resulting in a fourth-level stress level test scenario. Here, we... Figure 4 The analysis is performed under four stress levels, where the "?" sign indicates that the specimen under that stress level either did not fail after being tested or under hypothetical testing for a given number of cycles, or failed before reaching the given number of cycles. Since the survival rate calculation is independent of the testing sequence, Figure 4 The specimens that failed at least once under stress level S3 are placed last. That is, if the total number of specimens tested under stress level S3 is less than n... p Considering n under stress level S3 p The number of possible test results at each experimental point increases the number of samples available for analysis. Specifically, if conditions permit, the number of specimens tested at stress level S3 may be less than n. p At that time, n can be tested under stress level S3. p Based on the analysis of a sample, specific results can be obtained.

[0109] With n p Taking d = 7 as an example, Table 1 gives the values ​​when d = 0.05S1. Figure 4The figure shows the dimensionless mean estimate, standard deviation estimate, and fatigue strength lower limit under different numbers of unfailed specimens (m3) at stress level S3 under the four stress levels. For other typical confidence levels and failure probabilities, the corresponding one-sided error limit coefficient can be obtained from Table B.1 in the literature (ISO 12107:2003, Metallic materials—Fatigue testing—Statistical planning and analysis of data [S]; GB / T24176-2009, Statistical scheme and analysis method for fatigue test data of metallic materials [S]). Then, it is substituted together with the mean estimate and standard deviation estimate in Table 1 into equation (18) to obtain the fatigue strength lower limit under that confidence level and failure probability.

[0110] When the stress step d takes other values, the dimensionless mean and standard deviation estimates corresponding to different numbers of unfailed samples m3 in Table 1 can be substituted into equation (20) to first obtain the corresponding mean and standard deviation estimates:

[0111]

[0112] Then, according to Table B.1 in the literature (ISO 12107:2003, Metallic materials—Fatigue testing—Statistical planning and analysis of data[S]; GB / T 24176-2009, Statistical scheme and analysis method for fatigue test data of metallic materials[S]), the one-sided error limit coefficient under the given typical confidence level and failure probability is obtained. Then, it is substituted together with the obtained mean and standard deviation estimates into equation (18) to obtain the lower limit of fatigue strength under the given confidence level and failure probability.

[0113] Using Table 1, when the number of specimens tested at stress level S3 is 7, specific values ​​of the fatigue strength lower limit under several typical confidence levels and failure probabilities can be obtained. When the number of specimens tested at stress level S3 is 2, 3, ..., 6, a conservative estimate can be made based on the actual number of unfailed specimens. Of course, similar analytical methods can also be used to calculate based on the specific test results at stress level S3.

[0114] Table 1 shows the dimensionless mean and standard deviation estimates for different numbers of unfailed specimens (m³) under stress level S3 when d = 0.05S1, and the lower limit of fatigue strength at different confidence levels and failure probabilities.

[0115]

[0116]

[0117] For the third-level stress case ( Figure 5 a) If we assume that the nth stress level is S3 p One sample was destroyed, and the remaining n samples were destroyed. p -1 specimens did not fail, and n under stress level S4 p If none of the samples were damaged, then it can be passed. Figure 5 The fourth-level stress case shown in b approximates the third-level stress case with a given confidence level 1-β, failure probability p, and degrees of freedom v = 2n. p The lower limit of fatigue strength at +1. Specifically, with n... p Taking m = 7 and d = 0.05S1 as examples, Table 1 shows that when m3 = 6, the lower limit of fatigue strength at a confidence level of 95% and a failure probability of 5% is 0.8457S1, and the lower limit of fatigue strength at a confidence level of 95% and a failure probability of 1% is 0.8047S1.

[0118] c. Level 5 stress condition. If Figure 2 M3(1) tested under S3 stress level <M3≤n p Of the 100 samples tested, one failed before reaching the given number of cycles. The stress level S4 was tested at M4 (1≤M4≤n). p Of the 100 samples tested, one failed before reaching the given number of cycles. The n samples tested at stress level S5... p None of the specimens failed within the given number of cycles, resulting in a five-level stress level test scenario. Here, we... Figure 6 The analysis is performed under the five stress levels shown, where the "?" sign indicates that the specimen under that stress level either failed after being tested or under hypothetical testing for a given number of cycles, or failed before reaching the given number of cycles. In other words, if the number of specimens tested under stress levels S3 or S4 is less than n... p All of them take n into consideration p The potential results of each test specimen increase the number of samples available for analysis. If conditions permit, when the number of specimens tested at stress levels S3 or S4 is less than n... p When this happens, it can be supplemented with tests up to n. p The following analysis was used to obtain specific results for each sample.

[0119] With n p Taking d = 7 as an example, Table 2 gives the values ​​when d = 0.05S1. Figure 6The figure shows the dimensionless mean estimate, standard deviation estimate, and fatigue strength lower limit under several typical confidence levels and failure probabilities for different combinations of the number of unfailed specimens (m3, m4) under stress levels S3 and S4. For other typical confidence levels and failure probabilities, the corresponding one-sided error limit coefficient can be obtained from Table B.1 in the literature (ISO 12107:2003, Metallic materials—Fatigue testing—Statistical planning and analysis of data[S]; GB / T24176-2009, Statistical scheme and analysis method for fatigue test data of metallic materials[S]). Then, it is substituted together with the mean estimate and standard deviation estimate in Table 2 into equation (18) to obtain the fatigue strength lower limit under that confidence level and failure probability.

[0120] When d takes other values, the dimensionless mean and standard deviation estimates corresponding to different combinations of the number of unfailed samples (m3, m4) in Table 2 can be substituted into equation (20) to obtain the corresponding mean and standard deviation estimates. Then, by referring to Table B.1 in the literature (ISO 12107:2003, Metallic materials—Fatigue testing—Statistical planning and analysis of data [S]; GB / T 24176-2009, Statistical scheme and analysis method for fatigue test data of metallic materials [S]), the one-sided error limit coefficient under the given typical confidence level and failure probability can be obtained. Then, it can be substituted together with the obtained mean and standard deviation estimates into equation (18) to obtain the lower limit of fatigue strength under the given confidence level and failure probability.

[0121] Table 2 shows the dimensionless mean and standard deviation estimates, as well as the lower limit of fatigue strength at different confidence levels and failure probabilities, for different combinations of the number of unfailed specimens (m3, m4) under stress levels S3 and S4 when d = 0.05S1.

[0122]

[0123]

[0124]

[0125] Using Table 2, when the number of specimens tested under both stress levels S3 and S4 is 7, specific values ​​of the fatigue strength lower limit under several typical confidence levels and failure probabilities can be obtained. In other cases, a conservative estimate can be made based on the actual number of unfailed specimens tested under stress levels S3 and S4. Of course, similar analytical methods can also be used to calculate based on the specific test results under stress levels S3 and S4.

[0126] Example 1

[0127] In this embodiment, G20Mn5QT steel 10 7 Taking the fatigue strength of each cycle as an example, using n p The fatigue strength of G20Mn5QT steel was evaluated using a continuous method with a coefficient of 7. In the test, 10... 7 The estimated average fatigue strength per cycle was selected as 240 MPa, and the stress step d was selected as 5% of the estimated fatigue strength.

[0128] Figure 7 The test results of the continuous stress method for G20Mn5QT steel are presented. A fourth-level stress condition is used here. Figure 7 The test results shown are analyzed. Substituting S1 = 240 MPa directly into the case of m3 = 6 in Table 1, we obtain the result for G20Mn5QT steel 10. 7 Table 3 shows the estimated mean and standard deviation of fatigue strength for each cycle, as well as the lower limit of fatigue strength at different failure probabilities with a 95% confidence level.

[0129] Due to the occurrence of such stress levels under three consecutive stress levels Figure 2 As shown by the asterisk (*), 240 MPa is marked as stress level S1. Figure 7 The S4 stress level is not shown in the diagram.

[0130] Table 3 G20Mn5QT steel 10 7 Estimated mean and standard deviation of fatigue strength over cycles, and the lower limit of fatigue strength at 95% confidence level and different failure probabilities.

[0131]

[0132] The method proposed in this invention (i.e., the continuous method) can test multiple specimens simultaneously. Therefore, if conditions permit, fatigue testing can usually be completed with only two test cycles corresponding to a given number of cycles. First, individual specimens under the estimated fatigue strength and at different stress levels near the estimated fatigue strength are tested simultaneously to obtain... Figure 2 The case marked with an asterisk (*) is then considered; subsequently, n is tested simultaneously at stress levels S3, S4, and S5. p -1 or n p One sample.

[0133] Taking the case of three-level stress in the continuous method as an example, when n p =7 and n p When the stress ratio is 14, the continuous method requires at least 9 and 16 samples to be tested, respectively. However, approximate analysis can be performed using a four-level stress scenario, yielding 16 and 30 samples for analysis, respectively. In contrast, the traditional rise-fall method requires at least 16 and 30 samples to obtain the same number of samples. Therefore, the continuous method requires fewer samples to obtain the same number of samples for analysis.

[0134] Because the stress level of the subsequent specimen in the stress-level test needs to be determined based on the test results of the previous specimen, when the stress level is level three, at least 7 specimens (sample size 16) and 14 specimens (sample size 30) exceeded the given number of cycles (i.e., fatigue life) without failure. When the stress level is level four, at least 6 specimens (sample size 16) and 13 specimens (sample size 30) exceeded the given fatigue life without failure. When the stress level is level five, at least 6 specimens (sample size 16) and 13 specimens (sample size 30) exceeded the given fatigue life without failure.

[0135] Figure 8 A comparison of test times for the continuous method and the rising / falling method is given under the same test frequency. Figure 8 In the above, for the lifting method, stress levels three to five are considered, but the test time for specimens that fail before reaching the given fatigue life is not taken into account. From Figure 8 It can be seen that, under suitable conditions, the continuous method significantly improves testing efficiency compared to the gradual increase / decrease method. When the number of samples used for fatigue strength analysis is 16, the testing time of the continuous method is 1 / 5 to 1 / 3 of that of the traditional gradual increase / decrease method; when the number of samples used for fatigue strength analysis is 30, the testing time of the continuous method is 1 / 8.5 to 1 / 6.5 of that of the traditional gradual increase / decrease method. It should be noted that when the gradual increase / decrease method results in a third-level stress condition, fatigue strength cannot be evaluated based on the test results in some cases. However, the continuous method provided by this invention can transform the third-level stress condition into a fourth-level stress condition, and obtain the fatigue strength evaluation result through statistical analysis.

[0136] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A fatigue strength testing method, characterized in that, Includes the following steps: (1) Under multiple stress levels initially estimated for fatigue strength, fatigue tests are conducted on individual specimens until the test specimens under three consecutive stress levels show the following situation: among the three adjacent stress levels, the specimen under the highest stress level fails within a given number of cycles, while the specimens under the other two stress levels do not fail within a given number of cycles. The highest stress level is marked as S1, and the two adjacent stress levels are marked as S2 and S3. (2) Select stress level S3 for fatigue testing. If the measured n under this stress level p If none of the samples fail, the experiment is stopped; otherwise, the experiment continues to the next stress level until n samples are tested at that stress level. p None of the samples were damaged.

2. The fatigue strength testing method according to claim 1, characterized in that, Fatigue tests on multiple specimens can be conducted simultaneously under the same stress level.

3. The fatigue strength testing method according to claim 1, characterized in that, Fatigue tests on specimens can be conducted simultaneously under different stress levels.

4. The fatigue strength testing method according to claim 3, characterized in that, If fatigue tests on a single specimen are performed simultaneously at different stress levels in step (1); After testing, if a specimen fails within a given number of cycles at a certain stress level, but specimens at more than two adjacent low stress levels do not fail within the given number of cycles, then the data from the first three stress levels are used. The stress level where failure occurs is marked as S1, and the two adjacent low stress levels are marked as S2 and S3 from high to low, respectively.

5. The fatigue strength testing method according to claim 1, characterized in that, After the fatigue test, the experimental data were used to estimate the sample parameters and calculate the survival rate. Then, the survival rate of any given data was obtained using formula (14). fatigue strength Formula (14) is: (14) In the formula, S1 is the first stress level, and d is the stress step. , and For dimensionless parameters, , and These represent the mean and standard deviation of fatigue strength, respectively.

6. The fatigue strength testing method according to claim 1, characterized in that, After the fatigue test, the experimental data were subjected to sample parameter estimation and one-sided error limit analysis. Then, the given confidence level was obtained by formula (18). Failure probability p and degrees of freedom The lower limit of fatigue strength Formula (18) is: (18) In the formula, S1 is the first stress level. and These are the estimated values ​​of the mean and standard deviation of fatigue strength, respectively. , and For dimensionless parameters, , , d represents the stress step, and the parameter is... ,in For upper quantiles, For degrees of freedom Non-central parameters are non-central The distribution function of the distribution.

7. The fatigue strength testing method according to claim 6, characterized in that, After the fatigue test is completed, the sample parameters are estimated based on the test data and the assumed fatigue strength follows a normal distribution, combined with the likelihood function, to obtain the estimated values ​​of the mean and standard deviation.

8. A fatigue strength testing method according to any one of claims 1-7, characterized in that, In fatigue tests, the stress step d between two adjacent stress levels is the same.

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