A low-temperature metal fatigue life evaluation method considering uncertainty factors

Abstract

The present application relates to the technical field of low-temperature metal fatigue life analysis, and particularly relates to a low-temperature metal fatigue life evaluation method considering uncertainty factors. The method comprises the following steps: collecting low-temperature metal material fatigue life test data; determining a low-temperature metal material fatigue life prediction model parameter distribution range; obtaining a jth membership value of an ith fuzzy number; judging whether all fuzzy numbers are valued; determining all fuzzy number values under the jth membership; calculating a low-temperature fatigue life interval of the metal material under the jth membership; judging whether all memberships are calculated; and obtaining a low-temperature metal fatigue life analysis result considering uncertainty factors. The improved low-temperature metal material fatigue life prediction model proposed in the method fully considers material performance degradation under low-temperature conditions, improves fatigue life prediction accuracy, and fully considers parameter uncertainty in the low-temperature fatigue life prediction model, so that the prediction result is more referable.

Description

Technical Field

[0001] This invention relates to the field of low-temperature metal fatigue life analysis technology, and in particular to a method for assessing the fatigue life of low-temperature metals that takes into account uncertainties. Background Technology

[0002] With the expansion of global energy development into polar regions and the accelerated construction of large-scale infrastructure in cold regions, metallic materials are widely used in critical areas such as polar offshore platforms, bridges in cold regions, and wind turbine towers. During their service life, these materials must withstand the coupled effects of cyclic loading and extreme low temperatures, significantly increasing the risk of fatigue failure and seriously threatening engineering safety. However, the uncertainties in fatigue life analysis of low-temperature metallic materials, such as load and environmental fluctuations, increase the difficulty of fatigue life analysis and lead to inaccurate prediction results. Therefore, research on fatigue life assessment methods for low-temperature metallic materials is urgently needed.

[0003] Current low-temperature fatigue life analysis of metals still relies on traditional fracture mechanics theory as its core framework, characterizing the fatigue damage evolution of materials under low-temperature environments by introducing key parameters such as the fatigue crack propagation threshold. However, low temperatures induce performance degradation in metallic materials, and traditional methods do not fully consider the coupling effect between the environment and material properties, leading to significant deviations between their predicted fatigue life and experimental data. Furthermore, the evolution of key model parameters in existing fatigue models at low temperatures remains unclear, and traditional deterministic analysis methods struggle to quantify the impact of these uncertainties. Consequently, they cannot accurately assess the true fatigue life of low-temperature metallic materials, hindering the safe design and improved service reliability of engineering structures under extreme low-temperature environments. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a low-temperature metal fatigue life assessment model that considers uncertainties. The core of this model is to construct a metal fatigue life prediction model under low-temperature conditions by establishing the correlation between key parameters of the model and ambient temperature. At the same time, fuzzy theory is used to describe the uncertainty of key parameters in the model, thereby quantifying the low-temperature metal fatigue life considering uncertainties.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for assessing the fatigue life of low-temperature metals considering uncertainties includes the following steps: S1. Collect fatigue life test data of low-temperature metallic materials; The experimental data includes the initial crack length a0 of the metallic material and the critical crack length a0 of the metallic material. c Elastic modulus E(T0) of metallic materials at room temperature, temperature factor b of elastic modulus, temperature factor q of material fatigue limit, size correction factor Y, and maximum stress of material. Fatigue limit of metallic materials at room temperature Fatigue crack propagation threshold of metallic materials at room temperature .

[0006] S2. Determine the parameter distribution range of the fatigue life prediction model for low-temperature metallic materials; Specifically, this includes: calculating the mean and standard deviation of the fuzzy parameters in the model based on the collected experimental data, and using the mean ± 3 times the standard deviation as the distribution range of the fuzzy parameters.

[0007] S3. Obtain the j-th membership value of the ith fuzzy number; Specifically, it includes: Assume that there are n independent fuzzy variables in the low-temperature metal fatigue life prediction model. The mean and standard deviation of each interval variable are respectively and ; Each fuzzy variable Performing α-cut decomposition, we obtain the following set of intervals: (1) in, (2) In formula (2) Let the i-th fuzzy variable be at the membership level μ j The formula for calculating the membership level of the corresponding interval is as follows: (3) In formula (2) and These represent the membership level μ of the i-th fuzzy parameter. j lower interval The lower and upper bounds are calculated using the following expression: (4) The i-th fuzzy variable is set at the membership level μ. j The corresponding interval below Further transform it into an array of the following form : (5) in: (6) (7) That is, the j-th membership value of the i-th fuzzy number.

[0008] S4. Determine whether to take values ​​for all membership degrees of all fuzzy numbers; Specifically, it includes: S3 is iterated over in a two-level loop structure. The first level loops over i, with a range of 1 to n. The second level loops over j, with a range of 0 to m. When i>n and j>m, it is considered that the values ​​of all fuzzy variables under all membership degrees have been obtained.

[0009] S5. Determine the values ​​of all fuzzy numbers under the j-th membership degree; Specifically, it includes: Since the value of the i-th fuzzy number at the j-th membership degree Given an array containing m-j+1 elements, combine all the values ​​of the fuzzy numbers in pairs, resulting in a total of (m-j+1) values. n The method involves using an array to calculate the k-th value of all fuzzy numbers for the j-th membership degree. express: (8).

[0010] S6. Calculate the low-temperature fatigue life range of metallic materials at the j-th membership degree; Specifically, it includes: Take the value of the fuzzy number under the j-th membership degree calculated in S5. Substitute other model parameters into the proposed low-temperature metal fatigue life assessment model as shown in equation (9), and calculate the results of the low-temperature metal fatigue life assessment model for the k-th value. ; (9) Repeat the above steps to calculate the low-temperature fatigue life assessment results for all possible values ​​of the metallic material under the j-th membership degree, and calculate the maximum and minimum values ​​of all results; (10) Then the low-temperature fatigue life range of the metallic material at the j-th membership degree It can be represented as .

[0011] The detailed derivation of the low-temperature metal fatigue life assessment model (9) is as follows: The fatigue life assessment model for metals at room temperature can be solved using the following expression: (11) Where a is the crack length, N f It is the number of cyclic loads the structure experiences before fatigue failure, B is the fatigue crack propagation coefficient, and ΔK is the stress intensity factor amplitude. th The fatigue crack propagation threshold is calculated using the following expressions:

[0012] Where E is the material's elastic modulus, and Y is a size-related correction factor. It is the maximum stress. This is the critical length of the crack. This refers to the material's fatigue limit. Considering the temperature dependence of the fatigue crack propagation threshold, its expression can be further rewritten as: (15) Where T and T0 represent low temperature and room temperature, respectively, with room temperature being 20℃. △K th (T) and △K th (T0) represents the fatigue crack propagation thresholds at low temperature and room temperature, respectively, and σ R (T) and σ R (T0) represents the material fatigue limit at low temperature and room temperature, respectively; Substituting equations (12)-(15) into equation (11), we get: (16) By integrating the above equation, we can obtain: (17) Where a0 is the initial crack length, a c It is the critical crack length; To further consider the material property degradation process under low-temperature conditions, a temperature factor is introduced to describe the changes in material fatigue limit and elastic modulus with temperature:

[0013] In the formula, q and b are temperature factors related to the fatigue limit and elastic modulus of the material, respectively; Substituting equations (18) and (19) into equation (17), we get: (20) S7. Determine whether to calculate all membership degrees; Specifically, this includes: iterating through the values ​​of membership degree j in S6, with the iteration range being from 0 to m. When j > m, it is considered that the calculation of material fatigue life under all membership degrees has been completed.

[0014] S8. Obtain the results of low-temperature metal fatigue life analysis considering uncertainties; Specifically, this includes: the low-temperature fatigue life range for each membership degree in S7. Organize and obtain the low-temperature fatigue life assessment results for all membership degrees. .

[0015] The improved low-temperature fatigue life prediction model for metallic materials proposed in this invention fully considers the degradation of material properties under low-temperature conditions, thereby improving the accuracy of fatigue life prediction; it also fully considers the parameter uncertainties in the low-temperature fatigue life prediction model, making the prediction results more reliable. Attached Figure Description

[0016] Figure 1 This is a flowchart of the evaluation method of the present invention; Figure 2 The fatigue life prediction results for Q345qD steel at 0℃ in the examples are shown. Figure 3 The fatigue life prediction results for Q345qD steel at -20℃ are shown in the examples. Figure 4 The fatigue life prediction results for Q345qD steel at -40℃ are shown in the examples. Figure 5 The fatigue life prediction results for Q345qD steel at -60℃ are shown in the examples. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0018] Example 1

[0019] A method for assessing the fatigue life of low-temperature metals that takes into account uncertainties, such as Figure 1 As shown, it includes the following steps: S1. Collect fatigue life test data of low-temperature metallic materials; The experimental data includes the initial crack length a0 of the metallic material and the critical crack length a0 of the metallic material. c Elastic modulus E(T0) of metallic materials at room temperature, temperature factor b of elastic modulus, temperature factor q of material fatigue limit, size correction factor Y, and maximum stress of material. Fatigue limit of metallic materials at room temperature Fatigue crack propagation threshold of metallic materials at room temperature .

[0020] S2. Determine the parameter distribution range of the fatigue life prediction model for low-temperature metallic materials; Specifically, this includes: calculating the mean and standard deviation of the fuzzy parameters in the model based on the collected experimental data, and using the mean ± 3 times the standard deviation as the distribution range of the fuzzy parameters.

[0021] S3. Obtain the j-th membership value of the ith fuzzy number; Specifically, it includes: Assume that there are n independent fuzzy variables in the low-temperature metal fatigue life prediction model. The mean and standard deviation of each interval variable are respectively and ; Each fuzzy variable Performing α-cut decomposition, we obtain the following set of intervals: (1) in, (2) In formula (2) Let the i-th fuzzy variable be at the membership level μ j The formula for calculating the membership level of the corresponding interval is as follows: (3) In formula (2) and These represent the membership level μ of the i-th fuzzy parameter. j lower interval The lower and upper bounds are calculated using the following expression: (4) The i-th fuzzy variable is set at the membership level μ. j The corresponding interval below Further transform it into an array of the following form : (5) in: (6) (7) That is, the j-th membership value of the i-th fuzzy number.

[0022] S4. Determine whether to take values ​​for all membership degrees of all fuzzy numbers; Specifically, it includes: S3 is iterated over in a two-level loop structure. The first level loops over i, with a range of 1 to n. The second level loops over j, with a range of 0 to m. When i>n and j>m, it is considered that the values ​​of all fuzzy variables under all membership degrees have been obtained.

[0023] S5. Determine the values ​​of all fuzzy numbers under the j-th membership degree; Specifically, it includes: Since the value of the i-th fuzzy number at the j-th membership degree Given an array containing m-j+1 elements, combine all the values ​​of the fuzzy numbers in pairs, resulting in a total of (m-j+1) values. n The method involves using an array to calculate the k-th value of all fuzzy numbers for the j-th membership degree. express: (8).

[0024] S6. Calculate the low-temperature fatigue life range of metallic materials at the j-th membership degree; Specifically, it includes: Take the value of the fuzzy number under the j-th membership degree calculated in S5. Substitute other model parameters into the proposed low-temperature metal fatigue life assessment model as shown in equation (9), and calculate the results of the low-temperature metal fatigue life assessment model for the k-th value. ; (9) Repeat the above steps to calculate the low-temperature fatigue life assessment results for all possible values ​​of the metallic material under the j-th membership degree, and calculate the maximum and minimum values ​​of all results; (10) Then the low-temperature fatigue life range of the metallic material at the j-th membership degree It can be represented as .

[0025] The detailed derivation of the low-temperature metal fatigue life assessment model (9) is as follows: The fatigue life assessment model for metals at room temperature can be solved using the following expression: (11) Where a is the crack length, N f It is the number of cyclic loads the structure experiences before fatigue failure, B is the fatigue crack propagation coefficient, and ΔK is the stress intensity factor amplitude. th The fatigue crack propagation threshold is calculated using the following expressions:

[0026] Where E is the material's elastic modulus, and Y is a size-related correction factor. It is the maximum stress. This is the critical length of the crack. This refers to the material's fatigue limit. Considering the temperature dependence of the fatigue crack propagation threshold, its expression can be further rewritten as: (15) Where T and T0 represent low temperature and room temperature, respectively, with room temperature being 20℃. △K th (T) and △K th (T0) represents the fatigue crack propagation thresholds at low temperature and room temperature, respectively, and σ R (T) and σ R (T0) represents the material fatigue limit at low temperature and room temperature, respectively; Substituting equations (12)-(15) into equation (11), we get: (16) By integrating the above equation, we can obtain: (17) Where a0 is the initial crack length, a c It is the critical crack length; To further consider the material property degradation process under low-temperature conditions, a temperature factor is introduced to describe the changes in material fatigue limit and elastic modulus with temperature:

[0027] In the formula, q and b are temperature factors related to the fatigue limit and elastic modulus of the material, respectively; Substituting equations (18) and (19) into equation (17), we get: (20) S7. Determine whether to calculate all membership degrees; Specifically, this includes: iterating through the values ​​of membership degree j in S6, with the iteration range being from 0 to m. When j > m, it is considered that the calculation of material fatigue life under all membership degrees has been completed.

[0028] S8. Obtain the results of low-temperature metal fatigue life analysis considering uncertainties; Specifically, this includes: the low-temperature fatigue life range for each membership degree in S7. Organize and obtain the low-temperature fatigue life assessment results for all membership degrees. .

[0029] Example 2 The following uses Q345qD steel as an example to illustrate the evaluation method described in Example 1.

[0030] Based on historical test data, the elastic modulus E(T0) of Q345qD metallic material at room temperature is 209 MPa, the temperature factor of elastic modulus b is 110, the material fatigue limit temperature factor q is 0.00188, the size correction factor Y is 1.0, and the fatigue limit σ of the metallic material at 20℃ is... R (T0) = 252.6 MPa, fatigue crack propagation threshold ΔK for metallic materials at room temperature. th (T0) = 3.106, assuming the initial crack length a0 and the critical crack length a of the metallic material. c Maximum stress of material Fatigue crack propagation threshold ΔK in metallic materials at low temperatures th The variables are fuzzy, and their mean and standard deviation are shown in Table 1.

[0031] Table 1. Range of fuzzy parameters for Q345qD steel under low temperature conditions.

[0032] In the calculation, it is assumed that the distribution range of the above fuzzy variables is ±3 standard deviations from the mean, and each fuzzy variable is divided into 10 membership degrees. Based on the above steps, the fatigue life prediction results for Q345qD steel at different temperatures considering parameter uncertainties are as follows: Figures 2-5 As shown.

[0033] Figure 2 As shown, at 0℃, the fatigue life test value is 92070. When the membership degree μ=0.9, the estimated value calculated by the proposed method is 97698, and the relative error of the calculation result is 6.11%, which verifies the accuracy of the model.

[0034] Figure 3 As shown, at -20℃, the fatigue life test value is 129410. When the membership degree μ=0.9, the estimated value calculated by the proposed method is 122548, and the relative error of the calculation result is 5.30%, which verifies the accuracy of the model.

[0035] Figure 4 As shown, at -40℃, the fatigue life test value is 365596. When the membership degree μ=0.9, the estimated value calculated by the proposed method is 386189, and the relative error of the calculation result is 5.63%, which verifies the accuracy of the model.

[0036] Figure 5 As shown, at -60℃, the fatigue life test value is 438751. When the membership degree μ=0.9, the estimated value calculated by the proposed method is 431006, and the relative error of the calculation result is 1.77%, which verifies the accuracy of the model.

[0037] Table 2 compares the predicted fatigue life of Q345qD steel with experimental results at different temperatures using the proposed model when the membership degree is 0.9. The results in Table 2 demonstrate that the proposed model can effectively predict the fatigue life of Q345qD steel under low-temperature conditions, with an error controlled within approximately 5%, thus verifying the model's effectiveness and reliability.

[0038] Table 2. Estimated average fatigue life of Q345qD steel at different temperatures

[0039] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be included within the scope of protection of the present invention.

Claims

1. A method for assessing the fatigue life of low-temperature metals considering uncertainties, characterized in that, Includes the following steps: S1. Collect fatigue life test data of low-temperature metallic materials; S2. Determine the parameter distribution range of the fatigue life prediction model for low-temperature metallic materials; S3. Obtain the j-th membership value of the ith fuzzy number; S4. Determine whether to take values ​​for all membership degrees of all fuzzy numbers; S5. Determine the values ​​of all fuzzy numbers under the j-th membership degree; S6. Calculate the low-temperature fatigue life range of metallic materials at the j-th membership degree; S7. Determine whether to calculate all membership degrees; S8. Obtain the results of low-temperature metal fatigue life analysis considering uncertainties.

2. The method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, In S1, the experimental data includes the initial crack length a0 of the metallic material and the critical crack length a of the metallic material. c Elastic modulus E(T0) of metallic materials at room temperature, temperature factor b of elastic modulus, temperature factor q of material fatigue limit, size correction factor Y, and maximum stress of material. Fatigue limit of metallic materials at room temperature Fatigue crack propagation threshold of metallic materials at room temperature .

3. The method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, S2 specifically includes: calculating the mean and standard deviation of the fuzzy parameters in the model based on the collected experimental data, and taking the mean ± 3 times the standard deviation as the distribution range of the fuzzy parameters.

4. A method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, S3 specifically includes: Assume that there are n independent fuzzy variables in the low-temperature metal fatigue life prediction model. The mean and standard deviation of each interval variable are respectively and ; Each fuzzy variable Performing α-cut decomposition, we obtain the following set of intervals: (1) in, (2) In formula (2) Let the i-th fuzzy variable be at the membership level μ j The formula for calculating the membership level of the corresponding interval is as follows: （3） In formula (2) and These represent the membership level μ of the i-th fuzzy parameter. j lower interval The lower and upper bounds are calculated using the following expression: （4） The i-th fuzzy variable is set at the membership level μ. j The corresponding interval below Further transform it into an array of the following form : （5） in: (6) （7） That is, the j-th membership value of the i-th fuzzy number.

5. The method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, S4 specifically includes: S3 is iterated over in a two-level loop structure. The first level loops over i, with a range of 1 to n. The second level loops over j, with a range of 0 to m. When i>n and j>m, it is considered that the values ​​of all fuzzy variables under all membership degrees have been obtained.

6. The method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, S5 specifically includes: Since the value of the i-th fuzzy number at the j-th membership degree Given an array containing m-j+1 elements, combine all the values ​​of the fuzzy numbers in pairs, resulting in a total of (m-j+1) values. n The method involves using an array to calculate the k-th value of all fuzzy numbers for the j-th membership degree. express: （8）。 7. The method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, S6 specifically includes: Take the value of the fuzzy number under the j-th membership degree calculated in S5. Substitute other model parameters into the proposed low-temperature metal fatigue life assessment model as shown in equation (9), and calculate the results of the low-temperature metal fatigue life assessment model for the k-th value. ; （9） Repeat the above steps to calculate the low-temperature fatigue life assessment results for all possible values ​​of the metallic material under the j-th membership degree, and calculate the maximum and minimum values ​​of all results; （10） Then the low-temperature fatigue life range of the metallic material at the j-th membership degree It can be represented as.

8. The method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 7, characterized in that, The detailed derivation of the low-temperature metal fatigue life assessment model (9) is as follows: The fatigue life assessment model for metals at room temperature can be solved using the following expression: （11） Where a is the crack length, N f It is the number of cyclic loads the structure experiences before fatigue failure, B is the fatigue crack propagation coefficient, and ΔK is the stress intensity factor amplitude. th The fatigue crack propagation threshold is calculated using the following expressions: Where E is the material's elastic modulus, and Y is a size-related correction factor. It is the maximum stress. This is the critical length of the crack. This refers to the material's fatigue limit. Considering the temperature dependence of the fatigue crack propagation threshold, its expression can be further rewritten as: （15） Where T and T0 are low temperature and room temperature, respectively, and ΔK th (T) and △K th (T0) represents the fatigue crack propagation thresholds at low temperature and room temperature, respectively, and σ R (T) and σ R (T0) represents the material fatigue limit at low temperature and room temperature, respectively; Substituting equations (12)-(15) into equation (11), we get: （16） By integrating the above equation, we can obtain: （17） Where a0 is the initial crack length, a c It is the critical crack length; To further consider the material property degradation process under low-temperature conditions, a temperature factor is introduced to describe the changes in material fatigue limit and elastic modulus with temperature: ； In the formula, q and b are temperature factors related to the fatigue limit and elastic modulus of the material, respectively; Substituting equations (18) and (19) into equation (17), we get: （20）。 9. The method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, Specifically, S7 includes: iterating through the values ​​of membership degree j in S6, with the iteration range being from 0 to m. When j > m, it is considered that the calculation of material fatigue life under all membership degrees has been completed.

10. A method for assessing the fatigue life of low-temperature metals considering uncertainties according to claim 1, characterized in that, S8 specifically includes: the low-temperature fatigue life range for each membership degree in S7. Organize and obtain the low-temperature fatigue life assessment results for all membership degrees. .

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