A method for predicting fatigue crack growth rate in the hysteresis effect influence zone under single peak overload condition

Abstract

The application provides a fatigue crack propagation rate prediction method for a hysteresis effect influence area under single-peak overload conditions, and belongs to the technical field of metal material fatigue crack propagation tests. y The size of a monotonic plastic zone under overload conditions is calculated, and the fatigue crack propagation rate of the hysteresis effect influence area under single-peak overload conditions is predicted through a modified Paris formula. The prediction method directly modifies the physical size of the plastic zone by introducing the strain hardening effect, fully considers the influence of the overload factor on the fatigue mechanism factor, solves the problem that the classic model cannot predict the overload hysteresis effect, the prediction result rate is closer to the actual test value, the model has clear physical meaning and simple calculation, and reliable basis is provided for fatigue life assessment of engineering structures.

Description

Technical Field

[0001] This invention belongs to the field of fatigue crack propagation testing technology for metallic materials, and particularly relates to a method for predicting the single-peak overload fatigue crack propagation rate based on strain hardening effect correction. Background Technology

[0002] Fatigue is one of the main causes of failure in metal structures during service, and its crack propagation behavior is heavily influenced by the load history. In practical engineering, structures often bear variable amplitude loads, among which a single tensile overload (i.e., "single-peak overload") is a fundamental and important load event that triggers a significant reduction in the subsequent fatigue crack propagation rate (i.e., the "hysteresis effect"). Accurately predicting the crack propagation behavior within the hysteresis effect zone is crucial for assessing the remaining life of the structure under complex loads and ensuring safety. Mechanisms such as residual compressive stress, plastic-induced crack closure, crack tip blunting, and crack bifurcation have been proposed to address the hysteresis phenomenon after a single peak overload. However, the classic Paris formula fatigue crack propagation model cannot accurately describe the fatigue crack propagation rate in the hysteresis effect zone under overload conditions. These problems make it difficult to guarantee the safe and reliable use of metal components and the prevention of fatigue failure, thus restricting the widespread use of high-performance metal structural materials.

[0003] To simulate overload hysteresis effects, various models have been proposed in existing technologies. For example, patent CN106886632B discloses a method for characterizing the hysteresis process using residual stress intensity factors and piecewise functions, and introduces overload cutoff ratio functions and compressive overload weakening factors. This model is relatively complex, and some of its assumptions differ from experimental observations. Patent CN118211382A focuses on quantifying the influence of residual stress in the crack wake by experimentally measuring the crack opening stress intensity factor, thereby determining the effective stress intensity factor range. This method relies on specific experimental testing methods. Another patent, CN120145724A, uses a cyclic cohesion model for numerical simulation, introducing strain hardening and strain rate hardening terms to simulate crack propagation under high-frequency variable amplitude loads. However, this is a computationally expensive finite element analysis method. Overall, existing prediction methods either rely on complex multi-parameter models and calculations or require specific experimental data, which limits their ease of use and universality in engineering applications. Furthermore, they fail to establish a clear physical relationship between the intrinsic mechanical properties of materials (such as strain hardening characteristics) and overload hysteresis effects in a concise and direct manner.

[0004] Therefore, it is urgent to study the fatigue crack propagation behavior in the hysteresis zone under a single tensile overload and to provide relevant prediction methods, which will help to accurately predict fatigue life under variable amplitude cyclic loading and guide loading control in engineering. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention provides a method for predicting the fatigue crack propagation rate in the hysteresis effect zone under single-peak overload conditions, comprising the following steps:

[0006] S1. Obtain the strain hardening exponent n and yield strength σ of the material to be predicted based on uniaxial tensile tests. y ;

[0007] S2. Based on the strain hardening exponent n and fatigue crack propagation experiments, the size of the monotonic plastic zone is calculated using the following formula:

[0008] Equation (1)

[0009] Equation (2)

[0010] Where, r m It is the size of the monotonic plastic region under a modified constant amplitude load, r ol It is the size of the monotonic plastic zone under modified overload conditions, K max It is the maximum stress intensity factor under constant amplitude load. It is the maximum stress intensity factor when the fatigue crack propagation rate reaches its minimum after applying overload;

[0011] S3. Based on the calculated size r of the monotonic plastic zone under the overload condition. ol The fatigue crack propagation rate da / dN in the hysteresis effect zone under the single-peak overload condition is predicted using the following formula:

[0012] Equation (3)

[0013] Equation (4)

[0014] Where C, m, and m1 are material constants, and a is the corresponding fatigue crack length. ol , These are the crack length and the maximum stress intensity factor when the fatigue crack propagation rate reaches its minimum after applying overload.

[0015] Furthermore, the strain hardening exponent n is obtained by fitting the true stress-true strain curve obtained from the uniaxial tensile test of the material using equation (7):

[0016] Equation (5)

[0017] Where σ is the true stress, ε is the true strain, β is a constant, and E is Young's modulus.

[0018] Furthermore, the stress intensity factor ΔK is calculated using the following formula:

[0019] Equation (6)

[0020] Where B is the fatigue specimen thickness, W is the fatigue specimen width, α is the ratio of the corresponding fatigue crack length to the fatigue specimen width, and ΔP is the difference between the maximum and minimum loading forces in the fatigue test.

[0021] Furthermore, the crack length 'a' is the minimum crack length when the fatigue crack propagation rate is minimized after the overload is applied. ol and the corresponding maximum stress intensity factor The material constants C, m, and m1 were obtained through single-peak overload fatigue crack propagation tests; these constants were determined by nonlinear regression fitting of fatigue crack propagation test data of the same material under single-peak overload conditions.

[0022] Compared with the prior art, the method of the present invention has the following advantages:

[0023] (1) High prediction accuracy and clear physical meaning: By introducing the strain hardening exponent n, an intrinsic property of the material, the size of the monotonic plastic zone under overload conditions is physically corrected, and a modified Paris model based on the ratio of plastic zone size is constructed. This method clearly establishes the physical relationship between the intrinsic hardening behavior of the material and the hysteresis effect, and the mechanism is transparent. Compared with the classic Paris model, which cannot describe the hysteresis phenomenon, or other analytical models that rely on complex parameters and assumptions, this method can more accurately predict the fatigue crack propagation rate in the unimodal overload hysteresis influence zone. Its prediction results are in excellent agreement with experimental values, with a correlation coefficient of up to 0.998.

[0024] (2) The model is simple, computationally efficient, and easy to apply in engineering: This invention provides a semi-empirical prediction method based on explicit analytical formulas, whose core parameters (such as strain hardening exponent n, yield strength σ) are relatively simple. y All of these (such as tensile strength) can be obtained through conventional uniaxial tensile testing of materials, without relying on expensive specialized experimental equipment or complex numerical simulations. This avoids the high computational costs and time consumption associated with numerical methods such as finite element analysis, enabling rapid evaluation and design iteration.

[0025] (3) Providing a reliable tool for the safety assessment and life management of engineering structures: By providing a high-precision and easy-to-implement method for predicting fatigue crack propagation rate, this invention can more reliably assess the remaining fatigue life of defective metal components (such as aerospace structures, bridges, pressure vessels, etc.) under variable amplitude loads. This helps to formulate more scientific maintenance strategies and provides a theoretical basis and practical tool for further research on how to actively extend the life of structures using controllable overloads (overload life extension), which is of great value to improving the safety and economy of critical infrastructure and equipment. Attached Figure Description

[0026] Figure 1 This is a comparison between the predicted fatigue crack propagation rate in the hysteresis effect zone under single-peak overload conditions using the method of this invention and the experimental results.

[0027] Figure 2 The stress intensity factor range (ΔK) and fatigue crack propagation rate (ΔK) are shown in different embodiments and comparative examples of the present invention. The fitted curve of ). Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings, specific embodiments and comparative methods. However, the present invention is not limited to the following embodiments and should not be construed as limiting the scope of protection of the present invention.

[0029] Example 1

[0030] 1. Obtain basic material performance parameters:

[0031] DP780 duplex steel plate with a thickness of B=1.418mm was selected and processed into standard tensile specimens and compact tensile (CT) fatigue specimens, wherein the width of the CT specimen was W=28mm. Uniaxial tensile tests were performed on the tensile specimens, and the load-displacement data were recorded and converted into true stress-true strain curves. These curves were then analyzed using equation (5). By fitting the plastic segment of the curve, the yield strength σ of the material can be obtained. y =546MPa, Young's modulus E=195GPa, strain hardening exponent n=7.257.

[0032] 2. Conduct fatigue crack propagation tests:

[0033] Fatigue crack propagation tests were conducted on CT specimens using an MTS810 testing machine. The experimental environment was ambient temperature and atmospheric conditions, and the loading waveform was a sine wave with a frequency of 4 Hz.

[0034] Constant amplitude loading stage: Apply constant amplitude load, maximum loading force P max The minimum loading force is 1000N, the stress ratio is 0.1, and the minimum loading force is P. min The load is 100N, and the load difference ΔP is 900N.

[0035] Overload event: When the fatigue crack stably propagates to a length a of 9.0 mm, a single-peak overload is applied, with an overload load P. ol The load was 1500N (overload ratio = 1500 / 1000 = 1.5), and then the load was restored to the original constant amplitude load to continue the test. This specimen is recorded as OL1.5-9.

[0036] Data acquisition: The crack length 'a' was monitored in real time using the crack tip opening displacement (COD) gauge and compliance method, and the corresponding number of cycles 'N' was recorded. The crack length 'a' was then calculated. -a curve.

[0037] 3. Rate prediction and parameter fitting:

[0038] For each data point (a, after overload) First, calculate the ratio α (a / W) of the corresponding fatigue crack length to the fatigue specimen width, and then use equation (6). ΔK is calculated.

[0039] Calculate r m Using the geometric factor function of equation (1), the maximum stress intensity factor K under constant amplitude load is calculated. max Then substitute it into equation (1). Calculate r m .

[0040] Calculate r ol Based on experimental data, find the point where the crack propagation rate da / dN reaches its minimum after applying overload, and record the crack length a at this point. ol and the corresponding maximum stress intensity factor Given n=7.257, σ y =546MPa and Substitution formula (2) Calculate r ol .

[0041] Parameter fitting: The experimentally measured... The calculated ΔK and r m and r ol Substitution formula (3) (4) The model parameters were obtained by fitting the data in the overload hysteresis region using the least squares method.

[0042] Technical effect: The model parameters obtained by fitting in this embodiment are: C=1.002×10 -26 m=15.622, m1=-0.02393. Substituting these parameters into the model yields a predicted curve and experimental data points (e.g., Figure 1 The results of the two methods were compared, and the correlation coefficient of the fitting results was as high as 0.985, which proves that the method of the present invention can accurately predict the fatigue crack propagation rate under this working condition.

[0043] Example 2

[0044] Fatigue crack propagation rate experiments were conducted using the same DP780 duplex steel as in Example 1 to obtain its stress intensity factor range (ΔK) and fatigue crack propagation rate (ΔK). Data. The constant amplitude fatigue loading stress ratio was 0.1, and the maximum loading force was 1000N. An overload of 2000N was applied at a fatigue crack length of 9mm (the specimen was denoted as OL2.0-9). The true stress-true strain curve of DP780 steel was obtained by uniaxial tensile test, and the strain hardening index n was obtained by fitting with equation (5). Then, the fatigue crack propagation rate in the hysteresis zone was predicted by using equations (1) to (4) and equation (6) in the same way as in Example 1.

[0045] Technical effect: The model parameters obtained by fitting in this embodiment are: C=1.815×10 -55 m=34.195, m1=-0.81013. Substituting these parameters into the model yields a predicted curve and experimental data points (e.g., Figure 1 The results of the two fitting results were compared, and the correlation coefficient was as high as 0.998, which proves that the method of the present invention can accurately predict the fatigue crack propagation rate under this working condition.

[0046] Example 3

[0047] Fatigue crack propagation rate experiments were conducted using the same DP780 duplex steel as in Example 1 to obtain its stress intensity factor range (ΔK) and fatigue crack propagation rate (ΔK). Data. The constant amplitude fatigue loading stress ratio was 0.1, and the maximum loading force was 1000N. An overload of 2000N was applied at a fatigue crack length of 11mm (the specimen was denoted as OL2.0-11). The true stress-true strain curve of DP780 steel was obtained by uniaxial tensile test, and the strain hardening index n was obtained by fitting with equation (5). Then, the fatigue crack propagation rate in the hysteresis zone was predicted by using equations (1) to (4) and equation (6) in the same way as in Example 1.

[0048] Technical effect: The model parameters obtained by fitting in this embodiment are: C=1.279×10 -53 m=30.416, m1=-0.9939. Substituting these parameters into the model, the resulting prediction curve and experimental data points are shown below. Figure 1 The results show a high correlation coefficient of 0.997 between the two fitting results, demonstrating that the method of this invention can accurately predict the fatigue crack propagation rate under this working condition.

[0049] Table 1 shows the parameters obtained by fitting the method provided by this invention in the three sets of embodiments.

[0050]

[0051] Comparative Example 1

[0052] Fatigue crack propagation rate experiments were conducted using the same DP780 duplex steel as in Example 1 to obtain its stress intensity factor range (ΔK) and fatigue crack propagation rate (ΔK). Data. The constant amplitude fatigue loading stress ratio is 0.1, and the maximum loading force is 1000N. No overload load (denoted as CA) is applied.

[0053] Figure 2 The stress intensity factor range (ΔK) and fatigue crack propagation rate obtained from the three sets of embodiments and comparative examples are... The data shows that, in a log-log coordinate system, ΔK and... The relationship is linear, which is consistent with the characteristics of the classic Paris model. However, all three overloaded examples exhibited hysteresis, and the fatigue crack propagation rate decreased significantly after the overload was applied, thus making it impossible to predict using the classic Paris model.

[0054] In summary, the present invention provides a method for predicting the fatigue crack propagation rate in the hysteresis effect zone under unimodal overload conditions. This method can accurately predict the fatigue crack propagation rate in the hysteresis effect zone under unimodal overload conditions, solving the problem that the Paris classical model cannot explain the overload hysteresis effect phenomenon. The predicted rate is closer to the actual test value, making it more reliable as a basis for materials engineering applications.

[0055] The above description is a preferred embodiment of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for predicting the fatigue crack propagation rate in the hysteresis zone under single-peak overload conditions, characterized in that, Includes the following steps: S1. Obtain the strain hardening exponent n and yield strength σ of the material to be predicted based on uniaxial tensile tests. y ; S2. Based on the strain hardening exponent n and fatigue crack propagation experiments, the size of the monotonic plastic zone is calculated using the following formula: Equation (1) Equation (2) Where, r m It is the size of the monotonic plastic region under a modified constant amplitude load, r ol It is the size of the monotonic plastic zone under modified overload conditions, K max It is the maximum stress intensity factor under constant amplitude load. It is the maximum stress intensity factor when the fatigue crack propagation rate reaches its minimum after applying overload; S3. Based on the calculated size r of the monotonic plastic zone under the overload condition. ol The fatigue crack propagation rate da / dN in the hysteresis effect zone under the single-peak overload condition is predicted using the following formula: Equation (3) Equation (4) Where C, m, and m1 are material constants, and a is the corresponding fatigue crack length. ol , These are the crack length and the maximum stress intensity factor when the fatigue crack propagation rate reaches its minimum after applying overload.

2. The method for predicting the fatigue crack propagation rate in the hysteresis effect zone under single-peak overload conditions according to claim 1, characterized in that, The strain hardening exponent n is obtained by fitting the true stress-true strain curve obtained from the uniaxial tensile test of the material using equation (7): Equation (5) Where σ is the true stress, ε is the true strain, β is a constant, and E is Young's modulus.

3. The method for predicting the fatigue crack propagation rate in the hysteresis effect zone under single-peak overload conditions according to claim 1 or 2, characterized in that, The stress intensity factor ΔK is calculated using the following formula: Equation (6) Where B is the fatigue specimen thickness, W is the fatigue specimen width, α is the ratio of the corresponding fatigue crack length to the fatigue specimen width, and ΔP is the difference between the maximum and minimum loading forces in the fatigue test.

4. The method for predicting the fatigue crack propagation rate in the hysteresis effect zone under single-peak overload conditions according to claim 1, characterized in that, The crack length 'a' that reaches the minimum fatigue crack propagation rate after applying overload. ol and the corresponding maximum stress intensity factor The material constants C, m, and m1 were obtained through single-peak overload fatigue crack propagation tests; these constants were determined by nonlinear regression fitting of fatigue crack propagation test data of the same material under single-peak overload conditions.

Images