Method for predicting high-cycle fatigue life of welded joint based on equivalent stress

Abstract

The invention discloses a method for predicting the high-cycle fatigue life of a welded joint based on equivalent cyclic stress, and relates to the technical field of prediction of the high-cycle fatigue life of the welded joint. The high-cycle fatigue life of the welded joint is predicted by utilizing the equivalent cyclic stress and combining a high-cycle fatigue coefficient and a high-cycle fatigue strength index of a welded joint material. Specifically, sigma eq is equal to sigma'f (2Nf) b. According to the method, the continuously changing cyclic stress in the fatigue process is considered, the high-cycle fatigue life of the welded joint is predicted through the equivalent cyclic stress, the problems that in the prior art, the prediction process is complex, the applicability is not high, and the limitation of a prediction model is large are solved, a theoretical basis and data support are laid for safe and reliable evaluation of components, and the method is suitable for popularization and application. Therefore, the method is suitable for popularization and application.

Description

Technical Field

[0001] The invention relates to the technical field of high cycle fatigue life prediction of welded joints, and in particular to a high cycle fatigue life prediction method for welded joints based on equivalent stress. Background Art

[0002] The key load-bearing structures of high-speed transport equipment such as aerospace and rail transit are often subjected to high-frequency cyclic loads during service, resulting in high-cycle fatigue failure. Therefore, it is necessary to carry out high-cycle fatigue life assessment on the key load-bearing structures of high-speed transport equipment to lay a theoretical foundation and data support for their safe and reliable service.

[0003] High cycle fatigue life is related to materials, organization, load and service environment, among which the sensitivity of cyclic loading reflects the characteristics of SN curve and is an important basis for evaluating the high cycle fatigue performance of welded joints. At present, the main methods for predicting high cycle fatigue life include: constant stress method, finite element simulation method and critical plane method.

[0004] The constant stress method for predicting the high cycle fatigue life of welded joints mainly relies on the analysis of local stresses in welded joints, which include but are not limited to the overall structural form, local joint form, load size and loading form, boundary constraints on the joint, local joint geometry, and residual stress. The constant stress method for predicting the high cycle fatigue life of welded joints is a complex process that needs to consider the influence of multiple factors. Therefore, its prediction process is time-consuming and labor-intensive, and is not easy to promote in actual engineering.

[0005] The finite element simulation method is mainly based on three-dimensional finite element simulation and dynamic response test. By studying the fatigue crack initiation and propagation characteristics of welded joints, the three stages of fatigue crack propagation are defined by using the relationship between simulated crack length and natural frequency. Then, the local stress-strain method is used to predict the high-cycle fatigue life of welded joints. However, for welded joints with different base materials, the high cycle fatigue life predicted by this method has a large deviation. For example, for welded joints with dual-phase TC4 titanium alloy as the base material, the high cycle fatigue life deviation range obtained by the finite element simulation method and the authoritative literature: "Microstructure and poresensitivities in very high cycle fatigue behaviors of titanium alloy weldedjoints under stress ratios" (Liu, F., Chen, Y., He, C., Li, L., Wang, C., Wang, Q., Liu, Y. 2024. Engineering Fracture Mechanics 295, 109801. hereinafter referred to as "Document 1") can reach up to 50%; for another example, for welded joints with aluminum alloy as the base material, similarly, the finite element simulation method and the authoritative literature: "Microstructure and fatigue properties of laser-MIG hybrid welding of medium-thickness 6005Aaluminum alloy”(Duan, C., Hao, X., Luo, X., Cao, X., Xu, H., Zhu, Z., 2024. Engineering Failure Analysis 165, 108753. hereinafter referred to as “Reference 2”) The deviation range of high cycle fatigue life obtained can reach up to 50%. Therefore, the finite element simulation method is not applicable to the prediction of high cycle fatigue life of welded joints of some materials.

[0006] The critical plane method can reveal the influence of cyclic load on fatigue life while considering the physical characteristic parameters in the fatigue process. In the critical plane method, the Matake model cannot reflect the influence of average stress on fatigue strength, the Susmel model is too complicated, and the Findley model mainly relies on the stress Mohr circle to establish a quantitative relationship between normal stress / shear stress and fatigue life, so it is an effective high-cycle fatigue life prediction method. At present, the research based on the Findley model mainly constructs the stress Mohr circle based on the maximum cyclic stress, thereby establishing a high-cycle fatigue life prediction model to predict the high-cycle fatigue life. However, during the fatigue process, the cyclic stress changes continuously. It is unreasonable to use the cyclic stress at a certain moment to establish a fatigue life prediction model, and it cannot well reflect the overall high-cycle fatigue life assessment of the welded joint.

[0007] In summary, the existing high-cycle fatigue life prediction methods cannot meet the high-cycle fatigue life prediction needs of key load-bearing structures of high-speed transport equipment due to problems such as complex prediction process, poor applicability, and large limitations of prediction models. Summary of the invention

[0008] The purpose of the present invention is to provide a method for predicting the high-cycle fatigue life of welded joints based on equivalent stress, which takes into account the continuously changing cyclic stress during the fatigue process and predicts the high-cycle fatigue life of welded joints through equivalent cyclic stress, thereby solving the problems of complex prediction process, poor applicability, and large limitations of the prediction model in the prior art.

[0009] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0010] A method for predicting the high cycle fatigue life of welded joints based on equivalent cyclic stress is used to predict the high cycle fatigue life of welded joints by combining the high cycle fatigue coefficient and high cycle fatigue strength index of the welded joint material. The specific method is as follows:

[0011] σ eq =σ′ f (2N f ) b

[0012] Among them, N f is the predicted value of high cycle fatigue life of welded joint; σ′ f is the high cycle fatigue coefficient; b is the high cycle fatigue strength index;

[0013] σ eq is the equivalent cyclic stress, which is calculated by the following formula:

[0014]

[0015] Where θ is the angle between the critical plane normal and the principal stress axis; σ max is the maximum cyclic stress.

[0016] Preferably, the σ′ f The values ​​of and b are obtained by fitting high cycle fatigue experimental data.

[0017] The design principle of the present invention is as follows:

[0018] Research has shown that at the same critical plane angle, the relationship between normal stress and shear stress corresponding to different stress Mohr circles is similar; and the relationship between normal stress and shear stress determines the fatigue strength of the material. Therefore, if these two relationships can be linked, an equivalent cyclic stress Mohr circle can be constructed, and an equivalent cyclic stress can be derived, a high-cycle fatigue life prediction model can be established while considering the continuous cyclic stress changes, making the high-cycle fatigue life prediction more reasonable and accurate.

[0019] The details are as follows:

[0020] 1. Equivalent cyclic stress σ eq Derivation:

[0021] In the initial state, the stress in the three directions (X, Y and Z directions) is: σ1 = σ2 = σ3 = 0; after cyclic loading, the stress in the three directions becomes: σ′1 = σ n , σ′2=σ′3=0, where the stress Mohr circle normal stress σ corresponding to any cyclic stress n And the shear stress △τ can be expressed as:

[0022]

[0023] Based on the T / 4 cycle loading characteristics, the normal stress and shear stress corresponding to the initial loading stress Mohr circle at the critical plane angle are: The normal stress and shear stress corresponding to the maximum load corresponding to the stress Mohr circle at the critical plane angle are:

[0024] From the initial loading to the maximum cyclic loading, the normal stress and shear stress corresponding to the stress Mohr circle at the critical plane angle for different cyclic stresses are all on the line connecting the initial loading and maximum loading normal stress and shear stress. This straight line can be expressed as:

[0025]

[0026] For any critical plane, the normal stress and shear stress satisfy the following relationship:

[0027]

[0028] In the above formula, κ is a material parameter, usually 0.3; f is the fatigue strength of the material. Combining formulas 3 and 4, the normal stress σ and shear stress τ corresponding to the equivalent cyclic stress Mohr circle at the critical plane angle can be obtained:

[0029]

[0030] According to the above normal stress and shear stress, the diameter of the stress Mohr circle at this time is calculated, which is the equivalent cyclic stress σ eq According to formula 1, the following equation holds:

[0031]

[0032] 2. Derivation of high cycle fatigue life prediction model based on equivalent cyclic stress:

[0033] Based on the Basquin formula, the relationship between cyclic stress and fatigue life can be expressed as:

[0034] σ a =σ′ f (2N f ) b , (8)

[0035] Substituting formula 7 into formula 9, we can get:

[0036]

[0037] Finally, based on the experimental fatigue data (obtained from room temperature high-cycle fatigue tests and high-temperature high-cycle fatigue tests), the high-cycle fatigue life corresponding to different equivalent cyclic stresses is obtained. Then, these experimental data are fitted to obtain a high-cycle fatigue life prediction model, and the high-cycle fatigue life of the welded joint is predicted (the software used for fitting is Origin).

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] (1) Based on the consideration of the continuously changing cyclic stress during the fatigue process, the present invention introduces equivalent cyclic stress, and combines the high-cycle fatigue coefficient and high-cycle fatigue strength index of the welded joint material to predict the high-cycle fatigue life of the welded joint. The verification results show that the predicted value of the present invention is close to the experimental value in the authoritative literature (such as literature 1 and 2), which shows that the prediction model designed by the present invention is effective. Thus, compared with the critical plane method, since the present invention takes into account the continuously changing cyclic stress during the fatigue process, the high-cycle fatigue life prediction is more reasonable, comprehensive and accurate, and better reflects the overall high-cycle fatigue life assessment of the welded joint.

[0040] Moreover, compared with the constant stress method, the prediction process of the present invention is very simple and the prediction means is more convenient. It only needs to use the angle between the normal line of the critical plane and the principal stress axis and the maximum cyclic stress to construct an equivalent cyclic stress, and then obtain the prediction result through the relationship between the cyclic stress and the fatigue life. Compared with the fatigue life prediction method using finite element analysis, with reference to Documents 1 and 2, the deviation of the prediction value of the present invention is much smaller than the deviation of the prediction value of the finite element simulation method. Therefore, the present invention can more accurately reflect the high-cycle fatigue life of the welded joint (especially the prediction of the high-cycle fatigue life of the welded joint of the alloy material).

[0041] (2) In the present invention, the values ​​of the high-cycle fatigue coefficient and the high-cycle fatigue strength index are directly obtained by fitting the high-cycle fatigue experimental data, which is not only convenient and real-time to obtain, but also can better reflect the material properties of the welded joint in the high-cycle fatigue performance evaluation, providing a guarantee for accurately predicting the high-cycle fatigue life of the welded joint.

[0042] (3) The present invention is ingeniously designed, easy to use, and has high prediction accuracy. It can better lay a theoretical foundation and data support for the safety and reliability evaluation of key load-bearing structures of high-speed carrier equipment, and thus serve the application of key load-bearing structures of high-speed carrier equipment such as aerospace, rail transit, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of the fitting results of the relationship between the equivalent cyclic stress and fatigue life of a welding joint in an embodiment of the present invention.

[0044] Figure 2 This is a schematic diagram of the fitting results of the relationship between the equivalent cyclic stress and fatigue life of another welded joint in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The present invention is further described below in conjunction with various embodiments and drawings. The embodiments of the present invention include but are not limited to the following embodiments.

[0046] Example

[0047] This embodiment provides a prediction scheme for the high cycle fatigue life of a welded joint, by establishing a high cycle fatigue life prediction model based on equivalent cyclic stress, and using equivalent cyclic stress to predict the high cycle fatigue life of a welded joint. The prediction model used in this embodiment is as follows:

[0048] σ eq =σ′ f (2N f ) b

[0049] Among them, σ eq is the equivalent cyclic stress, Nf is the predicted value of high cycle fatigue life of welded joint; σ′ f is the high cycle fatigue coefficient (unit: MPa); b is the high cycle fatigue strength index (dimensionless unit); in this embodiment, σ′ f The values ​​of and b are obtained by fitting the high cycle fatigue experimental data. It should be noted that, unlike the dimensionless unit of the traditional strain-controlled low cycle fatigue strength coefficient, σ′ in this embodiment f It is the stress-controlled high cycle fatigue coefficient, so the unit is MPa.

[0050] In the above model, σ eq It is calculated by the following formula:

[0051]

[0052] Where θ is the angle between the critical plane normal and the principal stress axis; σ max is the maximum cyclic stress (unit: MPa).

[0053] Among them, σ max It is directly obtained through the APDL (ANSYS Parametric Design Language) method of ANSYS software; θ is obtained by the following method:

[0054] (1) Determine the direction of the principal stress axis using analytical or graphical methods. The analytical method and the graphical method have their own characteristics. The analytical method directly obtains the result through mathematical calculation; while the graphical method intuitively displays the stress state through graphics. In practical applications, the direction of the principal stress axis can be determined according to the specific situation. For details, please refer to "A Simple Method for Determining the Direction of the Principal Stress under Plane Stress State" (Tao Jianxin, Gansu Science and Technology, Vol. 38, No. 5, 2009);

[0055] (2) Using the critical plane method to determine the orientation of the critical plane and obtain the normal line of the critical plane;

[0056] (3) Compare the direction vector of the principal stress axis with the normal vector of the critical plane to obtain the angle between the two vectors, that is, θ.

[0057] Two cases are selected below to verify the effectiveness of the model in this embodiment.

[0058] Case 1

[0059] The dual-phase TC4 titanium alloy was selected as the base material, and the TC4 titanium alloy flat plate was butt-jointed using the laser-arc hybrid welding technology. The specific welding process can be referred to the experimental part in the literature "Effect of three-stage heat treatment on mechanical properties and micro-deformation mechanism of TC4 titanium alloy welded joint" (Su R, Li H, Wang D, et al. Journal of Materials Research and Technology, 2024, 30: 6753-6770).

[0060] High cycle fatigue tests of the composite welded joints with different maximum cyclic stresses (310MPa, 330MPa, 350MPa, 370MPa and 390MPa) were carried out at room temperature, and the high cycle fatigue life under different maximum cyclic stresses was recorded.

[0061] Then, according to the experimental data obtained, the equivalent cyclic stress corresponding to each maximum cyclic stress is calculated, and the equivalent cyclic stress σ is established. eq and fatigue life prediction value N f The corresponding relationship between σ and σ is then fitted using Formula 9. eq and N f The value of can be used to get the predicted value of high cycle fatigue life of the welded joint. The fitted curve is as follows Figure 1 shown.

[0062] After fitting, the following model is obtained:

[0063] σ eq =1026.62×(2N f ) -0.099

[0064] Among them, the experimentally fitted σ′ f It is 1026.62MPa and b is -0.099.

[0065] Verify the above model:

[0066] The above model is verified using the experimental data in Reference 1. Figure 1 The dots in the figure represent the experimental data points in Reference 1, and the square data points represent the data in the above model. It can be seen that the experimental values ​​in Reference 1 are very close to the fitting curve. For example, according to Figure 1 The results show that when the equivalent cyclic stress is 300MPa, the experimental value of fatigue life is 185518, while the fatigue life prediction value N corresponding to the above model isf The calculated result is 118293, so the deviation of the predicted value is 36.23%; when the equivalent cyclic stress is 285MPa, the experimental value of fatigue life is 301995, and the fatigue life N corresponding to the above model is f The calculated result is 204824, and the deviation of the predicted value is 32.17%. Therefore, the overall deviation range of the above model fitting curve is mainly concentrated below 36%, which is much smaller than the 50% deviation range of the predicted value of the finite element simulation method, which shows that the use of this embodiment can more accurately reflect the high cycle fatigue life of the welded joint.

[0067] Case 2

[0068] Aluminum alloy was selected as the base material, and the aluminum alloy plates were butt-jointed using laser-arc hybrid welding technology. The specific welding process can be referred to the experimental part in the literature "Keyhole-induced pore formation mechanism in laser-MIG hybrid welding of aluminum alloy based on experiment and multiphase numerical model" (Huang S, Xu L, Lou M, et al. Journal of Materials Processing and Technology, 2023, 314: 117903).

[0069] High cycle fatigue tests were carried out on the composite welded joints at room temperature with different maximum cyclic stresses (120MPa, 130MPa, 140MPa and 150MPa), and the high cycle fatigue life under different maximum cyclic stresses was recorded.

[0070] Then, according to the experimental data obtained, the equivalent cyclic stress corresponding to each maximum cyclic stress is calculated, and the equivalent cyclic stress σ is established. eq and fatigue life prediction value N f The corresponding relationship between σ and σ is then fitted using Formula 9. eq and N f The value of can be used to get the predicted value of high cycle fatigue life of the welded joint. The fitted curve is as follows Figure 2 shown.

[0071] After fitting, the following model is obtained:

[0072] σ eq =362.18×(2N f ) -0.086

[0073] Among them, the experimentally fitted σ′f is 362.18MPa, and b is -0.086.

[0074] Verify the above model:

[0075] The above model is verified using the experimental data in Reference 2. Figure 2 The dots in the figure represent the experimental data points in document 2, and the square data points represent the data in this embodiment. It can be seen that the experimental values ​​in document 2 are very close to the fitting curve. For example, according to Figure 2 The results show that when the equivalent cyclic stress is 120MPa, the experimental value of fatigue life is 211522, while the fatigue life prediction value N corresponding to the above model is f The calculated result is 189439, so the deviation of the predicted value is 10.44%; the overall deviation range of the above model fitting curve is mainly concentrated around 10%, which is much smaller than the 50% deviation range of the predicted value of the finite element simulation method.

[0076] The scheme of the present invention seems simple, but it is not easy to think of. Only by deeply understanding the high-cycle fatigue failure mechanism of welded joints and making creative efforts on the basis of existing technologies can we achieve the prediction of high-cycle fatigue life of welded joints in a simple, reasonable and effective way and improve the accuracy of prediction, so as to better lay a theoretical foundation and data support for the safety and reliability assessment of key bearing structures of high-speed carrying equipment. Therefore, compared with the existing technologies, the present invention has outstanding substantive features and significant progress.

[0077] The above embodiments are only preferred implementation modes of the present invention and should not be used to limit the protection scope of the present invention. Any changes or modifications that are made to the main design concept and spirit of the present invention and have no substantive significance, and the technical problems they solve are still consistent with the present invention, should be included in the protection scope of the present invention.

Claims

1. A method for predicting high cycle fatigue life of welded joints based on equivalent cyclic stress, characterized in that: The high cycle fatigue life of welded joints is predicted by using an equivalent cyclic stress combined with the high cycle fatigue coefficient and high cycle fatigue strength index of the welded joint material. The specific method is as follows: s eq =σ′ f (2N f ) b Among them, N f is the predicted value of high cycle fatigue life of welded joint; σ′ f is the high cycle fatigue coefficient; b is the high cycle fatigue strength index; σ eq is the equivalent cyclic stress, which is calculated by the following formula: Where θ is the angle between the critical plane normal and the principal stress axis; σ max is the maximum cyclic stress.

2. The method for predicting high cycle fatigue life of welded joints based on equivalent cyclic stress according to claim 1, characterized in that: The σ′ f The values ​​of and b are obtained by fitting high cycle fatigue experimental data.

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