A multi-shaft high-cycle fatigue life prediction method suitable for out-of-phase loading working conditions

Abstract

The application provides a multi-axle high-cycle fatigue life prediction method suitable for out-of-phase loading conditions, and the main steps include: selecting damage control parameters based on the critical plane method and performing calculation and analysis; summarizing the influence law of the load path on the damage control parameters under the out-of-phase loading condition; redefining the non-proportionality from the stress angle, and defining the additional damage coefficient by considering the additional strengthening property of the material itself; and establishing a multi-axle high-cycle fatigue life prediction model capable of reflecting the rapid reduction of fatigue life with the increase of the phase difference. The model established by the application can simultaneously consider simple loading, biaxial in-phase loading and out-of-phase loading, is simple in form, easy to determine parameters and convenient for engineering application.

Description

Technical Field

[0001] This invention relates to the field of service safety assessment of mechanical components, and more specifically to the research on high-cycle fatigue life prediction methods under multi-axis heterogeneous loading conditions, and particularly to a multi-axis high-cycle fatigue life prediction method applicable to heterogeneous loading conditions. Background Technology

[0002] Fatigue is a process in which mechanical components undergo localized permanent structural changes after being subjected to sufficient cyclic disturbance loads. In modern industry, fatigue failure is the most common form of damage. In real life, the service environment of mechanical components is extremely complex, making research on multiaxial fatigue life prediction a hot topic, especially research on multiaxial high-cycle fatigue under heterogeneous loading, which can more effectively meet the current demands for complex service environments, high quality, and long service life of mechanical components.

[0003] Existing multiaxial high-cycle fatigue failure criteria cannot comprehensively cover all possible situations, but for certain specific cases, some criteria are still quite accurate in prediction. Representative examples include the equivalent stress criterion, the stress invariant criterion, and the critical surface stress criterion. The critical surface method, proposed based on the crack initiation and propagation mechanism, focuses on the fatigue failure surface, has clear physical meaning, and provides high accuracy in calculation results, making it widely accepted. The Matake criterion uses the surface with the maximum shear stress amplitude as the critical surface and constructs fatigue damage control parameters by linearly combining it with the maximum normal stress on that surface; it is a classic criterion in the critical surface method. Ohka-Wa and Vu et al., when using crack replication technology to study the crack initiation and propagation behavior of S45C and C35 steels, found that under multiaxial loading, crack propagation is divided into a first stage (propagation along the plane of maximum shear stress) and a second stage (propagation along axial stress), and the transition length of the second stage is affected by the stress amplitude ratio and phase difference. Verreman et al. conducted multiaxial high-cycle fatigue tests on 1045 steel and found that the stress amplitude ratio significantly affects the crack propagation shape along the depth direction. Liu Jia et al. selected strain as the damage control parameter based on the critical surface principle and predicted the fatigue life of four materials, including 1045HR steel, with relatively ideal prediction results. Jiang Chao et al. established a new multiaxial low-cycle fatigue life prediction model by analyzing the critical surface strain parameter and considering plastic strain. The method is simple and has good prediction results, but it does not further consider the applicability of multiaxial high-cycle fatigue from the perspective of stress. Most of the above methods are applicable to low-cycle fatigue and fail to fully consider the additional strengthening behavior caused by heterogeneous loading paths. Summary of the Invention

[0004] The existing fatigue prediction methods mentioned above are mostly applicable to low-cycle fatigue and fail to fully consider the additional strengthening behavior caused by heterogeneous loading paths. Therefore, this invention provides a multi-axis high-cycle fatigue life prediction method applicable to heterogeneous loading conditions. This invention is simple in principle, convenient for engineering applications, and can simultaneously consider simple loading as well as multi-axis in-phase and heterogeneous loading conditions.

[0005] The technical means employed in this invention are as follows:

[0006] A method for predicting the multiaxial high-cycle fatigue life under heterogeneous loading conditions includes the following steps:

[0007] S1. Perform stress state analysis on a standard thin-walled circular tube test specimen to obtain the maximum shear stress value at any angle θ to the axial direction of the specimen.

[0008] S2. Based on the critical surface method, damage control parameters are selected and calculated and analyzed to obtain the curve of the maximum shear stress history of the critical surface under the heterogeneous loading path.

[0009] S3. Based on the results of damage control parameter calculation and analysis, define the influence parameter g of the heterogeneous loading path;

[0010] S4. Based on the above-mentioned heterogeneous loading path influence parameter g, and considering the overall additional strengthening degree of the entire angle domain, define the non-proportional degree L;

[0011] S5. Taking into account the inherent strengthening properties of the material and the non-proportionality of the load path L, define the non-proportional additional damage coefficient ρ.

[0012] S6. By introducing a non-proportional additional damage coefficient ρ, a multi-axis high-cycle fatigue life prediction model based on the critical surface and comprehensively considering the influence of heterogeneous loading paths and the additional strengthening properties of the material itself is established using the Von-Mises form. Multi-axis high-cycle fatigue life prediction is performed based on the multi-axis high-cycle fatigue life prediction model.

[0013] Furthermore, stress state analysis was performed on the standard thin-walled circular tube specimen to obtain the maximum shear stress value at any angle θ to the specimen's axis, including:

[0014] Under combined tension and torsion loading, the specimen surface is in a plane stress state, with a normal stress σ on the plane at an angle θ to the specimen axis. θ and shear stress τ θ Expressed as:

[0015]

[0016]

[0017] Where, σ x For axial stress, σx =σ m +σ a sinwt,τ xy For shear stress, σ a and τ a These are the axial and tangential stress amplitudes, σ and σ', respectively. m and τ m Here, σ0 represents the axial and tangential mean stresses, respectively, and w represents the loading frequency. The phase angle;

[0018] Based on the normal stress σ on the plane that makes an angle θ with the axial direction of the specimen... θ and shear stress τ θ The expression for the maximum shear stress value at any angle θ to the specimen axis is derived as follows:

[0019]

[0020] Where λ=τ a / σ a The stress ratio is given.

[0021] Furthermore, based on the critical surface method, damage control parameters were selected and calculated and analyzed to obtain the variation curve of the maximum shear stress at the critical surface under the heterogeneous loading path, including:

[0022] The critical surface is defined as the surface where the maximum shear stress is located, and the maximum shear stress and the normal stress on this surface are selected as damage control parameters.

[0023] The Mohr's circle theory was used to analyze the time evolution of damage control parameters under uniaxial and biaxial in-phase loading. Based on the maximum shear stress τ at an arbitrary angle θ to the specimen axis, the analysis was conducted. max,θ Expression analysis of the time evolution of damage control parameters under biaxial heterogeneous loading.

[0024] Furthermore, the formula for the influence parameter g of the heterogeneous loading path is:

[0025]

[0026] Where, minτ max,θ,np minτ max,θ,p These represent the minimum values ​​of the maximum shear stress on each plane at an angle θ to the axial direction under both non-phase and in-phase loading conditions. θ0 represents the maximum shear stress on the critical surface under heterogeneous and in-phase loading conditions, respectively. The subscripts p and np represent biaxial in-phase loading and biaxial heterogeneous loading, respectively, and θ0 indicates the location of the critical surface.

[0027] Furthermore, the formula for expressing the non-proportionality L of the load path is:

[0028]

[0029] in, The maximum shear stress at the critical surface is denoted by , and m is a proportionality coefficient representing the degree of additional hardening by the loading path within the angular domain. denoted as phase angle, and g is the parameter affecting the out-of-phase loading path.

[0030] Furthermore, the formula for expressing the non-proportional additional damage coefficient ρ is:

[0031]

[0032] Where L is the non-proportional loading path and α is the material additional strengthening coefficient.

[0033] Furthermore, the formula for expressing the multiaxial high-cycle fatigue life under heterogeneous loading conditions is as follows:

[0034]

[0035] Where, σ Hm For the mean hydrostatic stress, σ M Let N be the Mises equivalent stress, f(N) be the stress-life relationship, and the most commonly used Basquin power function expression be used here. ρ is the non-proportional additional damage coefficient.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] This invention takes fatigue fracture mechanism as its starting point, selects and analyzes damage control parameters based on the critical surface, clarifies the variation law of critical surface damage control parameters with time and phase angle under different loading methods, and considers the additional strengthening degree of heterogeneous loading path from the perspective of domain. Combining the material's own additional strengthening properties, a non-proportional additional damage coefficient ρ is introduced. Using the Von-Mises form, a stress-expressed multiaxial high-cycle fatigue life prediction model is established. The model is simple in form, the parameters are easy to determine, and it is convenient for engineering applications. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart of a multi-axis high-cycle fatigue life prediction method applicable to heterogeneous loading conditions according to the present invention.

[0040] Figure 2 This is a schematic diagram of plane stress analysis under a simple loading path in this invention.

[0041] Figure 3 This is a graph showing the variation of the maximum shear stress at the critical surface in this invention.

[0042] Figure 4 Hereinafter, the angle domains A and B are defined in this invention.

[0043] Figure 5 This is a graph showing the variation of the influence parameter g with the phase angle under different stress ratios in this invention.

[0044] Figure 6 This is a graph showing the variation of the influence parameter g with stress ratio under different phase differences in this invention.

[0045] Figure 7 This is a comparison chart of the multi-model predicted life and the experimental life of the LY12CZ aluminum alloy material involved in this invention.

[0046] Figure 8 This is a comparison chart of the multi-model predicted life and the experimental life of the 30CrMnSiA steel material involved in this invention.

[0047] Figure 9 This is a comparison chart of the multi-model predicted life and the experimental life of the 0.51% high carbon steel material involved in this invention. Detailed Implementation

[0048] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0049] This invention selects stress as the damage control parameter based on the critical surface method and performs calculations and analyses. It summarizes the variation law of the damage control parameter under heterogeneous loading and defines the path influence parameter g. Considering the overall influence of the load path in the angular domain, a new non-proportional additional damage coefficient ρ is further defined. This coefficient is then combined with the damage control parameter selected based on the critical surface to establish a new multiaxial high-cycle fatigue life prediction model based on the Mises form. Specifically, as follows... Figure 1 As shown, the method of the present invention specifically includes the following steps:

[0050] S1. Perform stress state analysis on a standard thin-walled circular tube test specimen to obtain the maximum shear stress value at any angle θ to the specimen's axial direction.

[0051] Specifically, considering the relatively thin wall thickness of the specimen, the radial stress gradient difference is ignored. Under the combined tension and torsion loading state, the surface of the specimen is in a plane stress state, and the normal stress σ on the plane with an angle of θ with the specimen axis is... θ and shear stress τ θ Expressed as:

[0052]

[0053] Where, σ x For axial stress, σ x =σ m +σ a sinwt,τ xy For shear stress, σ a and τ a These are the axial and tangential stress amplitudes, σ and σ', respectively. m and τ m Here, σ0 represents the axial and tangential mean stresses, respectively, and w represents the loading frequency. This is the phase angle.

[0054] Based on the above, the normal stress σ on the plane with an angle θ to the axial direction of the specimen is obtained. θ and shear stress τ θ The expression for the maximum shear stress at any angle θ to the specimen axis was derived as follows:

[0055]

[0056] Where λ=τ a / σ a The stress ratio is given.

[0057] S2. Based on the critical surface method, damage control parameters are selected and calculated and analyzed to obtain the curve of the maximum shear stress history of the critical surface under the heterogeneous loading path.

[0058] Specifically, based on the fact that fatigue cracks mostly initiate in the plane of maximum shear stress, and that the propagation rate is determined by the range of maximum shear stress, while normal stress promotes crack initiation, the critical surface is defined as the plane of maximum shear stress. The maximum shear stress and the normal stress on this plane are selected as damage control parameters. The Mohr's circle theory is used to analyze the time-varying history of the damage control parameters under uniaxial and biaxial in-phase loading. Based on the maximum shear stress τ at an arbitrary angle θ to the specimen axis... max,θ Expression analysis of the time evolution of damage control parameters under biaxial heterogeneous loading.

[0059] S3. Based on the above damage control parameter calculation and analysis, define the parameter g that affects the heterogeneous loading path, and explain the rationality of this parameter.

[0060] Specifically, the formula for the parameter g, which is influenced by the out-of-phase loading path, is as follows:

[0061]

[0062] Where, minτ max,θ,np minτ max,θ,p These represent the minimum values ​​of the maximum shear stress on each plane at an angle θ to the axial direction under both non-phase and in-phase loading conditions. θ0 represents the maximum shear stress on the critical surface under heterogeneous and in-phase loading conditions, respectively. The subscripts p and np represent biaxial in-phase loading and biaxial heterogeneous loading, respectively, and θ0 indicates the location of the critical surface.

[0063] Analyzing the variation characteristics of the influence parameter *g* of the non-proportional loading path under different stress ratios with the phase angle reveals that the trend of *g*'s variation is consistent with the trend of the degree of non-proportionality, effectively reflecting the additional strengthening effect of the heterogeneous loading path. Further analysis shows that when the phase angle is 0°, the influence parameter *g* remains 0, indicating that it does not affect the calculation and analysis under in-phase loading conditions. When the phase angle is 90°, the influence parameter *g* remains at its maximum, which is consistent with the phenomenon that the degree of additional strengthening increases with the increase of the loading phase difference, proving the rationality of the defined parameter *g*.

[0064] S4. Based on the above-mentioned heterogeneous loading path influence parameter g, and considering the overall additional strengthening degree of the entire angular domain, define the non-proportional degree L.

[0065] Specifically, the influence parameter g of the heterogeneous loading path is defined by calculating, analyzing, and summarizing the laws governing damage parameters selected based on the critical surface criterion, taking into account τ in the angle domains A and B. max,θ The maximum and minimum values ​​change continuously with the phase difference, that is, only the value of τ on a plane at an angle θ to the axis is considered. max,θ Since the overall additional enhancement degree of the entire angular domain is not considered, a scaling factor m is introduced to characterize the additional enhancement degree within the angular domain, thus establishing the non-scalability L:

[0066]

[0067] in, The maximum shear stress at the critical surface is denoted by , and m is a proportionality coefficient representing the degree of additional hardening by the loading path within the angular domain. denoted as phase angle, and g is the parameter affecting the out-of-phase loading path.

[0068] S5. Taking into account the inherent strengthening properties of the material itself and the non-proportional load path L mentioned above, a non-proportional additional damage coefficient ρ is defined.

[0069] Specifically, most metallic materials are collections of numerous tiny grains, which are broadly classified into cubic and hexagonal grains. Furthermore, anisotropy exists within each individual grain. Grain type, size, and different aggregation and slip systems all contribute to variations in the inherent strengthening properties of different materials. According to literature reports, the formula for calculating the inherent strengthening coefficient α of a material is:

[0070]

[0071] Where α is the additional strengthening coefficient, β is the static strengthening coefficient, and σ u For tensile strength, σ y It represents the yield strength.

[0072] Taking into account both the path nonproportionality and the material's inherent strengthening properties on multiaxial fatigue life, a new nonproportional additional damage coefficient ρ is defined:

[0073]

[0074] Where L is the non-proportional loading path and α is the material additional strengthening coefficient.

[0075] S6. By introducing a non-proportional additional damage coefficient ρ, a multiaxial high-cycle fatigue life prediction model based on the critical surface and comprehensively considering the influence of heterogeneous loading paths and the additional strengthening properties of the material itself is established using the Von-Mises form.

[0076]

[0077] Where, σ Hm For the mean hydrostatic stress, σ M For Mises equivalent stress, f(N) is the stress-life relationship. Here, the most commonly used Basquin power function expression is selected, and ρ is the non-proportional additional damage coefficient.

[0078] The following specific application examples will further illustrate the solution and effects of the present invention.

[0079] The multiaxial high-cycle fatigue life prediction method given in this embodiment includes the following steps:

[0080] Step 1: Under room temperature conditions, standard thin-walled circular tube specimens of different materials are subjected to uniaxial, in-phase, and out-of-phase tensile-torsional biaxial sinusoidal loading, and stress state analysis is performed to obtain the maximum shear stress value at any angle θ to the specimen axis.

[0081]

[0082] Step 2: Based on the fact that fatigue cracks mostly initiate in the plane of maximum shear stress, and the propagation rate is determined by the range of maximum shear stress, while normal stress promotes crack initiation, the critical surface is defined as the plane of maximum shear stress. The maximum shear stress and the normal stress on this surface are selected as damage control parameters. The Mohr's circle theory is used to analyze the time evolution of the damage control parameters (maximum shear stress and normal stress at the critical surface) at arbitrary points on the surface of thin-walled circular tube specimens under uniaxial and biaxial in-phase loading. For example... Figure 2 As shown. Based on the above, the maximum shear stress τ at any angle θ to the specimen axis... max,θ Expression analysis of the time evolution of damage control parameters under biaxial heterogeneous loading, such as Figure 3 As shown. Figure 2 By comparing the maximum shear stress on the critical surface and the normal stress on the surface under uniaxial tension / compression, pure torsion, and in-phase tension / torsion loading, it was found that: under uniaxial tension / compression, the maximum shear stress on the critical surface is equal to the normal stress on the surface, and the critical surface forms a 45° angle with the axial direction; under pure torsion loading, the critical surface always forms a 0° angle with the axial direction, and the normal stress on the critical surface is always 0; under in-phase loading, the position of the critical surface depends on the magnitude of the tension / torsion load. The position of the critical surface is different depending on the tension / torsion load stress ratio, but the position of the critical surface does not change with time. Figure 3 Under heterogeneous loading paths, when the stress ratio is The variation of the maximum shear stress in each plane with the phase angle when the equivalent Mises stress is 200 MPa reveals that the maximum shear stress τ between the planes near the critical surface is... max,θ The magnitude of τ decreases as the phase angle increases; when the phase angle is 90°, τ max,θ To reach a minimum. Observing the variation of the maximum shear stress in various planes at different phase angles, it can be found that the maximum shear stress in some planes increases with the increase of the phase angle, defined as angular domain A; while the maximum shear stress in some planes decreases with the increase of the phase angle, defined as angular domain B; and angular domain A = angular domain B = 45°, such as... Figure 4 As shown. τ of each plane in the angular domain B. max,θ The degree to which the phase angle decreases with increasing phase angle is greater than that of τ in each plane of the angular domain A. max,θ The increase with increasing phase angle is much smaller. And when the phase angle is 90°, τ in the angle domain A... max,θ To reach its maximum, τ in the angle domain B max,θ It reaches its minimum. This phenomenon is caused by the continuous change in the direction of the principal stress, and it becomes more pronounced as the degree of rotation increases.

[0083] Step 3, through Figure 3 , Figure 4Analysis revealed that the loading path has a certain influence on the defined damage control parameters. The influence law is summarized, and the parameter g of the heterogeneous loading path influence is defined as follows:

[0084]

[0085] Where, minτ max,θ,np minτ max,θ,p These represent the minimum values ​​of the maximum shear stress on each plane at an angle θ to the axial direction under both non-phase and in-phase loading conditions. These represent the maximum shear stress values ​​on the critical surface under heterogeneous and homogeneous loading conditions, respectively.

[0086] Analyze the characteristics of the influence parameter g of the non-proportional loading path under different stress ratios as a function of phase angle, such as... Figure 5 As shown, from Figure 5 The variation trend of g can be observed to be consistent with the variation trend of the non-proportional loading degree, which well reflects the additional strengthening degree of the heterogeneous loading path. Analysis of the variation trend of the non-proportional loading path influence parameter g with stress ratio, such as... Figure 6 As shown, when the phase angle is 0°, the influence parameter g is always 0, indicating that the influence parameter g does not affect the calculation and analysis under in-phase loading. When the phase angle is 90°, the influence parameter g remains at its maximum, which is consistent with the phenomenon that the degree of non-proportional additional strengthening increases with the increase of the loading phase difference, proving the rationality of the defined parameter g. Moreover, when the stress ratio λ = 0.6, the influence parameter g reaches its peak value, indicating that the loading path with α = 90° and λ = 0.6 has the greatest impact on the degree of additional strengthening of the material, and this loading path should be avoided as much as possible in engineering practice.

[0087] Step 4: Based on the above-mentioned heterogeneous loading path influence parameter g, consider the overall additional strengthening degree of the entire angular domain and define the non-proportional degree L.

[0088] The influence parameter g of the heterogeneous loading path is defined by calculating, analyzing, and summarizing the laws governing damage parameters selected based on the critical surface criterion, taking into account τ in the angle domains A and B. max,θ The maximum and minimum values ​​change continuously with the phase difference, that is, only the value of τ on a plane at an angle θ to the axis is considered. max,θ Since the overall additional enhancement degree of the entire angular domain is not considered, a scaling factor m is introduced to characterize the additional enhancement degree within the angular domain, thus establishing the non-scalability L:

[0089]

[0090] Among them, among them, The maximum shear stress at the critical surface is denoted by , and m is a proportionality coefficient representing the degree of additional hardening by the loading path within the angular domain. denoted as phase angle, and g is the parameter affecting the out-of-phase loading path.

[0091] Step 5: Taking into account the inherent strengthening properties of the material and the non-proportional load path L mentioned above, define the non-proportional additional damage coefficient ρ.

[0092] Most metallic materials are collections of numerous tiny grains, which are broadly classified into cubic and hexagonal grains. Anisotropy exists within each individual grain, and the type, size, aggregation, and slip system of the grains all contribute to differences in the inherent strengthening properties of different materials. According to literature reports, the formula for calculating the inherent strengthening coefficient α of a material is:

[0093]

[0094] Where α is the additional strengthening coefficient, β is the static strengthening coefficient, and σ u For tensile strength, σ y It represents the yield strength.

[0095] Taking into account both the path nonproportionality and the material's inherent strengthening properties on multiaxial fatigue life, a new nonproportional additional damage coefficient ρ is defined:

[0096]

[0097] Where L is the non-proportional loading path and α is the material additional strengthening coefficient.

[0098] Step 6: Since materials exhibit anisotropy in tension and compression, tensile stress is often detrimental to fatigue, and this effect can be represented by the magnitude of the mean stress. Considering the relatively low stress level in high-cycle fatigue, the influence of the mean stress becomes even more important. This invention introduces stress triaxiality. To consider the influence of mean stress; and by introducing a non-proportional additional damage coefficient ρ, a multiaxial high-cycle fatigue life prediction model based on the critical surface and comprehensively considering the influence of heterogeneous loading paths and the inherent strengthening properties of the material is established using the Von-Mises form:

[0099]

[0100] Where, σ Hm For the mean hydrostatic stress, σ M Let f(N) be the Mises equivalent stress, f(N) be the stress-life relationship, and the most commonly used Basquin power function expression is selected here. ρ is the non-proportional additional damage coefficient.

[0101] To verify the model's accuracy, three materials were extracted from three published papers: LY12CZ aluminum alloy, 30CrMnSiA steel, and 0.51% high-carbon steel. All three materials are isotropic or weakly anisotropic to ensure the applicability of the Mises equivalent stress method. Multiaxial fatigue test data for the three materials were then analyzed... Figure 1 The computational process in the model is used to perform lifetime prediction analysis, and the predicted lifetime is compared with the experimental lifetime, as well as with the predicted lifetimes of various other models. The results are as follows: Figure 7 , Figure 8 , Figure 9 As shown in the figure, the life prediction results of this model for different materials are basically within the three-fold error band, and 87% of the data are within the two-fold error band. Compared with other models, it has higher prediction accuracy and is more suitable for multi-axis high-cycle fatigue life prediction.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the multiaxial high-cycle fatigue life under heterogeneous loading conditions, characterized in that, Includes the following steps: S1. Perform stress state analysis on a standard thin-walled circular tube test specimen to obtain stress values ​​at any angle relative to the specimen's axis. The maximum shear stress values ​​include: Under combined tension and torsion loading, the specimen surface is in a plane stress state, with an angle of [angle missing] with the specimen axis. Normal stress on a plane and shear stress Expressed as: in, For axial stress, , For shear stress, , and These are the axial and tangential stress amplitudes, respectively. and These are the axial and tangential mean stresses, respectively. For loading frequency, Phase angle; Based on the obtained angle with the axial direction of the specimen... Normal stress on a plane and shear stress Calculate the angle between the specimen axis and the axis of the specimen. The expression for the maximum shear stress value: in, Stress ratio; S2. Based on the critical surface method, damage control parameters are selected and calculated and analyzed to obtain the variation curve of the maximum shear stress at the critical surface under the heterogeneous loading path. S3. Based on the results of damage control parameter calculation and analysis, define the influence parameter g of the heterogeneous loading path; S4. Based on the above-mentioned heterogeneous loading path influence parameter g, and considering the overall additional strengthening degree of the entire angle domain, define the load path non-proportional degree L. S5. Taking into account the inherent strengthening properties of the material and the non-proportional load path L, define a non-proportional additional damage coefficient. ; S6. By introducing a non-proportional additional damage coefficient A multiaxial high-cycle fatigue life prediction model based on the critical surface and taking into account the influence of heterogeneous loading paths and the additional strengthening properties of the material itself is established using the Von-Mises form. Multiaxial high-cycle fatigue life prediction is performed based on the multiaxial high-cycle fatigue life prediction model.

2. The method for predicting the multi-axis high-cycle fatigue life under heterogeneous loading conditions according to claim 1, characterized in that, Damage control parameters were selected and calculated based on the critical surface method, and the variation curve of the maximum shear stress at the critical surface under heterogeneous loading path was obtained, including: The critical surface is defined as the surface where the maximum shear stress is located, and the maximum shear stress and the normal stress on this surface are selected as damage control parameters. The Mohr's circle theory was used to analyze the time evolution of damage control parameters under uniaxial and biaxial in-phase loading. Based on the above, the parameters were adjusted at any angle to the specimen axis. Maximum shear stress value Expression analysis of the time evolution of damage control parameters under biaxial heterogeneous loading.

3. The method for predicting the multiaxial high-cycle fatigue life under heterogeneous loading conditions according to claim 1, characterized in that, The formula for the influence parameter g of the heterogeneous loading path is: in, , The angles with the axial direction under different phase and same phase loading conditions are respectively: The minimum value of the maximum shear stress on each plane, , These represent the maximum shear stress values ​​on the critical surface under heterogeneous and homogeneous loading conditions, respectively, with subscripts indicating the values. and These represent biaxial in-phase loading and biaxial out-of-phase loading, respectively. This indicates the location of the critical surface.

4. The method for predicting the multiaxial high-cycle fatigue life under heterogeneous loading conditions according to claim 1, characterized in that, The formula for expressing the nonproportionality L of the load path is: in, The maximum shear stress at the critical surface. m This is a scaling factor, representing the degree of reinforcement added to the loading path within the angular domain. denoted as phase angle, and g is the parameter affecting the out-of-phase loading path.

5. The method for predicting the multiaxial high-cycle fatigue life under heterogeneous loading conditions according to claim 1, characterized in that, The non-proportional additional damage coefficient The formula for expressing it is: in, For loading path non-proportional, Add a strengthening factor to the material.

6. The method for predicting the multiaxial high-cycle fatigue life under heterogeneous loading conditions according to claim 1, characterized in that, The formula for expressing the multiaxial high-cycle fatigue life under heterogeneous loading conditions is: in, For the average hydrostatic stress, For Mises equivalent stress, For the stress-life relationship, the most commonly used Basquin power function expression is chosen here. This is a non-proportional additional damage coefficient. This represents the maximum shear stress at the critical surface.

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