A fatigue life prediction method

Abstract

The application discloses a fatigue life prediction method, which determines a fatigue dangerous point by calculating the strain energy density of each point on the notch edge line of a test piece, determines the fatigue crack initiation direction at the fatigue dangerous point by calculating the negative gradient direction of the strain energy density at the fatigue dangerous point, then fits the strain energy density field at the fatigue dangerous point, combines the crack initiation direction, and calculates the equivalent strain energy density based on the negative gradient of the strain energy density field and the point method and the line method in the critical distance method, so as to take the equivalent strain energy density as a damage parameter and evaluate the life of the test piece. When the energy accumulation caused by deformation of the material reaches a certain degree in each cyclic load, failure and damage occur. The life of the material is evaluated by taking the strain energy density as a fatigue damage parameter, so that the situation that the prediction result has a large error caused by taking the maximum stress and stress distribution as parameters is avoided, that is, the accurate evaluation of the life of the material is realized.

Description

Technical Field

[0001] This invention relates to the technical field of reliability analysis, and specifically to a method for predicting fatigue life. Background Technology

[0002] Fatigue failure is the phenomenon where a material, under cyclic loading at a level far below its static strength, develops progressively propagating fatigue cracks, eventually leading to fracture. In structural design, steps, holes, grooves, and other structures are unavoidable; these are collectively referred to as notches. Notched structures cause localized stress concentrations in components under load, and these weak points become initiation sites for fatigue cracks, significantly reducing the structure's fatigue strength. Furthermore, the crack initiation period for fatigue failure is long, making it difficult to detect before rapid propagation. This leads to major accidents and substantial economic losses every year. Therefore, fatigue life prediction has immense guiding value for the design and application of engineering materials.

[0003] The existing, relatively mature method for predicting fatigue life is the local stress-strain method. This method works on the principle that the local stress-strain history at the notch root of a notched component made of the same material is the same as that of a smooth component, and therefore they have the same fatigue life. Under uniaxial fatigue loading, the fatigue damage parameter of the local stress-strain method is the maximum local stress (σ) or local strain (ε) at the notch root; while under multiaxial fatigue loading, the fatigue damage parameter of the local stress-strain method is the equivalent local stress or equivalent local strain at the notch root.

[0004] However, the aforementioned local stress-strain method only considers the local maximum stress (or strain) and ignores the influence of notch geometry and local stress-strain distribution of the notch. Therefore, the prediction results are often conservative. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is that the existing technology only considers the local maximum stress (or strain) and ignores the influence of notch geometry and local stress and strain distribution of the notch. Therefore, the prediction results are often conservative.

[0006] Therefore, the present invention provides a fatigue life prediction method, comprising:

[0007] S1: Calculate the strain energy density at each point on the notch edge of the test piece, and select the point corresponding to the maximum strain energy density as the fatigue hazard point;

[0008] S2: Calculate the negative gradient direction of the strain energy density at the fatigue critical point, which is the crack initiation direction;

[0009] S3: Fit the strain energy density field at the fatigue critical point, combine it with the crack initiation direction, and calculate the equivalent strain energy density based on the negative gradient of the strain energy density field and the point method and line method in the critical distance method.

[0010] S4: Substitute the equivalent variable energy density into the fatigue life equation to obtain the life prediction result.

[0011] Optionally, the fatigue life prediction method described above, in step S1, further includes:

[0012] For a point on the test specimen under triaxial stress, the strain energy density formula is:

[0013]

[0014] Among them, υ ε Let σ1, σ2, and σ3 be the first principal stress, the second principal stress, and the third principal stress, respectively, and ε1, ε2, and ε3 be the first principal strain, the second principal strain, and the third principal strain, respectively. x σ y σ z Let τ represent the normal stress components along the x-axis, y-axis, and z-axis in a rectangular coordinate system, respectively. xy τ yz τ zx These represent the shear stress components along the xoy plane, the yoz plane, and the zox plane in the rectangular coordinate system, respectively.

[0015] Optionally, the fatigue life prediction method described above, in step S1, further includes:

[0016] For points on the test specimen within the linear elastic range, the strain energy density formula is:

[0017]

[0018] Where E is the elastic modulus of the material, μ is the Poisson's ratio of the material, and G is the shear modulus of the material.

[0019] Optionally, in the above fatigue life prediction method, for points on the notch edge of the test piece under uniaxial stress, step S1 specifically includes:

[0020] S11: The analytical solution of the distribution functions of principal stress and principal strain on the notch edge of the test specimen during one loading cycle is:

[0021] σ1=σ1(x,y,t)=σ1(θ,t)

[0022] ε1=ε1(x,y,t)=ε1(θ,t);

[0023] S12: Based on the distribution functions of principal stress and principal strain in S11, the distribution function of instantaneous strain energy density within one loading cycle is obtained, as shown in the following equation:

[0024]

[0025] σ1 is the principal stress, ε1 is the principal strain, θ is the angle, t is the time, and υ is the principal strain. ε (θ,t) is the strain energy density at time t of the point located at angle θ on the edge of the notch.

[0026] S13: The total strain energy density over one loading cycle is obtained based on the distribution function of the instantaneous strain energy density in S12, as shown in the following formula:

[0027]

[0028] Among them, υ ε (θ) represents the sum of strain energy densities at a point located at angle θ on the notch edge during one fatigue loading cycle, where T is the fatigue loading cycle;

[0029] S14: The angle value corresponding to the point of maximum strain energy density is obtained by calculation using the following formula:

[0030]

[0031] θ d The angle value is the point where the strain energy density is maximum.

[0032] 5. The fatigue life prediction method according to claim 2, characterized in that,

[0033] For a point on the notch edge of the test piece, under uniaxial stress, step S1 is as follows:

[0034] S11: According to the finite element method, the non-proportional load is uniformly discretized into n load cases within one period, denoted as C1-C. n C for each operating condition i The corresponding instantaneous stress state (σ) i , τ i ), arrange grid nodes on the edge of the gap and divide the surrounding area into grids, dividing the edge of the gap into m nodes on average;

[0035] S12: In C i Under the operating condition, the strain energy density at node j on the notch edge is as follows:

[0036]

[0037] Where, σ ijLet ε be the principal stress at node j on the notch edge under condition Ci. ij Let be the principal strain at node j on the notch edge under working condition Ci.

[0038] S13: The total strain energy density at node j over the entire non-proportional loading period is as follows:

[0039]

[0040] S14: Calculate the total strain energy density of each node, and obtain the maximum strain energy density by comparison. The node corresponding to the maximum strain energy density is the fatigue danger point.

[0041]

[0042]

[0043] d represents the fatigue hazard point.

[0044] Optionally, in the above fatigue life prediction method, step S2 further includes:

[0045] For a center hole notch test specimen subjected to uniaxial tension, step S2 is specifically as follows:

[0046] S21: Obtain the analytical solution of stress in the notched component;

[0047] S22: Transform the stress components in polar coordinates into stress components in rectangular coordinates;

[0048] S23: Combine the strain energy density expression to obtain the strain energy density in polar coordinates in the region near the notch;

[0049] S24: Based on the strain energy density gradient formula and the coordinates of the fatigue critical point, the negative gradient of strain energy at the fatigue critical point can be obtained.

[0050] Optionally, in the above fatigue life prediction method, step S2 further includes:

[0051] For metal notched specimens under non-proportional fatigue loads, step S2 specifically involves:

[0052] S21: Discretize the non-proportional load into n load cases, denoted as C1-Cn, where each load case Ci corresponds to a certain instantaneous stress state (σ). i , τ i The metal notched component under non-proportional fatigue load is meshed using finite element methods. A rectangular coordinate system is established with the fatigue hazard point as the origin, denoted as the local coordinate system of the fatigue hazard point.

[0053] S22: The strain energy density at nodes near the fatigue-critical point is determined by finite element method, denoted as υ.εij ;

[0054] S23: The coordinates of node j in the local coordinate system of the fatigue danger point are (x j y j The sum of the strain energies of the nodes under all operating conditions during the entire non-proportional load period is υ. εj As shown in the following formula:

[0055]

[0056] S24: Take k nodes in the region near the fatigue hazard point. Based on the sum of the local coordinates and strain energy density of the k nodes, fit the strain energy density field in the region near the fatigue hazard point using a function as follows:

[0057] υ ε (x,y)=a1x 3 +a2y 3 +a3xy 2 +a4x 2 y+a5x 2 +a6y 2 +a7xy+a8x+a9y+a 10 ;

[0058] Where a1,......,a 10 These are the fitted parameters in the function;

[0059] S25: Based on the strain energy density field function υ ε The negative gradient of the fatigue danger point (x, y) is as follows:

[0060]

[0061]

[0062]

[0063]

[0064] S26:υ ε The angle θ0 between the negative gradient direction (x,y) and the x-axis of the local coordinate system is as follows:

[0065]

[0066] Optionally, the fatigue life prediction method described above, in step S3, further includes:

[0067] S31: Strain energy density υ in the region near the fatigue critical point εGiven (x, y) and the fatigue crack initiation direction θ0, and combining the point method and line method in the critical distance method, we obtain the point method and line method based on the negative gradient of the strain energy density field, as shown in the following equation:

[0068]

[0069]

[0070] in, Let l0 be the equivalent energy density, and l0 be the critical distance, a key parameter in the critical distance method. This critical distance can be calculated using the ELHaddad empirical formula, as shown below:

[0071]

[0072] In the formula, ΔK th The range of the crack initiation threshold under symmetrical cyclic loading; Δσ -1 This represents the fatigue limit of the material under symmetrical cyclic loading.

[0073] Optionally, the fatigue life prediction method described above, in step S4, further includes:

[0074] S41: The load dispersion factor is calculated as follows:

[0075]

[0076] Among them, l f The load dispersion factor is related to the waveform of the fatigue load and the number of load dispersion conditions, but is independent of the loading method and the load non-proportionality. ε υ is the strain energy density calculated after discretization. εa The strain energy density corresponding to the original fatigue load stress amplitude;

[0077] S42: The high-cycle fatigue damage parameters and low-cycle fatigue damage parameters are calculated as follows:

[0078]

[0079] High-cycle fatigue:

[0080] Low-cycle fatigue:

[0081] Where K' is the cyclic strengthening coefficient and n' is the cyclic strain hardening exponent;

[0082] S43: Point and line methods based on the negative gradient of the strain energy density field, high-cycle fatigue damage parameters and low-cycle fatigue damage parameters, and fatigue life prediction based on fatigue life curves.

[0083] The technical solution provided by this invention has the following advantages:

[0084] 1. The fatigue life prediction method provided by this invention determines fatigue hazard points by calculating the strain energy density at each point on the notch edge of the test specimen. Fatigue hazard points are the potential initiation points of fatigue cracks on the test specimen. The direction of fatigue crack initiation at the fatigue hazard point is determined by calculating the negative gradient direction of the strain energy density at that point. Then, by fitting the strain energy density field at the fatigue hazard point and combining it with the crack initiation direction, the equivalent strain energy density is calculated based on the negative gradient of the strain energy density field and the point and line methods in the critical distance method. This equivalent strain energy density is used as a damage parameter to establish a fatigue life assessment equation, thereby achieving the assessment of the test specimen's life. Materials fail when the energy accumulation due to deformation reaches a certain level within each cyclic load. By using strain energy for material life assessment, the large errors in prediction results caused by using maximum stress and stress distribution as parameters are avoided, thus achieving an accurate assessment of material life.

[0085] 2. The fatigue life prediction method provided by the present invention can accurately determine the fatigue-prone parts of the test piece, predict the safe service life of the test piece, and avoid unexpected fatigue failure of the test piece during service.

[0086] 3. The fatigue life prediction method provided by this invention can provide a theoretical basis for structural optimization design, ensure the development progress, and reduce the time required for improvement when the requirements are not met in the subsequent testing stage. Attached Figure Description

[0087] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific 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 from these drawings without creative effort.

[0088] Figure 1 A flowchart of the fatigue life testing method provided by the present invention;

[0089] Figure 2 A notched test piece with a circular hole diameter of 1 mm is provided for the fatigue life testing method of this invention;

[0090] Figure 3 A notched test piece with a circular hole diameter of 2 mm is provided for the fatigue life testing method of this invention;

[0091] Figure 4 The notched test piece with an oblong hole provided for the fatigue life testing method of the present invention;

[0092] Figure 5 This is a comparison chart of the fatigue life test values ​​and predicted values ​​of the test specimens in this invention. Detailed Implementation

[0093] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0094] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0095] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0096] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0097] Example 1

[0098] This embodiment provides a fatigue life testing method, including:

[0099] S1: Calculate the strain energy density at each point on the notch edge of the test specimen, and select the point corresponding to the maximum strain energy density as the fatigue hazard point. Due to the different working environments of the test specimens, different strain energy density formulas are selected based on the stress state at each point on the notch edge of the test specimen to calculate the strain energy density. For a point on the test specimen under triaxial stress, when all three normal stresses are non-zero, the point is said to be under triaxial stress, and its strain energy density formula is:

[0100]

[0101] Among them, υ ε Let σ1, σ2, and σ3 be the first principal stress, the second principal stress, and the third principal stress, respectively, and ε1, ε2, and ε3 be the first principal strain, the second principal strain, and the third principal strain, respectively. x σ y σ z Let τ represent the normal stress components along the x-axis, y-axis, and z-axis in a rectangular coordinate system, respectively. xy τ yz τ zx These represent the shear stress components along the xoy plane, the yoz plane, and the zox plane in the rectangular coordinate system, respectively.

[0102] For points on the test specimen within the linear elastic range, the range is defined as the point where the stress is below the yield strength. The strain energy density formula for this range is:

[0103]

[0104] Where E is the elastic modulus of the material, μ is the Poisson's ratio of the material, and G is the shear modulus of the material.

[0105] For a point on the notch edge of the test piece, and under uniaxial stress, the stress state at a point in the member can be completely determined by the normal stress on its cross-section. This stress state is called uniaxial stress state. Step S1 is as follows:

[0106] S11: The analytical solution of the distribution functions of principal stress and principal strain on the notch edge of the test specimen during one loading cycle is:

[0107] σ1=σ1(x,y,t)=σ1(θ,t)

[0108] ε1=ε1(x,y,t)=ε1(θ,t);

[0109] S12: Based on the distribution functions of principal stress and principal strain in S11, the distribution function of instantaneous strain energy density within one loading cycle is obtained, as shown in the following equation:

[0110]

[0111] σ1 is the principal stress, ε1 is the principal strain, θ is the angle, t is the time, and υ is the principal strain. ε (θ,t) is the strain energy density at time t of the point located at angle θ on the edge of the notch.

[0112] S13: The total strain energy density over one loading cycle is obtained based on the distribution function of the instantaneous strain energy density in S12, as shown in the following formula:

[0113]

[0114] Among them, υ ε (θ) represents the sum of strain energy densities at a point located at angle θ on the notch edge during one fatigue loading cycle, where T is the fatigue loading cycle;

[0115] S14: The angle value corresponding to the point of maximum strain energy density is obtained by calculation using the following formula:

[0116]

[0117] θ d The angle value is the point where the strain energy density is maximum.

[0118] S2: Calculate the negative gradient direction of the strain energy density at the fatigue critical point, which is the crack initiation direction;

[0119] For a center hole notch test specimen subjected to uniaxial tension, step S2 is specifically as follows:

[0120] S21: Obtain the analytical solution of stress in the notched component;

[0121] S22: Transform the stress components in polar coordinates into stress components in rectangular coordinates;

[0122] S23: Combine the strain energy density expression to obtain the strain energy density in polar coordinates in the region near the notch;

[0123] S24: Based on the strain energy density gradient formula and the coordinates of the fatigue critical point, the negative gradient of strain energy at the fatigue critical point can be obtained.

[0124] S3: Fit the strain energy density field at the fatigue critical point, combine it with the crack initiation direction, and calculate the equivalent strain energy density based on the negative gradient of the strain energy density field and the point method and line method in the critical distance method.

[0125] S31: Strain energy density υ in the region near the fatigue critical point ε Given (x, y) and the fatigue crack initiation direction θ0, and combining the point method and line method in the critical distance method, we obtain the point method and line method based on the negative gradient of the strain energy density field, as shown in the following equation:

[0126]

[0127]

[0128] Where l0 is the critical distance, a key parameter in the critical distance method, which can be calculated using the El Haddad empirical formula. This represents the equivalent variable energy density.

[0129] S4: Substitute the equivalent variable energy density into the fatigue life equation to obtain the life prediction result.

[0130] S41: The load dispersion factor is calculated as follows:

[0131]

[0132] Among them, l f The load dispersion factor is related to the waveform of the fatigue load and the number of load dispersion conditions, but is independent of the loading method and the load non-proportionality. ε υ is the strain energy density calculated after discretization. εa The strain energy density corresponding to the original fatigue load stress amplitude;

[0133] S42: The high-cycle fatigue damage parameters and low-cycle fatigue damage parameters are calculated as follows:

[0134]

[0135] High-cycle fatigue:

[0136] Low-cycle fatigue:

[0137] Where K' is the cyclic strengthening coefficient and n' is the cyclic strain hardening exponent;

[0138] S43: Based on the point method and line method of the negative gradient of the strain energy density field, high-cycle fatigue damage parameters and low-cycle fatigue damage parameters, the fatigue life curve is obtained from a large number of fatigue life tests, and fatigue life is predicted based on the fatigue life curve.

[0139] The fatigue life prediction method provided in this embodiment is based on the principle that material failure occurs when the energy accumulated due to deformation reaches a certain level in each cyclic load. A fatigue prediction method based on strain energy has been developed based on this principle. The sum of the elastic and plastic deformation energies generated by the material in each cycle is the total strain energy density. Fatigue life can be predicted by calculating the maximum total strain energy density at the root of the notched part and comparing it with the test results of a standard part. Fatigue hazard points are determined by calculating the strain energy density at each point on the notch edge of the test piece. These hazard points are the possible initiation points of fatigue cracks on the test piece. The direction of fatigue crack initiation at the hazard point is determined by calculating the negative gradient direction of the strain energy density at that hazard point. Then, by fitting the strain energy density field at the hazard point and combining it with the crack initiation direction, the equivalent strain energy density is calculated based on the negative gradient of the strain energy density field and the point and line methods in the critical distance method. This equivalent strain energy density is used as a damage parameter to establish a fatigue life assessment equation, thereby achieving the assessment of the test piece's life. Material failure occurs when the energy accumulated due to deformation reaches a certain level during each cyclic load. By using strain energy to assess the life of materials, we can avoid the large errors in prediction results caused by using the maximum stress and stress distribution as parameters, thus achieving an accurate assessment of material life.

[0140] Example 2

[0141] This embodiment provides a fatigue life testing method. The calculation of fatigue critical points can also be obtained through engineering methods. For points on the notch edge of the test piece, under uniaxial stress, step S1 specifically involves:

[0142] S11: According to the finite element method, the non-proportional load is uniformly discretized into n load cases within one period, denoted as C1-C. n C for each operating condition i The corresponding instantaneous stress state (σ) i , τ i ), arrange grid nodes on the edge of the gap and divide the surrounding area into grids, dividing the edge of the gap into m nodes on average;

[0143] S12: In C i Under the operating condition, the strain energy density at node j on the notch edge is as follows:

[0144]

[0145] Where, σ ij Let ε be the principal stress at node j on the notch edge under condition Ci. ij Let be the principal strain at node j on the notch edge under working condition Ci.

[0146] S13: The total strain energy density at node j over the entire non-proportional loading period is as follows:

[0147]

[0148] S14: Calculate the total strain energy density of each node, and obtain the maximum strain energy density by comparison. The node corresponding to the maximum strain energy density is the fatigue danger point.

[0149]

[0150]

[0151] d represents the fatigue hazard point.

[0152] This embodiment uses notched test specimens with a circular hole diameter of 1 mm, notched test specimens with a circular hole diameter of 2 mm, and oblong hole specimens for verification. The comparison between the test values ​​and predicted values ​​of fatigue hazard points is shown in the table below:

[0153]

[0154] The calculation of the negative gradient direction of strain energy density can also be obtained through engineering methods. For metal notched specimens under non-proportional fatigue loads, step S2 is as follows:

[0155] S21: Discretize the non-proportional load into n load cases, denoted as C1-Cn, where each load case Ci corresponds to a certain instantaneous stress state (σ). i , τ i The metal notched component under non-proportional fatigue load is meshed using finite element methods. A rectangular coordinate system is established with the fatigue hazard point as the origin, denoted as the local coordinate system of the fatigue hazard point.

[0156] S22: The strain energy density at nodes near the fatigue-critical point is determined by finite element method, denoted as υ. εij ;

[0157] S23: The coordinates of node j in the local coordinate system of the fatigue danger point are (x j y j The sum of the strain energies of the nodes under all operating conditions during the entire non-proportional load period is υ. εj As shown in the following formula:

[0158]

[0159] S24: Take k nodes in the region near the fatigue hazard point. Based on the sum of the local coordinates and strain energy density of the k nodes, fit the strain energy density field in the region near the fatigue hazard point using a function as follows:

[0160] υ ε (x,y)=a1x 3 +a2y 3 +a3xy 2 +a4x 2 y+a5x 2 +a6y 2 +a7xy+a8x+a9y+a 10 ;

[0161] Where a1,......,a 10 These are the fitted parameters in the function;

[0162] S25: Based on the strain energy density field function υ ε The negative gradient of the fatigue danger point (x, y) is as follows:

[0163]

[0164]

[0165]

[0166]

[0167] S26:υ ε The angle θ0 between the negative gradient direction (x,y) and the x-axis of the local coordinate system is as follows:

[0168]

[0169] The comparison between the experimental and predicted values ​​of crack initiation direction for the three test specimens in this embodiment is shown in the table below:

[0170]

[0171] In this embodiment, the comparison chart of fatigue life test values ​​and predicted values ​​for a notched test specimen with a 1mm diameter circular hole is shown below. Figure 5 As shown:

[0172] in:

[0173] ESDF-PM - A point method based on strain energy density method

[0174] ESDF-PM - A linear method based on strain energy density method

[0175] M-TCD-critical distance method.

[0176] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A fatigue life prediction method, characterized in that, include: S1: Calculate the strain energy density at each point on the notch edge of the test piece, and select the point corresponding to the maximum strain energy density as the fatigue hazard point; S2: Calculate the negative gradient direction of the strain energy density at the fatigue critical point, which is the crack initiation direction; S3: Fit the strain energy density field at the fatigue critical point, combine it with the crack initiation direction, and calculate the equivalent strain energy density based on the negative gradient of the strain energy density field and the point method and line method in the critical distance method. S4: Substitute the equivalent variable energy density into the fatigue life equation to obtain the life prediction result.

2. The fatigue life prediction method according to claim 1, characterized in that, The above S1 step also includes: For a point on the test specimen under triaxial stress, the strain energy density formula is: Among them, υ ε Let σ1, σ2, and σ3 be the first principal stress, the second principal stress, and the third principal stress, respectively, and ε1, ε2, and ε3 be the first principal strain, the second principal strain, and the third principal strain, respectively. x σ y σ z Let τ represent the normal stress components along the x-axis, y-axis, and z-axis in a rectangular coordinate system, respectively. xy τ yz τ zx These represent the shear stress components along the xoy plane, the yoz plane, and the zox plane in the rectangular coordinate system, respectively.

3. The fatigue life prediction method according to claim 1, characterized in that, The above S1 step also includes: For points on the test specimen within the linear elastic range, the strain energy density formula is: Where E is the elastic modulus of the material, μ is the Poisson's ratio of the material, and G is the shear modulus of the material.

4. The fatigue life prediction method according to claim 2, characterized in that, For the point on the notch edge of the test piece, since it is under uniaxial stress, step S1 is as follows: S11: The analytical solution of the distribution functions of principal stress and principal strain on the notch edge of the test specimen during one loading cycle is: σ1=σ1(x,y,t)=σ1(θ,t) ε1=ε1(x,y,t)=ε1(θ,t); S12: Based on the distribution functions of principal stress and principal strain in S11, the distribution function of instantaneous strain energy density within one loading cycle is obtained, as shown in the following equation: σ1 is the principal stress, ε1 is the principal strain, θ is the angle, t is the time, and υ is the principal strain. ε (θ,t) is the strain energy density at time t of the point located at angle θ on the edge of the notch. S13: The total strain energy density over one loading cycle is obtained based on the distribution function of the instantaneous strain energy density in S12, as shown in the following formula: in, Let T be the sum of the strain energy densities of the point located at angle θ on the notch edge during one fatigue loading cycle, where T is the fatigue loading cycle. S14: The angle value corresponding to the point of maximum strain energy density is obtained by calculation using the following formula: θ d The angle value is the point where the strain energy density is maximum.

5. The fatigue life prediction method according to claim 2, characterized in that, For a point on the notch edge of the test piece, under uniaxial stress, step S1 is as follows: S11: According to the finite element method, the non-proportional load is uniformly discretized into n load cases within one period, denoted as C1-C. n C for each operating condition i The corresponding instantaneous stress state (σ) i , τ i ), arrange grid nodes on the edge of the gap and divide the surrounding area into grids, dividing the edge of the gap into m nodes on average; S12: In C i Under the operating condition, the strain energy density at node j on the notch edge is as follows: Where, σ ij Let ε be the principal stress at node j on the notch edge under condition Ci. ij The principal strain at node j on the notch edge under working condition Ci; S13: The total strain energy density at node j over the entire non-proportional loading period is as follows: S14: Calculate the total strain energy density of each node, and obtain the maximum strain energy density by comparison. The node corresponding to the maximum strain energy density is the fatigue danger point. d represents the fatigue hazard point.

6. The fatigue life prediction method according to claim 2 or 3, characterized in that, Step S2 above also includes: For a center hole notch test specimen subjected to uniaxial tension, step S2 is specifically as follows: S21: Obtain the analytical solution of stress in the notched component; S22: Transform the stress components in polar coordinates into stress components in rectangular coordinates; S23: Combine the strain energy density expression to obtain the strain energy density in polar coordinates in the region near the notch; S24: Based on the strain energy density gradient formula and the coordinates of the fatigue critical point, the negative gradient of strain energy at the fatigue critical point can be obtained.

7. The fatigue life prediction method according to claim 2 or 3, characterized in that, Step S2 above also includes: For metal notched specimens under non-proportional fatigue loads, step S2 specifically involves: S21: Discretize the non-proportional load into n load cases, denoted as C1-Cn, where each load case Ci corresponds to a certain instantaneous stress state (σ). i , τ i The metal notched component under non-proportional fatigue load is meshed using finite element methods. A rectangular coordinate system is established with the fatigue hazard point as the origin, denoted as the local coordinate system of the fatigue hazard point. S22: The strain energy density at nodes near the fatigue-critical point is determined by finite element method, denoted as υ. εij ; S23: The coordinates of node j in the local coordinate system of the fatigue danger point are (x j y j The sum of the strain energies of the nodes under all operating conditions during the entire non-proportional load period is υ. εj As shown in the following formula: S24: Take k nodes in the region near the fatigue hazard point. Based on the sum of the local coordinates and strain energy density of the k nodes, fit the strain energy density field in the region near the fatigue hazard point using a function as follows: υ ε (x,y)=a1x 3 +a2y 3 +a3xy 2 +a4x 2 y+a5x 2 +a6y 2 +a7xy+a8x+a9y+a 10 ; Where a1,......,a 10 These are the fitted parameters in the function; S25: Based on the strain energy density field function υ ε The negative gradient of the fatigue danger point (x, y) is as follows: S26:υ ε The angle θ0 between the negative gradient direction (x,y) and the x-axis of the local coordinate system is as follows:

8. The fatigue life prediction method according to claim 7, characterized in that, The above S3 step also includes: S31: Strain energy density υ in the region near the fatigue critical point ε Given (x, y) and the fatigue crack initiation direction θ0, and combining the point method and line method in the critical distance method, we obtain the point method and line method based on the negative gradient of the strain energy density field, as shown in the following equation: Dot method: Line method: in, Let l0 be the equivalent energy density, and l0 be the critical distance, a key parameter in the critical distance method, which can be calculated using the El Haddad empirical formula, as shown below: In the formula, ΔK th The range of the crack initiation threshold under symmetrical cyclic loading; Δσ -1 This represents the fatigue limit of the material under symmetrical cyclic loading.

9. The fatigue life prediction method according to claim 8, characterized in that, The above S4 step also includes: S41: The load dispersion factor is calculated as follows: Among them, l f The load dispersion factor is related to the waveform of the fatigue load and the number of load dispersion conditions, but is independent of the loading method and the load non-proportionality. ε υ is the strain energy density calculated after discretization. εa The strain energy density corresponding to the original fatigue load stress amplitude; S42: The high-cycle fatigue damage parameters and low-cycle fatigue damage parameters are calculated as follows: High-cycle fatigue: Low-cycle fatigue: Where K' is the cyclic strengthening coefficient and n' is the cyclic strain hardening exponent; S43: Point and line methods based on the negative gradient of the strain energy density field, high-cycle fatigue damage parameters and low-cycle fatigue damage parameters, and fatigue life prediction based on fatigue life curves.

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