Aero-engine coating treatment blade fatigue limit prediction method

Abstract

The application discloses an aero-engine coating treatment blade fatigue limit prediction method and belongs to the technical field of aero-engines. The method comprises the following steps: obtaining the stress-strain curve of a stainless steel blade substrate through a single-axis tensile test, determining the constitutive model of the coating through a nano-indentation inversion analysis method; carrying out a coating blade fatigue test on a vibration table; establishing a coating blade finite element model in Abaqus; simulating the fatigue test of the coating blade on the vibration table by using a finite element method; establishing a blade fatigue limit prediction model considering coating treatment; extracting the circumferential effective stress parameters of the dangerous point position of the coating blade; substituting the effective stress parameters into the established prediction model to obtain fatigue limit prediction results; and verifying the prediction results with the test results. The aero-engine coating treatment blade fatigue limit prediction method has the advantages that the influence of coating treatment on the fatigue performance of the blade is considered, the fatigue limit of the coating treatment blade can be predicted, and the prediction result has high precision.

Description

Technical Field

[0001] This invention relates to the field of aero-engine technology, and in particular to a method for predicting the fatigue limit of coated blades for aero-engines. Background Technology

[0002] Aero-engine blades are among the most numerous and operate in the harshest environments within aero-engines. During service, aero-engine blades endure vibration stresses induced by various aerodynamic and mechanical factors. Because aero-engine blades operate under complex environments such as high temperature, humidity, and alternating stress for extended periods, anti-corrosion coatings effectively protect them from corrosive media. However, coating treatments can affect the surface condition and high-cycle fatigue performance of stainless steel blades. Therefore, factors such as coating and blade configuration must be considered when constructing fatigue limit prediction models suitable for aircraft engine blades. This paper establishes a fatigue limit prediction model for simulated stainless steel blades that considers the coating-matrix stress gradient effect, and verifies the model's errors through simulated blade vibration fatigue tests. The established fatigue limit prediction model for coated stainless steel blades for aircraft engines provides theoretical support and guidance for setting safe operating loads for engine blades, which is of positive significance for ensuring the safe operation of aircraft engines. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting the fatigue limit of coated blades in aero-engines, taking into account the influence of coating treatment on the fatigue performance of the blades, and predicting the fatigue limit of coated blades.

[0004] To achieve the above objectives, the present invention provides a method for predicting the fatigue limit of coated blades for aero-engines, comprising the following steps:

[0005] S1. The stress-strain curve of the stainless steel blade substrate was obtained by uniaxial tensile test, and the constitutive model of the coating was determined by nanoindentation inversion analysis.

[0006] S2. Conduct fatigue tests on the coated blades on a vibration table, and determine the fatigue limit of the coated blades by finding the frequency and using the step-by-step load loading method.

[0007] S3. Establish a finite element model of the coated blade in Abaqus;

[0008] S4. Use the finite element method to simulate the fatigue test of the coated blade on the vibration table;

[0009] S5. Establish a blade fatigue limit prediction model that takes into account coating treatment;

[0010] S6. Extract the effective circumferential stress parameters of the critical points of the coated blade and import them into the prediction model to calculate the fatigue limit.

[0011] S7. Substitute the effective stress parameters into the established prediction model to obtain the fatigue limit prediction results, and verify the prediction results with the experimental results.

[0012] Preferably, the specific steps of S1 are as follows:

[0013] S11. The stress-strain curve of the stainless steel blade matrix was obtained by uniaxial tensile test, and the JC constitutive model of formula (1) was obtained by fitting.

[0014] σ = 1296 + 1716ε 0.765 (1)

[0015] Where σ is stress and ε is strain;

[0016] S12. Since the coating is relatively thin, the constitutive model of the coating is determined by nanoindentation inversion analysis, the hardness and elastic modulus of the coating are determined by nanoindentation test, and the characteristic stress σ is calculated by formula (2) and formula (3). r and characteristic strain ε r ;

[0017]

[0018]

[0019] Among them, E r H represents the composite elastic modulus, and H represents the coating hardness.

[0020] S13. Determine the hardening exponent n and yield strength σ using formulas (4) and (5). r ;

[0021]

[0022]

[0023] Among them, h r h represents the residual depth after unloading. m For the maximum indentation depth, σ y The yield stress;

[0024] S14. The final constitutive model of the coating is determined to be Equation (6);

[0025] σ = 936.99(1 + 73.97ε) 0.681 (6).

[0026] Preferably, in step S2, the stress ratio R = -1 in the fatigue test of the coated blade.

[0027] Preferably, in step S3, the size ratio of the finite element model of the coated blade to that of the test piece is 1:1.

[0028] Preferably, the specific steps of S4 are as follows:

[0029] S41. Omnidirectional fixation of the petiole;

[0030] S42. Through harmonic response analysis, the first natural frequency of the blade was found to be around 1053 Hz.

[0031] S43. In the simulation experiment, a vertical excitation force is applied to simulate the loading conditions in the real test.

[0032] Preferably, the specific steps of S5 are as follows:

[0033] S51. Combining the Basquin and Walker models, we obtain formula (7). Taking the logarithm of both sides of formula (7), we obtain the fatigue limit prediction model, which is formula (8).

[0034]

[0035]

[0036] Where a is the material parameter, N f For fatigue life, σ max y is the fatigue limit, y is the average stress influence parameter, and R is the stress ratio;

[0037] S52. Calculate the omnidirectional gradient stress influence factor ΔT;

[0038] S53, Calculate the stress concentration influence factor K s ;

[0039] S54. Introduce the omnidirectional gradient stress influence factor ΔT and the stress concentration influence factor K. s A fatigue limit prediction model for simulating the omnidirectional gradient stress field of a blade was established, and the fatigue limit σ of the simulated blade was calculated. max ;

[0040] S55. Substitute each parameter into the fatigue limit prediction model of the omnidirectional gradient stress field of the coating-substrate multilayer structure to obtain the fatigue limit of the coated stainless steel blade.

[0041] Preferably, the specific steps of S52 are as follows:

[0042] S521. Taking the fatigue failure hazard point as the base point, take a series of equidistant points in four directions: the tip direction, the axis of symmetry direction, the petiole direction, and the thickness direction of the blade, and record the corresponding stress values.

[0043] S522. Normalize the distance and stress values ​​of the four groups of gradient stress fields respectively, and plot the distance-stress normalization curve.

[0044] S523. The omnidirectional gradient stress influence factor ΔT is calculated from the stress gradient value and the influence distance value of the gradient stress field obtained from the simulation, as shown in the following formula:

[0045] ΔT=(b1·S1)+(b2·S2)+(b3·S3)+(b4·S4) (9)

[0046] Where S1, S2, S3, and S4 are the areas enclosed by the distance-stress normalization curves in the four directions of the blade tip, axis of symmetry, petiole, and thickness, respectively, and b1, b2, b3, and b4 are weighting coefficients, with b1+b2+b3+b4=1.

[0047] The formulas for calculating s1, s2, and S3 are as follows:

[0048]

[0049] The formula for calculating S4 is as follows:

[0050]

[0051] The formula for calculating χ(r) is as follows:

[0052]

[0053] Where L is the influence distance of the gradient stress field at the peak stress point of the blade in this direction, σ(r) is the stress field, r is the field diameter, χ(r) is the stress gradient, t is the coating thickness, and T is the blade thickness.

[0054] Preferably, the specific steps of S53 are as follows:

[0055] S531. In order to study and analyze the actual impact of stress concentration effect on fatigue failure risk points, under the same loading conditions, finite element simulation experiments of actual simulated blade aerodynamic uniform load loading and finite element simulation experiments of simulated blade aerodynamic uniform load loading without draft angle were carried out to study the stress concentration effect caused by draft angle.

[0056] S532, Obtain the stress concentration influence factor K s The formula is as follows:

[0057]

[0058] Where σ1 is the maximum stress value at the fatigue failure point of the actual simulated blade, and σ2 is the stress value at the corresponding point of the simulated blade without draft.

[0059] Preferably, the specific steps of S54 are as follows:

[0060] S541. Introduce the omnidirectional gradient stress influence factor ΔT and the stress concentration influence factor K. s Formula (14) is obtained;

[0061]

[0062] S542. Taking the logarithm of both sides of formula (14), we obtain the fatigue limit prediction model of the simulated blade omnidirectional gradient stress field as formula (15).

[0063]

[0064] S543, The material parameter a, stress gradient influence factor ΔT, and stress concentration influence factor K are included. s Substituting into the fatigue limit prediction model, the fatigue life N f The fatigue limit σ was calculated. max When N f =10 7 At that time, the fatigue limit σ of the simulated blade was obtained. max .

[0065] Preferably, the fatigue limit prediction model for the omnidirectional gradient stress field of the coating-substrate multilayer structure in S55 is as follows:

[0066]

[0067] Where, N f For fatigue life, σ max Let be the fatigue limit, 'a' be a material parameter, 'y' be a value, 'R' be a value, and 'K' be a value. s ΔT is the stress concentration influencing factor, and ΔT is the omnidirectional gradient stress influencing factor.

[0068] Therefore, the present invention employs the above-mentioned method for predicting the fatigue limit of coated blades for aero-engines, which has the following beneficial effects:

[0069] (1) Considering the thin and brittle characteristics of the coating, the constitutive parameters of the coating were effectively obtained by using the nanoindentation inversion analysis method;

[0070] (2) The influence of the coating on the fatigue limit of the blade was considered from the perspective of the stress field. An omnidirectional gradient stress field coating blade fatigue limit prediction model was proposed, which improves the calculation efficiency while ensuring the calculation accuracy.

[0071] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0072] Figure 1This is a flowchart of a method for predicting the fatigue limit of coated blades for aero-engines according to the present invention;

[0073] Figure 2 The fatigue limit prediction method for coated blades of aero-engines of this invention was obtained through simulation of 15 materials with different elastic moduli (50-150 GPa) and characteristic stresses (0.5-2 GPa). With lnε r Distribution relationship diagram;

[0074] Figure 3 The hardening index n of the present invention is used to predict the fatigue limit of coated blades for aero-engines. A three-dimensional surface plot composed of three parameters;

[0075] Figure 4 This is a top view of the finite element model of the fatigue limit prediction method for the coating treatment blade of an aero-engine according to the present invention.

[0076] Figure 5 This is a front view of the finite element model of the fatigue limit prediction method for the coating treatment blade of an aero-engine according to the present invention.

[0077] Figure 6 This is a side view of the finite element model of the fatigue limit prediction method for the coating treatment blade of an aero-engine according to the present invention.

[0078] Figure 7 This invention presents four sets of normalized curves showing the influence of gradient stress fields on distance and stress values ​​in a method for predicting the fatigue limit of coated blades for aero-engines. (a) is the distance-stress normalized curve in the blade tip direction, (b) is the distance-stress normalized curve in the blade stem direction, (c) is the distance-stress normalized curve in the blade surface direction, and (d) is the distance-stress normalized curve in the thickness direction.

[0079] Figure 8 The figure shows the finite element simulation results of the actual simulated blade aerodynamic uniformly distributed load loading of the method for predicting the fatigue limit of coated blades of the present invention.

[0080] Figure 9 The figure shows the finite element simulation results of a uniformly distributed aerodynamic load on a blade without draft angle, based on the fatigue limit prediction method for aero-engine coated blades according to the present invention. Detailed Implementation

[0081] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0082] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0083] Example

[0084] like Figure 1 As shown, this invention provides a method for predicting the fatigue limit of coated blades for aero-engines, comprising the following steps:

[0085] S1. The stress-strain curve of the stainless steel blade substrate was obtained by uniaxial tensile test, and the constitutive model of the coating was determined by nanoindentation inversion analysis.

[0086] S11. The stress-strain curve of the stainless steel blade matrix was obtained by uniaxial tensile test, and the JC constitutive model of formula (1) was obtained by fitting.

[0087] σ = 1296 + 1716ε 0.765 (1)

[0088] Where σ is stress and ε is strain.

[0089] S12. Since the coating is relatively thin, the constitutive model of the coating is determined by nanoindentation inversion analysis, the hardness and elastic modulus of the coating are determined by nanoindentation test, and the characteristic stress σ is calculated by formula (2) and formula (3). r and characteristic strain ε r .

[0090]

[0091] Among them, E r H represents the composite elastic modulus, and H represents the coating hardness.

[0092] Fifteen materials with different elastic moduli (50-150 GPa) and characteristic stresses (0.5-2 GPa) were designed and simulated to obtain... With lnε r Distribution relationship diagram, such as Figure 2 As shown, the functional relationship of formula (3) is obtained by fitting the distribution relationship between the two.

[0093]

[0094] S13. Determine the hardening exponent n and yield strength σ using formulas (4) and (5).r ; Figure 3 For the hardening index n, The three-dimensional surface diagram composed of the three parameters, and the coating hardening index model are determined by formula (4);

[0095]

[0096]

[0097] Among them, h r h represents the residual depth after unloading. m For the maximum indentation depth, σ y This is the yield stress.

[0098] S14. The final constitutive model of the coating is determined as Equation (6).

[0099] σ = 936.99(1 + 73.97ε) 0.681 (6)

[0100] S2. Conduct fatigue tests on the coated blades on a vibration table. Determine the fatigue limit of the coated blades by finding the frequency and using the step-by-step load method. The stress ratio of the coated blade fatigue test is R = -1.

[0101] S3, such as Figures 4-6 As shown, a finite element model of the coated blade was established in Abaqus, with the size ratio of the finite element model of the coated blade to that of the test piece being 1:1.

[0102] S4. Use the finite element method to simulate the fatigue test of the coated blade on the vibration table.

[0103] S41. Omnidirectional fixation of the petiole;

[0104] S42. The first natural frequency of the blade was determined to be 1053 Hz through harmonic response analysis.

[0105] S43. In the simulation experiment, a vertical excitation force is applied to simulate the loading conditions in the real test.

[0106] S5. Establish a blade fatigue limit prediction model that takes into account coating treatment.

[0107] S51. Combining the Basquin and Walker models, we obtain formula (7). Taking the logarithm of both sides of formula (7), we obtain the fatigue limit prediction model, which is formula (8).

[0108]

[0109]

[0110] Where a is the material parameter, Nf For fatigue life, σ max y is the fatigue limit, y is the average stress influence parameter, and R is the stress ratio;

[0111] S52. Calculate the omnidirectional gradient stress influence factor ΔT.

[0112] S521. Using the fatigue failure hazard point as the base point, take a series of equidistant points in four directions: the tip direction, the axis of symmetry direction, the petiole direction, and the thickness direction of the blade, and record the corresponding stress values.

[0113] S522. Normalize the influence distance and stress values ​​of the four sets of gradient stress fields respectively, and plot the distance-stress normalization curve, as follows. Figure 7 As shown, the horizontal axis represents the distance normalized value, and the vertical axis represents the stress normalized value.

[0114] S523. The formula for calculating the omnidirectional gradient stress influence factor ΔT is obtained from the stress gradient value and the influence distance value of the gradient stress field obtained from the simulation.

[0115] ΔT=(b1·S1)+(b2·S2)+(b3·S3)+(b4·S4)=(0.2×(0.2×0.297416)+0.422886)+(0.2×0.419779)+(0.4×0.764789)≈0.5339318 (9)

[0117] Where S1, S2, S3, and S4 are the areas enclosed by the distance-stress normalization curves in the four directions of the blade tip, axis of symmetry, petiole, and thickness, respectively, and b1, b2, b3, and b4 are weighting coefficients, with b1+b2+b3+b4=1.

[0118] The formulas for calculating S1, S2, and S3 are as follows:

[0119]

[0120] The formula for calculating S4 is as follows:

[0121]

[0122] The formula for calculating χ(r) is as follows:

[0123]

[0124] Where L is the influence distance of the gradient stress field at the peak stress point of the blade in this direction, σ(r) is the stress field, r is the field diameter, χ(r) is the stress gradient, t is the coating thickness, and T is the blade thickness.

[0125] S53, Calculate the stress concentration influence factor K s .

[0126] S531. To investigate the actual impact of stress concentration on fatigue failure hazard points, finite element simulation experiments were conducted under the same loading conditions, including actual simulated blade aerodynamic uniformly distributed load loading and simulated blade aerodynamic uniformly distributed load loading without draft angle. The stress concentration effect caused by draft angle was studied, and the experimental results are as follows: Figure 8 and Figure 9 As shown;

[0127] S532, Obtain the stress concentration influence factor K s Formula and calculation;

[0128]

[0129] Where σ1 is the maximum stress value at the fatigue failure point of the actual simulated blade, and σ2 is the stress value at the corresponding point of the simulated blade without draft.

[0130] S54. Introduce the omnidirectional gradient stress influence factor ΔT and the stress concentration influence factor K. s A fatigue limit prediction model for simulating the omnidirectional gradient stress field of a blade was established, and the fatigue limit σ of the simulated blade was calculated. max .

[0131] S541. Introduce the omnidirectional gradient stress influence factor ΔT and the stress concentration influence factor K. s Formula (11) is obtained;

[0132]

[0133] S542. Taking the logarithm of both sides of formula (11), we obtain the fatigue limit prediction model of the simulated blade omnidirectional gradient stress field as formula (12).

[0134]

[0135] S543, The material parameter a, stress gradient influence factor ΔT, and stress concentration influence factor K are included. s Substituting into the fatigue limit prediction model, the fatigue life N f The fatigue limit σ was calculated. max When N f =10 7 At that time, the fatigue limit σ of the simulated blade was obtained. max .

[0136] S55. Substitute each parameter into the fatigue limit prediction model of the omnidirectional gradient stress field of the coating-substrate multilayer structure to obtain the fatigue limit of the coated stainless steel blade.

[0137] The fatigue limit prediction model for the omnidirectional gradient stress field of the coating-substrate multilayer structure is as follows:

[0138]

[0139] Where, N f For fatigue life, σ max Let be the fatigue limit, 'a' be a material parameter, 'y' be a value, 'R' be a value, and 'K' be a value. s ΔT is the stress concentration influencing factor, and ΔT is the omnidirectional gradient stress influencing factor.

[0140] Given N f =10 7 Given a = 0.0000468041, y = 0.61627907, R = -1, K = 1.314172, and ΔT = 0.5339318, the fatigue limit of the coated stainless steel blade, calculated by the omnidirectional gradient stress field fatigue limit prediction model for the coating-substrate multilayer structure, is 667.03 MPa.

[0141] S6. Extract the effective circumferential stress parameters of the critical points of the coated blade and import them into the prediction model to calculate the fatigue limit.

[0142] S7. Substitute the effective stress parameters into the established prediction model to obtain the fatigue limit prediction results, and verify the prediction results predicted by the fatigue prediction model with the experimental results.

[0143] Therefore, the present invention adopts the above-mentioned method for predicting the fatigue limit of coated blades, which takes into account the influence of coating treatment on the fatigue performance of blades, and can predict the fatigue limit of coated blades with high accuracy.

[0144] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the fatigue limit of coated blades for aero-engines, characterized in that, Includes the following steps: S1. The stress-strain curve of the stainless steel blade substrate was obtained by uniaxial tensile test, and the constitutive model of the coating was determined by nanoindentation inversion analysis. S2. Conduct fatigue tests on the coated blades on a vibration table, and determine the fatigue limit of the coated blades by finding the frequency and using the step-by-step load loading method. S3. Establish a finite element model of the coated blade in Abaqus; S4. Use the finite element method to simulate the fatigue test of the coated blade on the vibration table; S5. Establish a blade fatigue limit prediction model that considers coating treatment, including: S51. Combining the Basquin and Walker models, we obtain formula (7). Taking the logarithm of both sides of formula (7), we obtain the fatigue limit prediction model, which is formula (8). （7） （8） wherein is a material parameter, is the fatigue life, is the fatigue limit, y is an average stress influence parameter, is the stress ratio; S52, calculate the omni-directional gradient stress influence factor T; S53, calculating a stress concentration influence factor ; S54, introducing T and , a fatigue limit prediction model of the simulated blade omni-directional gradient stress field is established, and the fatigue limit of the simulated blade is calculated ; S55. Substitute each parameter into the fatigue limit prediction model of the omnidirectional gradient stress field of the coating-substrate multilayer structure to obtain the fatigue limit of the coated stainless steel blade. S6. Extract the effective circumferential stress parameters of the critical points of the coated blade and import them into the prediction model to calculate the fatigue limit. S7. Substitute the effective stress parameters into the established prediction model to obtain the fatigue limit prediction results, and verify the prediction results with the experimental results.

2. The method of claim 1, wherein, The specific steps of S1 are as follows: S11. The stress-strain curve of the stainless steel blade matrix was obtained by uniaxial tensile test, and the JC constitutive model of formula (1) was obtained by fitting. （1） in, For stress, In response to the situation; S12, determine the constitutive model of the coating by the method of nanoindentation inversion analysis, determine the hardness and elastic modulus of the coating by nanoindentation test, and calculate the characteristic stress and the characteristic strain by formulas (2) and (3) （2） （3） wherein, Gc is the complex elastic modulus, Gc is the coating hardness; S13, determining the hardening index by formula (4) and formula (5) and the yield strength ; （4） （5） wherein, is the residual depth after unloading, is the maximum indentation depth, is the yield stress; S14. The final constitutive model of the coating is determined to be Equation (6). （6）。 3. The method of claim 1, wherein: In step S2, the stress ratio R = -1 in the fatigue test of the coated blade.

4. The method of claim 1, wherein: In step S3, the finite element model of the coated blade is 1:1 in size to the test piece.

5. The method of claim 1, wherein, The specific steps for S4 are as follows: S41. Omnidirectional fixation of the petiole; S42. The first natural frequency of the blade was determined to be 1053 Hz through harmonic response analysis. S43. In the simulation experiment, a vertical excitation force is applied to simulate the loading conditions in the real test.

6. The method of claim 1, wherein, The specific steps of S52 are as follows: S521. Taking the fatigue failure hazard point as the base point, take a series of equidistant points in four directions: the tip direction, the axis of symmetry direction, the petiole direction, and the thickness direction of the blade, and record the corresponding stress values. S522. Normalize the distance and stress values ​​of the four groups of gradient stress fields respectively, and plot the distance-stress normalization curve. S523、the omni-directional gradient stress influence factor is calculated according to the stress gradient value and the gradient stress field influence distance value obtained by simulation T, the formula is as follows: （9） in, , , , These represent the areas enclosed by the normalized stress curves along four directions: the leaf tip direction, the axis of symmetry direction, the petiole direction, and the thickness direction. , , , These are weighting coefficients. ; , , The calculation formula is as follows: （10） The calculation formula is as follows: （11） The calculation formula is as follows: （12） where L is the gradient stress field influence distance of the blade stress peak point in the direction, is the stress field, r is the field radius, is the stress gradient, t is the coating thickness, and T is the blade thickness.

7. The method of claim 1, wherein, The specific steps of S53 are as follows: S531. Under the same loading conditions, conduct finite element simulation experiments of actual simulated blade aerodynamic uniform load loading and finite element simulation experiments of simulated blade aerodynamic uniform load loading without draft angle to study the stress concentration effect caused by draft angle. S532, Obtain the stress concentration influence factor The formula is as follows: （13） wherein, is the maximum stress value at the fatigue failure point of the actual blade, is the stress value at the corresponding point of the non-pullout blade.

8. The method of claim 7, wherein the method further comprises: The specific steps of S54 are as follows: S541、introducing an isotropic gradient stress influence factor T and stress concentration influence factor Equation (14) is obtained. （14） S542. Taking the logarithm of both sides of formula (14), we obtain the fatigue limit prediction model of the simulated blade omnidirectional gradient stress field as formula (15). （15） S543, the material parameter a, the stress gradient influence factor , the stress concentration influence factor into the fatigue limit prediction model, the fatigue life is calculated to obtain the fatigue limit , when , the simulated blade fatigue limit is obtained.

9. The method of claim 8, wherein the method further comprises: The fatigue limit prediction model for the omnidirectional gradient stress field of the coating-substrate multilayer structure in S55 is as follows: （16） in, For fatigue life, The fatigue limit, Here, y is a material parameter, and y is a parameter related to the influence of average stress. Stress ratio, Stress concentration influencing factor, This is the omnidirectional gradient stress influence factor.

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