Method for predicting ultrahigh-cycle multi-axis tension-torsion composite variable-amplitude fatigue life of titanium alloy

Abstract

The invention discloses a method for predicting the ultra-high-cycle multi-axis tension-torsion composite variable-amplitude fatigue life of a titanium alloy. The method relates to data acquisition, processing and life calculation of ultra-high-cycle uniaxial fatigue tests under three different stress ratios, ultra-high-cycle multi-axial fatigue tests with different shear / axial stress ratios under symmetrical circulation and ultra-high-cycle multi-axial tension-torsion composite variable-amplitude fatigue tests. A stress ratio correction model in the ultra-high cycle field is established based on a Goodman equation, a new multi-axis parameter is introduced to replace a shear / axial stress ratio, and a shear stress influence factor is proposed to correct Mises equivalent stress which is suitable for fatigue limit equivalence. By analyzing a new multi-axis parameter, a shear stress influence factor in a fatigue limit under different shear / axial stress ratios and a relationship between an S-N curve slope and a fatigue index in a Basquin equation, actual tests verify that the calculation is simple and convenient, the accuracy is high, and the method has great practical significance.

Description

Technical Field

[0001] The present invention can be used in the field of ultra-high cycle multi-axial variable amplitude fatigue life prediction of titanium alloy materials, including an equivalent evaluation method for ultra-high cycle multi-axial load of titanium alloy and a high cycle-ultra-high cycle composite multi-axial fatigue life prediction method, which can be applicable to the life prediction research of titanium alloy under ultra-high cycle variable amplitude multi-axial fatigue load. Background Art

[0002] Key components in the aerospace field are usually subjected to complex multi-axial fatigue loads. With the gradual increase in the service life requirements of high-end equipment, there is an urgent need for a fatigue life prediction method under multi-axial variable amplitude loading suitable for the ultra-high cycle field.

[0003] At present, the low-cycle / high-cycle fatigue life prediction methods and the traditional infinite life design methods based on fatigue limit have shown serious shortcomings. Therefore, it is urgently necessary to study the equivalent evaluation method of multi-axial loads in the ultra-high cycle field, so as to form a life prediction method under multi-axial tension-torsion composite variable amplitude loads suitable for the ultra-high cycle field. This is of great strategic significance to the research and development of machinery in aerospace and other fields. Summary of the invention

[0004] The technical solution adopted by the present invention is a life prediction method for ultra-high cycle multi-axis tension-torsion composite variable amplitude fatigue of titanium alloy.

[0005] For low-cycle and high-cycle fatigue, life prediction methods have become mature, but there are no research reports on multi-axial ultra-high cycle fatigue life prediction methods, especially for ultra-high cycle life prediction methods under multi-axial tension-torsion composite different shear / axial stress ratio loads. Therefore, the present invention mainly studies ultra-high cycle tension-torsion composite multi-axial variable amplitude fatigue life prediction methods. The present invention first obtains basic test data through fatigue tests under ultra-high cycle uniaxial, obtains experimental data under three stress ratios of -1, 0.06, and 0.5, establishes a stress ratio correction model in the ultra-high cycle field based on the Goodman equation, and then obtains test data by ultra-high cycle multi-axial fatigue tests under three different shear / axial stress ratios through an ultra-high cycle multi-axial tension-torsion composite testing machine. A new multiaxial parameter is introduced to replace the shear / axial stress ratio, and a modified Mises equivalent stress suitable for the field of ultra-high cycle multiaxial fatigue is proposed. By analyzing the relationship between the new multiaxial parameter and the shear stress influencing factor in the fatigue limit under different shear / axial stress ratios and the slope of the SN curve, i.e. the fatigue exponent in the Basquin equation, an equivalent multiaxial evaluation method for ultra-high cycle multiaxial tension-torsion combined fatigue is proposed. Finally, a nonlinear fatigue damage accumulation method considering the influence of multi-level loading is used to realize the prediction of ultra-high cycle variable amplitude multiaxial fatigue life.

[0006] The life prediction method proposed by the present invention comprises the following steps:

[0007] Step (1): The specimen used in the ultra-high cycle uniaxial symmetrical fatigue test is an hourglass-shaped specimen. An ultra-high cycle fatigue test with a stress ratio of -1 is performed on an ultra-high cycle fatigue testing machine to obtain corresponding test data for subsequent analysis;

[0008] Step (2): By analyzing the ultra-high cycle fatigue test data under symmetrical cycles, the test data is fitted through a variant of the Basquin formula to express the ultra-high cycle fatigue life prediction model under symmetrical cycles. The formula is as follows:

[0009] σ a =σ' f (2N f ) b (1)

[0010]

[0011] Among them, N f represents the predicted fatigue life, σ a represents the stress amplitude under symmetrical cyclic loading, σ, f represents fatigue strength coefficient, b represents fatigue strength index;

[0012] Step (3): conducting ultra-high cycle fatigue tests at two different stress ratios with a stress ratio greater than 0 on an ultra-high cycle hourglass-shaped specimen under asymmetric cycles to obtain experimental data in order to derive a stress ratio correction model under ultra-high cycles;

[0013] Step (4): After analyzing the data of the three stress ratios of -1, 0.06, and 0.5, the fatigue life of 10 7 , 10 8 , 10 9 The stress amplitude and average stress are calculated as follows:

[0014] σ a =σ, f (2N f ) b (3)

[0015] Among them, σ a represents the stress amplitude under this stress ratio, σ, f Indicates fatigue strength coefficient, N f represents the fatigue life under this stress ratio, and b represents the fatigue strength index;

[0016] Step (5): The fatigue life is fitted to 10 by using the modified Goodman equation as shown below: 7 , 10 8 , 10 9The stress amplitude and average stress are used to obtain the stress ratio correction model in the ultra-high cycle field;

[0017]

[0018] Among them, p and q are experimental fitting parameters, σ b is the tensile strength of the material;

[0019] Step (6): The fatigue life under p, q and stress ratio of -1 is 10 by fitting the following formula: 7 , 10 8 , 10 9 The relationship between the data is calculated as follows:

[0020] p=a+b·σ -1 (5)

[0021] q=m+n·σ -1 (6)

[0022] Among them, a, b, m and n are fitting parameters.

[0023] Step (7): Integrate formula (d), formula (e), and formula (f) to finally obtain the stress ratio correction model in the ultra-high cycle field, as shown in the following formula;

[0024]

[0025] Step (8): The ultra-high cycle multi-axial tension-torsion composite fatigue test needs to be carried out on an ultra-high cycle fatigue testing machine. Compared with the uniaxial test, a special multi-axial amplitude change rod with an inclined groove and a double-arc specimen are used to carry out fatigue tests with three different shear / axial stress ratio loads of 1.37 / 1.95 / 3.53 to obtain the corresponding test data;

[0026] Step (9): After analyzing the data of the above three stress ratios, the SN curves under the three shear / axial stress ratios of 1.37 / 1.95 / 3.53 are described by the Basquin formula respectively, and the 10 9 Fatigue strength and fatigue index for three shear / axial stress ratios under life.

[0027] σ a =σ, f (2N f ) b (8)

[0028] Among them, σ a represents the stress amplitude under uniaxial profit state, σ, f Indicates fatigue strength coefficient, N frepresents the fatigue life under this stress ratio, and b represents the fatigue strength index;

[0029] Step (10): A new multi-axial parameter ρ in the ultra-high frequency range is adopted, and the expression is as follows, which represents the effect of normal stress under tension-torsion combined loading conditions in the ultra-high frequency range.

[0030]

[0031] Among them, σ represents the normal stress in tension-torsion combined loading, τ represents the shear stress in tension-torsion combined loading, and σ mises It indicates the magnitude of the mises equivalent stress in tension-torsion combined loading;

[0032] Step (11): Introduce the shear stress influence factor λ and modify the mises formula as follows, taking the case where the shear / axial stress ratio is 0 (i.e., under uniaxial tension and compression load) as 10 9 The fatigue limit σ0 of life is taken as the benchmark, and the fatigue limit under each shear / axial stress ratio is calculated to be applicable to the mises shear stress influence factor λ under ultra-high cyclic tension-torsion combined loading.

[0033]

[0034] Among them, σ ρ It represents the fatigue limit size under multiaxial parameter ρ load, that is, 10 9 Fatigue strength under life; σ represents the normal stress in tension-torsion combined loading, τ represents the shear stress in tension-torsion combined loading, and λ represents the mises shear stress influence factor applicable to ultra-high cycle tension-torsion combined loading. It is worth noting that in previous studies, the failure mechanism of Ti60 material under ultra-high cycle multi-axial loading was divided into two forms, and there is a threshold of shear / axial stress ratio. Here we can consider the shear / axial stress ratio to be 1, that is, the shear / axial stress is equivalent as the dividing point of the two failure forms. The shear stress influence coefficient λ of the load condition where the shear stress is greater than the tensile stress can be taken as a negative value to express the stress state dominated by shear stress.

[0035] Step (12): Fit the relationship between fatigue index b, shear stress influence coefficient λ and ultra-high cycle multiaxial parameter ρ under three shear / axial stress ratios by the following formula:

[0036] b=C1+C2ρ (11)

[0037] λ=P+Ae Sρ (12)

[0038] Among them, C1, C2, P, A, and S are fitting parameters.

[0039] Step (13): Integrate formula (8) with formula (9), formula (10), formula (11), and formula (12) to calculate the fatigue strength coefficient σ under a multi-axial parameter ρ working condition load: , f , the SN curve equation under arbitrary shear / axial stress ratio working load is further depicted as follows, and the fatigue life under ultra-high cycle multi-axial tension-torsion combined load is predicted.

[0040]

[0041] Among them, σ a,mises represents the applied Mises equivalent stress, is the fatigue limit value under single-cycle tension and compression load when the shear / axial stress ratio is 0; R represents the shear / axial stress ratio, and C1, C2, P, A, and S are fitting parameters;

[0042] Step (14): A high-cycle-ultra-high-cycle composite multi-axial variable amplitude fatigue test of Ti60 titanium alloy material with variable amplitude loading is carried out by using the developed high-cycle-ultra-high-cycle multi-axial fatigue testing machine. Since Miner's theorem is insensitive to the loading sequence of high-low or low-high loads, the life predicted by Miner will be too high, which is dangerous for engineering applications. Therefore, a classical nonlinear fatigue damage accumulation method that considers the interaction of multi-level loads is adopted, and a sequential load influence factor α is introduced, and the expression is shown in the following formula;

[0043]

[0044] The meaning of each parameter in the above formula:

[0045] The meaning of each parameter in formula (13): D i,mp Represents the residual damage after level i loading; N fi represents the fatigue life until failure under the cyclic load of level i; n i Indicates the number of cycles of load level i; σ i represents the stress load under level i loading; α represents the sequential load influence factor, and its expression is shown in formula (13), where σ and τ are the axial stress and shear stress applied by the ultra-high cycle, respectively.

[0046] Step (15): A high-cycle-ultra-high-cycle composite multiaxial variable amplitude fatigue test of Ti60 titanium alloy material with variable amplitude loading is carried out by using the developed high-cycle-ultra-high-cycle multiaxial fatigue testing machine, where the actual frequency of the ultra-high cycle load is 20 kHz; the load spectrum is decomposed into high-frequency ultra-high cycle multiaxial load and low-frequency high-cycle average stress, and the ultra-high cycle uniaxial variable amplitude load under symmetrical cycle is obtained according to the ultra-high cycle multiaxial equivalent evaluation method and stress ratio correction method proposed in the previous article combined with the high-cycle average stress, and finally the life prediction is carried out by using the nonlinear damage accumulation method to further verify the accuracy of the proposed model.

[0047] The formula proposed in the present invention has the following advantages: a titanium alloy high-cycle and ultra-high-cycle multi-axial tension-torsion composite fatigue equivalent evaluation method and a titanium alloy high-cycle-ultra-high-cycle composite multi-axial variable amplitude fatigue life prediction method are proposed. The method is simple to calculate, and the SN curve under other arbitrary shear / axial stress ratio conditions can be inferred through experiments under three shear / axial stress ratio conditions, and the high-cycle-ultra-high-cycle composite multi-axial variable amplitude fatigue life prediction of titanium alloy is realized by combining the stress ratio correction model and the nonlinear damage accumulation model. It greatly saves the energy required for the experiment and has high economic value and practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Uniaxial very high cycle fatigue specimen shape under symmetrical cycles.

[0049] Figure 2 Shape of multiaxial very high cycle fatigue specimen under symmetrical cycles.

[0050] Figure 3 Very high cycle fatigue test platform under symmetrical cycles.

[0051] Figure 4 Ultra-high cycle SN curve fitting effect diagram under symmetrical cycle.

[0052] Figure 5 Fitting diagram of shear stress influencing factors.

[0053] Figure 6 Fatigue strength index fitting diagram.

[0054] Figure 7 Comparison of ultra-high cycle fatigue life test results and prediction results under different shear / axial stress ratios. Figure 8 It is a fitting result diagram of the relationship between the fatigue index b, the shear stress influence coefficient λ and the ultra-high cycle multi-axial parameter ρ under three shear / axial stress ratios. Fig. 9 It is a typical variable amplitude load spectrum; Fig.10 It is a life prediction diagram using the nonlinear damage accumulation method; Fig.11 yes Fig.10 Prediction result graph. DETAILED DESCRIPTION

[0055] The present invention is described with reference to the accompanying drawings.

[0056] Step (1): The specimen used in the ultra-high cycle uniaxial symmetrical fatigue test is an hourglass-shaped specimen, such as Figure 1 As shown in the uniaxial symmetric test piece, Figure 3 Perform ultra-high cycle fatigue tests with a stress ratio of -1 on an ultra-high cycle fatigue testing machine to obtain relevant test data for subsequent analysis;

[0057] Step (2): By analyzing the ultra-high cycle fatigue test data under symmetrical cycles, the test data is fitted through a variant of the Basquin formula to express the ultra-high cycle fatigue life prediction model under symmetrical cycles. The formula is as follows:

[0058] σ a =σ' f (2N f ) b (1)

[0059]

[0060] Among them, N f represents the predicted fatigue life, σ a represents the stress amplitude under symmetrical cyclic loading, σ, f represents fatigue strength coefficient, b represents fatigue strength index;

[0061] Step (3): If Figure 1 As shown in the figure, the ultra-high cycle hourglass specimen under asymmetric cycle was subjected to ultra-high cycle uniaxial loading tests with different stress ratios using an MTS-809 fatigue testing machine. Figure 4 As shown, ultra-high cycle fatigue tests are carried out under two different stress ratios with a stress ratio greater than 0 to obtain experimental data in order to derive a stress ratio correction model under ultra-high cycles;

[0062] Step (4): After analyzing the fatigue test data of uniaxial asymmetric cyclic load, i.e., two different stress ratios of 0.06 and 0.5, the fatigue life is calculated to be 10 7 , 10 8 , 10 9 The stress amplitude and average stress are calculated as follows:

[0063] σ a =σ, f (2N f ) b (3)

[0064] Among them, σ arepresents the stress amplitude under this stress ratio, σ, f Indicates fatigue strength coefficient, N f represents the fatigue life under this stress ratio, and b represents the fatigue strength index;

[0065] Step (5): The fatigue life is fitted to 10 by using the modified Goodman equation as shown below: 7 , 10 8 , 10 9 The stress amplitude and average stress are used to obtain the stress ratio correction model in the ultra-high cycle field;

[0066]

[0067] Among them, p and q are experimental fitting parameters, σ b is the tensile strength of the material;

[0068] Step (6): The fatigue life under p, q and stress ratio of -1 is 10 by fitting the following formula: 7 , 10 8 , 10 9 The relationship between the data is calculated as follows:

[0069] p=a+b·σ -1 (5)

[0070] q=m+n·σ -1 (6)

[0071] Among them, a, b, m and n are fitting parameters.

[0072] Step (7): Integrate formula (4), formula (5), and formula (6) to finally obtain the stress ratio correction model in the ultra-high cycle field. The fitting results are as follows: Figure 5 As shown;

[0073]

[0074] Step (8): The ultra-high cycle multi-axial tension-torsion composite fatigue test needs to be carried out on an ultra-high cycle fatigue testing machine, such as Figure 3 As shown; compared with the uniaxial test, a special multi-axial amplitude rod with inclined grooves and double arc specimens were used to carry out fatigue tests with three different shear / axial stress ratios of 1.37 / 1.95 / 3.53 to obtain the corresponding test data;

[0075] Step (9): After analyzing the data of the above three stress ratios, the SN curves under the three shear / axial stress ratios of 1.37 / 1.95 / 3.53 are described by the Basquin formula, as shown in Figure 6 As shown, according to the following formula, 10 9Fatigue strength and fatigue index for three shear / axial stress ratios under life.

[0076] σ a =σ, f (2N f ) b (8)

[0077] Among them, σ a represents the stress amplitude under uniaxial profit state, σ, f Indicates fatigue strength coefficient, N f represents the fatigue life under this stress ratio, and b represents the fatigue strength index;

[0078] Step (10): A new multi-axial parameter ρ in the ultra-high frequency range is adopted, and the expression is as follows, which represents the effect of normal stress under tension-torsion combined loading conditions in the ultra-high frequency range.

[0079]

[0080] Among them, σ represents the normal stress in tension-torsion combined loading, τ represents the shear stress in tension-torsion combined loading, and σ mises It indicates the magnitude of the mises equivalent stress in tension-torsion combined loading;

[0081] Step (11): Introduce the shear stress influence factor λ and modify the mises formula as follows, taking the case where the shear / axial stress ratio is 0 (i.e., under uniaxial tension and compression load) as 10 9 The fatigue limit σ0 of life is taken as the benchmark, and the fatigue limit under each shear / axial stress ratio is calculated to be applicable to the mises shear stress influence factor λ under ultra-high cyclic tension-torsion combined loading.

[0082]

[0083] Among them, σ ρ It represents the fatigue limit size under multiaxial parameter ρ load, that is, 10 9 Fatigue strength under life; σ represents the normal stress in tension-torsion combined loading, τ represents the shear stress in tension-torsion combined loading, and λ represents the mises shear stress influence factor applicable to ultra-high cycle tension-torsion combined loading. It is worth noting that in previous papers, the failure mechanism of Ti60 material under ultra-high cycle multi-axial loading was divided into two forms, and there is a threshold of shear / axial stress ratio. Here we can consider the shear / axial stress ratio to be 1, that is, the shear / axial stress is equivalent as the dividing point of the two failure forms. The shear stress influence coefficient λ of the load condition where the shear stress is greater than the tensile stress can be taken as a negative value to express the stress state dominated by shear stress.

[0084] Step (12): The relationship between fatigue index b, shear stress influence coefficient λ and ultra-high cycle multiaxial parameter ρ under three shear / axial stress ratios is fitted by the following formula. The fitting results are as follows: Figure 7 , Figure 8 As shown:

[0085] b=C1+C2ρ (11)

[0086] λ=P+Ae Sρ (12)

[0087] Among them, C1, C2, P, A, and S are fitting parameters.

[0088] Step (13): Integrate formula (8) with formula (9), formula (10), formula (11), and formula (12) to calculate the fatigue strength coefficient σ under a multi-axial parameter ρ working condition load. f , the SN curve equation under arbitrary shear / axial stress ratio working load is further depicted as follows, and the fatigue life under ultra-high cycle multi-axial tension-torsion combined load is predicted.

[0089]

[0090] Among them, σ a,mises represents the applied Mises equivalent stress, is the fatigue limit value under single-cycle tension and compression load when the shear / axial stress ratio is 0; R represents the shear / axial stress ratio, and C1, C2, P, A, and S are fitting parameters;

[0091] Step (14): Since Miner's theorem is insensitive to the loading sequence of high-low or low-high loads, the life predicted by Miner will be too high, which is dangerous for engineering applications. Therefore, a classical nonlinear fatigue damage accumulation method that considers the interaction of multi-level loads is adopted, and the sequential load influence factor α is introduced. The expression is shown in the following formula:

[0092]

[0093] The meaning of each parameter in the above formula:

[0094] The meaning of each parameter in formula (m): D i,mp Represents the residual damage after level i loading; N fi represents the fatigue life until failure under the cyclic load of level i; n i Indicates the number of cycles of load level i; σ i represents the stress load under level i loading; α represents the sequential load influence factor, and its expression is shown in formula (m), where σ and τ are the axial stress and shear stress applied by the ultra-high cycle, respectively.

[0095] Step (15): A high-cycle-ultra-high-cycle composite multi-axial variable amplitude fatigue test of Ti60 titanium alloy material with variable amplitude loading is carried out by using the developed high-cycle-ultra-high-cycle multi-axial fatigue testing machine. The typical variable amplitude load spectrum is as follows: Fig. 9 As shown in the figure, the actual frequency of the ultra-high cycle load is 20kHz; Fig.10 As shown in the figure, the load spectrum is decomposed into high-frequency ultra-high-cycle multiaxial load and low-frequency high-cycle average stress. According to the ultra-high-cycle multiaxial equivalent evaluation method and stress ratio correction method proposed in the previous article, combined with the high-cycle average stress, the ultra-high-cycle uniaxial variable amplitude load under symmetrical cycle is obtained, and finally the life prediction is carried out through the nonlinear damage accumulation method. The prediction results are shown in Fig.11 As shown, most of the errors are within the three-fold band, which further verifies the accuracy of the proposed model.

[0096] The present invention provides a method for predicting the ultra-high cycle multi-axis variable amplitude fatigue life of titanium alloy. Through the ultra-high cycle stress ratio correction model, ultra-high cycle multi-axis equivalent evaluation method, and nonlinear fatigue damage accumulation method considering the influence of multi-level load interaction of the present invention, the ultra-high cycle multi-axis variable amplitude fatigue life prediction is made more accurate. The method steps are: step (1): conduct an ultra-high cycle fatigue test with a stress ratio of -1 to obtain valid test data; step (2): establish a uniaxial ultra-high cycle fatigue life prediction model under symmetrical cycles; step (3): conduct ultra-high cycle fatigue tests under two different stress ratios with a stress ratio greater than 0 to obtain valid test data; step (4): calculate the fatigue life under different stress ratios by the Basquin formula as 10 7 , 10 8 , 10 9 Stress amplitude and average stress; Step (5): Fit the fatigue life under different stress ratios by specifying the formula to be 10 7 , 10 8 , 10 9 The stress amplitude and average stress data are used to obtain the ultra-high cycle stress ratio correction model; Step (6): By fitting the fatigue life of 10 under p, q and stress ratio of -1 by specifying the formula 7 , 10 8 , 10 9data; Step (7): obtain the stress ratio correction model in the ultra-high cycle field; Step (8): conduct ultra-high cycle tension-torsion multiaxial fatigue experiments under symmetrical cycles to obtain effective test data; Step (9): analyze the multiaxial test data, and use the Basquin formula to describe the SN curves under three shear / axial stress ratios of 1.37 / 1.95 / 3.53; Step (10): propose to use a new multiaxial parameter ρ in the ultra-high cycle field; Step (11): introduce the shear stress influence factor λ, modify the mises formula, and apply it to the fatigue limit calculation under different shear / axial stress ratios; Step (12): by pointing A relationship is determined to fit the relationship between the fatigue index b, the shear stress influence coefficient λ and the ultra-high cycle multi-axial parameter ρ under three shear / axial stress ratios; step (13): integrating the relationship to obtain the SN curve equation under any shear / axial stress ratio working load; step (134): adopting a classic nonlinear fatigue damage accumulation method considering the influence of multi-stage load interaction, and introducing the sequential load influence factor α; step (15): combining the proposed ultra-high cycle stress ratio correction method, the ultra-high cycle multi-axial equivalent evaluation method and the nonlinear fatigue damage accumulation method considering the influence of multi-stage load interaction to predict the high-cycle-ultra-high cycle composite multi-axial variable amplitude fatigue life of titanium alloy.

Claims

1. A method for predicting fatigue life of titanium alloy under ultra-high cycle multi-axis tension-torsion combined variable amplitude, characterized in that: The specific calculation process of this life prediction method is as follows: Step (1): The specimen used in the ultra-high cycle uniaxial symmetrical fatigue test is an hourglass-shaped specimen. An ultra-high cycle fatigue test with a stress ratio of -1 is performed on an ultra-high cycle fatigue testing machine to obtain corresponding test data for subsequent analysis; Step (2): By analyzing the ultra-high cycle fatigue test data under symmetrical cycles, the test data is fitted through a variant of the Basquin formula to express the ultra-high cycle fatigue life prediction model under symmetrical cycles. The formula is as follows: s a =s' f (2N f ) b (1) Among them, N f represents the predicted fatigue life, σ a represents the stress amplitude under symmetrical cyclic loading, σ' f represents fatigue strength coefficient, b represents fatigue strength index; Step (3): conducting ultra-high cycle fatigue tests at two different stress ratios with a stress ratio greater than 0 on an ultra-high cycle hourglass-shaped specimen under asymmetric cycles to obtain experimental data in order to derive a stress ratio correction model under ultra-high cycles; Step (4): After analyzing the data of the three stress ratios of -1, 0.06, and 0.5, the fatigue life of 10 7 , 10 8 , 10 9 The stress amplitude and average stress are calculated as follows: s a =in' f (2N f ) b (3) Among them, σ a represents the stress amplitude under this stress ratio, σ' f Indicates fatigue strength coefficient, N f represents the fatigue life under this stress ratio, and b represents the fatigue strength index; Step (5): The fatigue life is fitted to 10 by using the modified Goodman equation as shown below: 7 , 10 8 , 10 9 The stress amplitude and average stress are used to obtain the stress ratio correction model in the ultra-high cycle field; Among them, p and q are experimental fitting parameters, σ b is the tensile strength of the material; Step (6): The fatigue life under p, q and stress ratio of -1 is 10 by fitting the following formula: 7 , 10 8 , 10 9 The relationship between the data is calculated as follows: p=a+b·s -1 (5) q=m+n·σ -1 (6) Among them, a, b, m and n are fitting parameters. Step (7): Integrate formula (d), formula (e), and formula (f) to finally obtain the stress ratio correction model in the ultra-high cycle field, as shown in the following formula; Step (8): The ultra-high cycle multi-axial tension-torsion composite fatigue test needs to be carried out on an ultra-high cycle fatigue testing machine. Compared with the uniaxial test, a special multi-axial amplitude change rod with an inclined groove and a double-arc specimen are used to carry out fatigue tests with three different shear / axial stress ratios of 1.37 / 1.95 / 3.53 to obtain corresponding test data; Step (9): After analyzing the data of the above three stress ratios, the SN curves under the three shear / axial stress ratios of 1.37 / 1.95 / 3.53 are described by the Basquin formula respectively, and the 10 9 Fatigue strength and fatigue index for three shear / axial stress ratios under life. s a =s' f (2N f ) b (8) Among them, σ a represents the stress amplitude under uniaxial stress state, σ' f Indicates fatigue strength coefficient, N f represents the fatigue life under this stress ratio, and b represents the fatigue strength index; Step (10): A multi-axial parameter ρ in the ultra-high frequency range is adopted, and the expression is as follows, which represents the effect of normal stress under tension-torsion combined loading conditions in the ultra-high frequency range. Among them, σ represents the normal stress in tension-torsion combined loading, τ represents the shear stress in tension-torsion combined loading, and σ mises It indicates the magnitude of the mises equivalent stress in tension-torsion combined loading; Step (11): Introduce the shear stress influence factor λ and modify the mises formula as follows, taking the shear / axial stress ratio as 0, i.e. 10 under uniaxial tension and compression load 9 The fatigue limit σ0 of life is taken as the benchmark, and the fatigue limit under each shear / axial stress ratio is calculated to be applicable to the mises shear stress influence factor λ under ultra-high cyclic tension-torsion combined loading. Among them, σ ρ It represents the fatigue limit size under multiaxial parameter ρ load, that is, 10 9 Fatigue strength under life; σ represents the magnitude of normal stress in tension-torsion combined loading, τ represents the magnitude of shear stress in tension-torsion combined loading, and λ represents the mises shear stress influence factor applicable to ultra-high cycle tension-torsion combined loading; the shear stress influence coefficient λ of the load condition where the shear stress is greater than the tensile stress is taken as a negative value to express the stress state dominated by shear stress. Step (12): Fit the relationship between fatigue index b, shear stress influence coefficient λ and ultra-high cycle multiaxial parameter ρ under three shear / axial stress ratios by the following formula: b=C1+C2ρ (11) λ=P+Ae Sρ (12) Among them, C1, C2, P, A, and S are fitting parameters. Step (13): Integrate formula (8) with formula (9), formula (10), formula (11), and formula (12) to calculate the fatigue strength coefficient σ' under a multi-axial parameter ρ working condition load f , the equation of the SN curve under any shear / axial stress ratio working load is depicted as follows, and then the fatigue life under ultra-high cycle multi-axial tension-torsion combined load is predicted. Among them, σ a,mises represents the applied Mises equivalent stress, is the fatigue limit value under single-cycle tension and compression load when the shear / axial stress ratio is 0; R represents the shear / axial stress ratio, and C1, C2, P, A, and S are fitting parameters; Step (14): a high-cycle-ultra-high-cycle composite multi-axial variable amplitude fatigue test of Ti60 titanium alloy material with variable amplitude loading is carried out by using a developed high-cycle-ultra-high-cycle multi-axial fatigue testing machine. A classical nonlinear fatigue damage accumulation method considering the interaction of multi-level loads is adopted, and a sequential load influence factor α is introduced. The expression is shown in the following formula; The meaning of each parameter in the above formula: The meaning of each parameter in formula (m): D i,mp Represents the residual damage after level i loading; N fi represents the fatigue life until failure under the cyclic load of level i; n i Indicates the number of cycles of load level i; σ i represents the stress load under level i loading; α represents the sequential load influence factor, and its expression is shown in formula (12), where σ and τ are the axial stress and shear stress applied by the ultra-high cycle, respectively. Step (15): A high-cycle-ultra-high-cycle composite multiaxial variable amplitude fatigue test of Ti60 titanium alloy material with variable amplitude loading is carried out by using the developed high-cycle-ultra-high-cycle multiaxial fatigue testing machine, where the actual frequency of the ultra-high cycle load is 20 kHz; the load spectrum is decomposed into high-frequency ultra-high cycle multiaxial load and low-frequency high-cycle average stress, and the ultra-high cycle uniaxial variable amplitude load under symmetrical cycle is obtained according to the ultra-high cycle multiaxial equivalent evaluation method and the stress ratio correction method combined with the high-cycle average stress, and finally the life prediction is carried out by using the nonlinear damage accumulation method to further verify the accuracy of the proposed model.

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