Titanium alloy high-cycle-ultra-high-cycle combined amplitude fatigue life prediction method

Abstract

The application discloses a titanium alloy high-cycle-ultra-high-cycle compound amplitude fatigue life prediction method, relates to data collection, processing and life calculation of ultra-high-cycle fatigue tests, high-cycle fatigue tests and high-cycle-ultra-high-cycle compound amplitude fatigue tests under different stress ratios, and belongs to the field of fatigue performance of titanium alloy materials under high-cycle-ultra-high-cycle loads. The method combines typical stress ratio correction models, introduces a corrected ultra-high-cycle stress ratio correction model, and compares the test data of the ultra-high-cycle load loading under different stress ratios, wherein the results are all within three times of the band, the prediction effect is good, and the application is based on the Miner theorem, introduces the influence of the loading sequence on the ultra-high-cycle amplitude load, establishes a corrected high-cycle-ultra-high-cycle amplitude fatigue life prediction model, and the use of the model is more accurate in calculating the high-cycle-ultra-high-cycle amplitude fatigue life. The method is simple to calculate and has high accuracy, and has great practical significance.

Description

Technical Field

[0001] This invention can be used in the field of variable amplitude fatigue life prediction of titanium alloy materials under high-cycle-ultra-high-cycle stepped load loading, and is a method for predicting the high-cycle-ultra-high-cycle composite variable amplitude fatigue life of titanium alloys. Background Technology

[0002] Ti60 titanium alloy is a near-alpha type high-temperature titanium alloy belonging to the Ti-Al-Sn-Zr-Mo-Nb-Ta-Si system, strengthened through multi-component composite strengthening methods. This alloy was independently designed and developed in my country and possesses independent intellectual property rights. Titanium alloys can reduce aircraft weight and improve the thrust-to-weight ratio; therefore, they are often referred to as the backbone of the aerospace industry and are frequently used in this field.

[0003] When designing aero-engines, high-frequency vibration must be a primary consideration. During operation, critical components frequently face the risk of stress concentration, and coupled with the need to withstand continuous cyclic loads, fatigue fracture becomes their most common failure mode. With the continuous advancement of aero-engine technology, the challenge of fatigue failure in critical components is becoming increasingly apparent. Therefore, for important aero-engine components, researching the high-cycle-ultra-high-cycle fatigue life of their manufacturing material—titanium alloy—is particularly important. Summary of the Invention

[0004] This invention discloses a method for predicting the life of high-cycle and ultra-high-cycle composite variable amplitude fatigue in titanium alloys. Since life prediction methods for high-cycle fatigue are relatively mature, this invention will employ a commonly used high-cycle life prediction model. However, research on life prediction methods for ultra-high-cycle fatigue is still scarce, especially for ultra-high-cycle fatigue life prediction methods under different stress ratios. Therefore, this invention mainly focuses on the research of ultra-high-cycle fatigue life prediction methods. First, this invention obtains experimental data from ultra-high-cycle fatigue tests under different stress ratios. Based on the Basquin equation, it establishes an ultra-high-cycle fatigue life prediction model under symmetric cyclic conditions. Then, it establishes ultra-high-cycle fatigue life prediction models under different stress ratios using a modified stress ratio model. Finally, it introduces a loading sequence factor, proposes a modified Miner's theorem, and establishes a high-cycle and ultra-high-cycle composite variable amplitude fatigue life prediction model.

[0005] The lifetime prediction method proposed in this invention comprises the following steps:

[0006] Step (1): The specimens used in the ultra-high cycle fatigue test are all hourglass-shaped specimens. The fatigue test is an ultra-high cycle fatigue test with a stress ratio of -1 to obtain the corresponding test data for subsequent analysis.

[0007] Step (2): By analyzing the ultra-high cycle fatigue test data under R=-1, the test data are fitted using a variation of the Basquin formula to express the ultra-high cycle fatigue life prediction model under R=-1. The formula is as follows:

[0008]

[0009] Where, N f σ represents the predicted fatigue life. a σ represents the stress amplitude under symmetrical cyclic loading. f represents the fatigue strength coefficient, and b represents the fatigue strength index;

[0010] Step (3): The specimens used in the ultra-high cycle fatigue test are all hourglass-shaped specimens. The fatigue test is an ultra-high cycle fatigue test under two different stress ratios with a stress ratio greater than 0, in order to obtain the corresponding test data for subsequent analysis.

[0011] Step (4): After analyzing the data of the above three stress ratios, the stress level of 10 is calculated using the following formula. 7 10 8 10 9 The stress amplitude and average stress are calculated using the following formulas:

[0012] σ a =σ, f (2N f ) b (b)

[0013] Where, σ a σ represents the stress amplitude at this stress ratio. f N represents the fatigue strength coefficient. f represents the fatigue life under this stress ratio, and b represents the fatigue strength index;

[0014] Step (5): Fit the stress level for different stress ratios using the following formula: 10 7 10 8 10 9 Based on the stress amplitude and average stress data, the stress ratio correction model is obtained, and the calculation formula is as follows:

[0015]

[0016] Where α and β are experimental fitting parameters, σ s It is the yield strength of the material;

[0017] Step (6): Fit α, β and the stress level at a stress ratio of -1 to 10 using the following formula. 7 10 8 10 9The relationship between the data, and its calculation formula, are as follows:

[0018] α=a-bσ -1 (d)

[0019] β=c-dσ -1 (e)

[0020] Where a, b, c, and d are the fitting parameters.

[0021] Step (7): Substituting formulas (d) and (e) into formula (c) yields the final stress ratio correction model for ultra-high cycles. The final expression of the stress ratio correction model is shown below:

[0022]

[0023] Where, σ a σ is the stress amplitude at this stress ratio. m The average stress at this stress ratio is σ. -1 This is the corrected stress amplitude under this stress ratio;

[0024] Step (8): Calculate the corrected stress amplitude σ under different stress ratios using formula (f). -1 Substituting its value into formula (a) yields the predicted value of ultra-high cycle fatigue life under different stress ratios.

[0025] Step (9): High-cycle fatigue tests were conducted using an MTS-809 fatigue testing machine to obtain high-cycle fatigue test data for Ti60 titanium alloy material at R = -1. The Goodman stress ratio correction model was substituted into formula (a) to establish a high-cycle fatigue life prediction model under different stress ratios. The expression is shown in the following formula:

[0026]

[0027] Where, σ -1 It is the stress amplitude under this stress ratio, σ m It is the average stress under this stress ratio, σ b It is the tensile strength of the material, σ. f is the fatigue strength coefficient of the material, and b is the fatigue strength index of the material;

[0028] Step (10): High-cycle-ultra-high-cycle composite variable amplitude fatigue test of Ti60 titanium alloy material under stepped load was carried out using the developed high-cycle-ultra-high-cycle fatigue testing machine. Considering that the ultra-high-cycle load is a small stress level, the influence factor of the loading sequence was introduced, and its expression is shown in the following formula (h). A high-cycle-ultra-high-cycle composite variable amplitude fatigue life prediction model was established, and the variable amplitude test life was predicted using this model, and its expression is shown in the following formula (i):

[0029]

[0030] The meanings of the parameters in equation (h) are as follows: α VHCF,i This represents the influence factor of the i-th order loading sequence under a load block. Specifically, when i is 1, α... VHCF,i =1; D i This represents the damage amount under the ultra-high cycle load at the i-th stress level under a load block, i.e. n i N represents the fatigue life under ultra-high cycle load at the i-th stress level under a load block. i D represents the total fatigue life under ultra-high cycle load at the i-th stress level; i-1 D represents the damage amount under ultra-high cycle load at the (i-1)th stress level in a load block; k This represents the damage amount under the k-th stress level of a load block under ultra-high cycle load;

[0031] The meanings of each parameter in equation (i): N f Indicates the predicted fatigue life; n VHCF,1 N represents the fatigue life under ultra-high cycle load at the first stress level under a load block. VHCF,1 This represents the total fatigue life under ultra-high cycle load at the first stress level; This represents the damage amount under the first-order ultra-high cycle load in a load cell; α VHCF,i This represents the influence factor of the i-th order loading sequence under a load block (i≥2); n VHCF,i N represents the fatigue life under ultra-high cycle load at the i-th stress level under a load block. VHCF,i This represents the total fatigue life under ultra-high cycle load at the i-th stress level; This represents the damage amount under the i-th order ultra-high cycle load in a load block; n HCF,i N represents the fatigue life under high-cycle load at the i-th stress level in a load block. HCF,i This represents the total fatigue life under high-cycle load at the i-th stress level; This represents the damage amount under the i-th order high-cycle load in a load block.

[0032] The formula proposed in this invention has the following advantages: It proposes a method for predicting the high-cycle-ultra-high-cycle composite amplitude fatigue life of titanium alloys. This method is simple to calculate. Through ultra-high-cycle fatigue tests at R=-1 and two different stress ratios, and high-cycle fatigue tests at R=-1, the predicted high-cycle and ultra-high-cycle fatigue lifes at different stress ratios can be obtained by calculation. Then, the high-cycle-ultra-high-cycle composite amplitude fatigue life can be obtained by calculation through the amplitude prediction model. This greatly saves the effort required for the test and has high economic and practical value. Attached Figure Description

[0033] Figure 1 Shape and size of ultra-high cycle fatigue specimens under R=-1;

[0034] Figure 2 Ultra-high cycle fatigue test platform with R=-1

[0035] Figure 3 Figure of fitting effect of ultra-high frequency SN curve under R=-1

[0036] Figure 4 Shape and dimensions of ultra-high cycle fatigue specimens with stress ratio greater than 0;

[0037] Figure 5 Ultra-high cycle variable stress ratio fatigue test platform;

[0038] Figure 6 Figures showing the fitting results of the isochronous lifetime curves at different orders of magnitude;

[0039] Figure 7 A graph showing the relationship between test parameters and stress amplitude;

[0040] Figure 8 Comparison of test results and prediction results of ultra-high cycle fatigue life under different stress ratios;

[0041] Figure 9 MTS-809 fatigue testing machine;

[0042] Figure 10 Comparison of high-cycle and ultra-high-cycle composite amplitude fatigue life test results with predicted results. Detailed Implementation

[0043] The present invention will be described in conjunction with the accompanying drawings.

[0044] Step (1): The specimens used in the ultra-high cycle fatigue test are all hourglass-shaped specimens, and the specimen dimensions are as follows: Figure 1 As shown, the fatigue test is an ultra-high cycle fatigue test with a stress ratio of -1, and the fatigue test platform used is as follows: Figure 2 As shown, this is to obtain the relevant experimental data for subsequent analysis;

[0045] Step (2): Analysis of ultra-high cycle fatigue test data under R=-1

[0046] The experimental data were fitted using a variation of the Basquin formula, and the fitting effect was as follows: Figure 3 As shown, the ultra-high cycle fatigue life prediction model under R=-1 is described by the following formula:

[0047]

[0048] Where, N f σ represents the predicted fatigue life. a σ represents the stress amplitude under symmetrical cyclic loading. f represents the fatigue strength coefficient, and b represents the fatigue strength index;

[0049] Step (3): The specimens used in the ultra-high cycle fatigue test are all hourglass-shaped specimens, and the specimen dimensions are as follows: Figure 4 As shown, the fatigue tests were ultra-high cycle fatigue tests under two different stress ratios of 0.06 and 0.5. The fatigue test platform used was as follows: Figure 5 As shown, this is to obtain the relevant experimental data for subsequent analysis;

[0050] Step (4): After analyzing the data with stress ratios of -1, 0.06, and 0.5, the stress level of 10 is calculated using the following formula. 7 10 8 10 9 The stress amplitude and average stress are calculated using the following formulas:

[0051] σ a =σ, f (2N f ) b (b)

[0052] Where, σ a σ represents the stress amplitude at this stress ratio. f N represents the fatigue strength coefficient. f represents the fatigue life under this stress ratio, and b represents the fatigue strength index;

[0053] Step (5): Fit the stress levels with stress ratios of -1, 0.06, and 0.5 using the following formula, resulting in a stress level of 10. 7 10 8 10 9 The stress amplitude and mean stress data, the fitting effect is as follows Figure 6 As shown, the stress ratio correction model is obtained, and the calculation formula is as follows:

[0054]

[0055] Where α and β are experimental fitting parameters, σ s It is the yield strength of the material;

[0056] Step (6): Fit α, β and the stress level at a stress ratio of -1 to 10 using the following formula. 7 10 8 10 9 The relationship between the data and the fitting effect are as follows: Figure 7 As shown, its calculation formula is as follows:

[0057] α=a-bσ -1 (d)

[0058] β=c-dσ -1 (e)

[0059] Where a, b, c, and d are the fitting parameters.

[0060] Step (7): Substituting formulas (d) and (e) into formula (c) yields the final stress ratio correction model for ultra-high cycles. The final expression of the stress ratio correction model is shown below:

[0061]

[0062] Where, σ a σ is the stress amplitude at this stress ratio. m The average stress at this stress ratio is σ. -1 This is the corrected stress amplitude under this stress ratio;

[0063] Step (8): Calculate the corrected stress amplitude σ under different stress ratios using formula (f). -1 Substituting this value into formula (a) yields the predicted ultra-high cycle fatigue life under different stress ratios, such as... Figure 8 The results show a comparison between the test results and the predicted results of ultra-high cycle fatigue life under different stress ratios. The errors are mostly within three times the band, thus verifying the accuracy of the model.

[0064] Step (9): Conduct high-cycle testing using an MTS-809 fatigue testing machine, such as... Figure 9 As shown, high-cycle fatigue test data of Ti60 titanium alloy material under R=-1 were obtained. Substituting the Goodman stress ratio correction model into formula (a), a high-cycle fatigue life prediction model under different stress ratios was established, and its expression is shown in the following formula:

[0065]

[0066] Where, σ -1 It is the stress amplitude under this stress ratio, σ m It is the average stress under this stress ratio, σ b It is the tensile strength of the material, σ. f is the fatigue strength coefficient of the material, and b is the fatigue strength index of the material;

[0067] Step (10): Conduct high-cycle-ultra-high-cycle composite amplitude fatigue tests on Ti60 titanium alloy materials under stepped load using the developed high-cycle-ultra-high-cycle fatigue testing machine. The testing machine is as follows: Figure 5As shown, considering that the ultra-high cycle load is a low stress level, the influence factor of the loading sequence is introduced, and its expression is shown in equation (h) below. A high-cycle-ultra-high-cycle composite variable amplitude fatigue life prediction model is established, and the variable amplitude test life is predicted using this model, and its expression is shown in equation (i) below:

[0068]

[0069]

[0070] The meanings of the parameters in equation (h) are as follows: α VHCF,i This represents the influence factor of the i-th order loading sequence under a load block. Specifically, when i is 1, α... VHCF,i =1; D i This represents the damage amount under the ultra-high cycle load at the i-th stress level under a load block, i.e. n i N represents the fatigue life under ultra-high cycle load at the i-th stress level under a load block. i D represents the total fatigue life under ultra-high cycle load at the i-th stress level; i-1 D represents the damage amount under ultra-high cycle load at the (i-1)th stress level in a load block; k This represents the damage amount under the k-th stress level of a load block under ultra-high cycle load;

[0071] The meanings of each parameter in equation (i): N f Indicates the predicted fatigue life; n VHCF,1 N represents the fatigue life under ultra-high cycle load at the first stress level under a load block. VHCF,1 This represents the total fatigue life under ultra-high cycle load at the first stress level; This represents the damage amount under the first-order ultra-high cycle load in a load cell; α VHCF,i This represents the influence factor of the i-th order loading sequence under a load block (i≥2); n VHCF,i N represents the fatigue life under ultra-high cycle load at the i-th stress level under a load block. VHCF,i This represents the total fatigue life under ultra-high cycle load at the i-th stress level; This represents the damage amount under the i-th order ultra-high cycle load in a load block; n HCF,i N represents the fatigue life under high-cycle load at the i-th stress level in a load block. HCF,i This represents the total fatigue life under high-cycle load at the i-th stress level; This represents the damage amount under the i-th order high-cycle load in a load block.

[0072] like Figure 10The results of the variable amplitude fatigue life test were compared with the predicted results. The errors were mostly within three bands, thus verifying the accuracy of the model.

[0073] This invention provides a method for predicting the high-cycle and ultra-high-cycle composite amplitude fatigue life of titanium alloys. Through the ultra-high-cycle stress ratio correction model of this invention, and by introducing the Miner's theorem to correct the influence factor of the ultra-high-cycle amplitude load loading sequence, the prediction of the high-cycle and ultra-high-cycle composite amplitude fatigue life becomes more accurate. The method consists of the following steps: Step (1): Obtaining ultra-high-cycle fatigue test life data with a stress ratio of -1; Step (2): Establishing an ultra-high-cycle fatigue life prediction model under R = -1; Step (3): Obtaining ultra-high-cycle fatigue test life data under two different stress ratios with a stress ratio greater than 0; Step (4): Calculating the stress level of 10 under different stress ratios using a specified formula. 7 10 8 10 9 The stress amplitude and average stress; Step (5): Fit the stress level of 10 under different stress ratios using the specified formula. 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): Fit α, β and stress level of 10 with stress ratio of -1 using the specified formula. 7 10 8 10 9 The relationship between the data; Step (7): Substitute the data from the above steps into the specified formula to obtain the final stress ratio correction model for the ultra-high cycle; Step (8): Calculate the corrected stress amplitude σ under different stress ratios using the formula from step (7). -1 Substituting its value into the formula in step (2) yields the predicted value of ultra-high cycle fatigue life under different stress ratios; Step (9): Obtain high cycle fatigue test data under R = -1, and establish a high cycle fatigue life prediction model under different stress ratios using the specified formula; Step (10): Propose a high cycle-ultra-high cycle composite amplitude fatigue life prediction model that considers the influence of loading sequence, and substitute the high cycle-ultra-high cycle composite amplitude fatigue test data with stepped loading into the model to calculate the predicted fatigue life value.

Claims

1. A method for predicting the fatigue life of titanium alloys using high-cycle and ultra-high-cycle composite amplitude modulation, characterized in that, The specific calculation process of this lifetime prediction method is as follows: Step (1): The specimens used in the ultra-high cycle fatigue test are all hourglass-shaped specimens. The fatigue test is an ultra-high cycle fatigue test with a stress ratio of -1 to obtain the corresponding test data for subsequent analysis. Step (2): By analyzing the ultra-high cycle fatigue test data under R=-1, the test data are fitted using a variation of the Basquin formula to express the ultra-high cycle fatigue life prediction model under R=-1. The formula is as follows: Where, N f σ represents the predicted fatigue life. a σ represents the stress amplitude under symmetrical cyclic loading. f represents the fatigue strength coefficient, and b represents the fatigue strength index; Step (3): The specimens used in the ultra-high cycle fatigue test are all hourglass-shaped specimens. The fatigue test is an ultra-high cycle fatigue test under two different stress ratios with a stress ratio greater than 0, in order to obtain the corresponding test data for subsequent analysis. Step (4): After analyzing the data of the above three stress ratios, the stress level of 10 is calculated using the following formula. 7 10 8 10 9 The stress amplitude and average stress are calculated using the following formulas: s a =s, f (2N f ) b (b) Where, σ a σ represents the stress amplitude at this stress ratio. f N represents the fatigue strength coefficient. f represents the fatigue life under this stress ratio, and b represents the fatigue strength index; Step (5): Fit the stress level for different stress ratios using the following formula: 10 7 10 8 10 9 Based on the stress amplitude and average stress data, the stress ratio correction model is obtained, and the calculation formula is as follows: Where α and β are experimental fitting parameters, σ s It is the yield strength of the material; Step (6): Fit α, β and the stress level at a stress ratio of -1 to 10 using the following formula. 7 10 8 10 9 The relationship between the data, and its calculation formula, are as follows: α=a-bσ -1 (d) β=c-dσ -1 (e) Where a, b, c, and d are the fitting parameters; Step (7): Substituting formulas (d) and (e) into formula (c) yields the final stress ratio correction model for ultra-high cycles. The final expression of the stress ratio correction model is shown below: Where, σ a σ is the stress amplitude at this stress ratio. m The average stress at this stress ratio is σ. -1 This is the corrected stress amplitude under this stress ratio; Step (8): Calculate the corrected stress amplitude σ under different stress ratios using formula (f). -1 Substituting its value into formula (a) yields the predicted value of ultra-high cycle fatigue life under different stress ratios. Step (9): High-cycle fatigue tests were conducted using an MTS-809 fatigue testing machine to obtain high-cycle fatigue test data for Ti60 titanium alloy material at R = -1. The Goodman stress ratio correction model was substituted into formula (a) to establish a high-cycle fatigue life prediction model under different stress ratios. The expression is shown in the following formula: Where, σ -1 It is the stress amplitude under this stress ratio, σ m It is the average stress under this stress ratio, σ b It is the tensile strength of the material, σ. f is the fatigue strength coefficient of the material, and b is the fatigue strength index of the material; Step (10): High-cycle-ultra-high-cycle composite variable amplitude fatigue test of Ti60 titanium alloy material under stepped load was carried out using the developed high-cycle-ultra-high-cycle fatigue testing machine. Considering that the ultra-high-cycle load is a small stress level, the influence factor of the loading sequence was introduced, and its expression is shown in the following formula (h). A high-cycle-ultra-high-cycle composite variable amplitude fatigue life prediction model was established, and the variable amplitude test life was predicted using this model, and its expression is shown in the following formula (i): The meanings of the parameters in equation (h) are as follows: α VHCF,i This represents the influence factor of the i-th order loading sequence under a load block. Specifically, when i is 1, α... VHCF,i =1; D i This represents the damage amount under the ultra-high cycle load at the i-th stress level under a load block, i.e. n i N represents the fatigue life under ultra-high cycle load at the i-th stress level under a load block. i D represents the total fatigue life under ultra-high cycle load at the i-th stress level; i-1 D represents the damage amount under ultra-high cycle load at the (i-1)th stress level in a load block; k This represents the damage amount under the k-th stress level of a load block under ultra-high cycle load; The meanings of each parameter in equation (i): N f Indicates the predicted fatigue life; n VHCF,1 N represents the fatigue life under ultra-high cycle load at the first stress level under a load block. VHCF,1 This represents the total fatigue life under ultra-high cycle load at the first stress level; This represents the damage amount under the first-order ultra-high cycle load in a load cell; α VHCF,i This represents the influence factor of the i-th order loading sequence under a load block, where i ≥ 2; n VHCF,i N represents the fatigue life under ultra-high cycle load at the i-th stress level under a load block. VHCF,i This represents the total fatigue life under ultra-high cycle load at the i-th stress level; This represents the damage amount under the i-th order ultra-high cycle load in a load block; n HCF,i N represents the fatigue life under high-cycle load at the i-th stress level in a load block. HCF,i This represents the total fatigue life under high-cycle load at the i-th stress level; This represents the damage amount under the i-th order high-cycle load in a load block.

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