CN108491570B - Bending fatigue life prediction method for SPFDB three-layer plate hollow sandwich structure - Google Patents
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Abstract
The invention provides a bending fatigue life prediction method for an SPF/DB three-layer plate hollow sandwich structure, which is characterized in that a fatigue life prediction model with a wider application range is established by extracting sandwich structures with different thicknesses and capable of reflecting the structural characteristics of hollow fan blades and taking the maximum bending normal stress after considering different thicknesses and stress ratios as damage parameters, and the model can provide a basis for the design and strength evaluation of wide-chord hollow fan blades. Meanwhile, a numerical simulation method is adopted to carry out simulation calculation on the impact damage process of the foreign object, so that the residual stress distribution after impact damage and the stress concentration coefficient at the damage position are obtained, and a fatigue life prediction model of the sandwich structure after FOD is considered is established. The method for predicting the service life is suitable for predicting the fatigue life of the wide-chord hollow fan blade at any position and under different damage states, and has a better engineering application value.
Description
Technical Field
The invention relates to the field of prediction of fatigue life of fan blades of an aeroengine, in particular to a method for predicting the bending fatigue life of a wide-chord hollow fan blade formed by a superplastic forming/diffusion bonding (SPF/DB) combined process.
Background
In the actual work of an aircraft engine, the fan blades can be subjected to complex loads such as centrifugal force load, pneumatic load and the like, and the complex loads bring harsh test to the blade strength. Particularly, the wide-chord hollow fan blade contains a hollow structure, additional bending moment can be generated at the hollow part under pneumatic load, and bending deformation is mainly generated when the blade vibrates, so that the hollow structure is in a complex stress state. The diffusion welding structure in the hollow blade is a weak part which is stressed actually, so that the method is particularly important for evaluating the bending fatigue performance of the diffusion welding hollow structure. At the same time, fan blades are also prone to Foreign Object Damage (FOD) events, i.e., hard objects from the external environment, such as flying stones, grit, etc., enter the engine airflow path along with the high velocity airflow. This can lead (depending on the degree of influence) to direct blade fracture or failure, crack formation and deformation, which greatly affects the performance and life of the broad-chord hollow blade. Such harsh operating environments and complex stress conditions provide significant challenges to the safe operation of the hollow fan blades. Therefore, a reliable bending fatigue life prediction model needs to be established.
Disclosure of Invention
The invention provides a method for predicting the bending fatigue life of a wide-chord hollow fan blade in different damage states, which aims to solve the problems of strength analysis of the fan blade of an aeroengine and safety evaluation of the fan blade after FOD (form of the device), and can more accurately predict the bending fatigue life of the wide-chord hollow fan blade at different positions and after FOD.
The invention adopts the following technical scheme:
and extracting a hollow sandwich structure test piece of the hollow fan blade, and taking the maximum bending normal stress as a damage parameter. An S-N curve of a test piece with a thickness hollow sandwich structure under the condition that the stress ratio R is 0.1 is established through a three-point bending test and is shown as a formula (1)
lgσα＝algNf+b (1)
Correcting the test pieces with different thicknesses of the hollow sandwich structure by combining a theoretical normal stress calculation formula, wherein W in the formula (2) is shown as a formula (2)0The effective bending-resistant section coefficient of the hollow sandwich structure test piece in the bending fatigue test is shown, and W is the effective bending-resistant section coefficient of the hollow sandwich structure test piece with any thickness, and can be directly calculated in modeling software.
And correcting the stress ratio by adopting a Gerber stress ratio correction formula. And (3) combining the vertical type (1) and the formula (2) to obtain a bending fatigue life prediction model of the hollow sandwich structure under the consideration of different thicknesses and stress ratios, as shown in the formula (3). Wherein sigmaα' is the maximum bending normal stress after the stress ratio correction.
For predicting the fatigue life of the FOD rear hollow sandwich structural member, the invention adopts a linear superposition method for processing. The specific implementation process comprises the following steps:
(1) numerical simulation is carried out on the FOD process of the hollow sandwich structure test piece based on FEM, and the residual stress sigma in the direction of normal stress loading of the dangerous part of the hollow sandwich structural member is obtained through calculationres，
(2) Theoretical stress concentration coefficient K at notch under bending load of FEM-based hollow sandwich structure test piece with impact notcht；
(3) When residual stresses are applied to cyclic loads, they substantially affect the fatigue life of the hollow sandwich structure by affecting the average stress. If the superposition of residual stress is introduced, the service life can be predicted by mean stress correction. And (3) superposing the notch residual stress and the bending normal stress corrected by considering the notch effect to obtain the equivalent bending normal stress, wherein the equivalent bending stress ratio is shown as a formula (4) and a formula (5). And according to the thickness-to-stress ratio correction method, a bending fatigue life prediction model of the FOD rear hollow sandwich structure can be established, as shown in the formula (6).
σequ＝Ktσα+σres(4)
Has the advantages that: compared with the prior art, the method for predicting the bending fatigue life of the three-layer plate hollow sandwich structural member formed by the superplastic forming/diffusion bonding (SPF/DB) combined process has the following advantages: the method for predicting the service life is suitable for predicting the fatigue life of the wide-chord hollow fan blade at any position and under different damage states, and has a better engineering application value.
Drawings
FIG. 1 is a flow chart of the prediction of the bending fatigue life of the hollow sandwich structure in the invention.
FIG. 2 is a geometric dimension diagram of a test piece of a hollow sandwich structure used in the test verification of the invention.
FIG. 3 is a load-life curve of a hollow sandwich structure specimen in the process of embodying the present invention.
FIG. 4 is a comparison of the predicted life and the test life of the non-damaged hollow sandwich structure test piece of the present invention.
FIG. 5 is a cloud diagram of the distribution of residual stress in the bending normal stress direction obtained by FOD numerical simulation in the present invention.
FIG. 6 is a cloud chart of the distribution of the bending normal stress obtained by the numerical value of the test piece with the notch hollow sandwich structure.
FIG. 7 is a comparison of the predicted life and the test life of the test piece with different thicknesses of the hollow sandwich structure after FOD in the invention.
Detailed Description
The invention provides a method for predicting the bending fatigue life of a three-layer plate hollow sandwich structural member formed by a superplastic forming/diffusion bonding (SPF/DB) combined process. Meanwhile, a numerical simulation method is adopted to carry out simulation calculation on the impact damage process of the foreign object, so that the residual stress distribution after impact damage and the stress concentration coefficient at the damage position are obtained, and a fatigue life prediction model of the sandwich structure after FOD is considered is established. The method for predicting the service life is suitable for predicting the fatigue life of the wide-chord hollow fan blade at any position and under different damage states, and has a better engineering application value.
The invention is further described with reference to the following figures and examples.
The flow chart of the prediction method provided by the invention is shown in figure 1, and two hollow sandwich structure test pieces with the total thickness, namely 7mm test pieces and 9mm test pieces, are designed and processed, as shown in figure 2. Firstly, three-point bending fatigue tests are carried out on hollow sandwich structure test pieces in different damage states to obtain load-life curves of the test pieces, as shown in fig. 3.
A three-point bending fatigue test result of a 7mm hollow sandwich structure test piece under the condition that the stress ratio R is 0.1 is taken as a basis, and an S-N curve is established by taking the maximum bending normal stress as a damage parameter, wherein the S-N curve is shown as a formula (1).
lgσα＝-0.1078lg Nf+3.45 (1)
The maximum bending normal stress on the middle loading section of the hollow sandwich structure test piece can be calculated by adopting the formula (2). In the formula sigmaαMaximum bending normal stress under bending load, FmaxFor maximum bending cycle loads, L is the test 1/2 effective span (60 mm in this experiment), W is the effective bending section modulus for hollow core test pieces.
σα＝FmaxL/2W (2)
As the bending moments on the same section of the blade are the same, according to the formula (2), when other conditions are the same, the influence of the thickness on the stress on the section with the maximum bending stress is mainly determined by the effective bending-resistant section coefficient. With a test piece with the thickness of 7mm as a reference, the maximum normal stress of the section under any thickness condition under the same load grade can be calculated by the formula (3), and the maximum normal stress is substituted into the S-N curve equation (1) of the test piece with the hollow sandwich structure of 7mm to obtain the formula (4). The model is a fatigue life prediction model of the hollow sandwich structure test piece considering the influence of different thicknesses.
lgσ＝-0.1078lgNf-lgW0+lgW+3.45 (4)
In the formula W0The effective bending-resistant section coefficient of a 7mm hollow sandwich structure test piece, and W is the effective bending-resistant section coefficient of a hollow sandwich structure test piece with any thicknessThe coefficients can be directly obtained in modeling software.
For the influence of the stress ratio, the invention adopts Gerber equation to carry out equivalent conversion on the normal stress, and also takes an S-N curve when the stress ratio R of a 7mm hollow sandwich structure test piece is 0.1 as a reference to carry out equal-life conversion. Thereby obtaining a fatigue life prediction model of the hollow sandwich structure test piece under the influence of the section thickness and the stress ratio in comprehensive consideration:
lgσ'a＝-0.1078lgNf-lgW0+lgW+3.41 (5)
wherein sigmaαThe stress ratio is the corrected maximum bending normal stress. Using the above model, life prediction was performed for the 9mm hollow sandwich structure specimen stress at a ratio R of 0.1 and for the 7mm hollow sandwich structure specimen stress at a ratio R of 0.3, for example. A comparison of the predicted lifetime with the actual test results is obtained as shown in figure 4. As can be seen from FIG. 4, the error band is within 2 times, the prediction result is good, and the validity of the model is verified.
And predicting the bending fatigue life of the FOD rear hollow sandwich structure by adopting a linear superposition method. The specific implementation process comprises the following steps:
(1) numerical simulation is carried out on the FOD process of a 7mm hollow sandwich structure test piece based on FEM, and the surface center of the hollow sandwich structure test piece is impacted, wherein the impact speed is 397m/s, and the impact angle is 55 degrees. The residual stress distribution in the direction of the normal bending stress after the hollow sandwich structure test piece FOD is obtained, as shown in FIG. 5. Residual stress sigma in the direction of normal stress loaded at dangerous part of output hollow sandwich structure test pieceres＝138.4MPa；
(2) Numerical simulation of the hollow sandwich structure test piece with the impact notch under bending load based on FEM (finite element analysis), as shown in FIG. 6, is performed, and the theoretical stress concentration coefficient K at the notch is obtained through calculationt1.60, which is defined as the ratio of the maximum normal stress at the edge of the gap of the hollow sandwich structure test piece under the same load to the theoretical maximum bending normal stress of the smooth hollow sandwich structure test piece;
(3) when residual stress acts on cyclic load, the essence is to influence the fatigue life of the hollow sandwich structure test piece by influencing the average stress. Then if a superposition of residual stresses is introduced, the lifetime prediction can be made by mean stress correction. And (4) superposing the residual stress of the notch and the corrected bending normal stress in consideration of the notch effect to obtain equivalent bending normal stress and equivalent stress ratio, as shown in formulas (6) and (7). And according to the thickness and stress amplitude correction method, a bending fatigue life prediction model of the FOD rear hollow sandwich structure can be established, as shown in the formula (8).
σequ＝Ktσα+σres(6)
Compared with the bending fatigue test result under the same condition, as shown in fig. 7, the error is within 2 times of tolerance band, which indicates that the prediction method is good.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (2)
1. A bending fatigue life prediction method for an SPF/DB three-layer plate hollow sandwich structure is characterized by comprising the following steps: the method comprises the following steps:
1) by extracting sandwich structures with different thicknesses and taking the maximum bending normal stress as a damage parameter, a bending fatigue life prediction model under different thicknesses and stress ratios is established, and the specific method comprises the following steps:
extracting a hollow sandwich structure test piece of the hollow fan blade, taking the maximum bending normal stress as a damage parameter, and establishing an S-N curve of the hollow sandwich structure test piece with the corresponding thickness under the condition that the stress ratio R is 0.1 through a three-point bending test:
lgσα＝algNf+b (1)
in the formula NfIs threeThe bending fatigue life of the laminated plate hollow sandwich structure is prolonged; a and b are material constants and are obtained by fitting test data;
the hollow sandwich structure fatigue life prediction model considering the influences of different thicknesses and stress ratios specifically comprises the following steps: maximum positive stress sigma on any thickness section under the same load classWAnd (3) calculating according to the formula (2), substituting the formula (2) into an S-N curve equation measured in a bending fatigue test to obtain a formula (3), namely a bending fatigue life prediction model of the hollow sandwich structure considering the influence of different thicknesses:
lgσα＝algNf-lgW0+lgW+b (3)
in the formula sigmaαMaximum bending normal stress under bending load, W0The effective bending-resistant section coefficient of the hollow sandwich structure test piece is W, and the effective bending-resistant section coefficient of the hollow sandwich structure with any thickness is W;
meanwhile, performing equivalent conversion on the bending normal stress under different stress ratios by adopting a Gerber curve equation, and performing equal-life conversion by taking the S-N curve as a reference to obtain the maximum bending normal stress under any stress ratio; the fatigue life prediction model of the hollow sandwich structure under the influence of the section thickness and the stress ratio is comprehensively considered and is shown as a formula (4):
lgσ′α＝algNf-lgW0+lgW+b (4)
wherein sigma'αThe maximum bending normal stress after the stress ratio is corrected;
2) adopting a numerical simulation method to carry out simulation calculation on the impact damage process of the foreign object to obtain the residual stress distribution after impact damage and the stress concentration coefficient K at the damage positiontEstablishing a model for predicting the fatigue life of the sandwich structure after FOD consideration, wherein the specific method comprises the following steps:
correcting the maximum bending normal stress by combining a theoretical bending normal stress calculation formula and a stress ratio correction formula to obtain a bending fatigue life prediction model of the hollow sandwich structure test piece under the influence of the section thickness and the stress ratio;
for the prediction of the bending fatigue life of the FOD rear hollow sandwich structure, a linear superposition method is adopted for processing, and the specific implementation process is as follows:
(1) according to FOD numerical simulation, calculating to obtain a residual stress numerical value sigma in the direction of normal stress loading of the dangerous part of the hollow sandwich structure test pieceres；
(2) Calculating the normal stress distribution and theoretical stress concentration coefficient K at the notch under the bending load of the hollow sandwich structure test piece containing the impact notcht；
(3) And superposing the residual stress in the direction of the notch normal stress and the maximum normal stress under the bending load, and correcting according to the notch effect and the stress ratio to obtain the equivalent bending normal stress and the equivalent stress ratio.
2. The method for predicting the bending fatigue life of the SPF/DB three-layer hollow sandwich structure according to claim 1, characterized in that: the specific FOD post-equivalent bending normal stress is as shown in a formula (5), the equivalent stress ratio is as shown in a formula (6), and the bending normal stress is further corrected by adopting a linear superposition and stress ratio correction method to obtain the equivalent bending normal stress sigma'equAnd finally, establishing a bending fatigue life prediction model after the hollow sandwich structure FOD is as the formula (7):
σequ＝Ktσα+σres(5)
lgσ′equ＝algNf-lgW0+lgW+b (7)
wherein R isequIs an equivalent stress ratio, σequ，minFor minimum equivalent bending cyclic stress, σequ，maxIs the maximum equivalent bending cyclic stress, σ'equThe stress ratio is the corrected maximum bending normal stress.
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| CN109522592B (en) * | 2018-10-10 | 2023-04-25 | 南京航空航天大学 | Method for determining FOD (field of view) allowable repair limit of aero-engine blade |
| CN110006636A (en) * | 2019-03-15 | 2019-07-12 | 南京航空航天大学 | A kind of FOD repeated bend test part and its design method |
| CN110987389B (en) * | 2019-11-27 | 2021-07-27 | 南京航空航天大学 | Foreign object damage notch calibration method with stress concentration coefficient not less than 3 |
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