A method for determining resonance fatigue acceleration factor based on continuum damage mechanics

Abstract

The invention discloses a method for determining a resonance fatigue acceleration factor based on continuous damage mechanics. The determination method comprises the following steps: step S1, constructing a relationship between the excitation magnitude of a sinusoidal load and fatigue life according to an inverse power-rate model; step S2, establishing a finite element model of an engineering structure, initializing material parameters of the structure, and setting an initial damage value of the structure to 0. In the invention, based on continuous damage mechanics, a fatigue damage accumulation process of the structure is simulated, and a nonlinear evolution process of quantitatively characterizing the damage amount can be achieved, so that the fatigue life of the structure can be predicted more accurately. Compared with the resonance state of traditional sinusoidal load excitation, the excitation frequency of the sinusoidal load takes into account the change of the macroscopic frequency of the structure caused by the generation of damage, so that the resonance fatigue process is more in line with engineering practice.

Description

Technical Field

[0001] The invention relates to the technical field of engineering structure vibration fatigue, and in particular to a method for determining a resonance fatigue acceleration factor based on continuum damage mechanics. Background Art

[0002] Structural vibration fatigue seriously threatens the reliability and safety of engineering structures. Therefore, during the product development phase, it is necessary to conduct structural vibration fatigue tests to verify whether the product's life meets the design requirements. However, with the continuous improvement of the reliability of engineering structures, the vibration fatigue life of structures is getting longer and longer, and the time cost of vibration fatigue tests is greatly increased. In order to ensure that the defects of engineering structures can be fully exposed in vibration fatigue tests, vibration fatigue accelerated tests are an inevitable choice.

[0003] The vibration fatigue life prediction method has important guiding significance for the vibration fatigue accelerated test. The vibration fatigue life prediction method based on continuous damage mechanics describes the relationship between the degree of structural damage and the mechanical properties of the material by introducing continuous damage variables. Compared with the traditional fatigue life prediction method, the use of continuous damage mechanics theory to predict the fatigue life of the structure can describe the damage process of the structure from a multi-scale perspective, which has better physical significance and theoretical basis for the study of the mechanism of structural fatigue damage.

[0004] The determination of the acceleration factor is a key link in the vibration fatigue acceleration test. At present, the most commonly used method for calculating the acceleration factor is to use the inverse power rate model. For example, GJB 150.16A, automotive electrical and electronic equipment test standard GB / T 28046.3, MIL-STD-810G and other industry standards all use the inverse power rate model to calculate the acceleration factor. In the research on the method of using the inverse power rate model to calculate the acceleration factor, most of them focus on the study of broadband random vibration fatigue acceleration factors, and rarely involve the study of resonance fatigue acceleration factors under sinusoidal loads. Moreover, the determination of the acceleration factor relies too much on engineering experience and intensive test, lacking effective theoretical guidance. Therefore, it is urgent to propose a corresponding method for determining the resonance fatigue acceleration factor to solve the above problems. Summary of the invention

[0005] The purpose of the present invention is to solve the above-mentioned problem and to propose a method for determining the resonance fatigue acceleration factor based on continuum damage mechanics.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for determining a resonance fatigue acceleration factor based on continuum damage mechanics, the method comprising the following steps:

[0008] Step S1: construct the relationship between the sinusoidal load excitation magnitude and fatigue life according to the inverse power rate model Where T s Indicates the design life under actual service conditions; T t Indicates the equivalent accelerated test time; A s Indicates the vibration acceleration amplitude under actual service conditions; A t It is expressed as the vibration acceleration amplitude under equivalent acceleration test conditions, and m is the fatigue index of the material;

[0009] Step S2, establishing a finite element model of the engineering structure, initializing the material parameters of the structure, and setting the initial damage value of the structure to 0;

[0010] Step S3, using finite element analysis software to perform modal analysis on the finite element model of the engineering structure to obtain the first-order natural frequency of the structure;

[0011] Step S4, determine whether the structure has fatigue failure, set the evaluation standard of the first-order natural frequency drop of the structure, when the natural frequency drop reaches a preset value, end the cycle and output the fatigue life result of the structure, otherwise, execute the next step S5;

[0012] Step S5, applying a sinusoidal load excitation with a frequency of the first-order natural frequency of the structure and an amplitude of A to the finite element model of the structure, performing a harmonic response analysis of the finite element model, and extracting multi-axial stress values ​​of dangerous points of the structure under a resonance state;

[0013] Step S6, substituting the multiaxial stress value obtained in step S5 into the multiaxial damage evolution equation to calculate the damage evolution rate;

[0014] Step S7, superimposing the damage value of the structure and updating the real-time cycle number;

[0015] Step S8, equating the structural defects caused by structural fatigue to a decrease in structural stiffness, expressed by an elastic modulus E, updating the elastic modulus of the structure, and returning to step S3;

[0016] Step S9, repeating steps S2-S8 to obtain the fatigue life of the structure under different excitation levels, and fitting the excitation level and the structure prediction fatigue life data to determine the material fatigue index m of the structure;

[0017] Step S10: Determine the resonance fatigue acceleration factor when the material fatigue index m is known

[0018] As a further description of the above technical solution:

[0019] The evaluation standard in step S4 is that the decrease in the first-order natural frequency of the structure reaches 5% of the first-order initial natural frequency of the structure.

[0020] As a further description of the above technical solution:

[0021] Before repeating steps S2 to S8 in step S9, the excitation level A of the sinusoidal load needs to be changed.

[0022] As a further description of the above technical solution:

[0023] The frequency of the sinusoidal load excitation applied to the finite element model of the structure in step S5 is the first-order natural frequency of the structure, and the natural frequency is the result of the modal analysis of the finite element model in step S3.

[0024] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0025] In the present invention, the fatigue damage accumulation process of the structure is simulated based on continuous damage mechanics, which can realize the quantitative characterization of the nonlinear evolution process of the damage amount and more accurately predict the fatigue life of the structure. Compared with the resonance state of the traditional sinusoidal load excitation, the excitation frequency of the sinusoidal load takes into account the change of the macroscopic frequency of the structure caused by the occurrence of damage, so that the resonant fatigue process is more in line with engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the working process in the present invention;

[0027] Figure 2 It is a specific flow chart of the resonance fatigue life prediction module based on continuum damage mechanics in the present invention;

[0028] Figure 3 This is a finite element model diagram of the satellite return capsule structure in the present invention;

[0029] Figure 4 It is a curve diagram of damage accumulation and first-order natural frequency change of dangerous points of the satellite return capsule structure in the present invention;

[0030] Figure 5 A curve diagram showing the relationship between magnitude and life under sinusoidal load excitation of the satellite return capsule structure in the present invention;

[0031] Figure 6 It is a sinusoidal load excitation magnitude diagram of the satellite return capsule structure in the present invention;

[0032] Figure 7 It is the material parameter diagram of 7A09 aluminum alloy in the present invention;

[0033] Figure 8It is the first order natural frequency diagram of the satellite return capsule structure in the present invention;

[0034] Fig. 9 This is a diagram of fatigue life data (25°C) of a smooth sample of 7A09 aluminum alloy in the present invention;

[0035] Fig.10 It is a parameter diagram of the damage evolution model of 7A09 aluminum alloy in the present invention;

[0036] Fig.11 This is a diagram of the vibration fatigue life of the return capsule under different levels of excitation in the present invention. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] Embodiment 1:

[0039] See also Figure 1-11 , a method for determining a resonance fatigue acceleration factor based on continuum damage mechanics, comprising the following steps:

[0040] Step S1, constructing a relationship (2) between the sinusoidal load excitation magnitude and fatigue life according to the inverse power rate model (1);

[0041]

[0042]

[0043] Where, T s Indicates the design life under actual service conditions; T t Indicates the equivalent accelerated test time; A s It represents the root mean square value of vibration acceleration under actual service conditions (for sinusoidal load, this value is the amplitude of sinusoidal load); A t It is expressed as the root mean square value of vibration acceleration under equivalent acceleration test conditions (for sinusoidal load, this value is the amplitude of sinusoidal load), and m is the fatigue index of the material;

[0044] Step S2, establishing a finite element model of the engineering structure, initializing the material parameters of the structure, and setting the initial damage value D of the structure to 0;

[0045] Step S3, using finite element analysis software to perform modal analysis on the finite element model of the engineering structure to obtain the first-order natural frequency of the structure;

[0046] Step S4, determine whether the structure is fatigue-failed, and take the decrease of the first-order natural frequency of the structure to 5% of the first-order initial natural frequency of the structure as the evaluation standard of structural fatigue failure. When the decrease of the natural frequency reaches a preset value, the cycle ends and the fatigue life result of the structure is output. Otherwise, execute step S5;

[0047] Step S5, based on the structural modal analysis, a sinusoidal load excitation with a frequency of the first-order natural frequency f of the structure and an amplitude of A is applied to the finite element model of the structure, a harmonic response analysis of the finite element model is carried out, and the multi-axial stress value of the structural dangerous point under the resonance state is extracted;

[0048] Step S6, substituting the multiaxial stress value obtained in step S5 into the multiaxial damage evolution equation (3) to calculate the damage evolution rate;

[0049]

[0050] Where D is the damage value, N is the number of cycles, which can be determined by material fatigue test, and σ H，mean is the average hydrostatic stress in the cycle, A II is the octahedral stress amplitude.

[0051] Step S7, superimposing the damage value of the structure according to formula (4), and updating the real-time cycle number according to formula (5);

[0052]

[0053] N (i+1) =N (i) +ΔN (i+1) (5)

[0054] In the formula, j represents the node number, and i represents the number of times the current loop block is executed.

[0055] Step S8, the structural defects caused by fatigue of the structure are equivalent to the decrease of structural stiffness, which is expressed by elastic modulus E, and the updated damage value is substituted into formula (6) to update the elastic modulus of the structure, and then return to step S3;

[0056]

[0057] Step S9, change the excitation level A of the sinusoidal load, repeat steps S2-S8, obtain the fatigue life of the structure under different excitation levels, and fit the excitation level and the structure prediction fatigue life data according to the relationship (2) to determine the material fatigue index of the structure.

[0058] Step S10: When the material fatigue index is known, determine the resonance fatigue acceleration factor according to formula (7).

[0059]

[0060] In the formula, α represents the acceleration factor.

[0061] S110. Construct a relationship between the excitation magnitude of the sinusoidal load and the fatigue life based on the inverse power-rate model.

[0062] Preferably, the inverse power rate model is:

[0063]

[0064] Taking the logarithm of both sides of the above equation, we get:

[0065]

[0066] Taking the logarithm of the life ratio and the logarithm of the magnitude (amplitude) ratio as the horizontal and vertical coordinates of the coordinate axis, the above formula can be represented as a straight line passing through the origin, and the slope is the fatigue index m of the structural material. Furthermore, given the magnitudes of different sinusoidal loads and predicting the fatigue life of the structure under each magnitude, sufficient data can be obtained to fit the above formula and then determine the material fatigue index m of the structure. For the satellite return capsule structure of this embodiment, it is set as follows Figure 6 The excitation levels are shown.

[0067] S120. A resonance fatigue life prediction module based on continuum damage mechanics predicts fatigue life under various excitation levels.

[0068] Specifically, step S120 includes the following steps:

[0069] S121. Establish a finite element model of the engineering structure, initialize the material parameters of the structure, and set the damage value D of the structure to 0.

[0070] The finite element model of the satellite return capsule structure is established using finite element analysis software. Figure 3 As shown. And follow Figure 7 The material parameters of the structure shown are set, and the damage value D of the structure is set to 0.

[0071] S122. Conduct modal analysis of the finite element model to obtain the first-order natural frequency f of the structure.

[0072] For the finite element model of the satellite return capsule structure, a model analysis was carried out to obtain the first-order natural frequency of the structure. The results are as follows: Figure 8 shown.

[0073] S123, determine whether the structure has fatigue failure, that is, whether the decrease in the first-order natural frequency of the structure has reached a preset value. If the decrease in the natural frequency has reached the preset value, proceed to step S128, otherwise, proceed to step S124.

[0074] It should be noted that in continuum damage mechanics, the concept of effective stress is introduced to describe the load concentration borne by the damage on the effective section. Assuming that the normal direction of the damaged section remains unchanged before and after the damage, the effective stress The expression is:

[0075]

[0076] Where P is the load acting on the cross section, σ is the theoretical stress value, E is the elastic modulus of the undamaged material, and ε e is the strain value of the structure, S is the cross-sectional area, S D is the damaged cross-sectional area. For isotropic materials and multiaxial loading, the above formula can be written as

[0077] σ=E(1-D)ε e =E D ε e (11)

[0078] Where E D It is the elastic modulus of the material after being damaged. On a macro scale, it manifests as a change in the dynamic characteristics of the structure. As an important characteristic quantity of the dynamic characteristics of the structure, the change in the structural elastic modulus can directly lead to a change in the natural frequency of the structure. Therefore, in the present invention, the decrease in the first-order natural frequency of the structure is used as a basis for determining whether the structure has fatigue failure. Furthermore, considering that in actual applications, the structure is considered to have failed when the damage reaches a certain level, and the structure does not need to be completely damaged and destroyed, the present invention uses the decrease in the first-order natural frequency of the structure to 5% of the initial first-order natural frequency as a criterion for determining whether the structure is fatigue damaged.

[0079] S124. Conduct harmonic response analysis to determine the multi-axial stress values ​​at dangerous points of the structure.

[0080] For the finite element model of the satellite return capsule structure, a sinusoidal load excitation with a frequency of the first-order natural frequency and an amplitude of the set excitation magnitude is applied to carry out harmonic response analysis of the structure, and various stress values ​​of the satellite return capsule structure are extracted for calculation of the damage evolution rate in step S125.

[0081] S125. Calculate the damage evolution rate using the multi-axis damage evolution equation.

[0082] Preferably, the multiaxial damage evolution equation is:

[0083]

[0084] Where A Ⅱ is the octahedral stress amplitude, which takes into account the equivalent effect of multiaxial loading and is expressed as:

[0085]

[0086] In the formula, S ij,max is the maximum stress deviator during the cycle, S ij,min is the minimum value of the stress deviator in the cycle, σ 1 , σ 2 and σ 3 are the stress amplitudes corresponding to the three principal stresses respectively.

[0087] The expression corresponding to α in the damage accumulation equation is:

[0088]

[0089] Where a is the material parameter, σ u is the ultimate tensile strength, σ e,max is the maximum equivalent von Mises stress in cyclic loading, The multiaxial fatigue limit is obtained using the Sines fatigue limit criterion. The expression is:

[0090]

[0091] In the formula, σ l0 is the fatigue stress corresponding to the infinite life of the object under symmetrical cyclic loading, b 1 is the material parameter. The meaning of the < > operator is:

[0092]

[0093] When the cyclic load satisfies the following relationship, the life of the structure will tend to infinity.

[0094]

[0095] In order to conveniently determine the values ​​of the parameters in the above formula, the uniaxial form of the damage evolution equation can be integrated to obtain:

[0096]

[0097] Where σ m is the mean stress, σ a is the stress amplitude, σ a =σ max -σ min In the derivation process of the whole model, there are β, M 0 、b 1 、b 2 Five parameters need to be determined, including β and aM 0 -βIt can be obtained by fitting the fatigue SN curve under symmetrical load, and b 1 and b 2 It can be obtained by fitting the fatigue SN curve under asymmetric load, and a can be solved using numerical methods.

[0098] The tensile strength of 7A09 aluminum alloy is 540MPa. The fatigue limit of the aluminum alloy under symmetrical load is obtained by extrapolation using the Basquin formula. The logarithm of the Basquin formula can be obtained as follows:

[0099] lgN H =m 0 lgσ a +n (19)

[0100] according to Fig. 9 The fatigue life data of 7A09 aluminum alloy at different stress ratios are given, and the m in the above formula is obtained by fitting the test data with R = -1. 0 and n we get:

[0101]

[0102] Take the stress cycle number N H =1×10 7 According to the above formula, we can get (the corresponding fatigue limit value when R = -1). σ l0 =76.38Mpa.

[0103] The SN curve when R = -1 is fitted using formula (18), and β and aM are obtained. 0 -β The value of , and then use the SN curve when R≠1 and the obtained β and aM 0 -β value, we can fit b 1 and b 2 Finally, the numerical method proposed in the literature is used to obtain the parameter a. The result is as follows Fig.10 shown.

[0104] S126. Structural damage is superimposed and the number of cycles is updated at the same time.

[0105] The damage evolution rate obtained in step S125 is Substitution The damage is accumulated in (i+1) =N (i) +ΔN (i+1)Update the number of cycles. It should be noted that, since the structural fatigue damage process shows a trend of first slow and then rapid accumulation, in order to reduce the calculation cost, the present invention adopts a step-by-step algorithm, that is, in the early stage of structural damage accumulation, the number of cycles ΔN takes a larger value, and in the later stage of damage accumulation, the number of cycles ΔN gradually decreases, and it is assumed that within a certain cycle period ΔN, the stress and damage values ​​of the structure remain unchanged.

[0106] S127. Update the elastic modulus E and return to step S122.

[0107] Substitute the updated damage value D into the following formula to update the elastic modulus E of the structure.

[0108]

[0109] S128. Output structural fatigue life results.

[0110] S129: For the satellite return capsule structure, use step S120 to predict the fatigue life of the structure under various excitation levels. Fig.11 Among them, under a certain excitation level, the damage evolution process of the dangerous point of the satellite return capsule structure is as follows: Figure 4 As shown. Figure 4 It can be seen that the damage process of the structure experienced an accumulation process that was first slow and then fast, which shows that the resonant fatigue life prediction method based on continuous damage can accurately simulate the nonlinear evolution process of structural damage.

[0111] S130, fitting the relationship curve between magnitude and life, and determining the material fatigue index m.

[0112] according to Fig.11 The data results of structural vibration fatigue life are plotted as follows Figure 5 The logarithmic curve of magnitude ratio-life ratio is shown, and a linear fit is performed on the original data. The slope of the fitting line is the material fatigue index m of the structure.

[0113] S140. Determine the structural fatigue acceleration factor α.

[0114] After the fatigue index of the material is determined, the fatigue acceleration factor of the structure can be determined according to the following formula.

[0115]

[0116] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for determining the resonance fatigue acceleration factor based on continuum damage mechanics, It is characterized in that The determination method comprises the following steps: Step S1: construct the relationship between the sinusoidal load excitation magnitude and fatigue life according to the inverse power rate model Where T s Indicates the design life under actual service conditions; T t Indicates the equivalent accelerated test time; A s Indicates the vibration acceleration amplitude under actual service conditions; A t It is expressed as the vibration acceleration amplitude under equivalent acceleration test conditions, and m is the fatigue index of the material; Step S2, establishing a finite element model of the engineering structure, initializing the material parameters of the structure, and setting the initial damage value of the structure to 0; Step S3, using finite element analysis software to perform modal analysis on the finite element model of the engineering structure to obtain the first-order natural frequency of the structure; Step S4, determine whether the structure has fatigue failure, set the evaluation standard of the first-order natural frequency drop of the structure, when the natural frequency drop reaches a preset value, end the cycle and output the fatigue life result of the structure, otherwise, execute step S5; Step S5, applying a sinusoidal load excitation with a frequency of the first-order natural frequency of the structure and an amplitude of A to the finite element model of the structure, performing a harmonic response analysis of the finite element model, and extracting multi-axial stress values ​​of dangerous points of the structure under a resonance state; Step S6, substituting the multiaxial stress value obtained in step S5 into the multiaxial damage evolution equation to calculate the damage evolution rate; Step S7, superimposing the damage value of the structure and updating the real-time cycle number; Step S8, equating the structural defects caused by structural fatigue to a decrease in structural stiffness, expressed by an elastic modulus E, updating the elastic modulus of the structure, and returning to step S3; Step S9, repeating steps S2-S8 to obtain the fatigue life of the structure under different excitation levels, and fitting the excitation level and the structure prediction fatigue life data to determine the material fatigue index m of the structure; Step S10: Determine the resonance fatigue acceleration factor when the material fatigue index m is known 2. The method for determining the resonance fatigue acceleration factor based on continuum damage mechanics according to claim 1, It is characterized in that The evaluation standard in step S4 is that the decrease in the first-order natural frequency of the structure reaches 5% of the first-order initial natural frequency of the structure.

3. The method for determining the resonance fatigue acceleration factor based on continuum damage mechanics according to claim 1, It is characterized in that Before repeating steps S2 to S8 in step S9, the amplitude A of the sinusoidal load excitation needs to be changed.

4. The method for determining the resonance fatigue acceleration factor based on continuum damage mechanics according to claim 1, It is characterized in that The frequency of the sinusoidal load excitation applied to the finite element model of the structure in step S5 is the first-order natural frequency of the structure, and the natural frequency is the result of the modal analysis of the finite element model in step S3.

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