A method for constructing a high-temperature fretting fatigue life prediction model considering surface hardness

Abstract

The present invention discloses a method for constructing a high-temperature fretting fatigue life prediction model considering surface hardness. It belongs to the field of fretting fatigue life prediction simulation; the model is based on a nonlinear fatigue cumulative damage model, and according to the difference in surface hardness of heterogeneous contact materials, a damage accumulation rate factor considering hardness is introduced to obtain a life model suitable for fretting fatigue. Since hardness changes with temperature, a temperature-related damage rate factor is introduced to consider the influence of temperature on the fretting fatigue behavior of the structure. The application method of the model requires the use of ANSYS finite element software, and the specific steps are: 1) establish a finite element model; 2) perform finite element simulation calculations on contact problems; 3) post-process the calculation results; 4) perform parameter fitting; 5) obtain the fretting fatigue prediction life. The model and application method can effectively predict the high-temperature fretting fatigue life under heterogeneous material contact, which has important engineering significance.

Description

Technical Field

[0001] The present invention belongs to the field of fretting fatigue life prediction simulation, and relates to a method for constructing a high-temperature fretting fatigue life prediction model taking into account surface hardness, and in particular to a high-temperature fretting fatigue life prediction model based on continuous medium damage and taking into account material surface hardness, as well as an establishment method and an application method. Background Art

[0002] Fretting fatigue is a common form of fatigue failure. It refers to the phenomenon that under the action of cyclic loads, a part of the surface produces small-amplitude relative sliding with other contact surfaces, which leads to reduced fatigue strength or early fracture of the component. Fretting fatigue is a typical form of structural failure of components in the aviation field. Under fretting conditions, the fatigue life of components can be reduced to 2 / 3 of the normal fatigue life or even lower. A typical feature of fretting fatigue is that the fretting action significantly accelerates the nucleation of cracks and early crack propagation. In order to effectively predict the fretting fatigue behavior and life, the continuum damage mechanics method uses damage variables to describe the damage evolution process of the material to predict the failure life of the material. This method has been continuously developed and improved in recent years.

[0003] In aircraft engines, fretting fatigue usually occurs in the turbine tenon connection structure. In the current turbine tenon connection structure, the materials of the turbine disk and the blade are usually two different materials, and the surface hardness of the two materials is different. Therefore, in order to ensure that the turbine tenon connection structure does not fail, it is very important to predict the high-temperature fretting fatigue life of the dissimilar materials in contact. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a high-temperature fretting fatigue life prediction model based on continuous medium damage and taking into account the surface hardness of the material, as well as its establishment method and application method, so as to effectively predict the fretting fatigue life of dissimilar material contact pairs under high-temperature working conditions.

[0005] The steps for deriving the lifespan model are as follows:

[0006] Step 1: Obtain a nonlinear cumulative fatigue damage life prediction model.

[0007] The nonlinear cumulative fatigue damage model describes the progressive degradation process before the macro crack initiation; the damage variable D is 0 in the initial undamaged state and when the crack propagates to the life N = N f When D = 1, the loading parameter considered is the maximum stress σ of each cycle. max and mean stress Expressing the damage rate in cycles is:

[0008]

[0009] The damage rate in equation (1) depends on the current damage state and allows for nonlinear evolution under cyclic loading; this is similar to the relationship between fatigue crack growth rate and crack length; nonlinear evolution is not sufficient to describe nonlinear accumulation; in addition, the function has an inseparable variable σ max and D, used to describe nonlinear damage accumulation and sequence effects; separable variables always lead to linear accumulation;

[0010] The specific form of formula (1) can be written as:

[0011]

[0012] in:

[0013]

[0014]

[0015] choose To describe the linear dependence of mean stress and fatigue limit, in terms of equivalent amplitude, it can be written as:

[0016]

[0017] M0, b2 and β are all material-dependent coefficients; to make the identification of the nonlinear cumulative fatigue damage model easier, the form of α is specified in the following way, which corresponds to the formula used so far:

[0018]

[0019]

[0020] σ l0 is the fatigue limit under reverse stress conditions, is the fatigue limit under non-zero mean stress, <> takes a positive sign, for equation (6), when the maximum stress σ max Below the fatigue limit at non-zero mean stress When , <>=0, α=1; Simultaneously combining equations (4) and (6), we obtain:

[0021]

[0022] When σ max =σ b When N f =0; when When N f =∞.

[0023] N f It can be determined by the form of formula (4); Substituting formula (5) and (7) into (8) we get:

[0024]

[0025] Let equation (9)

[0026]

[0027] Then equation (9) can be written as:

[0028]

[0029] Step 2: Redefine the life model in step 1 under fretting fatigue.

[0030] A large number of experiments have shown that the average tensile stress affects the fatigue limit in tension or torsion, while the average shear stress does not affect the fatigue limit in tension or torsion. These results have led to the introduction of the average hydrostatic pressure as a parameter of the multiaxial fatigue limit criterion, replacing the average stress with the average hydrostatic stress:

[0031]

[0032] is the multiaxial fatigue limit, σ H,mean is the mean hydrostatic pressure, which is expressed as follows:

[0033]

[0034] The equivalent stress amplitude under multiaxial fatigue loading is A II , is defined in proportional loading as follows:

[0035]

[0036] σ′ ij,max and σ′ ij,min are the maximum and minimum values ​​of each stress deviator in the cycle, respectively.

[0037] Step 3: In order to consider the strengthening effect under multiaxial non-proportional loading conditions, the critical equivalent plastic strain amplitude is introduced as shown in formula (15), thereby reflecting the influence of plastic normal strain and plastic shear strain on fretting fatigue damage;

[0038]

[0039] Among them, Δγ max is the maximum shear strain range, is the equivalent strain range, ε n is positive strain;

[0040] Then the nonlinear cumulative damage model of fretting fatigue can be written as:

[0041]

[0042] Integrating the above formula, we can obtain the fretting fatigue life prediction model based on continuum damage mechanics, as shown in formula (17):

[0043] Step 4: In order to consider the influence of surface hardness on the cumulative damage rate and life of fretting fatigue, and taking into account the high temperature softening effect of the material, this paper introduces a hardness-related damage accumulation rate factor Formula (17) is modified to obtain a high-temperature nonlinear continuous damage fretting fatigue life model considering surface hardness;

[0044] Damage accumulation rate factor considering surface hardness It is directly related to the surface hardness and temperature of the contact material, and its expression is:

[0045]

[0046] Will Substituting into formula (16), the high temperature fretting fatigue nonlinear cumulative damage model considering surface hardness is obtained as shown in formula (19):

[0047]

[0048] By integrating the above formula, we can obtain the high temperature nonlinear cumulative damage fretting fatigue life model considering the surface hardness, as shown in formula (20):

[0049]

[0050] Where N f is the fretting fatigue cycle life, β, α, b1, b2 and M0 are material fitting constants and can be determined by uniaxial fatigue test, k and w are the fretting fatigue parameters of the material; σ b is the ultimate strength of the material, σ l0 is the material fatigue strength, R t is the temperature ratio, A II is the equivalent stress amplitude under multiaxial fatigue loading, σ H,mean is the average hydrostatic stress in the cycle, is the critical equivalent plastic strain amplitude, η is the hardness correlation coefficient, m is the temperature correlation coefficient, which can be obtained by fitting the fretting fatigue test data. H1 and H2 are the surface hardness of the fretting pad and the test piece material in the single-clamp fretting fatigue test, respectively. T m1 and T m2 In the single-chuck fretting fatigue test, they are the melting point temperatures of the fretting pad and the test piece material;

[0051] In the model, The effect of surface hardness on the fretting fatigue damage rate was considered; the wear performance of metal alloys is directly related to the surface hardness of the material. For the contact of dissimilar materials, due to the different surface hardnesses of the two contacting materials, the material with higher surface hardness will produce a stronger plowing effect on the surface of the material with lower surface hardness, causing its wear rate to be higher than the wear rate generated when the material with lower surface hardness contacts itself.

[0052] In the model, Taking into account the influence of high temperature softening, as the temperature rises, the material properties of most metal materials will gradually decrease, so the temperature influence factor is corrected and introduced into the hardness; the nonlinear cumulative damage model is corrected by introducing a damage accumulation rate factor that takes into account the surface hardness;

[0053] In the model, The influence of the current damage degree on the fretting fatigue damage rate is considered, nonlinear evolution under cyclic loading is allowed, and the nonlinear damage accumulation is described by the inseparable variable D.

[0054] In the model, The effects of multiaxial fatigue state and mean hydrostatic stress on fretting fatigue damage rate are considered.

[0055] In the model, The effects of plastic normal strain and plastic shear strain on the fretting fatigue damage rate are considered.

[0056] Beneficial effects: Compared with the prior art, the characteristics of the present invention are: 1. The present invention can effectively predict the high-temperature micro-motion fatigue life of dissimilar material contacts, which has important engineering significance; 2. The present invention can effectively predict the micro-motion fatigue life of structural contact parts in the range from normal temperature to maximum operating temperature of dissimilar material contacts; 3. The present invention can predict the micro-motion fatigue life of different types of structural contact parts, such as the tenon connection structure of the compressor and turbine disc, the arc end tooth structure connecting the wheel disc and the wheel disc, and the sleeve tooth structure connecting the wheel disc and the transmission shaft. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is an operation flow chart of the present invention;

[0058] Figure 2 It is a schematic diagram of the method of use of the present invention. DETAILED DESCRIPTION

[0059] The specific implementation method of the present invention is: the application method of the model needs to use ANSYS finite element software, and the specific steps are as follows: 1) establish a finite element model and perform finite element simulation calculation on the contact problem; 2) post-process the calculation results; 3) perform parameter fitting; 4) obtain the predicted life of fretting fatigue; the model and application method can effectively predict the high-temperature fretting fatigue life of dissimilar material contact pairs, which has important engineering significance. The specific steps are as follows:

[0060] Step a, establish a finite element model for the fretting fatigue test piece under different temperatures and different load conditions, and perform nonlinear contact calculation. Since the axial load in the fretting fatigue test has peak and valley values, the corresponding finite element calculation should be loaded in multiple steps, with the first load step applying the load valley value and the second load step applying the load peak value;

[0061] Step b, post-processing the finite element results, selecting the contact area between the micro-motion pad and the test piece as the research object, compiling a calculation formula for any oblique section on the unit, wherein the increment of the oblique section angle in the calculation formula is Δθ=1°, and the angle θ on the oblique section ranges from 0° to 180°, thereby obtaining the stress-strain values ​​at different angles on each unit, and extracting the stress-strain values ​​at different angles of each unit in the contact area under the peak load and the valley load respectively;

[0062] Step c, write the calculation formulas for each parameter in the life prediction model, substitute the stress-strain values ​​of each unit at different angles in the contact area under the load peak and load valley into formulas (12) to (15), and obtain the fatigue limit under multi-axial fatigue load. Equivalent stress amplitude A II , the average hydrostatic stress σ in the cycle H,mean , critical equivalent plastic strain amplitude The hardness of different contact materials is measured using a nanoindentation testing machine to obtain parameters H1 and H2. The parameters in the life prediction model formula are fitted with the actual fretting fatigue test life to obtain four parameters: m, η, k, and w. A high-temperature fretting fatigue life prediction model considering surface hardness is established.

[0063] Step d, after the model formula is completed, calculate the fretting fatigue life value under the given working condition, assign the working temperature and load to the corresponding variables of the ANSYS program, and adjust the material related constants according to the temperature working condition and the contact material, repeat the above steps a to c, substitute the parameter fitting results into formula (20) to calculate the fretting fatigue life of all units, and the unit corresponding to the minimum life value among all units in the overall life zone is located at the crack initiation position.

[0064] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for constructing a high-temperature fretting fatigue life prediction model considering surface hardness, It is characterized in that The specific steps are as follows: (1) Measure the surface hardness of the test piece through the test, and conduct the test to obtain the fretting fatigue life of the test piece; (2) By establishing a finite element model, prestress is applied to the test piece, and the stress and strain values ​​of each unit are obtained under peak and valley loads; (3) Calculate the equivalent strain amplitude, average hydrostatic pressure and equivalent strain amplitude of all units; Specifically:

1. The damage evolution equation of nonlinear cumulative damage fatigue is: Among them, the form of α is as follows: D is the damage variable, σ b is the ultimate strength of the material, σ max is the maximum stress for each cycle, is the mean stress, M 0 ,β are coefficients that depend on the material and are obtained by fitting the uniaxial fatigue test; σ l0 is the fatigue limit under reverse stress conditions, is the fatigue limit under non-zero mean stress; a is the initial contact half width, is the fatigue limit under non-zero mean stress; <> takes a positive sign. For α, when the maximum stress v max Lower than When , <>=0, α=1; Second, introduce the fatigue limit and equivalent stress amplitude under multiaxial fatigue, and redefine the parameters in formula (1) under multiaxial fatigue; replace the average stress with the average hydrostatic stress v H,mean , the multiaxial fatigue limit is calculated The equivalent stress amplitude under multiaxial fatigue loading is A II , the formula is as follows: σ′ ij,max and σ′ ij,min are the maximum and minimum values ​​of each stress deviator in the cycle, σ 1 , σ 2 , σ 3 is the principal stress amplitude; The redefined α is: Wherein, the average hydrostatic stress σ H,mean The calculation formula is as follows: Among them, v 11 ,σ 22 ,σ 33 are the three principal stresses, σ H,max and σ H,min are the maximum hydrostatic stress and the minimum hydrostatic stress, respectively; (4) Use k, w, b1, b2, β, α and M0 obtained by calculation and fitting to build a complete fretting fatigue life prediction model; Specifically: The critical equivalent plastic strain amplitude is introduced; the critical equivalent plastic strain amplitude is shown in formula (4): Among them, Δγ max is the maximum shear strain range, is the equivalent strain range, ε n is positive strain; Then the nonlinear cumulative damage model of fretting fatigue can be written as: The fretting fatigue life prediction model based on continuum damage mechanics is obtained by integrating the above formula, as shown in formula (6): Where σ eqv,max is the maximum equivalent stress calculated in the finite element model in step (2); Among them, the β, α, M 0 Determined by the stress-life curve of the uniaxial fatigue test of the material under symmetrical cycles; b 1 , b 2 Determined by the stress-life curve of the uniaxial fatigue test of the material under asymmetric cycles; k and w are the fretting fatigue parameters of the material, and the specific method for fitting the fretting fatigue test results in step (1) is as follows: A II , σ H,mean and Substitute it into formula (6) and fit it with the fretting fatigue life data in step (1); (5) Substituting the material's η, m, H1, H2, Tm1 and Tm2, ​​we finally get a high-temperature fretting fatigue life prediction model that takes into account surface hardness; Specifically: Introducing a hardness-related damage accumulation rate factor Correct formula (6): The expression is: Will Substituting into formula (5), we can obtain the high temperature fretting fatigue nonlinear cumulative damage model considering the surface hardness, as shown in formula (8): By integrating the above formula, we can obtain the high temperature nonlinear cumulative damage fretting fatigue life model considering the surface hardness, as shown in formula (9): Wherein, η is the hardness correlation coefficient, m is the temperature correlation coefficient, which can be obtained by fitting the fretting fatigue test data, and H 1 and H 2 are the surface hardness of the fretting pad and the test piece in the single-chuck fretting fatigue test, obtained from step (1), T m1 and T m2 In the single-chuck fretting fatigue test, they are the melting point temperatures of the fretting pad and the test piece material.

2. A method for constructing a high temperature fretting fatigue life prediction model considering surface hardness according to claim 1, It is characterized in that In step (2), the stress-strain value of each unit is obtained by establishing a finite element model: (2.1) Establish a finite element model and set contact pairs, boundary conditions and applied loads; (2.2), solve the load peak and valley values; (2.3) and extract the stress-strain components at the peak and valley values ​​of all unit loads.

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