Metal material creep deformation analysis method considering complex temperature field

Abstract

The application discloses a metal material creep deformation analysis method considering a complex temperature field, and comprises the following steps: S1, obtaining a first parameter, a first conversion time and a second conversion time under each temperature stress condition according to a creep test curve of a metal material; S2, calculating a second parameter according to the first parameter, the first conversion time and the second conversion time, and combining a first formula; the first formula is a creep model parameter and temperature, stress correlation expression formula; S3, fitting a third parameter of the first formula according to the first parameter, the second parameter and the creep test curve; S4, substituting the first parameter, the second parameter, the third parameter, the first conversion time and the second conversion time into a preset model to calculate the creep deformation under any temperature and stress condition. The application can be used for creep analysis under a wide range of real engine working conditions and a wide range of temperature fields.

Description

Technical Field

[0001] This invention relates to the field of aero-engine structural strength technology, specifically to a method for analyzing creep deformation of metallic materials considering complex temperature fields. Background Technology

[0002] In engineering, creep deformation cannot be ignored when the absolute temperature exceeds half the melting point. In aero-engine gas turbines, many components, such as the turbine disk and turbine blades, operate at high temperatures and are prone to creep deformation. Taking the turbine disk rim as an example, excessive creep can cause blades to rub against the casing, affect disk / blade assembly, and even lead to disk tenon fracture. This problem becomes even more pronounced as turbine inlet temperatures increase further. Therefore, aero-engine design must analyze the creep of hot-end components and provide corresponding criteria to ensure operational safety throughout the engine's lifespan.

[0003] Commercial software integrates various creep models, and some finite element software has a relatively rich variety of creep models. However, the creep models in commercial software can only calculate and analyze the creep deformation in the first two stages, and cannot characterize the third stage of creep deformation. Furthermore, they are difficult to use in the case of a wide range of temperature fields under real engine operating conditions.

[0004] Therefore, it is necessary to develop a creep analysis method that can be used over a wide temperature range to analyze the creep deformation of hot-end components of aero-engines under real operating conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a creep deformation analysis method for metallic materials that considers complex temperature fields, in order to overcome the shortcomings of the prior art. It can be used for creep estimation under a wide range of real engine operating conditions and temperature fields.

[0006] This invention provides a method for creep deformation analysis of metallic materials considering complex temperature fields, comprising the following steps:

[0007] S1. Obtain the first parameter, first transition time, and second transition time under each temperature stress condition based on the creep test curve of the metallic material;

[0008] S2, calculate the second parameter based on the first parameter, the first transition time, and the second transition time, combined with the first formula; the first formula is an expression for the correlation between creep model parameters and temperature and stress;

[0009] S3, based on the first parameter, the second parameter and the creep test curve, the third parameter of the first formula is obtained by fitting;

[0010] S4, substitute the first parameter, second parameter, third parameter, first conversion time and second conversion time back into the preset model to calculate creep deformation under arbitrary temperature and stress conditions.

[0011] In the above-described method for analyzing the creep deformation of metallic materials considering complex temperature fields, the first parameter optionally includes the initial creep rate and the steady-state creep rate.

[0012] In the above-described method for analyzing creep deformation of metallic materials considering complex temperature fields, the second parameter is optionally an apparent activation energy parameter.

[0013] The creep deformation analysis method for metallic materials considering complex temperature fields as described above, wherein, optionally, the preset model includes a first-stage model;

[0014] The first-stage model is represented by the following formula:

[0015] ε P =βln(αt+1)t≤t P / S ;

[0016]

[0017] Where, ε P The creep deformation represents the first stage, and β and α are the model parameters for the first stage. Let t be the creep rate, and t be the time. P / S This is the first transition moment.

[0018] The creep deformation analysis method for metallic materials considering complex temperature fields as described above, wherein, optionally, the preset model further includes a second-stage model;

[0019] The second-stage model is represented by the following formula:

[0020]

[0021] Where, ε S ε represents the creep deformation that has occurred at the current moment when the second stage is in progress. P / S This refers to the creep deformation that occurs in the first stage. Let t be the steady-state creep rate, and t be time. P / S For the first transition time, t S / T This is the second transition moment.

[0022] The creep deformation analysis method for metallic materials considering complex temperature fields, as described above, optionally includes a third-stage model in the preset model.

[0023] The third-stage model is represented by the following formula:

[0024] ε T =θ(exp[ω(tt) S / T )]-1)t>t S / T ;

[0025]

[0026] Where, ε T The creep deformation occurs at the current moment in the third stage, where θ and ω are both parameters of the third stage model; t is time. S / T This is the second transition time. The creep deformation rate of the third-stage model. The steady-state creep rate.

[0027] The method for analyzing creep deformation of metallic materials considering complex temperature fields, as described above, optionally includes the following: The first formula is...

[0028]

[0029] in, The initial creep rate, α is the steady-state creep rate, ω is the first-stage model parameter, a0 and a1 are both second parameters, T is the temperature, σ is the creep stress, E is the elastic modulus of the metallic material, a2, a3, a4 and a5 are all third parameters, and τ is the bilinear inflection point.

[0030] In the above-described method for analyzing creep deformation of metallic materials considering complex temperature fields, optionally, the first transition time is calculated using the following formula.

[0031]

[0032] Among them, t P / S This is the first transition moment. The initial creep rate, Let α be the steady-state creep rate, and α be the model parameter for the first stage.

[0033] The above-described method for analyzing creep deformation of metallic materials considering complex temperature fields optionally includes a method for calculating the third-stage model parameter ω using the formula...

[0034]

[0035] The third-stage curve of the creep test under each temperature and stress was obtained by fitting the least squares method.

[0036] The creep deformation analysis method for metallic materials considering complex temperature fields, as described above, optionally includes step S2 where the second parameter is calculated by fitting 1 / T and... The slope and intercept of the graph are used to obtain the second parameter.

[0037] Compared with existing technologies, this invention divides the creep process into three stages through a first and second transition time, and calculates the second parameter using a first formula. Since the first formula is an expression relating creep model parameters to temperature and stress, it allows for the calculation of creep deformation results to adapt to a wider temperature range when the first, second, and third parameters, as well as the first and second transition times, are substituted back into the preset model. This method is applicable to calculating the three-stage creep deformation of metallic materials under temperature field conditions, addressing the engineering needs of creep calculation for hot-end components of aero-engines, and has strong engineering application value. Attached Figure Description

[0038] Figure 1 This is a flowchart of the steps of the present invention;

[0039] Figure 2 This is a schematic diagram of the typical three-stage creep deformation curves and parameters;

[0040] Figure 3 This is a schematic diagram of the apparent activation energy fitting during the creep steady-state stage;

[0041] Figure 4 It is the bilinear characteristic of the steady-state creep rate of a certain steady-state creep rate material to stress;

[0042] Figure 5 It represents the linear characteristic of the steady-state creep rate of a certain steady-state creep rate material to stress;

[0043] Figure 6 This is a comparison between the creep curve calculated using this method and the experimental curve. Detailed Implementation

[0044] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0045] In existing technologies, models are typically classified according to their ability to describe creep deformation curves.

[0046] (1) For the first stage of creep, there are several basic model forms that describe the hardening behavior in which the creep rate gradually decreases over time:

[0047] 1) Time-hardening model form:

[0048] ε=βt α (1)

[0049] 2) Strain hardening model form

[0050] ε=βε α t (2)

[0051] 3) Exponential model form

[0052] ε=β(1-e -αt (3)

[0053] 4) Logarithmic model form

[0054] ε=βln(αt+1) (4)

[0055] Where β and α are model constants, ε is creep deformation, and t is time.

[0056] (2) For the second stage of creep, most tests show that the steady-state creep strain rate at a given temperature is related to stress:

[0057]

[0058]

[0059] Where A and n are constants related to material properties and temperature, and σ is stress.

[0060] (3) For the third stage of creep, there are usually two model forms to represent it: one is to introduce the damage formula into the creep model, such as the Kachanov-Rabotnov damage model; the other is an exponential formula, such as the second formula in the θ parameter method.

[0061]

[0062] The models listed in commercial software can all be seen as evolutions of the above basic model forms.

[0063] In engineering, since components are usually exposed to complex temperature fields, the above model establishes a relationship with temperature in the form of apparent activation energy:

[0064]

[0065] Where Q, R, and T represent the apparent activation energy, the gas state constant, and the absolute temperature, respectively. However, the above model cannot achieve good creep deformation calculation accuracy over a wide range of temperature and stress conditions.

[0066] To calculate the creep deformation of components under temperature conditions using the above model, linear interpolation of temperature is typically used to solve for the creep model parameters. However, because the model parameter values ​​obtained by fitting creep test data at typical temperature points may differ by a large order of magnitude, the interpolated model may not converge in the creep finite element calculation, resulting in ineffective creep deformation calculation results. Therefore, for creep calculation problems caused by temperature fields, stress and temperature are also used as control factors, and the formula is constructed using parameter fitting to establish the influence of creep deformation on temperature. A common fitting formula is:

[0067] parameter=a+bσ+cT+dσT (9)

[0068] The above formula actually assumes that the creep model parameters are linearly related to stress at the same temperature. This assumption is not appropriate for a wider temperature and stress range or for certain materials, and may lead to deviations in creep calculations.

[0069] Therefore, the present invention proposes the following embodiments.

[0070] Example 1

[0071] For a typical three-stage creep curve, the creep initiation stage has a relatively high initial creep rate. During the first stage of creep, its creep rate Gradually decrease until at the first transition time t of creep. P / S Reduce to steady-state creep rate In the second stage, the creep rate will continue to be maintained, and then at the second creep transition time t S / T The creep rate will gradually increase until it fractures and fails.

[0072] This embodiment provides a three-stage creep deformation analysis and calculation method for hot-end components of an aero-engine under complex temperature field conditions. The overall scheme is as follows:

[0073] This study addresses the first, second, and third stages of creep deformation; the first stage is the initial stage, and the second stage is the steady-state stage. Model formulas are established to simulate the initial stage where the deformation rate gradually decreases over time, the steady-state stage where the creep rate remains constant, and the third stage where the creep rate gradually increases. Corresponding models are established to characterize the duration of each creep stage, and the total creep deformation is obtained by summing the creep deformation of each stage. The relationships between the creep model formula parameters and temperature and stress for each stage are established in the form of apparent activation energy to characterize the influence of the temperature field.

[0074] The specific technical solution of this method is as follows:

[0075] (1) Segmented characterization of creep deformation curve

[0076] 1) For the first stage of creep, the deformation is characterized using a logarithmic time model, i.e.:

[0077] ε P =βln(αt+1) t≤t P / S (10)

[0078]

[0079] At time t=0, the initial creep rate The value of is equal to αβ; where, where, ε P The creep deformation represents the first stage, and β and α are the model parameters for the first stage. Let t be the creep rate, and t be the time. P / S This is the first transition moment.

[0080] 2) During the steady-state creep stage, the creep rate remains constant, and the total creep deformation is:

[0081]

[0082] Where, ε S ε represents the creep deformation that has occurred at the current moment when the second stage is in progress. P / S This refers to the creep deformation that occurs in the first stage. Let t be the steady-state creep rate, and t be time. P / S For the first transition time, t S / T This is the second transition moment.

[0083] 3) For the third stage of creep, the creep deformation in this stage is characterized by an exponential function of time.

[0084] ε T =θ(exp[ω(tt) S / T )]-1) t>t S / T (13)

[0085] At t=t S / T At any given moment, the steady-state creep rate and the initial creep rate in the third stage must satisfy the continuity condition, which yields: Therefore, the creep rate in the third stage is:

[0086]

[0087] Where, ε T The creep deformation occurs at the current moment in the third stage, where θ and ω are both parameters of the third stage model; t is time. S / T This is the second transition time. The creep deformation rate of the third-stage model. The steady-state creep rate.

[0088] (2) Determination of the timing of creep stage transition

[0089] 1) The transition time t between the first and second stages of creep P / S for:

[0090]

[0091] Among them, t P / S This is the first transition moment. The initial creep rate, Let α be the steady-state creep rate, and α be the model parameter for the first stage.

[0092] 2) The second transition time t in the creep steady-state stage and the third stage S / T From the first transition time t P / S The duration of the second stage is obtained by superimposing the duration of the second stage, which can be obtained by fitting an nth-order polynomial with respect to the steady-state creep rate, depending on the material. In specific implementation, n is a positive integer not less than 3.

[0093] (3) Expression of the temperature-stress correlation of creep model parameters

[0094] For creep model parameters in the first stage of creep α; Creep rate in the second stage of creep And the model parameter ω for the third stage of creep, each parameter is expressed by a combination of formulas (16), and the corresponding expression relationship is selected according to the regular characteristics of the creep parameters of specific materials. For example, term a2 indicates that the temperature-corrected parameters have an exponential relationship with the stress after the elastic modulus is normalized; term a3 indicates that the temperature-corrected model parameters have a two-segment linear relationship with the stress after the elastic modulus is normalized; term a4 indicates that the temperature-corrected model parameters have a hyperbolic sine relationship with the stress after the elastic modulus is normalized.

[0095]

[0096] in, The initial creep rate, α is the steady-state creep rate, ω is the first-stage model parameter, a0 and a1 are both second parameters, T is the temperature, σ is the creep stress, E is the elastic modulus of the metallic material, a2, a3, a4 and a5 are all third parameters, and τ is the bilinear inflection point.

[0097] In summary, a complete creep curve has been established to express the creep load conditions that can be adapted to a wide range of temperature and stress fields.

[0098] Example 2

[0099] For different metallic materials, the parameters will differ when processed using the method described in Example 1. Therefore, this embodiment proposes a method for determining model parameters. This method is based on Example 1, and the similarities will not be repeated.

[0100] This embodiment proposes a method for analyzing the creep deformation of metallic materials considering complex temperature fields, which includes the following steps:

[0101] S1. Obtain the first parameter, first transition time, and second transition time under each temperature stress condition based on the creep test curve of the metallic material; wherein, the first parameter includes the initial creep rate and the steady-state creep rate.

[0102] S2, calculate the second parameter based on the first parameter, the first conversion time, and the second conversion time, combined with the first formula; the first formula is the expression for the correlation between creep model parameters and temperature and stress. In specific implementation, the first formula is formula (16); the second parameter includes the apparent energy parameter.

[0103] S3. Based on the first parameter, the second parameter, and the creep test curve, the third parameter of the first formula is obtained by fitting; specifically, the third parameter is the parameter of the first formula.

[0104] S4. Substitute the first parameter, second parameter, third parameter, first transition time, and second transition time back into the preset model to calculate creep deformation under arbitrary temperature and stress conditions. By substituting the first parameter, second parameter, third parameter, first transition time, and second transition time back into the preset model, the final model that can be used for calculation can be obtained, enabling the calculation of creep deformation under arbitrary temperature and stress conditions.

[0105] By following the steps above, the parameters of the preset model can be determined to obtain the final model that can be used to calculate creep deformation under arbitrary temperature and stress conditions.

[0106] Example 3

[0107] This embodiment is a specific application of Embodiment 2. The similarities will not be repeated here. Only the differences will be explained below.

[0108] S1, Measure the statistical creep test curve.

[0109] According to the creep test curve, such as Figure 2 As shown, the initial creep rate under each temperature stress condition was directly measured and statistically analyzed. Steady-state creep rate Creep first transition time t P / S and the second creep transition time t S / T Among them, the initial creep rate Steady-state creep rate That is, the first parameter.

[0110] S2, calculate the second parameter.

[0111] The calculation of the second parameter includes the following steps:

[0112] S21, Calculate the model parameters for the first stage of creep;

[0113] According to formula (17), the parameters under each temperature and stress condition are obtained from the measurements. Calculate the model parameters α for the first stage of creep at each temperature and stress.

[0114] Formula (17) is:

[0115]

[0116] Among them, t P / S This is the first transition moment. The initial creep rate, Let α be the steady-state creep rate, and α be the model parameter for the first stage.

[0117] Then, β is calculated according to formula (18).

[0118]

[0119] in, Let α be the initial creep rate, and β be the model parameters for the first stage.

[0120] S22, Calculate the model parameters for the third stage of creep;

[0121] According to formula (19), the least squares method is used to fit the third stage curve of the creep test under each temperature and stress to obtain the model parameter ω of the third stage of creep.

[0122] Formula (19) is:

[0123]

[0124] in, Let ω be the steady-state creep rate, ω be the third-stage model parameter, and t be time. S / T This is the second transition moment.

[0125] S23, Calculate the apparent activation energy parameters;

[0126] Combining formula (16), based on the same temperature T and different initial creep rates... Steady-state creep rate The experimental data for the first-stage model parameter α and the third-stage model parameter ω were fitted using the least squares method to 1 / T and The slope and intercept of the graph are used to calculate the apparent activation energy parameters a0 and a1, such as for steady-state creep rate. See Figure 3 As shown.

[0127] S3, calculate temperature and stress-related parameters;

[0128] Combining formula (16) and the initial creep rate calculated in the preceding steps Steady-state creep rate The first-stage model parameter α and the third-stage model parameter ω are obtained by fitting the parameter values ​​of a2, a3, a4, and a5 using the least squares method based on the parameter characteristics exhibited in the creep test. Figure 4 and Figure 5 As shown.

[0129] S4, calculate creep deformation;

[0130] The creep model parameters obtained in steps S1-S3 are used for parameter back-substitution calculations, and then substituted back into formulas (10) to (13) to calculate creep deformation under arbitrary temperature and stress conditions. The calculation results are shown in [the table below]. Figure 6 .

[0131] Through Examples 1 to 3 above, this invention constructs a method for determining the creep deformation of various high-temperature alloy material structures used in aero-engines. The calculation method and process are provided, and the specific implementable procedures for each step are clarified. A corresponding creep model program is also developed using a secondary development interface of commercial finite element software. This method can be used to analyze and calculate the creep deformation of hot-end components of aero-engines within a wide temperature field and stress range, improving calculation efficiency and accuracy. It is a relatively accurate, convenient, and reliable method.

[0132] It should be noted that in this application, It means ln(α) or ln(α); that is, All four parameters, α and ω, can be fitted using formula (16).

[0133] The above description, based on the embodiments shown in the figures, details the structure, features, and effects of the present invention. The above description is only a preferred embodiment of the present invention, but the present invention is not limited to the scope of implementation shown in the figures. Any changes made in accordance with the concept of the present invention, or equivalent embodiments modified to have equivalent changes, that do not exceed the spirit covered by the specification and figures, should be within the protection scope of the present invention.

Claims

1. A method for analyzing creep deformation of metallic materials considering complex temperature fields, characterized in that: Includes the following steps, S1. Obtain the first parameter, first transition time, and second transition time under each temperature stress condition based on the creep test curve of the metallic material; S2, calculate the second parameter based on the first parameter, the first transition time, and the second transition time, combined with the first formula; the first formula is an expression for the correlation between creep model parameters and temperature and stress; S3, based on the first parameter, the second parameter and the creep test curve, the third parameter of the first formula is obtained by fitting; S4, substitute the first parameter, second parameter, third parameter, first conversion time and second conversion time back into the preset model to calculate the creep deformation under arbitrary temperature and stress conditions; The preset model includes a first-stage model; The first-stage model is represented by the following formula: e P =βln(αt+1)t≤t P / S ; Where, ε P The creep deformation is represented by β and α, which are the model parameters for the first stage. Let t be the creep rate, and t be the time. P / S This is the first transition moment; The first formula is, in, The initial creep rate, For steady-state creep rate, α is the first-stage model parameter, ω is the third-stage model parameter, a0 and a1 are both second parameters, T is temperature, σ is creep stress, E is the elastic modulus of the metallic material, a2, a3, a4 and a5 are all third parameters, and τ is the bilinear inflection point. The first transition time is calculated using the following formula. Among them, t P / S This is the first transition moment. The initial creep rate, Let α be the steady-state creep rate, and α be the model parameter for the first stage.

2. The method for creep deformation analysis of metallic materials considering complex temperature fields according to claim 1, characterized in that: The first parameter includes the initial creep rate and the steady-state creep rate.

3. The method for creep deformation analysis of metallic materials considering complex temperature fields according to claim 2, characterized in that: The second parameter is the apparent activation energy parameter.

4. The method for creep deformation analysis of metallic materials considering complex temperature fields according to claim 3, characterized in that: The preset model also includes a second-stage model; The second-stage model is represented by the following formula: Where, ε S ε represents the creep deformation that has occurred at the current moment when the second stage is in progress. P / S This refers to the creep deformation that occurs in the first stage. Let t be the steady-state creep rate, and t be time. P / S For the first transition time, t S / T This is the second transition moment.

5. The method for creep deformation analysis of metallic materials considering complex temperature fields according to claim 4, characterized in that: The preset model also includes a third-stage model; The third-stage model is represented by the following formula: ε T =θ(exp[ω(t-t S / T )]-1)t>t S / T ; Where, ε T The creep deformation occurs at the current moment in the third stage, where θ and ω are both parameters of the third stage model; t is time. S / T This is the second transition time. The creep deformation rate of the third-stage model. The steady-state creep rate.

6. The method for creep deformation analysis of metallic materials considering complex temperature fields according to claim 5, characterized in that: The calculation method for the third-stage model parameter ω is based on the following formula: The third-stage curves of the creep test at each temperature and stress were obtained by fitting the least squares method.

7. The method for creep deformation analysis of metallic materials considering complex temperature fields according to claim 1, characterized in that: In step S2, the second parameter is calculated by fitting 1 / T and using the least squares method. The slope and intercept of the graph are used to obtain the second parameter.

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