CN110688788B - High-temperature material creep deformation and service life prediction method - Google Patents
High-temperature material creep deformation and service life prediction method Download PDFInfo
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Abstract
The invention discloses a high-temperature material creep deformation and service life prediction method and a model, which comprises the following steps: (1) converting an extensometer displacement-time curve obtained through a test into a creep strain-time curve; (2) normalizing the creep test stress by using the tensile strength of the material; (3) model of creep
The parameters β, δ, μ and ζ in (a) are expressed as a function of stress and temperature; in the above formula, the first and second carbon atoms are,
for creep strain rate, t is creep time, β, δ, μ, ζ are stress and temperature dependent material parameters, c6Is a material constant; (4) the creep strain-time curve obtained in the step (1) and the normalized curve obtained in the step (2) are usedFitting the stress data to obtain creep model parameters; (5) and (4) realizing creep analysis on the actual structure by using finite element software. The method not only reflects the whole process of material creep deformation, but also can predict the creep life of the material through parameters in the model; by means of finite element subroutines, the model can be applied in creep analysis of actual structures.
Description
Technical Field
The invention relates to a mathematical model capable of predicting creep deformation and service life of a high-temperature material and a method for applying the mathematical model in finite element software, and belongs to the technical field of high-temperature structural strength.
Background
The problem of creep of materials has a long history and there has been much research experience and effort in this field. These studies can be broadly divided into three categories: (1) determining a method for describing creep property and service life of the material through material macro test data; (2) studies based on the microstructure of the material reveal the intrinsic nature of the material creep problem; (3) a method for reflecting creep macro features is established based on the microstructure of the material. The creep process for most metallic materials can be divided into three phases, namely a first phase in which the creep rate decreases rapidly, a second phase in which the creep rate remains relatively stable, and a third phase in which the creep rate increases rapidly. Many researchers have proposed their own models to describe the different stages of creep based on different methods, but the constitutive equations that can describe the overall creep process are very limited. Among these, the most widely used full creep constitutive model is: theta-projection (1986), Batsoulas (1997) and sequential damage mechanics (CDM) methods. These models may reflect the characteristics of the three stages of creep, and CDM models may predict creep life by considering the damage evolution process.
In studying a creep life model of a material, researchers have attempted to relate creep life, temperature, and stress by different parameters. The thermal parameter equation based on the L-M parameter and the Wilshire equation has higher accuracy. However, none of these methods can be embedded in a creep constitutive model of the material, and thus it is difficult to apply them to creep life analysis of the structure. In order to better predict creep deformation and life of a material or structure, a model is needed that can both describe the overall process of material creep and reflect the creep life of the material.
Disclosure of Invention
The invention aims to provide a method and a model for predicting creep deformation and service life of a high-temperature material, so as to realize the purposes of describing the whole process of material creep and reflecting the creep service life of the material.
In order to achieve the purpose, the invention adopts the following technical scheme:
a high-temperature material creep deformation and service life prediction method comprises the following steps:
(1) converting an extensometer displacement-time curve obtained through a test into a creep strain-time curve;
(2) normalizing the creep test stress by using the tensile strength of the material;
(3) model of creep
The parameters β, δ, μ and ζ in (a) are expressed as a function of stress and temperature; in the above formula, the first and second carbon atoms are,
for creep strain rate, t is creep time, β, δ, μ, ζ are stress and temperature dependent material parameters, c6Is a material constant;
(4) fitting the creep strain-time curve obtained in the step (1) with the normalized stress data obtained in the step (2) to obtain creep model parameters;
(5) and (4) realizing creep analysis on the actual structure by using finite element software.
In the step (1), through extensometer displacement-time data measured through tests, a creep deformation-time curve is obtained after plastic deformation generated by loading is removed.
In the step (2), the tensile strength sigma of the material is utilizedTSNormalizing the stress sigma of the creep test to obtain sigma/sigmaTS。
In the step (3), the temperature and stress function expressions of the parameters β, δ, μ and ζ are respectively:
ζ＝exp(c5/(RT))
where σ is the stress of the creep test, σTSThe tensile strength of the material at the corresponding temperature is shown, R is a gas constant, and T is the test temperature; the above expression is simplified to:
ζ＝c5。
in the step (4), the parameter c is obtained by fitting by using a parameter fitting function in 1stOpt software and adopting a quart method and a general global optimization methodiSubscript i is 1 to 8.
In the step (5), the creep model is modeled by using a user creep subprogram carried by finite element software ANSYS
Compiling into the self-defined subprogram, then compiling and linking with the ANSYS main program to form an ANSYS version capable of executing the self-defined creep model, and realizing creep deformation analysis of the actual structure by using the version.
In the step (5), when writing the finite element creep subroutine usercreep, providing a creep strain increment delcr, a derivative dcrda (1) of the creep strain increment to the equivalent stress and a derivative dcrda (2) of the creep strain increment to the creep strain; when the test temperatures are the same, the expressions are respectively as follows:
dcrda(2)＝Δt·(μ·c6(c6-1)·t(c6-2)-β·δ·(ln(δ·t+c6)+1)/((δ·t+c5)2(ln(δ·t+c5))2))·1/(μ·c6·t(c6-1)+β/(δ·t+c5)/ln(δ·t+c5))
in the above equation, Δ t is the time increment in the software calculation.
A creep model describing the overall creep process and life of a material, which is an expression of creep strain rate, as shown in formula (1):
in the above formula, the first and second carbon atoms are,
for creep strain rate, t is creep time, β, δ, μ, ζ are stress and temperature dependent material parameters, c6Is a material constant.
In the formula (1), beta, delta, mu and zeta are parameters of a creep process of the reaction material, and can reflect a first creep stage in which the creep rate of the reaction material is gradually reduced, a second creep stage in which the creep rate is constant and a third creep stage in which the creep rate is rapidly increased; the creep life of the material can be predicted by the parameters δ and ζ.
Meanwhile, the second term on the right of the equal sign in the formula (1) corrects the third stage of creep deformation, so that the model can better describe the creep deformation rule of the material.
Has the advantages that: the model and the method provided by the invention not only reflect the whole process of material creep deformation, but also can predict the creep life of the material through parameters in the model. By writing finite element subroutines, the model of the present invention can be applied to creep analysis of actual structures.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic representation of a typical creep curve and its three stages;
FIG. 3 is a creep strain diagram of TC11 material at 500 ℃ under 5 stress conditions;
FIG. 4 is a graph comparing creep curves of 5 stress condition tests at 500 ℃ for TC11 material with model fitting curves;
FIG. 5 is a graph comparing the model predicted creep life at 500 ℃ of TC11 material with the test life.
Detailed Description
The method and the model for predicting the creep deformation and the service life of the high-temperature material can describe the whole process of material creep and reflect the creep service life of the material. The creep model of the invention is an expression of creep strain rate, and is shown in formula (1):
in the above formula, the first and second carbon atoms are,
for creep strain rate, t is creep time, β, δ, μ, ζ are stress and temperature dependent material parameters, c6Is a material constant.
In the formula (1), beta, delta, mu and zeta are parameters of a creep process of the reaction material, and can reflect a first creep stage in which the creep rate of the reaction material is gradually reduced, a second creep stage in which the creep rate is constant and a third creep stage in which the creep rate is rapidly increased; the creep life of the material can be predicted by the parameters δ and ζ.
Meanwhile, the second term on the right of the equal sign in the formula (1) corrects the third stage of creep deformation, so that the model can better describe the creep deformation rule of the material.
The invention discloses a high-temperature material creep deformation and service life prediction method, which comprises the following steps:
(1) converting an extensometer displacement-time curve obtained through a test into a creep strain-time curve;
removing plastic deformation generated by loading through extensometer displacement-time data measured by tests to obtain a creep deformation-time curve;
(2) normalizing the creep test stress by using the tensile strength of the material;
by means of the tensile strength σ of the materialTSNormalizing the stress sigma of the creep test to obtain sigma/sigmaTS；
(3) Model of creep
The parameters β, δ, μ and ζ in (a) are expressed as a function of stress and temperature; in the above formula, the first and second carbon atoms are,
for creep strain rate, t is creep time, β, δ, μ, ζ are stress and temperature dependent material parameters, c6Is a material constant;
the temperature and stress function expressions for parameters β, δ, μ and ζ are:
ζ＝exp(c5/(RT))
where σ is the stress of the creep test, σTSThe tensile strength of the material at the corresponding temperature is shown, R is a gas constant, and T is the test temperature; the above expression is simplified to:
ζ＝c5
(4) fitting the creep strain-time curve obtained in the step (1) with the normalized stress data obtained in the step (2) to obtain creep model parameters;
the parameter c is obtained by utilizing the parameter fitting function in the 1stOpt software and adopting a quart method and a general global optimization methodiSubscript i is 1 to 8;
(5) realizing creep analysis of an actual structure by using finite element software;
compiling the creep model shown in the formula (1) into a self-defined subprogram by using a user critical subprogram of finite element software ANSYS, compiling and linking the creep model with an ANSYS main program to form an ANSYS version capable of executing the self-defined creep model, and realizing creep deformation analysis of an actual structure by using the version;
writing a finite element creep subroutine usercreep requires providing a creep strain increment delcr, a derivative of creep strain increment to equivalent stress dcrda (1), and a derivative of creep strain increment to creep strain dcrda (2); when the test temperatures are the same, the expressions are respectively as follows:
dcrda(2)＝Δt·(μ·c6(c6-1)·t(c6-2)-β·δ·(ln(δ·t+c6)+1)/((δ·t+c5)2(ln(δ·t+c5))2))·1/(μ·c6·t(c6-1)+β/(δ·t+c5)/ln(δ·t+c5))
in the above equation, Δ t is the time increment in the software calculation.
The invention is further illustrated by the following examples.
Examples
The implementation flow of the method for predicting creep deformation and service life of the high-temperature material in the embodiment is shown in fig. 1, a typical material creep curve is shown in fig. 2, and the application of the method in creep deformation analysis of the TC11 titanium alloy material at 500 ℃ comprises the following steps:
(1) converting the extensometer displacement-time curve of the TC11 material obtained by the test at 500 ℃ into a creep strain-time curve, as shown in figure 3;
(2) tensile strength sigma for creep test stress of TC11 material at 500 DEG CTSCarrying out normalization; wherein, the creep stress of the TC11 material at 500 ℃ is 558MPa, 580MPa, 604MPa, 630MPa, 660MPa and 675MPa respectively. Tensile strength of the material at this temperatureTS775.63 MPa;
(3) expressing the parameters β, δ, μ and ζ as a function of stress and temperature; the temperature and stress function expressions for the parameters β, δ, μ and ζ are:
ζ＝exp(c5/(RT))，
the above expression can be simplified to the same temperature under each test condition
And ζ ═ c5。
(4) Fitting creep model parameters by using the test data, comparing the fitted creep curve with the test curve as shown in FIG. 4, and comparing the predicted service life of the model parameters with the test service life as shown in FIG. 5;
the parameter c is obtained by utilizing the parameter fitting function in the 1stOpt software and adopting the Marquardt method and the general global optimization methodiThe index i is from 1 to 8, and the parameter c obtained by fitting the creep test data of the TC11 material at 500 ℃ and 6 stresses1～c8Respectively as follows:
c1＝24.1980,
c2＝-4.2460，
c3＝13.0467，
c4＝-1.9547，
c5＝0.0005823，
c6＝4.0612，
c7＝34.1804,
c8＝-16.2901；
(5) embedding the model into finite element software to realize creep analysis of the actual structure;
writing a finite element creep subroutine usercreep requires providing a creep strain increment delcr, a derivative of creep strain increment to equivalent stress dcrda (1), and a derivative of creep strain increment to creep strain dcrda (2); taking the condition that the test temperatures are the same as an example, the expressions are respectively:
dcrda(2)＝Δt·(μ·c6(c6-1)·t(c6-2)-β·δ·(ln(δ·t+c6)+1)/((δ·t+c5)2(ln(δ·t+c5))2))·1/(μ·c6·t(c6-1)+β/(δ·t+c5)/ln(δ·t+c5))
the foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A high-temperature material creep deformation and service life prediction method is characterized in that: the method comprises the following steps:
(1) converting an extensometer displacement-time curve obtained through a test into a creep strain-time curve;
(2) normalizing the creep test stress by using the tensile strength of the material;
(3) model of creep
The parameters β, δ, μ and ζ in (a) are expressed as a function of stress and temperature; in the above formula, the first and second carbon atoms are,
for creep strain rate, t is creep time, β, δ, μ, ζ are stress and temperature dependent material parameters, c6Is a material constant;
the temperature and stress function expressions for parameters β, δ, μ and ζ are:
ζ＝exp(c5/(RT))
where σ is the stress of the creep test, σTSThe tensile strength of the material at the corresponding temperature is shown, R is a gas constant, and T is the test temperature; the above expression is simplified to:
ζ＝c5
(4) fitting the creep strain-time curve obtained in the step (1) and the normalized stress data obtained in the step (2) by using a parameter fitting function in 1stOpt software and adopting a Marquardt method and a general global optimization method to obtain a creep model parameter ciSubscript i is 1 to 8;
(5) and (4) realizing creep analysis on the actual structure by using finite element software.
2. The method of claim 1, wherein the creep deformation and life prediction method comprises: in the step (1), through extensometer displacement-time data measured through tests, a creep deformation-time curve is obtained after plastic deformation generated by loading is removed.
3. The method of claim 1, wherein the creep deformation and life prediction method comprises: in the step (2), the tensile strength sigma of the material is utilizedTSNormalizing the stress sigma of the creep test to obtain sigma/sigmaTS。
4. The method of claim 1, wherein the creep deformation and life prediction method comprises: in the step (5), the creep model is modeled by using a user creep subprogram carried by finite element software ANSYS
Compiling into the self-defined subprogram, then compiling and linking with the ANSYS main program to form an ANSYS version capable of executing the self-defined creep model, and realizing creep deformation analysis of the actual structure by using the version.
5. The method of claim 4, wherein the creep deformation and life prediction method comprises: in the step (5), when writing the finite element creep subroutine usercreep, providing a creep strain increment delcr, a derivative dcrda (1) of the creep strain increment to the equivalent stress and a derivative dcrda (2) of the creep strain increment to the creep strain; when the test temperatures are the same, the expressions are respectively as follows:
dcrda(2)＝Δt·(μ·c6(c6-1)·t(c6-2)-β·δ·(ln(δ·t+c6)+1)/((δ·t+c5)2(ln(δ·t+c5))2))·1/(μ·c6·t(c6-1)+β/(δ·t+c5)/ln(δ·t+c5))
in the above equation, Δ t is the time increment in the software calculation.
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| CN112163359A (en) * | 2020-10-09 | 2021-01-01 | 南京航空航天大学 | Inversion optimization algorithm-based creep large-deformation endurance life prediction method |
| CN112630044A (en) * | 2020-11-19 | 2021-04-09 | 西北工业大学 | Creep life prediction method of nickel-based single crystal alloy based on crystal orientation |
| CN113866008A (en) * | 2021-09-07 | 2021-12-31 | 南京航空航天大学 | Creep life prediction method based on threshold stress and tensile strength |
| CN114295491A (en) * | 2021-12-14 | 2022-04-08 | 南京航空航天大学 | Prediction method for creep damage and time evolution behavior of deformation |
| CN114462147B (en) * | 2022-01-28 | 2023-02-03 | 中国人民解放军陆军工程大学 | Method for constructing damage-containing propellant creep deformation constitutive model and method for applying finite element |
| CN116665800B (en) * | 2023-04-07 | 2024-02-20 | 南京航空航天大学 | Nickel-based superalloy corrosion creep behavior prediction method |
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