CN110705019B - High-temperature creep damage equivalent acceleration method - Google Patents

High-temperature creep damage equivalent acceleration method Download PDF

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CN110705019B
CN110705019B CN201910802096.6A CN201910802096A CN110705019B CN 110705019 B CN110705019 B CN 110705019B CN 201910802096 A CN201910802096 A CN 201910802096A CN 110705019 B CN110705019 B CN 110705019B
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creep
damage
equivalent
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creep damage
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宋迎东
叶文明
胡绪腾
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a high-temperature creep damage equivalent acceleration method, which introduces a creep damage tolerance parameter lambda and enables the uniaxial creep property and creep deformation of a material to be improvedConsidering creep damage variables, simultaneously applying a load factor phi, taking a loading condition as an index of the creep damage variables, and obtaining acceleration time for converting a long-time working state into a short-time working state by a damage equivalent method according to the principle that creep damages of materials under different loading conditions are consistent, wherein the loading condition comprises stress sigma, temperature T and minimum creep rate
Figure DDA0002182617140000011
Creep damage equivalent acceleration of a material is determined by the following equation
Figure DDA0002182617140000012
To be implemented. The invention can obtain the acceleration time for converting the long-time working state into the short-time working state by a damage equivalent method, and is a creep damage equivalent acceleration method considering the creep performance and the loading condition of the material.

Description

High-temperature creep damage equivalent acceleration method
Technical Field
The invention relates to an equivalent acceleration method for high-temperature creep damage, and belongs to the technical field of high-temperature structural strength.
Background
The life of the aero-engine is usually tested in the process of development and use, and with the continuous improvement of the life of the aero-engine, the test cost is higher and higher in the whole life cycle of 1:1, the cycle is longer and longer, and even the test is unacceptable in engineering. In order to save the expenditure and shorten the development period, an accelerated task trial technology is required. During the process of accelerating the task trial run, the using load of the engine needs to be simulated, the engine is classified according to the type of damage of the structure of the aeroengine, and the load borne by the engine mainly comprises low-cycle fatigue, thermal shock, creep, vibration and the like. In order to shorten the test run time in the acceleration task test run, the equivalent simulation is usually performed by using the longer continuous working time under the small load of each stage and the shorter continuous test run time under the large load, so that a method for equivalently accelerating the high-temperature creep damage of the material needs to be established.
Disclosure of Invention
In order to realize equivalent acceleration of creep damage in an acceleration task trial run, the invention aims to provide a high-temperature creep damage equivalent acceleration method, which can convert a small load into a large load under the condition of ensuring the equivalent creep damage.
In order to achieve the purpose, the invention adopts the technical scheme that:
a high-temperature creep damage equivalent acceleration method is characterized in that a creep damage tolerance parameter lambda is introduced, the uniaxial creep performance and creep deformation of a material are considered in a creep damage variable, a load factor phi is applied, a loading condition is used as an index of the creep damage variable, and acceleration time for converting a long-time working state into a short-time working state through a damage equivalent method is obtained according to the principle that the creep damage of the material under different loading conditions is consistent, wherein the loading conditions comprise stress sigma, temperature T and minimum creep rate
Figure BDA0002182617120000011
Creep damage equivalent acceleration of a material is achieved by the following equation:
Figure BDA0002182617120000012
in the formula, ω is creep damage,
Figure BDA0002182617120000013
for creep damage tolerance variable,. DELTA.. dicIn order to increase the creep strain by an amount,
Figure BDA0002182617120000014
for minimum rate of creep, tfIn order to achieve a creep life, it is preferred that,
Figure BDA0002182617120000015
is the load factor, σ is the stress, T is the temperature, A, B is the material constant;
Figure BDA0002182617120000016
in order to be tolerant to fracture creep damage,
Figure BDA0002182617120000017
is creep rupture strain; when creep damage Δ λ ═ λfWhen the material is broken(ii) a When two load conditions are experienced during the material's working history, the cumulative creep damage is expressed as:
Figure BDA0002182617120000021
wherein D is the accumulated creep damage, Δ λ1Is a temperature T1Stress σ1Lower operation Δ t1Creep damage tolerance after time, Δ λ2Is a temperature T2Stress σ2Lower operation Δ t2Creep damage tolerance after time, lambdaf1、λf2Tolerance for fracture creep damage under corresponding loading conditions;
Figure BDA0002182617120000022
wherein
Figure BDA0002182617120000023
To load the load factor corresponding to condition 1,
Figure BDA0002182617120000024
a, B is a material constant for the load factor corresponding to load condition 2; when the accumulated creep damage D is equal to 1, the material fractures; creep rupture life t of material under loaded condition 1f1Greater than the creep rupture life t of the material under the loading condition 2f2And equating the damage generated under the loading condition 1 to the loading condition 2 by a creep damage equivalence method to obtain the corresponding working time delta t'2And has Δ t'2<<Δt1Thereby realizing the purpose of accelerating the damage; obtaining the equivalent creep damage tolerance according to the formula (2)
Figure BDA0002182617120000025
Then working time delta t 'is obtained through uniaxial creep test data or constitutive equation of the material under the loading condition 2'2。
The method comprises the following steps:
step 1, obtaining different temperatures of materials according to a uniaxial creep testCreep strain-time curve under stress, minimum creep rate
Figure BDA0002182617120000026
Strain at rupture creep
Figure BDA0002182617120000027
And fracture life tf；
Step 2, selecting a creep constitutive equation, and fitting through a uniaxial creep test to obtain material parameters of the creep constitutive equation;
step 3, obtaining the creep test data according to two simple two-stage variable load by fitting
Figure BDA0002182617120000028
Parameter A, B;
step 4, calculating the equivalent creep damage tolerance variable converted to the large load condition under the small load condition through the formula (2)
Figure BDA0002182617120000029
Step 5, obtaining equivalent creep strain increment under the condition of large load according to the definition of delta lambda
Figure BDA00021826171200000210
Step 6, according to the material creep constitutive equation and equivalent creep strain increment obtained in the step 2
Figure BDA00021826171200000211
Calculating to obtain action time delta t 'equivalent to damage under large load'2。
In the step 1, the minimum creep rate is obtained by deriving the creep strain-time curve
Figure BDA00021826171200000212
In the step 2, a constitutive model capable of completely describing three creep stages is selected, and material parameters of a creep constitutive equation are obtained through fitting of a creep strain-time curve obtained in the step 1.
In the step 3, when the formula (2) is applied to the damage evaluation of creep rupture under the two-stage loading condition, the damage evaluation is represented as:
Figure BDA0002182617120000031
if the above formulae are all expressed in terms of strain:
Figure BDA0002182617120000032
according to the data of the two-stage variable load creep test and the uniaxial creep test, fitting to obtain a parameter A, B, and calculating an index
Figure BDA0002182617120000033
The value of (c).
In the step 4, the creep strain increment generated by the material under the action of a small load is recorded according to the test
Figure BDA0002182617120000034
Calculating to obtain damage tolerance variable delta lambda1And calculating the equivalent creep damage tolerance under the condition of converting from the small load to the large load by using the parameter A, B obtained in the step 3
Figure BDA0002182617120000035
In the step 5, the equivalent creep damage tolerance calculated in the step 4 is used
Figure BDA0002182617120000036
And
Figure BDA0002182617120000037
calculating to obtain equivalent creep strain increment
Figure BDA0002182617120000038
In the step 6, the equivalent strain obtained according to the step 5
Figure BDA0002182617120000039
And calculating a creep constitutive equation in the step 2 to obtain an action time delta t 'from the small load equivalent conversion to the large load'2。
Has the advantages that: the invention introduces a creep damage tolerance parameter lambda, considers the uniaxial creep performance and creep deformation of the material into a creep damage variable, and applies a load factor phi to load conditions (including stress sigma, temperature T and minimum creep rate)
Figure BDA00021826171200000310
) As an index of a creep damage variable, according to the principle that creep damages of materials under different loading conditions are consistent, the acceleration time for converting a long-time working state into a short-time working state through a damage equivalent method can be obtained, and the creep damage equivalent acceleration method considering the creep performance of the materials and the loading conditions is provided.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a comparison of a creep constitutive equation fitting curve and a test curve of a TC11 material at 500 ℃;
FIG. 3 is a relationship between creep damage tolerance parameters and load factor;
FIG. 4 is a graph of the low-high variable load creep deformation of TC11 material at two stages at 500 ℃;
FIG. 5 is a graph of high-low variable load creep deformation of TC11 material at two stages at 500 ℃.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The high-temperature creep damage equivalent acceleration method introduces a creep damage tolerance parameter lambda, considers the uniaxial creep performance and creep deformation of the material into a creep damage variable, simultaneously applies a load factor phi, takes a loading condition as an index of the creep damage variable, and takes the creep damage of the material under different loading conditions as oneObtaining the acceleration time of the long-time working state converted into the short-time working state by a damage equivalent method according to the principle, wherein the loading condition comprises stress sigma, temperature T and minimum creep rate
Figure BDA0002182617120000041
Creep damage equivalent acceleration of a material is achieved by the following equation:
Figure BDA0002182617120000042
in the formula, ω is creep damage,
Figure BDA0002182617120000043
for creep damage tolerance variables, Δ ε c is the creep strain delta,
Figure BDA0002182617120000044
for minimum rate of creep, tfIn order to achieve a creep life, it is preferred that,
Figure BDA0002182617120000045
is the load factor, σ is the stress, T is the temperature, A, B is the material constant;
Figure BDA0002182617120000046
in order to be tolerant to fracture creep damage,
Figure BDA0002182617120000047
is creep rupture strain; when creep damage Δ λ ═ λfWhen the material is broken; when two load conditions are experienced during the material's working history, the cumulative creep damage is expressed as:
Figure BDA0002182617120000048
wherein D is the accumulated creep damage, Δ λ1Is a temperature T1Stress σ1Lower operation Δ t1Creep damage tolerance after time, Δ λ2Is a temperature T2Stress σ2Lower operation Δ t2Creep damage tolerance after time, lambdaf1、λf2Tolerance for fracture creep damage under corresponding loading conditions;
Figure BDA00021826171200000412
wherein
Figure BDA0002182617120000049
To load the load factor corresponding to condition 1,
Figure BDA00021826171200000410
a, B is a material constant for the load factor corresponding to load condition 2; when the accumulated creep damage D is equal to 1, the material fractures; creep rupture life t of material under loaded condition 1f1Greater than the creep rupture life t of the material under the loading condition 2f2And equating the damage generated under the loading condition 1 to the loading condition 2 by a creep damage equivalence method to obtain the corresponding working time delta t'2And has Δ t'2<<Δt1Thereby realizing the purpose of accelerating the damage; obtaining the equivalent creep damage tolerance according to the formula (2)
Figure BDA00021826171200000411
Then working time delta t 'is obtained through uniaxial creep test data or constitutive equation of the material under the loading condition 2'2。
As shown in fig. 1, the method of the present invention comprises the steps of:
step 1, obtaining creep strain-time curves and minimum creep rates of materials under different temperatures and stresses according to a uniaxial creep test
Figure BDA0002182617120000051
Strain at rupture creep
Figure BDA0002182617120000052
And fracture life tf(ii) a Therein, lead toMinimum creep rate by derivation of creep strain-time curve
Figure BDA0002182617120000053
Step 2, selecting a constitutive model capable of completely describing three creep stages, and fitting a creep strain-time curve obtained in the step 1 to obtain material parameters of a creep constitutive equation;
step 3, obtaining the creep test data according to two simple two-stage variable load by fitting
Figure BDA0002182617120000054
Parameter A, B; the method specifically comprises the following steps: when the formula (2) is applied to the damage evaluation of creep rupture under the two-stage loading condition, the damage evaluation is expressed as:
Figure BDA0002182617120000055
if the above formulae are all expressed in terms of strain:
Figure BDA0002182617120000056
according to the data of the two-stage variable load creep test and the uniaxial creep test, fitting to obtain a parameter A, B, and calculating an index
Figure BDA0002182617120000057
A value of (d);
step 4, calculating the equivalent creep damage tolerance variable converted to the large load condition under the small load condition through the formula (2)
Figure BDA0002182617120000058
The method specifically comprises the following steps: according to the experimental record, the creep strain increment generated by the material under the action of small load
Figure BDA0002182617120000059
Calculating to obtain damage tolerance variable delta lambda1And calculating the equivalent creep damage tolerance under the condition of converting from the small load to the large load by using the parameter A, B obtained in the step 3
Figure BDA00021826171200000510
Step 5, obtaining the equivalent creep damage tolerance according to the calculation in the step 4
Figure BDA00021826171200000511
And
Figure BDA00021826171200000512
calculating to obtain equivalent creep strain increment
Figure BDA00021826171200000513
Step 6, obtaining the equivalent strain according to the step 5
Figure BDA00021826171200000514
And calculating a creep constitutive equation in the step 2 to obtain an action time delta t 'from the small load equivalent conversion to the large load'2。
The present invention will be further described with reference to specific examples and figures, which are included to provide a better understanding of the present invention. However, those skilled in the art will readily appreciate that the specific material ratios, process conditions and results thereof described in the examples are illustrative only and should not be taken as limiting the invention as detailed in the claims.
Examples
In this embodiment, the high-temperature creep damage equivalent acceleration method of the present invention is applied to the calculation of the variable load creep damage of the TC11 titanium alloy material at 500 ℃, and includes the following steps:
(1) obtaining creep strain-time curves and minimum creep rate of TC11 material under different stresses at 500 ℃ according to uniaxial creep test
Figure BDA0002182617120000061
Strain at rupture creep
Figure BDA0002182617120000062
And fracture life tfAs shown in fig. 2; wherein after obtaining the creep curve of the material, the minimum creep rate is obtained by derivation
Figure BDA0002182617120000063
(2) Selecting a constitutive model capable of completely describing three creep stages, and fitting through a uniaxial creep test to obtain creep constitutive parameters of the TC11 material at 500 ℃, as shown in the attached figure 2;
wherein, the selected constitutive model capable of describing the creep complete deformation process is as follows:
Figure BDA0002182617120000064
in the formula: epsiloncFor creep strain, σ is stress, tfRespectively creep time and fracture life of the material under specified temperature and stress, wherein k, eta and alpha are stress and temperature related material parameters, and when the temperature under each test condition is the same, k is equal to c1+c2σ、η＝c3+c4σ、α＝c5+c6And sigma. Parameter c is obtained by fitting experimental data1～6Comprises the following steps:
c1＝-596952.8358,
c2＝1004.7019，
c3＝3391572.9972，
c4＝-5438.5501，
c5＝0.2274，
c6＝1.9544E-7。
(3) according to two simple two-stage variable load creep test deformations of the TC11 material at 500 ℃, as shown in attached figures 4 and 5, parameters A and B are obtained by fitting and damage indexes are obtained by calculation
Figure BDA0002182617120000065
Value of (1), creepThe relationship between the variable damage tolerance λ and the load factor Φ, as shown in fig. 3;
wherein, the parameters A and B are respectively 0.0261 and-0.0297 according to the data of the two-stage variable load creep test and the uniaxial creep test;
(4) according to the experimental record of the creep strain increment generated by the material under the action of the first-stage load
Figure BDA0002182617120000071
Calculating to obtain damage tolerance variable delta lambda1And calculating the equivalent creep damage tolerance converted from the small load to the large load through the parameter A, B fitted in the step 3
Figure BDA0002182617120000072
Wherein, the creep strain increment generated by the material under the small load according to the test record
Figure BDA0002182617120000073
Calculating to obtain damage tolerance variable delta lambda12.9591 and 1.5178, and calculating the equivalent creep damage tolerance delta lambda 'for the conversion from the first stage load to the second stage load by using the parameter A, B fitted in the step 3'21.8614 and 1.5446;
(5) according to the equivalent creep damage tolerance calculated in the previous step
Figure BDA0002182617120000074
And
Figure BDA0002182617120000075
calculating to obtain equivalent creep strain increment
Figure BDA0002182617120000076
And 0.05229;
(6) equivalent strain obtained from the previous step
Figure BDA0002182617120000077
And the present in step 2 describing the three phases of creepEquation, calculating to obtain action time delta t 'from equivalent conversion of small load to large load'22.08 and 8.03 hours.
The time after creep damage equivalent transformation at 500 ℃ of the TC11 material and the test time are shown in Table 1.
TABLE 1 comparison of time after creep damage equivalent transformation of TC11 Material at 500 ℃ with test time
Figure BDA0002182617120000078
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 (8)

1. A high-temperature creep damage equivalent acceleration method is characterized by comprising the following steps: introducing a creep damage tolerance parameter lambda, considering the uniaxial creep performance and creep deformation of the material into a creep damage variable, simultaneously using a load factor phi, using a loading condition as an index of the creep damage variable, and obtaining acceleration time converted from a long-time working state to a short-time working state by a damage equivalent method according to the principle that the creep damage of the material under different loading conditions is consistent, wherein the loading condition comprises stress sigma, temperature T and minimum creep rate
Figure FDA0002923045180000011
Creep damage equivalent acceleration of a material is achieved by the following equation:
Figure FDA0002923045180000012
in the formula, ω is creep damage,
Figure FDA0002923045180000013
for creep damage tolerance variable,. DELTA.. dicIn order to increase the creep strain by an amount,
Figure FDA0002923045180000014
for minimum rate of creep, tfIn order to achieve a creep life, it is preferred that,
Figure FDA0002923045180000015
is the load factor, σ is the stress, T is the temperature, A, B is the material constant;
Figure FDA0002923045180000016
in order to be tolerant to fracture creep damage,
Figure FDA0002923045180000017
is creep rupture strain; when creep damage Δ λ ═ λfWhen the material is broken; when two load conditions are experienced during the material's working history, the cumulative creep damage is expressed as:
Figure FDA0002923045180000018
wherein D is the accumulated creep damage, Δ λ1Is a temperature T1Stress σ1Lower operation Δ t1Creep damage tolerance after time, Δ λ2Is a temperature T2Stress σ2Lower operation Δ t2Creep damage tolerance after time, lambdaf1、λf2Tolerance for fracture creep damage under corresponding loading conditions;
Figure FDA0002923045180000019
wherein
Figure FDA00029230451800000110
To load the load factor corresponding to condition 1,
Figure FDA00029230451800000111
a, B is a material constant for the load factor corresponding to load condition 2; when the accumulated creep damage D is equal to 1, the material fractures; creep rupture life t of material under loaded condition 1f1Greater than the creep rupture life t of the material under the loading condition 2f2And equating the damage generated under the loading condition 1 to the loading condition 2 by a creep damage equivalence method to obtain the corresponding working time delta t'2And has Δ t'2＜＜Δt1Thereby realizing the purpose of accelerating the damage; obtaining the equivalent creep damage tolerance according to the formula (2)
Figure FDA00029230451800000112
Then working time delta t 'is obtained through uniaxial creep test data or constitutive equation of the material under the loading condition 2'2。
2. The high temperature creep damage equivalent acceleration method according to claim 1, characterized by: the method comprises the following steps:
step 1, obtaining creep strain-time curves and minimum creep rates of materials under different temperatures and stresses according to a uniaxial creep test
Figure FDA0002923045180000021
Strain at rupture creep
Figure FDA0002923045180000022
And fracture life tf；
Step 2, selecting a creep constitutive equation, and fitting through a uniaxial creep test to obtain material parameters of the creep constitutive equation;
step 3, obtaining the target material according to the two-stage variable load creep test data fitting
Figure FDA0002923045180000023
Parameter A, B;
step 4, calculating the conversion from the small load condition to the large load condition through the formula (2)Equivalent creep damage tolerance variable
Figure FDA0002923045180000024
Step 5, obtaining equivalent creep strain increment under the condition of large load according to the definition of delta lambda
Figure FDA0002923045180000025
Step 6, according to the material creep constitutive equation and equivalent creep strain increment obtained in the step 2
Figure FDA0002923045180000026
Calculating to obtain action time delta t 'equivalent to damage under large load'2。
3. The high temperature creep damage equivalent acceleration method according to claim 2, characterized by: in the step 1, the minimum creep rate is obtained by deriving the creep strain-time curve
Figure FDA0002923045180000027
4. The high temperature creep damage equivalent acceleration method according to claim 2, characterized by: in the step 2, a constitutive model capable of completely describing three creep stages is selected, and material parameters of a creep constitutive equation are obtained through fitting of a creep strain-time curve obtained in the step 1.
5. The high temperature creep damage equivalent acceleration method according to claim 2, characterized by: in the step 3, when the formula (2) is applied to the damage evaluation of creep rupture under the two-stage loading condition, the damage evaluation is represented as:
Figure FDA0002923045180000028
if the above formulae are all expressed in terms of strain:
Figure FDA0002923045180000029
according to the data of the two-stage variable load creep test and the uniaxial creep test, fitting to obtain a parameter A, B, and calculating an index
Figure FDA00029230451800000210
The value of (c).
6. The high temperature creep damage equivalent acceleration method according to claim 2, characterized by: in the step 4, the creep strain increment generated by the material under the action of a small load is recorded according to the test
Figure FDA00029230451800000211
Calculating to obtain damage tolerance variable delta lambda1And calculating the equivalent creep damage tolerance under the condition of converting from the small load to the large load by using the parameter A, B obtained in the step 3
Figure FDA0002923045180000031
7. The high temperature creep damage equivalent acceleration method according to claim 2, characterized by: in the step 5, the equivalent creep damage tolerance calculated in the step 4 is used
Figure FDA0002923045180000032
And
Figure FDA0002923045180000033
calculating to obtain equivalent creep strain increment
Figure FDA0002923045180000034
8. The high temperature creep damage equivalent acceleration method according to claim 2, characterized by: in the step 6, the equivalent strain obtained according to the step 5
Figure FDA0002923045180000035
And calculating a creep constitutive equation in the step 2 to obtain an action time delta t 'from the small load equivalent conversion to the large load'2。
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