CN115204013A - Method for predicting service life of material in multi-axis stress state - Google Patents

Method for predicting service life of material in multi-axis stress state Download PDF

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CN115204013A
CN115204013A CN202210809588.XA CN202210809588A CN115204013A CN 115204013 A CN115204013 A CN 115204013A CN 202210809588 A CN202210809588 A CN 202210809588A CN 115204013 A CN115204013 A CN 115204013A
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creep
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notch
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张冬旭
吕盟辉
郭晓钥
李晓闻
罗壮
宋智超
李夏霜
李海涛
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Shaanxi University of Science and Technology
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Abstract

The invention discloses a method for predicting the service life of a material in a multiaxial stress state, and belongs to the field of material service life prediction. The method specifically comprises the following steps: the method comprises the following steps: obtaining relevant material parameters in the continuous damage mechanical model through a uniaxial creep experiment; step two: defining a material creep-damage constitutive model based on a continuous damage mechanical model in finite element software; step three: obtaining node positions corresponding to different gaps through a node position curve; step four: calculating the maximum main stress at each node on the cross section of the related notch according to finite element
Figure DDA0003740121390000011
Stress of von Mises
Figure DDA0003740121390000012
Step five: obtained based on step four
Figure DDA0003740121390000013
And with
Figure DDA0003740121390000014
And calculating the service life of the material by using a node stress method and a service life calculation formula. The method for predicting the creep-fracture life of the material in the multi-axis stress state can more efficiently, conveniently and accurately predict the creep life of the material in the multi-axis stress state.

Description

Method for predicting service life of material in multi-axis stress state
Technical Field
The invention belongs to the field of material life prediction, and particularly relates to a life prediction method of a material in a multi-axis stress state.
Background
In the aerospace and nuclear power fields, there are many important parts that are subjected to high temperature, high pressure, high speed loads during operation, such as turbine disks of aircraft engines and gas turbines, where most of the failure to break occurs in the slot connection structure. As these high-load hot-end members, there are many factors that affect the life of the tank connection structure, including creep deformation and fracture under high-temperature long-time operation, low-cycle fatigue caused by repeated changes in operating conditions, high-cycle fatigue caused by vibration, high-temperature gas corrosion, oxidation, and the like. Generally, creep rupture and low cycle fatigue play a decisive role, and generally these components are all exposed to a complex multiaxial stress field. The research on the creep behavior and the multi-axial creep life prediction of the materials is of great significance.
In the current engineering field design, material data under a uniaxial stress state is mostly adopted, and a design method and an evaluation means which accord with the structure reliability under the multiaxial stress are lacked. In recent years, in the academic field, researchers at home and abroad have developed a great deal of research on creep rupture behavior in a multiaxial stress state, and have proposed a great deal of creep-damage calculation models based on commercial finite element software, such as a crystal plasticity model, a continuous damage mechanics model, and a description of creep behavior by a constitutive model only. The crystal plastic model can accurately describe the stress-strain behavior of a microscopic level in a creep process, is suitable for basic scientific research, but is difficult to be used for macroscopic performance evaluation in engineering; the continuous damage mechanical model can accurately reflect the creep behavior of the material under the multi-axis stress state, and is also the most widely applied calculation model in the related research at present, but most of the related service life prediction methods at present have complex structure and complicated process, and are difficult to effectively apply to the engineering field; a large number of non-uniform phenomenological constitutive models can be used for carrying out qualitative research on a creep process, but are not suitable for predicting the service life of creep rupture under multi-axial stress. Various prediction methods are either cumbersome or inaccurate and comprehensive, and therefore, an effective method for multi-axial creep life prediction is currently lacking in the engineering field.
Disclosure of Invention
The invention aims to overcome the defects and provide a simple, convenient, efficient and accurate method for predicting the creep life under the multi-axis stress state, so that the residual life prediction, the performance evaluation and the design optimization of a hot-end high-temperature component are realized with lower cost and higher efficiency.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for predicting the service life of a material in a multi-axis stress state comprises the following steps:
the method comprises the following steps: performing a material uniaxial creep rupture experiment, respectively obtaining creep curves of the material under a plurality of uniaxial stress loads, and obtaining material parameters in the continuous damage mechanical model based on the plurality of uniaxial creep curves;
step two: establishing a finite element model in ABAQUS, and defining a material creep-damage constitutive model based on a continuous damage mechanical model by using a user subprogram UMAT;
step three: obtaining node positions corresponding to different gaps through a node position curve;
step four: calculating to obtain the maximum main stress at each node on the corresponding notch section when the stress of the relevant section is loaded based on a crop module in finite element software ABAQUS
Figure BDA0003740121370000021
And Mises stress
Figure BDA0003740121370000022
Step five: based on the results obtained in step four
Figure BDA0003740121370000023
And with
Figure BDA0003740121370000024
And calculating the creep-damage life under the corresponding multi-axis stress state by using a node stress method and a life calculation formula.
The material parameters in the first step comprise A, B, M, n, M and n 0 Chi and phi, A, B, M, n, M, n 0 And chi and phi are material constants related to temperature in a continuous damage mechanics model and are calculated by fitting a uniaxial creep test curve.
The uniaxial creep curve fitting method is as follows:
Figure BDA0003740121370000025
wherein A and n are Norton's equations
Figure BDA0003740121370000026
The material parameters in (2) need to be determined by at least two uniaxial creep curves of different stresses at least the same temperature,
Figure BDA0003740121370000027
is a minimum creep strain rate, which is independent of applied stress and temperature;
Figure BDA0003740121370000028
wherein t is f For uniaxial creep life, σ is uniaxial cross-sectional stress;
based on the formula
Figure BDA0003740121370000029
And obtaining M, chi and phi by using creep life fitting corresponding to different stresses.
The material creep-damage constitutive model based on the continuous damage mechanical model in the step two is as follows:
Figure BDA00037401213700000210
Figure BDA00037401213700000211
σ rep ＝ασ 1 +(1-α)σ e
wherein
Figure BDA00037401213700000212
For creep rate, the magnitude of the value of ω from 0 to 1 represents the creep damage, σ 1 Is the maximum principal stress, σ e Is the equivalent stress, σ rep Is a representative stress, alpha is a parameter related to the material creep failure mechanism, and the numerical value is from 0 to 1.
The process of obtaining the node positions corresponding to different gaps through the node position curve in the third step is as follows: firstly, counting node positions corresponding to different notch morphology parameters, then fitting to obtain a curve equation, namely a node position curve, and based on the curve, directly calculating the node positions through the notch morphology in an actual problem, wherein the method specifically comprises the following steps:
given creep rate
Figure BDA00037401213700000213
And load, selecting a Nuon model constant n, and obtaining the load through a formula
Figure BDA00037401213700000214
And calculating corresponding A values, inputting different n values and corresponding A values into a user subprogram UMAT based on a Nonton model, performing creep simulation in ABAQUS, and drawing a distribution curve of Mises stress at the notch section along the notch section when reaching a second creep stage, wherein the intersection point of a plurality of curves is the node position.
The parameter process and curve equation for drawing the node position curve are as follows:
notch sharpness is expressed by 2 r/(D-D), (D-D)/D shows notch depth, and normalized node position is expressed by 2 r/(D-D). Wherein D is the diameter of the section of the notch of the smooth sample, D is the diameter of the section of the notch, r is the radius of the notch, r is the diameter of the notch * The distance between the node position and the root of the notch is (D-D)/2, the actual notch depth is obtained, when the notch degree is more than or equal to 1, the notch is a C-shaped notch, and when the notch degree is less than 1, the notch is a U-shaped notch;
drawing a notch position curve by the notch acutance and the corresponding normalized node position, wherein the curve equation is as follows:
y＝0.7410x 0.5483
where x =2 r/(D-D) is expressed as notch sharpness, y =2r * and/D-D is expressed as normalized node position.
The creep-damage life calculation process in the multiaxial stress state described in the step five is as follows:
Figure BDA0003740121370000031
Figure BDA0003740121370000032
wherein t is f For creep life under multiaxial stress, σ rep For the reference stress in the multi-axial stress state,
Figure BDA0003740121370000033
is the maximum principal stress at the node point,
Figure BDA0003740121370000034
is the Mises stress at the node, σ net Is section stress, alpha is a stress correction parameter;
wherein when σ rep /σ net >1, the notch has a weakening effect on the specimen, when σ rep /σ net <1, the notch has a strengthening effect on the sample; and the number of the first and second electrodes,
Figure BDA0003740121370000035
the method for obtaining the stress correction parameter α is as follows:
selecting alpha value, from formula
Figure BDA0003740121370000036
Calculating to obtain corresponding sigma rep And then by the formula
Figure BDA0003740121370000037
Calculating the creep life, taking the value of alpha as an abscissa and the creep life as an ordinate, making a transverse line parallel to the abscissa at the ordinate according to the known creep life, finding that the intersection point of the transverse line and the life curve is a straight line perpendicular to the coordinate and finally intersects the abscissa, and the value of alpha at the intersection point of the transverse line and the abscissa is the accurate value of alpha.
Compared with the prior art, the invention has the following beneficial effects:
the method for predicting the service life of the material in the multi-axis stress state is suitable for predicting the creep life of various metal materials and various temperature states, only relevant material parameters in a continuous damage mechanical model need to be changed, the application range is wide, the method for predicting the creep life is simple and convenient to operate, and design optimization, performance evaluation and residual life prediction of hot-end high-temperature components are achieved with low cost and high efficiency. Is convenient for popularization and application. Secondly, the method respectively obtains creep curves of the material under the loading of a plurality of uniaxial stresses by carrying out uniaxial creep rupture experiments on the material, obtains material parameters in the continuous damage mechanical model based on the plurality of uniaxial creep curves, is accurate and reliable in material parameters, and improves the accuracy of experimental results. In addition, the method is different from other researches in notch morphology parameter description, provides innovative parameter description, more scientifically, reasonably and accurately describes the notch morphology, and further improves the accuracy of the experimental result.
Furthermore, the creep-damage life prediction method of the material under the c-type notch structure based on the node stress method comprises a universal node position curve, the node position can be directly calculated according to the notch appearance in the actual engineering, and the workload of searching for the node is greatly reduced.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a view of a notched cylinder specimen according to an embodiment of the present invention;
FIG. 3 is a creep curve of GH4169 nickel-based single crystal superalloy at 650 ℃ under different uniaxial stress loads;
FIG. 4 is a simplified finite element model of the numerical simulation set up in ABAQUS according to the present invention;
FIG. 5 is a view showing the positions of the nodes of a test sample having a notch with a radius of 1 mm;
FIG. 6 is a comparison graph of the positions of nodes under the same notch structure and different section diameters;
FIG. 7 is a plot of nodal locations for a material of the present invention;
FIG. 8 is a graph comparing calculated node positions with node position errors in a correlation study;
fig. 9 is an accurate determination of the material parameter α of the present invention, with two dashed horizontal lines indicating the creep test life at η =0.2 and η =0.4, respectively;
FIG. 10 is a graph of predicted life versus experimental life error;
FIG. 11 (a) is the damage evolution over creep time on the notch cross section at 0.2 notch sharpness for 0.001tf;
FIG. 11 (b) is the damage evolution tf along with creep time on the notch cross section when the notch sharpness is 0.2;
FIG. 12 (a) is the damage evolution over creep time on the notch cross section at a notch sharpness of 1.6, 0.001tf;
FIG. 12 (b) is the evolution tf of the damage with creep time on the notch cross section for a notch sharpness of 1.6.
Detailed Description
The invention is further described below with reference to fig. 1-12.
As shown in fig. 1, a method for predicting the life of a material in a multiaxial stress state includes the following steps:
the method comprises the following steps: performing a material uniaxial creep rupture experiment, respectively obtaining creep curves of the material under a plurality of uniaxial stress loads, and obtaining material parameters in the continuous damage mechanical model based on the plurality of uniaxial creep curves;
step two: establishing a finite element model in ABAQUS, and defining a material creep-damage constitutive model based on a continuous damage mechanical model by using a user subprogram UMAT;
step three: obtaining node positions corresponding to different gaps through a node position curve;
step four: calculating to obtain the maximum main stress at each node on the corresponding notch section when the stress of the relevant section is loaded based on a crop module in finite element software ABAQUS
Figure BDA0003740121370000051
And Mises stress
Figure BDA0003740121370000052
Step five: based on the results obtained in step four
Figure BDA0003740121370000053
And
Figure BDA0003740121370000054
and calculating the creep-damage life under the corresponding multiaxial stress state by using a node stress method and a life calculation formula.
Further, the material parameters in the first step include A, B, M, n, M, n 0 Chi and phi, A, B, M, n, M, n 0 And chi and phi are material constants related to temperature in a continuous damage mechanics model and are calculated by fitting a uniaxial creep test curve.
The uniaxial creep curve fitting method is as follows:
Figure BDA0003740121370000055
wherein A and n are Norton's equations
Figure BDA0003740121370000056
The material parameters in (2) need to be determined by at least two uniaxial creep curves of different stresses at least the same temperature,
Figure BDA0003740121370000057
is the minimum creep strain rate, which is independent of applied stress and temperature;
Figure BDA0003740121370000058
wherein t is f For uniaxial creep life, σ is uniaxial cross-sectional stress;
based on the formula
Figure BDA0003740121370000059
And obtaining M, chi and phi by using creep life fitting corresponding to different stresses.
Further, the material creep-damage constitutive model based on the continuous damage mechanical model in the step two is as follows:
Figure BDA00037401213700000510
Figure BDA00037401213700000511
σ rep ＝ασ 1 +(1-α)σ e
wherein
Figure BDA00037401213700000512
For creep rate, the magnitude of ω is 0 to 1 representing creep damage, σ 1 Is the maximum principal stress, σ e Is the equivalent stress, σ rep Is a representative stress, alpha is a parameter related to the material creep failure mechanism, and the numerical value is from 0 to 1.
Further, the creep-damage constitutive model described in step two is embedded in ABAQUS by FORTRAN language. The C-notch finite element model of the cylindrical bar of the study object is established as follows:
a simplified two-dimensional model of a cylindrical bar with a C-shaped notch is established on the ABAQUS/CAE, as shown in figure 2, material attributes are set, grids are divided, a creep analysis step is established, and relevant required output variables are defined to an ODB file.
Further, the process of obtaining the node positions corresponding to different gaps through the node position curve in the third step is as follows: firstly, counting node positions corresponding to different notch morphology parameters, then fitting to obtain a curve equation, namely a node position curve, and based on the curve, directly calculating the node positions through the notch morphology in an actual problem, wherein the method specifically comprises the following steps:
given creep rate
Figure BDA00037401213700000513
The load is 200MPa, and a Noton model constant n =1, 3, 5, 7 or 10 is taken to pass through the formula
Figure BDA00037401213700000514
And calculating corresponding A values, inputting five groups of different n values and corresponding A values into a user subprogram UMAT based on a Nonton model, performing creep simulation in ABAQUS, and drawing a distribution curve of Mises stress at the notch section along the notch section when reaching a creep second stage, wherein the intersection point of a plurality of curves is the node position.
Preferably, the node stress method is also called bone point stress method, which means that the stress value at one point is approximately constant all the time along with the change of time in the creep process under the multi-axis stress state of the component. Furthermore, when the stress index n of the material is different, the stress value at this point also remains approximately constant. This point is called a node or bone point.
Further, the parameter process and curve equation for drawing the node position curve are as follows:
notch sharpness is expressed by 2 r/(D-D), (D-D)/D shows notch depth, and normalized node position is expressed by 2 r/(D-D). Wherein D is the diameter of the section of the notch of the smooth sample, D is the diameter of the section of the notch, r is the radius of the notch, and r is * The distance between the node position and the root of the notch is (D-D)/2, the actual notch depth is (D-D)/2, the notch is a C-shaped notch when the notch degree is larger than or equal to 1, the notch is a U-shaped notch when the notch degree is smaller than 1, the notch depth has no influence on the normalized notch position, and the notch sharpness has a functional relation with the normalized node position.
Drawing a notch position curve by the notch acutance and the corresponding normalized node position, wherein the curve can be suitable for all the problems of the same type of notches in the engineering practice, and the curve equation is as follows:
y＝0.7410x 0.5483
where x =2 r/(D-D) is expressed as notch sharpness, y =2r * and/D-D is expressed as normalized node position.
Further, the calculation process of the creep-damage life under the multi-axial stress state in the step five is as follows:
after obtaining the relevant stress in the third step and the fourth step, based on the formula
Figure BDA0003740121370000061
And formulas
Figure BDA0003740121370000062
Figure BDA0003740121370000063
Longevity of lifeAnd (5) calculating.
Wherein t is f For creep life under multiaxial stress, σ rep For the reference stress in the multi-axial stress state,
Figure BDA0003740121370000064
is the maximum principal stress at the node point,
Figure BDA0003740121370000065
is the Mises stress at the node, σ net Is section stress, alpha is a stress correction parameter;
wherein when σ rep /σ net >1, the notch has a weakening effect on the sample, when σ rep /σ net <1, the notch has a strengthening effect on the sample; and also,
Figure BDA0003740121370000066
the method for obtaining the stress correction parameter α is as follows:
take α =0, 0.2, 0.4, 0.6, 0.8 or 1, from the formula
Figure BDA0003740121370000067
Calculating to obtain corresponding sigma rep And then by the formula
Figure BDA0003740121370000068
The creep life is calculated, as shown in fig. 9, by taking the value of α as the abscissa and the creep life as the ordinate, and making a horizontal line parallel to the abscissa at the ordinate according to the known creep life, it is found that the intersection point of the horizontal line and the life curve is a straight line perpendicular to the coordinate and finally intersects the abscissa, and the value of α at the intersection point with the abscissa is the accurate value of α.
Preferably, the following is the creep-damage life prediction of the second generation nickel-based single crystal superalloy GH4169 material under the C-notch multiaxial stress shown in FIG. 2.
Table 1 shows the material composition (wt%) of second generation nickel-based single crystal superalloy GH 4169.
Figure BDA0003740121370000071
Table 2 shows the dimensions of the notch structures in each set of FIG. 2.
Figure BDA0003740121370000072
Creep-strain curves of the GH4169 superalloy under 750MPa and 700MPa loading stresses were obtained by a single axis creep rupture test at 650 ℃. And performing related calculation based on the plurality of uniaxial creep curves to obtain material parameters in the continuous damage mechanical model. Wherein the continuous injury mechanics model is as follows
Figure BDA0003740121370000073
Figure BDA0003740121370000074
σ rep ＝ασ 1 +(1-α)σ e (3)
Wherein
Figure BDA0003740121370000075
For creep rate, the magnitude of ω is 0 to 1 representing creep damage, σ 1 Is the maximum principal stress, σ e Is the equivalent stress, σ rep Is a representative stress, alpha is a parameter related to the material creep failure mechanism, and the numerical value is from 0 to 1. A. B, M, n, M, n 0 And chi and phi are temperature-dependent material constants in the continuous damage mechanics model, calculated from uniaxial creep test curve fitting. The parameter fitting process of the GH4169 superalloy material at 650 ℃ is as follows:
FIG. 3 is a creep curve of GH4169 nickel-base single crystal superalloy at 650 ℃ under different uniaxial stress loads. The material parameters a and n were calculated from the 2 creep curves of fig. 3 by Norton equation (4).
Figure BDA0003740121370000076
Wherein
Figure BDA0003740121370000077
Is the minimum creep strain rate, which is independent of applied stress and temperature.
Based on equation (5), chi and M (1 + phi) were calculated using the creep life corresponding to the different stresses shown in FIG. 3.
Figure BDA0003740121370000078
Wherein t is f For uniaxial creep life, σ is uniaxial cross-sectional stress.
Then substituting M into
Figure BDA0003740121370000079
And performing curve fitting by using data processing software to obtain phi.
Table 3 shows creep life and creep strain corresponding to different notch sizes of GH4169 nickel-based single crystal superalloy under multiaxial stress at 650 ℃ and a section load of 750 MPa. The method comprises the following specific steps:
Figure BDA0003740121370000081
table 4 shows the parameters of GH4169 superalloy materials at 650 ℃.
Figure BDA0003740121370000082
Embedding the creep-damage constitutive model into ABAQUS via FORTRAN language by the method described in step two. FIG. 4 is a simplified two-dimensional model of a cylindrical bar stock with a C-shaped notch built in ABAQUS/CAE.
Obtaining the section only corresponding to the notch structure morphology as described in the third stepPoint position curves. Given creep rate
Figure BDA0003740121370000083
The load was 200MPa, and the corresponding a value was calculated by equation (4) using the norton model constant n =1, 3, 5, 7, or 10. For five different sets of n values and corresponding a values, input into the user subroutine UMAT based on the norton model, creep simulations were performed in ABAQUS. When the creep second stage is reached, drawing a distribution curve of Mises stress at the notch section along the notch section, wherein the intersection point of a plurality of curves is the node position. FIG. 5 shows the node positions of the test sample piece with the notch radius of 1mm, and the distance from the node to the root of the notch is about 1.125mm.
In both references 1 and 2, the notch size is described using the degree of notch d/r in order to better define the notch topographic size. Fig. 6 (a) (b) shows the mises stress distribution of the notch section of the notch sample at D =10, D =6, r =2 and D =20, D =16, r =2, respectively, at n =1, 3, 5, 7, or 10, and it was found that the node positions are all approximately 1.5mm from the notch root. This means that when the difference between D and D is not changed, the values of D and D are increased or decreased simultaneously, and the distance from the node to the root of the gap is not changed all the time without changing the radius of the gap. That is to say, the size of D is independent of the position of the node on the premise that D-D is not changed. Therefore, in order to more accurately represent the notch size parameters influencing the node positions, the notch sharpness is represented by 2 r/(D-D), the relative notch depth is represented by (D-D)/D, and the relative node positions are represented by 2 r/(D-D). Where (D-D)/2 is the actual notch depth distance, and a notch is described as a C-type notch when the notch sharpness is greater than or equal to 1, and a notch can be described as a U-type notch when the notch sharpness is less than 1.
Reference to the literature
[1]S.Goyal,K.Laha,Creep life prediction of 9Cr–1Mo steel under multiaxial state of stress,Materials Science and Engineering:A.615(2014)348–360.https://doi.org/10.1016/j.msea.2014.07.096.
[2]Y.Chang,H.Xu,Y.Ni,X.Lan,H.Li,The effect of multiaxial stress state on creep behavior and fracture mechanism of P92 steel,Materials Science and Engineering:A.636(2015)70–76.https://doi.org/10.1016/j.msea.2015.03.056.
TABLE 5 finite element simulation of distances from the nodes of the sample pieces with different notch sizes to the root of the notch
Figure BDA0003740121370000091
Figure BDA0003740121370000101
The node position curve in fig. 7 is obtained by analyzing and fitting the positions of these nodes, and the fitting formula is equation (6). Fig. 8 is a graph of the relative error of the curve predicted node position from the node positions described in references 1 and 2. The relative error is within two times of the error band. The node position can be directly calculated in the engineering practice by equation (6).
Step four, determining the maximum main stress of the GH4169 nickel-based single crystal superalloy at the node on the notch section through finite element simulation
Figure BDA0003740121370000102
And Mises stress
Figure BDA0003740121370000103
And step five, after the relevant stress is obtained in the step three and the step four, calculating the creep-damage life under the multi-axial stress state based on the formula (7) and the formula (8).
Figure BDA0003740121370000104
Figure BDA0003740121370000105
Wherein t is f For creep life under multiaxial stress, σ rep For the reference stress in the multi-axial stress state,
Figure BDA0003740121370000106
is the maximum principal stress at the node point,
Figure BDA0003740121370000107
is the Mises stress at the node, σ net Is the section stress. Alpha is a stress correction parameter.
When σ is rep /σ net >1, the notch has a weakening effect on the specimen, when σ rep /σ net <1, the notch has a reinforcing effect on the sample. In addition to this, the present invention is,
Figure BDA0003740121370000108
the relationship of (c) always exists.
Further, the method for obtaining the stress correction parameter α is as follows:
taking α =0, 0.2, 0.4, 0.6, 0.8 or 1, the corresponding σ is obtained by calculation from formula (8) rep Then, the creep life is calculated from the formula (7). As shown in fig. 9, when the value α is plotted on the abscissa and the creep life is plotted on the ordinate, and a horizontal line parallel to the abscissa is plotted on the ordinate according to the known creep life, it is found that the intersection of the horizontal line and the life curve is a straight line perpendicular to the ordinate and finally intersects the abscissa, and the value α at the intersection with the abscissa is the accurate value α. And calculating the stress correction parameter alpha =0.51 of the GH4169 nickel-based single crystal superalloy at 650 ℃.
Based on the obtained material stress correction parameter α, the creep damage life of the notched sample can be calculated from the formula (7) and the formula (8). FIG. 10 is a comparison graph of calculated lifetime and experimental lifetime, and the error is found to be within 13.02%, so that the method is practical, convenient and effective in engineering practice.
In addition, fig. 11 and 12 show the progress of damage with creep time in the notch cross section when the notch sharpness is 0.2 and 1.6, respectively, where fig. 11 (a) and 12 (a) are 0.001tf and fig. 11 (b) and 12 (b) are tf.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1.A method for predicting the service life of a material in a multiaxial stress state is characterized by comprising the following steps:
the method comprises the following steps: performing a material uniaxial creep rupture experiment, respectively obtaining creep curves of the material under a plurality of uniaxial stress loads, and obtaining material parameters in the continuous damage mechanical model based on the plurality of uniaxial creep curves;
step two: establishing a finite element model in ABAQUS, and defining a material creep-damage constitutive model based on a continuous damage mechanical model by using a user subprogram UMAT;
step three: obtaining node positions corresponding to different gaps through a node position curve;
step four: calculating to obtain the maximum main stress at each node on the corresponding notch section when the stress of the relevant section is loaded based on a crop module in finite element software ABAQUS
Figure FDA0003740121360000011
And Mises stress
Figure FDA0003740121360000012
Step five: obtained based on step four
Figure FDA0003740121360000013
And
Figure FDA0003740121360000014
and calculating the creep-damage life under the corresponding multi-axis stress state by using a node stress method and a life calculation formula.
2. A method of predicting the lifetime of a material under multiaxial stress conditions as recited in claim 1, characterized in that the material parameters in the first step comprise A,B、M、n、m、n 0 Chi and phi, A, B, M, n, M, n 0 And chi and phi are material constants related to temperature in a continuous damage mechanics model and are calculated by fitting a uniaxial creep test curve.
3. The method of claim 2, wherein the uniaxial creep curve fitting method is as follows:
Figure FDA0003740121360000015
wherein A and n are Norton's equations
Figure FDA0003740121360000016
The material parameters in (2) need to be determined by at least two uniaxial creep curves of different stresses at least the same temperature,
Figure FDA0003740121360000017
is a minimum creep strain rate, which is independent of applied stress and temperature;
Figure FDA0003740121360000018
wherein t is f For uniaxial creep life, σ is uniaxial section stress;
based on the formula
Figure FDA0003740121360000019
And obtaining M, chi and phi by using creep life fitting corresponding to different stresses.
4. The method for predicting the service life of the material under the multiaxial stress state as recited in claim 1, wherein the material creep-damage constitutive model based on the continuous damage mechanical model in the second step is as follows:
Figure FDA00037401213600000110
Figure FDA00037401213600000111
σ rep ＝ασ 1 +(1-α)σ e
wherein
Figure FDA00037401213600000112
For creep rate, the magnitude of ω is 0 to 1 representing creep damage, σ 1 Is the maximum principal stress, σ e Is the equivalent stress, σ rep Is representative of stress, alpha is a parameter related to the material creep failure mechanism, and the numerical value is from 0 to 1.
5. The method for predicting the service life of the material in the multiaxial stress state as claimed in claim 1, wherein the process of obtaining the node positions corresponding to different notches through the node position curve in the third step is as follows: firstly, counting node positions corresponding to different notch morphology parameters, then fitting to obtain a curve equation, namely a node position curve, and based on the curve, directly calculating the node positions through the notch morphology in an actual problem, wherein the method specifically comprises the following steps:
given creep rate
Figure FDA0003740121360000021
And load, selecting a Nuon model constant n, and obtaining the load through a formula
Figure FDA0003740121360000022
Calculating corresponding A values, inputting different n values and corresponding A values into a user subprogram UMAT based on a Nonton model, carrying out creep simulation in ABAQUS, and drawing a distribution curve of Mises stress at the notch section along the notch section when reaching a second stage of creep,the intersection of the curves is the node position.
6. The method for predicting the service life of the material under the multiaxial stress state as recited in claim 5, wherein a parametric process and a curve equation for drawing a node position curve are as follows:
using 2 r/(D-D) to represent the notch sharpness, (D-D)/D to represent the notch depth, and 2 r/(D-D) to represent the normalized nodal position, wherein D is the smooth specimen notch cross-section diameter, D is the diameter at the notch cross-section, r is the notch radius * The distance between the node position and the root of the notch is (D-D)/2, the actual notch depth is, when the notch degree is more than or equal to 1, the notch is a C-shaped notch, and when the notch degree is less than 1, the notch is a U-shaped notch;
drawing a notch position curve by the notch acutance and the corresponding normalized node position, wherein the curve equation is as follows:
y＝0.7410x 0.5483
where x =2 r/(D-D) is expressed as notch sharpness, y =2r * and/D-D is expressed as normalized node position.
7. The method for predicting the service life of the material under the multiaxial stress state as claimed in claim 1, wherein the calculation process of the creep-damage service life under the multiaxial stress state in the step five is as follows:
Figure FDA0003740121360000023
Figure FDA0003740121360000024
wherein t is f For creep life under multiaxial stress, σ rep For the reference stress in the multi-axial stress state,
Figure FDA0003740121360000025
is the most at the nodeThe high principal stress is a function of the stress,
Figure FDA0003740121360000026
is the Mises stress at the node, σ net Is section stress, alpha is a stress correction parameter;
wherein when σ rep /σ net >1, the notch has a weakening effect on the sample, when σ rep /σ net <1, the notch has a reinforcing effect on the sample, and,
Figure FDA0003740121360000027
8. the method for predicting the service life of the material under the multiaxial stress state as recited in claim 7, wherein the stress correction parameter α is obtained as follows:
selecting alpha value, from formula
Figure FDA0003740121360000028
Calculating to obtain corresponding sigma rep And then by the formula
Figure FDA0003740121360000031
Calculating the creep life, taking the value of alpha as an abscissa and the creep life as an ordinate, and making a transverse line parallel to the abscissa at the ordinate according to the known creep life, wherein the intersection point of the transverse line and the life curve is a straight line perpendicular to the coordinate and is finally intersected with the abscissa, and the value of alpha at the intersection point of the transverse line and the abscissa is the accurate value of alpha.
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Publication number Priority date Publication date Assignee Title
CN115982958A (en) * 2022-12-07 2023-04-18 南京工业大学 Material creep fatigue life prediction method based on engineering damage mechanics

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115982958A (en) * 2022-12-07 2023-04-18 南京工业大学 Material creep fatigue life prediction method based on engineering damage mechanics
CN115982958B (en) * 2022-12-07 2023-10-13 南京工业大学 Material creep fatigue life prediction method based on engineering damage mechanics

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