A method for predicting the life of a material under a multi-axial stress state
A method combining material experiments and finite element analysis using ABAQUS software addresses the challenge of multi-axial stress lifespan prediction, offering efficient and accurate lifespan prediction for high-temperature components.
Patent Information
- Application Number
- CN202210809588.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-07-11
- Publication Date
- 2025-07-15
- Estimated Expiration
- 2042-07-11
AI Technical Summary
In the fields of aerospace and nuclear power, there is a lack of effective methods for predicting creep life of materials under multi-axis stress. The existing methods are cumbersome or inaccurate and difficult to apply to engineering design.
The continuous damage mechanics model was used to obtain material parameters through uniaxial creep fracture experiments, and a finite element model was established in ABAQUS. The creep-damage life calculation was performed under multi-axis stress state using the node stress method, including material parameter fitting and the drawing of node position curves.
It provides a simple, convenient and efficient method for creep life prediction under multi-axis stress states, which improves the accuracy and applicability of prediction, is suitable for various metal materials and temperature states, and reduces the cost of design optimization and performance evaluation.
Smart Images
Figure CN115204013B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of material life prediction, and in particular relates to a method for predicting the life of a material under a multi-axial stress state. Background Art
[0002] In the fields of aerospace and nuclear power, there are many important components that are subject to high temperature, high pressure, and high-speed loads during operation, such as the turbine disks of aircraft engines and gas turbines, most of which fracture failures occur in the slot connection structure. As these high-load hot end components, there are many factors that affect the life of the slot connection structure, including creep deformation and fracture under high temperature and long-term operation, low-cycle fatigue caused by repeated changes in working conditions, high-cycle fatigue caused by vibration, high-temperature gas corrosion, oxidation, etc. Generally speaking, creep fracture and low-cycle fatigue play a decisive role, and these components are usually in a complex multi-axial stress field. The study of the creep behavior of these materials and the prediction of multi-axial creep life is of great significance.
[0003] In the current engineering field, most of the material data under uniaxial stress state are used, and there is a lack of design methods and evaluation means that meet the reliability of structures under multiaxial stress. In recent years, domestic and foreign researchers have carried out a lot of research on creep rupture behavior under multiaxial stress state in the academic field, and proposed a large number of creep-damage calculation models based on commercial finite element software, such as crystal plasticity model, continuous damage mechanics model and phenomenological constitutive model to describe creep behavior. Among them, the crystal plasticity model can accurately describe the stress-strain behavior at the microscopic level during creep, which is suitable for basic scientific research, but it is difficult to use for macro performance evaluation in engineering; the continuous damage mechanics model can accurately reflect the creep behavior of materials under multiaxial stress state, and it is also the most widely used calculation model in related research, but most of the current related life prediction methods are complex and cumbersome, and it is difficult to effectively apply them to the engineering field; and a large number of non-unified phenomenological constitutive models are acceptable for qualitative research on creep process, but they are not suitable for life prediction of creep rupture under multiaxial stress. Various prediction methods are either cumbersome or inaccurate and comprehensive. Therefore, there is currently a lack of effective multiaxial creep life prediction methods in the engineering field. Summary of the invention
[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a simple, convenient, efficient and accurate method for predicting creep life under multi-axial stress state, so as to realize the remaining life prediction, performance evaluation and design optimization of hot end high-temperature components at a lower cost and more efficiently.
[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:
[0006] A method for predicting the life of a material under a multiaxial stress state comprises the following steps:
[0007] Step 1: Conduct a uniaxial creep fracture experiment on the material to obtain the creep curves of the material under multiple uniaxial stress loadings respectively. Based on the multiple uniaxial creep curves, obtain the material parameters in the continuous damage mechanics model.
[0008] Step 2: Establish a finite element model in ABAQUS and use the user subroutine UMAT to define the creep-damage constitutive model of the material based on the continuous damage mechanics model.
[0009] Step 3: Obtain the node positions corresponding to different notches through the node position curve.
[0010] Step 4: Calculate the maximum principal stress at each node on the notch cross-section corresponding to the relevant cross-section stress loading based on the creep module in the finite element software ABAQUS and the Mises stress
[0011] Step 5: Based on those obtained in Step 4 and Use the node stress method and the life calculation formula to calculate the creep-damage life under the corresponding multiaxial stress state.
[0012] The material parameters described in Step 1 include A, B, M, n, m, n0, χ, and φ. A, B, M, n, m, n0, χ, and φ are material constants related to temperature in the continuous damage mechanics model, which are obtained by fitting and calculating the uniaxial creep test curves.
[0013] The uniaxial creep curve fitting method is as follows:
[0014]
[0015] Among them, A and n are the material parameters in the Norton equation , and at least two uniaxial creep curves with different stresses at the same temperature are required to determine them. is the minimum creep strain rate, which is independent of the applied stress and temperature;
[0016]
[0017] where t f is the uniaxial creep life and σ is the uniaxial cross-section stress;
[0018] Based on the formula Use the creep life corresponding to different stresses to fit and obtain M, χ, and φ.
[0019] The creep-damage constitutive model of the material based on the continuous damage mechanics model described in Step 2 is as follows:
[0020]
[0021]
[0022] σ rep = ασ1 + (1 - α)σ e
[0023] where is the creep rate, the value of ω ranges from 0 to 1 representing creep damage, σ1 is the maximum principal stress, and σ e is the equivalent stress, and σ rep is the representative stress, and α is a parameter related to the creep failure mechanism of the material, with a value ranging from 0 to 1.
[0024] The process of obtaining the node positions corresponding to different notches through the node position curve in Step 3 is as follows: First, count the node positions corresponding to different notch morphology parameters, and then perform fitting to obtain the curve equation, that is, the node position curve. Based on this curve, in practical problems, the node positions can be directly calculated through the notch morphology, as follows:
[0025] Given the creep rate and the load, select the Norton model constant n, and calculate the corresponding A value through the formula Input the different n values and the corresponding A values into the user subroutine UMAT based on the Norton model, and perform creep simulation in ABAQUS. When reaching the second stage of creep, plot the distribution curve of the Mises stress along the notch cross-section at the notch cross-section. The intersection points of multiple curves are the node positions.
[0026] The parameter process of plotting the node position curve and the curve equation are as follows:
[0027] Use 2r / (D - d) to represent the notch sharpness, (D - d) / D to represent the notch depth, and 2r* / (D - d) to represent the normalized node position. Where D is the diameter of the smooth specimen notch cross-section, d is the diameter at the notch cross-section, r is the notch radius, and r * is the distance of the node position from the notch root, (D - d) / 2 is the actual notch depth, and when the notch degree ≥ 1, the notch is a C-type notch, and when the notch degree < 1, the notch is a U-type notch;
[0028] Plot the notch position curve from the notch sharpness and the corresponding normalized node position. The curve equation is as follows:
[0029] y = 0.7410x 0.5483
[0030] where x = 2r / (D - d) represents the notch sharpness, and y = 2r * / (Dd) represents the normalized node position.
[0031] The creep-damage life calculation process under the multiaxial stress state described in step 5 is as follows:
[0032]
[0033]
[0034] where t f is the creep life under multiaxial stress, σ rep is the reference stress under multiaxial stress state, is the maximum principal stress at the node, is the Mises stress at the node, σ net is the cross-sectional stress, α is the stress correction parameter;
[0035] When σ rep / σ net >1, the notch has a weakening effect on the specimen. rep / σ net <1, the notch has a strengthening effect on the specimen; and
[0036] The method for obtaining the stress correction parameter α is as follows:
[0037] Select the value of α, according to the formula Calculate the corresponding σ rep , and then by the formula To calculate the creep life, take the value of α as the horizontal coordinate and the creep life as the vertical coordinate. Draw a horizontal line parallel to the horizontal coordinate at the vertical coordinate based on the known creep life. At this time, you will find that the intersection of the horizontal line and the life curve is connected to a straight line perpendicular to the coordinate, and finally intersects at the horizontal coordinate. At this time, the α value of the intersection with the horizontal coordinate is the precise α value.
[0038] Compared with the prior art, the present invention has the following beneficial effects:
[0039] The method for predicting the life of materials under multi-axial stress states of the present invention is applicable to various metal materials and the creep life prediction under various temperature states. Only by changing the relevant material parameters in the continuous damage mechanics model, it has a wide range of applications. This creep life prediction method is simple and convenient to operate, and can realize the design optimization, performance evaluation and remaining life prediction of hot-end high-temperature components with lower cost and higher efficiency. It is convenient for popularization and use. Secondly, by conducting uniaxial creep fracture experiments on materials, the creep curves of materials under multiple uniaxial stress loadings are respectively obtained. Based on multiple uniaxial creep curves, the material parameters in the continuous damage mechanics model are obtained. The material parameters are accurate and reliable, which improves the accuracy of experimental results. In addition, the present invention is different from other studies in the description of notch morphology parameters, and proposes an innovative parameter description, which describes the notch morphology more scientifically, reasonably and accurately, and further improves the accuracy of experimental results.
[0040] Furthermore, the creep-damage life prediction method of materials based on the nodal stress method under the c-notch structure of the present invention includes a universal nodal position curve. In engineering practice, the nodal position can be directly calculated from the notch morphology, which greatly reduces the workload of finding nodes. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 is a flowchart of the implementation mode of the present invention;
[0042] Figure 2 is a structural diagram of a notched cylindrical specimen under one implementation mode of the present invention;
[0043] Figure 3 is the creep curve of GH4169 nickel-based single crystal superalloy at 650 °C under different uniaxial stress loadings;
[0044] Figure 4 is the simplified finite element model established by the numerical simulation of the present invention in ABAQUS;
[0045] Figure 5 is the nodal position of the test specimen with a notch radius of 1 mm;
[0046] Figure 6 is the comparison diagram of the nodal positions under the same notch structure and different cross-sectional diameters;
[0047] Figure 7 is the nodal position curve of the materials of the present invention;
[0048] Figure 8 is the error comparison diagram of the calculated nodal position and the nodal position in related research;
[0049] Figure 9For the accurate determination of the material parameter α of the present invention, the two horizontal dashed lines are respectively the creep test lives at η = 0.2 and η = 0.4;
[0050] Figure 10 It is a comparison chart of the error between the predicted life and the experimental life;
[0051] Figure 11(a) shows the damage evolution at 0.001tf with creep time on the notch cross-section when the notch sharpness is 0.2;
[0052] Figure 11(b) shows the damage evolution with creep time on the notch cross-section when the notch sharpness is 0.2 at tf;
[0053] Figure 12(a) shows the damage evolution at 0.001tf with creep time on the notch cross-section when the notch sharpness is 1.6;
[0054] Figure 12(b) shows the damage evolution with creep time on the notch cross-section when the notch sharpness is 1.6 at tf. Specific implementation manner
[0055] The following further describes the present invention in conjunction with Figure 1-1 Appendix 2.
[0056] As Figure 1 shown, a method for predicting the life of a material under a multiaxial stress state includes the following steps:
[0057] Step 1: Conduct a uniaxial creep fracture experiment on the material, respectively obtain the creep curves of the material under multiple uniaxial stress loadings, and based on the multiple uniaxial creep curves, obtain the material parameters in the continuous damage mechanics model;
[0058] Step 2: Establish a finite element model in ABAQUS, and use the user subroutine UMAT to define the material creep-damage constitutive model based on the continuous damage mechanics model;
[0059] Step 3: Obtain the node positions corresponding to different notches through the node position curve;
[0060] Step 4: Based on the creep module in the finite element software ABAQUS, calculate the maximum principal stress at each node on the notch cross-section corresponding to the relevant cross-section stress loading and the Mises stress
[0061] Step 5: Based on the and obtained in Step 4, use the node stress method and the life calculation formula to calculate the creep-damage life under the corresponding multiaxial stress state.
[0062] Furthermore, the material parameters in Step 1 include A, B, M, n, m, n0, χ, and φ. A, B, M, n, m, n0, χ, and φ are material constants related to temperature in the continuous damage mechanics model, which are obtained by fitting and calculating the uniaxial creep test curve.
[0063] The method for fitting the uniaxial creep curve is as follows:
[0064]
[0065] Among them, A and n are the material parameters in the Norton equation and need to be determined by at least two uniaxial creep curves with different stresses at the same temperature. is the minimum creep strain rate, which is independent of the applied stress and temperature;
[0066]
[0067] where t f is the uniaxial creep life, and σ is the uniaxial cross-section stress;
[0068] Based on the formula M, χ, and φ are obtained by fitting the creep life corresponding to different stresses.
[0069] Furthermore, the material creep-damage constitutive model based on the continuous damage mechanics model in Step 2 is as follows:
[0070]
[0071]
[0072] σ rep = ασ1 + (1 - α)σ e
[0073] where is the creep rate, the value of ω represents creep damage from 0 to 1, σ1 is the maximum principal stress, σ e is the equivalent stress, σ rep is the representative stress, and α is a parameter related to the material creep failure mechanism, with a value ranging from 0 to 1.
[0074] Furthermore, the creep-damage constitutive model in Step 2 is embedded into ABAQUS through FORTRAN language. The finite element model of the C-notch of the cylindrical bar as the research object is established as follows:
[0075] In ABAQUS / CAE, a simplified two-dimensional model of the cylindrical bar with a C-notch is established, as Figure 2As shown, set the material properties, divide the mesh, establish a creep analysis step, and define the relevant required output variables to the ODB file.
[0076] Further, the process of obtaining the node positions corresponding to different notches through the node position curve in step three is as follows: First, count the node positions corresponding to different notch morphology parameters, and then perform fitting to obtain the curve equation, that is, the node position curve. Based on this curve, in practical problems, the node positions can be directly calculated through the notch morphology, specifically as follows:
[0077] Given the creep rate The load is 200 MPa, and the Norton model constants n = 1, 3, 5, 7, or 10 are taken. Through the formula Calculate the corresponding A values. For the five groups of different n values and the corresponding A values, input them into the user subroutine UMAT based on the Norton model, and perform creep simulation in ABAQUS. When the second stage of creep is reached, plot the distribution curve of the Mises stress along the notch cross-section at the notch cross-section. The intersection point of multiple curves is the node position.
[0078] Preferably, the node stress method, also known as the bone point stress method, indicates that in a multi-axial stress state of a component, as time changes during the creep process, the stress value at a certain point remains approximately constant. In addition, when the stress exponent n of the material is different, the stress value at this point also remains approximately constant. This point is called the node or bone point.
[0079] Further, the parameter process and curve equation for plotting the node position curve are as follows:
[0080] Use 2r / (D - d) to represent the notch sharpness, (D - d) / D to represent the notch depth, and 2r* / (D - d) to represent the normalized node position. Where D is the diameter of the smooth specimen notch cross-section, d is the diameter at the notch cross-section, r is the notch radius, and r * * is the distance of the node position from the notch root, (D - d) / 2 is the actual notch depth, and when the notch degree ≥ 1, the notch is a C-type notch, and when the notch degree < 1, the notch is a U-type notch. It is found that the notch depth has no effect on the normalized notch position, and there is a functional relationship between the notch sharpness and the normalized node position.
[0081] Draw the notch position curve from the notch sharpness and the corresponding normalized node position. This curve can be applied to all problems of the same type of notch in engineering practice. The curve equation is as follows:
[0082] y = 0.7410x 0.5483
[0083] Where, x = 2r / (D - d) represents the notch sharpness, and y = 2r * * / (D - d) represents the normalized node position.
[0084] Further, the creep-damage life calculation process under the multi-axial stress state described in Step 5 is as follows:
[0085] After obtaining the relevant stresses in Steps 3 and 4, based on the formula and the formula the life is calculated.
[0086] Where t f is the creep life under multi-axial stress, σ rep is the reference stress under the multi-axial stress state, is the maximum principal stress at the node, is the Mises stress at the node, σ net is the sectional stress, and α is the stress correction parameter;
[0087] Where when σ rep / σ net > 1, the notch has a weakening effect on the specimen, and when σ rep / σ net < 1, the notch has a strengthening effect on the specimen; and,
[0088] The method for obtaining the stress correction parameter α is as follows:
[0089] Take α = 0, 0.2, 0.4, 0.6, 0.8 or 1, and calculate the corresponding σ using the formula, and then calculate the creep life using the formula rep . As shown in , taking the value of α as the abscissa and the creep life as the ordinate, draw a horizontal line parallel to the abscissa at the known creep life on the ordinate. At this time, it will be found that the intersection points of the horizontal line and the life curve are connected by a straight line perpendicular to the coordinate, and finally intersect at the abscissa. At this time, the α value at the intersection point with the abscissa is the accurate α value. Figure 9 Preferably, the following is the creep-damage life prediction of the second-generation nickel-based single-crystal superalloy GH4169 material under the C-type notch multi-axial stress shown in
[0090] . Figure 2 Table 1 shows the material composition (wt%) of the second-generation nickel-based single-crystal superalloy GH4169.
[0091] Table 2 shows the dimensions of the notch structures in
[0092]
[0093] . Figure 2 each group.
[0094]
[0095] The creep-strain curves of GH4169 superalloy under loading stresses of 750 MPa and 700 MPa are obtained through uniaxial creep fracture experiments at 650 °C. Based on multiple uniaxial creep curves, relevant calculations are carried out to obtain the material parameters in the continuous damage mechanics model. The continuous damage mechanics model is as follows
[0096]
[0097]
[0098] σ rep = ασ1+(1 - α)σ e (3)
[0099] Where is the creep rate, the value of ω ranges from 0 to 1 representing creep damage, σ1 is the maximum principal stress, σ e is the equivalent stress, σ rep is the representative stress, α is a parameter related to the creep failure mechanism of the material, and its value ranges from 0 to 1. A, B, M, n, m, n0, χ, and φ are material constants related to temperature in the continuous damage mechanics model, which are obtained by fitting calculation from the uniaxial creep test curves. The fitting process of the material parameters of GH4169 superalloy at 650 °C is as follows
[0100] Figure 3 is the creep curve of GH4169 nickel-based single crystal superalloy at 650 °C under different uniaxial stress loads. From Figure 3 two creep curves, the material parameters A and n are calculated through the Norton equation (4).
[0101]
[0102] Where is the minimum creep strain rate, which is independent of the applied stress and temperature.
[0103] Based on formula (5), χ and M(1 + φ) are calculated using the creep lives corresponding to different stresses shown in Figure 3 .
[0104]
[0105] Where t f is the uniaxial creep life, and σ is the uniaxial cross-section stress.
[0106] Then M is substituted into and curve fitting is performed using data processing software to obtain φ.
[0107] Table 3 shows the creep life and creep strain corresponding to different notch sizes of GH4169 nickel-based single crystal superalloy under multiaxial stress at a cross-sectional load of 750 MPa and a temperature of 650 °C. The details are as follows:
[0108]
[0109] Table 4 shows the material parameters of GH4169 superalloy at 650 °C.
[0110]
[0111] Through the method described in Step 2, the creep-damage constitutive model is embedded in ABAQUS using FORTRAN language. Figure 4 It is a simplified two-dimensional model of a C-notch cylindrical bar established in ABAQUS / CAE.
[0112] As described in Step 3, a node position curve corresponding only to the notch structure morphology needs to be obtained. Given the creep rate When the load is 200 MPa, taking the Norton model constants n = 1, 3, 5, 7, or 10, the corresponding A values are calculated through formula (4). For the five groups of different n values and the corresponding A values, they are input into the user subroutine UMAT based on the Norton model, and creep simulation is carried out in ABAQUS. When the second stage of creep is reached, the distribution curve of the Mises stress along the notch cross-section at the notch cross-section is plotted, and the intersection of multiple curves is the node position. Figure 5 This is the node position of the test specimen with a notch radius of 1 mm, and the distance from the node to the notch root is approximately 1.125 mm.
[0113] In References 1 and 2, in order to better define the notch morphology size, the notch degree d / r is used to describe the notch size. Figure 6 Figures (a) and (b) respectively show the mises stress distributions of the notch cross-sections of notch specimens with D = 10, d = 6, r = 2 and D = 20, d = 16, r = 2 at n = 1, 3, 5, 7, or 10, and it is found that the node positions are approximately at 1.5 mm from the notch root. This shows that when the difference between D and d remains unchanged, while increasing or decreasing the values of D and d simultaneously without changing the notch radius, the distance from the node to the notch root always remains unchanged. That is to say, on the premise that D - d remains unchanged, the size of d has nothing to do with the position of the node. Therefore, in order to more accurately represent the notch size parameter affecting the node position, in the present invention, 2r / (D - d) is used to represent the notch sharpness, (D - d) / D is used to represent the relative notch depth, and 2r* / (D - d) is used to represent the relative node position. Among them, (D - d) / 2 is the actual notch depth distance, and when the notch sharpness ≥ 1, the notch is described as a C-notch, and when the notch sharpness < 1, the notch can be described as a U-notch.
[0114] References
[0115] [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.
[0116] [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.
[0117] Table 5 shows the distance from the nodes of the specimens with different notch sizes to the notch root obtained by finite element simulation
[0118]
[0119]
[0120] The position curves of the nodes in Figure 7 were obtained by fitting through the analysis of the positions of these nodes, and the fitting formula is Equation (6). Figure 8 is the relative error between the predicted node positions of this curve and the node positions described in References 1 and 2. The relative error is within twice the error band. Then the node positions can be directly calculated by Equation (6) in engineering practice.
[0121] Step 4 Determine the maximum principal stress at the nodes on the notch section of the GH4169 nickel-based single crystal superalloy by finite element simulation and the Mises stress
[0122] Step 5 After obtaining the relevant stresses in Steps 3 and 4, calculate the creep-damage life under multiaxial stress state based on Formulas (7) and (8).
[0123]
[0124]
[0125] where t f is the creep life under multiaxial stress, σ rep is the reference stress under multiaxial stress state, is the maximum principal stress at the node, is the Mises stress at the node, σ net is the cross-sectional stress. α is the stress correction parameter.
[0126] 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 specimen. In addition, always exists.
[0127] Furthermore, the method for obtaining the stress correction parameter α is as follows:
[0128] Take α = 0, 0.2, 0.4, 0.6, 0.8 or 1, and calculate the corresponding σ rep by formula (8), and then calculate the creep life by formula (7). As Figure 9 shown, with the value of α as the abscissa and the creep life as the ordinate, draw a horizontal line parallel to the abscissa at the ordinate according to the known creep life. At this time, it will be found that the connection of the intersection points of the horizontal line and the life curve is a straight line perpendicular to the coordinate, and finally intersects the abscissa. At this time, the α value at the intersection point with the abscissa is the accurate α value. The stress correction parameter α of the GH4169 nickel-based single crystal superalloy at 650 °C is calculated to be 0.51.
[0129] Based on the obtained material stress correction parameter α, the creep damage life of the notched specimen can be calculated by formula (7) and formula (8). Figure 10 is the comparison diagram of the calculated life and the experimental life. It is found that the error is within 13.02%. Therefore, the present invention is practical, convenient and effective in engineering practice.
[0130] In addition, FIGS. 11 and 12 are the damage evolutions of the notch cross-section with creep time when the notch sharpness is 0.2 and 1.6 respectively. FIGS. 11(a) and 12(a) are 0.001tf, and FIGS. 11(b) and 12(b) are tf.
[0131] In summary, the above are only the preferred embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims
1. A method for predicting the life of a material under a multi-axial stress state, characterized in that, It includes the following steps: Step 1: Conduct a uniaxial creep fracture experiment on the material to obtain the creep curves of the material under multiple uniaxial stress loadings respectively. Based on the multiple uniaxial creep curves, obtain the material parameters in the continuous damage mechanics model; Step 2: Establish a finite element model in ABAQUS and use the user subroutine UMAT to define the material creep-damage constitutive model based on the continuous damage mechanics model; Step 3: Obtain the node positions corresponding to different notches through the node position curve; Step 4: Calculate the maximum principal stress at each node on the notch cross-section corresponding to the stress loading of the relevant cross-section based on the creep module in the finite element software ABAQUS and the Mises stress Step 5: Based on what is obtained in Step 4 and use the node stress method and the life calculation formula to calculate the creep-damage life under the corresponding multiaxial stress state; The calculation process of the creep-damage life under the multiaxial stress state is as follows: where t f is the creep life under multiaxial stress, σ rep is the reference stress under multiaxial stress state, is the maximum principal stress at the node, is the Mises stress at the node, σ net is the sectional stress, and α is the stress correction parameter; Where 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 specimen, and, 2. The life prediction method of a material under a multi-axial stress state according to claim 1, characterized in that, The material parameters in Step 1 include A, B, M, n, m, n0, χ, and φ. A, B, M, n, m, n0, χ, and φ are temperature-related material constants in the continuous damage mechanics model, which are obtained by fitting calculation from the uniaxial creep test curves.
3. The life prediction method of a material under a multi-axial stress state according to claim 2, characterized in that, The uniaxial creep curve fitting method is as follows: where A and n are material parameters in the Norton equation and need to be determined using at least two uniaxial creep curves at different stresses at the same temperature is the minimum creep strain rate, which is independent of the applied stress and temperature; where t f is the uniaxial creep life and σ is the uniaxial cross-sectional stress; Based on the formula M, χ, and φ are obtained by fitting the creep lives corresponding to different stresses.
4. A method for predicting the life of a material under a multi-axial stress state according to claim 2, characterized in that, The material creep-damage constitutive model based on the continuous damage mechanics model in Step 2 is as follows: σ rep = ασ1+(1 - α)σ e Among them is the creep rate, the value of ω ranges from 0 to 1 representing creep damage, σ1 is the maximum principal stress, σ e is the equivalent stress, σ rep is the representative stress, α is a parameter related to the creep failure mechanism of the material, and its value ranges from 0 to 1.
5. The method for predicting the life of a material under a multi-axial stress state according to claim 2, wherein The process of obtaining the node positions corresponding to different notches through the node position curve in Step 3 is as follows: First, count the node positions corresponding to different notch morphology parameters, and then perform fitting to obtain the curve equation, that is, the node position curve. Based on this curve, in practical problems, the node positions can be directly calculated through the notch morphology, specifically as follows: Given creep rate and load, select the Norton model constant n, and calculate the corresponding A value through the formula For different n values and their corresponding A values, input them into the user subroutine UMAT based on the Norton model, and perform creep simulation in ABAQUS. When the second stage of creep is reached, plot the distribution curve of the Mises stress along the notch cross-section at the notch cross-section. The intersection point of multiple curves is the node position.
6. The life prediction method of a material under a multi-axial stress state according to claim 5, characterized in that, The parameter process for drawing the node position curve and the curve equation are as follows: The notch sharpness is represented by 2r / (D-d), the notch depth is represented by (D-d) / D, and the normalized node position is represented by 2r* / (D-d), where D is the diameter of the smooth specimen notch cross-section, d is the diameter at the notch cross-section, r is the notch radius, and r * is the distance from the node position to the notch root, (D-d) / 2 is the actual notch depth, and when the notch degree ≥ 1, the notch is a C-type notch, and when the notch degree < 1, the notch is a U-type notch; Draw the notch position curve from the notch sharpness and the corresponding normalized node position. The curve equation is as follows: y = 0.7410x 0.5483 Among them, x = 2r / (D - d) represents the notch sharpness, and y = 2r * / (D - d) represents the normalized node position.
7. The life prediction method of a material under a multi-axial stress state according to claim 1, wherein, The method for obtaining the stress correction parameter α is as follows: Select the value of α, according to the formula Calculate the corresponding σ rep , and then by the formula To calculate the creep life, take the value of α as the horizontal coordinate and the creep life as the vertical coordinate. Draw a horizontal line parallel to the horizontal coordinate at the vertical coordinate based on the known creep life. At this time, you will find that the intersection of the horizontal line and the life curve is connected to a straight line perpendicular to the coordinate, and finally intersects at the horizontal coordinate. At this time, the α value of the intersection with the horizontal coordinate is the precise α value.