General model and method for predicting fatigue life of structure with defects

Abstract

The invention relates to the technical field of fatigue strength evaluation of mechanical structures, and provides a universal model and method for predicting the fatigue life of a structure with defects, finite element models with defects are respectively established according to different defect information, and the fatigue life of the structure with the defects is solved based on fatigue analysis software; in combination with a Z parameter model, obtaining a Z parameter under each defect according to the established finite element model containing the defects; establishing linear correlation between the obtained fatigue life and a Z parameter, and fitting all obtained data points to obtain a fatigue life prediction formula; and calculating a Z parameter value according to actually detected defect information, and substituting the Z parameter value into a fatigue life prediction formula to complete fatigue life prediction. By expanding the applicability of the Z parameter to the whole service cycle of short service life and long service life and perfecting related parameters in the Z parameter, a universal model and method are provided for predicting the fatigue life of a structure containing defects.

Description

Technical Field

[0001] This invention relates to the technical field of fatigue strength assessment of mechanical structures, and in particular to a general model and method for predicting the fatigue life of structures with defects. Background Technology

[0002] The increasing complexity of engineering structures and the harsher service environments have led to the growing prevalence of defective structures. These defects may originate from material smelting, manufacturing, assembly processes, or cumulative damage during long-term service. For example, defects are inevitably introduced during the forming or manufacturing of metal structures, especially welded structures, and their presence significantly reduces service life. For structures subjected to cyclic loading, fatigue failure is one of the most prevalent failure modes, characterized by its suddenness and catastrophic nature. Among the many factors inducing fatigue failure, internal structural defects (such as inclusions and porosity) are widely recognized as the most threatening source. Compared to surface defects, internal defects are often more concealed, making it difficult for conventional non-destructive testing methods to effectively identify and accurately assess their condition, resulting in insufficient assessment of the severity of internal defects in engineering practice. In fact, under cyclic loading, these internal defects easily become areas of high stress concentration, becoming the source of microcrack initiation and propagation, ultimately leading to component fracture after long-term service at relatively low stress levels.

[0003] As long-term structural service life becomes a new trend, traditional design methods based on material fatigue limits are no longer sufficient to address the new challenges to structural safety and reliability. There is an urgent need to develop new fracture prevention methods, and damage caused by internal defects has become a critical problem that must be overcome. For example, Chinese patent CN117171943A, entitled "A Method for Fatigue Life Reliability Analysis of Welded Joints Considering Defect Distribution Laws," constructs a fatigue life model for welded structures containing defects. Chinese patent CN112881208A, entitled "A Method for Equivalent Initial Defect Size Measurement and Evaluation," achieves fatigue safety assessment of structures by simulating group fatigue tests of materials under durability load spectra. Existing technologies also explore the influence of the distribution density and size of surface and internal inclusion defects on crack initiation from a probability distribution perspective. However, existing solutions still cannot establish the relationship between defects and fatigue life, and cannot predict the fatigue life of components containing internal defects.

[0004] Therefore, there is an urgent need for those skilled in the art to design a model and method that can link defects to both short and long lifespans, providing a general model and method for predicting the fatigue life of structures with defects. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for predicting the fatigue life of a defective structure, the method comprising: S1. Based on different defect information, establish finite element models containing defects, and solve for the fatigue life of the defective structure using fatigue analysis software; the defect information includes the location, size, type, and shape of the defect. S2, combined Z The parametric model, based on the established finite element model containing defects, obtains the parameters for each defect. Z Parameters; S3, combine the fatigue life obtained in step S1 with... Z A linear relationship is established between the parameters, and all the obtained data points are fitted to obtain the fatigue life prediction formula; S4 is calculated based on the actual detected defect information. Z The parameter values ​​are substituted into the fatigue life prediction formula to complete the fatigue life prediction. The prediction is also calculated using defect information detected by methods such as ultrasound, X-ray, or CT. Z Parameter value.

[0006] Furthermore, the finite element model containing defects is established as a flat plate.

[0007] Furthermore, the finite element model containing defects undergoes the following processing: a. Set boundary conditions for the finite element model and apply fatigue loads. The boundary conditions are as follows: One side of the finite element model is completely fixed, and a fixed fatigue load (monotropic load) is applied to the other side. In order to ensure the uniform deformation of the finite element model as a whole, the displacement in the non-force direction in the entire finite element model is constrained. b. Mesh the finite element model. The specific steps for mesh generation are as follows: The finite element model is divided along the three dividing planes by creating a plane along the circumferential, axial and radial directions of the defect. In order to ensure the accuracy of the calculation results around the defect, it is necessary to refine the local mesh around the defect. The method of local mesh refinement is to use a transition mesh with decreasing mesh size around the defect to achieve local refinement.

[0008] Furthermore, the specific steps for obtaining the fatigue life of a defective structure based on fatigue analysis software are as follows: First, the finite element model is solved using finite element software to obtain a result file containing the stress and strain of the model. The result file is in odb format and contains principal stresses, principal strains, shear strains, and nodal stresses. The results file is then imported into fatigue analysis software. Material parameters, fatigue life model, and load spectrum are set, and the fatigue life of the defective structure is obtained. The fatigue analysis software is Fe-safe (a finite element software plugin). The number of fatigue cycles is counted using the rainflow counting algorithm at each node of the fatigue life model, and the fatigue life can be solved. Finally, the fatigue life results of the defective structure and the life result cloud map are obtained.

[0009] Furthermore, the material parameter is only the elastic modulus. During the fatigue analysis software calculation, the Neuber formula is used to perform an elastoplastic transformation of the material to improve the accuracy of the calculation. The Neuber formula is:

[0010] In the formula, This is the theoretical stress concentration factor. ,in The solution is an elastic finite element method (the stress at the root of the notch is calculated directly through linear elastic finite element analysis (FEA), neglecting plastic deformation). , E The elastic modulus of the material; The nominal stress (average stress away from the notch); The stress concentration factor is... ,in This is the Neuber method modified solution (which modifies the elastic solution into an elastoplastic solution through energy equivalence); The strain concentration factor is... ,in In order to respond nominally, ; Furthermore, by selecting defect-free materials and processing them into standard specimen sizes for fatigue testing, the parameters required for the fatigue life model are obtained, specifically: The fatigue life model is the SWT fatigue life model. Defect-free material is processed into standard fatigue specimens, and fatigue tests are conducted on a hydraulic servo fatigue testing machine. The obtained fatigue test results are plotted on a double logarithmic coordinate system, and the plastic strain amplitude of the fatigue test results is expressed as... With fatigue life N f Perform linear regression to obtain the intercept A and slope B, and then calculate the fatigue strength index. b and fatigue ductility index c The value of is used to determine the plastic strain amplitude-life relationship in the plastic dominant region.

[0011] Furthermore, since a fixed fatigue load (monotonic load) is applied to the other side of the finite element model, a load spectrum is defined in the fatigue analysis software. Then, the stress-strain parameters from the final incremental step in the finite element analysis are input into the fatigue analysis software, the stress ratio and time history are defined, and the required load spectrum is generated. For nonlinear problems, the relationship between displacement and load is nonlinear, so the entire analysis step cannot be solved in one step. Therefore, it is necessary to decompose the entire analysis step into multiple incremental steps and solve them sequentially, gradually obtaining the final response of the entire analysis step along the path of nonlinear response change.

[0012] Furthermore, the aforementioned Z The parametric model is:

[0013] in, α and C All are fitting constants; N f For fatigue life; β Material parameters; σ a √area represents the stress amplitude (in MPa); √area represents the defect size (in μm). D Indicates the relative depth of micro-defects. , d inc This represents the shortest distance from the defect center to the free surface of the specimen. d Indicates the sample size; D The range is 0.5~1, when D When =1, it indicates that the defect is a surface defect. D A value of 0.5 indicates that the defect is located in the center. This is when considering the micro-defect depth parameter. D In this case, Z The parametric model tracked the transformation of crack initiation from the specimen surface to the specimen interior. The more internal micro-defects, the larger the fisheye size. Under conditions where matrix softening, surface compressive stress, and oxidation promote internal cracking, the parametric model... D Especially important. Index β The degree of promotion effect was quantified. Parameters D With overall stress amplitude The combination of these factors represents the contribution of local stress at micro-defects to internal cracks, providing a good basis for mechanical modeling of fatigue life.

[0014] Furthermore, the fatigue life obtained in step S1 is compared with... Z Establish linear relationships based on parameters, according to Obtain the fitting parameters β , α andC The value of is then used; therefore, the fatigue life prediction formula is: .

[0015] Another aspect of the present invention provides a general model for predicting the fatigue life of structures with defects. The general model for lifespan prediction is:

[0016] in, Z The parameters are based on the established finite element model containing the defects for each defect. Calculated; The fatigue life of the defective structure is obtained by solving the established finite element model containing the defect using fatigue analysis software. Z Establish linear relationships based on parameters, according to Obtain the fitting parameters β , α and C The value; Calculated based on the actual detected defect information. Z By substituting the parameter values ​​into the general life prediction model, fatigue life prediction can be completed. In the formula, α and C All are fitting constants; N f For fatigue life; β Material parameters; σ a √area represents the stress amplitude; √area represents the defect size. D Indicates the relative depth of micro-defects. , d inc This represents the shortest distance from the defect center to the free surface of the specimen. d Indicates the sample size.

[0017] By increasing the simulation quantities of different materials, a database for predicting the fatigue life of defective structures made of different materials is established.

[0018] The present invention has the following beneficial effects: (1) This invention establishes a finite element model of a defective structure, applies the material elastoplastic constitutive model, introduces different types of volumetric defects, considers the influence of factors such as the location, size, and shape of the defects, and constructs a correlation model between defects and fatigue life. Z The applicability of the parameters has been extended to the entire service life of both short-life and long-life applications, and has been improved. Z The relevant parameters in the parameters provide a general model and method for predicting the fatigue life of structures with defects; (2) The present invention can obtain the fatigue life calculation formula through finite element calculation, and can predict the life of structures with different defects. Compared with the traditional test method, the present invention can greatly reduce the amount of experiment, shorten the time, save costs, and ensure the accuracy and reliability of the prediction results. (3) By increasing the simulation quantities of different materials, this invention can systematically establish a complete database for predicting the fatigue life of structures with defects in different materials, providing a more convenient way for direct application in engineering, and has important practical significance for the prevention and control of structural material fracture. Attached Figure Description

[0019] Figure 1 This is a flowchart of fatigue life prediction in this invention.

[0020] Figure 2 This is a schematic diagram of a finite element model containing defects.

[0021] Figure 3 This is a schematic diagram of setting boundary conditions for a finite element model.

[0022] Figure 4 This is a schematic diagram of edge placement when meshing using the finite element method.

[0023] Figure 5 This is a diagram showing the result after the finite element mesh has been generated.

[0024] Figure 6 For Z A schematic diagram showing the fitting results of parameters as control parameters for fatigue life.

[0025] Figure 7 This is a schematic diagram comparing the predicted lifetime with the experimental lifetime results. Detailed Implementation

[0026] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. However, these embodiments are not intended to limit the present invention. Any similar structures and similar variations of the present invention should be included in the protection scope of the present invention. The commas in the present invention all indicate the relationship between and. The English letters in the present invention are case-sensitive.

[0027] To verify this invention, fatigue life prediction was performed on a certain 316 austenitic stainless steel material, such as... Figure 1 As shown, the specific method is as follows: S1. Based on different defect information, establish finite element models containing defects respectively, and obtain the fatigue life of the defective structure based on fatigue analysis software; A finite element model of a flat plate with a length of 200 mm, a width of 200 mm, and a thickness of 20 mm was created in the finite element software. A pore defect with a sphere radius of 6 mm was introduced inside the finite element model. Figure 2As shown; one side of the finite element model is completely fixed, while the other side ( Figure 3 A fixed fatigue load (stress ratio of -1) is applied along the y-direction. To ensure uniform deformation of the entire model, the non-force-applied directions are constrained. Figure 3 Displacement in the x and z directions (e.g.) Figure 3 As shown.

[0028] The finite element model is meshed, and a structured mesh, i.e. a hexahedral mesh, is generated during the meshing process. The specific steps for mesh generation are as follows: The finite element model is divided along three dividing planes by creating partitioning planes along the circumferential, axial, and radial directions of the defect using the plane creation function; edge seeding is performed during mesh generation, such as... Figure 4 As shown, the mesh size is determined, and the result after meshing is as follows. Figure 5 As shown. To ensure the accuracy of the calculation results around the defect, it is necessary to refine the local mesh around the defect. The method of local mesh refinement is to use a transition mesh with decreasing mesh size around the defect to achieve local refinement.

[0029] First, the finite element model is solved using finite element software to obtain a result file containing the stress and strain of the model. The result file is in odb format and contains principal stresses, principal strains, shear strains, and nodal stresses. The results file is then imported into fatigue analysis software. Material parameters, fatigue life model, and load spectrum are set, and the fatigue life of the defective structure is obtained. The fatigue analysis software is Fe-safe (a finite element software plugin). The number of fatigue cycles is counted using the rainflow counting algorithm at each node of the fatigue life model, and the fatigue life can be solved. Finally, the fatigue life results of the defective structure and the life result cloud map are obtained.

[0030] The material parameter used is only the elastic modulus. During the fatigue analysis software calculation, the Neuber formula is used to perform an elastic-plastic transformation of the material to improve the accuracy of the calculation. The Neuber formula is:

[0031] In the formula, This is the theoretical stress concentration factor. ,in The solution is an elastic finite element method (the stress at the root of the notch is calculated directly through linear elastic finite element analysis (FEA), neglecting plastic deformation). , E The elastic modulus of the material; The nominal stress (average stress away from the notch); The stress concentration factor is... ,in This is the Neuber method modified solution (which modifies the elastic solution into an elastoplastic solution through energy equivalence); The strain concentration factor is... ,in In order to respond nominally, ; Specifically, fatigue tests were conducted using defect-free materials processed into standard specimen sizes to obtain the parameters required for the fatigue life model. The details are as follows: The fatigue life model is the SWT fatigue life model, and its expression is:

[0032] Defect-free material is processed into standard fatigue specimens, and fatigue tests are conducted on a hydraulic servo fatigue testing machine. The obtained fatigue test results are plotted on a double logarithmic coordinate system, and the plastic strain amplitude of the fatigue test results is expressed. With fatigue life N f Perform linear regression to obtain the intercept A and slope B, and then calculate the fatigue strength index. b and fatigue ductility index c The value of is used to determine the plastic strain amplitude-life relationship in the plastic dominant region.

[0033] To ensure the conservatism of the overall calculation results, the SWT fatigue life model was used to predict fatigue life under different defect conditions. , , b and c The values ​​are 703.4, 0.476, 0.0835 and -0.5142, respectively.

[0034] Since a fixed fatigue load (monotonic load) is applied to the other side of the finite element model, the load spectrum is defined in the fatigue analysis software. The stress-strain parameters of the last incremental step are input into the fatigue analysis software, the stress ratio and time history are defined, and the required load spectrum is generated.

[0035] Pore ​​defects of different sizes were introduced into the finite element model to analyze their variation trends. The fatigue life of four pores with different diameters was calculated, which were 6.35 mm, 6.5 mm, 6.8 mm and 7 mm.

[0036] Different defect shapes are represented by changing the aspect ratio of the pore defects. When the aspect ratio is 1, the defect is circular. As the aspect ratio increases, the defect shape becomes flatter. The fatigue life of pores with different shapes is calculated, and the fatigue life variation trend of the aspect ratios from 1 to 5 is statistically analyzed.

[0037] By gradually reducing the distance between the defect center and the nearest surface, fatigue life curves for four different porosity defect locations (L / T = 1 / 2, 7 / 16, 3 / 8, and 1 / 4) were calculated to analyze the influence of different defect locations on the structural fatigue life.

[0038] Hard inclusions are introduced by changing the ratio of the elastic modulus of the defect to that of the material matrix. E d / E m ( E d Defect elastic modulus, E m If the matrix elastic modulus is 0, then it is a porosity. E d / E m =1 indicates a defect-free case. E d / E m A value between 1 and 2 indicates a hard inclusion. The fatigue life was calculated by repeating the process with pore defects of different sizes, varying the aspect ratio of the pore defects, and gradually decreasing the distance between the defect center and the nearest surface.

[0039] S2, combined Z The parametric model, based on the established finite element model containing defects, obtains the parameters for each defect. Z Parameter Z The parametric model is:

[0040] in, α and C All are fitting constants; N f For fatigue life; β Material parameters; σ a √area represents the stress amplitude; √area represents the defect size. D Indicates the relative depth of micro-defects. , d inc This represents the shortest distance from the defect center to the free surface of the specimen. d Indicates the sample size.

[0041] S3, combine the fatigue life obtained in step S1 with... Z A linear relationship was established using parameters, resulting in a total of 253 data points. These 253 data points were then used according to... Perform fitting and obtain fitting parameters. β , α and CThe value;, with Z The fitting results of the parameters as control parameters for fatigue life are as follows: Figure 6 As shown; The formula for predicting low- and high-cycle fatigue of this material is as follows:

[0042] The formula for predicting ultra-high cycle fatigue life is as follows:

[0043] S4, using CT flaw detection, obtained information on internal structural defects and calculated... Z The parameters are then substituted into the fatigue life prediction formula to complete the fatigue life prediction. Simultaneously, fatigue tests are conducted on a hydraulic servo fatigue testing machine to obtain the experimental life. The predicted life and experimental life results are shown below. Figure 7 , Figure 7 The 2x error and 3x error in the text define the lifetime prediction effect, relative to the case of no error (when the predicted lifetime equals the experimental lifetime). The "2x error band" refers to the error range of the measurement results, indicating that the error of the predicted lifetime is twice the experimental lifetime; the "3x error band" refers to the error range of the measurement results, indicating that the error of the predicted lifetime is three times the experimental lifetime.

[0044] This invention also provides a general model for predicting the fatigue life of structures with defects. The general model for lifespan prediction is:

[0045] in, Z The parameters are based on the established finite element model containing the defects for each defect. Calculated; The fatigue life of the defective structure is obtained by solving the established finite element model containing the defect using fatigue analysis software. Z Establish linear relationships based on parameters, according to Obtain the fitting parameters β , α and C The value; Calculated based on the actual detected defect information. Z By substituting the parameter values ​​into the general life prediction model, fatigue life prediction can be completed. In the formula, α and C All are fitting constants; N f For fatigue life; β Material parameters; σ a √area represents the stress amplitude; √area represents the defect size. DIndicates the relative depth of micro-defects. , d inc This represents the shortest distance from the defect center to the free surface of the specimen. d Indicates the sample size.

[0046] By increasing the simulation quantities of different materials, a database for predicting the fatigue life of defective structures made of different materials is established.

[0047] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

Claims

1. A method for fatigue life prediction of a structure containing defects, characterized by, The method comprises: S1, respectively establishing a finite element model containing defects according to different defect information, and solving the fatigue life of the structure containing defects based on fatigue analysis software; S2, bind Z Parametric model, according to the established finite element model containing defects, get each defect under Z Parameter; S3, the fatigue life obtained in step S1 is compared with Z The parameters are established to linearly correlate, and all obtained data points are fitted to obtain a fatigue life prediction formula. S4, calculating according to the actually detected defect information Z The parameter value is substituted into the fatigue life prediction formula to complete fatigue life prediction.

2. The method of claim 1, wherein, The finite element model containing defects is a flat plate.

3. The method of claim 1, wherein, The finite element model containing defects is processed as follows: a. Set boundary conditions for the finite element model and apply fatigue load, the boundary conditions are: One side of the finite element model is completely fixed, and a fixed fatigue load is applied to the other side, in order to ensure uniform deformation of the entire finite element model, the displacement in the direction not applying force in the entire finite element model is constrained; b. Grid division is performed on the finite element model, and the specific steps of grid division are: Divide the finite element model along the circumferential, axial and radial directions of the defect by creating a plane, and divide the finite element model along the three division planes; in order to ensure the accuracy of the calculation results around the defect, local grid refinement is performed around the defect, and the local grid refinement is a transition grid with decreasing grid size around the defect.

4. The method of claim 1, wherein, The specific steps of solving the fatigue life of the structure containing defects based on fatigue analysis software are: First, solve the finite element model by finite element software to obtain a result file containing model stress and strain, the result file is an odb format file containing principal stress, principal strain, shear strain and node stress; Then, import the result file into the fatigue analysis software, set material parameters, fatigue life model and define load spectrum, solve the fatigue life of the structure containing defects; use rainflow counting algorithm to count the number of fatigue cycles at each node of the fatigue life model, which can solve the fatigue life, and finally obtain the fatigue life result and life result cloud map of the structure containing defects.

5. The method for predicting the fatigue life of a structure containing defects according to claim 4, characterized in that, The material parameter is only the elastic modulus, and the Neuber formula is used for elastic-plastic conversion of the material in the calculation process of the fatigue analysis software to improve the accuracy of the calculation, the Neuber formula is: wherein is the theoretical stress concentration factor, wherein is the elastic finite element solution, , E is the modulus of elasticity of the material; is the nominal stress; is the stress concentration factor, wherein is the Neuber method modified solution; is the strain concentration factor, wherein is the nominal strain, .

6. The method of predicting fatigue life of a structure containing defects according to claim 4, wherein A standard specimen size is selected to process a fatigue test, and the required parameters of the fatigue life model are obtained, specifically: The fatigue life model is an SWT fatigue life model. A standard fatigue specimen is processed from a non-defective material, fatigue test is performed on a hydraulic servo fatigue testing machine, the fatigue test results are plotted in a double logarithmic coordinate system, the plastic strain amplitude and fatigue life N f Linear regression is performed to obtain an intercept A and a slope B, and then fatigue strength index b and fatigue ductility index c are calculated, so as to determine the plastic strain amplitude-life relationship in the plasticity dominant zone.

7. The method of claim 4, wherein the fatigue life prediction of a structure containing defects is characterized by, Since a fixed fatigue load is applied to the other side of the finite element model, define the load spectrum in the fatigue analysis software, input the stress and strain parameters of the last step increment in the finite element software analysis into the fatigue analysis software, define the stress ratio and time history, and generate the required load spectrum.

8. The method of predicting fatigue life of a structure containing defects according to claim 1, wherein, The Z The parametric model is: wherein α and C are fitting constants; N f is the fatigue life; β is a material parameter; σ a is the stress amplitude; and D denotes the relative depth of the microdefect, , d inc denotes the shortest distance from the defect center to the free surface of the specimen; d denotes the specimen size.

9. The method of claim 8, wherein, The specific process of step S3 is: The fatigue life obtained in step S1 is correlated with Z the parameter to establish a linear correlation, and the correlation is fitted according to to obtain the values of the fitting parameters β , α and C ; The fatigue life prediction formula is: .

10. A general model for fatigue life prediction of structures containing defects, characterized in that, The general model is obtained by the prediction method of any one of claims 1-9, and the life prediction general model is: ; wherein, Z The parameters are calculated for each defect from the finite element model established with the defect, calculated; The fatigue life of the structure with the defects is solved based on the fatigue analysis software according to the established finite element model with defects for each defect and Z The linear correlation is established according to The values of the fitting parameters β 、 α and C are obtained The fatigue life prediction is completed by substituting the parameter value into a general life prediction model according to actually detected defect information. Z The fatigue life prediction is completed by substituting the parameter value into a general life prediction model according to actually detected defect information. wherein α and C are fitting constants; N f is the fatigue life; β is a material parameter; σ a is the stress amplitude; and D denotes the relative depth of the microdefect, , d inc denotes the shortest distance from the defect center to the free surface of the specimen; d denotes the specimen size.

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