Ultrahigh-cycle fatigue crack stress intensity factor solving method

Abstract

The invention provides an ultra-high cycle fatigue crack stress intensity factor solving method, and relates to the technical field of ultra-high cycle fatigue performance analysis and fracture characterization, and the method comprises the following steps: establishing an ultrasonic fatigue sample finite element model containing a precrack; carrying out modal analysis on the sample containing the precracks; carrying out steady-state dynamic response analysis on the sample containing the pre-cracks; dividing a finite element model according to the most dangerous section, and sequentially obtaining a plurality of sections where the required crack front edge is located; nodes are sequentially selected along the cracks on the section, and corresponding displacement parameters at the nodes are extracted to serve as crack opening displacement; calculating a stress intensity factor value at each node under the ultrasonic fatigue load by combining a node displacement method; and a node stress intensity factor is pushed to the crack tip by using a linear regression method, and the value of the node stress intensity factor is used as the stress intensity factor value of the crack tip of the section. The method is suitable for solving and analyzing the stress intensity factor of the crack front edge of the sample under ultrasonic fatigue loading, and is simple and convenient to implement and reliable in precision.

Description

Technical Field

[0001] The present invention relates to the field of analysis of very high cycle fatigue performance and fracture characterization of metallic materials, and more particularly to a method for solving and analyzing the numerical value and distribution of the stress intensity factor at the crack front of very high cycle fatigue cracks. Background Art

[0002] With the development requirements of high speed, long life and high reliability of modern mechanical equipment, the fatigue life of many key components has far exceeded tens of millions of cycles, belonging to the category of very high cycle fatigue research. Very High Cycle Fatigue (VHCF) refers to a phenomenon in which fatigue damage may still occur when the number of cyclic loadings on a material exceeds one million cycles. With the improvement of the service performance requirements of materials in fields such as aerospace, energy equipment and the automotive industry, very high cycle fatigue research has gradually become a hot topic in material fatigue science. Traditional fatigue research methods are mostly based on low cycle fatigue and high cycle fatigue theories, and the damage and fracture failure mechanisms of materials in very high cycle fatigue have not been fully understood. As the most effective means for studying the very high cycle fatigue performance of metallic materials, ultrasonic resonance technology obtains the required displacement and load levels through the resonance of specimens in the test system. However, based on the ultrasonic fatigue test system and operation mode, the actual physical measurement of the process parameters in the very high cycle fatigue test is still complex and difficult. And currently, fatigue tests on specimens containing physical cracks are still in the category of traditional fatigue and rarely involve the field of very high cycle fatigue.

[0003] The crack propagation behavior is a key link in the very high cycle fatigue failure of materials. In the very high cycle fatigue range, crack propagation usually occurs under low stress conditions and exhibits different characteristics from traditional fatigue, such as cracks may initiate and propagate from internal defects, the crack propagation rate is extremely low, and the microscopic behavior at the crack tip dominates the entire propagation process. Studying the crack propagation law helps to reveal the failure mechanism of very high cycle fatigue and provides a scientific basis for crack life prediction. The stress intensity factor is an important parameter that describes the stress field distribution at the crack tip and the driving force for crack propagation, and is also a key parameter for judging the fracture of a cracked structure and calculating the crack propagation rate. In the study of very high cycle fatigue cracks, the solution of the stress intensity factor is also crucial. It can not only reflect the mechanical state of the local area at the crack tip under very high cycle service conditions, be used to predict the crack propagation path, propagation rate and final failure mode, but also reveal the correlation between crack propagation and the material microstructure, helping to predict the service behavior of materials under very high cycle conditions.

[0004] Therefore, the solution of the stress intensity factor is of great significance for promoting the in-depth study and engineering application of very high cycle fatigue crack behavior.

[0005] At present, the methods for solving the stress intensity factor of fatigue cracks mainly include theoretical analytical methods, numerical simulation methods (such as finite element methods), and experimental measurement methods. The theoretical analytical method relies on classical fracture mechanics formulas and has strong applicability to specific geometric shapes and loading conditions. The experimental measurement method directly obtains crack propagation data through experimental means and inversely calculates the stress intensity factor by combining the definition of the stress intensity factor. The finite element method uses numerical calculation techniques to calculate the stress intensity factor by establishing a crack model and solving the stress field distribution. In addition, as the most effective means for studying the very high cycle fatigue performance of metallic materials, the ultrasonic resonance technique can obtain the required displacement and load levels for experiments through the resonance of specimens in the experimental system.

[0006] However, due to its special loading conditions, there are many technical challenges in solving the stress intensity factor of very high cycle fatigue cracks. The theoretical analytical method in the traditional fatigue field is limited in terms of the unconventional specimen structure and the accuracy of theoretical analysis of ultrasonic fatigue, and it is difficult to meet the complex requirements of very high cycle fatigue cracks. In terms of experimental measurement, very high cycle fatigue usually involves complex working conditions such as ultra-high frequency vibration, ultrasonic vibration, and asymmetric loads. The crack propagation rate is extremely low, and the measurement accuracy of crack initiation and propagation is limited. At the same time, factors such as the crack initiation competition mechanism, the diversity and randomness of crack propagation, and the significant influence of the material microstructure in very high cycle fatigue all increase the measurement difficulty. In addition, the process measurement under the loading conditions of the ultrasonic fatigue test system is complex and expensive, which limits its wide application. Although the finite element method has the advantages of a wide application range, high calculation accuracy, and the ability to simulate complex working conditions in solving the stress intensity factor of very high cycle fatigue cracks, under the loading conditions of unconventional specimens in ultrasonic fatigue, the traditional finite element method still has deficiencies in terms of loading conditions, the construction of finite element models containing cracks, and the ability to solve fracture parameters, and it is difficult to efficiently and accurately simulate the crack tip stress field and optimize the prediction of crack propagation laws. Summary of the Invention

[0007] Aiming at the existing ultrasonic fatigue test system, based on engineering practice and test objectives, and combining classical fracture mechanics theory and finite element analysis methods, the present invention has developed a method for solving the stress intensity factor of very high cycle fatigue cracks, providing a simulation model basis and research ideas for the theoretical analysis and experimental innovation of very high cycle fatigue of structures with prefabricated cracks.

[0008] The technical means adopted by the present invention are as follows:

[0009] The present invention provides a method for solving the stress intensity factor of very high cycle fatigue cracks, including:

[0010] Establishing a finite element model of an ultrasonic fatigue specimen containing a prefabricated crack;

[0011] Perform modal analysis on the finite element model of the ultrasonic fatigue specimen with a prefabricated crack to verify that the natural frequency of the ultrasonic fatigue specimen with a prefabricated crack under the required vibration mode meets the test frequency requirements;

[0012] Perform steady-state dynamic response analysis on the finite element model of the ultrasonic fatigue specimen with a prefabricated crack to simulate the ultrasonic fatigue loading condition;

[0013] Divide the finite element model of the ultrasonic fatigue specimen with a prefabricated crack according to the required crack front to obtain the required crack front and multiple cross-sections along the crack propagation direction;

[0014] Select nodes sequentially along the cracks on the cross-section, and extract the corresponding displacement parameters at each node as the crack opening displacement;

[0015] Take the nodes on each cross-section as a group, and combine the node displacement method to calculate the stress intensity factor values at each group of nodes under ultrasonic fatigue load;

[0016] Use the linear regression method to extrapolate the stress intensity factor values at multiple nodes to the crack tip to obtain the stress intensity factor at the crack tip on the crack tip cross-section.

[0017] Further, it also includes:

[0018] Calculate the maximum value of the crack tip stress intensity factor on multiple cross-sections, and perform evaluation and fracture analysis of ultra-high cycle fatigue crack propagation based on the maximum value of the crack tip stress intensity factor on the multiple cross-sections.

[0019] Further, the types of prefabricated cracks include one or more of surface cracks, embedded cracks, corner cracks, and through cracks.

[0020] Further, establishing a finite element model of an ultrasonic fatigue specimen with a prefabricated crack includes:

[0021] According to the test requirements and common ultrasonic fatigue specimen analytical design methods, determine the geometric parameters of the conventional specimen, and establish a finite element model of the conventional specimen;

[0022] Set the material parameters and perform mesh division, where the material parameters include the elastic modulus, Poisson's ratio, and density of the material;

[0023] Divide the finite element model of the conventional specimen into a local area where the crack is to be inserted and the remaining part without crack insertion;

[0024] According to the type and geometric parameters of the prefabricated crack, generate a crack defect that meets the requirements and insert it into the corresponding position in the local area, and divide a fine mesh near the crack tip by inputting the mesh parameters to ensure the calculation accuracy of the stress and displacement of the nodes during crack analysis;

[0025] Perform three-dimensional fracture analysis and verification on the overall finite element model of the obtained cracked specimen.

[0026] Furthermore, perform modal analysis on the finite element model of the ultrasonic fatigue specimen with a prefabricated crack to verify that the natural frequency of the ultrasonic fatigue specimen with a prefabricated crack under the required vibration mode meets the test frequency requirements, including:

[0027] Fix one end of the ultrasonic fatigue specimen on the concentrator of the ultrasonic fatigue test system and analyze the natural frequency under the free vibration of the structure itself;

[0028] If the natural frequency is less than the design frequency, reduce the resonance length and re-establish the finite element model of the ultrasonic fatigue specimen with a prefabricated crack;

[0029] If the natural frequency is greater than the design frequency, increase the resonance length and re-establish the finite element model of the ultrasonic fatigue specimen with a prefabricated crack;

[0030] When the natural frequency is equal to the design frequency, the natural frequency of the ultrasonic fatigue specimen with a prefabricated crack under the required vibration mode meets the test frequency requirements.

[0031] Furthermore, perform steady-state dynamic response analysis on the finite element model of the ultrasonic fatigue specimen with a prefabricated crack to realize the simulation of the ultrasonic fatigue loading condition, including:

[0032] Based on the specimen model in which the natural frequency of the ultrasonic fatigue specimen with a prefabricated crack under the required vibration mode meets the test frequency requirements, keep its material parameters and mesh attributes unchanged, specify the frequency range of the required dynamic response analysis for the test, and perform steady-state dynamic response - direct method analysis and calculation under linear perturbation to calculate the specific values and distribution laws of the vibration displacement, stress, and strain of the specimen; define the corresponding displacement loading boundary conditions according to the ultrasonic fatigue test condition during the analysis, and the displacement amplitude is the displacement amplitude actually input to the specimen end face during the test.

[0033] Furthermore, the nodal displacement method is a method for estimating the stress intensity factor by calculating the displacements of the crack tip nodes in finite element analysis;

[0034] Take the nodes on each cross-section as a group, and combine the nodal displacement method to calculate the stress intensity factor values at each group of nodes under ultrasonic fatigue loading, including:

[0035] Analyze the crack tip displacement field, including: According to the classical linear elastic fracture mechanics theory, assume that the crack tip on each cross-section is a two-dimensional problem, and the displacement field near the crack tip is expressed as:

[0036]

[0037] where, u x 、uy is the displacement component at the crack tip; K I is the stress intensity factor (Mode I); E' is the equivalent elastic modulus; r is the radial distance from the node to the crack tip; f x (θ), f y (θ) is the angle between the node and the crack surface;

[0038] Extract the displacement components (u x , u y ) and the r value of the corresponding nodes. Usually, the nodes along the crack propagation direction are selected to calculate the stress intensity factors at all nodes:

[0039]

[0040] Furthermore, divide the finite element model of the ultrasonic fatigue specimen with a prefabricated crack according to the required crack front, including:

[0041] Divide the finite element model of the ultrasonic fatigue specimen with a prefabricated crack according to the most dangerous section.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] The present invention simplifies the crack analysis process by using the finite element method. By solving the crack tip stress intensity factor on the dangerous section of the specimen, the stress intensity factor distribution of the prefabricated crack front can be obtained, effectively improving the accuracy and efficiency of crack analysis. This method reduces the actual measurement difficulty of very high cycle fatigue, avoids the empirical errors that may occur in traditional methods and experimental measurements, and thus provides reliable analysis results for the fracture behavior of cracks.

[0044] The present invention is not only applicable to crack analysis under different types of conventional ultrasonic fatigue specimen loading, but also can realize the insertion of multiple types, characteristics and different numbers of cracks, the remeshing of complex crack models, and the reconstruction of the finite element model with cracks. By performing finite element modeling and analysis on multi-mode cracks and multi-type specimens, the applicable range of this solution is effectively broadened, providing fracture analysis support under very high cycle fatigue conditions.

[0045] The present invention is based on the classical fracture mechanics theory. By innovating the traditional fatigue analysis method, it is applicable to the simulation of very high cycle fatigue. This method provides an effective theoretical basis and model foundation for the indirect measurement of process parameters in actual physical experiments, and provides new research ideas for the analysis of the propagation behavior and failure mode of very high cycle fatigue cracks. It has practical significance for the analysis of the crack action state under very high cycle cyclic loading conditions, the experimental study of initial crack propagation, and the exploration of the evolution process of very high cycle fatigue defects. Description of the Drawings

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0047] Figure 1 It is the flowchart of the method of the present invention;

[0048] Figure 2 It is a schematic diagram of a fatigue specimen with a prefabricated crack involved in an embodiment of the present invention;

[0049] Figure 3 It is the crack insertion result of an embodiment of the present invention;

[0050] Figure 4 It is the axial vibration displacement and strain distribution diagram of an embodiment of the present invention;

[0051] Figure 5 Stress distribution along the thickness direction of the specimen at the crack front;

[0052] Figure 6 Node selection on the crack in the middle section of an embodiment of the present invention;

[0053] Figure 7 Stress intensity factor at the crack tip of an embodiment of the present invention. Detailed implementation manners

[0054] In order to enable those skilled in the art of the present technology to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0055] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above accompanying drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such used data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any of their deformations are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily need to be limited to those clearly listed steps or units, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0056] The object of the present invention is to carry out simulation and fracture calculation of an ultra-high cycle fatigue specimen with a prefabricated crack, provide ideas for the indirect measurement of the parameters in the actual physical test process, enrich the fracture characterization methods of the ultra-high cycle fatigue crack structure, and provide a model basis and innovative ideas for the ultrasonic fatigue physical test research of unconventional specimens and their synchronous finite element simulation analysis.

[0057] Taking an ultrasonic fatigue specimen with a single-edge through straight crack in the middle of a dog-bone-shaped thin plate as an example for analysis, the basic shape and dimensions of the specimen are shown as Figure 2 shown, and the material parameters and specimen dimensions are shown in Table 1.

[0058]

[0059]

[0060] As Figure 1 shown, a method for solving the stress intensity factor at the crack front of an ultra-high cycle fatigue crack provided in an embodiment of the present invention specifically includes the following steps:

[0061] Step 1, establish a finite element model of an ultrasonic fatigue specimen with a prefabricated crack;

[0062] Among them, considering actual conditions such as engineering structures, material forming processes, and common ultrasonic fatigue specimen types, the types of prefabricated cracks can include surface cracks, embedded cracks, corner cracks, through cracks, etc. Based on the parameters of the ultrasonic fatigue physical test system and specimen parameters, carry out the modeling and finite element model preprocessing work of the specimen with a prefabricated crack.

[0063] In specific implementation, Step 1 is executed according to the following steps:

[0064] S11. According to the test requirements and the analytical design method of common ultrasonic fatigue specimens, select a dog-bone-shaped thin plate ultrasonic fatigue specimen as the initial shape, use numerical calculation software (such as Matlab) to determine the basic geometric parameters of the conventional specimen (see Table 1), and use finite element analysis software (such as ABAQUS) to establish its finite element model.

[0065] S12. Input material parameters.

[0066] Given that the elastic modulus of aluminum alloy AL6061 material is 69000 MPa, the Poisson's ratio is 0.33, the density is 2.7E-9 t / mm 3 , and the structural damping coefficient is taken as 0.0001.

[0067] S13. Carry out mesh division, where the element type is defined, and surface elements or volume elements are selected according to its model type. The structure of the conventional specimen is simple, appropriately refine the number of element seeds, and directly carry out mesh division;

[0068] S14. Establish task Job_1, export the finite element model.inp file under this task, and read it into a three-dimensional fracture mechanics analysis software (such as FRANC3D).

[0069] S15. Offset the finite element model 4 mm up and down along the middle radial section, and respectively divide the local area (local model) where the crack is to be inserted and the remaining part without crack insertion (global model).

[0070] S16. Select the type of prefabricated through straight crack and combine its geometric parameters (see Table 2) to generate a crack defect that meets the requirements and insert it into the corresponding position in the local model. That is, a 0.5-mm deep three-dimensional through straight crack prefabricated on one side of the middle section of the specimen is obtained, and by inputting the mesh parameters, a fine mesh is divided near the crack tip to ensure the calculation accuracy of the stress and displacement of the nodes during crack analysis. The result is as Figure 3 shown.

[0071] S17. Export the overall finite element model full.inp file of the specimen with crack to the finite element analysis software for analysis and verification.

[0072] Step 2. Conduct modal analysis on the specimen with prefabricated crack to verify that its natural frequency under the required vibration mode meets the test frequency requirements.

[0073] Among them, one end of the ultrasonic fatigue specimen is fixed on the concentrator of the ultrasonic fatigue test system, and the natural properties of the structure under free vibration are analyzed, that is, no boundary conditions are applied, and free modal analysis is adopted. In this embodiment, the designed frequency when prefabricating the crack specimen is 20,000 Hz, and the specimen is in the axial vibration mode at this frequency. The specific steps include the following:

[0074] S21. Set the modal analysis step step1, select the linear perturbation - frequency to define the modal analysis step, use the Lanczos solver to solve the eigenvalues, and select the modal analysis order to be 40 orders.

[0075] S22. Submit the modal analysis task Job_2 and output the.dat file containing the natural frequencies and natural vibration mode data of the specimen in the free vibration mode. In this embodiment, only longitudinal tensile and compressive loads are generated on the specimen under the ultrasonic vibration load, that is, the deformation only occurs along the axial direction, and no other mixed vibration modes such as bending and torsion are superimposed. That is, it is required that the natural vibration mode is vibration along the axial direction (Y direction) of the specimen. That is, extract the modal order (MODE NO) and the natural frequency (FREQUENCY) of this order of the mode that meet the conditions of Y-COMPONENT>0, X-COMPONENT≤0, Z-COMPONENT≤0, and Y-ROTATION≤0 in the participation coefficients of each order of the mode under the.dat file. After verification, extract the modal extraction order and its response frequency that meet the experimental requirements of the vibration mode, and compare them with the experimental design frequency to determine the size adjustment measures of the specimen with cracks. Within the actual machinable dimensional accuracy (0.1mm in this embodiment), the smaller the frequency error, the better; if the natural frequency is less than the design frequency (-500Hz), reduce the resonant length of the specimen; if the natural frequency is greater than the design frequency (+500Hz), increase the resonant length of the specimen.

[0076] S23. After adjusting the resonant length of the specimen with a prefabricated crack, modify the ABAUQS / Python script and re-model and submit the modal analysis.

[0077] Among them, the material parameters, element types, mesh division, and boundary conditions remain unchanged until the natural frequency under the required vibration mode meets the experimental design frequency.

[0078] In the output result of the modal analysis of this embodiment, the 14th order mode of the specimen is the lowest order mode of the axial vibration state required for the ultrasonic fatigue test design. At this time, the natural frequency is 20014Hz, which meets the frequency range required for the ultrasonic fatigue test. That is, at this time, the specimen will resonate, resulting in resonant fatigue.

[0079] Step 3. Conduct a steady-state dynamic response analysis on the specimen with a prefabricated crack to verify that the specimen meets the resonant requirements of the ultrasonic fatigue test and realize the simulation of the ultrasonic fatigue loading condition.

[0080] Specifically, Step 3 includes the following steps:

[0081] S31. Based on the geometric model of the specimen finally subjected to modal analysis in Step 2, keep its material parameters, mesh attributes, etc. unchanged, define the steady-state dynamic response - direct method analysis step step2 under linear perturbation, and specify the frequency range of 19500Hz - 20500Hz required for the dynamic response analysis of the experiment;

[0082] S32. Define the sine displacement loading boundary condition along the axial direction of the specimen according to the ultrasonic fatigue test conditions in step 2. The displacement amplitude is the sine displacement loading amplitude U0 = 0.01 mm actually input to the specimen end face in the test.

[0083] S33. Create Job_3 and submit the calculation. Subsequently, extract the calculation result file to obtain specific numerical values such as the vibration displacement, stress, and strain of the specimen and their distribution laws.

[0084] In this embodiment, in the extracted result file, the dynamic response analysis results of the specimen at the required design frequency of 20,000 Hz are output, including the axial vibration displacement, axial stress diagram, etc. of the specimen. Combining Figure 4 It can be found that at this time, the specimen still meets the resonance requirements of the actual ultrasonic fatigue test. That is, it meets the requirements that at the ultrasonic vibration frequency, the amplitude at the end is the largest, the stress and strain are the smallest, the amplitude at the central section is the smallest, the stress and strain are the largest, and the most dangerous section is the central section. At the same time, as a single-sided penetrating straight crack, Figure 5 The Mises stress distribution along the thickness direction of the specimen at the leading edge of the straight crack is given. The stress in the center of the thickness direction is the largest and gradually decreases towards both sides, and the minimum value appears on the specimen surface and near the surface. This indicates that the possibility of crack propagation at the center of the leading edge of the penetrating straight crack is the greatest, and the most dangerous section of the pre-cracked specimen is the central thickness section.

[0085] Step Four. Divide the finite element model according to the most dangerous section or research plan.

[0086] Divide n cross-sections along the thickness direction of the specimen. In this embodiment, since the dangerous section where the crack front and the crack propagation direction are located has been analyzed, only one cross-section needs to be divided along the center thickness of the specimen.

[0087] Step Five. Select nodes r n_i in sequence along the crack propagation direction on the crack lips of each cross-section, and extract the corresponding displacement parameters at the nodes as the crack opening displacement.

[0088] Among them, r n_i represents n groups of nodes at different distances from the crack tip.

[0089] To avoid the influence of the crack tip singular field, the nodes cannot be selected too close to the crack tip when selecting nodes. Taking the middle cross-section as an example, a group of nodes on it is selected as shown in Figure 6.

[0090] Step Six. Take the nodes on each cross-section as a group, and combine the node displacement method to calculate the stress intensity factor values at each group of nodes under the ultrasonic fatigue load.

[0091] Among them, the node displacement method is a method for estimating the stress intensity factor by calculating the displacements of the nodes at the crack tip in finite element analysis. Its basic principle is to derive the stress intensity factor by using the relationship between the displacement field near the crack tip and the analytical solution of classical fracture mechanics theory. Under the ultra-high cycle fatigue loading condition, the crack displacement field conforms to the assumptions of linear elastic fracture mechanics, that is, small deformation and elastic conditions.

[0092] In specific implementation, it includes the following steps:

[0093] S61. Analysis of the displacement field at the crack tip.

[0094] According to the classical linear elastic fracture mechanics theory, the displacement field near the crack tip (assuming that the crack tip on each cross-section is a two-dimensional problem, usually studying Mode I crack) can be expressed as:

[0095]

[0096] Among them, u x , u y are the displacement components at the crack tip; K I is the stress intensity factor (Mode I); E' is the equivalent elastic modulus; r is the radial distance from the node to the crack tip; f x (θ), f y (θ) is the angle between the node and the crack surface. In this embodiment, under the design frequency loading, the specimen only undergoes axial deformation, so each node only generates an axial, that is, the displacement component in the u y direction, and the crack propagation mode is Mode I cracking.

[0097] S62. Extract the node displacement component u y_n in each group and the radial distance r n_i from each node to the crack tip;

[0098] Among them, r is the radial distance from this node on the finite element model to the crack tip, n is the nth cross-section, and i is the ith node.

[0099] S63. After converting formula (1) to obtain formula (3), use formula (3) to calculate the stress intensity factors at all nodes.

[0100]

[0101] The distribution of the stress intensity factors at all nodes on this middle cross-section is shown by the solid dots in Figure 7.

[0102] Step seven, using the linear regression method, extrapolate the discrete stress intensity factor values obtained for each group of nodes to r nAt =0, the obtained stress intensity factor value is used as the stress intensity factor value at the crack tip on this cross-section.

[0103] Among them, r n =0 means that the distance from this point to the crack tip is 0, that is, this point is the crack tip point.

[0104] This cross-section is the crack tip cross-section at r=0, while r in the nodal displacement method cannot be equal to 0. Therefore, calculate point by point from far to near, and obtain the stress intensity factor at the crack tip through regression.

[0105] Such as Figure 7 shown, the stress intensity factor value K I at the crack tip on this middle cross-section is 2.436 Mpa·m 1 / 2 .

[0106] Step eight, based on the maximum stress intensity factor at the crack tip on n cross-sections as the physical model and research basis for subsequent prefabricated crack specimen design and experimental analysis, for the evaluation and fracture analysis of ultra-high cycle fatigue crack propagation.

[0107] In this embodiment, it has been analyzed that the most dangerous cross-section of this specimen is the central thickness cross-section, and there is no need to divide and calculate the stress intensity factor at the crack tip on more cross-sections. Conducting subsequent research based on the stress intensity factor value at the most dangerous location will greatly improve the safety and reliability of specimen design and actual physical experiments.

[0108] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for solving the stress intensity factor of ultra-high cycle fatigue cracks, characterized in that: include: Establish a finite element model of ultrasonic fatigue specimen with prefabricated cracks; Performing modal analysis on the finite element model of the ultrasonic fatigue specimen containing prefabricated cracks to verify that the natural frequency of the ultrasonic fatigue specimen containing prefabricated cracks under the required vibration mode meets the test frequency requirement; Performing steady-state dynamic response analysis on the finite element model of the ultrasonic fatigue specimen containing the prefabricated cracks to achieve ultrasonic fatigue loading condition simulation; Dividing the finite element model of the ultrasonic fatigue specimen containing the prefabricated crack according to the required crack front to obtain the required crack front and multiple cross sections along the crack propagation direction; Nodes are selected one by one along the crack on the cross section, and the corresponding displacement parameters at each node are extracted as the crack opening displacement; The nodes on each section are grouped together, and the stress intensity factor value at each group of nodes under ultrasonic fatigue load is calculated by combining the node displacement method. The stress intensity factor values ​​at multiple nodes are extrapolated to the crack tip using the linear regression method to obtain the stress intensity factor at the crack tip on the crack tip section.

2. A method for solving the stress intensity factor of ultra-high cycle fatigue crack according to claim 1, characterized in that: Also includes: The maximum values ​​of the crack tip stress intensity factors on multiple cross sections are calculated, and the evaluation of ultra-high cycle fatigue crack growth and fracture analysis are performed based on the maximum values ​​of the crack tip stress intensity factors on the multiple cross sections.

3. The method for solving the stress intensity factor of ultra-high cycle fatigue crack according to claim 1, characterized in that: The prefabricated crack types include one or more of surface cracks, embedded cracks, corner cracks, and through cracks.

4. A method for solving the stress intensity factor of ultra-high cycle fatigue crack according to claim 3, characterized in that: Establish a finite element model of ultrasonic fatigue specimen with prefabricated cracks, including: According to the test requirements and the commonly used ultrasonic fatigue specimen analytical design method, the geometric parameters of the conventional specimen are determined, and the finite element model of the conventional specimen is established; Set material parameters and perform meshing, where material parameters include elastic modulus, Poisson's ratio and density; Dividing the finite element model of the conventional specimen into a local area where cracks are to be inserted and the remaining area where no cracks are inserted; According to the prefabricated crack type and geometric parameters, a crack defect that meets the requirements is generated and inserted into the corresponding position of the local area. By inputting the mesh parameters, a fine mesh is divided near the crack tip to ensure the calculation accuracy of the stress and displacement of the node during crack analysis. The obtained overall finite element model of the cracked specimen was subjected to three-dimensional fracture analysis and verification.

5. The method for solving the stress intensity factor of ultra-high cycle fatigue crack according to claim 1, characterized in that: Performing modal analysis on the finite element model of the ultrasonic fatigue specimen containing prefabricated cracks to verify that the natural frequency of the ultrasonic fatigue specimen containing prefabricated cracks under the required vibration mode meets the test frequency requirements, including: Fix one end of the ultrasonic fatigue specimen on the energy concentrator of the ultrasonic fatigue test system to analyze the natural frequency of the structure under free vibration. If the natural frequency is less than the design frequency, the resonance length is reduced and the finite element model of the ultrasonic fatigue specimen with prefabricated cracks is re-established; If the natural frequency is greater than the design frequency, the resonance length is increased and the finite element model of the ultrasonic fatigue specimen with prefabricated cracks is re-established; When the natural frequency is equal to the design frequency, the natural frequency of the ultrasonic fatigue specimen containing the prefabricated cracks under the required vibration mode meets the test frequency requirement.

6. A method for solving the stress intensity factor of ultra-high cycle fatigue crack according to claim 5, characterized in that: The steady-state dynamic response analysis is performed on the finite element model of the ultrasonic fatigue specimen containing the prefabricated cracks to realize the ultrasonic fatigue loading condition simulation, including: Based on the specimen model whose natural frequency of the ultrasonic fatigue specimen containing prefabricated cracks under the required vibration mode meets the test frequency requirements, its material parameters and grid properties are kept unchanged, the frequency range of dynamic response analysis required for the test is given, and the steady-state dynamic response-direct method analysis and calculation under linear perturbation is performed to calculate the specific values ​​of the vibration displacement, stress, and strain of the specimen and their distribution law; during the analysis, the corresponding displacement loading boundary conditions are defined according to the ultrasonic fatigue test conditions, and the displacement amplitude is the displacement amplitude of the end face of the actual test input specimen.

7. A method for solving the stress intensity factor of ultra-high cycle fatigue crack according to claim 6, characterized in that: The node displacement method is a method for estimating stress intensity factors by calculating the displacement of crack tip nodes in finite element analysis; The nodes on each section are grouped together, and the stress intensity factor value at each group of nodes under ultrasonic fatigue load is calculated by combining the node displacement method, including: Analyze the displacement field at the crack tip, including: According to the classical linear elastic fracture mechanics theory, assuming that the crack tip on each section is a two-dimensional problem, the displacement field near the crack tip is expressed as: Among them, u x 、u y is the displacement component at the crack tip; K I is the stress intensity factor; E' is the equivalent elastic modulus; r is the radial distance from the node to the crack tip; f x (θ), f y (θ) is the angle between the node and the crack surface; Extract the displacement component (u x ,u y ) and r value, usually the nodes along the crack propagation direction are selected to calculate the stress intensity factor at all nodes: or.

8. The method for solving the stress intensity factor of ultra-high cycle fatigue crack according to claim 1, characterized in that: The finite element model of the ultrasonic fatigue specimen with prefabricated cracks is divided according to the required crack front, including: The finite element model of the ultrasonic fatigue specimen containing prefabricated cracks is divided according to the most dangerous section.

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