Steel rail welded joint fatigue crack initiation and propagation full-life prediction method and device

By establishing a finite element model and calculating the initiation and extension life of fatigue cracks, combined with the shear stress amplitude ratio, the problem of low accuracy in the prediction of the full life of fatigue cracks at rail welded joints in the existing technology is solved, and more accurate prediction and safety management are achieved .

CN119272562APending Publication Date: 2025-01-07SANYA SCI & EDUCATION INNOVATION PARK WUHAN UNIV OF TECH +1
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Patent Information

Application Number
CN202411300059.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-18
Publication Date
2025-01-07

AI Technical Summary

Technical Problem

The prior art is difficult to accurately predict the full life of fatigue cracks in rail welded joints, resulting in low prediction accuracy and difficult to combine research on crack initiation and expansion stages, which has the problem of insufficient prediction.

Method used

By obtaining the data of rail welded joints and parent material, a finite element model is established to calculate the fatigue crack initiation life and extended life, and combining the ratio of the shear stress amplitude to the positive stress amplitude, the full life of fatigue crack initiation is calculated to improve the prediction accuracy.

Benefits of technology

Accurate prediction of the full life of fatigue crack initiation of rail welded joints is achieved, and the prediction accuracy is improved, and it can be used for rail safety management.

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Abstract

The invention discloses a steel rail welded joint fatigue crack initiation and propagation full-life prediction method and device. The method comprises the following steps: acquiring steel rail welded joint data and base metal data; establishing a steel rail finite element model according to the steel rail welding joint data and the base metal data; calculating a fatigue crack initiation life prediction key position and a corresponding stress component time history according to the steel rail finite element model; calculating a ratio of a shear stress amplitude to a normal stress amplitude according to the fatigue crack initiation life prediction key position and the stress component time history; calculating the fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude; according to the fatigue crack initiation life and the initiation position, the fatigue crack initiation and propagation full life is calculated, and the fatigue crack initiation and propagation full life is used for steel rail safety management. According to the method, fatigue crack initiation and propagation full-life prediction is realized, and the prediction accuracy is improved. The method can be widely applied to the technical field of track engineering.
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Description

Technical Field

[0001] The invention relates to the technical field of track engineering, and in particular to a method and device for predicting the full life of fatigue crack initiation and propagation of a rail welded joint. Background Art

[0002] Railways are important infrastructures. High-speed train rails use advanced high-speed seamless rails. Flash welding is the preferred welding method for seamless rail welded joints. Due to the influence of many factors such as process level and maintenance, the strength and stability of welded joints are not as good as those of the parent material, which causes fatigue failure of welded joints under long-term alternating loads. Fatigue cracks appear at welded joints, which can easily lead to rail breakage accidents. In traditional fatigue life prediction methods for rail welded joints, only the influencing factors of fatigue crack initiation in welded joints and the crack propagation pattern are usually analyzed. The initiation stage and the propagation stage are studied separately, making it difficult to predict the fatigue life of welded joints throughout the entire process, and the prediction accuracy is low.

[0003] In summary, the technical problems existing in the relevant technologies need to be improved. Summary of the invention

[0004] The embodiments of the present invention provide a method and device for predicting the entire life of fatigue crack initiation and propagation of a rail welded joint, which effectively improves the prediction accuracy.

[0005] On the one hand, an embodiment of the present invention provides a full life prediction method for fatigue crack initiation and propagation of a rail welded joint, comprising the following steps:

[0006] Obtain rail welding joint data and parent material data;

[0007] Establishing a rail finite element model according to the rail welding joint data and the parent material data;

[0008] Calculating the key positions for predicting fatigue crack initiation life and the corresponding stress component time history according to the rail finite element model;

[0009] Calculating the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the stress component time history;

[0010] Calculating fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude;

[0011] The fatigue crack initiation life and initiation position are used to calculate the fatigue crack initiation and propagation life, and the fatigue crack initiation and propagation life is used for rail safety management.

[0012] In some embodiments, establishing a rail finite element model according to the rail welding joint data and the parent material data includes:

[0013] Calculate the processing dimensions of the joint sample according to the rail welding joint data;

[0014] Calculate the processing size of the parent material sample according to the parent material data;

[0015] According to the processing size of the joint sample, a tensile test is performed on the rail welded joint to obtain a joint stress-strain curve;

[0016] According to the processing size of the base material sample, a tensile test is performed on the base material to obtain a stress-strain curve of the base material;

[0017] According to the joint stress-strain curve and the parent material stress-strain curve, a finite element model of the rail is established by using a finite element analysis method.

[0018] In some embodiments, the step of calculating the fatigue crack initiation life prediction key position and the corresponding stress component time history according to the rail finite element model includes:

[0019] Calculate the dynamic load time history according to the EMU train combination status;

[0020] Loading the dynamic load time history onto the rail finite element model to obtain the stress field at the rail weld under the wheel rolling state;

[0021] The position where the equivalent stress in the rail weld area is greater than a preset stress threshold is used as the key position for predicting the fatigue crack initiation life;

[0022] The stress component time history at the key position for predicting the fatigue crack initiation life is extracted from the stress field.

[0023] In some embodiments, the calculating the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the stress component time history includes:

[0024] According to the fatigue crack initiation life prediction of the equivalent stress time history of the key position, the number of stress cycles and the start and end times are calculated by the rain flow counting method;

[0025] Calculate the shear stress time history and the normal stress time history corresponding to each stress cycle according to the number of stress cycles, the start and end times, and the stress component time history;

[0026] According to the shear stress time history and the normal stress time history, a plane with the largest shear stress in the rail weld region is taken as a critical surface;

[0027] According to the critical surface, the ratio of the shear stress amplitude to the normal stress amplitude is calculated.

[0028] In some embodiments, the calculating the fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude comprises:

[0029] Calculating a ratio threshold value according to the ratio of the shear stress amplitude to the normal stress amplitude;

[0030] Calculating the number of fatigue failures corresponding to each stress cycle according to the ratio of the shear stress amplitude to the normal stress amplitude, the ratio threshold, the shear stress amplitude, and the number of cycles corresponding to the reference shear stress;

[0031] Calculating the fatigue damage value caused by the bicycle group according to the fatigue failure number and the number of full cycles;

[0032] Calculating fatigue damage values ​​caused by multiple train sets according to the fatigue damage value caused by the single train set and the number of train sets;

[0033] The time period during which the fatigue damage value caused by the multi-vehicle set increases from 0 to 1 is taken as the fatigue crack initiation life.

[0034] In some embodiments, the calculating the fatigue crack initiation and propagation life according to the fatigue crack initiation life and initiation position includes:

[0035] According to the initiation position, an initial crack is set, wherein the direction of the initial crack is parallel to the maximum shear stress plane in the rail weld area;

[0036] According to the fatigue crack initiation life, the crack occurrence time is sorted to obtain the crack initiation sequence;

[0037] Calculating the relationship between the crack propagation path and the number of stress cycles according to the initial crack and the crack initiation sequence;

[0038] When the crack depth or crack width increases to a critical threshold, the number of stress cycles is calculated according to the relationship between the crack extension path and the number of stress cycles;

[0039] Calculating fatigue crack growth life according to the number of stress cycles;

[0040] When the load-bearing capacity at the rail weld is less than a preset load-bearing threshold, the total fatigue crack growth life is calculated according to the plurality of fatigue crack growth lives;

[0041] The fatigue crack initiation and growth total life is calculated according to the fatigue crack initiation and growth total life.

[0042] In some embodiments, the calculating the fatigue damage value caused by the bicycle group according to the fatigue failure number and the number of full cycles includes:

[0043] According to the fatigue failure times and the number of full cycles, the fatigue damage value caused by the bicycle group is calculated by the fatigue damage value calculation formula, and the fatigue damage value calculation formula is:

[0044]

[0045] Where D n is the fatigue damage value caused by the bicycle group, n is the number of full cycles, N fi is the fatigue failure number.

[0046] In some embodiments, the relationship between the crack propagation path and the number of stress cycles is expressed as:

[0047]

[0048] Where α is the crack depth, N is the number of stress cycles, C and m are material parameters, and ΔK is the amplitude of the stress intensity factor.

[0049] On the other hand, an embodiment of the present invention provides a full life prediction device for fatigue crack initiation and propagation of a rail welded joint, comprising:

[0050] The first module is used to obtain rail welding joint data and parent material data;

[0051] The second module is used to establish a rail finite element model according to the rail welding joint data and the parent material data;

[0052] The third module is used to calculate the key position for predicting fatigue crack initiation life and the corresponding stress component time history according to the rail finite element model;

[0053] A fourth module is used to calculate the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the stress component time history;

[0054] A fifth module is used to calculate the fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude;

[0055] The sixth module is used to calculate the fatigue crack initiation and extension life according to the fatigue crack initiation life and initiation position, and the fatigue crack initiation and extension life is used for rail safety management.

[0056] In another aspect, an embodiment of the present invention provides a computer device, comprising:

[0057] at least one processor;

[0058] at least one memory for storing at least one program;

[0059] When the at least one program is executed by the at least one processor, the at least one processor implements the described method.

[0060] The beneficial effects of the present invention are as follows:

[0061] The embodiment of the present invention first obtains rail welding joint data and parent material data, and establishes a rail finite element model according to the rail welding joint data and the parent material data, and then calculates the key position for fatigue crack initiation life prediction and the corresponding stress component time history according to the rail finite element model, and calculates the ratio of shear stress amplitude to normal stress amplitude according to the key position for fatigue crack initiation life prediction and the corresponding stress component time history, and then calculates the fatigue crack initiation life according to the ratio of shear stress amplitude to normal stress amplitude, and finally calculates the fatigue crack initiation life and initiation position. The full life of fatigue crack initiation and propagation is calculated, so that the fatigue crack initiation life and fatigue crack propagation life can be combined to realize the full life prediction of fatigue crack initiation and propagation, thereby improving the prediction accuracy.

[0062] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0064] Figure 1 This is a flow chart of a method for predicting the full life of fatigue crack initiation and propagation of a rail weld joint according to an embodiment of the present invention;

[0065] Figure 2 A schematic diagram of a rail finite element model according to an embodiment of the present invention;

[0066] Figure 3 A schematic diagram of a dangerous point for fatigue crack initiation according to an embodiment of the present invention;

[0067] Figure 4 A schematic diagram of a critical surface position angle according to an embodiment of the present invention;

[0068] Figure 5 A schematic diagram of a crack morphology in an embodiment of the present invention;

[0069] Figure 6A schematic diagram of the relationship between a crack propagation path and the number of stress cycles according to an embodiment of the present invention;

[0070] Figure 7 A schematic diagram of an overall process for predicting the full life of a rail joint according to an embodiment of the present invention;

[0071] Figure 8 This is a schematic structural diagram of a full-life prediction device for fatigue crack initiation and propagation of a rail welded joint according to an embodiment of the present invention;

[0072] Fig. 9 The figure is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of the present application. They are only examples of devices and methods consistent with some aspects of the embodiments of the present application as detailed in the attached claims.

[0074] It is understood that the terms "first", "second", etc. used in this application can be used to describe various concepts in this article, but unless otherwise specified, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another concept. For example, without departing from the scope of the embodiment of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the words "if" and "if" as used herein can be interpreted as "at the time of" or "when" or "in response to determination".

[0075] The terms "at least one", "multiple", "each", "any", etc. used in this application, at least one includes one, two or more, multiple includes two or more, each refers to each of the corresponding multiple, and any refers to any one of the multiple.

[0076] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0077] Before describing the embodiments of the present application in detail, some nouns and terms involved in the embodiments of the present application are first described. The nouns and terms involved in the embodiments of the present application are subject to the following explanations.

[0078] Fatigue life: refers to the service life of a material or component before fatigue rupture occurs after multiple stress cycles under a specific load. This process involves the initiation of cracks at the stress concentration site after a certain number of cycles under the action of alternating stress (or strain). As the use time increases, the cracks gradually expand and eventually lead to rupture. The calculation of fatigue life is usually based on nominal stress and can be divided into infinite life calculation and finite life calculation. The relationship between stress and strain level can be described by SN curve (stress-life curve) and ε-N curve (strain-life curve).

[0079] Among the related technologies, railways are strategic, leading and key national infrastructure, and are the main arteries of the national economy and the backbone of the comprehensive transportation system. In transportation construction, railways are required to take the lead and be a good pioneer. The total operating mileage of high-speed railways has reached a relatively high level, accounting for most of the total mileage of high-speed railways in the world, and the construction scale ranks among the top. At present, high-speed train rails use advanced high-speed seamless rails, and flash welding is the preferred welding method for seamless rail welded joints. Due to the limitations of many factors such as process level, maintenance and repair, in most cases, the strength and stability of welded joints are not as good as those of the parent material, so that welded joints will fail due to fatigue under the long-term action of alternating loads, which is easy to cause rail breakage accidents. For example, a high-speed train derailed due to rail breakage in a certain place, resulting in many deaths and injuries; a rail breakage occurred on a railway bridge in a certain place, and a train was blocked for about half an hour due to this accident; a train derailed due to track breakage, causing the last 6 carriages to derail. The causes of these accidents are fatigue cracks at the welded joints, which eventually caused rail breakage. At present, most studies focus on the fatigue research of rails, and less on the fatigue research of welded joints. For the prediction of rail fatigue life, firstly, a two-dimensional wheel-rail non-steady-state cyclic rolling contact finite element model is established, and elastic-plastic rolling contact finite element analysis is adopted; then, combined with the multi-axial fatigue damage model, the SN curve of the rail material is referred to, and the fatigue damage accumulation value is calculated using the linear fatigue cumulative damage theory; finally, the fatigue crack initiation life or crack formation life of the rail is analyzed. And by analyzing the fatigue crack propagation mechanism of the rail, the crack propagation rate is determined to analyze the crack propagation behavior of the rail. Therefore, the fatigue life prediction research of the rail only gives the crack initiation life, and no full life prediction method for the rail from crack initiation to propagation is established. For the prediction of fatigue life of rail welded joints, most of the research is on the analysis of the influencing factors of fatigue crack initiation of welded joints, as well as the mode of crack propagation, etc. Only a few studies involve the establishment of a rail fatigue crack initiation prediction model, but no fatigue crack initiation life prediction method for rail welded joints is established, let alone a full life prediction method for fatigue of rail welded joints. The limitations of existing research have led to the following problems: (1) Since the current research studies the fatigue crack initiation and propagation of rail welded joints separately, it is difficult to establish a full life prediction method for fatigue cracks in welded joints from initiation to propagation, and the prediction accuracy is low. (2) In the study of the fatigue crack initiation stage of rail welded joints, it is difficult to establish a numerical model that can reflect the mechanical properties of the weld and the heat-affected zone, which makes it impossible to predict the fatigue crack initiation life of rail welded joints. (3) In the study of the fatigue crack propagation stage of rail welded joints, since the position and direction of the initial fatigue crack are mostly based on assumptions, not the actual fatigue crack initiation, the crack propagation obtained based on this analysis is used to predict the fatigue crack propagation life of the rail, which does not conform to the actual situation.

[0080] In view of this, the present embodiment first obtains the mechanical properties of the parent material, the weld and the heat affected zone according to the test, and establishes a finite element model of the rail welded joint; then adopts the critical surface multi-axial stress fatigue theory to predict the fatigue crack initiation life of each key position; then, the initial crack is set according to the initiation position obtained by analysis, and at the same time, the crack direction is parallel to the maximum shear stress plane with the largest number of occurrences; finally, the occurrence time of each crack is defined in the order of the crack initiation life from short to long, starting with the first crack to initiate, and the Paris formula is used to calculate the relationship between the crack propagation path and the number of cycles; when the number of cycles reaches the second crack, the relationship between the two crack propagation paths and the number of cycles is calculated; and so on, until the bearing capacity at the rail weld drops to 85% of the intact state, the rail weld can be considered to have failed, thereby obtaining the full life of fatigue crack initiation and propagation at the rail weld.

[0081] The full life prediction method of fatigue crack initiation and extension of rail welded joints provided in the embodiment of the present application relates to the field of rail engineering technology. The full life prediction method of fatigue crack initiation and extension of rail welded joints provided in the embodiment of the present application can be applied to a terminal, can also be applied to a server, and can also be software running in a terminal or a server. In some embodiments, the terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, and a vehicle-mounted terminal, etc., but is not limited to this; the server side can be configured as an independent physical server, or it can be configured as a server cluster or a distributed system composed of multiple physical servers, and can also be configured as a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network; the software can be an application that implements the full life prediction method of fatigue crack initiation and extension of rail welded joints, etc., but is not limited to the above forms.

[0082] The present application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc. The present application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments, in which tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media including storage devices.

[0083] The following is a detailed explanation of the embodiments of the present application in conjunction with the accompanying drawings:

[0084] Figure 1 is an optional flow chart of the full life prediction method for fatigue crack initiation and propagation of rail welded joints provided in the embodiment of the present application. Figure 1 The method may include but is not limited to steps S101 to S106.

[0085] Step S101, obtaining rail welding joint data and parent material data;

[0086] Step S102, establishing a rail finite element model according to rail welding joint data and parent material data;

[0087] Step S103, calculating the key positions for predicting fatigue crack initiation life and the corresponding stress component time history according to the rail finite element model;

[0088] Step S104, calculating the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the corresponding stress component time history;

[0089] Step S105, calculating the fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude;

[0090] Step S106: Calculate the fatigue crack initiation and propagation life according to the fatigue crack initiation life and initiation position. The fatigue crack initiation and propagation life is used for rail safety management.

[0091] Steps S101 to S106 shown in the embodiment of the present application realize the full life prediction of fatigue crack initiation and propagation, and improve the prediction accuracy.

[0092] In step S101 of some embodiments, the rail welding joint data and the base material data may be obtained through a rail database or field sampling. The rail welding joint data and the base material data may also be obtained through other methods, not limited thereto. For example, in field sampling, sampling may be performed according to the requirements of the tensile test method.

[0093] In some embodiments, in step S102, a rail finite element model is established according to the rail welding joint data and the base material data, which may include but is not limited to the following steps:

[0094] Calculate the processing dimensions of the joint specimen according to the rail welding joint data;

[0095] Calculate the processing size of the parent material sample according to the parent material data;

[0096] According to the processing size of the joint sample, the rail welding joint is subjected to tensile test to obtain the joint stress-strain curve;

[0097] According to the processing size of the parent material sample, the parent material is subjected to a tensile test to obtain the parent material stress-strain curve;

[0098] According to the stress-strain curve of the joint and the stress-strain curve of the parent material, the finite element model of the rail is established by using the finite element analysis method.

[0099] In some embodiments, the processing size of the joint sample can be calculated according to the requirements of the room temperature test method and the rail welding joint data, and the processing size of the parent material sample can be calculated according to the parent material data, so as to perform a tensile test later. Then, according to the processing size of the joint sample, the rail welding joint is subjected to a tensile test to obtain a joint stress-strain curve, and according to the processing size of the parent material sample, the parent material is subjected to a tensile test to obtain a parent material stress-strain curve. Finally, according to the joint stress-strain curve and the parent material stress-strain curve, a finite element model of the rail is established using the finite element analysis method. Exemplarily, the finite element analysis method can be implemented using finite element analysis software, and a finite element model of a rail with a welded joint can be established using finite element analysis software according to the joint stress-strain curve and the parent material stress-strain curve, so as to obtain the stress field later. Exemplarily, the geometric model of the physical rail and the high-speed rail wheel can be first established using SolidWorks software, and they are meshed and locally refined using HyperMesh software. The wheel-rail model was imported into the Abaqus finite element software for simulation analysis, and the material properties of the rail base material, welded joint and wheel were assigned respectively. The material properties of the rail (i.e., stress-strain curve) were obtained by performing monotonic tensile tests on the rail base material and welded joint weld material. The tangential behavior between the wheel and rail is contact based on the "penalty" formula, and the normal behavior is hard contact. It can be understood that the "penalty" formula is a penalty friction formula, which is a way to define interaction in the Abaqus software. Under default conditions, the friction coefficient is a constant, and the shear force is proportional to the friction coefficient. In this embodiment, the tangential behavior between the wheel and rail is set. Then the axle weight applied to the center of the wheel, that is, a concentrated force is applied at the center of the wheel. The wheel is given a speed of 350Km / h to make it roll on the rail. The established rail finite element model is as follows. Figure 2 shown.

[0100] In some embodiments, in step S103, calculating the fatigue crack initiation life prediction key position and the corresponding stress component time history according to the rail finite element model may include but is not limited to the following steps:

[0101] Calculate the dynamic load time history according to the EMU train combination status;

[0102] The dynamic load time history is applied to the rail finite element model to obtain the stress field at the rail weld under the wheel rolling state.

[0103] The position where the equivalent stress in the rail weld area is greater than the preset stress threshold is taken as the key position for fatigue crack initiation life prediction;

[0104] The stress component time history at the key location for fatigue crack initiation life prediction is extracted from the stress field.

[0105] In some embodiments, the dynamic load time history can be calculated first according to the combined state of the EMU train, and then the dynamic load time history can be loaded onto the finite element model of the rail, and the stress field at the rail weld under the wheel rolling state can be obtained by nonlinear finite element analysis, and then the position where the equivalent stress in the rail weld area is greater than the preset stress threshold is used as the key position for fatigue crack initiation life prediction, that is, according to the larger value of the equivalent stress in the rail weld area, several key positions for fatigue crack initiation life prediction can be determined, and finally the stress component time history of the key position for fatigue crack initiation life prediction can be extracted from the stress field, and the stress component time history corresponding to each key position for fatigue crack initiation life prediction can be obtained. Exemplarily, the stress state (i.e., stress field) of the rail is calculated, and it can be seen from the results that when the high-speed rail wheel passes over the rail, the maximum Mises stress appears at a position about 3 mm from the top of the rail, i.e., the dangerous point for fatigue crack initiation, such as Figure 3 At the same time, the time history of each stress component at this position is extracted.

[0106] In some embodiments, in step S104, calculating the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the corresponding stress component time history may include but is not limited to the following steps:

[0107] The equivalent stress history of key positions is predicted based on the fatigue crack initiation life, and the number of stress cycles and the start and end times are calculated by the rain flow counting method;

[0108] According to the number of stress cycles, start and end times and stress component time history, the shear stress time history and normal stress time history corresponding to each stress cycle are calculated;

[0109] According to the shear stress time history and normal stress time history, the plane with the maximum shear stress in the rail weld area is taken as the critical surface;

[0110] Based on the critical surface, calculate the ratio of the shear stress amplitude to the normal stress amplitude.

[0111] In some embodiments, the equivalent stress history of the key position can be predicted based on the fatigue crack initiation life, and the number of stress cycles and the corresponding start and end times can be calculated by the rain flow counting method. It can be understood that in fatigue calculation, the irregular equivalent stress history can be converted into a series of stress cycles, and the stress cycle can be determined by the rain flow counting method to obtain the number of cycles that the stress history can be converted into and the corresponding amplitude. Then, according to the number of stress cycles, the start and end times of each full cycle and the stress component history, the shear stress history and the normal stress history corresponding to each stress cycle are calculated. It can be understood that the equivalent stress history is different from the stress component history. The equivalent stress history is a numerical value that can be calculated using the Mises criterion and can also be called Mises stress. The stress component history includes the normal stress history and the shear stress history in all directions. According to the shear stress history and the normal stress history, the plane with the largest shear stress in the rail weld area is taken as the critical surface. For example, the maximum shear stress plane can be found as the critical surface. Finally, according to the critical surface, the ratio ρ of the shear stress amplitude Δτ to the normal stress amplitude Δσ on the critical surface is calculated. For example, the equivalent stress time history at the key position of fatigue crack initiation life prediction is counted by rain flow counting to determine the number of cycles and their start and end times. According to the time history of each stress component at the key position of fatigue crack initiation life prediction, the shear stress and normal stress time history corresponding to each full cycle are determined, and the maximum shear stress amplitude plane is found as the critical surface. Figure 4 As shown, by searching, (the angle of the critical surface) is determined The maximum value corresponds to the position (156, 1) in the 360×360 matrix, that is, the position of the critical surface is θ=156°. Calculate the ratio ρ of the normal stress amplitude Δσ to the shear stress amplitude Δτ on the plane, where

[0112] In some embodiments, in step S105, the fatigue crack initiation life is calculated according to the ratio of the shear stress amplitude to the normal stress amplitude, which may include but is not limited to the following steps:

[0113] According to the ratio of the shear stress amplitude to the normal stress amplitude, a ratio threshold is calculated;

[0114] The number of fatigue failures corresponding to each stress cycle is calculated according to the ratio of the shear stress amplitude to the normal stress amplitude, the ratio threshold, the shear stress amplitude and the number of cycles corresponding to the reference shear stress;

[0115] The fatigue damage value caused by the bicycle group was calculated based on the number of fatigue failures and the number of full cycles;

[0116] According to the fatigue damage value caused by a single train set and the number of EMU train combinations, the fatigue damage value caused by multiple train sets is calculated;

[0117] The time period during which the fatigue damage value caused by the multi-vehicle set increases from 0 to 1 is taken as the fatigue crack initiation life.

[0118] In some embodiments, the critical surface multi-axial stress fatigue theory can be used to predict the fatigue crack initiation life of each fatigue crack and predict the fatigue crack initiation life of the key position. The ratio threshold can be calculated based on the ratio of the shear stress amplitude to the normal stress amplitude, where the calculation formula of the ratio threshold is: In the formula, ρ lim is the ratio threshold, τ A,Ref is the fatigue parameter, and ρ is the ratio of the shear stress amplitude to the normal stress amplitude. Then, according to the ratio of the shear stress amplitude to the normal stress amplitude, the ratio threshold, the shear stress amplitude, and the number of cycles corresponding to the reference shear stress, the number of fatigue failures corresponding to each stress cycle is calculated, where the calculation formula for the number of fatigue failures is: In the formula,

[0119] N f is the number of fatigue failures, Δτ is the shear stress amplitude on the critical surface in the corresponding full cycle, N A is the number of cycles corresponding to the reference shear stress, which can be taken as 2×10 6 , τ A,Ref and k τ are fatigue parameters. It can be understood that the number of cycles N A The corresponding reference shear stress τ A,Ref (ρ) and k τ (ρ) can be a correction for any value of ρ The reverse slope of the curve. It can be obtained from τ with ρ = 1 and ρ = 0 A,Ref (ρ) and k τ (ρ) is determined. The reference shear stress is the number of cycles reaching 2×10 6 The stress time history is the stress response of the structure under a certain load. In the uniaxial tension and compression fatigue test, the normal stress is σ, and the angle between the maximum shear stress plane and the axial direction is θ = 45°, then ρ = σ 45 / τ 45 =0.5σ / 0.5σ=1. The critical surface of uniaxial tension and compression fatigue failure is ρ=1, where ρ=1 is the ratio of normal stress to shear stress on the critical surface of uniaxial tension and compression fatigue failure. The critical surface of uniaxial torsion high-cycle fatigue is ρ=0. τ can be obtained by conducting uniaxial tension and compression and torsion high-cycle fatigue tests, or by establishing a finite element model of a standard specimen based on the mechanical properties of the welded joint, and simulating the uniaxial high-cycle fatigue test. A,Ref (ρ=1), τ A,Ref (ρ=0), k τ (ρ=1), k τ (ρ=0).

[0120] Then, according to the ρ corresponding to each full cycle, N can be calculated f , denoted as N fi Based on Miner's linear fatigue cumulative damage theory, according to the number of fatigue failures and the number of full cycles, when the EMU train is combined into one group, the fatigue damage value at a key position of the fatigue crack initiation life prediction of the rail welding joint caused by the single train group is calculated by the fatigue damage value calculation formula, where the fatigue damage value calculation formula is: Where D n is the fatigue damage value caused by the bicycle group, n is the number of full cycles, N fi is the number of fatigue failures. The number of EMU train combinations per day is m. Based on the fatigue damage value of the rail weld joint caused by a single train set and the number of EMU train combinations, the fatigue damage value (mD) caused by multiple train sets at a certain fatigue crack initiation life prediction key position of the rail weld joint caused by multiple train sets per day can be calculated. n ). Finally, the fatigue damage value (mD n ) is taken as the time period from 0 to 1. It can be understood that when the fatigue damage value of the rail weld joint caused by multiple train sets reaches 1, the fatigue crack initiation life of the rail weld joint predicts the crack initiation at the key position, which is the fatigue crack initiation life of the rail weld. The fatigue crack initiation life is a time period, which refers to the time from intact to the beginning of crack initiation. The same calculation process can be used to predict the crack initiation at the key position of other fatigue crack initiation life. Exemplarily, the fatigue life N within the first full cycle is obtained. f =1.37×10 10 The fatigue life calculation under the remaining cycles is the same as the first full cycle fatigue life calculation. Based on Miner's linear fatigue cumulative damage theory, when a wheel passes through the rail welding joint, the fatigue damage value caused by the single vehicle group to that position is D n =9.2779×10 -8 Based on the first day of operation of a high-speed railway, 14 trains pass through the line every day, each train has 16 carriages, and each carriage has 4 high-speed rail wheels on one side. The fatigue damage value of the rail welding joint caused by multiple train sets every day is mD n =8.313×10 -5 When the fatigue damage value caused by multiple train sets reaches 1, the fatigue crack initiation life of the welded joint is about 33 years.

[0121] In some embodiments, in step S106, the fatigue crack initiation and propagation life is calculated according to the fatigue crack initiation life and the initiation position, which may include but is not limited to the following steps:

[0122] According to the initiation position, the initial crack is set, and the direction of the initial crack is parallel to the maximum shear stress plane in the rail weld area;

[0123] According to the fatigue crack initiation life, the crack occurrence time is sorted to obtain the crack initiation sequence;

[0124] According to the initial crack and crack initiation sequence, the relationship between the crack propagation path and the number of stress cycles is calculated;

[0125] When the crack depth or crack width increases to a critical threshold, the number of stress cycles is calculated based on the relationship between the crack extension path and the number of stress cycles;

[0126] Calculate fatigue crack growth life based on the number of stress cycles;

[0127] When the load-bearing capacity at the rail weld is less than the preset load-bearing threshold, the total fatigue crack growth life is calculated based on multiple fatigue crack growth lives;

[0128] The total life of fatigue crack initiation and growth is calculated based on the fatigue crack initiation life and the total life of fatigue crack growth.

[0129] In some embodiments, the initial crack can be set according to the initiation position, wherein the direction of the initial crack is parallel to the maximum shear stress plane in the rail weld area. More importantly, the direction of the initiation crack at each fatigue crack initiation life prediction key position is parallel to the maximum shear stress plane with the largest number of occurrences. Then, according to the fatigue crack initiation life, the crack occurrence time is sorted, and the crack occurrence time is defined in the order of crack initiation life from short to long to obtain the crack initiation order. Then, according to the initial crack and the crack initiation order, the Paris formula is used to calculate the relationship between the crack propagation path and the number of stress cycles, wherein the expression of the relationship between the crack propagation path and the number of stress cycles is: Wherein, α is the crack depth or crack width, N is the number of stress cycles, C and m are both material parameters, and ΔK is the stress intensity factor amplitude. It is understandable that the direction of the crack is known, and the crack depth or crack width α combined with the crack extension is the path. When the crack depth or crack width increases to the critical threshold, the number of stress cycles can be calculated based on the relationship between the crack extension path and the number of stress cycles, and the fatigue crack extension life can be calculated based on the number of stress cycles. It is understandable that when α expands to the critical length (that is, increases to the critical threshold, or reaches the surface of the object), the number of stress cycles corresponding to the expansion is the fatigue crack extension life of this crack. The crack extension angle can be determined based on the maximum circumferential stress failure criterion. When the bearing capacity at the rail weld is less than the preset bearing threshold, the total fatigue crack extension life is calculated based on multiple fatigue crack extension lives.

[0130] Exemplarily, the preset load threshold can be set to 85% of the intact state. The number of stress cycles is caused by the load, and the load history is related to the train combination. The number of trains in a day is the length of the load history, and the number of cycles in a day and the fatigue damage caused can be calculated. When the fatigue damage value is 1, the crack initiates. When the number of cycles reaches the time difference between the initiation of the first and second cracks, the second crack appears, and the relationship between the crack propagation path of the two cracks and the number of stress cycles is calculated; and so on, until the bearing capacity at the rail weld drops to 85% of the intact state, the rail weld can be considered to have failed, and the total life of fatigue crack propagation at the rail weld from the initiation of the first crack to this point. It can be understood that there are generally multiple cracks at the joint, and the position with the largest equivalent stress will first initiate cracks and enter the crack propagation stage. As time increases, the position with the second largest equivalent stress will appear after the initiation of the first crack and enter the crack propagation stage. When multiple cracks propagate and cause the load-bearing capacity of the rail weld to drop to 85% of that in good condition, the rail joint fails. The total fatigue crack propagation life of the rail joint is from the initiation of the first crack to the failure of the rail. The deformation of the rail weld joint when the load is applied when it is intact is equal to the deformation of the rail weld joint when the load is reduced to 15% after the crack appears, that is, the bearing capacity of the rail weld is considered to be 85% of that in good condition. Finally, the fatigue crack initiation and extension life is calculated based on the fatigue crack initiation life and the total fatigue crack extension life. Exemplarily, the fatigue crack initiation life and the total fatigue crack extension life can be added to obtain the fatigue crack initiation and extension life. More importantly, the fatigue crack initiation and extension life can be used for rail safety management.

[0131] In some embodiments, in the experiment, the initial crack can be set according to the initiation position obtained by analysis, a key position set is established in Abaqus, and it is imported into Franc 3d to define the crack length and shape. The crack set in this embodiment is as follows: Figure 5 As shown in the figure, the innermost semicircle is the initial crack, which extends downward from the semicircle, and the line represents the crack extension. Then use the Paris formula Calculate the relationship between the crack propagation path and the number of stress cycles, and calculate the length and direction of crack propagation. Among them, C and m are material parameters that can be obtained through experiments. The relationship between the crack propagation path and the number of stress cycles is obtained as follows Figure 6As shown. When α expands to the critical length (that is, reaches the surface), the corresponding number of stress cycles is the expansion life of the crack. The crack expansion angle is determined according to the maximum circumferential stress failure criterion. In this embodiment, in order to simplify the calculation, a wheel passing through the crack is equivalent to a load. Under this load, the number of cycles reaches 3447932 times, and the crack reaches the expansion amount specified in the specification, and the calculation is stopped, that is, the crack expansion amount corresponding to a wheel rolling over is 1 / 3447932. Also based on the first day of operation of a certain high-speed railway, the total life of fatigue crack expansion of the rail is converted to 10.5 years. It can be further obtained that the full life of fatigue crack initiation and expansion of the rail welded joint is 33+10.5=43.5 years.

[0132] In some embodiments, the overall process of predicting the full life of a rail joint is as follows: Figure 7 As shown in the figure, a finite element model of a rail welded joint can be established based on the mechanical properties of the tested parent material, weld and heat-shadow zone, and then the stress field at the rail weld under the rolling state of the wheel is extracted, and the fatigue crack initiation life with a large Mises equivalent stress is calculated to predict the time history curves of each stress component at the key position. Then, the critical surface multi-axial stress fatigue theory is used to calculate the fatigue crack initiation life of each fatigue crack and predict the fatigue crack initiation life at the key position to determine whether fatigue crack initiation exists. If fatigue crack initiation exists, the length and direction of the crack are set, and the relationship between the crack propagation path and the number of cycles is calculated using the Paris formula. When the bearing capacity at the rail weld drops to 85% of the intact state, the full life of fatigue crack initiation and propagation of the rail joint is calculated. This embodiment can predict the fatigue life of the rail welded joint; and the implementation process is simple. The fatigue crack initiation life of the rail welded joint can be determined by analyzing the fatigue crack initiation in a certain EMU train combination, and the initiation position and direction can be determined at the same time. On this basis, the crack propagation life is further analyzed until multiple cracks initiate and propagate, causing the bearing capacity of the rail weld to drop to 85% of the intact state, thereby obtaining the fatigue crack initiation and propagation life of the rail welded joint.

[0133] In some embodiments, the current prediction of fatigue life of rail welded joints can only predict the initiation of fatigue cracks, and obtain the crack initiation life at a certain position of the rail welded joint. However, there is still a long fatigue crack propagation life from crack initiation to failure of the rail welded joint. Therefore, the full life of fatigue crack initiation to propagation of the rail welded joint can be predicted to reasonably evaluate the fatigue performance of the rail welded joint. This embodiment first adopts the critical surface multi-axial stress fatigue theory to predict the fatigue crack initiation life of each key position of the rail welded joint, and sets the initial crack position and direction based on this, and then analyzes the relationship between the initiation crack propagation path and the number of cycles based on the Paris formula. Finally, when the bearing capacity at the rail weld drops to 85% of the intact state, the rail welded joint fails, and the full life of fatigue crack initiation and propagation of the rail welded joint is obtained by analysis, and the process is simple to implement. In addition, the current research is to study the fatigue crack initiation stage and the expansion stage of the rail welded joint separately. The research on the fatigue crack initiation stage of the rail welded joint rarely considers the changes in the mechanical properties of the weld and heat-affected zone of the welded joint, so the fatigue crack initiation life obtained has a large error; at the same time, in the research on the fatigue crack expansion stage of the rail welded joint, the position and direction of the initial crack are based on assumptions, which are inconsistent with the actual situation, resulting in the analysis results may not be consistent with the actual situation. Therefore, the full life prediction of fatigue crack initiation and expansion of the rail welded joint proposed in this embodiment is obtained by sampling the base material, heat-affected zone and weld of the rail welded joint, and using experiments to obtain their mechanical properties, and the position and direction of crack initiation are obtained by analyzing the fatigue crack initiation of the rail welded joint, so the fatigue life of the rail welded joint obtained by the method of the present invention is not only more in line with reality, but also has higher accuracy.

[0134] The beneficial effects of implementing the embodiments of the present invention include: the embodiments of the present invention first obtain rail welding joint data and parent material data, and establish a rail finite element model based on the rail welding joint data and the parent material data, and then calculate the key position for fatigue crack initiation life prediction and the corresponding stress component time history based on the rail finite element model, and calculate the ratio of shear stress amplitude to normal stress amplitude based on the key position for fatigue crack initiation life prediction and the corresponding stress component time history, and then calculate the fatigue crack initiation life based on the ratio of shear stress amplitude to normal stress amplitude, and finally calculate the fatigue crack initiation life and initiation position. The full life of fatigue crack initiation and extension is calculated, so that the fatigue crack initiation life and fatigue crack extension life can be combined to achieve fatigue crack initiation and extension The full life prediction improves the prediction accuracy.

[0135] like Figure 8 As shown, the embodiment of the present invention also provides a full life prediction device for fatigue crack initiation and propagation of rail welded joints, comprising:

[0136] The first module 801 is used to obtain rail welding joint data and parent material data;

[0137] The second module 802 is used to establish a rail finite element model according to the rail welding joint data and the parent material data;

[0138] The third module 803 is used to calculate the key position for predicting fatigue crack initiation life and the corresponding stress component time history according to the rail finite element model;

[0139] The fourth module 804 is used to calculate the ratio of the shear stress amplitude to the normal stress amplitude based on the fatigue crack initiation life prediction key position and the corresponding stress component time history;

[0140] The fifth module 805 is used to calculate the fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude;

[0141] The sixth module 806 is used to calculate the fatigue crack initiation and propagation life according to the fatigue crack initiation life and initiation position. The fatigue crack initiation and propagation life is used for rail safety management.

[0142] The contents of the above method embodiments are all applicable to the present device embodiments. The functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0143] like Fig. 9 As shown, an embodiment of the present invention further provides a computer device, including:

[0144] at least one processor 901;

[0145] At least one memory 902, used to store at least one program;

[0146] When at least one program is executed by at least one processor, the at least one processor implements Figure 1 The method shown.

[0147] The contents of the above method embodiments are all applicable to the present device embodiments. The functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0148] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights of the present invention.

Claims

1. A full life prediction method for fatigue crack initiation and growth of rail welded joints, characterized in that: The following steps are involved: Obtain rail welding joint data and parent material data; Establishing a rail finite element model according to the rail welding joint data and the parent material data; Calculating the key positions for predicting fatigue crack initiation life and the corresponding stress component time history according to the rail finite element model; Calculating the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the stress component time history; Calculating fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude; The fatigue crack initiation life and initiation position are used to calculate the fatigue crack initiation and propagation life, and the fatigue crack initiation and propagation life is used for rail safety management.

2. The method according to claim 1, characterized in that The step of establishing a rail finite element model according to the rail welding joint data and the parent material data comprises: Calculate the processing dimensions of the joint sample according to the rail welding joint data; Calculate the processing size of the parent material sample according to the parent material data; According to the processing size of the joint sample, a tensile test is performed on the rail welded joint to obtain a joint stress-strain curve; According to the processing size of the base material sample, a tensile test is performed on the base material to obtain a stress-strain curve of the base material; According to the joint stress-strain curve and the parent material stress-strain curve, a finite element model of the rail is established by using a finite element analysis method.

3. The method according to claim 1, characterized in that: The step of calculating the key position for predicting fatigue crack initiation life and the corresponding stress component time history according to the rail finite element model includes: Calculate the dynamic load time history according to the EMU train combination status; Loading the dynamic load time history onto the rail finite element model to obtain the stress field at the rail weld under the wheel rolling state; The position where the equivalent stress in the rail weld area is greater than a preset stress threshold is used as the key position for predicting the fatigue crack initiation life; The stress component time history at the key position for predicting the fatigue crack initiation life is extracted from the stress field.

4. The method according to claim 1, characterized in that: The calculating the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the stress component time history comprises: According to the fatigue crack initiation life prediction of the equivalent stress time history of the key position, the number of stress cycles and the start and end times are calculated by the rain flow counting method; Calculate the shear stress time history and the normal stress time history corresponding to each stress cycle according to the number of stress cycles, the start and end times, and the stress component time history; According to the shear stress time history and the normal stress time history, a plane with the largest shear stress in the rail weld region is taken as a critical surface; According to the critical surface, the ratio of the shear stress amplitude to the normal stress amplitude is calculated.

5. The method according to claim 1, characterized in that The calculating of the fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude comprises: Calculating a ratio threshold value according to the ratio of the shear stress amplitude to the normal stress amplitude; Calculating the number of fatigue failures corresponding to each stress cycle according to the ratio of the shear stress amplitude to the normal stress amplitude, the ratio threshold, the shear stress amplitude, and the number of cycles corresponding to the reference shear stress; Calculating the fatigue damage value caused by the bicycle group according to the fatigue failure number and the number of full cycles; According to the fatigue damage value caused by the single train set and the number of EMU train combinations, the fatigue damage value caused by the multiple train sets is calculated; and the time period for the fatigue damage value caused by the multiple train sets to increase from 0 to 1 is taken as the fatigue crack initiation life.

6. The method according to claim 1, characterized in that The calculating of the fatigue crack initiation and propagation life according to the fatigue crack initiation life and initiation position comprises: According to the initiation position, an initial crack is set, wherein the direction of the initial crack is parallel to the maximum shear stress plane in the rail weld area; According to the fatigue crack initiation life, the crack occurrence time is sorted to obtain the crack initiation sequence; Calculating the relationship between the crack propagation path and the number of stress cycles according to the initial crack and the crack initiation sequence; When the crack depth or crack width increases to a critical threshold, the number of stress cycles is calculated according to the relationship between the crack extension path and the number of stress cycles; Calculating fatigue crack growth life according to the number of stress cycles; When the load-bearing capacity at the rail weld is less than a preset load-bearing threshold, the total fatigue crack growth life is calculated according to the plurality of fatigue crack growth lives; The fatigue crack initiation and growth total life is calculated according to the fatigue crack initiation and growth total life.

7. The method according to claim 5, characterized in that The step of calculating the fatigue damage value caused by the bicycle group according to the fatigue failure number and the number of full cycles includes: According to the fatigue failure times and the number of full cycles, the fatigue damage value caused by the bicycle group is calculated by the fatigue damage value calculation formula, and the fatigue damage value calculation formula is: Where D n is the fatigue damage value caused by the bicycle group, n is the number of full cycles, N fi is the fatigue failure number.

8. The method according to claim 6, characterized in that The expression for the relationship between the crack propagation path and the number of stress cycles is: Where α is the crack depth, N is the number of stress cycles, C and m are material parameters, and ΔK is the amplitude of the stress intensity factor.

9. A full life prediction device for fatigue crack initiation and growth of rail welded joints, characterized in that: include: The first module is used to obtain rail welding joint data and parent material data; The second module is used to establish a rail finite element model according to the rail welding joint data and the parent material data; The third module is used to calculate the key position for predicting fatigue crack initiation life and the corresponding stress component time history according to the rail finite element model; A fourth module is used to calculate the ratio of the shear stress amplitude to the normal stress amplitude according to the fatigue crack initiation life prediction key position and the stress component time history; A fifth module is used to calculate the fatigue crack initiation life according to the ratio of the shear stress amplitude to the normal stress amplitude; The sixth module is used to calculate the fatigue crack initiation and extension life according to the fatigue crack initiation life and initiation position, and the fatigue crack initiation and extension life is used for rail safety management.

10. A computer device, characterized in that: include: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method according to any one of claims 1 to 8.

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