Discrete ballastless track tension and compression fatigue damage rapid calculation method

Abstract

The invention provides a discrete ballastless track tension-compression fatigue damage rapid calculation method, which comprises the following steps of: uniformly measuring a complex stress state and a simple stress state through a damage energy release rate, and decomposing tension-compression effective stress by utilizing a fourth-order projection tensor, so that the tension-compression effective stress value is equivalent to a uniaxial tension-compression stress value under a uniaxial loading condition; constructing a hyperbolic function with a natural constant as a base and a damage variable as an index on the basis of the damage energy release rate and in combination with three-stage damage characteristics of high-cycle fatigue of the material; carrying out integration on fatigue loading times through tension and compression damage, and deducing to obtain a discrete transcendental differential function of the damage related to the loading times; function variables are defined, an initial value is set, an iteration format is established, the discrete transcendental differential function is solved through a numerical integration method, and a calculation result graph is drawn. The model is simplified, and the calculation efficiency is improved; a high-order tensor stress updating algorithm does not need to be constructed, redundant calculation is reduced, and the data processing efficiency and the calculation speed during parameter analysis are greatly improved.

Description

Technical Field

[0001] This invention relates to the field of ballastless track technology, and in particular to a rapid calculation method for tensile and compressive fatigue damage of discrete ballastless track. Background Technology

[0002] Current Status and Damage Issues of Ballastless Track Applications: Ballastless track is the main structural type of high-speed railways. During its service design life, it needs to withstand tens of millions or even hundreds of millions of high-cycle fatigue loads from trains. Continuous repeated loads can cause damage such as cracking and spalling of track slabs, which degrades the mechanical properties of the track. If not detected in time, it will further weaken the structural durability and shorten the service life. Therefore, scientific and reasonable damage prediction technology is needed.

[0003] Limitations of traditional damage calculation methods: Existing concrete fatigue damage constitutive models are mostly composed of governing equations and damage evolution functions. Common methods include the linear damage accumulation method, the microplane method, and the competition mechanism method based on damage energy release rate (the latter is the most representative, which decomposes the effective tensile and compressive stresses by fourth-order projection tensile tensile tensile tensile and compressive damage energy release rate functions respectively).

[0004] Traditional models have significant drawbacks: the algorithms are complex (including descriptions of plastic behavior, while the service stress of ballastless track is far below the yield value, and plastic deformation is not reflected, leading to model redundancy); the fatigue damage equation uses a semi-empirical formula, which has poor adaptability to different train load characteristics and requires recalibration; the computational efficiency during parameter analysis is low, and there is a lack of fast calculation methods that can efficiently feed back parameter relationships and value rules. Summary of the Invention

[0005] This invention provides a rapid calculation method for tensile and compressive fatigue damage of discrete ballastless tracks to solve one or more of the problems mentioned above.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A rapid method for calculating discrete tensile and compressive fatigue damage of ballastless tracks includes: S1. The damage energy release rate is used to express the material damage state, realizing a unified measurement of complex stress state and simple stress state. The effective stress of tension and compression is decomposed by the fourth-order projection tensor to describe the stress state of fatigue damage under tension and compression respectively, so that the stress value under uniaxial loading is equivalent to the uniaxial tensile and compressive stress value. S2. Based on the tensile and compressive effective stress and damage energy release rate obtained from S1, and combined with the three-stage damage characteristics of high-cycle fatigue of materials, a hyperbolic function with the natural constant as the base and the damage variable as the exponent is constructed. This function serves as the core function of tensile and compressive fatigue damage evolution and adapts to the variation law of damage rate in the three stages. S3. Obtain train load characteristic parameters through field testing or theoretical simulation. Using these parameters as loading conditions, perform fatigue loading number integration on tensile and compressive damage based on the hyperbolic function in S2. Transform the derivative of damage with respect to time into the derivative with respect to the number of loading times, and derive the discrete transcendental differential function related to the number of loading times. S4. Define function variables and set initial values. The function variables include train load characteristic parameters and concrete tensile and compressive fatigue damage characteristic parameters. Move the right-hand side of the discrete transcendental differential equation in S3 to the left-hand side to form an iterable equation. Construct an iterative format of F(d)=0 and use the solution function of the numerical calculation tool to solve it iteratively. Plot the calculation results with the normalized cycle ratio of loading times as the x-axis and the damage variable as the y-axis.

[0007] In this specification, complex stress states include three normal stress components and three shear stress components, while simple stress states include uniaxial tensile stress states and uniaxial compressive stress states. A unified metric is established for both through damage energy release rate.

[0008] In this specification, after the effective stress of tension and compression is decomposed by the fourth-order projection tensor in S1, the stress states of tensile fatigue damage and compressive fatigue damage are described independently without interference, ensuring the accurate characterization of the evolution law of tensile and compressive damage.

[0009] In this specification, the three-stage damage characteristics of the material under high-cycle fatigue are as follows: In the first stage, stress concentration is caused by micro-defects inside the material, resulting in microcracks and rapid decay of the material's mechanical properties; In the second stage, crack propagation releases internal energy, and the energy accumulation and release reach a relatively stable state, with the material's mechanical properties decaying slowly, and this stage accounts for the highest proportion; In the third stage, microcracks continue to propagate, internal defects are aggravated, the energy balance is broken, and the material's mechanical properties decay again at an accelerated pace.

[0010] In this specification, the domain of the hyperbolic function is from 0 to 1, and the function value is always greater than 0. The variation law of its derivative is consistent with the damage rate of the three stages of high cycle fatigue, that is, the derivative is first less than 0, then equal to 0, and finally greater than 0 and gradually increases, which respectively correspond to the process of rapid decay of damage rate, tendency to stabilize, and accelerated accumulation.

[0011] In this specification, the specific process of obtaining train load characteristic parameters in S3 is as follows: First, collect train wheel-rail force data through field testing or theoretical simulation, draw a wheel-rail force frequency histogram to determine the load extreme value range, then calculate the stress in combination with the ballastless track structure, extract the stress data at the most unfavorable load position, and finally determine the load characteristic parameters, which include average stress, stress amplitude and load frequency.

[0012] In this specification, when integrating the fatigue loading cycles for tensile and compressive damage in S3, considering that the damage does not increase during unloading, the integration is only performed within the effective load range, and the integration term in the unloading range is ignored to simplify the calculation process.

[0013] In this specification, the range and spacing of the characteristic parameters of concrete tensile and compressive fatigue damage in S4 are determined by the controlled variable method, combined with the position of the characteristic parameters of concrete tensile and compressive fatigue damage in the formula and whether they are in the exponential term. Specifically, some parameters are fixed, and multiple sets of values ​​are assigned to the target parameters. The damage curves under different values ​​are calculated, with the parameter value at which the second obvious three-stage phenomenon appears as the lower boundary and the value near the asymptote as the upper boundary. The value spacing is determined based on the sensitivity of the trial values ​​to the damage curve. In the initial values, the initial value of the damage variable is set to 0, and the initial values ​​of the other parameters are adjusted according to engineering experience or trial calculation benchmark values.

[0014] In this specification, when constructing the iterative format in S4, a two-dimensional array is set to store the normalized cycle ratio of the loading times and the corresponding damage variables. The damage values ​​under different loading times are obtained sequentially through iterative calculation. The solution function of the numerical calculation tool is used to solve the iterable equation to obtain the damage variables corresponding to each cycle.

[0015] In this manual, the calculation result graph drawn by S4 is labeled with the normalized cycle ratio on the horizontal axis and the damage variable on the vertical axis. The graph includes a clear title and legend, distinguishing between tensile fatigue damage curves and compressive fatigue damage curves, and intuitively presenting the correspondence between the number of loading cycles and damage accumulation.

[0016] In summary, the present invention has at least the following beneficial effects: Simplify the model and improve computational efficiency: Filter out the influence of material plasticity on fatigue damage, focus on elastic fatigue damage evolution, and reduce model complexity; eliminate the need to build high-order tensor stress update algorithms, reduce redundant calculations, and significantly improve data processing efficiency and computation speed during parameter analysis.

[0017] Optimize damage description and improve accuracy: Based on the concrete fatigue curve results under train load characteristics, propose a self-consistent tensile fatigue damage evolution equation under different tensile stress levels. This solves the irrationality of the traditional model using a uniform equation to describe the anisotropic tensile and compressive damage of concrete, and more accurately characterizes the fatigue characteristics of ballastless track concrete.

[0018] Clearly define the damage correlation to facilitate engineering applications: Transform the correlation between fatigue damage and "time" into a direct correlation with "number of loading cycles," intuitively reflecting the cumulative effect of damage; Combined with simple numerical integration methods, the "number of loading cycles - damage" relationship can be quickly obtained, making it easier for engineers to understand the development law of track damage and support the safety assessment and maintenance decisions of ballastless tracks. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the rapid calculation method for tensile and compressive fatigue damage of discrete ballastless track involved in this invention.

[0021] Figure 2 This is a schematic diagram of the damage evolution in the three stages of high-cycle fatigue in the embodiment.

[0022] Figure 3 This is a schematic diagram illustrating the physical meaning of the average nominal stress and the nominal stress amplitude in the embodiment.

[0023] Figure 4 This is a schematic diagram of the train load type curve in the embodiment.

[0024] Figure 5 The diagram shows damage curves at different stress levels in the embodiment.

[0025] Figure 6 This is a comparison diagram of the fast calculation solution and the finite element solution of compressive fatigue damage in the example.

[0026] Figure 7 This is a comparison diagram between the fast calculation solution and the finite element solution of tensile fatigue damage in the example. Detailed Implementation

[0027] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0028] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0029] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0030] like Figure 1 As shown, this embodiment provides a rapid calculation method for discrete tensile and compressive fatigue damage of ballastless tracks, including: S1. The damage energy release rate is used to express the material damage state, realizing a unified measurement of complex stress state and simple stress state. The effective stress of tension and compression is decomposed by the fourth-order projection tensor to describe the stress state of fatigue damage under tension and compression respectively, so that the stress value under uniaxial loading is equivalent to the uniaxial tensile and compressive stress value. S2. Based on the tensile and compressive effective stress and damage energy release rate obtained from S1, and combined with the three-stage damage characteristics of high-cycle fatigue of materials, a hyperbolic function with the natural constant as the base and the damage variable as the exponent is constructed. This function serves as the core function of tensile and compressive fatigue damage evolution and adapts to the variation law of damage rate in the three stages. S3. Obtain train load characteristic parameters through field testing or theoretical simulation. Using these parameters as loading conditions, perform fatigue loading number integration on tensile and compressive damage based on the hyperbolic function in S2. Transform the derivative of damage with respect to time into the derivative with respect to the number of loading times, and derive the discrete transcendental differential function related to the number of loading times. S4. Define function variables and set initial values. The function variables include train load characteristic parameters and concrete tensile and compressive fatigue damage characteristic parameters. Move the right-hand side of the discrete transcendental differential equation in S3 to the left-hand side to form an iterable equation. Construct an iterative format of F(d)=0 and use the solution function of the numerical calculation tool to solve it iteratively. Plot the calculation results with the normalized cycle ratio of loading times as the x-axis and the damage variable as the y-axis.

[0031] In some embodiments, a complex stress state includes three normal stress components and three shear stress components, and a simple stress state includes a uniaxial tensile stress state and a uniaxial compressive stress state. Both are measured by a unified metric based on the damage energy release rate.

[0032] The three normal stress components are oriented in the same direction as the normal to the surface of application (i.e., perpendicular to the surface), primarily reflecting the stress tendency of an object under tension or compression. For precise positioning, a spatial rectangular coordinate system (x, y, z axes) needs to be established. The three normal stress components correspond to three mutually perpendicular surfaces, that is, the surfaces are perpendicular to the x, y, and z axes, and the stress directions are along the x, y, and z axes.

[0033] The three shear stress components are parallel to the stress surface (i.e., along the tangent of the surface) and mainly reflect the force tendency of the object to "shear or shift". They are: the surface is perpendicular to the x-axis and the shear stress direction is along the y-axis; the surface is perpendicular to the y-axis and the shear stress direction is along the z-axis; the surface is perpendicular to the z-axis and the shear stress direction is along the x-axis.

[0034] In some embodiments, after the effective tensile and compressive stresses are decomposed by the fourth-order projection tensor in S1, the stress states of tensile fatigue damage and compressive fatigue damage are described independently and do not interfere with each other, ensuring the accurate characterization of the tensile and compressive damage evolution law.

[0035] In some embodiments, the three-stage damage characteristics of the material during high-cycle fatigue are as follows: In the first stage, stress concentration is caused by micro-defects inside the material, resulting in microcracks and rapid decay of the material's mechanical properties; in the second stage, crack propagation releases internal energy, and energy accumulation and release reach a relatively stable state, with the material's mechanical properties decaying slowly, and this stage accounting for the highest proportion; in the third stage, microcracks continue to propagate, internal defects are aggravated, the energy balance is broken, and the material's mechanical properties decay again at an accelerated pace.

[0036] In some embodiments, the domain of the hyperbolic function is 0 to 1, and the function value is always greater than 0. The variation law of its derivative is consistent with the damage rate of the three stages of high cycle fatigue, that is, the derivative is first less than 0, then equal to 0, and finally greater than 0 and gradually increases, which respectively correspond to the process of rapid decay of damage rate, tendency to stabilize, and accelerated accumulation.

[0037] In some embodiments, the specific process of obtaining train load characteristic parameters in S3 is as follows: first, train wheel-rail force data are collected through field testing or theoretical simulation, a wheel-rail force frequency histogram is plotted to determine the load extreme range, then the stress is calculated in combination with the ballastless track structure, the stress data at the most unfavorable load position is extracted, and finally the load characteristic parameters are determined. The load characteristic parameters include average stress, stress amplitude and load frequency.

[0038] In some embodiments, when integrating the fatigue loading cycles for tensile and compressive damage in S3, considering that the damage does not increase during the unloading process, the integration is only performed within the effective load range, and the integral term in the unloading range is ignored to simplify the calculation process.

[0039] In some embodiments, the range and spacing of the concrete tensile and compressive fatigue damage characteristic parameters in S4 are determined by the control variable method in combination with the position of the concrete tensile and compressive fatigue damage characteristic parameters in the formula and whether they are in the exponential term. Specifically, some parameters are fixed, multiple sets of values ​​are assigned to the target parameters, and the damage curves under different values ​​are calculated. The parameter value at which the second obvious three-stage phenomenon appears is taken as the lower boundary, and the value near the asymptote is taken as the upper boundary. The value spacing is determined by trial calculation of the sensitivity of the values ​​to the damage curve. In the initial values, the initial value of the damage variable is set to 0, and the initial values ​​of the other parameters are adjusted according to engineering experience or trial calculation benchmark values.

[0040] In some embodiments, when constructing the iterative format in S4, a two-dimensional array is set to store the normalized cycle ratio of the number of loadings and the corresponding damage variables. The damage values ​​under different loading numbers are obtained sequentially through iterative calculation. The solution function of the numerical calculation tool is used to solve the iterable equation to obtain the damage variables corresponding to each cycle.

[0041] In some embodiments, the calculation result graph drawn by S4 is labeled with the normalized cycle ratio on the horizontal axis and the damage variable on the vertical axis. The graph includes a clear title and legend, distinguishing between tensile fatigue damage curves and compressive fatigue damage curves, and intuitively presenting the correspondence between the number of loading cycles and damage accumulation.

[0042] The technical concept of this invention is as follows: A rapid calculation method for discrete tensile and compressive fatigue damage of ballastless track includes the following steps: Step 1: Express the material damage state using damage energy release rate to distinguish between complex and simple stress states. This serves as a unified measure for both complex and simple stress states, making them equivalent to uniaxial tensile and compressive stress values ​​under uniaxial loading conditions.

[0043] In step 1, the complex stress state includes along x Normal stress ,along y Normal stress ,along z Normal stress ,exist x Normal plane pointing y shear stress in the direction ,exist y Normal plane pointing z shear stress in the direction ,exist x Normal plane pointing z shear stress in the direction Simple stress states include uniaxial tension and uniaxial compression.

[0044] In step 1, the effective stress after tensile and compressive stress decomposition is used to define the damage energy release rate under tension and compression. The tensile and compressive stress decomposition is performed using a fourth-order projection tensor. accomplish, , This represents the eigenvector corresponding to the principal stresses of the effective stress. For the Heaviside function, when the effective principal stress The value is 0 when ≤0 and 1 when >0. α =1, 2, 3. Based on the different components of the fourth-order projection tensor of the principal stress state of the effective stress, such as the effective principal stress... ≤0, effective principal stress ≤0, effective principal stress ≤0, then , >0, ≤0, ≤0, then , >0, >0, ≤0, then ,when >0, >0, >0, then Then, the effective stress and the fourth-order projection tensor are combined. The result obtained is the effective tensile stress, through , Perform tensor shrinking operation on a unit-consistent tensor. The result obtained is the effective compressive stress.

[0045] The stress state descriptions of tensile and compressive fatigue damage evolution are given separately, as shown in equation (1): (1) In the formula, tension is positive and compression is negative. For the effective stress tensor of tension and compression in ( i , j The component at the position, where the variable being multiplied appears twice in the expression is a repetition indicator. i , j , k , n These are all indices of the stress tensor. All repeated indices need to be summed within their domain, i.e., they must conform to Einstein's summation convention: such as... , If position "11" is taken as the direction of single-axis loading, when the single axis is under compression... When a single axis is under tension The formula for damage release rate is adapted from "Research on Constitutive Model of Elastic-Plastic Damage in Concrete I: Basic Formulas": any meaningful monotonic function can be used as a damage criterion to control damage development. The definition of this function is based on the expressions of the third and fourth strength theories of mechanics of materials, which state that regardless of the stress state of the material, changes in internal variables such as plasticity / damage are caused by a certain judgment condition reaching a threshold. This represents the initial Poisson's ratio.

[0046] Step 2: Based on the damage energy release rate defined by the effective stress of tension and compression, and combined with the three-stage damage characteristics of material fatigue, a function reflecting the three-stage changes is constructed using the natural constant as the base and the damage variable as the exponent. High-cycle fatigue of materials often exhibits a three-stage damage evolution: In the first stage, micro-cracks are generated due to stress concentration caused by microscopic defects in the internal structure of concrete, leading to a rapid decline in the mechanical properties of the concrete specimen. In the second stage, crack propagation releases the energy accumulated inside the concrete, and under load, energy accumulation and release reach a relatively stable state, thus mitigating the decline in the mechanical properties of the concrete. In the third stage, micro-cracks propagate, internal defects intensify, the relative balance is eventually broken, and internal damage intensifies, causing its mechanical properties to decline again at an accelerated pace. The three-stage damage is as follows: Figure 2 As shown.

[0047] The function has a steep slope in the first stage, indicating rapid damage accumulation. The second stage is relatively gentle, with a slow accumulation rate, and it accounts for the largest proportion of the three stages. An equation can describe all three stages; in this invention, a hyperbolic function is used. The function's value is greater than 0 within its domain [0,1]. The first derivative initially shows a value less than 0, then greater than 0, indicating that the damage rate initially increases rapidly, then gradually slows down. When the first derivative equals 0, the damage stops increasing and tends to stabilize. The final derivative is greater than 0 and gradually increases, indicating that the damage rate is continuously accelerating. Therefore, this function aligns well with the three stages of fatigue development and is well-suited for characterizing the fatigue damage evolution of materials. The rate of damage in the first stage can be controlled; the larger the value, the faster the damage decays, and the smaller the value, the slower the damage decays. The damage rate in the third stage is controlled; the larger the value, the faster the damage accumulation rate, and the smaller the value, the slower the damage accumulation rate. Based on the flexural-tensile damage curve of concrete, the damage accumulation rate in the second stage is greater than that in the compressive fatigue damage accumulation curve, and the constructed function... The inability to balance the large differences in damage curves under different stress levels results in significant deviations in tensile damage curves at different stress levels; therefore, [the following is used]... , To optimize the cumulative effect of the first and second stages of damage curves under different loading stress levels, using... The distance between damage evolution relationships under different stress levels is narrowed; the tensile and compressive fatigue damage functions of ballastless track concrete under different stress levels are reorganized into formulas based on the fatigue tensile and compressive damage laws under different stress levels, as shown in equations (2) and (3), where Representing tensile and compressive damage variables ( Represents tensile damage variable, (Representing compressive damage variables), characteristic parameters of concrete tensile-compressive fatigue damage include: , , , , , , . Parameters related to the fatigue accumulation process of the tensile / compressive exponential term ( For parameters related to the fatigue accumulation process of the exponential term, (Parameters related to the fatigue accumulation process of the exponential term). The parameters related to the tensile / compressive energy dissipation density caused by fatigue microcrack propagation ( The parameters related to tensile dissipation energy density caused by fatigue microcrack propagation are as follows: (This refers to the energy density related parameters of pressure dissipation caused by fatigue microcrack propagation). , These are the parameters for accelerating and inhibiting tensile / compressive damage in the first and third stages of fatigue, respectively. , For hyperbolic functions, tension / compression and front / back distribution coefficients ( For the Lagrange and pre-distributive coefficients of hyperbolic functions, For hyperbolic functions, the compression and pre-distribution coefficients are... For the Lagrange and post-distribution coefficients of hyperbolic functions, (For hyperbolic functions, compression and post-distribution coefficients). Parameters related to the fatigue accumulation process of the tensile / compressive constant term ( For parameters related to the fatigue accumulation process of the constant term, (Parameters related to the fatigue accumulation process of the pressure constant term). (2) (3) Step 3: Obtain the discrete transcendental differential function expression by integrating the fatigue loading times with respect to tensile and compressive damage, and obtain the discrete fast calculation expression.

[0048] In parametric analysis, simple loading conditions are generally used for calculation and analysis. Considering that finite element calculation requires element meshing, model building, material property allocation, material subroutine programming, overall stiffness matrix construction, and algorithm development for consistent tangent stiffness matrix, the results calculation and analysis store stress and strain in different coordinate axis directions, damage values ​​and displacements under different loading times, etc., which introduces redundant costs to parametric analysis under simple loading in terms of both calculation time and storage space. At the same time, the model is a damage accumulation function directly related to time, and it is difficult to intuitively obtain the relationship between the number of loading cycles and damage accumulation under constant amplitude loading conditions. Therefore, an analytical expression of fatigue damage and the number of loading cycles is sought to save calculation and storage costs and to directly and clearly define the relationship between the number of cycles and damage. Under 1D uniaxial tensile and compressive fatigue loading, the tensile and compressive damage energy release rate is... It can be simplified to effective tensile and compressive stresses , Therefore, the left sides of equations (2) and (3) remain unchanged, while the right sides are replaced by effective tensile and compressive stresses, respectively. The terms on the right side regarding the damage variable are then... , By moving the terms to the left side of the equation and combining like terms, we can obtain the damage expression after separating the variables, and then derive the analytical expression based on this.

[0049] Since the derivation process of analytical functions for tension and compression is the same, the following example uses uniaxial compressive fatigue. By analyzing the statistical characteristics of train loads, the maximum and minimum values ​​of train loads, the mean and variance of frequency characteristics, and the amplitude range of the 3x root mean square error confidence interval are obtained. This provides load assumptions for the actual loading conditions of the track structure. The eigenvalues ​​are used as key parameters of the loading function to calculate the maximum compressive stress borne by the track structure components. Based on this, the nominal stress of the load is calculated. According to the sine function expression, as shown in equation (4): (4) In the formula , These are the average nominal stress and the nominal stress amplitude, respectively. Figure 3 As shown, f For the load frequency, three load characteristic parameters are used to define load variation. These characteristics are obtained through train load statistics and stress calculations based on the track structure; the effective stress is the nominal stress. Therefore, the effective stress is times higher. The nominal stress can be divided by 1- To express oneself.

[0050] The effective stress of the load versus time t Find the derivative, where time is the factor. t The relevant variables are and By differentiating by parts, we obtain equation (5): (5) Because of the existence of the formula This affects the existence of the solution when deriving the fast calculation expression for the loading period and damage in the subsequent process. Therefore, the damage is frozen and assumed to remain unchanged over time. Based on the form of the ignored terms, it can be seen that when the damage is small... It is relatively close to 1, and then with When multiplied, the calculated value of the entire term will be much smaller than that of the first term. Calculated value. But as the accumulated damage increases, The value will approach 0, and the calculated value of the entire term will increase rapidly, affecting the overall calculation result and causing a large deviation between the rapid calculation expression and the direct finite element solution in the second and third stages of fatigue loading. However, through trial calculations, it was found that this term has little impact on the exploration of parameter laws. Therefore, a certain degree of accuracy is sacrificed to find a rapid calculation expression for the result in order to improve the efficiency of parameter analysis. Thus, equation (5) will Ignoring this, only the first term remains on the right side of equation (5).

[0051] To make the expression concise, let Substituting the simplified equation (5) into equation (2) after combining like terms, we can obtain the damage evolution function related to the average nominal stress, nominal stress amplitude, and load frequency.

[0052] Due to the current The equation is a differential with respect to time t, while the load is a constant-amplitude, constant-frequency excitation. Therefore, the load is discussed within each complete loading cycle. The advantages of this approach are: ① By integrating the cycles, these complex time-varying characteristics can be averaged or simplified, resulting in a more manageable and analytical equation about the cyclic period; ② For problems requiring long-term simulations or iterative solutions, directly solving the original differential equation is very time-consuming. Integrating the cycles simplifies the problem to an equation about the cyclic period, significantly reducing computational complexity; ③ The equation after period integration has a simpler form, making it easier to apply various mathematical tools for parameter analysis, further revealing the material's fatigue parameter sensitivity, and providing an efficient calculation method for quickly determining material parameters.

[0053] The loading period is the reciprocal of the frequency. Therefore, within one period, the derivative of the left side of the equation with respect to time t This will be transformed into the derivative with respect to the number of iterations. Integrating the right side of the equation over one cycle, we obtain the integral of the damage with respect to the number of cycles as shown in equation (6): (6) Considering that the damage does not increase during unloading, During unloading, it automatically becomes 0, and the integral term on the right side of equation (6) is arranged according to a period [0, Piecewise representation, only in the interval [0, ]and[ , The integral term on the right side of the equation becomes not equal to 0. .

[0054] Substituting the integral result into equation (6), we obtain the transcendental differential expression function of the number of cycles and damage as shown in equation (7): (7) Since the left side of equation (7) is a transcendental differential equation, it cannot be directly integrated. By using numerical integration, multiple sets of equations with equal spacing can be constructed and solved to obtain a discrete system of equations. The spacing of the discrete equations can be adjusted automatically. Taking a spacing of 1 as an example, as shown in equation (8): (8) It belongs to the set of natural numbers and is represented by 0, 1, 2...; Similarly, based on the uniaxial tension condition, the transcendental differential expression function of tensile damage and fatigue loading cycles is derived as shown in equation (9): (9) in .

[0055] Step 4: Solve the discrete fast calculation expression using numerical integration and plot the calculation results.

[0056] Step 4 specifically involves: (1) Define function variables; The variables that need to be defined in expressions (8) and (9) are: , , , , , , , , , ; in, , The load characteristics of the train can be used to determine the maximum load range. First, a wheel-rail force frequency histogram is plotted using the train wheel-rail force dataset obtained from on-site or theoretical simulations. This yields the maximum and minimum possible wheel-rail forces within a certain confidence interval. Second, the track slab directly bears the rail support pressure transmitted from the rails. The load is determined by the superposition of the front and rear wheels, forming an "M"-shaped load time history curve with one bogie as the unit. Figure 4 Using the trough between the two peaks of the "M"-shaped curve as the minimum value, the maximum and minimum load ratio of the train was found through analysis of the load range of the time-history curve. / Between 0.36 and 0.4, a cyclic load curve can be set, which can then be imported into the finite element model of the ballastless track to calculate the stress on the ballastless track under the cyclic load curve and extract the maximum stress at the most unfavorable load location. With minimum stress ,but , .

[0057] , The damage rate can be determined by observing the changes in the damage accumulation curve at different stages. (Based on the hyperbola) It can be seen that the damage rate values ​​at x=0, x=1 and x=0.5 differ significantly, and it is impossible to simultaneously satisfy the condition. Figure 5 Two curves under different stress levels are shown, therefore it is necessary to reduce the initial damage rate and the difference between the first and second stage damage rates, which can be achieved by... In Add above , ,make =0、 The value of =1 and A smaller difference in the value of 0.5 can reduce the difference in damage rates between the first and second stages of fatigue, by adjusting the... Change , The trial calculations show that when the damage rate in the first stage decreases from 1 to 0.026, and the difference between the damage rate in the first stage and the damage rate in the second stage decreases from 1 - 0.625 = 0.375 to 0.026 - 0.007 = 0.018, the following can be obtained. =0.08, =1.15.

[0058] , , , , The parameters were determined one by one using the controlled variable method, with the value range for each parameter determined through trial calculations. The stress was set to a fixed tensile stress level of 0.3. , Under a tensile stress level of 0.5 , , , If you want to clarify ,Will , ,, , Assign a fixed value, and Different value ranges are assigned for each value calculation. The value range is determined based on its role in the damage energy release rate index; it cannot be too large, while also considering the difference in damage curves between different stress levels. Trial calculations determined that a value within [0,1] was appropriate. This value was then applied to a rapid calculation method, where a second, clearly defined three-stage phenomenon was observed. The value is determined by the lower boundary and the asymptote as the upper boundary. The range of values ​​and the interval between values, Take [0.05 0.1 0.15 0.2 0.3 0.5 0.8], The value range is based on its damage energy release rate and The reason for the exponential part of the ratio is that, based on the range of 0 to 1, by substituting values, an asymptote is found near -20. The range is [-20 -12.0 -8.0 -5.0 -0.5 0.5 5.0 8.012 20]. The values ​​of other parameters are based on the same criteria and range. The main consideration is the position of the parameter in the formula, whether it is in the exponential term. The lower boundary is the parameter value where the three-stage phenomenon appears for the second time, and the upper boundary is the value near the asymptote. The interval between values ​​is determined by calculating the sensitivity of the values ​​to the damage curve. Take [3.0 4.0 5.0 6.0 8.0 10.0], Take [0.5 1.0 2.0 4.0 8.0 20.0 100.0], Take [1.6 2.0 2.6 3.0 50.0 200.01000.0], Take [22.0 23.0 24.0 32.0 64.0 96.0 250.0 350.0 390.0], Take [42.0 45.0 48.0 51.0 54.0 100.0 200.0], Take [27.0 30.0 34.0 38.0 100.0 300.0 500.0 700.0], Take [4.0 4.5 5.0 5.5 8.0 10.0 20.0], The influence of different values ​​[25.0 27.5 30.0 35.5 40.0] on the damage curve was analyzed. The influence of different values ​​on the damage curve was calculated using the discrete track slab damage rapid calculation method.

[0059] (2) Set initial values ​​for the variables, and adjust each initial value as needed; Obtaining a constant, under pressure: ; Pulled: ; (3) Establish the iterative format; (3.1) Set the maximum number of loops; the value can be defined by yourself. (3.2) Set the initial value for the iteration count variable; (3.3) Set a two-dimensional empty set, with the row dimension of the set being the maximum number of iterations. N The column dimension is 2, which are used to store the cycle ratio. n / N With damage variables d A for loop is used to construct an iterative calculation scheme for the damage; the constructed iterative scheme adopts... F ( x =0, move the right side of the original equation (9) to the left side, and construct the equation as follows: F ( d The iterable equation with )=0 is solved using the fsolve function in MATLAB, and damage calculations are performed using a for loop for different loading cycles. Taking compressive fatigue as an example, the specific iterative code is as follows: for i = 1:N sum = sum + 1; y0=Y(sum,2); (sum+1,2)=fsolve(@(y)(y-y0). / (exp(-a1*(b1+y))+exp(-a2*(b2-y))).*(1-y)^(1-m)-k,y0); Y(sum+1,1) = sum / N; end. Where N is the total number of loading attempts, sum is the accumulated loading variable, which can be incremented by 1 for each loop (the increment interval is adjustable), Y() is an array storing the damage variable and the number of loading attempts, and a1 and a2 represent respectively... , y represents pressure damage m is k is a constant obtained in the second step: y0 represents the damage result from the previous iteration, initially set to 0.

[0060] (4) Draw a graph of the calculation results; Normalized loop ratio of loading count n / N Plot the damage variable as the ordinate on the x-axis, including setting the graph title, setting the legend, and setting the names of the y-axis and ordinate for damage and cycle number.

[0061] In this embodiment, the normalized damage-fatigue number obtained from the fast calculation solutions of finite element method and discrete method are plotted simultaneously. Figure 6 and Figure 7 As can be seen, the curves obtained by both methods are quite consistent in the first and second stages of fatigue, but there is a certain error in the third stage. In the application scenario of parameter analysis, both the discrete fast calculation solution and the finite element solution can characterize the variation law of the curve under different parameter conditions. The calculation time used by the finite element method is about 105s, while the calculation time of the discrete fast calculation solution is only about 2.67s, which significantly improves the calculation efficiency.

[0062] In parametric analysis, it is unnecessary to construct a high-order tensor stress update algorithm to participate in the finite element calculation. The idea is to ensure the specificity of the calculation as much as possible, without considering how the consistent tangent stiffness tensor is derived, how it participates in the finite element calculation, or how it is updated. Instead, more emphasis is placed on the evolution of damage. At the same time, the relationship between fatigue damage and time is transformed into a relationship with the number of cyclic loading cycles, which more intuitively describes the cumulative effect of damage behavior.

[0063] This method optimizes the driving factors of damage, unifying elasticity and plasticity into elastic fatigue damage, thus avoiding the problem that plasticity is not applicable at low stress levels. The tensile fatigue damage function needs to be reconstructed by considering the differences in damage curves under different tensile stress levels. This solves the problem of using a consistent damage equation to describe the damage of anisotropic concrete under tension and compression, making the fatigue damage equation more targeted for the analysis of damage behavior of ballastless track under train load.

[0064] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0065] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

[0066] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention. The above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

[0067] It should be noted that the above description of the process is for illustrative purposes only and does not limit the scope of this specification. Those skilled in the art can make various modifications and changes to the process under the guidance of this specification. However, these modifications and changes remain within the scope of this specification.

[0068] The basic concepts have been described above. Obviously, for those skilled in the art who have read this application, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore, such modifications, improvements, and corrections still fall within the spirit and scope of the exemplary embodiments of this application.

[0069] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different positions in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0070] Furthermore, those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Therefore, aspects of this application can be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. All of the above hardware or software can be referred to as a “unit,” “module,” or “system.” Furthermore, aspects of this application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0071] The computer program code required for the operation of each part of this application can be written in any one or more programming languages, including object-oriented programming languages ​​such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, and Python; general programming languages ​​such as C; Visual Basic, Fortran2103, Perl, COBOL2102, PHP, and ABAP; dynamic programming languages ​​such as Python, Ruby, and Groovy; or other programming languages. This program code can run entirely on the user's computer, or as a standalone software package on the user's computer, or partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer via any network, such as a local area network (LAN) or wide area network (WAN), or connected to an external computer (e.g., via the Internet), or in a cloud computing environment, or used as a service such as Software as a Service (SaaS).

[0072] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this application are not intended to limit the order of the processes and methods of this application. Although some currently considered useful embodiments of the invention have been discussed in the foregoing disclosure by way of various examples, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the substance and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a purely software solution, such as an installation on an existing server or mobile device.

[0073] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this approach of the present application should not be construed as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject of the invention should possess fewer features than in any single embodiment described above.

Claims

1. A discrete type of ballastless track tension-compression fatigue damage rapid calculation method, characterized in that, The application relates to a method for calculating the fatigue damage of concrete under complex stress state, which comprises the following steps: S1, a damage energy release rate is used to express the material damage state, a unified measurement is realized between the complex stress state and the simple stress state, the tensile and compressive effective stresses are decomposed by a fourth-order projection tensor, and the stress states of the tensile and compressive fatigue damages are respectively described, so that the stress value under the uniaxial loading condition is equivalent to the uniaxial tensile and compressive stress values; S2, based on the tensile and compressive effective stresses and the damage energy release rate obtained in S1, a hyperbolic function with a natural constant as a base and a damage variable as an index is constructed according to the three-stage damage characteristics of the material high-cycle fatigue, the function is used as a core function of the tensile and compressive fatigue damage evolution, and the variation law of the three-stage damage speed is adapted; S3, train load characteristic parameters are obtained through field testing or theoretical simulation, the parameters are used as loading conditions, the hyperbolic function in S2 is used for the fatigue loading time integration of the tensile and compressive damages, the derivative of the damage with respect to time is converted into the derivative of the damage with respect to the loading time, and a discrete transcendental differential function related to the damage and the loading time is derived; S4, function variables are defined and initial values are set, wherein the function variables include train load characteristic parameters and concrete tensile and compressive fatigue damage characteristic parameters, the right side item of the discrete transcendental differential equation in S3 is moved to the left side to form an iterative equation, an iterative format of F(d)=0 is constructed, a solving function of a numerical calculation tool is used for cyclic solving, and a calculation result graph is drawn with the normalized cyclic ratio of the loading time as the horizontal coordinate and the damage variable as the vertical coordinate.

2. The method according to claim 1, wherein the method is characterized by, The complex stress state comprises three normal stress components and three shear stress components, and the simple stress state comprises a uniaxial tensile stress state and a uniaxial compressive stress state, and the two are unified by the damage energy release rate.

3. The method according to claim 1, wherein the method is characterized by, After the tensile and compressive effective stresses are decomposed by the fourth-order projection tensor in S1, the stress states of the tensile and compressive fatigue damages are independently described, and do not interfere with each other, so that the evolution law of the tensile and compressive damages can be accurately characterized.

4. The method according to claim 1, wherein, The three-stage damage characteristics of the material high-cycle fatigue are as follows: in the first stage, stress concentration is caused by internal micro defects of the material, micro cracks are generated, and the mechanical properties of the material are rapidly degraded; in the second stage, the cracks expand to release internal energy, energy accumulation and release reach a relative stability, the mechanical properties of the material are slowly degraded, and the proportion of the second stage is the highest; in the third stage, the micro cracks continuously expand, the internal defects are aggravated, the energy balance is broken, and the mechanical properties of the material are again accelerated to degrade.

5. The method according to claim 1, wherein the method is characterized by, The definition domain of the hyperbolic function is 0 to 1, the function value is always greater than 0, the derivative variation law is consistent with the high-cycle fatigue three-stage damage speed, that is, the derivative is first less than 0, then equal to 0, and finally greater than 0 and gradually increases, which respectively corresponds to the processes of the rapid degradation, the stability and the accelerated accumulation of the damage speed.

6. The method according to claim 1, wherein the method is a method for quickly calculating the tensile and compressive fatigue damage of a discrete type of ballastless track, characterized in that, In S3, the specific process of obtaining the train load characteristic parameters is as follows: first, train wheel-rail force data are collected through field testing or theoretical simulation, a wheel-rail force frequency histogram is drawn to determine the load extreme value range, then stress calculation is carried out in combination with the ballastless track structure, stress data of the most unfavorable load position are extracted, and finally the load characteristic parameters are determined, wherein the load characteristic parameters include an average stress, a stress amplitude and a load frequency.

7. The method according to claim 1, wherein the method is a method for quickly calculating the tensile and compressive fatigue damage of a discrete type of ballastless track, characterized in that, In S3, when integrating the fatigue loading times of tensile and compressive damage, considering that the damage does not increase during unloading, only the integral calculation is performed in the interval of effective load, and the integral term in the unloading interval is ignored to simplify the calculation process.

8. The method according to claim 1, wherein the method is a method for quickly calculating the tensile and compressive fatigue damage of a discrete type of ballastless track, characterized in that, In S4, the value range and interval of the concrete tensile and compressive fatigue damage characteristic parameters are determined by the control variable method combined with the formula position of the concrete tensile and compressive fatigue damage characteristic parameters and whether it is in the exponential term. Specifically, fix the part parameters, assign multiple values to the target parameters, calculate the damage curve under different values, and take the parameter value of the second time when the three-stage phenomenon appears obviously as the lower boundary. Take the value near the asymptote as the upper boundary, and determine the value interval by the sensitivity of the trial value to the damage curve. In the initial value, the initial value of the damage variable is set to 0, and the initial value of the remaining parameters is adjusted according to the engineering experience or trial benchmark value.

9. The method according to claim 1, wherein the method is a method for quickly calculating the tensile and compressive fatigue damage of a discrete type of ballastless track, characterized in that, In S4, when constructing the iteration format, a two-dimensional array is set to store the normalized cycle ratio of loading times and the corresponding damage variable. The damage value under different loading times is obtained by loop calculation in turn. The solving function of the numerical calculation tool is used to solve the iterative equation to obtain the damage variable corresponding to each cycle.

10. The method according to claim 1, wherein the method is a method for quickly calculating the tensile and compressive fatigue damage of a discrete type of ballastless track, characterized in that, In the calculation result graph drawn in S4, the horizontal coordinate is labeled as the normalized cycle ratio, and the vertical coordinate is labeled as the damage variable. The graph contains a clear title and legend, respectively distinguishing the tensile fatigue damage curve and the compressive fatigue damage curve, and intuitively presenting the corresponding relationship between the loading times and the damage accumulation.

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