Rail fatigue crack simulation method and system based on fracture phase field fatigue model

Abstract

The application provides a steel rail fatigue crack simulation method and system based on a fracture phase field fatigue model, relates to the technical field of track traffic structure safety and computational mechanics, and comprises the following steps: acquiring the geometry, material and wheel load parameters of a steel rail; constructing a three-dimensional steel rail finite element model according to the basic data, and setting a local encryption grid in a key area such as wheel-rail contact; on this basis, a fracture phase field model capable of describing natural crack initiation and propagation is established; a fatigue degradation model is further integrated to simulate the crack resistance attenuation caused by fatigue, thereby forming a phase field fatigue coupling model; finally, a moving wheel load is simulated through envelope loading, and a high-efficiency calculation is performed by applying a cycle transition strategy, so that the accurate simulation of the steel rail fatigue crack initiation position, propagation path and damage field distribution is realized. The application can naturally predict crack evolution and significantly improve the high-cycle fatigue analysis efficiency.

Description

Technical Field

[0001] This invention relates to the field of rail transit structural safety and computational mechanics technology, and more specifically, to a method and system for simulating rail fatigue cracks based on a fracture phase field fatigue model. Background Technology

[0002] In the field of rail transit structural safety and computational mechanics, the accurate prediction of fatigue cracks in rails, as key components directly bearing train wheel loads, has always been a core challenge for ensuring operational safety. Because rails are subjected to high-frequency cyclic moving loads during long-term service, fatigue cracks are prone to initiation and propagation within them. This damage behavior is characterized by its complex nature, starting from scratch, uncertain path, and frequent occurrence on subsurface surfaces. Traditional crack simulation methods mainly rely on fracture mechanics with pre-set initial cracks or numerical techniques requiring mesh re-division. When dealing with complex three-dimensional structures like rails, these methods often struggle to naturally describe the crack initiation process and cannot effectively handle topological changes such as path bifurcation during crack propagation. Furthermore, given the enormous number of cycles involved in high-cycle fatigue analysis, existing methods often suffer from excessively low computational efficiency, failing to meet the practical needs of engineering solutions. Therefore, developing a rail fatigue crack simulation method that can naturally describe crack initiation and propagation and efficiently handle high-cycle fatigue problems has become a critical technological bottleneck that urgently needs to be overcome in this field. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for simulating rail fatigue cracks based on a fracture phase-field fatigue model, in order to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0004] Firstly, this application provides a method for simulating rail fatigue cracks based on a fracture phase-field fatigue model, including:

[0005] Obtain basic data of railway rails, including the rail's geometric parameters, material properties, and wheel load parameters, wherein the material properties are the test values ​​of the physical properties of the rail material;

[0006] Based on the aforementioned basic data, a three-dimensional rail finite element model is constructed. By establishing a three-dimensional finite element model that includes the rail head, rail web, and rail bottom, and setting locally refined meshes in the wheel-rail contact area and potential crack initiation area, an optimized three-dimensional rail finite element model is obtained.

[0007] The fracture phase field model is constructed based on the optimized three-dimensional rail finite element model to obtain a fracture phase field model that can describe the natural initiation and propagation of cracks.

[0008] Based on the fracture phase field model, fatigue degradation model integration processing is performed. By simulating the degradation of crack resistance caused by fatigue, a phase field fatigue coupling model containing the fatigue degradation mechanism is obtained.

[0009] Based on the phase-field fatigue coupling model, the evolution of rail fatigue cracks was simulated to obtain the initiation location, propagation path, and damage field distribution of rail fatigue cracks.

[0010] Secondly, this application also provides a rail fatigue crack simulation system based on a fracture phase field fatigue model, comprising:

[0011] The acquisition unit is used to acquire basic data of railway rails, including the rail's geometric parameters, material properties, and wheel load parameters, wherein the material properties are the physical performance test values ​​of the rail material;

[0012] The construction unit is used to construct a three-dimensional rail finite element model based on the basic data. By establishing a three-dimensional finite element model including the rail head, rail web and rail bottom, and setting local mesh refinement in the wheel-rail contact area and potential crack initiation area, an optimized three-dimensional rail finite element model is obtained.

[0013] The processing unit is used to construct a fracture phase field model based on the optimized three-dimensional rail finite element model to obtain a fracture phase field model that can describe the natural initiation and propagation of cracks.

[0014] An integration unit is used to perform fatigue degradation model integration processing based on the fracture phase field model, and obtain a phase field fatigue coupling model containing the fatigue degradation mechanism by simulating the degradation of crack resistance caused by fatigue.

[0015] The simulation unit is used to perform rail fatigue crack evolution simulation processing based on the phase-field fatigue coupling model to obtain the initiation location, propagation path and damage field distribution results of rail fatigue cracks.

[0016] The beneficial effects of this invention are as follows:

[0017] This invention acquires basic data of railway rails, constructs a three-dimensional finite element model of the rails with locally refined meshes, establishes a fracture phase field model to describe the natural initiation and propagation of cracks, integrates a fatigue degradation model to simulate the decay of crack resistance caused by fatigue, and employs envelope loading and cyclic transition strategies to simulate the evolution of rail fatigue cracks. This achieves natural prediction of rail fatigue cracks from scratch, handling complex path evolution without pre-setting cracks. The threshold-driven and history field mechanisms effectively avoid spurious damage and unloading closure problems in low-stress zones, ensuring the physical rationality and irreversibility of crack evolution. The fatigue degradation model maps cumulative damage to fracture toughness decay, accurately reflecting the performance degradation behavior of the rail under cyclic loading. The envelope loading and cyclic transition strategies significantly improve the computational efficiency of high-cycle fatigue simulation, making it suitable for efficient analysis of complex three-dimensional rail structures.

[0018] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the rail fatigue crack simulation method based on the fracture phase field fatigue model described in this embodiment of the invention.

[0021] Figure 2 This is a schematic diagram of the rail fatigue crack simulation system based on the fracture phase field fatigue model described in this embodiment of the invention.

[0022] In the diagram: 701, acquisition unit; 702, construction unit; 703, processing unit; 704, integration unit; 705, simulation unit. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0024] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0025] Example 1:

[0026] This embodiment provides a method for simulating rail fatigue cracks based on a fracture phase field fatigue model.

[0027] See Figure 1 The figure shows that the method includes steps S1, S2, S3, S4 and S5.

[0028] Step S1: Obtain basic data of railway rails, including the geometric parameters, material properties and wheel load parameters of the rails, wherein the material properties are the physical performance test values ​​of the rail materials;

[0029] It is understandable that the geometric parameters in this step include key dimensions such as the working edge curvature of the rail head, the thickness of the rail web, and the width of the rail base. These dimensions directly determine the geometric relationship and stress distribution characteristics of the wheel-rail contact. The determination of material properties relies on standardized physical performance tests of the rail material. For example, tensile tests are used to obtain the elastic modulus and Poisson's ratio, and fatigue tests are used to obtain cyclic stress-life curves. These data provide a realistic material response basis for the constitutive relationship in the phase-field model. Wheel load parameters are collected through sensors, including time-history data such as the vertical force, lateral force, and torque acting on the rail when the train passes. These dynamic load sequences are the core inputs for reproducing the actual stress state of the rail. This step emphasizes the use of direct measurement and test data, aiming to ensure the physical authenticity and engineering reliability of the simulation model input parameters from the source, laying a solid data foundation for the subsequent establishment of a fracture phase-field model that can accurately reflect actual service conditions.

[0030] Step S2: Based on the basic data, construct a three-dimensional rail finite element model. By establishing a three-dimensional finite element model including the rail head, rail web and rail bottom, and setting local mesh refinement in the wheel-rail contact area and potential crack initiation area, the optimized three-dimensional rail finite element model is obtained.

[0031] Understandably, this step first involves constructing a three-dimensional finite element model of the rail. By extracting the actual dimensional information from the geometric parameters, the three-dimensional geometry of the rail head, web, and base is precisely defined, and corresponding mechanical constitutive relations are assigned based on material properties, thereby establishing a complete three-dimensional finite element model of the rail. On this basis, considering the unique service scenarios of railway rails, high stress concentration areas such as the wheel-rail contact area and potential crack initiation areas are identified. The discrete element size of these key areas is refined by setting local mesh densification to ensure that stress gradient changes and crack initiation details can be accurately captured in subsequent phase field simulations. In this step, step S2 includes steps S21, S22, and S23.

[0032] Step S21: Based on the basic data, perform rail geometric model construction processing. By extracting the geometric parameters from the actual size measurement values ​​of the rail, and defining the three-dimensional geometric shapes of the rail head, rail web and rail bottom based on the geometric parameters, an initial three-dimensional rail geometric model is obtained.

[0033] Understandably, this step begins with constructing a geometric model of the rail. By extracting geometric parameters from the actual measured dimensions of the rail, such as the contour curve of the rail head, the thickness of the rail web, and the width of the rail base, key geometric features are obtained. Based on these parameters, the three-dimensional geometry of the rail head, rail web, and rail base is precisely defined, thus obtaining an initial three-dimensional rail geometric model. This process ensures that the geometric model strictly corresponds to the physical dimensions of the actual rail, providing a high-fidelity geometric foundation for subsequent finite element mesh generation and phase field simulation.

[0034] Step S22: Perform finite element mesh generation processing based on the initial three-dimensional rail geometric model. By identifying the wheel-rail contact area and potential crack initiation area unique to railway rails, and setting locally refined meshes in these areas, a three-dimensional rail finite element model with locally refined meshes is obtained.

[0035] Understandably, this step first identifies key areas such as the wheel-rail contact area and potential crack initiation areas based on the specific scenario of railway rails bearing cyclic moving loads during service. The wheel-rail contact area refers to the high-stress concentration zone where the wheel and rail surfaces directly interact, while potential crack initiation areas typically include vulnerable locations determined based on mechanical analysis or historical damage data (data exceeding a preset damage threshold or load threshold), such as the working edge of the rail head and the transition zone of the rail web. Then, locally refined meshes are set in these areas, that is, the mesh dispersion is refined by reducing the element size, so that the mesh distribution adapts to the numerical resolution required for stress gradient changes and crack initiation. This local refinement process is tailored to the characteristics of the rail structure, increasing the mesh density only in high-risk areas, thereby effectively capturing subtle features of contact stress and potential crack origination while ensuring computational efficiency. Finally, a three-dimensional finite element model of the rail with locally refined meshes is obtained. This model provides a high-precision discretization basis for subsequent phase-field simulations, ensuring the reliability of fatigue crack evolution analysis.

[0036] Step S23: Optimize the mesh size of the three-dimensional rail finite element model with locally refined mesh by matching the size of the locally refined mesh with the phase field length scale parameter, so that the mesh size is less than or equal to one-third of the phase field length scale parameter, and obtain the three-dimensional rail finite element model with optimized mesh size.

[0037] It is understandable that the phase field length scale parameter in this step is a key intrinsic parameter controlling the width of the crack dispersion zone in fracture phase field theory, determining the physical width of the crack zone in the numerical simulation. To ensure the finite element model can accurately analyze the evolution of this crack zone, the mesh size needs to be small enough to capture its gradient changes. By setting the size of the locally refined mesh to be less than or equal to one-third of the phase field length scale parameter, a sufficient number of elements are included within each crack zone width, ensuring a smooth spatial transition of phase field variables and meeting computational accuracy requirements. This matching process is a key optimization for simulating high-cycle fatigue cracks in railway rails. It ensures that in the high stress gradient region of wheel-rail contact, the numerical model can accurately describe the details of crack initiation and propagation while avoiding computational resource waste due to overly dense meshes or numerical errors caused by overly coarse meshes.

[0038] Step S3: Based on the optimized three-dimensional rail finite element model, a fracture phase field model is constructed to obtain a fracture phase field model that can describe the natural initiation and propagation of cracks.

[0039] Understandably, this step first introduces a phase field variable as a continuous damage descriptor. This variable ranges from zero to one, representing the intact state of the material and the complete fracture state, respectively. The intermediate value represents the gradual damage transition zone within the crack propagation band. Based on this, a driving function is set based on the elastic strain energy density or its tensile portion to quantify the driving effect of local tensile energy on the crack. A threshold control mechanism ensures that phase field evolution is only allowed when the driving function exceeds a set threshold, thereby avoiding non-physical spurious damage to the rail in low-stress areas. Furthermore, by combining the historical field records of the maximum value of the driving function from the start of the analysis to the current moment, the phase field evolution is made dependent on the historical field rather than the instantaneous value to simulate the irreversible physical characteristic of cracks once they are generated. Finally, these elements are integrated into the phase field evolution equation to construct a fracture phase field model that can naturally describe the crack initiation and propagation of the rail under cyclic moving loads. This model can handle complex path changes without pre-setting cracks and is particularly suitable for physically reasonable simulation of crack behavior in high-cycle fatigue scenarios of railway rails. Step S3 includes steps S31, S32 and S33.

[0040] Step S31: Based on the optimized three-dimensional rail finite element model, the phase field variables and driving function are defined. By considering the wheel-rail contact stress distribution characteristics of railway rails, phase field variables are introduced to characterize the material damage state, and the driving function is set based on the elastic strain energy density or its tension part to obtain the initial phase field model.

[0041] Understandably, firstly, considering the complex stress state of railway rails under cyclic wheel loads, especially the high-gradient stress distribution characteristics in the wheel-rail contact area and subsurface, a continuous phase field variable is introduced to characterize the material's damage state. This variable, as a scalar field function between zero and one, changes continuously, intuitively describing the progressive damage process from a healthy state to complete fracture. This transforms the discrete crack topology problem into an evolution problem of a continuous field variable, avoiding the limitation of traditional methods that require pre-defining cracks. Subsequently, a driving function is set as the physical driving force controlling the phase field evolution. This function is defined based on the elastic strain energy density or its tensile component at a material point. In the service scenario of rails, the tensile stress component often plays a dominant role in the initiation and propagation of fatigue cracks. Therefore, the driving function based on tensile strain energy can more accurately reflect the actual driving force of cracks in the wheel-rail contact, ensuring that the model can sensitively capture those potential damage areas dominated by tension. By combining the phase field variable with the physically meaningful driving function, an initial phase field model that can preliminarily describe the damage behavior of rail materials is obtained. The driving function of this invention... From elastic strain energy density Or its tensile portion is defined to measure whether local tensile energy is sufficient to drive crack propagation, wherein the driving function is a function that defines the driving force for crack propagation based on the elastic strain energy density or its tensile portion.

[0042] Step S32: Perform threshold control mechanism integration processing based on the initial phase field model. By combining the high-cycle fatigue scenario of railway rails, set the threshold of the driving function. Phase field evolution is performed only when the local driving function is greater than the threshold of the driving function, thus obtaining a phase field model with threshold control.

[0043] Understandably, this step, by considering the characteristics of rails subjected to cyclic moving loads, sets a driving function threshold. This threshold, determined based on material fatigue characteristics or experimental data, represents the minimum energy level required to drive crack initiation. Only when the local driving function exceeds this threshold is the phase field variable allowed to evolve; otherwise, the phase field remains stable. This threshold control mechanism ensures that crack evolution only occurs in high-stress areas such as wheel-rail contact, avoiding spurious damage to the rail structure in low-stress areas, thus providing a more physically reasonable description of the selective initiation of cracks under high-cycle fatigue. Ultimately, a phase field model with threshold control is obtained, which enhances the accuracy of damage evolution and provides a reliable foundation for subsequent fatigue degradation behavior simulation. Specifically, to suppress non-physical damage in low-stress areas, this invention introduces threshold control into the phase field evolution equation: the phase field is allowed to grow only when the local driving function exceeds the set threshold; when the driving function is below the threshold, the phase field remains unchanged, preventing crack initiation. This step, through a threshold control mechanism, achieves the effect that the phase field variable remains at 0 in regions far from the crack and with low stress levels, preventing the generation of pseudo-cracks. Furthermore, the phase field only gradually evolves from 0 to 1 when approaching the fatigue crack initiation and propagation region and reaching a certain energy level.

[0044] Step S33: Perform historical field loading processing according to the phase field model with threshold control. Record the maximum value of the driving function from the start of the analysis to the current moment through the preset historical field, and load the historical field into the phase field model with threshold control to obtain the fracture phase field model describing the natural initiation and propagation of cracks.

[0045] Understandably, this step employs a historical field method to ensure that cracks, once formed, cannot "self-heal." Record the maximum drive level of the material throughout the entire loading process. The history field is defined as:

[0046] ;

[0047] in, For the historical field, For any time The historical field is taken from the beginning of the analysis to the current moment. The maximum value of the driving function up to this point. In practice, the phase-field evolution equation does not directly depend on the instantaneous driving force. Instead, it relies on the historical field. Therefore, during the loading phase, if the stress continues to increase, the historical field... As it increases, the phase field can continue to evolve forward; when unloaded or reloaded to a lower level, although the instantaneous driving function decreases, the historical field... Maintaining the crack level ensures that existing damage will not be "recovered" during unloading, thus demonstrating the irreversibility of crack evolution.

[0048] This step incorporates length measurement. Historical Field The phase field evolution equation can be written as an elliptic equation similar to the following:

[0049] ;

[0050] Wherein, represents the phase field length scale parameter, which is a material parameter that controls the width of the crack dispersion zone (the crack and the surrounding damage area) and is used to regularize the topology of sharp cracks; This represents the Laplace calculation, used to describe the spatial gradient change of phase field variables; : Represents the phase field variable. Used to characterize the damage state of a material, its value range is usually [0, 1], where 0 represents the material is intact and 1 represents complete fracture; In this formula, the historical field variables are represented. That is, as mentioned above The value at the current moment. It records the maximum tensile elastic strain energy density experienced by the material, used to drive crack propagation and prevent crack healing upon unloading (ensuring irreversibility).

[0051] The above-described form, combined with the fatigue degradation model of this invention, ensures that in regions of high stress and significant fatigue accumulation, the phase field gradually increases, leading to natural crack initiation and propagation; in low-stress regions, the phase field remains close to zero, preventing non-physical decomposition; after unloading, the crack does not close or heal, and the phase field evolution exhibits a clear irreversible characteristic. Therefore, this invention, through a fracture phase field model based on "threshold-driven + history field constraint," achieves a physically reasonable and numerically stable description of crack initiation and propagation within the three-dimensional finite element framework of steel rails, providing a reliable damage field basis for subsequent fatigue degradation and cyclic transition strategies.

[0052] Step S4: Perform fatigue degradation model integration processing based on the fracture phase field model. By simulating the degradation of crack resistance caused by fatigue, obtain a phase field fatigue coupling model that includes the fatigue degradation mechanism.

[0053] Understandably, this step first introduces a local fatigue life variable as a scalar field describing the accumulation of fatigue damage at material points, based on the fracture phase-field model. This variable starts from zero and increases with the number of load cycles, quantifying the fatigue history of local regions. Next, based on fatigue experimental data of railway rail materials, a fracture toughness degradation function is defined. This function maps the fatigue accumulation variable to a decrease in fracture toughness through mathematical relationships, thus characterizing the gradual weakening of the material's ability to resist crack propagation with increasing fatigue damage. During integration, the fracture toughness degradation function is embedded into the fracture energy term of the phase-field model, so that the evolution of the phase-field variable is controlled not only by the driving function and the history field but also modulated by the fatigue accumulation variable, thereby reflecting the accelerated effect of crack initiation and propagation in rails under high-cycle fatigue scenarios. In this step, step S4 includes steps S41, S42, and S43.

[0054] Step S41: Perform fatigue accumulation variable initialization processing according to the fracture phase field model. Introduce local fatigue life variables at each grid point of the phase field model and initialize the life variables to zero to indicate no cumulative damage, thereby obtaining an initial phase field model containing fatigue accumulation variables.

[0055] Understandably, this step introduces a local fatigue life variable at each grid point in the phase-field model. This variable records the number of load cycles experienced by the material point or the equivalent cumulative damage. By initializing the local fatigue life variable at each grid point to zero, it indicates that the rail material has not yet experienced any load cycles at the start of the simulation and is therefore in an initial state without accumulated damage. This ensures that the fatigue simulation starts from a clean starting point, avoiding non-physical initial deviations. This initialization process is a key prerequisite for the integration of the fatigue degradation model. It expands the fracture phase-field model from merely describing crack evolution to simultaneously tracking fatigue accumulation, resulting in an initial phase-field model that includes fatigue accumulation variables.

[0056] Step S42: Based on the initial phase-field model containing fatigue accumulation variables, the fracture toughness degradation function is defined. Using fatigue test data based on railway rail materials, the fracture toughness degradation function is defined to obtain a phase-field model with the degradation function.

[0057] Understandably, this step first relies on fatigue test data of railway rail materials. This data is typically obtained through standard laboratory fatigue tests and reflects the decay law of rail materials' resistance to crack propagation under cyclic loading. Then, a fracture toughness degradation function is defined. This function is a mathematical expression used to quantitatively describe how the material's fracture toughness (i.e., its ability to resist crack propagation) gradually decreases with increasing fatigue accumulation. In the actual scenario of high-cycle fatigue in railway rails, the material does not fail suddenly, but its crack resistance slowly deteriorates with increasing load cycles. The fracture toughness degradation function is precisely designed to accurately characterize this gradual material performance degradation behavior. By embedding this function into the phase-field model, the evolution of the phase-field variables is not only driven by stress but also modulated by the material performance weakening effect caused by fatigue accumulation, thus more realistically reflecting the damage evolution law of rails under long-term service conditions.

[0058] The fracture toughness degradation function is shown below:

[0059] ;

[0060] in, The fracture toughness degradation function is a dimensionless scalar function used to describe the proportionality of the material’s ability to resist crack propagation (i.e., fracture toughness) as fatigue damage accumulates. This represents the cumulative fatigue variable (or cumulative damage variable). Its value range is usually from 0 to 1, where 0 indicates that the material is intact and undamaged, and 1 indicates that the material has completely failed due to fatigue. This represents the fatigue threshold parameter (or residual toughness coefficient). It is a model constant representing the condition when the material reaches a state of complete fatigue damage. At that time, the material retains the minimum fracture toughness ratio to prevent singularities in numerical calculations; This represents the degradation shape parameter (or degradation index), which is a fitting parameter used to control the rate and shape of the nonlinear decay of fracture toughness with fatigue damage.

[0061] Among them, the life calculation for cumulative stress amplitude control adopts the Miner linear accumulation criterion:

[0062] ;

[0063] ;

[0064] in, Indicates the first Damage increment caused by secondary load cycles; This represents the fatigue life under the corresponding stress amplitude. That is, at the [stress level]... The total number of cycles that the rail material can withstand to the point of fatigue failure under the stress level of the next cycle (usually obtained from the SN curve of the material).

[0065] Step S43: Perform fatigue degradation mechanism integration processing based on the phase-field model with degradation function. By embedding the fracture toughness degradation function into the fracture energy term in the phase-field evolution equation, the evolution of phase-field variables is modulated by fatigue accumulation variables, simulating the progressive damage process of rails under cyclic load, and obtaining a phase-field fatigue coupling model containing fatigue degradation mechanism.

[0066] Understandably, this step first embeds the fracture toughness degradation function defined in the previous step into the fracture energy term in the phase-field evolution equation. The fracture energy term is originally used to characterize the material's intrinsic ability to resist crack propagation. Through this embedding operation, the evolution of the phase-field variables no longer depends solely on instantaneous stress driving, but is simultaneously modulated by fatigue accumulation variables. That is, as the number of load cycles increases, the fatigue accumulation variable increases, leading to a decrease in fracture toughness, which weakens the constraint effect of the fracture energy term on the phase-field evolution and accelerates damage accumulation. In the high-cycle fatigue scenario of railway rails, this mechanism can physically and reasonably simulate the gradual degradation behavior of the rail's crack resistance due to fatigue accumulation under long-term cyclic moving loads, thus more accurately describing the gradual damage process from crack initiation to propagation. Finally, through this integrated processing, a phase-field fatigue coupling model containing the fatigue degradation mechanism is obtained. This model organically unifies fatigue damage and fracture evolution, providing a complete numerical basis for the full life cycle simulation of rail fatigue cracks.

[0067] Step S5: Perform rail fatigue crack evolution simulation processing based on the phase-field fatigue coupling model to obtain the initiation location, propagation path and damage field distribution results of rail fatigue cracks.

[0068] Understandably, this step first employs an envelope loading method to simulate the effect of wheel load moving across the rail surface. Envelope loading is a loading strategy that organizes the entire process of the wheelset passing through the contact zone as a single fatigue cycle. It includes four stages: applying a load at the initial contact position to establish wheel-rail contact, maintaining the load amplitude and moving the load position to simulate the wheelset rolling through, unloading to near zero to simulate wheel load departure, and resetting the load position back to the starting point under low load conditions to prepare for the next cycle. This loading method can accurately reproduce the cyclic moving load history that railway rails experience in actual service, ensuring that the spatiotemporal changes in stress distribution are consistent with the real scenario. Next, to efficiently handle the large number of cycles involved in high-cycle fatigue, a cyclic transition strategy is applied. This strategy is based on fatigue accumulation stability. The system assumes a fixed-stage approach, using a constant damage increment to jump through multiple cycles, thus skipping redundant calculations. When the difference between the damage variable or phase field variable and the preset failure threshold is less than 0.1, the jump step size is automatically reduced to maintain the resolution of the near-failure stage, significantly improving computational efficiency without sacrificing physical rationality. Then, by numerically solving the coupled equations of the displacement field and phase field variables, the fatigue accumulation variable and historical field are dynamically updated to simulate the evolution of the phase field variable with load cycles, thereby capturing the continuous process from crack initiation to propagation. Finally, by extracting the spatial distribution and evolution history of the phase field variable, the initiation location, corresponding cycle number, crack propagation path, and damage field distribution of the rail fatigue crack are obtained, providing a complete description of the fatigue damage behavior of the three-dimensional rail structure under long-term cyclic moving loads. In this step, step S5 includes steps S51, S52, and S53.

[0069] Step S51: Perform rail movement wheel load simulation processing based on the phase-field fatigue coupling model containing the fatigue degradation mechanism to obtain complete load history data for a single wheelset passage;

[0070] Understandably, this step first applies a load at the initial contact position to establish wheel-rail contact, then maintains the load amplitude and moves the load position to simulate the wheelset rolling through, then unloads to near zero to simulate wheel load leaving, and finally resets the load position back to the starting point under low load conditions to prepare for the next cycle. This loading method is designed for the characteristics of continuous wheel load movement in high-cycle fatigue scenarios of railway rails, and can accurately reproduce the dynamic changes in the spatiotemporal distribution of load on the rail surface, avoiding stress simulation deviations caused by simplified loading, thereby obtaining complete load history data for a single wheelset passage.

[0071] Step S52: Perform fatigue acceleration calculation processing based on the complete load history data of the single wheelset passage. By applying a cyclic transition strategy in the fatigue accumulation and stabilization stage, a preset number of cycles are transitioned with a constant damage increment. When the difference between the damage variable or phase field variable and the preset failure threshold is less than 0.1, the preset transition step size is automatically reduced to obtain the cumulative damage field and phase field evolution results of the rail under cyclic load.

[0072] It is understandable that in high-cycle fatigue simulation, this step assumes that the stress amplitude within a certain cycle is approximately stable with respect to the plastic history, and takes the stable damage increment. For example, a constant. The system then jumps through multiple loops to improve efficiency. When the fatigue accumulation variable or phase field variable approaches the failure threshold (the preset failure threshold is set to 0.9), the stable damage increment is reduced (e.g., by 10 times) to ensure resolution in the near-failure stage.

[0073] Step S53: Extract and process the crack evolution results based on the cumulative damage field and phase field evolution results. Update the fatigue cumulative variables and historical fields by solving the field variables of the displacement field and phase field, and extract the spatial distribution and evolution history of the phase field variables to obtain the initiation location, corresponding cycle number, crack propagation path and damage field distribution results of the rail fatigue crack.

[0074] Understandably, in this step, the displacement field and phase field variables are solved first by using an implicit scheme (using the displacement and phase field variables of the current step as the variables to be solved, establishing a set of nonlinear equations containing unknowns. The coefficient matrix of this set of equations depends on the current value of the unknowns themselves. Then, the solution of the set of equations is gradually approximated by the Newton-Raphson method until the convergence criterion is met, and then the solution result is obtained). The displacement field and phase field variables are solved, and the fatigue accumulation variables and phase field variables are updated. A two-layer shared nodal degree of freedom structure can be adopted: the first layer solves the displacement field and updates the stress, fatigue accumulation variables, and phase field variables, and the second layer solves the evolution of the phase field variables. The global variables are transferred between the two layers to achieve synchronous updates of mechanical response and damage evolution. The displacement field reflects the macroscopic deformation of the rail structure, while the phase field variables characterize the microscopic damage state inside the material. During the solution process, the fatigue accumulation variables and historical fields are updated in real time according to the current stress state and load history to ensure the physical rationality of fatigue damage accumulation and crack evolution process. Subsequently, the spatial distribution and evolution history of the phase field variables are extracted. Through phase field time series analysis, the location where the phase field variables begin to increase from zero can be accurately identified as the crack initiation point. The number of cycles corresponding to reaching the critical damage value is recorded as the crack initiation life. Simultaneously, tracing the connectivity path of the high-value region of the phase field can determine the crack propagation trajectory. Finally, by systematically integrating this information, the initiation location, corresponding cycle number, crack propagation path, and damage field distribution of rail fatigue cracks are obtained. This provides a complete description of the fatigue damage evolution behavior of the three-dimensional rail structure under long-term cyclic moving loads, offering a quantitative basis for rail remaining life assessment and maintenance decisions.

[0075] Example 2:

[0076] like Figure 2 As shown, this embodiment provides a rail fatigue crack simulation system based on a fracture phase field fatigue model. See [link to relevant documentation]. Figure 2 The system includes an acquisition unit 701, a construction unit 702, a processing unit 703, an integration unit 704, and a simulation unit 705.

[0077] The acquisition unit 701 is used to acquire basic data of railway rails, including the geometric parameters, material properties and wheel load parameters of the rails, wherein the material properties are the physical performance test values ​​of the rail materials;

[0078] The construction unit 702 is used to construct a three-dimensional rail finite element model based on the basic data. By establishing a three-dimensional finite element model including the rail head, rail web and rail bottom, and setting local mesh refinement in the wheel-rail contact area and potential crack initiation area, an optimized three-dimensional rail finite element model is obtained.

[0079] The processing unit 703 is used to perform fracture phase field model construction processing based on the optimized three-dimensional rail finite element model to obtain a fracture phase field model that can describe the natural initiation and propagation of cracks.

[0080] The integration unit 704 is used to perform fatigue degradation model integration processing based on the fracture phase field model, and obtain a phase field fatigue coupling model containing the fatigue degradation mechanism by simulating the degradation of crack resistance caused by fatigue.

[0081] The simulation unit 705 is used to perform rail fatigue crack evolution simulation processing based on the phase-field fatigue coupling model to obtain the initiation location, propagation path and damage field distribution results of rail fatigue cracks.

[0082] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0083] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0084] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for simulating rail fatigue cracks based on a fracture phase-field fatigue model, characterized in that, include: Obtain basic data of railway rails, including the rail's geometric parameters, material properties, and wheel load parameters, wherein the material properties are the test values ​​of the physical properties of the rail material; Based on the aforementioned basic data, a three-dimensional rail finite element model is constructed. By establishing a three-dimensional finite element model that includes the rail head, rail web, and rail bottom, and setting locally refined meshes in the wheel-rail contact area and potential crack initiation area, an optimized three-dimensional rail finite element model is obtained. The fracture phase field model is constructed based on the optimized three-dimensional rail finite element model to obtain a fracture phase field model that can describe the natural initiation and propagation of cracks. Based on the fracture phase field model, fatigue degradation model integration processing is performed. By simulating the degradation of crack resistance caused by fatigue, a phase field fatigue coupling model containing the fatigue degradation mechanism is obtained. The fatigue crack evolution of rails was simulated using the phase-field fatigue coupling model to obtain the initiation location, propagation path, and damage field distribution of rail fatigue cracks. Specifically, based on the fracture phase-field model, a fatigue degradation model integration process is performed. By simulating the degradation of crack resistance caused by fatigue, a phase-field fatigue coupling model containing the fatigue degradation mechanism is obtained, including: The fatigue accumulation variable initialization process is performed based on the fracture phase field model. Local fatigue life variables are introduced into each grid point of the phase field model and initialized to zero to indicate no cumulative damage, thus obtaining an initial phase field model containing fatigue accumulation variables. The fracture toughness degradation function is defined based on the initial phase-field model containing fatigue accumulation variables. The fracture toughness degradation function is defined using fatigue test data based on railway rail materials, resulting in a phase-field model with degradation function. The fatigue degradation mechanism is integrated based on the phase-field model with degradation function. By embedding the fracture toughness degradation function into the fracture energy term in the phase-field evolution equation, the evolution of phase-field variables is modulated by fatigue accumulation variables, simulating the progressive damage process of rails under cyclic load, and obtaining a phase-field fatigue coupling model containing fatigue degradation mechanism. The simulation of rail fatigue crack evolution based on the phase-field fatigue coupling model includes: Based on the phase-field fatigue coupling model containing the fatigue degradation mechanism, the rail moving wheel load simulation processing is performed to obtain complete load history data for a single wheelset passage; Based on the complete load history data of the single wheelset passage, fatigue acceleration calculation is performed. By applying a cyclic transition strategy in the fatigue accumulation and stabilization stage, a preset number of cycles are transitioned with a constant damage increment. When the difference between the damage variable or phase field variable and the preset failure threshold is less than 0.1, the preset transition step size is automatically reduced to obtain the cumulative damage field and phase field evolution results of the rail under cyclic load. Based on the cumulative damage field and phase field evolution results, crack evolution results are extracted and processed. By solving the field variables of displacement field and phase field, fatigue cumulative variables and historical field are updated, and the spatial distribution and evolution history of phase field variables are extracted to obtain the initiation location, corresponding cycle number, crack propagation path and damage field distribution results of rail fatigue crack.

2. The method for simulating rail fatigue cracks based on a fracture phase-field fatigue model according to claim 1, characterized in that, Based on the aforementioned basic data, a three-dimensional finite element model of the rail is constructed, including: Based on the aforementioned basic data, a rail geometric model is constructed. By extracting the geometric parameters from the actual dimensions of the rail, and defining the three-dimensional geometric shapes of the rail head, web, and bottom based on these geometric parameters, an initial three-dimensional rail geometric model is obtained. Based on the initial three-dimensional rail geometric model, finite element meshing is performed. By identifying the wheel-rail contact area and potential crack initiation area unique to railway rails, and setting locally refined meshes in these areas, a three-dimensional rail finite element model with locally refined meshes is obtained. The mesh size of the three-dimensional rail finite element model with locally refined mesh is optimized by matching the size of the locally refined mesh with the phase field length scale parameter, so that the mesh size is less than or equal to one-third of the phase field length scale parameter, thus obtaining a three-dimensional rail finite element model with optimized mesh size.

3. The method for simulating rail fatigue cracks based on a fracture phase-field fatigue model according to claim 1, characterized in that, The fracture phase field model is constructed based on the optimized three-dimensional rail finite element model, including: Based on the optimized three-dimensional rail finite element model, the phase field variables and driving functions are defined. By considering the wheel-rail contact stress distribution characteristics of railway rails, phase field variables are introduced to characterize the material damage state, and the driving function is set based on the elastic strain energy density or its tension part to obtain the initial phase field model. The threshold control mechanism is integrated based on the initial phase field model. By combining the high-cycle fatigue scenario of railway rails, a threshold for the driving function is set. Phase field evolution is performed only when the local driving function is greater than the threshold, resulting in a phase field model with threshold control. The historical field loading process is performed on the phase field model with threshold control. The maximum value of the driving function from the start of the analysis to the current moment is recorded by the preset historical field, and the historical field is loaded into the phase field model with threshold control to obtain the fracture phase field model describing the natural initiation and propagation of cracks.

4. A rail fatigue crack simulation system based on a fracture phase-field fatigue model, characterized in that, include: The acquisition unit is used to acquire basic data of railway rails, including the rail's geometric parameters, material properties, and wheel load parameters, wherein the material properties are the physical performance test values ​​of the rail material; The construction unit is used to construct a three-dimensional rail finite element model based on the basic data. By establishing a three-dimensional finite element model including the rail head, rail web and rail bottom, and setting local mesh refinement in the wheel-rail contact area and potential crack initiation area, an optimized three-dimensional rail finite element model is obtained. The processing unit is used to construct a fracture phase field model based on the optimized three-dimensional rail finite element model to obtain a fracture phase field model that can describe the natural initiation and propagation of cracks. An integration unit is used to perform fatigue degradation model integration processing based on the fracture phase field model, and obtain a phase field fatigue coupling model containing the fatigue degradation mechanism by simulating the degradation of crack resistance caused by fatigue. The simulation unit is used to perform rail fatigue crack evolution simulation processing based on the phase-field fatigue coupling model to obtain the initiation location, propagation path and damage field distribution results of rail fatigue cracks. The integrated unit includes: The first integrated subunit is used to perform fatigue accumulation variable initialization processing according to the fracture phase field model. Local fatigue life variables are introduced into each grid point of the phase field model and initialized to zero to indicate no cumulative damage, so as to obtain an initial phase field model containing fatigue accumulation variables. The second integrated subunit is used to define the fracture toughness degradation function based on the initial phase field model containing fatigue accumulation variables. By using fatigue test data based on railway rail materials, the fracture toughness degradation function is defined to obtain a phase field model with degradation function. The third integration subunit is used to perform fatigue degradation mechanism integration processing based on the phase field model with degradation function. By embedding the fracture toughness degradation function into the fracture energy term in the phase field evolution equation, the evolution of phase field variables is modulated by fatigue accumulation variables, simulating the progressive damage process of rails under cyclic load, and obtaining a phase field fatigue coupling model containing fatigue degradation mechanism. The simulation unit includes: The first simulation subunit is used to perform rail movement wheel load simulation processing based on the phase-field fatigue coupling model containing the fatigue degradation mechanism, and obtain complete load history data for a single wheelset passage; The second simulation subunit is used to perform fatigue acceleration calculation processing based on the complete load history data of the single wheelset passage. By applying a cyclic transition strategy in the fatigue accumulation and stabilization stage, a preset number of cycles are transitioned with a constant damage increment. When the difference between the damage variable or phase field variable and the preset failure threshold is less than 0.1, the preset transition step size is automatically reduced to obtain the cumulative damage field and phase field evolution results of the rail under cyclic load. The third simulation subunit is used to extract and process crack evolution results based on the cumulative damage field and phase field evolution results. By solving the field variables of the displacement field and phase field, the fatigue cumulative variable and historical field are updated, and the spatial distribution and evolution history of the phase field variable are extracted to obtain the initiation location, corresponding cycle number, crack propagation path and damage field distribution results of rail fatigue crack.

5. The rail fatigue crack simulation system based on the fracture phase field fatigue model according to claim 4, characterized in that, The building unit includes: The first construction subunit is used to construct a rail geometric model based on the basic data. By extracting the geometric parameters from the actual size measurement values ​​of the rail, and defining the three-dimensional geometric shapes of the rail head, rail web and rail bottom based on the geometric parameters, an initial three-dimensional rail geometric model is obtained. The second construction sub-unit is used to perform finite element meshing processing based on the initial three-dimensional rail geometric model. By identifying the wheel-rail contact area and potential crack initiation area unique to railway rails, and setting locally refined meshes in these areas, a three-dimensional rail finite element model with locally refined meshes is obtained. The third construction sub-unit is used to optimize the mesh size of the three-dimensional rail finite element model with locally refined mesh. By matching the size of the locally refined mesh with the phase field length scale parameter, the mesh size is made less than or equal to one-third of the phase field length scale parameter, thus obtaining a three-dimensional rail finite element model with optimized mesh size.

6. The rail fatigue crack simulation system based on the fracture phase field fatigue model according to claim 4, characterized in that, The processing unit includes: The first processing subunit is used to define phase field variables and driving functions based on the optimized three-dimensional rail finite element model. By considering the wheel-rail contact stress distribution characteristics of railway rails, phase field variables are introduced to characterize the material damage state, and the driving function is set based on the elastic strain energy density or its tension part to obtain the initial phase field model. The second processing subunit is used to perform threshold control mechanism integration processing based on the initial phase field model. By combining the high cycle fatigue scenario of railway rails, a driving function threshold is set. Phase field evolution is performed only when the local driving function is greater than the driving function threshold, thus obtaining a phase field model with threshold control. The third processing subunit is used to perform historical field loading processing according to the phase field model with threshold control. It records the maximum value of the driving function from the start of the analysis to the current moment through a preset historical field record, and loads the historical field into the phase field model with threshold control to obtain a fracture phase field model describing the natural initiation and propagation of cracks.

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