A high-speed wheel-rail contact crack prediction method based on crystal plasticity-phase field method

Abstract

The application discloses a high-speed wheel-rail contact crack prediction method based on a crystal plasticity-phase field method, and comprises the following steps: S1, a high-speed wheel-rail model is established through a finite element analysis software, and a local wheel-rail contact area is divided into a cubic; S2, corresponding to the simulation model, a cubic with consistent geometric size is cut in a wheel-rail head contact area, and the cubic is processed for shooting an EBSD image to obtain crystal size and crystal orientation statistical characteristics of the wheel-rail; S3, a crystal plasticity-phase field coupling model is established and tested; S4, statistical parameters of crack forms, crack propagation rates and crack geometries under different load frequencies, load intensities and crystal fracture forms are obtained, and a BP neural network optimized by a sparrow algorithm is trained through the statistical parameters, so that the relationship between the wide-range load frequencies, load intensities, crystal fracture forms and the crack forms, crack propagation rates and crack geometries is obtained, and high-speed wheel-rail contact cracks under different loads are predicted.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of damage-fracture calculation, and particularly relates to a high-speed wheel-rail contact crack prediction method based on a crystal plasticity-phase field method. BACKGROUND

[0002] High-speed trains are an important part of the layout of China's transportation hub system and bear most of the domestic key transport demand. High-speed train tracks are usually not frequently replaced due to high manufacturing costs. During the operation of high-speed trains, relative movement between the wheel-rail and the train wheel produces rolling contact, and with the increase of load, micro-cracks are generated in the surface layer material of the track, and gradually develop into macro-cracks, until the material is damaged, thereby affecting the smooth operation of the train and even causing safety accidents. The traditional crack prediction method is the dispersion crack phase field method, but the phase field method only predicts the initiation and growth of cracks from a macroscopic perspective, without considering the microstructure of the material crystal, and for high-speed wheel-rail crack prediction, the traditional crack prediction method does not fully consider the rolling friction contact conditions in the wheel-rail contact area, resulting in poor prediction effect for high-speed wheel-rail. Therefore, it is particularly urgent to realize a method for predicting high-speed wheel-rail contact cracks, which needs to meet certain prediction reliability and can accurately predict wheel-rail cracks. SUMMARY

[0003] The purpose of the application is to solve the above problems and provide a high-speed wheel-rail contact crack prediction method based on crystal plasticity-phase field method, which is efficient, accurate and can greatly improve the prediction accuracy of high-speed wheel-rail contact cracks and ensure the accuracy of the results.

[0004] To solve the above technical problems, the technical scheme of the application is: a high-speed wheel-rail contact crack prediction method based on crystal plasticity-phase field method, comprising the following steps:

[0005] S1, a high-speed wheel-rail model is established by a finite element analysis software, and a local wheel-rail contact area is divided into a cube;

[0006] S2, corresponding to the simulation model, a cube with consistent geometric size is cut in the wheel-rail head contact area, and the cube is processed for shooting EBSD images to obtain the crystal size and crystal orientation statistical characteristics of the wheel-rail;

[0007] S3, a crystal plasticity-phase field coupling model is established and tested;

[0008] S4, obtain the statistical parameters of crack form, crack propagation rate and crack geometry under different load frequency, load intensity and crystal fracture form, and train the BP neural network optimized by sparrow algorithm to obtain the relationship between wide range of load frequency, load intensity, crystal fracture form and crack form, crack propagation rate and crack geometry, thereby predicting high-speed wheel-rail contact cracks under different loads.

[0009] Further, the S1 comprises the following sub-steps:

[0010] S11, a model is established in a finite element software according to wheel-rail geometry;

[0011] S12, a local 1*1*1mm cube is cut in the wheel-rail contact area, and mesh refinement is performed according to the cutting condition.

[0012] Further, the S2 comprises the following sub-steps:

[0013] S21, a cube with consistent geometry is cut in the wheel-rail head contact area corresponding to the simulation model, and the cube is processed for shooting EBSD image, so as to obtain the crystal size and crystal orientation statistical characteristics of the wheel-rail;

[0014] S22, the local 1*1*1mm cube is divided into Voronoi unit according to the crystal size and crystal orientation statistical characteristics obtained in S21 by Neper software;

[0015] S23, a program is written to read the Voronoi unit division information obtained by Neper software and the mesh node information of the local cutting cube in step one, and the mesh node information of the former two is compared to set the mesh unit of the cube in step one to the corresponding Voronoi unit set, and the finite element model in step one is reimported, thereby completing the Voronoi unit division of the local cube of the finite element model.

[0016] Further, the S3 comprises the following sub-steps:

[0017] S31, a cylindrical sample is cut in the wheel-rail head contact area, and the cylindrical sample is subjected to a tensile test to obtain a wheel-rail stress-strain curve, and at the same time, a tensile test of the wheel-rail cut cylindrical sample is also performed in the finite element software; the tensile stress-strain curve obtained by simulation is compared with the curve obtained by experiment to adjust the simulation phase field fracture energy density, so that the tensile stress-strain curve obtained by simulation coincides with the curve obtained by experiment, and the phase field fracture energy density parameter is obtained;

[0018] S32, on the premise of realizing the above steps, a crystal plasticity-phase field coupling model of the cutting area is derived and established, and the finite element model of S12 is combined with the phase field and crystal plasticity expansion;

[0019] S33, contact rolling fatigue load is applied, and wheel rail crack initiation and propagation are predicted.

[0020] Further, the statistical parameters in S4 include mean values, equations, and standard deviation statistical parameters of different load frequencies, load intensities, crack forms under different crystal fracture forms, crack propagation rates, and crack geometries.

[0021] Further, the specific method for training the sparrow algorithm through the statistical parameters in S4 is: the random initialization population method and the position updating strategy of the improved sparrow search algorithm are improved, and the BP neural network program optimized by the improved sparrow search algorithm is written; the obtained load parameters are taken as inputs, and the obtained crack parameters are taken as outputs to train the neural network; and the relationship between the wide range of load frequencies, load intensities, crystal fracture forms and crack types, crack propagation rates, and crack geometries is obtained through verification.

[0022] The present application has the following advantages:

[0023] 1. The high-speed wheel rail contact crack prediction method based on the crystal plasticity-phase field method provided by the present application establishes a wheel rail finite element model, performs crystal characteristic testing and phase field fracture energy calibration testing on a 1*1*1 mm cube in a local contact area of a wheel head, and divides the local contact area cube into Voronoi units, thereby establishing a high-speed wheel rail crystal plasticity-phase field finite element model by applying a wheel rail rolling contact load.

[0024] 2. The present application trains a BP neural network optimized by a sparrow algorithm using crystal crack statistical parameters obtained from finite element results to predict high-speed train wheel rail contact cracks. The crack prediction method utilizes the advantages of the phase field method, combines the micro characteristics of material crystals, and fully considers the wheel rail contact conditions, thereby ensuring the accuracy of the wheel rail contact crack prediction.

[0025] 3. The present application is different from traditional phase field crack prediction methods. Based on the phase field method, the present application considers the micro characteristics of materials by establishing crystal Voronoi units and considers the wheel rail contact conditions by applying a rolling contact load. As a prediction method considering the micro characteristics of materials and the wheel rail contact load, the present application can greatly improve the accuracy of high-speed wheel rail contact crack prediction and ensure the accuracy of the results. The entire application is efficient, accurate, simple to implement, and has strong practical value and application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 is a step diagram of the high-speed wheel rail contact crack prediction method based on the crystal plasticity-phase field method of the present application;

[0027] Figure 2is a high-speed wheel-rail finite element model and a local section of a rail head contact area of the application;

[0028] Figure 3 is a Voronoi cell grid establishment process diagram of the application;

[0029] Figure 4 is a section schematic diagram of a crystal plasticity-phase field model of the application;

[0030] Figure 5 is a normal force load distribution diagram of the application;

[0031] Figure 6 is a tangential force load distribution diagram of the application;

[0032] Figure 7 is a contact crack propagation diagram of the application;

[0033] Figure 8 is a stress distribution and load movement process diagram of the application. DETAILED DESCRIPTION

[0034] The application will be further described below in combination with the drawings and specific embodiments:

[0035] As shown in the drawings, Figures 1 to 4 a high-speed wheel-rail contact crack prediction method based on a crystal plasticity-phase field method provided by the application includes the following steps:

[0036] S1, a high-speed wheel-rail model is established by a finite element analysis software, and a local wheel-rail contact area is sectioned into a cube.

[0037] Step S1 includes the following sub-steps:

[0038] S11, a model is established in the finite element software according to wheel-rail geometry.

[0039] S12, a local 1x1x1mm cube is sectioned in the wheel-rail contact area, and mesh refinement is performed according to sectioning conditions.

[0040] S2, corresponding to the simulation model, a cube with consistent geometry size is cut in the wheel-rail head contact area, and the cube is processed for shooting an EBSD image to obtain crystal size and crystal orientation statistical characteristics of the wheel-rail.

[0041] Step S2 includes the following sub-steps:

[0042] S21, corresponding to the simulation model, a cube with consistent geometry size is cut in the wheel-rail head contact area, and the cube is processed for shooting an EBSD image to obtain crystal size and crystal orientation statistical characteristics of the wheel-rail.

[0043] S22, Voronoi cell partitioning is performed on the 1*1*1 mm local cubic section by Neper software according to the crystal size and crystal orientation statistical characteristics obtained from S21.

[0044] S23, a program is written to read the Voronoi cell partitioning information obtained by Neper software and the grid node information of the local cubic section in step one, and the grid node information of the former two is compared to set the grid cell of the cubic section in step one to the corresponding Voronoi cell set, and the finite element model in step one is reimported, completing the Voronoi cell partitioning of the local cubic section of the finite element model. As shown in Figure 3 , this method makes the nodes of the local cubic section area completely coincide with the nodes of the remaining area of the finite element model, avoiding the node misalignment problem caused by the conventional tied link method, thereby improving the result accuracy.

[0045] S3, a crystal plasticity-phase field coupling model is established and tested.

[0046] Step S3 includes the following sub-steps:

[0047] S31, the cylindrical sample is cut in the wheel-rail head contact area, and the cylindrical sample is subjected to a tensile test to obtain a wheel-rail stress-strain curve, and at the same time, the finite element software also performs a tensile test on the wheel-rail cut cylindrical sample; the tensile test results and the simulation results are compared, the simulation phase field fracture energy density is adjusted, the tensile stress-strain curve obtained by simulation is coincided with the curve obtained by experiment, and the phase field fracture energy density parameter is obtained.

[0048] S32, on the premise of realizing the above steps, a crystal plasticity-phase field coupling model of the partitioned area is derived and established, which is combined with the finite element model of S12 extended by phase field and crystal plasticity.

[0049] (1) Derive the crystal plasticity phase field control equation:

[0050] ψ = ψ e + ψ p + ψ φ ;

[0051] In the formula, ψ is the total system energy, ψ e is the elastic strain energy, ψ p is the plastic strain energy, and ψ φ is the fracture energy.

[0052]

[0053] In the formula, g(φ) is a degradation function, E e is the elastic strain, L e is the material elastic stiffness matrix, and φ is the phase field.

[0054]

[0055] where, is the shear stress intensity of each slip direction of the crystal, γ i is the shear slip rate of each direction, N is the number of all slip planes of the crystal.

[0056]

[0057] where ω c is the specific fracture energy per unit volume, C is the right Cauchy-Green deformation tensor, ▽0 is the gradient operator of the reference configuration.

[0058]

[0059] where H is the crack driving energy, l φ is the phase field length size factor.

[0060] (2) Derivation of the crystal plasticity constitutive equation and hardening law:

[0061]

[0062] where ρ i is the dislocation density of each slip plane direction, b is the Burgers vector length, v0 is the reference dislocation velocity, τ i is the analytical shear stress, n is the rate sensitivity coefficient.

[0063]

[0064] where k multi and k annih are the dislocation multiplication constant and dislocation annihilation constant.

[0065]

[0066] where c is the proportional constant, G is the shear modulus, χ ij is the Taylor coefficient matrix.

[0067] (3) After the spatial and temporal discretization operations of the above equations, the finite element differential balance equation is obtained, and then the crystal plasticity and the phase field method are coupled. The coupling mode is: the phase field method degeneration function g(φ) controls the evolution process of the plastic slip rate in the crystal plasticity; and the accumulation of the plastic work of each direction of the crystal plasticity further controls the phase field evolution equation.

[0068] S33, apply contact rolling fatigue load, predict wheel-rail crack initiation and propagation.

[0069] As Figures 5 to 6As shown in the figure, fatigue load is added to the wheel-rail contact area. The fatigue load consists of normal load and tangential traction load. The wheel-rail contact surface is elliptical, and the Hertz contact theory determines the elliptical contact surface and ellipsoidal contact pressure distribution. The tangential traction load is divided into pure slip and adhesion parts. In the case of pure slip, the tangential traction distribution force q is proportional to the normal load distribution force p; however, under adhesion-slip conditions, the tangential traction distribution depends on the length of the pure slip and adhesion areas, which is determined by the strip theory. The tangential traction force and normal load distribution force in the strip theory are shown as follows:

[0070]

[0071] Where p max is the Hertz peak pressure, x and y are the load positions, x c 、y c is the maximum load position, a and b are half of the contact strip width in x (rolling direction) and y (lateral direction), respectively.

[0072] q(x)=q1(x)+q2(x);

[0073]

[0074] Where q1 is the sliding tangential traction load, q2 is the adhesion traction load, and μ is the friction coefficient.

[0075] S4, such as Figures 7 to 8 As shown in the figure, the statistical parameters of crack form, crack growth rate and crack geometry under different load frequencies, load intensities and crystal fracture forms are obtained. The BP neural network optimized by the sparrow algorithm is trained by using the statistical parameters to obtain the relationship between a wide range of load frequencies, load intensities, crystal fracture forms and crack form, crack growth rate and crack geometry, so as to predict high-speed wheel-rail contact cracks under different loads.

[0076] The statistical parameters in step S4 include different load frequencies, load intensities, crack forms under conditions of crystal fracture forms, crack growth rates, mean values, equations, and standard deviation statistical parameters of crack geometry.

[0077] The specific method of training the sparrow algorithm through statistical parameters in step S4 is: improving the random initialization population method and position update strategy of the sparrow search algorithm, writing a BP neural network program optimized by the improved sparrow search algorithm; using the obtained load parameters as input and the obtained crack parameters as output to train the neural network; and obtaining the relationship between a wide range of load frequency, load intensity, crystal fracture form and crack type, crack growth rate, and crack geometry through verification.

[0078] The application simplifies the analysis process by cutting the high-speed wheel-rail local contact area, couples the crystal plasticity-phase field method to consider the influence of material micro-plasticity on the contact crack, obtains the phase field fracture energy density of the wheel-rail material through the tensile experiment, programs the crystal plasticity model and the finite element model nodes to coincide to improve the analysis accuracy, applies the wheel-rail head contact load, and trains the BP neural network optimized by the sparrow search algorithm. Finally, the relationship between the wide range of load frequency, load intensity, crystal fracture form and crack form, crack propagation rate, crack geometry is obtained, and the high-speed wheel-rail contact crack is predicted and analyzed.

[0079] Those skilled in the art will realize that the embodiments described herein are for the purpose of illustration and should not be construed as limiting the scope of the present application. Those skilled in the art can make various modifications and combinations according to the technical spirit of the present application disclosed herein without departing from the scope of the present application.

Claims

1. A high-speed wheel-rail contact crack prediction method based on crystal plasticity-phase field method, characterized by: The following steps are involved: S1. Establish a high-speed wheel-rail model using finite element analysis software and divide the local wheel-rail contact area into cubes; S2. Cut the wheel / rail contact area into cubes of uniform geometric size corresponding to the simulation model, and process the cubes for taking EBSD images to obtain the crystal size and crystal orientation statistical characteristics of the wheel / rail; S3. Establish and test the crystal plasticity-phase field coupling model; S4. Obtain statistical parameters of crack form, crack growth rate, and crack geometry under different load frequencies, load intensities, and crystal fracture forms. Use these statistical parameters to train a BP neural network optimized by the Sparrow algorithm to obtain the relationship between a wide range of load frequencies, load intensities, crystal fracture forms, and crack form, crack growth rate, and crack geometry, thereby predicting high-speed wheel-rail contact cracks under different loads. The S3 includes the following sub-steps: S31, cutting a cylindrical specimen in the wheel-rail-rail head contact area and performing a tensile test on the cylindrical specimen to obtain a wheel-rail stress-strain curve. Simultaneously, a tensile test of the wheel-rail cut cylindrical specimen is also performed in finite element software; comparing the tensile test results with the simulation results, adjusting the simulated phase field fracture energy density so that the tensile stress-strain curve obtained by simulation coincides with the curve obtained by experiment, and obtaining a phase field fracture energy density parameter; S32, on the premise of achieving the above steps, deriving and establishing a crystal plasticity-phase field coupling model for the subdivided region, and expanding the finite element model of S12 by combining phase field and crystal plasticity; S33, applying contact rolling fatigue load to predict wheel-rail crack initiation and growth; The specific method of training the sparrow algorithm through statistical parameters in S4 is: improving the random initialization population method and position update strategy of the sparrow search algorithm, writing a BP neural network program optimized by the improved sparrow search algorithm; using the obtained load parameters as input and the obtained crack parameters as output to train the neural network; and obtaining the relationship between a wide range of load frequency, load intensity, crystal fracture form and crack type, crack growth rate, and crack geometry through verification.

2. The high-speed wheel-rail contact crack prediction method based on crystal plasticity-phase field method according to claim 1, characterized in that: The S1 comprises the following sub-steps: S11. Build a model in finite element software based on wheel-rail geometry; S12. Divide the wheel-rail contact area into a local 1×1×1 mm cube and refine the mesh according to the division conditions.

3. The high-speed wheel-rail contact crack prediction method based on crystal plasticity-phase field method according to claim 1, characterized in that: The S2 comprises the following sub-steps: S21, corresponding to the simulation model, cutting a cube of uniform geometric size in the wheel-rail rail head physical contact area, and processing the cube to take an EBSD image, thereby obtaining the crystal size and crystal orientation statistical characteristics of the wheel-rail; S22, using Neper software, perform Voronoi cell division on the split local 1 × 1 × 1 mm cube according to the crystal size and crystal orientation statistical characteristics obtained in S21; S23, write a program to read the Voronoi unit division information obtained by Neper software and the grid node information of the local subdivision cube in step one, compare the grid node information of the former two, set the grid unit of the cube in step one to the corresponding Voronoi unit set, and re-import the finite element model in step one to complete the Voronoi unit division of the local cube of the finite element model.

4. The high-speed wheel-rail contact crack prediction method based on crystal plasticity-phase field method according to claim 1, characterized in that: The statistical parameters in S4 include different load frequencies, load intensities, crack forms under conditions of crystal fracture forms, crack growth rates, mean values, equations, and standard deviation statistical parameters of crack geometry.

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