CN110926942B - Numerical analysis method for rolling contact fatigue cracks of rails in ABAQUS - Google Patents

Numerical analysis method for rolling contact fatigue cracks of rails in ABAQUS Download PDF

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CN110926942B
CN110926942B CN201911135451.5A CN201911135451A CN110926942B CN 110926942 B CN110926942 B CN 110926942B CN 201911135451 A CN201911135451 A CN 201911135451A CN 110926942 B CN110926942 B CN 110926942B
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track
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CN110926942A (en
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杨静
胡志伟
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Xian University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/006—Crack, flaws, fracture or rupture
    • G01N2203/0062—Crack or flaws
    • G01N2203/0066—Propagation of crack
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0073—Fatigue
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract

The invention discloses a numerical analysis method for rolling contact fatigue cracks of a rail in ABAQUS, which comprises the following steps: 1) establishing a finite element microscopic model of the track; 2) leading the model into an ABAQUS orbit calculation model; 3) collecting and initializing parameters, and setting boundary conditions of a track calculation model; 4) setting an analysis step and an increment step in the ABAQUS; 5) calculating the damage performance of the material; 6) loading a track calculation model; 7) analyzing the stress amplitude and the strain of the cohesive force unit; 8) analyzing cohesive force unit damage; 9) judging whether the cohesion unit fails or not; 10) revising the ABAQUS calculation model. The method realizes the fatigue damage failure numerical analysis of the cohesion unit by utilizing the UMAT subprogram of the ABAQUS, realizes the simulation analysis of the fatigue crack initiation and expansion of the rail under rolling contact in the ABAQUS, and predicts the reliability of the rail.

Description

Numerical analysis method for rolling contact fatigue cracks of rails in ABAQUS
Technical Field
The invention belongs to the technical field of structural fatigue crack monitoring, and relates to a numerical analysis method for rolling contact fatigue cracks of a rail in ABAQUS.
Background
The main problem of high-speed railway safety is rail surface crack caused by rolling contact, the train wheels continuously make rolling contact with the rail, and under the action of wheel-rail rolling contact fatigue, cracks are generated on the surface or the sub-surface of a rail material in a contact area and gradually expand in the depth direction, so that the rail material finally fails and breaks, and train derailment accidents are caused. The fatigue crack on the surface of the rail directly affects the reliability of the safe operation of the railway, however, the detection and maintenance cost of the rail crack is very high, so that the position of the rail crack initiation and the cycle number of the crack propagation to the dangerous length load are predicted, and a correct maintenance strategy is made to reduce the maintenance cost of the railway, and the method becomes a hot point of research of railway enterprises and academia.
A large number of researches show that the crack initiation and propagation of the metal material mostly occur at the grain boundary, and the influence of the grain topological structure on the fatigue of the polycrystalline material under the microscopic scale is great. Different from the condition that cracks of most engineering structures expand under the action of tensile load, the rolling contact cracks of the track further expand towards the interior of the track under the action of pressure generated by wheel-track contact, and crack simulation based on Paris formula of fracture mechanics and crack simulation of an expanded finite element can not analyze the crack initiation and expansion among crystal grains of the metal material of the track.
Disclosure of Invention
The invention aims to provide a numerical analysis method for rolling contact fatigue cracks of a rail in ABAQUS, and solves the problem that the maintenance cost is obviously improved due to the fact that the detection mode of the prior art for the rail cracks is not accurate enough.
The technical scheme adopted by the invention is that a numerical analysis method for rolling contact fatigue cracks of the rails in ABAQUS is implemented according to the following steps:
step 1: establishing a finite element microscopic model of the track,
setting a crack analysis area of a wheel in contact with a rail as 6b x 4b, wherein b is the contact half width of the rail in rolling contact with the wheel, and a 2b x b area is set as a central area;
step 2: importing the orbit finite element micro model established in the step 1 to generate an ABAQUS orbit calculation model,
importing a track finite element micro model file mode. inp embedded with Voronoi and a cohesion unit into the ABAQUS by utilizing an 'Import' function of the ABAQUS;
and step 3: collecting and initializing parameters, setting boundary conditions of a track calculation model,
initializing relevant parameters according to the material of the track: elastic modulus E of crystal grains, Poisson ratio gamma, maximum stress value T initially borne by grain boundary cohesion unit0Initial stiffness K of the cohesive force element0Energy of rupture GIC(ii) a And the fatigue degradation damage variable and the accumulated damage variable are initially assigned a value of 0, i.e., Ds＝0，Df＝0；
And, according to the working condition that the orbit contacts with wheel, limit the whole degree of freedom of the orbit bottom in ABAQUS;
and 4, step 4: setting an analysis step and an increment step in the ABAQUS;
and 5: calculating the damage performance of the material,
using fatigue degradation damage variable DfAnd accumulated damage variablesDsModifying the rigidity and the maximum bearing stress of the cohesive force unit of the material, and calculating to obtain the stress T which can be borne by the cohesive force unit after the degradationfCalculating to obtain the rigidity K of the damaged cohesion unit1；
Step 6: loading the track calculation model;
and 7: the stress amplitude delta tau and the strain delta of the cohesive force unit are analyzed,
obtaining the maximum stress amplitude delta tau and the maximum stress delta of the unit of the track model under the action of rolling contact load by utilizing the statics analysis function of ABAQUS;
and 8: the cohesive force units were analyzed for damage,
adding a P1.for subprogram on a jobinterface of ABAQUS, associating the UMAT subprogram P1.for failing the fatigue damage of the cohesion unit to a track analysis model, and calling the UMAT subprogram P1.for calculating the damage variable D of the cohesion unit of the track modelfAnd Ds；
And step 9: judging whether the cohesion unit fails or not,
if D issNot equal to 1, returning to the step 5 to calculate the material damage performance, and circularly loading and calculating;
if D issWhen the unit is failed, the step 10 is carried out;
step 10: the ABAQUS calculation model is revised, and the calculation model is revised,
if D issIndicating that the cohesive units have failed, removing the cohesive units of the grain boundary from the model, and marking the initiation of cracks in the model; then, returning to the step 5 to calculate the material damage performance, and circularly loading and calculating;
the ABAQUS submits the analysis model, and the ABAQUS circulates steps 5 to 10 in a numerical analysis algorithm of the rail rolling contact fatigue crack initiation and propagation according to the set analysis steps and increment steps, so that the initiation and propagation analysis of the rail crack is realized, and the analysis result is output in time.
The invention has the beneficial effects that: 1) the numerical analysis of the fatigue damage failure of the cohesive force unit is realized by utilizing the UMAT subprogram of ABAQUS; 2) a satellite orbit microscopic model embedded into a Voronoi unit and a cohesion unit is established by using Neper software, the mechanical properties of the material are more finely described by using a finite element model in the model, and simultaneously, the Voronoi unit represents grains randomly distributed in the material; the cohesion unit embedded among the grains simulates the properties of a grain boundary, so that the initiation and the expansion analysis of cracks among the grains are realized; 3) the method effectively simulates the initiation and the expansion of the fatigue crack of the rail under rolling contact, thereby predicting the service life and the reliability of the rail, providing a basis for formulating a rail maintenance strategy and reducing the maintenance cost of the railway.
Drawings
FIG. 1 is a stress-strain relationship for cohesive unit fatigue damage failure for use in the method of the present invention;
FIG. 2 is a UMAT subroutine flow for cohesive unit fatigue damage failure analysis employed in the method of the present invention;
FIG. 3 is a flow chart of a numerical analysis algorithm for the initiation and propagation of rolling contact fatigue cracks in the track in ABAQUS adopted by the method of the present invention;
FIG. 4 is a rail-to-wheel contact model used in the method of the present invention;
FIG. 5 is a orbital finite element microscopic model of a Voronoi and cohesion unit mosaic used in the method of the present invention;
FIG. 6 is a rail contact load of an embodiment of the method of the present invention;
FIG. 7 is a numerical simulation of rail cracking according to an embodiment of the method of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Referring to FIG. 1, which is a stress-strain relationship for fatigue damage failure of the cohesive unit employed in the method of the present invention, in FIG. 1, T is set0Initial maximum stress to be applied to the cohesive unit, K0Is unit stiffness, GICThe energy absorbed per unit length of the crack propagation (i.e., the fracture energy, which is the area encompassed by the stress-strain curve); when the stress borne by the cohesive force unit is less than T0When the unit is in the linear elastic stage; when the stress reaches T0At that time, the cohesive units begin to develop damage (initial damage)) Then the bearing capacity of the cohesive force unit begins to decline, and the displacement of the cohesive force unit gradually increases; when the displacement value of the cohesion unit reaches deltaf，δfDependent on the variable energy of rupture GIC，
Figure BDA0002279475440000051
When the load bearing capacity of the cohesive unit drops to 0, the cohesive unit fails completely.
The damage failure process of the cohesion unit under the alternating load is divided into two stages of fatigue degradation and damage evolution. The fatigue degradation stage is described as the cohesive unit stress is less than the maximum stress value that the cohesive unit can bear, at this time, the cohesive unit does not start to damage, but under the action of alternating load, the performance of the cohesive unit gradually attenuates.
The method adopts the strength attenuation of the cohesive force unit to describe the fatigue degradation process of the cohesive force unit and defines a fatigue degradation damage variable DfReferring to FIG. 1, as the load continues, the maximum stress capability that the cohesive units can withstand gradually decreases, using a fatigue degradation damage variable DfThe expression describing the cell performance decay is as follows:
Tf＝T0(1-Df) (1)
in the formula (1), TfThe unit of stress borne by the degraded cohesive force unit is MPa; t is0The initial maximum bearing stress of the cohesive force unit is expressed in MPa; dfIn order to provide a fatigue-degradation damage variable,
as the number of loads increases, DfThe evolution law of (2) is as follows:
Figure BDA0002279475440000052
in the formula (2), delta tau is stress amplitude and the unit is MPa; tau isrAnd m is a material constant; n is the loading times, then:
Figure BDA0002279475440000053
in the formula (3), the reaction mixture is,
Figure BDA0002279475440000054
the damage rate after the (i + 1) th loading is obtained;
Figure BDA0002279475440000055
the damage rate after the ith loading is obtained;
Figure BDA0002279475440000056
increment damage for the ith load;
when the cohesive unit stress is greater than TfThe cohesion unit enters the damage evolution stage under the action of load, as shown in figure 1, and an accumulated damage variable D is definedsDescribing the gradual reduction of the rigidity of the cohesive force unit in the damage evolution stage, the expression is as follows:
K1＝K0(1-Ds) (4)
in the formula (4), K0Is the initial stiffness value of the cohesive unit; k1Is the cohesive force unit stiffness after damage; dsIs a cumulative damage variable;
when D is presents1, δ ═ δfThe rigidity of the cohesive force unit becomes zero, the cohesive force unit does not have bearing capacity, and the cohesive force unit fails;
the displacement-based damage evolution rule expression is as follows:
Figure BDA0002279475440000061
in the formula (5), δ is a displacement value of a unit in mm; delta0Displacement values in mm for the initial damage of the cell; deltafThe displacement value when the unit fails is in mm;
referring to fig. 2, a flow of UMAT subroutine (p1.for) for cohesive cell fatigue damage failure, which was developed in Visual Studio using Fortran language, with program inputs: stress amplitude delta tau and strain delta borne by the cohesion unit; the program output is: cohesive force sheetThe damage variable of elements, including fatigue-degeneration damage variable DfAnd accumulated damage variable Ds(ii) a Elastic modulus E, Poisson ratio gamma and maximum stress value T initially borne by grain boundary cohesive force unit of the material in the procedure0Initial stiffness K of the cohesive unit0And breaking energy GICA constant amount, depending on the track material,
the working process of the UMAT subprogram is implemented according to the following steps:
the first step is as follows: the stress amplitude delta tau and the strain delta applied to the lead-in unit,
the UMAT subprogram obtains the stress amplitude delta tau and the strain delta value of the cohesion unit under the action of external load from the ABAQUS main program through a data communication interface;
the second step is that: judging whether the cohesive force unit starts to be damaged or not,
if Δ τ ≧ TfJudging that the cohesive force unit starts to be damaged; if Δ τ < TfJudging that the cohesion unit is not damaged and the cohesion unit is in a fatigue degradation stage;
the third step: calculating the damage variable D of the cohesion unitfAnd DS，
If Δ τ is not less than TfThe cohesive force unit begins to damage, and the cumulative damage variable D is calculated according to equation (5)S；
If Δ τ < TfThe cohesive force unit is not damaged, and the fatigue degradation damage variable D is calculated by the formula (2) and the formula (3)f；
Finally outputting accumulated damage variable DsOr fatigue degradation damage variable Df。
Under the Visual Studio interface, the program (p1.for) is associated into ABAQUS using the "attach" button, loaded into ABAQUS as a UMAT subroutine.
Referring to fig. 3, the numerical analysis method for rolling contact fatigue cracks of the rails in the ABAQUS of the present invention is implemented according to the following steps:
step 1: establishing a finite element microscopic model of the track,
setting a crack analysis area of a wheel in contact with a rail as 6b x 4b, wherein b is the contact half width of the rail in rolling contact with the wheel, and a 2b x b area is set as a central area, as shown in figure 4, the step uses Neper software to establish a Voronoi and track finite element micro model embedded with a cohesion unit in the crack analysis area of the rail, the Neper software is open source software based on a Linux system, and the specific process is that,
1.1) generating a Voronoi grain location file,
generating 700 crystal grain seed positions at random in a crack analysis area 6b x 4b of a track by utilizing a random number generation function rand ()' of Matlab, wherein the function is called, and storing all the crystal grain seed positions in a crystal grain position file c1.txt, in order to improve the calculation accuracy and reduce the calculation amount, generating 350 crystal grain seed positions at random in the central area of the crack analysis area, generating 350 crystal grain seed positions at other positions of the crack analysis area;
1.2) constructing a track Voronoi model,
a track Voronoi model file mode _ V.tess containing 700 grain positions is constructed by a grain position file c1.txt by using a-T command of the New, and the command format is as follows:
neper-T-n 700-dim 2-morphooptiini"coo:file(c1)"-domain"square(6b，4b)"-morpho gg-o mode_V；
1.3) dividing the embedded cohesion units and the finite element meshes,
carrying out finite element meshing on the orbit Voronoi model by using a-M command of Neper, wherein the type of a finite element mesh unit is CPE3, and embedding cohesive force units of the type COH2D4 among grains to generate an orbit finite element micro model file mode.inp of mosaic Voronoi and cohesive force units (an orbit model) is shown in figure 5, and the command format of the Neper is as follows:
neper-M mode_V.tess-dim all-nset 0，1，2，3-interface cohesive-format inp-rcl 0.5-o mode；
step 2: importing the orbit finite element micro model established in the step 1 to generate an ABAQUS orbit calculation model,
importing a track finite element micro model file mode. inp embedded with Voronoi and a cohesion unit into the ABAQUS by utilizing an 'Import' function of the ABAQUS;
and step 3: collecting and initializing parameters, setting boundary conditions of a track calculation model,
initializing relevant parameters according to the material of the track: elastic modulus E of crystal grains, Poisson ratio gamma, maximum stress value T initially borne by grain boundary cohesion unit0Initial stiffness K of the cohesive force element0Energy of rupture GIC(ii) a And the fatigue degradation damage variable and the accumulated damage variable are initially assigned a value of 0, i.e., Ds＝0，Df＝0；
And, according to the working condition that the orbit contacts with wheel, limit the whole degree of freedom of the orbit bottom in ABAQUS;
and 4, step 4: the analysis step and the increment step in the ABAQUS are set,
the ABAQUS can analyze a plurality of problems in one calculation, each problem is set as an analysis step, and software analyzes one by one according to the sequence, so that the analysis efficiency is improved; in the ABAQUS data calculation, each analysis step is divided into a plurality of incremental steps, one analysis step is set for the rolling contact load of the track, and the range of the incremental steps is set to be 0.001-0.01;
and 5: calculating the damage performance of the material,
using fatigue degradation damage variable DfAnd accumulated damage variable DsModifying the rigidity and the maximum bearing stress of the cohesive force unit in the material, and obtaining the stress T which can be born after the cohesive force unit is degraded by the formula (1)fThe post-injury cohesive force unit stiffness K is obtained from the formula (4)1；
Step 6: the orbit calculation model is loaded on the basis of the orbit calculation model,
when the wheel rolls on the track, the acting force between the wheel and the track is shown in fig. 6, which includes the normal force p (x) and the tangential force t (x) applied to the surface of the track, wherein the distribution expression of the normal force p (x) is as follows:
Figure BDA0002279475440000091
in the formula (6), xcIs the horizontal coordinate of the load center position; p is a radical ofmaxMaximum contact stress in Mpa; b is the contact half width of the rolling contact between the rail and the wheel, and the unit is mm;
the magnitude of the tangential force is related to the traction coefficient, and the expression is as follows:
t(x)＝μp(x) (7)
in the formula (7), mu is a traction coefficient;
and 7: the stress amplitude delta tau and the strain delta of the cohesive force unit are analyzed,
obtaining the maximum stress amplitude delta tau and the maximum stress delta of the unit of the track model under the action of rolling contact load by utilizing the statics analysis function of ABAQUS;
and 8: cohesive unit damage was analyzed (tune UMAT subroutine p1.for),
adding a P1.for subprogram on a jobinterface of ABAQUS, associating the UMAT subprogram P1.for failing the fatigue damage of the cohesion unit to a track analysis model, and calling the UMAT subprogram P1.for calculating the damage variable D of the cohesion unit of the track modelfAnd Ds；
And step 9: judging whether the cohesion unit fails or not,
if D issNot equal to 1, returning to the step 5 to calculate the material damage performance, and circularly loading and calculating;
if D issWhen the unit is failed, the step 10 is carried out;
step 10: the ABAQUS calculation model is revised, and the calculation model is revised,
if D issWhen the cohesive unit fails, deleting the cohesive unit of the grain boundary from the model (modifying the calculation model), and marking the initiation of crack in the model; then, returning to the step 5 to calculate the material damage performance, and circularly loading and calculating;
the ABAQUS submits the analysis model, and the ABAQUS circulates the steps 5 to 10 in the numerical analysis algorithm of the rail rolling contact fatigue crack initiation and propagation according to the set analysis steps and increment steps, so that the initiation and propagation analysis of the rail cracks is realized, the analysis result is timely output, the prediction of the rail service life is realized, and a basis is provided for formulating a rail maintenance strategy.
Example (b):
taking a 75kg/m type rail as an example, the length of the rail is 12.5m, the material is U78CrV type steel, and the specific parameters of the material are shown in the following table 1; the diameter of the wheel is 1250mm, and the material is CL65 steel. In the contact process of the wheels and the rails, the rails bear 95000N pressure load, and the maximum contact stress p borne by the rails can be calculated according to the Hertz theorymax847Mpa, contact half width b 7.3 mm.
TABLE 1 parameters of examples
Figure BDA0002279475440000101
According to the process setting of the method, firstly, a track finite element microscopic model of a 75kg/m type track embedded with Voronoi and a cohesion unit is established by utilizing Neper and is led into ABAQUS, then, according to the working condition that the track is in contact with wheels, the whole freedom degree of the bottom of the track is limited in the ABAQUS, and a track contact traction coefficient u is set to be 0.3; according to the analysis flow of fig. 3, the material parameters of the initialized U78 CrV-shaped steel are shown in table 1, 1 analysis step is set in ABAQUS, and the range of the increment step is 0.001-0.01; applying normal force p (x) and tangential force t (x) to the orbit model according to the figure 6; after the above orbit calculation model is prepared, the model is associated with the UMAT subroutine (p1.for) of the cohesion unit fatigue damage failure analysis in ABAQUS, and the analysis task is submitted in ABAQUS to obtain the crack numerical analysis result of the orbit of fig. 7 (a). In fig. 7(a), the right side (B region) shear stress is positive, the left side (a region) shear stress is negative, the maximum shear stress occurs at points a and B, the maximum stress amplitude Δ τ is 1580MPa, and the maximum shear stress depth is 0.42 mm. When the number of model loading times is N-2.9 multiplied by 105At this time, cracks initiated from near point a of maximum shear stress, see fig. 7 (b); FIG. 7(c) and FIG. 7(d) show the crack propagation and the change of the surrounding shear stress at different stages with increasing number of times of loading, and the black broken lines in FIG. 7(b), FIG. 7(c) and FIG. 7(d) are the crack propagation paths (failure paths), and it can be seen that the crack propagation paths (failure paths) are lower than the surface of the rail with loadingThe maximum shear stress begins to propagate toward the surface of the rail while the crack propagation process is at its maximum at the tip of the crack.
The method is based on a cohesive force model of damage mechanics, firstly, a local stress-strain constitutive model of fatigue damage failure of a cohesive force unit is given, a UMAT subprogram of fatigue damage failure analysis of the cohesive force unit of ABAQUS is written, on the basis, a track grain microscopic model is established by embedding Voronoi and the cohesive force unit on the basis of a track finite element model, and finally, the model is led into ABAQUS, so that the numerical analysis of the rolling contact fatigue crack of the track is realized. By implementing the numerical analysis of the rolling contact fatigue crack of the track in the ABAQUS, the initiation, the expansion and the failure process of the fatigue crack of the track under the rolling contact are better simulated, the method can effectively predict the service life and the reliability of the track, and provide a basis for formulating a track maintenance strategy, thereby reducing the maintenance cost of the railway.

Claims (6)

1. A numerical analysis method for rolling contact fatigue cracks of rails in ABAQUS is characterized by comprising the following steps:
step 1: establishing a finite element microscopic model of the track,
setting a crack analysis area of a wheel in contact with a rail as 6b x 4b, setting a b contact half width of the rail in rolling contact with the wheel, setting a 2b x b area as a central area, and establishing a Voronoi and cohesive force unit embedded rail finite element micro model in the rail crack analysis area by using Neper software;
step 2: importing the orbit finite element micro model established in the step 1 to generate an ABAQUS orbit calculation model,
importing a track finite element micro model file mode. inp embedded with Voronoi and a cohesion unit into the ABAQUS by utilizing an 'Import' function of the ABAQUS;
and step 3: collecting and initializing parameters, setting boundary conditions of a track calculation model,
initializing relevant parameters according to the material of the track: elastic modulus E of crystal grains, Poisson ratio gamma, and initial bearing capacity of grain boundary cohesion unitMaximum stress value T0Initial stiffness K of the cohesive force element0Energy of rupture GIC(ii) a And the fatigue degradation damage variable and the accumulated damage variable are initially assigned a value of 0, i.e., Ds＝0，Df＝0；
And, according to the working condition that the orbit contacts with wheel, limit the whole degree of freedom of the orbit bottom in ABAQUS;
and 4, step 4: setting an analysis step and an increment step in the ABAQUS;
and 5: calculating the damage performance of the material,
using fatigue degradation damage variable DfAnd accumulated damage variable DsModifying the rigidity and the maximum bearing stress of the cohesive force unit of the material, and calculating to obtain the stress T which can be borne by the cohesive force unit after the degradationfCalculating to obtain the rigidity K of the damaged cohesion unit1；
Step 6: loading the track calculation model;
and 7: the stress amplitude delta tau and the strain delta of the cohesive force unit are analyzed,
obtaining the maximum stress amplitude delta tau and the maximum stress delta of the unit of the track model under the action of rolling contact load by utilizing the statics analysis function of ABAQUS;
and 8: the cohesive force units were analyzed for damage,
adding a P1.for subprogram on a jobinterface of ABAQUS, associating the UMAT subprogram P1.for failing the fatigue damage of the cohesion unit to a track analysis model, and calling the UMAT subprogram P1.for calculating the damage variable D of the cohesion unit of the track modelfAnd Ds；
And step 9: judging whether the cohesion unit fails or not,
if D issNot equal to 1, returning to the step 5 to calculate the material damage performance, and circularly loading and calculating;
if D issWhen the unit is failed, the step 10 is carried out;
step 10: the ABAQUS calculation model is revised, and the calculation model is revised,
if D issWhen the cohesive units fail, the cohesive units of the grain boundary were removed from the model and the start of the mark in the modelInitiating cracks; then, returning to the step 5 to calculate the material damage performance, and circularly loading and calculating;
the ABAQUS submits the analysis model, and the ABAQUS circulates steps 5 to 10 in a numerical analysis algorithm of the rail rolling contact fatigue crack initiation and propagation according to the set analysis steps and increment steps, so that the initiation and propagation analysis of the rail crack is realized, and the analysis result is output in time.
2. The method for numerically analyzing rolling contact fatigue cracks of a railway rail according to claim 1, wherein: in the step 1, open source software Neper based on a Linux system is used for modeling, and the specific process is that,
1.1) generating a Voronoi grain location file,
generating a function rand () by using a random number of Matlab, randomly generating 700 crystal grain seed positions in a crack analysis area 6b x 4b of the track, and storing all the crystal grain seed positions in a crystal grain position file c1. txt;
1.2) constructing a track Voronoi model,
a track Voronoi model file mode _ V.tess containing 700 grain positions is constructed by a grain position file c1.txt by using a-T command of the New, and the command format is as follows:
neper-T-n 700-dim 2-morphooptiini"coo:file(c1)"-domain"square(6b，4b)"-morpho gg-o mode_V；
1.3) dividing the embedded cohesion units and the finite element meshes,
carrying out finite element meshing on the orbit Voronoi model by using a-M command of Neper, wherein the type of a finite element mesh unit is CPE3, and embedding cohesion units of COH2D4 among grains to generate an orbit finite element micro model file mode. inp embedded with the Voronoi and the cohesion units, and the command format of the Neper is as follows:
neper-M mode_V.tess-dim all-nset 0，1，2，3-interface cohesive-format inp-rcl 0.5-o mode。
3. the method for numerically analyzing rolling contact fatigue cracks of a railway rail according to claim 2, wherein: in the step 1.1), 350 grain seed positions are randomly generated in the central area of the crack analysis area, and 350 grain seed positions are generated in other positions of the crack analysis area.
4. The method for numerically analyzing rolling contact fatigue cracks of a railway rail according to claim 1, wherein: in the step 4, an analysis step is set for the rolling contact load of the track, and the range of the increment step is set to be 0.001-0.01.
5. The method for numerically analyzing rolling contact fatigue cracks of a railway rail according to claim 1, wherein: in the step 6, the specific process is,
when the wheel rolls on the track, the acting force between the wheel and the track comprises a normal force p (x) and a tangential force t (x) applied to the surface of the track, wherein the distribution expression of the normal force p (x) is as follows:
Figure FDA0002279475430000041
in the formula (6), xcIs the horizontal coordinate of the load center position; p is a radical ofmaxMaximum contact stress in Mpa; b is the contact half width of the rolling contact between the rail and the wheel, and the unit is mm;
the magnitude of the tangential force is related to the traction coefficient, and the expression is as follows:
t(x)＝μp(x)(7)
in the formula (7), μ is a traction coefficient.
6. The method for numerically analyzing rolling contact fatigue cracks of a railway rail according to claim 1, wherein: in the step 8, a UMAT subprogram P1.for failing from the fatigue damage of the cohesion unit is called,
the program inputs are: stress amplitude delta tau and strain delta borne by the cohesion unit;
the program output is: damage variables of cohesive units, including fatigue degradation lossesInjury variable DfAnd accumulated damage variable Ds(ii) a Elastic modulus E, Poisson ratio gamma and maximum stress value T initially borne by grain boundary cohesive force unit of the material in the procedure0Initial stiffness K of the cohesive unit0And breaking energy GICA constant value is set, and the constant value,
the working process of the UMAT subprogram is implemented according to the following steps:
the first step is as follows: the stress amplitude delta tau and the strain delta applied to the lead-in unit,
the UMAT subprogram obtains the stress amplitude delta tau and the strain delta value of the cohesion unit under the action of external load from the ABAQUS main program through a data communication interface;
the second step is that: judging whether the cohesive force unit starts to be damaged or not,
if Δ τ ≧ TfJudging that the cohesive force unit starts to be damaged; if Δ τ < TfJudging that the cohesion unit is not damaged and the cohesion unit is in a fatigue degradation stage;
the third step: calculating the damage variable D of the cohesion unitfAnd DS，
If Δ τ is not less than TfThe cohesive force unit begins to damage, and the cumulative damage variable D is calculated according to equation (5)S；
If Δ τ < TfCalculating the fatigue degeneration damage variable D when the cohesion unit is not damagedf；
Finally outputting accumulated damage variable DsOr fatigue degradation damage variable Df。
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