WO2021098169A1

WO2021098169A1 - Method for predicting fatigue life of geometrically discontinuous structure

Info

Publication number: WO2021098169A1
Application number: PCT/CN2020/091262
Authority: WO
Inventors: 张显程; 苑光健; 王润梓; 涂善东
Original assignee: 华东理工大学
Priority date: 2019-11-22
Filing date: 2020-05-20
Publication date: 2021-05-27
Also published as: CN110826285B; CN110826285A

Abstract

A method for predicting the fatigue life of a geometrically discontinuous structure, comprising the steps of: establishing a geometrically continuous first finite element model, defining a crystal plasticity constitutive equation, thereby obtaining a stress-strain relationship of a material under a given cyclic loading condition (S1); carrying out a uniaxial tensile test and a uniaxial fatigue test to obtain a tensile curve and a hysteresis loop (S2); obtaining the tensile curve and hysteresis loop by means of test parameter fitting, and acquiring material parameters and a critical value of fatigue plastic slip required by the crystal plasticity constitutive equation (S3); establishing a second finite element model of the geometrically discontinuous structure, and acquiring a stress-strain relationship of each cycle and a single-cycle fatigue plastic slip value (S4); and calculating the crack initiation life of a notched specimen (S5). The method for predicting the fatigue life of the geometrically discontinuous structure may better achieve the fatigue analysis of the geometrically discontinuous structure at different temperatures, and may also accurately predict the location of crack initiation. The method has the advantages of intuitiveness, strong applicability and high accuracy.

Description

A fatigue life prediction method for geometrically discontinuous structures

Technical field

The invention relates to the field of life prediction for structures containing notches, and in particular to a fatigue life prediction method based on ABAQUS.

Background technique

In the process of aeroengine manufacturing, due to the existence of objective reasons such as processing conditions, manufacturing processes and installation conditions, some important parts such as turbine disks inevitably have some surface micro-defects during the installation process. In addition, during the operation of the aircraft, the impact of suspended solids in the air can also cause serious damage to important components such as engine blades and turbine disks. It is precisely because of the existence of these micro-defects and small gaps that the initiation of fatigue cracks in important parts such as aero-engine turbine discs and blades has been accelerated, and the fatigue life of engine parts has been reduced. Therefore, in order to ensure economy and safety, it is very important to accurately assess the normal service life of engine components under the premise that engine components have defects.

In recent years, the development of finite element software can satisfy people's understanding of complex stress-strain behavior and provide the feasibility of accurate life prediction in this state. The ABAQUS finite element commercial software can not only analyze complex fixed mechanics and structural mechanics systems, but also supplement the imperfect functions of the ABAQUS pre-processing module through a powerful secondary development interface. Among them, the user-defined subroutine based on FORTRAN language expands the application of ABAQUS in constitutive equations, and realizes the functions of damage assessment and life prediction. Compared with the existing processing modules of the ABAQUS software, the user-defined subroutines adapted from the Fortran language can better compile the required constitutive model according to your own materials or needs.

Nowadays, fatigue analysis and life prediction of complex structures can mainly describe the continuous damage mechanics theory including crack initiation and propagation stages, which introduces a unified fatigue constitutive through damage variables to describe the process of damage accumulation to fracture under cyclic loading. . This type of method focuses on describing the fatigue behavior in the crack propagation stage. Its complex programming, poor convergence, and high computational cost determine that this type of method does not have a strong universality. In addition, this method is aimed at macro-level components and has a strong impact on micro-level components. The layer stress-strain response and mechanism analysis are not accurate. Due to the initiation of cracks, it is usually produced on a microscopic level. Therefore, how to more effectively evaluate the crack initiation life and analyze the causes of crack initiation is very important.

Summary of the invention

In view of the above-mentioned shortcomings in the prior art, the present invention provides a method for predicting the fatigue life of geometrically discontinuous structures, which can better realize the fatigue analysis of geometrically discontinuous structures, and has the advantages of intuitiveness, strong applicability, and high accuracy.

In order to achieve the above objective, the present invention provides a method for predicting the fatigue life of a geometrically discontinuous structure, which includes the following steps:

S1: Establish a geometrically continuous first ABAQUS finite element model containing multiple crystal grains of the material with the geometric discontinuous structure, and define the material during the cyclic load uniaxial fatigue test through the user subroutine UMAT The crystal plasticity constitutive equation of, to obtain the stress-strain relationship of the material under given cyclic loading conditions;

S2: Perform uniaxial tensile test and uniaxial fatigue test with different strain amplitudes on the material with the geometric discontinuous structure at the same temperature to obtain the tensile curve and hysteresis loop;

S3: Establish a fatigue damage calculation model, and obtain the tensile curve and hysteresis loop of the first ABAQUS finite element model through trial-parameter fitting, and then obtain the material parameters and fatigue plastic slip required by the crystal plastic constitutive equation Shift critical value;

S4: Establish a second ABAQUS finite element model of the geometric discontinuous structure, and combine the user subroutine UMAT of step S1 with the material parameters and fatigue plastic slip critical value of step S3, and use ABAQUS software to simulate the cycle Load uniaxial fatigue test to obtain the stress-strain relationship and single-cycle fatigue plastic slip value for each cycle;

S5: Combining the critical fatigue plastic slip value of step S3 and the single-cycle fatigue plastic slip value of step S4, calculate the crack initiation life of the notched sample.

Further, in the step S1, the crystal plasticity constitutive equation includes a master control equation, a slip flow criterion equation, and a back stress evolution equation.

Further, the step S1 includes:

S11: Establish the main control equations of the deformation gradient F and the deformation rate gradient L of the material with the geometric discontinuous structure in the crystal plastic constitutive equation, and the deformation gradient F and the deformation rate gradient L of the material with the geometric discontinuous structure are The main control equation is:

F=F _e ·F _p ,

L=L _e +L _p ,

Among them, F is the total deformation gradient, F _e is the elastic deformation gradient, F _{p is the} inelastic deformation gradient, L is the deformation rate gradient, _Le is the elastic deformation rate gradient, L _{p is the} inelastic deformation rate gradient,

Is the plastic slip rate of the α-th slip system _{, s α} _{is the slip direction vector of the α-th slip system, and m α} is the normal direction vector of the α-th slip system;

S12: Establish the slip flow criterion equation in the crystal plasticity constitutive equation. The slip flow criterion equation is:

among them,

Is the reference plastic slip rate, F ₀ is the thermal activation free energy, k is Boltzmann’s constant, θ is the absolute temperature, τ ^α is the decomposed shear stress of the α-th slip system, and σ is the stress value; B ^α is the first The back stress of the α slip system, μ and μ ₀ are the shear modulus at θ and 0K, respectively, τ ₀ , p, q are the material constants, S ^α is the slip resistance of the α-th slip system, h _s and d _D is the static hardening and dynamic recovery modulus respectively,

Is the initial slip resistance of the α-th slip system;

S13: Establish the back-stress inelastic follow-up strengthening equation in the crystal plastic constitutive equation, and the back-stress inelastic follow-up strengthening equation is:

Among them, h _B is the back-stress hardening constant, r _D is the dynamic recovery coefficient related to slip resistance, f _c is the coupling parameter related to internal variables, μ′ ₀ is the local slip shear modulus at 0K, and λ is the material constant.

Further, in the step S2, the shape of the sample used in the uniaxial tensile test and the uniaxial fatigue test is the same as the shape of the first ABAQUS finite element model in the step S1.

Further, in the step S3, the fatigue damage calculation model is established according to the first ABAQUS finite element model and the crystal plasticity constitutive equation in the step S1.

Further, in the step S3, the fatigue plastic slip critical value P _crit is:

Among them, L _{p is the} inelastic deformation rate gradient, and P _crit is the critical value of fatigue plastic slip.

Further, in the step S4, when simulating the uniaxial fatigue test of the cyclic load, the calculation formula adopts the crystal plastic constitutive equation defined by the user subroutine UMAT in the step S1, and the applied cyclic load The load is the same as that of the uniaxial fatigue test in step S2.

Further, the step S4 further includes: after establishing the second ABAQUS finite element model of the geometric discontinuous structure, applying reasonable boundary conditions and external loads to divide the model mesh.

Further, in the step S5, the crack initiation life is:

Where, N _i is the initiation of fatigue life, P _crit plastic slip fatigue threshold, P _cyc single cycle fatigue plastic slip value.

The present invention uses the fatigue plastic slip critical value P _crit as the fatigue indicator, and can use micro-scale parameters as damage parameters to evaluate life. The advantage of this method lies in the prediction on the micro-scale. Not only can the life be predicted, but also the accumulation map of plastic slip damage in each cycle can be obtained, thereby predicting the location of crack initiation.

The crystal plasticity constitutive in the user subroutine UMAT used in the fatigue life prediction method of the geometric discontinuous structure of the present invention is based on the classic crystal plasticity theory, and the stress and strain behavior of the geometric discontinuous structure under fatigue load can be obtained, and it adopts The slip flow criterion equation is a temperature-dependent power exponential slip flow criterion, which can simulate not only normal temperature but also high temperature, and can be used to describe the mechanical behavior of different temperature states, thereby making the geometric discontinuity of the present invention The fatigue life prediction method of structure can predict the structure life under high temperature.

The invention adopts the ABAQUS finite element model, which has strong intuitiveness, and can intuitively obtain the crack initiation position of the geometric discontinuous structure and predict the crack initiation life of the position.

Description of the drawings

Fig. 1 is a flowchart of a method for predicting fatigue life of a geometrically discontinuous structure according to an embodiment of the present invention;

2 is a schematic diagram of a first ABAQUS finite element model of a method for predicting fatigue life of a geometrically discontinuous structure according to an embodiment of the present invention;

Fig. 3 is a graph of the uniaxial tensile test and simulation curve fitting results of the method for predicting the fatigue life of a geometric discontinuous structure according to an embodiment of the present invention;

4 is a diagram of the hysteresis loop data of the uniaxial fatigue test and the fitting result diagram of the fitting curve of the fatigue life prediction method of the geometric discontinuous structure according to an embodiment of the present invention;

Figures 5(a)-5(h) are the finite element model diagrams of different notched specimens used in the fatigue life prediction method of the geometric discontinuous structure of the present invention, wherein Figures 5(a)-5(h) show Different notch sizes;

Fig. 6 is a diagram showing the linear growth trajectory of plastic strain accumulated in different cycles of different notched specimens in the fatigue life prediction method of the geometric discontinuous structure of the present invention;

Figure 7 is a comparison diagram of life prediction for different notched specimens;

FIG. 8 is a comparison diagram of the life prediction results of different notched specimens and the experimental verification results of the fatigue life prediction method of the geometric discontinuous structure of the present invention;

9 is a diagram of the relationship between different notch lengths and predicted life predicted by the fatigue life prediction method of the geometric discontinuous structure of the present invention;

Fig. 10 is a diagram of the relationship between the different notch areas predicted by the fatigue life prediction method of the geometric discontinuous structure of the present invention and the predicted life.

Detailed ways

Hereinafter, preferred embodiments of the present invention are given and described in detail according to the attached drawings 1-9, so that the functions and characteristics of the present invention can be better understood.

Please refer to FIG. 1 for a method for predicting fatigue life of a geometrically discontinuous structure disclosed in the present invention, which includes the following steps:

S1: Establish a first ABAQUS finite element model of a certain number of crystal grains that are geometrically continuous (that is, without gaps) and include the material with the geometric discontinuous structure, where the number of the crystal grains is usually multiple, and Define the crystal plastic constitutive equation of the material during the uniaxial fatigue test under cyclic loading through the user subroutine UMAT, so as to obtain the stress-strain relationship of the material under the given cyclic loading condition;

The first ABAQUS finite element model refers to a model modeled by the finite element software ABAQUS, the shape of which is shown in FIG. 2, and is used to describe the microstructure information of the material with the geometric discontinuous structure. The crystal plastic constitutive equations include master control equations, slip flow criterion equations, and back stress evolution equations (ie formulas 1 to 11 described below), which are used to describe the stress and strain of the material with the geometric discontinuous structure Relationship and used to embed the first ABAQUS finite element model for finite element calculations. The stress-strain relationship includes an elastic part and a plastic part, and the plastic part is calculated using the crystal plastic constitutive equation.

Wherein, step S1 further includes the steps:

S11: Establish a master control equation for the deformation gradient F and the deformation rate gradient L of the material with the geometric discontinuous structure in the crystal plasticity constitutive equation.

Wherein, the main control equations of the deformation gradient F and the deformation rate gradient L of the material with the geometric discontinuous structure are:

F=F _e ·F _p (1);

L=L _e +L _p (2);

S12: Establish the slip flow criterion equation in the crystal plastic constitutive equation. The slip flow criterion equation includes:

among them,

Is the plastic slip rate of the α-th slip system,

Is the reference plastic slip rate, F ₀ is the thermal activation free energy, the unit is kJ·mol ^-1 , k is Boltzmann's constant, θ(T) is the absolute temperature, τ ^α is the decomposition shear of the α-th slip system Stress, the unit is MPa, the evolution equation is shown in formula (5), σ is the stress value, the unit is MPa; B ^α is the back stress of the α-th slip system, the unit is MPa, μ and μ ₀ are respectively θ and 0K The unit of shear modulus at time is GPa, τ ₀ , p, q are material constants, and the unit of _{τ 0 is MPa.} The operation symbol <> means: when x>0, <x>=x; when x≤0, <x>=0. S ^α is the slip resistance of the α-th slip system, in MPa. Its evolution equation is shown in formula (6), h _s and d _D are static hardening and dynamic recovery modulus, respectively, in units of MPa,

Is the initial slip resistance of the α-th slip system, in MPa.

Since the slip flow criterion equation in the crystal plastic constitutive equation used in the fatigue life prediction method of the geometric discontinuous structure of the present invention is a power exponential slip flow criterion, compared with the traditional power function type, heat is embedded Temperature-related parameters such as activation energy can simulate the mechanical behavior of materials at different temperatures.

S13: Establish the back-stress inelastic follow-up strengthening equation in the crystal plastic constitutive equation, where the back-stress inelastic follow-up strengthening equation is:

Among them, h _B is the back stress hardening constant, the unit is MPa, r _D is the dynamic recovery coefficient related to slip resistance, the evolution equation is shown in formula (8), f _c is the coupling parameter related to internal variables, and μ′ ₀ is The local slip shear modulus at 0K, the unit is GPa, and λ is the material constant.

The fatigue life prediction method of the geometric discontinuous structure of the present invention adopts the back stress inelastic follow-up strengthening equation, thereby taking into account the temperature effect.

S2: Perform a uniaxial tensile test and a uniaxial fatigue test with different strain amplitudes on the material with the geometric discontinuous structure at the same temperature to obtain a tensile curve and a hysteresis loop. In this embodiment, the temperatures used are all room temperature, but the method of the present invention can also be applied to various service temperatures of materials.

Wherein, the shape of the sample used in the uniaxial tensile test and the uniaxial fatigue test is the same as the shape of the first ABAQUS finite element model in step S1.

S3: Establish a fatigue damage calculation model, and obtain the tensile curve and hysteresis loop of the first ABAQUS finite element model through trial-parameter fitting, until the obtained tensile curve and hysteresis loop are the same as in step S2 The tensile curve and hysteresis loop obtained from the test have a good degree of fit, and then the material parameters required for the crystal plasticity constitutive equation can be obtained

F ₀ ,p,q,τ ₀ ,s ₀ ,h _s ,d _D ,μ ₀ ,μ′ ₀ ,h _B ,f _C ,μ,λ and the critical fatigue plastic slip value P _crit . Among them, the fatigue plastic slip critical value P _crit is a new parameter relative to the prior art.

Wherein, the fatigue damage calculation model is established according to the first ABAQUS finite element model and the crystal plasticity constitutive equation in the step S1.

The calculation formula of fatigue plastic slip critical value P _{crit is as follows:}

Among them, L _{p is the} inelastic deformation rate gradient, P _crit is the critical value of fatigue plastic slip,

Is the rate of change of fatigue plastic slip.

Since the first ABAQUS finite element model of step S1 is geometrically continuous, that is, it does not contain gaps, it is used for parameter correction. Because the first ABAQUS finite element model can be fitted with the stretch curve and hysteresis loop in step S2, we use the first ABAQUS finite element model without gaps to fit the experiment to determine the parameters.

S4: Establish a second ABAQUS finite element model of the geometric discontinuous structure (that is, including gaps), apply reasonable boundary conditions and external loads, divide the model mesh, and combine the user subroutine UMAT of step S1 with all The material parameters and fatigue plastic slip critical value P _{crit of} step S3 are described. The ABAQUS software is used to simulate the uniaxial fatigue test of cyclic loading, and the stress-strain relationship and single-cycle fatigue of each cycle (each integration point) are obtained. The calculation of plastic slip value and single cycle fatigue plastic slip value also use formulas (9) and (10). The model shape and gap of the geometric discontinuous structure can be changed according to actual engineering conditions. Since it is the life prediction object of the present invention, a second finite element model with gaps is established to predict the life.

Wherein, the total number of cycle cycles may be the total cycle cycles up to the time of fatigue fracture. When simulating the uniaxial fatigue test under cyclic load, the calculation formula adopts the crystal plasticity constitutive equation defined by the user subroutine UMAT in step S1, and the applied cyclic load is the same as that of the uniaxial fatigue test in step S2. The load is the same, and the evolution of each cycle is calculated from this. As a result, the single-cycle fatigue plastic slip value and the evolution process of plastic slip per cycle as shown in Fig. 6 can be obtained.

Wherein, the crack initiation life is:

Where, N _i is the crack initiation life, P _crit plastic slip fatigue threshold, P _cyc single cycle fatigue plastic slip value.

Experimental results

In the following, the fatigue life prediction method of geometric discontinuous structure provided by the present invention is used to verify the effectiveness of the present invention for different notched specimens, and the initiation life information of the experiment is used. Among them, the material of the notched sample is nickel-based GH4169 superalloy, and the fatigue test is carried out in an air environment at room temperature. The external load applied at both ends of the specimen is the overall stress control. Due to the geometric discontinuity of the unilateral notch specimen, the weakest part of the notch is in a multiaxial stress-strain state.

The fatigue life prediction method of the geometric discontinuous structure of the present invention requires uniaxial tensile test under normal temperature air environment and uniaxial fatigue test with different strain amplitudes on samples without notches of the same material. The obtained test The result is used to determine the material parameters required by the crystal plastic constitutive equations of formulas (1) to (8) and (11) in step S2 of the fatigue life prediction method of the geometric discontinuous structure of the present invention. First, establish the ABAQUS model without notches as shown in Figure 2, and adjust the simulation results of uniaxial tensile and fatigue tests by the trial parameter method, so that it can be better matched with the uniaxial tensile and fatigue test data. The results are shown in Figure 3 and Figure 4. Among them, the fitting result is:

F ₀ =295kJ·mol ^-1 , θ = 293K, p = 0.31, q = 1.8, τ ₀ =810MPa, s ₀ =340MPa, h _s =513MPa, d _D =6030MPa, μ ₀ =192GPa, μ′ ₀ = 72.3GPa, h _B =540 MPa, f _C =0.41, μ=73.65GPa, λ=0.85.

By adopting the fatigue life prediction method of the geometric discontinuous structure of the present invention, the critical value P _{crit of} fatigue plastic slip can be determined according to the fitting result, and then the life prediction of materials with different notches can be carried out.

Figure 5 (a)-Figure 5 (h) show the ABAQUS model diagrams of different notched samples. The size of the model is the same, and different gap sizes are changed, where a represents the length of the gap and b represents the width of the gap. Figure 6 shows the fatigue cumulative plastic strain trajectory diagram for each cycle of different notched specimens. It can be seen that when the size of the gap is larger, the cumulative plastic slip is also larger. In addition, plastic accumulation is linear, so the above formula (11) can be used to calculate the fatigue initiation life of different specimens. Figure 7 shows the life prediction diagrams of different notched specimens. It can be seen that the fatigue life prediction method of the geometric discontinuous structure of the present invention uses cumulative plastic slip to predict the result of the initiation life, which is relatively close to the experimental result and within the range of 2 times the error band. Therefore, this numerical simulation is proved The method has high reliability. In addition, in the results of the numerical simulation, the location of crack initiation can also be predicted. Crack initiation is mainly concentrated in two areas, one is the stress concentration area at the root of the notch. This is because the root of the notch is a potential dangerous point in the fatigue process, and the stress concentration effect is more obvious; the other is at a location far away from the root, where the cracks are located in this area. The initiation is mainly caused by the large plastic deformation of local grains.

On the basis of the above-mentioned prediction results obtained by the fatigue life prediction method of the geometric discontinuous structure of the present invention, more models of the geometric discontinuous structure (the same size but different grain orientation) are established below, and the experiments are used to verify this The feasibility and applicability of the method.

Figure 8 shows the comparison diagram of the life prediction of different models and the experimental results. It can be seen from the figure that the life comparison of all the prediction results obtained by the present invention and the experimental results are within the range of 2 times the error band, which proves This numerical simulation method has high reliability and stability. In addition, the analysis of different notch length and notch area reveals that the life span has a great relationship with notch length and notch area. Figure 9 shows the life comparison diagram of different notch lengths. It can be seen from the figure that as the length of the notch increases, the fatigue life gradually decreases. In addition, after the length reaches a certain value, the life will reach a plateau. The length of the gap in the later period will have a smaller effect. Figure 10 shows the life comparison chart of different notch areas. It can be seen from the figure that as the notch area increases, the fatigue life gradually decreases. After the notch area increases, the plateau phenomenon will also appear. Moreover, there is a certain evolutionary relationship between notch area and fatigue life:

Wherein A is the area of the notch, N _i is the fatigue life.

The foregoing descriptions are only preferred embodiments of the present invention, and are not used to limit the scope of the present invention. Various changes can be made to the foregoing embodiments of the present invention. That is to say, all simple and equivalent changes and modifications made in accordance with the claims of the present invention and the contents of the description fall into the protection scope of the patent of the present invention.

Claims

A method for predicting the fatigue life of a geometrically discontinuous structure, which is characterized in that it comprises the following steps:

S1: Establish a geometrically continuous first ABAQUS finite element model containing multiple crystal grains of the material with the geometric discontinuous structure, and define the material during the cyclic load uniaxial fatigue test through the user subroutine UMAT The crystal plasticity constitutive equation of, to obtain the stress-strain relationship of the material under given cyclic loading conditions;

S2: Perform uniaxial tensile test and uniaxial fatigue test with different strain amplitudes on the material with the geometric discontinuous structure at the same temperature to obtain the tensile curve and hysteresis loop;

S3: Establish a fatigue damage calculation model, and obtain the tensile curve and hysteresis loop of the first ABAQUS finite element model through trial-parameter fitting, and then obtain the material parameters and fatigue plastic slip required by the crystal plastic constitutive equation Shift critical value;

S4: Establish a second ABAQUS finite element model of the geometric discontinuous structure, and combine the user subroutine UMAT of step S1 with the material parameters and fatigue plastic slip critical value of step S3, and use ABAQUS software to simulate the cycle Load uniaxial fatigue test to obtain the stress-strain relationship and single-cycle fatigue plastic slip value for each cycle;

S5: Combining the critical fatigue plastic slip value of step S3 and the single-cycle fatigue plastic slip value of step S4, calculate the crack initiation life of the notched sample.
The method for predicting the fatigue life of a geometric discontinuous structure according to claim 1, wherein in the step S1, the crystal plastic constitutive equation includes a master control equation, a slip flow criterion equation, and a back stress evolution equation .
The method for predicting the fatigue life of a geometrically discontinuous structure according to claim 2, wherein the step S1 comprises:

S11: Establish the main control equations of the deformation gradient F and the deformation rate gradient L of the material with the geometric discontinuous structure in the crystal plastic constitutive equation, and the deformation gradient F and the deformation rate gradient L of the material with the geometric discontinuous structure are The main control equation is:

F=F e ·F p ,

L=L e +L p ,

Among them, F is the total deformation gradient, F e is the elastic deformation gradient, F p is the inelastic deformation gradient, L is the deformation rate gradient, Le is the elastic deformation rate gradient, L p is the inelastic deformation rate gradient,
Is the plastic slip rate of the α-th slip system , s α is the slip direction vector of the α-th slip system, and m α is the normal direction vector of the α-th slip system;

S12: Establish the slip flow criterion equation in the crystal plasticity constitutive equation. The slip flow criterion equation is:

among them,
Is the reference plastic slip rate, F 0 is the thermal activation free energy, k is Boltzmann’s constant, θ is the absolute temperature, τ α is the decomposed shear stress of the α-th slip system, and σ is the stress value; B α is the first The back stress of the α slip system, μ and μ 0 are the shear modulus at θ and 0K, respectively, τ 0 , p, q are the material constants, S α is the slip resistance of the α-th slip system, h s and d D is the static hardening and dynamic recovery modulus respectively,
Is the initial slip resistance of the α-th slip system;

S13: Establish the back-stress inelastic follow-up strengthening equation in the crystal plastic constitutive equation, and the back-stress inelastic follow-up strengthening equation is:

Among them, h B is the back-stress hardening constant, r D is the dynamic recovery coefficient related to slip resistance, f c is the coupling parameter related to internal variables, μ′ 0 is the local slip shear modulus at 0K, and λ is the material constant.
The method for predicting the fatigue life of a geometric discontinuous structure according to claim 1, wherein in the step S2, the shape of the sample used in the uniaxial tensile test and the uniaxial fatigue test is the same as that of the The shape of the first ABAQUS finite element model in step S1 is the same.
The method for predicting the fatigue life of a geometric discontinuous structure according to claim 1, wherein in the step S3, the fatigue damage calculation model is based on the first ABAQUS finite element model and the crystal plasticity in the step S1 The constitutive equation is established.
The method for predicting the fatigue life of a geometrically discontinuous structure according to claim 1, wherein in the step S3, the fatigue plastic slip critical value P crit is:

Among them, L p is the inelastic deformation rate gradient, and P crit is the critical value of fatigue plastic slip.
The method for predicting the fatigue life of a geometric discontinuous structure according to claim 1, characterized in that, in the step S4, when simulating the uniaxial fatigue test of cyclic load, the calculation formula adopts the user in the step S1 The crystal plasticity constitutive equation defined by the subroutine UMAT, and the applied cyclic load is the same as the load of the uniaxial fatigue test in step S2.
The fatigue life prediction method of the geometric discontinuous structure according to claim 1, wherein the step S4 further comprises: after establishing a second ABAQUS finite element model of the geometric discontinuous structure, applying reasonable boundary conditions And external loads, and mesh the model.
The method for predicting the fatigue life of a geometrically discontinuous structure according to claim 1, wherein, in the step S5, the crack initiation life is:

Where, N i is the initiation of fatigue life, P crit plastic slip fatigue threshold, P cyc single cycle fatigue plastic slip value.