Method for simulating small fatigue crack propagation in polycrystalline metallic materials

Abstract

The present application relates to a kind of polycrystalline metal material fatigue small crack propagation simulation method, comprising: determining the accurate value of crystal plasticity constitutive model and each undetermined parameter thereof;Establish the crack propagation finite element model of polycrystalline metal material, and the crack propagation finite element model is embedded in crack propagation finite element model with each undetermined parameter having respective accurate value of crystal plasticity constitutive model and the crack propagation criterion obtained in advance;Load and boundary condition are applied to crack propagation finite element model, and crack propagation finite element analysis is carried out, to obtain finite element analysis result, including stress-strain data calculated based on crystal plasticity constitutive model and crack propagation data calculated based on crack propagation criterion and stress-strain data.The polycrystalline metal material fatigue small crack propagation simulation method of the present application introduces Hall-Petch size effect in crystal plasticity constitutive model to consider the influence of grain size on slip resistance, to improve the accuracy of simulation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fatigue numerical simulation, and more particularly to a polycrystalline metal material fatigue small crack propagation simulation method. BACKGROUND

[0002] In engineering, the service load of fatigue failure is lower than the yield point of the material, however, although the safety factor is considered after design and the inspection schedule is formulated, more than 80% of the parts cannot be detected by nondestructive testing (such as penetrating liquid) during the service life, just because the crack size is too small (less than 1mm). It is necessary to analyze the sensitivity of the crack from the microscopic point of view. The whole fatigue crack propagation is divided into two stages: stage I is related to small fatigue crack growth (FSCG), and stage II is related to long fatigue crack growth (LCG). In the whole fatigue life, the time of fatigue small crack propagation accounts for more than 85% of the total time, and the prediction of the propagation of fatigue cracks at the microstructure level is of great significance to many engineering industries, and the diversity of crack propagation at the microstructure length scale requires the use of existing modeling techniques to accurately predict the fatigue life. In polycrystalline microstructure, the short crack path has a great influence on the crack propagation rate, but it is difficult to accurately predict, especially the prediction of small crack propagation in HCP (hexagonal close-packed lattice structure) materials.

[0003] Crystal plasticity theory is a theory for describing the deformation behavior of materials at the microscale, which can consider the influence of grain orientation, grain size and grain boundary on crack propagation path and rate, and it is particularly important in the field of polycrystalline material fatigue small crack propagation. In the research process of crack propagation behavior, there are many theoretical models that can describe this property, such as the commonly used node release technique (VCCT), the cohesive zone model method (CZM), and the extended finite element technique (XFEM). Among them, with the development of computer technology, the XFEM method has obvious advantages. XFEM has the flexibility to simulate the arbitrary path of crack initiation and propagation, which enables the method to simulate crack propagation without re-meshing. XFEM is also the most accurate model, and is more suitable for predicting fatigue small crack propagation.

[0004] In the existing research on fatigue crack propagation at the microscale based on XFEM, numerical simulation of material fatigue crack propagation has been realized, but the existing crystal plasticity constitutive model does not consider the influence of grain size on the slip resistance, so the accuracy of the simulation results of polycrystalline metal materials is low. SUMMARY

[0005] The present application aims to provide a polycrystalline metal material small fatigue crack propagation simulation method, which introduces Hall-Petch size effect in a crystal plasticity constitutive model to consider the influence of grain size on slip resistance, thereby improving the accuracy of simulation.

[0006] To achieve the above object, the present application provides a polycrystalline metal material small fatigue crack propagation simulation method, comprising:

[0007] determining the crystal plasticity constitutive model and the accurate values of each undetermined parameter of the crystal plasticity constitutive model;

[0008] establishing a crack propagation finite element model of the polycrystalline metal material, and embedding the crystal plasticity constitutive model with each undetermined parameter having the accurate value and the pre-acquired crack propagation criterion into the crack propagation finite element model;

[0009] applying load and boundary conditions to the crack propagation finite element model and performing crack propagation finite element analysis to obtain finite element analysis results; the finite element analysis results include stress and strain data of the crack propagation finite element model calculated based on the crystal plasticity constitutive model and crack propagation data of the crack propagation finite element model calculated based on the crack propagation criterion and the stress and strain data.

[0010] Further, the crystal plasticity constitutive model comprises a kinematic model, a thermal activated flow law model and a hardening model.

[0011] Further, the kinematic model comprises:

[0012] F=F e F p

[0013]

[0014] wherein F is a deformation gradient tensor, F e represents elastic deformation, F p represents nonlinear plastic response, L p is a plastic velocity gradient, is a slip rate on an alpha slip system, m is a slip direction, n is a normal of a slip plane, N is a number of slip systems, alpha is a positive integer, and alpha ∈ [1, N].

[0015] Further, the thermal activated flow law model comprises:

[0016]

[0017]

[0018] h αβ =h s [ω+(1-ω)δαβ ]

[0019]

[0020] wherein, is the reference slip rate, X α and S α are the kinematic hardening and the slip resistance of the slip system a, T is the absolute temperature, k is the Boltzmann constant, τ α is the resolved shear stress, sgn is the sign function, p and q are the exponent and pre-exponent parameters, respectively, F0is the free energy required to overcome the lattice resistance; τ0is the lattice friction stress at the current temperature; the function by brackets <.> is such that for z > 0, <z>≡z, otherwise <z>≡ 0; S sat is the saturated sliding resistance, the initial value is S0; h s is the metal material parameter, δ αβ is the Kroner function, ω is the potential hardening ratio; S0 * is the initial sliding resistance with a conventional grain size, k s is the affected slope coefficient, d is the size of the grain considered.

[0021] Further, the dynamic hardening model comprises:

[0022]

[0023] wherein r D is the dynamic recovery parameter, h b is the hardening modulus, h b * is the critical hardening modulus of the homogeneous grain structure, k b is the hardening parameter induced by heterogeneous deformation, d n is the average size of the grains around the grain considered;

[0024] F0, τ0, ω, p, q, S0 * , k s , h s , r D , h b , k b are undetermined parameters.

[0025] Further, S0 * , k s are each first parameter, and the undetermined parameters other than S0 * , k s are each second parameter; determining the accurate values of the undetermined parameters of the crystal plasticity constitutive model comprises:

[0026] obtaining a first sample and a second sample made of a polycrystalline metal material, wherein the first sample and the second sample have different grain sizes;

[0027] respectively performing a quasi-static tensile test on the first sample and the second sample at room temperature to obtain stress-strain curves of the first sample and the second sample respectively;

[0028] respectively obtaining microstructure information of the first sample and the second sample, including average grain size and crystal orientation information;

[0029] establish a cubic crystal plasticity simulation model of the first sample according to the microstructure information of the first sample as a first simulation model; take a crystal plasticity constitutive model with preset fixed values of each first parameter as a first crystal plasticity constitutive model, embed the first crystal plasticity constitutive model into the first simulation model, and perform simulation analysis on the first simulation model to obtain a stress-strain curve of the first simulation model;

[0030] keep the fixed values of each first parameter of the first crystal plasticity constitutive model unchanged, and adjust the values of each second parameter of the first crystal plasticity constitutive model, so that the stress-strain curve of the first simulation model is the same as the stress-strain curve of the first sample; obtain the values of each second parameter at this time as the accurate values of each second parameter;

[0031] establish a cubic crystal plasticity simulation model of the second sample according to the microstructure information of the second sample as a second simulation model; take a crystal plasticity constitutive model with the accurate values of each second parameter as a second crystal plasticity constitutive model, embed the second crystal plasticity constitutive model into the second simulation model, and perform simulation analysis on the second simulation model to obtain a stress-strain curve of the second simulation model;

[0032] keep the values of each second parameter of the second crystal plasticity constitutive model unchanged, and adjust the values of each first parameter of the second crystal plasticity constitutive model, so that the stress-strain curve of the second simulation model is consistent with the stress-strain curve of the second sample; obtain the values of each first parameter at this time as the accurate values of each first parameter.

[0033] Further, a crack propagation finite element model of the polycrystalline metal material is established, specifically including:

[0034] obtain a third sample made of the polycrystalline metal material, the third sample including a first part and a second part, and a pre-crack being provided on the second part;

[0035] obtain microstructure information of the second part of the third sample;

[0036] establish a geometric model of the third sample, the geometric model including a macroscopic part and a microscopic part, the macroscopic part being constructed according to the first part of the third sample, and the microscopic part being constructed according to the microstructure information of the second part of the third sample;

[0037] divide the macroscopic part and the microscopic part into grids respectively, assign isotropic parameters to the macroscopic part, and connect the macroscopic part and the microscopic part in a common node manner to transmit stress and deformation, to obtain a crack propagation finite element model.

[0038] Further, the crystal plasticity constitutive model with each undetermined parameter having an accurate value and the pre-acquired crack propagation criterion are embedded into the crack propagation finite element model, specifically including:

[0039] The crystal plasticity constitutive model with each undetermined parameter having an accurate value and the pre-acquired crack propagation criterion are embedded into the micro part of the crack propagation finite element model.

[0040] Further, the crack propagation criterion is a cumulative strain energy criterion, and the cumulative strain energy criterion includes:

[0041]

[0042]

[0043] wherein G α is a cumulative strain energy value of a slip system alpha, G max is a maximum value of cumulative strain energy values of each slip system, G crit is a pre-set critical value of cumulative strain energy, and tol is a tolerance;

[0044] If G satisfies G , a crack propagation criterion is reached, and a crack propagation direction is a slip direction of a corresponding slip system. max

[0045] The polycrystalline metal material fatigue small crack propagation simulation method can introduce the Hall-Petch size effect equation into the crystal plasticity constitutive model, allocate a slip resistance ratio in parameters according to an experimental condition, combine an extended finite element, and define a crack criterion of cumulative strain energy, so that the influence of a microstructure on deflection and a rate of fatigue small crack propagation can be more accurately described, and the micro fatigue small crack propagation behavior of the polycrystalline metal material can be described. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 It is a flowchart of the polycrystalline metal material fatigue small crack propagation simulation method according to an embodiment of the present application;

[0047] Figure 2 It is a structural schematic diagram of a cubic crystal plasticity simulation model according to an embodiment of the present application;

[0048] Figure 3 It is a stress-strain curve diagram of a first sample, a second sample, a first simulation model and a second simulation model according to an embodiment of the present application;

[0049] Figure 4 It is a slip system starting result diagram of fatigue small crack propagation according to an embodiment of the present application;

[0050] ​ Figure 5 A schematic diagram of the crack length versus cycle number obtained after finite element analysis of a third sample with a first grain size and a second grain size according to an embodiment of the present invention.

[0051] Figure 6 A schematic diagram of the crack propagation rate versus stress intensity factor (ΔK) obtained after finite element analysis of a third sample with a first grain size and a second grain size according to an embodiment of the present invention. Detailed Implementation

[0052] The preferred embodiments of the present invention are given below with reference to the accompanying drawings and described in detail.

[0053] like Figure 1 As shown, this embodiment of the invention provides a method for simulating fatigue small crack propagation in polycrystalline metal materials, which includes the following steps S100-S300:

[0054] S100: Determine the accurate values ​​of the crystal plastic constitutive model and each undetermined parameter of the crystal plastic constitutive model.

[0055] Crystal plastic constitutive models predict the mechanical behavior of materials under external loads and their interaction with the microstructure by describing microscopic plastic deformation mechanisms such as crystal slip. Crystal plastic constitutive models include kinematic models, thermally activated flow law models, and kinematic hardening models. The kinematic model describes the geometric relationship of crystal deformation, the thermally activated flow law model defines the relationship between the plastic slip ratio and the decomposed shear stress of the slip system, and the kinematic hardening model characterizes the interaction between hardening and softening mechanisms, reflecting the dynamic hardening process of the slip system within the crystal.

[0056] The kinematic model is as follows:

[0057] F = F e F p (1)

[0058]

[0059] Where F is the deformation gradient tensor, F e F represents elastic deformation. p L represents the nonlinear plastic response. p For plastic velocity gradient, Let m be the slip ratio in the α slip system, m be the slip direction, n be the normal to the slip surface, N be the number of slip systems, and α be a positive integer, where α∈[1,N].

[0060] The thermally activated flow law model is as follows:

[0061]

[0062] wherein, is the reference slip rate, X α and S α are the hardening and the slip resistance of the slip system a, respectively, T is the absolute temperature, k is the Boltzmann constant, τ α is the resolved shear stress, sgn is the sign function. For a given slip system, the material constants are: the exponents and the pre-exponential parameters p and q, respectively; F0is the free energy required to overcome the lattice resistance; τ0is the lattice friction stress at the current temperature; in addition, the function is made by the brackets <.> such that for z > 0, <z>≡z, otherwise <z>= 0.

[0063] Slip resistance S α may be evolved as:

[0064]

[0065] where S sat is the saturated slip resistance, S0 is the initial value, β is a positive integer and β ∈ [1, N], h αβ is the slip hardening matrix. The slip hardening matrix h αβ may be evolved as:

[0066] h αβ = h s [ω + (1 - ω)δ αβ ] (5)

[0067] where h s is the metal material parameter, δ αβ is the Kronecker function, and ω is the potential hardening ratio. The hardening matrix h αβ represents the cross-hardening between slip systems.

[0068] Here, the Hall-Petch size effect equation is introduced to reflect the initial slip resistance S0 caused by grain boundary hardening, and the expression of S0 is:

[0069]

[0070] where S0 * is the initial slip resistance with a regular grain size, k s is the slope of the Hall-Petch size effect equation, and d is the size of the grain considered.

[0071] The dynamic hardening model is as follows:

[0072]

[0073] where r D is the dynamic recovery parameter, h b represents the hardening modulus, and is related to the material properties.

[0074] In the above crystal plasticity constitutive model, F0, τ0, ω, p, q, S0 * , k s , h s , r D , h b , k b are all undetermined parameters.

[0075] In some embodiments, S0 * , k s As each first parameter, S0 * , k s , and other undetermined parameters except S0

[0076] S110: Obtain a first sample and a second sample made of a polycrystalline metal material, wherein the first sample and the second sample have different grain sizes;

[0077] S120: Perform a quasi-static tensile test on the first sample and the second sample at room temperature respectively, and obtain a stress-strain curve of the first sample and the second sample respectively;

[0078] S130: Obtain microstructure information of the first sample and the second sample respectively, including average grain size (i.e. the average value of the grain sizes of the sample) and crystal orientation information;

[0079] S140: Establish a cubic crystal plasticity simulation model of the first sample according to the microstructure information of the first sample, as a first simulation model; embed a first crystal plasticity constitutive model into the first simulation model, and perform simulation analysis on the first simulation model to obtain a stress-strain curve of the first simulation model; wherein each first parameter of the first crystal plasticity constitutive model has a preset fixed value;

[0080] S150: Keep the fixed values of each first parameter of the first crystal plasticity constitutive model unchanged, and adjust the values of each second parameter of the first crystal plasticity constitutive model, so that the stress-strain curve of the first simulation model is the same as the stress-strain curve of the first sample; obtain the values of each second parameter at this time as the accurate values of each second parameter;

[0081] S160: Establish a cubic crystal plasticity simulation model of the second sample according to the microstructure information of the second sample, as a second simulation model; embed a second crystal plasticity constitutive model into the second simulation model, and perform simulation analysis on the second simulation model to obtain a stress-strain curve of the second simulation model; wherein the values of each second parameter of the second crystal plasticity constitutive model are the accurate values of each second parameter respectively;

[0082] S170: Keep the values of each second parameter of the second crystal plasticity constitutive model unchanged, and adjust the values of each first parameter of the second crystal plasticity constitutive model, so that the stress-strain curve of the second simulation model is consistent with the stress-strain curve of the second sample; obtain the values of each first parameter at this time as the accurate values of each first parameter.

[0083] Thus, the accurate values of each first parameter and each second parameter can be obtained, i.e. the accurate values of each undetermined parameter are obtained.

[0084] In step S150, since the values of the first parameters are randomly assigned values, when the values of the second parameters are adjusted, the stress-strain curve of the first simulation model can not be completely consistent with the stress-strain curve of the first sample, at this time, only the shapes of the two stress-strain curves need to be adjusted to be consistent, the same shape indicates that the second parameters have been adjusted to accurate values, but the first parameters are not accurate values. The accurate values of the first parameters need to be obtained through step S170. Since the accurate values of the second parameters have been obtained in step S150, in step S170, the second parameters need to remain unchanged, and only the values of the first parameters need to be adjusted, when the first parameters are adjusted to accurate values, the stress-strain curve of the second simulation model will be consistent with the stress-strain curve of the second sample. The crystal plasticity constitutive model with the accurate values of the first parameters and the second parameters can be applied to samples of any grain size, that is, any grain size sample uses the crystal plasticity constitutive model with the accurate values of the first parameters and the second parameters for simulation, and accurate stress-strain data can be obtained.

[0085] In some embodiments, the first simulation model and the second simulation model can be established in ABAQUS software. For example, a 10*10*10 cubic model can be established in ABAQUS, the model includes 1000 grains, each grain is divided into a unit, the microstructure information of the first sample is assigned to each grain, that is, the first simulation model is obtained, then the first crystal plasticity constitutive model is written into the UMAT subroutine of the ABAQUS software to embed it into the first simulation model; then the same load and boundary conditions as the quasi-static tensile test are applied to the first simulation model for simulation analysis, and the stress-strain curve of the first simulation model can be obtained; similarly, the microstructure information of the second sample is assigned to each grain, the second simulation model is obtained, and based on the same method as the first simulation model, the stress-strain curve of the second simulation model can be obtained.

[0086] In some embodiments, the grain size of the first sample is 10 microns, and the grain size of the second sample is 40 microns.

[0087] In some embodiments, the microstructure information of the first sample and the second sample can be obtained through experimental observation (such as scanning electron microscope SEM, transmission electron microscope TEM, electron backscatter diffraction EBSD, etc.) or literature research.

[0088] S200: Establish a crack propagation finite element model of a polycrystalline metal material, and embed the crystal plasticity constitutive model with accurate values of each to-be-determined parameter and the pre-obtained crack propagation criterion into the crack propagation finite element model.

[0089] In some embodiments, the method for establishing a crack propagation finite element model of a polycrystalline metal material comprises steps S210-S240 as follows:

[0090] S210: Obtain a third specimen made of the polycrystalline metal material, the third specimen comprising a first part and a second part, and the second part being provided with a pre-existing crack;

[0091] S220: Obtain microstructure information of the second part of the third specimen; for example, the microstructure information can be obtained through experimental observation (e.g., scanning electron microscope (SEM), transmission electron microscope (TEM), electron backscatter diffraction (EBSD), etc.) or literature research.

[0092] S230: Establish a geometric model of the third specimen, the geometric model comprising a macroscopic part and a microscopic part, the macroscopic part being constructed according to the first part of the third specimen, and the microscopic part being constructed according to the microstructure information of the second part of the third specimen;

[0093] S240: Divide the macroscopic part and the microscopic part of the geometric model into meshes respectively, and assign isotropic parameters (e.g., elastic modulus and Poisson's ratio) to the macroscopic part, and connect the macroscopic part and the microscopic part in a common node manner to transfer stress and deformation, so as to obtain the crack propagation finite element model.

[0094] Embed the crystal plasticity constitutive model with each undetermined parameter having an accurate value and the pre-obtained crack propagation criterion into the crack propagation finite element model, specifically comprising:

[0095] Embed the crystal plasticity constitutive model with each undetermined parameter having an accurate value and the pre-obtained crack propagation criterion into the microscopic part of the crack propagation finite element model.

[0096] S300: Apply load and boundary conditions to the crack propagation finite element model, and perform crack propagation finite element analysis to obtain finite element analysis results; the finite element analysis results comprise stress and strain data of the crack propagation finite element model calculated based on the crystal plasticity constitutive model, and crack propagation data of the crack propagation finite element model calculated based on the crack propagation criterion and the stress and strain data.

[0097] In some embodiments, steps S200 and S300 can be realized by using ABAQUS software; during the finite element analysis, ABAQUS will call the UMAT subprogram of the crystal plasticity constitutive model pre-written to solve the stress and strain data of each slip system of the model, and call the UDMGINI subprogram of the crack propagation criterion pre-written to solve the crack propagation data.

[0098] In some embodiments, the crack propagation criterion is a cumulative strain energy criterion, which is:

[0099]

[0100]

[0101] Among them, G α G represents the cumulative strain energy of the slip system α. max G represents the maximum cumulative strain energy of each slip system. crit The cumulative strain energy is a pre-set critical value, and tol is the tolerance. If formula (9) is satisfied, the crack initiation standard is met, and the crack propagation command is executed. The propagation direction is parallel to the sliding direction of the most active slip system (the slip system with the largest cumulative strain energy value is the most active slip system).

[0102] To accelerate computational efficiency, G is set... crit =1.1; To improve convergence, set tol =0.1.

[0103] In some embodiments, crack propagation data includes crack length, crack propagation rate, crack propagation direction, crack tip opening and closing stress, etc.

[0104] The following uses TA7 titanium alloy as an example to illustrate the application of the fatigue small crack propagation simulation method for polycrystalline metal materials of the present invention.

[0105] First, the exact values ​​of each undetermined parameter in the crystal plastic constitutive model and the values ​​of other material parameters were determined. The results are shown in Table 1 below:

[0106] Table 1. Accurate values ​​of each undetermined parameter and other material parameters for the crystal plastic constitutive model.

[0107]

[0108] In Table 1, d1 is the grain size of the first sample, d2 is the grain size of the second sample, E is the elastic modulus, and ν is Poisson's ratio. C11-C66 are the values ​​on the main diagonal of the local elastic stiffness matrix, which is a 6-row, 6-column matrix.

[0109] like Figure 2 The diagram shown is a schematic representation of the structure of the established cubic crystal plasticity simulation model. Figure 3 The figure shows the stress-strain curves of the first specimen, the second specimen, the first simulation model, and the second simulation model. Figure 3 It can be seen that the stress-strain curves obtained by the crystal plastic constitutive model with accurate values ​​for each undetermined parameter are consistent with the stress-strain curves obtained by the quasi-static tensile test, indicating that the crystal plastic constitutive model of the present invention has high accuracy and can be applied to samples with different grain sizes.

[0110] After obtaining the accurate value of the pending parameter, a crack propagation finite element model of the sample with an average grain size of 40 μm is established and finite element analysis is performed to obtain the analysis result Figure 4 To show only the effect of grain size on the fatigue small crack propagation, the model is reduced by 4 times in each grain size without changing the model geometry and orientation information to obtain a crack propagation model with an average grain size of 10 μm, and the crack propagation rates extracted from the two models are analyzed to obtain Figure 5 and Figure 6 It is found that fine grains have a strong hindering effect on cracks during the fatigue small crack propagation stage, and the hindering effect becomes smaller as the stress intensity factor increases.

[0111] The polycrystalline metal material fatigue small crack propagation simulation method of the embodiment can obtain the following prediction results:

[0112] 1) The Hell-Petch effect equation is introduced into the crystal plasticity constitutive model, which can more accurately predict the deflection and slip system start of the fatigue small crack.

[0113] 2) From the crack propagation rate prediction results of the two grain sizes, the fatigue small crack propagation rate of fine grains is significantly lower than that of coarse grains when the crack length is within 100 microns, i.e., the stress intensity factor is relatively low, which is consistent with the experimental phenomenon.

[0114] The polycrystalline metal material fatigue small crack propagation simulation method of the embodiment introduces the Hell-Petch size effect equation into the crystal plasticity constitutive model, allocates the slip resistance ratio in the parameters according to the experimental conditions, combines the propagation finite element, and defines the cumulative strain energy cracking criterion, which can more accurately describe the deflection and rate of the microstructure on the fatigue small crack propagation, and can describe the micro fatigue small crack propagation behavior of the polycrystalline metal material.

[0115] The above is only a preferred embodiment of the present application, and is not intended to limit the scope of the present application, and the above embodiment of the present application can be variously changed. That is, any simple, equivalent changes and modifications made in accordance with the content of the claims and description of the present application fall within the scope of the claims of the present application. The present application is not described in detail.< / z> < / z> < / z> < / z>

Claims

1. A method for simulating fatigue small crack propagation in polycrystalline metallic materials, characterized in that, The application relates to a method for determining the parameters of a crystal plasticity constitutive model. The method comprises the following steps: , , , , wherein, is the slip rate on the a slip system, a is a positive integer, a ∈ [1, N], N is the number of slip systems, is the reference slip rate, X α and S α are the kinematic hardening and the slip resistance of the slip system a, respectively, T is the absolute temperature, k is the Boltzmann constant, is the resolved shear stress, sgn is the sign function, p and q are the exponent and the pre-exponential parameter, respectively, F0 is the free energy required to overcome the lattice resistance; is the lattice friction stress at the current temperature; the function f is composed of the brackets such that for z ≥ 0, , otherwise ; S sat is the saturation slip resistance, with an initial value S0; β is a positive integer and β ∈ [1, N], h αβ is the slip hardening matrix; h s is the metallic material parameter, is the Kronecker function, is the potential hardening ratio; is the initial slip resistance with a regular grain size, k s is the slope of the Hall-Petch size effect equation, d is the size of the considered grain; A crystal plasticity constitutive model and accurate values of each undetermined parameter of the crystal plasticity constitutive model are determined; the crystal plasticity constitutive model comprises a kinematic model, a thermal-activated flow law model and a hardening model; the thermal-activated flow law model comprises: A crack propagation finite element model of a polycrystalline metal material is established, and the crystal plasticity constitutive model with each undetermined parameter having an accurate value and a pre-acquired crack propagation criterion are embedded into the crack propagation finite element model; A load and a boundary condition are applied to the crack propagation finite element model, and crack propagation finite element analysis is performed to obtain a finite element analysis result; the finite element analysis result comprises stress and strain data of the crack propagation finite element model calculated based on the crystal plasticity constitutive model and crack propagation data of the crack propagation finite element model calculated based on the crack propagation criterion and the stress and strain data; The method comprises the following steps: A third sample made of a polycrystalline metal material is acquired, the third sample comprising a first part and a second part, and a pre-crack being arranged on the second part; Microstructure information of the second part of the third sample is acquired; A geometric model of the third sample is established, the geometric model comprising a macroscopic part and a microscopic part, the macroscopic part being constructed according to the first part of the third sample, and the microscopic part being constructed according to the microstructure information of the second part of the third sample; The macroscopic part and the microscopic part are respectively meshed, isotropic parameters are assigned to the macroscopic part, and the macroscopic part and the microscopic part are connected in a shared node mode to transmit stress and deformation, so as to obtain a crack propagation finite element model; , , wherein, is a cumulative strain energy value of the slip system, is a cumulative strain energy value of the slip system, is a maximum value of the cumulative strain energy values of the slip systems, is a preset critical value of the cumulative strain energy, and tol is a tolerance. If satisfies , the crack opening criterion is reached, and the crack propagation direction is the sliding direction of the corresponding slip system.

2. The polycrystalline metal material fatigue small crack growth simulation method according to claim 1, characterized by, The crack propagation criterion is a cumulative strain energy criterion, and the cumulative strain energy criterion comprises: , , where F is the deformation gradient tensor, F e represents elastic deformation, F p represents nonlinear plastic response, L p is the plastic velocity gradient, m is the slip direction, and n is the normal to the slip plane.

3. The polycrystalline metal material fatigue small crack growth simulation method according to claim 1, characterized by, The kinematic model comprises: , wherein, h is a dynamic recovery parameter, b G is the modulus of rigidity; F0、 、 、 , p, q, , k s , h s , r D , h b are all undetermined parameters.

4. The polycrystalline metal material fatigue small crack growth simulation method according to claim 3, characterized by, Will k s As each of the first parameters, except k s Other undetermined parameters besides those mentioned above are designated as second parameters; the accurate values ​​of each undetermined parameter in the crystal plastic constitutive model are determined, specifically including: The hardening model comprises: A first sample and a second sample made of a polycrystalline metal material are acquired, wherein the first sample and the second sample have different grain sizes; Quasi-static tensile tests are respectively performed on the first sample and the second sample at room temperature, and stress and strain curves of the first sample and the second sample are respectively obtained; Microstructure information of the first sample and the second sample is respectively acquired, including average grain size and crystal orientation information; A cubic crystal plasticity simulation model of the first sample is established according to the microstructure information of the first sample, as a first simulation model; a crystal plasticity constitutive model with each first parameter having a preset fixed value is taken as a first crystal plasticity constitutive model, the first crystal plasticity constitutive model is embedded into the first simulation model, and simulation analysis is performed on the first simulation model to obtain a stress and strain curve of the first simulation model; The fixed values of each first parameter of the first crystal plasticity constitutive model are kept unchanged, and the values of each second parameter of the first crystal plasticity constitutive model are adjusted, so that the stress and strain curve of the first simulation model is identical in shape to the stress and strain curve of the first sample; the values of each second parameter at this time are taken as accurate values of each second parameter. According to the microstructure information of the second sample, a cubic crystal plasticity simulation model of the second sample is established as a second simulation model; a crystal plasticity constitutive model with values of each second parameter having a respective accurate value is taken as a second crystal plasticity constitutive model, the second crystal plasticity constitutive model is embedded into the second simulation model, and simulation analysis is performed on the second simulation model to obtain a stress-strain curve of the second simulation model; The values of each second parameter of the second crystal plasticity constitutive model are kept unchanged, and the values of each first parameter of the second crystal plasticity constitutive model are adjusted so that the stress-strain curve of the second simulation model is consistent with the stress-strain curve of the second sample; and the values of each first parameter at this time are taken as accurate values of each first parameter.

5. The polycrystalline metal material fatigue small crack growth simulation method according to claim 1, characterized by, The crystal plasticity constitutive model with each undetermined parameter having a respective accurate value and the pre-acquired crack propagation criterion are embedded into the crack propagation finite element model, specifically including: The crystal plasticity constitutive model with each undetermined parameter having a respective accurate value and the pre-acquired crack propagation criterion are embedded into the micro part of the crack propagation finite element model.

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