Metal material crack simulation method

Abstract

The present application relates to a kind of metal material crack simulation method, comprising: obtaining cohesive zone model, and determining each undetermined parameter of the cohesive zone model;Crystal plasticity constitutive model is obtained, and each undetermined parameter of the crystal plasticity constitutive model is determined;First microstructure finite element model of metal material is established, and the cohesive zone model and the crystal plasticity constitutive model are embedded in the first microstructure finite element model;Tensile load and boundary condition are applied to the first microstructure finite element model, and finite element analysis is carried out, to obtain first finite element analysis result;The first finite element analysis result includes the stress-strain data calculated based on the crystal plasticity constitutive model and the crack data calculated based on the cohesive zone model and stress-strain data.The metal material crack simulation method of the present application can accurately simulate the crack initiation and amplification behavior of metal material.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of crack calculation, and more particularly to a metal material crack simulation method. BACKGROUND

[0002] In the field of modern industry, materials play a crucial role, and their performance directly affects the quality and service life of products. Various engineering projects, such as construction, aerospace, automobile manufacturing, and energy equipment, have strict requirements for the strength, toughness, and corrosion resistance of materials. Therefore, the selection and optimization of materials are the core links in industrial design and production. In this context, how to accurately evaluate the mechanical properties of materials, especially their performance under complex stress conditions, is particularly important.

[0003] Among many materials, metal materials are the dominant materials in the industrial field due to their excellent mechanical properties and processability. Compared with ceramic, plastic and other materials, metal materials not only have high strength and toughness, but also have good electrical conductivity and thermal conductivity. These characteristics enable metal materials to maintain stable performance under extreme conditions such as high temperature, high pressure, and fatigue load, making them suitable for aerospace, construction, and mechanical manufacturing, which require high strength and high stability. Therefore, the selection of metal materials and their reliability research under different load conditions are important topics in various industries.

[0004] However, metal materials are prone to crack under complex load, leading to structural failure and posing a significant risk to industrial production and safety. Crack initiation and propagation are one of the main forms of material failure, so how to accurately simulate the propagation behavior of cracks in metal materials has become an important research direction in the field of materials science and engineering. SUMMARY

[0005] The purpose of the present application is to provide a metal material crack simulation method to accurately simulate the crack initiation and propagation behavior of metal materials.

[0006] To achieve the above purpose, the present application provides a metal material crack simulation method, comprising:

[0007] Obtaining a cohesive force model and determining the undetermined parameters of the cohesive force model;

[0008] Obtaining a crystal plasticity constitutive model and determining the undetermined parameters of the crystal plasticity constitutive model;

[0009] Establishing a first microstructure finite element model of the metal material, and embedding the cohesive force model and the crystal plasticity constitutive model into the first microstructure finite element model;

[0010] applying a tensile load and boundary conditions to the first microstructure finite element model, and performing finite element analysis to obtain a first finite element analysis result; the first finite element analysis result comprises stress-strain data calculated based on the crystal plasticity constitutive model and crack data calculated based on the cohesive zone model and the stress-strain data.

[0011] Further, the cohesive zone model comprises:

[0012]

[0013]

[0014] wherein F is the traction force, k1 is the stiffness in the linear elastic stage, x is the displacement, x1 is the critical damage displacement, F max is the critical damage stress, k2 is the slope of the traction-displacement curve in the damage evolution stage, b is the intercept of the traction-displacement curve in the damage evolution stage, x2 is the full damage displacement, k1, x1, F max , k2, b and x2 are to-be-determined parameters.

[0015] Further, determining the to-be-determined parameters of the cohesive zone model comprises:

[0016] performing molecular dynamics simulation on the metal material to obtain the critical damage stress, the critical damage displacement and the full damage displacement of the metal material;

[0017] determining the stiffness in the linear elastic stage according to the critical damage stress and the critical damage displacement;

[0018] determining the slope and the intercept of the traction-displacement curve in the damage evolution stage according to the critical damage stress, the critical damage displacement and the full damage displacement.

[0019] Further, the crystal plasticity constitutive model comprises a kinematic model, a thermal activated flow law model and a hardening model.

[0020] Further, the kinematic model comprises:

[0021] F=F e F p

[0022]

[0023] wherein F is the deformation gradient tensor, F e represents elastic deformation, F p represents nonlinear plastic response, L p is the plastic velocity gradient, for the slip rate on the alpha slip system, m is the slip direction, n is the normal to the slip plane, N is the number of slip systems, alpha is a positive integer, and alpha e [1, N].

[0024] Further, the heat-activated flow law model includes:

[0025]

[0026]

[0027] h αβ = h s [ω + (1 - ω) δ αβ ]

[0028] S sat = S0+ S inc

[0029]

[0030] where, plastic slip rate, X α and S α are the kinematic hardening and slip resistance of slip system alpha, T is the absolute temperature, k is the Boltzmann constant, tau α is the resolved shear stress, g and q are the exponential and pre-exponential parameters, respectively, F0 is the free energy required to overcome the lattice resistance; tau0 is the lattice friction stress at the current temperature; the function by the brackets <.> such that for z > 0, <z>≡z, otherwise <z>≡0; S sat is the saturated slip resistance, with an initial value of S0, S inc is the increased slip resistance during simulation; h s is the inherent hardening constant of the metal material, δ αβ is the Kronecker function, and ω is the potential hardening ratio; S0 * is the initial slip resistance with a regular grain size, k s is the size-related slope coefficient, and d is the size of the grain under consideration.

[0031] Further, the dynamic hardening model comprises:

[0032]

[0033]

[0034] wherein r D is the dynamic recovery coefficient, h b is the hardening modulus, h b * is the critical hardening modulus of a 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 under consideration.

[0035] F0, τ0, ω, g, q, S0 * , k s , S inc , h s , r D , h b * , k b are all undetermined parameters.

[0036] Further, the undetermined parameters of the crystal plasticity constitutive model are determined, and specifically comprising:

[0037] a second microstructure finite element model of the metal material is established, the crystal plasticity constitutive model is embedded into the second microstructure finite element model, a tensile load and boundary conditions are applied to the second microstructure finite element model, and finite element analysis is performed to obtain a stress-strain curve of the microstructure finite element model;

[0038] a tensile test is performed on the metal material to obtain a stress-strain curve of the metal material;

[0039] adjusting values of each undetermined parameter of the crystal plasticity constitutive model so that an error between a stress-strain curve of the second microstructure finite element model and a stress-strain curve obtained through a tensile test is within a preset range to determine the values of each undetermined parameter of the crystal plasticity constitutive model.

[0040] Further, the first microstructure finite element model of the metal material is established, and specifically includes:

[0041] obtaining microstructure data of the metal material;

[0042] establishing a geometric model according to the microstructure data;

[0043] performing meshing on the geometric model and assigning material properties to obtain the first microstructure finite element model.

[0044] Further, the crack data includes a number of cracks and a position and a size of each crack.

[0045] The metal material crack simulation method can effectively restore the tensile fracture behavior of the metal material and accurately predict the tensile crack of the metal material, has high precision, strong flexibility, can evaluate the fracture behavior of the metal material, and has the advantages of intuitive display. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 a flowchart of the metal material crack simulation method according to the embodiment of the present application;

[0047] Figure 2 a schematic diagram of stress-strain data of the metal material obtained after a tensile test and finite element simulation according to the embodiment of the present application;

[0048] Figure 3 a tensile crack simulation result schematic diagram of a non-uniform structure metal material under different grain orientations according to the embodiment of the present application, in which the entire morphology of fracture is shown;

[0049] Figure 4 a tensile crack simulation result schematic diagram of a non-uniform structure metal material according to the embodiment of the present application, in which a crack initiation position and a propagation direction are shown;

[0050] Figure 5 a schematic diagram of an optimization direction after a metal material crack initiation and propagation mechanism law analysis is completed according to the embodiment of the present application. DETAILED DESCRIPTION

[0051] The preferred embodiments of the present application will be described below in detail with reference to the accompanying drawings.

[0052] As shown in Figure 1 the present application provides a metal material crack simulation method, which comprises the following steps:

[0053] S100: obtaining a cohesive zone model, and determining each undetermined parameter of the cohesive zone model.

[0054] The cohesive zone model is a model for describing the behavior of the region near the crack tip based on the interaction force (i.e. cohesive force) between atoms or molecules of a substance, which can simulate the propagation, initiation and final fracture process of the crack during the stress process, thereby revealing the fracture mechanism of the material. The cohesive zone model can adopt a bilinear model for describing the relationship between the traction force and displacement of the metal material, and the relationship between the traction force and displacement in the cohesive zone model includes three stages, namely a linear elastic stage, a damage evolution stage and a complete failure stage, and the relationship between the traction force and displacement in each stage is as follows:

[0055] Linear elastic stage:

[0056] F=k1x (x≤x1) (1)

[0057]

[0058] wherein F is the traction force, k1 is the stiffness of the linear elastic stage, x is the displacement, x1 is the critical damage displacement, F max is the critical damage stress, and k1, x1 and F max are all undetermined parameters.

[0059] Damage evolution stage:

[0060] F=k2x+b (x1<x≤x2) (3)

[0061]

[0062]

[0063] wherein k2 is the stiffness (i.e. the slope of the traction-displacement curve) of the damage evolution stage, b is the intercept of the traction-displacement curve of the damage evolution stage, and x2 is the complete damage displacement, and k2, b and x2 are all undetermined parameters.

[0064] Complete failure stage:

[0065] F=0, x>x2 (6)

[0066] The cohesive zone model further includes:

[0067]

[0068] wherein t n , t s , t t respectively represent the stress of a certain position of the model in the normal direction, the first shear direction and the second shear direction, t0 n , t0 s , t0 t respectively represent the maximum stress of the model in the normal direction, the first shear direction and the second shear direction, wherein t0 n , t0 s , t0 t are all F max ; when a certain unit satisfies the above formula (7) in the finite element analysis process, it is indicated that the unit will generate a crack, and thus the crack data of the model can be obtained.

[0069] In some embodiments, the method for determining each undetermined parameter of the cohesive zone model is as follows:

[0070] Molecular dynamics simulation is performed on the metal material to obtain the critical damage stress F max , the critical damage displacement x1 and the complete damage displacement x2 of the metal material, then k1 is calculated according to formula (2), and k2 and b are calculated according to formulas (4) and (5), so that all the undetermined parameters of the cohesive zone model can be obtained, and the cohesive zone model is used in the later stage to calculate the crack data according to the stress-strain data. Molecular dynamics simulation is a many-body simulation method based on computer technology, which can obtain various properties and behaviors of the system by assigning an initial motion state to the molecular system and using the natural motion of molecules to extract samples in phase space for statistical calculation. Molecular dynamics simulation can be realized by using any suitable simulation software, including Gromacs, Amber, Namd, LAMMPS, etc.

[0071] S200: Obtain a crystal plasticity constitutive model, and determine each undetermined parameter of the crystal plasticity constitutive model.

[0072] The crystal plasticity constitutive model is based on a grain size difference strengthening model, and is obtained according to the parameters of the metal material, the slip system, the crystal orientation, the plastic flow and the hardening mechanism evolution. The crystal plasticity constitutive model includes a kinematic model, a thermal activated flow law model and a hardening model. The kinematic model is a mathematical model about crystal deformation. The thermal activated flow law model is a mathematical model about the plastic slip rate of the slip system and the decomposition of shear stress. The hardening model is a mathematical model about the interaction between the soft phase and the hard phase.

[0073] The kinematic model is:

[0074] F=F e F p (8)

[0075]

[0076] where F is the deformation gradient tensor, F e represents elastic deformation, F p represents a nonlinear plastic response, L p is the plastic velocity gradient, is the slip rate on the a slip system, m is the slip direction, n is the normal to the slip plane, N is the number of slip systems, a is a positive integer, and a e [1, N].

[0077] The thermal-activated flow rule model is:

[0078]

[0079] where, is the plastic slip rate, X α and S α are the hardening and 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, and sgn is the sign function. For a given slip system, the material constants are: the exponents and the pre-exponential parameters g and q; F0is the free energy required to overcome the lattice resistance; τ0is the lattice friction stress at the current temperature; in addition, the function f(z) is such that for z > 0, <z>≡z, otherwise <z>= 0.

[0080] Slip resistance S α may evolve as:

[0081]

[0082] where S sat is the saturated slip resistance, with an initial value S0, which can be expressed as: S sat = S0 + S inc , S inc is the increased slip resistance during the simulation, and β is a positive integer and β ∈ [1, N]. The slip hardening matrix h αβ may evolve as:

[0083] h αβ = h s [ω + (1 - ω)δ αβ ]

[0084] where h s is the inherent hardening constant of the metallic material, 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. Here, the Hall-Petch law is introduced to reflect the initial slip resistance caused by grain boundary hardening, and S0 evolves as:

[0085]

[0086] where S0 * is the initial slip resistance with a regular grain size, k s is the slope coefficient of the size dependence, which is a parameter affected by the slope determined by the Hall-Petch relationship, and d is the size of the considered grain.

[0087] The dynamic recovery model evolves as follows:

[0088]

[0089] where r D is the dynamic recovery coefficient, h b represents the hardening modulus, which is defined as a function of the considered grain size and the average size of the adjacent grains:

[0090]

[0091] where h b * is the critical hardening modulus of a homogeneous grain structure, k b is the hardening parameter induced by heterogeneous deformation, and d is the size of the considered grain (i.e., each grain in the model). n d and d n are the average size of the grains surrounding the considered grain, and d eq are obtained experimentally.

[0092] The local average cumulative strain of each slip system is denoted by the cumulative equivalent plastic strain ε p , whose evolution is given by:

[0093]

[0094] where t is the current time, τ is the integration variable, the symbol ":" denotes the double dot product of matrices, D p is the plastic strain rate, whose evolution is given by:

[0095]

[0096] where L p is the plastic velocity gradient matrix, (L T ) * is the transpose matrix of the plastic velocity gradient matrix, m is the slip direction vector, and n is the normal vector to the slip plane in the slip system.

[0097] In the crystal plasticity constitutive model, the free energy F0required to overcome the lattice resistance, the lattice friction stress τ0at the current temperature, the potential hardening ratio ω, g, q, the initial slip resistance S0of the homogeneous grain structure s , k inc , S s , h D , the critical hardening modulus h b * of the heterogeneous deformation-induced hardening parameter k b are undetermined parameters.

[0098] In some embodiments, the determination method of each undetermined parameter of the crystal plasticity constitutive model is as follows:

[0099] The second microstructure finite element model of the metal material is established, the crystal plasticity constitutive model is embedded into the second microstructure finite element model of the metal material, a tensile load and a boundary condition are applied to the second microstructure finite element model of the metal material, and finite element analysis is performed to obtain a second finite element analysis result, the second finite element analysis result including a stress-strain curve of the second microstructure finite element model; a tensile test is performed on the metal material to obtain a result of the tensile test, including a stress-strain curve of the metal material; values of each undetermined parameter of the crystal plasticity constitutive model are adjusted so that an error between the stress-strain curve of the second microstructure finite element model and the stress-strain curve of the tensile test is within a preset range (i.e., the result of the finite element analysis is consistent with the test result), and each undetermined parameter of the crystal plasticity constitutive model at this time is an accurate parameter value, so that the values of each undetermined parameter of the crystal plasticity constitutive model can be determined.

[0100] S300: A first microstructure finite element model of the metal material is established, and the cohesive force model and the crystal plasticity constitutive model are embedded into the first microstructure finite element model.

[0101] In some embodiments, the metal material can be subjected to finite element analysis by using ABAQUS software. First, microstructure data of the metal material, including grain shape, size distribution, grain boundary characteristics, and possible defects (such as pores, inclusions), etc., can be obtained through experimental observation (such as scanning electron microscopy SEM, transmission electron microscopy TEM, electron backscatter diffraction EBSD, etc.) or literature research, then a geometric model is established according to the microstructure data of the metal material, then the geometric model is subjected to meshing and is given material properties, thereby obtaining the first microstructure finite element model of the metal material. The crystal plasticity constitutive model can be stored in the UMAT subroutine of ABAQUS in the form of code to embed the crystal plasticity constitutive model into the first microstructure finite element model; the cohesive force model is realized by embedding a Cohesive unit in the first microstructure finite element model, and each undetermined parameter of the crystal plasticity constitutive model and the cohesive force model can be defined by using the User Material module of the ABAQUS software, so that each undetermined parameter is associated with the crystal plasticity constitutive model and the cohesive force model, respectively.

[0102] S400: A tensile load and a boundary condition are applied to the first microstructure finite element model, and finite element analysis is performed to obtain a first finite element analysis result; the first finite element analysis result including stress-strain data calculated based on the crystal plasticity constitutive model and crack data calculated based on the cohesive force model and the stress-strain data.

[0103] In some embodiments, the boundary conditions can be that the left side edge constrains the x-direction degree of freedom, the lower side edge constrains the y-direction degree of freedom, and the right side edge applies a preset tensile load. After the tensile load and the boundary conditions are applied, finite element analysis can be performed. During the finite element analysis process, the ABAQUS software calls the UMAT subroutine to calculate the stress-strain data of the first microstructure finite element model, and calculates crack data according to the stress-strain data through the Cohesive unit.

[0104] In some embodiments, the crack data includes the number of cracks and the position and size (e.g., length and width) of each crack.

[0105] After obtaining the crack data, the tensile crack initiation mechanism and propagation law can be determined according to the Schmitt factor and the crack data, including when the crack is intergranular fracture, when the crack is transgranular fracture, and in which grain orientation multiple cracks are likely to occur, etc. The calculation formula of the Schmitt factor is:

[0106] m = cosφ·cosλ (17)

[0107]

[0108]

[0109] where m is the Schmitt factor, φ is the angle between the external force direction and the normal line of the slip plane (normal angle), λ is the angle between the external force direction and the slip direction (slip angle), is the unit vector of the slip direction, is the normal vector direction of the slip plane, is the unit vector of the external stress direction.

[0110] In some embodiments, the relationship between the crack initiation mechanism and propagation law and the macroscopic mechanical properties of the metal material can also be determined according to the stress-strain data and the crack data of the first microstructure finite element model. Specifically, in the modeling process, each grain in the model can be given a different orientation. Therefore, through the fracture simulation of different orientation grain models, the positions where cracks are more likely to initiate and propagate can be summarized. Combined with the crack propagation position and the speed of the descending segment of the stress-strain curve, the influence of the direction in which the crack propagates on the descending segment of the stress-strain curve can be determined, thereby guiding the regulation of the grain orientation of the metal material in the actual manufacturing process and optimizing the anti-crack performance of the metal material.

[0111] In some embodiments, the optimization direction of the microstructure of the metal material can also be determined according to the relationship between the crack initiation mechanism and propagation law and the macroscopic mechanical properties of the metal material. Specifically, the structure with the best anti-fracture performance can be determined through the stress-strain data and the crack data, thereby determining the optimization direction.

[0112] The following takes CoCrFeMnNi high-entropy alloy metal material as an example to illustrate the specific application of the metal material crack simulation method of the present application.

[0113] First, the undetermined parameters of the cohesive zone model and the crystal plasticity constitutive model are determined, and the results are shown in Table 1 as follows:

[0114] Table 1: Undetermined parameters of the cohesive zone model and the crystal plasticity constitutive model

[0115]

[0116]

[0117] In Table 1, C11, C22, C44 are the values of the main diagonal of the elastic tensor matrix, E is the elastic modulus, and v is the Poisson's ratio.

[0118] After determining the undetermined parameters of the cohesive zone model and the crystal plasticity model, a microstructure finite element model of the metal material can be established in the ABAQUS software, and the cohesive zone model and the crystal plasticity model can be embedded in the finite element model. Then, boundary conditions and loads are applied to the finite element model to obtain the finite element analysis results. According to the finite element analysis results, the crack initiation mechanism and propagation law, the relationship between the macroscopic mechanical properties of the metal material and the optimization direction of the microstructure of the metal material can be determined. Through the crack simulation method of the present application, the following prediction results can be obtained:

[0119] 1. Macroscopic mechanical property prediction of homogeneous and heterogeneous polycrystalline materials:

[0120] Figure 2 The microstructure tensile stress-strain data of the metal material are shown, where the solid line represents the data obtained by finite element analysis, i.e. simulation data, and the circles represent the data obtained by tensile test, i.e. experimental data; from Figure 2 It can be seen that the simulation data and the experimental data can be well matched, proving that the crystal plasticity constitutive model of the present application can capture the macroscopic mechanical properties of the metal material.

[0121] 2. Crack data of non-uniform structure with different grain orientations

[0122] As Figure 3 shown, the non-uniform structure is also affected by the orientation, and similar to the results of the homogeneous structure, crack initiation always occurs in the grains with large Schmidt factors, or between the grains with large difference in Schmidt factors. In addition, the cracks of the non-uniform structure with different orientations are consistent with the experimental crack phenomenon, proving that the cohesive zone model of the present application can better predict the tensile cracks of the non-uniform structure. Figure 3 In the diagram, the left side represents the first orientation, and the right side represents the second orientation. The Schmidt factors corresponding to ①, ②, ③, and ④ on the left side are 0.4327, 0.4131, 0.3991, and 0.4375, respectively, while the Schmidt factors corresponding to ①, ②, ③, and ④ on the right side are 0.4318, 0.2456, 0.3894, and 0.3002, respectively.

[0123] 3. Crack Result Analysis of Non-homogeneous Structures

[0124] like Figure 4 As shown, the non-uniform structure exhibits the characteristic of multiple crack initiation and poor connectivity. In the non-uniform structure, the independent initiation of multiple cracks leads to the mutual influence of local stress fields. Compared with single crack initiation, multiple crack initiation can effectively absorb more external energy, improving the material's crack resistance. During the simulation, the high-stress areas of the non-uniform structure are distributed in the fine-grained region. According to the Hall-Page relation, compared with coarse grains, fine grains have higher strength and are less prone to crack initiation, thus playing a role in resisting crack initiation. In contrast, the coarse-grained region has more space and degrees of freedom within the grains to generate and propagate dislocations, resulting in the simultaneous activation of more slip systems. This means that in coarse-grained materials, dislocations are more likely to initiate and continue their movement, resulting in more plastic deformation. Compared to homogeneous structures, in heterogeneous structures, large grains absorb some stress through plastic deformation during loading, while small grains, due to their higher strength, can resist greater stress concentration, thus alleviating stress concentration in the overall material. Large grains can withstand larger plastic strains, providing stronger deformation capacity, while the presence of small grains limits excessive plastic deformation, thereby reducing dislocation accumulation and slip system activation. This structure allows large grains to bear most of the plastic deformation, while small grains enhance the overall material strength by providing higher resistance to deformation. This stress-strain distribution mechanism reduces excessive stress or strain at the individual grain scale, effectively delaying or inhibiting crack formation and extending the material's service life. In addition to improving material strength, heterogeneous structures also enhance ductility to some extent.

[0125] 4. Prediction of the direction of microstructure optimization in metallic materials

[0126] The synergistic effect between the fine and coarse grains in the non-uniform structure jointly enhances the strength and ductility of the material. Figure 4 It is known that cracks always propagate first in the fine-grained region and then deviate into the coarse-grained region. When the crack enters the coarse-grained region from the fine-grained region, the grain size suddenly increases, the grain boundary density decreases, and the crack propagation path changes. This abrupt change easily leads to uneven stress concentration distribution, and the crack may deflect or even branch during propagation. It can be inferred that the spatial arrangement and number of coarse-grained clusters with non-uniform structures in a given volume will affect its performance, such as... Figure 5 As shown, the irregular coarse grain cluster arrangement is likely to cause multiple deflection and branching of the crack path, absorb external energy, and reduce the material failure speed. Therefore, using the method to simulate the non-uniform structure of different coarse grain cluster spatial distribution can determine the direction for material microstructure optimization.

[0127] The metal material crack simulation method of the embodiment of the present application embeds the cohesive force model and the crystal plasticity constitutive model into the microstructure finite element model of the metal material, and accurate stress-strain data and crack data can be obtained after finite element analysis, so that the tensile fracture behavior of the metal material can be effectively restored, and the tensile crack of the metal material can be accurately predicted. The method has the advantages of high precision, strong flexibility, can evaluate the fracture behavior of the metal material, and has the advantage of intuitive display.

[0128] The above is only a preferred embodiment of the present application, not to limit the scope of the present application, the above embodiment of the present application can also be various changes. That is, the simple, equivalent changes and modifications made according to the content of the claims and the 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 of simulating a crack in a metal material, characterized by, The method comprises the following steps: obtaining a cohesive zone model and determining undetermined parameters of the cohesive zone model; obtaining a crystal plasticity constitutive model and determining undetermined parameters of the crystal plasticity constitutive model, the crystal plasticity constitutive model comprising a kinematic model, a thermal-activated flow law model and a hardening model; establishing a first microstructure finite element model of the metal material and embedding the cohesive zone model and the crystal plasticity constitutive model in the first microstructure finite element model; applying a tensile load and boundary conditions to the first microstructure finite element model and performing finite element analysis to obtain a first finite element analysis result; the first finite element analysis result comprising stress-strain data calculated based on the crystal plasticity constitutive model and crack data calculated based on the cohesive zone model and the stress-strain data; the thermal-activated flow law model comprising: ， ， ， ， ， where, is the plastic slip rate, X α and S α are the kinematic hardening and the slip resistance of the slip system α, respectively, is the slip rate on the slip system α, N is the number of slip systems, α is a positive integer, and α ∈ [1, N], T is the absolute temperature, k is the Boltzmann constant, is the resolved shear stress, g and q are the exponential 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(z) consists of the brackets such that for z ≥ 0, , otherwise ; S sat is the saturation slip resistance, the initial value is S0, S inc is the increased slip resistance during the simulation, β is a positive integer and β ∈ [1, N]; h αβ is the hardening matrix, h s is the hardening constant inherent to the metallic material, is the Kronecker function, is the potential hardening ratio; is the initial slip resistance with a regular grain size, k s is the slope coefficient of the size dependency, d is the size of the considered grain.

2. The metal material crack simulation method according to claim 1, characterized by, the cohesive zone model comprising: ， ， ， ， where F is the traction force, k1 is the stiffness in the linear elastic stage, x is the displacement, x1 is the critical damage displacement, F max is the critical damage stress, k2 is the slope of the traction-displacement curve in the damage evolution stage, b is the intercept of the traction-displacement curve in the damage evolution stage, x2 is the complete damage displacement, k1, x1, F max , k2, b, and x2 are all undetermined parameters.

3. The metal material crack simulation method according to claim 2, characterized by, determining the undetermined parameters of the cohesive zone model, specifically comprising: performing molecular dynamics simulation on the metal material to obtain a critical damage stress, a critical damage displacement and a complete damage displacement of the metal material; determining the stiffness of the linear elastic stage according to the critical damage stress and the critical damage displacement; determining the slope and intercept of the traction-displacement curve of the damage evolution stage according to the critical damage stress, the critical damage displacement and the complete damage displacement.

4. The metal material crack simulation method according to claim 1, characterized by, the kinematic model comprising: ， ， 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.

5. The metal material crack simulation method according to claim 4, characterized by, the hardening model comprising: ， ， where r D is the dynamic recovery coefficient, h b is the hardening modulus, is the critical hardening modulus for a homogeneous grain structure, k b is the hardening parameter induced by heterogeneous deformation, d n is the average size of the grains surrounding the grain under consideration; F0、 、 、 , g, q, , k s , S inc , h s , r D , , k b are all undetermined parameters.

6. The metal material crack simulation method according to claim 5, characterized by, determining the undetermined parameters of the crystal plasticity constitutive model, specifically comprising: establishing a second microstructure finite element model of the metal material, embedding the crystal plasticity constitutive model in the second microstructure finite element model, applying a tensile load and boundary conditions to the second microstructure finite element model and performing finite element analysis to obtain a stress-strain curve of the microstructure finite element model; performing a tensile test on the metal material to obtain a stress-strain curve of the metal material; adjusting the values of the undetermined parameters of the crystal plasticity constitutive model so that the error between the stress-strain curve of the second microstructure finite element model and the stress-strain curve obtained by the tensile test is within a preset range, to determine the values of the undetermined parameters of the crystal plasticity constitutive model.

7. The metal material crack simulation method according to claim 1, characterized by, establishing the first microstructure finite element model of the metal material, specifically comprising: obtaining microstructure data of the metal material; establishing a geometric model according to the microstructure data; performing meshing on the geometric model and assigning material properties to obtain the first microstructure finite element model.

8. The metal material crack simulation method according to claim 1, characterized by, the crack data comprising the number of cracks and the position and size of each crack.

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