A method for establishing a multi-scale crystal plasticity model based on dislocation density

Abstract

The application discloses a kind of multi-scale crystal plasticity model establishment methods based on dislocation density, specific steps are, S1: based on the grain information of metal material to obtain Fourier lattice, construct crystal plasticity model on Fourier lattice based on Orowan law, obtain the grain information of metal material on each Fourier point, slip system information and dislocation density information;S2: construct dislocation density evolution model, and based on the information of S1 to calculate the change of dislocation density on each Fourier point;S3: based on the change of dislocation density, update the slip system information and dislocation density information of the crystal plasticity model, and then realize the coupling of the dislocation density evolution model and the crystal plasticity model, obtain multi-scale crystal plasticity model based on dislocation density, this model can more accurately predict the mechanical properties and plastic deformation of different lattice type materials from physical meaning, and can also show the evolution law of dislocation density.

Description

Technical Field

[0001] This invention relates to the field of materials plastic deformation technology, and in particular to a method for establishing a multi-scale crystal plasticity model based on dislocation density. Background Technology

[0002] Plastic deformation of metals refers to the irreversible permanent deformation of metal parts under external forces. Understanding plastic deformation of metals is of great significance, as it can not only guide the design of metal material processing but also predict material deformation failure. Most existing studies on the plastic deformation of metal materials use traditional finite element models or more precise plastic crystal finite element models. Traditional finite element models require experimental data to obtain the corresponding constitutive relations to simulate the deformation of materials under external boundary conditions. Therefore, the accuracy of the simulation depends on the accuracy of the experimental data and lacks true physical meaning. Plastic crystal finite element models determine the occurrence of plastic deformation through dislocation slip, but their constitutive relations are still based on experimental data and usually only consider a small number of grains.

[0003] Therefore, there is a need for a method that can construct information at different scales, obtain macroscopic constitutive relations from microscopic mechanisms, thereby getting rid of the plastic model that directly obtains constitutive relations through experimental fitting, and is applicable to metals with different lattice types. It can also incorporate models with real physical meaning according to the mechanisms of different materials to trace the changes in the microstructure of the material. Summary of the Invention

[0004] This invention provides a method for establishing a multi-scale crystal plasticity model based on dislocation density, which overcomes the problem that the constitutive relations of the finite element model of plastic crystal are based on experimental data and lack physical meaning, and can usually only consider a small number of grains.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for establishing a multi-scale crystal plasticity model based on dislocation density, characterized by the following specific steps:

[0007] S1: Based on the grain information of the metal material, the Fourier lattice is obtained. Based on Orowan's law, a crystal plasticity model is constructed on the Fourier lattice to obtain the grain information, slip system information and dislocation density information of the metal material at each Fourier point.

[0008] S2: Construct a dislocation density evolution model, and calculate the change in dislocation density at each Fourier point based on the grain information, slip system information and dislocation density information;

[0009] S3: Based on the change in dislocation density obtained from the dislocation density evolution model, update the slip system information and dislocation density information of the crystal plasticity model, thereby realizing the coupling of the dislocation density evolution model and the crystal plasticity model, and obtaining a multi-scale crystal plasticity model based on dislocation density.

[0010] Specifically, in S2, a dislocation density evolution model is constructed. This model includes a movable dislocation evolution model and an immovable dislocation evolution model. The movable dislocation evolution model is used to calculate the movable dislocation evolution rate, using the following formula:

[0011]

[0012] The immovable dislocation evolution model is used to calculate the immovable dislocation evolution rate, and the formula is:

[0013]

[0014] In the formula, q1, q2, q3, q4, q5, q6, and q7 are parameters obtained through discrete dislocation dynamics simulation, respectively. For the mean free path, Let be the density of movable dislocations in the slip system s. Let R be the density of immovable dislocations in the slip system s. c The critical radius of dislocation interaction, P sβ Let be the cross-slip probability from slip system s to slip system β, and p be the probability of activating slip propagation. For the value-added model of dislocations, An annihilation model for dislocations caused by the interaction of two dislocations with opposite signs. The movable dislocation model is transformed into an immovable dislocation model when it is blocked. The immovable dislocation is transformed into a movable dislocation model. The cross-slip model for spiral dislocations. A model for the reduction in dislocation density caused by the interaction between dislocations and immovable dislocations on grain boundaries. A model for the formation of dislocation dipoles. This is a dislocation density flux model.

[0015] Specifically, in S1, a crystal plasticity model is constructed on the Fourier lattice based on Orowan's law to obtain the grain information, slip system information and dislocation density information of the metal material at each Fourier point. The grain information includes spatial location, grain size and grain orientation.

[0016] The crystal plasticity model based on Orowan's law includes a critical shear stress model based on the stress gradient model, which is used to calculate the critical shear stress at each Fourier point and determine the average dislocation velocity based on the critical shear stress; the crystal plasticity model also includes a strain gradient model based on the geometrically necessary dislocation density, which is used to calculate the strain gradient, i.e. the mean free path.

[0017] The formula for the crystal plasticity model constructed based on Orowan's law is as follows:

[0018]

[0019] in, Let be the shear rate of the slip system s, and b be the Burgers vector. Let be the density of movable dislocations in the slip system s. Let be the average dislocation velocity of the slip system s;

[0020] The critical shear stress model established based on the stress gradient model is as follows:

[0021]

[0022] in, For lattice friction, It is a hardening term caused by dislocation-dislocation interactions. It is a stress gradient model;

[0023] in The hardening term, based on Bailey-Hirsch strengthening, is represented as follows:

[0024]

[0025] Among them, Ω sβ It is the interaction matrix between the slip system s and the slip system β, c * It is a constant, and μ is the shear modulus; It is the total statistical storage dislocation density of the slip system β; It is the density of movable dislocations in the slip system β. It is the density of immovable dislocations in the slip system β.

[0026]

[0027] Where K is the Hall-Page constant, L is the grain size, and L′ is the average distance between obstacles that impede dislocation movement. It is the effective stress. It introduces an effective stress spatial gradient based on the intrinsic length scale;

[0028] The average dislocation velocity determined based on the critical shear stress is:

[0029]

[0030] Where v0 is the reference velocity, τ s It is the critical stress projected onto the slip surface by the stress on the grain, when τ s >0, sign(τ) s ) = 1; when τ s =0, sign(τ) s ) = 0; when τ s <0, sign(τ) s ) = -1;

[0031] The strain gradient model established based on the dislocation density required by geometry is as follows:

[0032]

[0033] Where c is a constant, w βs It is an interaction matrix; The dislocation density required for the geometry of the slip system β:

[0034]

[0035] Where A is the dislocation Nyes tensor, and in the plastic deformation gradient tensor -F P The intrinsic length scale is introduced in curl, and is expressed as:

[0036] A = curl(-F) P ).

[0037] Specifically, based on the dislocation density flux generated by dislocations flowing from one Fourier point to another, the dislocation density flux model formula is defined as follows:

[0038]

[0039] in, It is the distance between two adjacent Fourier points. The increase in dislocation density is due to dislocations moving from adjacent Fourier points into slip system s. The dislocation density decreases as a dislocation moves from the slip system s to the slip system at the adjacent Fourier point. To account for dislocation flux, the average dislocation velocity,

[0040] When the Fourier point is located at the grain boundary

[0041]

[0042]

[0043] Where, τ R It is the resistance that the grain boundaries themselves exert on the movement of dislocations;

[0044] When the Fourier point is located within the crystal.

[0045]

[0046]

[0047] p is the probability of activating the glide transfer, expressed as:

[0048]

[0049] N′ represents the partial shear stress of slip system β, where N′ is the slip system that may undergo transgranularity. It is the critical shear stress that needs to be overcome for dislocations to cross-grain in the slip system. Let be the shear stress of any slip system that may translocate at adjacent Fourier points. It represents the critical shear stress of any slip system that may translocate at adjacent Fourier points;

[0050] M′ si The geometric condition under which transgranularity may occur between slip system s in two different grains and any slip system i is expressed as:

[0051]

[0052] M′ sβ The geometric condition under which transgranularity may occur between two target slip systems s and β in two different grains is expressed as:

[0053]

[0054] in, For the slip normal of the slip system s, To find the slip normal of the slip system β, To determine the slip direction for entering the slip system s, The slip direction of the outflow slip system β To find the slip normal of slip system i, The direction of slip flow out of slip system i;

[0055] When M′ sβ When = 1, the Fourier point is located on the grain boundary. M′ represents the geometric eigenvalues ​​between two slip systems at different Fourier points;

[0056] When M′sβ When = 0, the Fourier point is located within the crystal. That is, the obstruction effect of grain boundaries is not considered in the dislocation flow.

[0057] Specifically, L = L.

[0058] Beneficial effects: By establishing a multi-scale crystal plasticity model based on dislocation density, this invention can more accurately predict the mechanical properties and plastic deformation of materials with different lattice types from a physical perspective, while also showing the evolution law of dislocation density. In addition, the computational efficiency of this multi-scale model is much higher than that of the full-field crystal plasticity finite element method and can consider polycrystalline materials with more grains. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 This is a flowchart of the method for establishing a multi-scale crystal plasticity model based on dislocation density in this invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] In practice, commonly used finite element models require experimental data to obtain the corresponding constitutive relations for simulating the deformation of materials under applied boundary conditions. Therefore, the accuracy of the simulation depends on the accuracy of the experimental data and lacks true physical meaning. While finite element methods for plastic crystals determine the occurrence of plastic deformation through dislocation slip, their constitutive relations are still based on experimental data and typically only consider a small number of grains. Multiscale simulations can obtain macroscopic constitutive relations by constructing information at different scales, starting from microscopic mechanisms. This avoids directly obtaining constitutive relations through experimental fitting and not only possesses isotropy (applicable to metals with different lattice types) but also allows for simulation based on the mechanisms of different materials. By incorporating a model with real physical meaning to trace changes in the microstructure of materials, this invention constructs a stress-strain constitutive relation based on dislocation density. Through this model, macroscopic mechanical properties are further calculated. Compared with the current crystal plasticity finite element model, the introduction of the dislocation density evolution model can more accurately predict the mechanical properties and plastic deformation of materials with different lattice types from a physical perspective, while also showing the evolution law of dislocation density. The computational efficiency of this multi-scale model is much higher than that of the full-field crystal plasticity finite element model and can consider polycrystalline materials with more grains. At the same time, this model can also be coupled with the crystal plasticity finite element code, and has a certain degree of scalability.

[0063] In this embodiment, the basic design principle is based on coupling processing using the VPSCFFT model (Viscoplastic Self-Locking Fast Fourier Transform model). The VPSCFFT model is a mean-field plastic crystal model that treats each grain as an ellipsoid embedded in a viscoelastic medium. To capture the grain size effect, information about neighboring grains and grain positions is needed. Therefore, the polycrystalline material is represented by a Fourier space lattice, and each Fourier point evaluated by VPSCFFT and the stress / strain state at that point are associated with each grain to obtain the lattice node information. VPSCFFT can not only simulate the macroscopic stress-strain curves of metals under different loading processes, but also analyze the evolution of microscopic deformation mechanisms and texture during deformation.

[0064] However, the VPSCFFT model has the following drawbacks: first, it cannot track the evolution of dislocation density within the crystal; second, it lacks intrinsic length to construct a model of grain size effect. The dislocation density evolution model can transform a single crystal shaping model into a multi-scale model capable of analyzing gradient materials with multi-scale microstructures.

[0065] Based on the above design principles and problems, this invention provides a method for establishing a multi-scale crystal plasticity model based on dislocation density, such as... Figure 1 As shown, the specific steps are as follows:

[0066] S1: Obtain grain information in a metallic material with an arbitrary crystal structure. Discretize the microstructure of the metallic material into a Fourier lattice based on the obtained grain information. Construct a crystal plasticity model on the Fourier lattice based on Orowan's law to obtain grain information, slip system information and dislocation density information of the metallic material at each Fourier point.

[0067] S2: Construct a dislocation density evolution model, and calculate the change in dislocation density at each Fourier point based on the grain information, slip system information and dislocation density information;

[0068] S3: Based on the change in dislocation density obtained from the dislocation density evolution model, update the slip system information and dislocation density information of the crystal plasticity model, thereby realizing the coupling of the dislocation density evolution model and the crystal plasticity model, and obtaining a multi-scale crystal plasticity model based on dislocation density, which is used to further calculate the macroscopic mechanical properties of metallic materials.

[0069] In a specific embodiment, in S2, a dislocation density evolution model is constructed based on several different dislocation motion mechanism models. This model includes a movable dislocation evolution model and an immovable dislocation evolution model. The movable dislocation evolution model is used to calculate the movable dislocation evolution rate, using the following formula:

[0070]

[0071] The immovable dislocation evolution model is used to calculate the immovable dislocation evolution rate, and the formula is:

[0072]

[0073] In the formula, q1, q2, q3, q4, q5, q6, and q7 are parameters obtained through discrete dislocation dynamics simulation, respectively. For the mean free path, Let be the density of movable dislocations in the slip system s. Let R be the density of immovable dislocations in the slip system s. c The critical radius of dislocation interaction, P sβ Let be the cross-slip probability from slip system s to slip system β, and p be the probability of activating slip propagation. For the value-added model of dislocations, An annihilation model for dislocations caused by the interaction of two dislocations with opposite signs. The movable dislocation model is transformed into an immovable dislocation model when it is blocked. The immovable dislocation is transformed into a movable dislocation model. The cross-slip model for spiral dislocations. A model for the reduction in dislocation density caused by the interaction between dislocations and immovable dislocations on grain boundaries. A model for the formation of dislocation dipoles. This is a dislocation density flux model.

[0074] In a specific embodiment, in S1, a crystal plasticity model is constructed on the Fourier lattice based on Orowan's law to obtain the grain information, slip system information and dislocation density information of the metal material at each Fourier point. The grain information includes spatial position, grain size and grain orientation.

[0075] The crystal plasticity model based on Orowan's law includes a critical shear stress model based on the stress gradient model, which is used to calculate the critical shear stress at each Fourier point and determine the average dislocation velocity based on the critical shear stress; the crystal plasticity model also includes a strain gradient model based on the geometrically necessary dislocation density, which is used to calculate the strain gradient, i.e. the mean free path.

[0076] The formula for the crystal plasticity model constructed based on Orowan's law is as follows:

[0077]

[0078] in, Let be the shear rate of the slip system s, and b be the Burgers vector. Let be the density of movable dislocations in the slip system s. Let be the average dislocation velocity of the slip system s;

[0079] The critical shear stress model established based on the stress gradient model is as follows:

[0080]

[0081] in, For lattice friction, It is a hardening term caused by dislocation-dislocation interactions. It is a stress gradient model;

[0082] in The hardening term, based on Bailey-Hirsch strengthening, is represented as follows:

[0083]

[0084] Among them, Ω sβ It is the interaction matrix between the slip system s and the slip system β, which can be obtained by fitting dislocation dynamics or experimentally. * It is a constant, and μ is the shear modulus; It is the total statistical storage dislocation density of the slip system β; It is the density of movable dislocations in the slip system β. The density of immovable dislocations in the slip system β

[0085] The linear stress gradient model is as follows:

[0086]

[0087] This embodiment employs a simplified stress gradient model to capture the effect of dislocation stacking on grain boundaries under non-uniform shear stress:

[0088]

[0089] Where K is the Hall-Page constant, L is the grain size, and L′ is the average distance between obstacles that impede dislocation movement. It is the effective stress. It introduces an effective stress spatial gradient based on the intrinsic length scale;

[0090] The average dislocation velocity determined based on the critical shear stress is:

[0091]

[0092] Where v0 is the reference velocity, τ s It is the critical stress projected onto the slip surface by the stress on the grain, when τ s >0, sign(τ) s ) = 1; when τ s =0, sign(τ) s ) = 0; when τ s <0, sign(τ) s ) = -1;

[0093] The strain gradient model established based on the dislocation density required by geometry is as follows:

[0094]

[0095] Where c is a constant, w βs It is an interaction matrix; The dislocation density required for the geometry of the slip system β:

[0096]

[0097] Where A is the dislocation Nyes tensor, and in the plastic deformation gradient tensor -F P The intrinsic length scale is introduced into curl to capture the grain size effect, expressed as:

[0098] A = curl(-F) P ).

[0099] Specifically, this embodiment employs a simplified transgranular model. Based on the dislocation density flux caused by dislocations flowing from one Fourier point to another, a dislocation density flux model is established to approximate the change in dislocation density when dislocations cross grain boundaries. The formula is as follows:

[0100]

[0101] in, It is the distance between two adjacent Fourier points. The increase in dislocation density is due to dislocations moving from adjacent Fourier points into slip system s. The dislocation density decreases as a dislocation moves from the slip system s to the slip system at the adjacent Fourier point. To account for dislocation flux, the average dislocation velocity,

[0102] When the Fourier point is located at the grain boundary

[0103]

[0104]

[0105] Wherein, τR is the resistance to dislocation movement caused by the grain boundary itself;

[0106] When the Fourier point is located within the crystal...

[0107]

[0108]

[0109] p is the probability of activating slip propagation, used to ensure that only some dislocations undergo transgranular propagation, and is expressed as:

[0110]

[0111] N′ represents the partial shear stress of slip system β, where N′ is the slip system that may undergo transgranularity. It is the critical shear stress that needs to be overcome for dislocations to cross-grain in the slip system. Let be the shear stress of any slip system that may translocate at adjacent Fourier points. It represents the critical shear stress of any slip system that may translocate at adjacent Fourier points;

[0112] M′ si The geometric condition under which transgranularity may occur between slip system s in two different grains and any slip system i is expressed as:

[0113]

[0114] M′ sβ The geometric conditions under which transgranular crossing may occur between two target slip systems s and β in two different grains are expressed as follows:

[0115]

[0116] in, For the slip normal of the slip system s, To find the slip normal of the slip system β, To determine the slip direction for entering the slip system s, The slip direction of the outflow slip system β For the slip normal of slip system i, The direction of slip flow out of slip system i;

[0117] When grain boundaries are impenetrable, the resistance comes entirely from the accumulation of dislocations near the grain boundaries, i.e., τ. SG However, when grain boundaries are permeable, dislocation accumulation will be eliminated, and slip will be triggered once the dislocation density in the outgoing slip system is greater than the dislocation density in the incoming slip system.

[0118] When M′ sβ When = 1, the Fourier point is located on the grain boundary. M′ represents the geometric eigenvalues ​​between two slip systems at different Fourier points;

[0119] For two Fourier points within the same grain, assuming they undergo cooperative deformation, this value is 0, i.e., when M′ sβ When = 0, the Fourier point is located within the crystal. That is, the obstruction effect of grain boundaries is not considered in the dislocation flow.

[0120] In this embodiment, since only the effect of grain boundaries is considered, L is set to = L. In practice, this model can be used to extend the study of dislocation accumulation caused by other defects.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for establishing a multi-scale crystal plasticity model based on dislocation density, characterized in that, The specific steps are as follows: S1: Based on the grain information of the metal material, the Fourier lattice is obtained. Based on Orowan's law, a crystal plasticity model is constructed on the Fourier lattice to obtain the grain information, slip system information and dislocation density information of the metal material at each Fourier point. In S1, a crystal plasticity model is constructed on the Fourier lattice based on Orowan's law to obtain the grain information, slip system information and dislocation density information of the metallic material at each Fourier point. The grain information includes spatial location, grain size and grain orientation. The crystal plasticity model based on Orowan's law includes a critical shear stress model based on the stress gradient model, which is used to calculate the critical shear stress at each Fourier point and determine the average dislocation velocity based on the critical shear stress; the crystal plasticity model also includes a strain gradient model based on the geometrically necessary dislocation density, which is used to calculate the strain gradient, i.e. the mean free path. The formula for the crystal plasticity model constructed based on Orowan's law is as follows: in For slip system shear rate, Burgers vector, For slip system The density of movable dislocations, For slip system Average dislocation velocity; The critical shear stress model established based on the stress gradient model is as follows: in, For lattice friction, It is a hardening term caused by dislocation-dislocation interactions. It is a stress gradient model; in The hardening term, based on Bailey–Hirsch strengthening, is represented as follows: in, It is a slip system and slip system The interaction matrix between them It is a constant. It is the shear modulus; It is a slip system Overall statistical storage dislocation density; It is a slip system The density of movable dislocations, Sliding system The density of immovable dislocations in, It is the Hall-Page constant. It refers to the grain size. It is the average distance between obstacles that impede the movement of dislocations. It is the effective stress. It introduces an effective stress spatial gradient based on the intrinsic length scale; The average dislocation velocity determined based on the critical shear stress is: in, This is a reference speed. It is the critical stress that is the projection of the stress on the grain onto the slip surface. when >0, sign( )=1; when =0, sign( )=0; when <0, sign( ) = -1; The strain gradient model established based on the dislocation density required by geometry is as follows: in, It is a constant. It is an interaction matrix; It is a slip system The required dislocation density for geometry: Where A is the dislocation Nyes tensor, and in the plastic deformation gradient tensor of The intrinsic length scale is introduced in the code, and it is expressed as: S2: Construct a dislocation density evolution model, and calculate the change in dislocation density at each Fourier point based on the grain information, slip system information and dislocation density information; In S2, a dislocation density evolution model is constructed, which includes a movable dislocation evolution model and an immovable dislocation evolution model. The movable dislocation evolution model is used to calculate the movable dislocation evolution rate, and the formula is: The immovable dislocation evolution model is used to calculate the immovable dislocation evolution rate, and the formula is: In the formula These are the parameters obtained through discrete dislocation dynamics simulation. For the mean free path, Let S be the density of immovable dislocations in the slip system s. Critical radius of dislocation interaction. For slip system arrive The cross-slip probability, To activate the probability of slip transfer, For the value-added model of dislocations, An annihilation model for dislocations caused by the interaction of two dislocations with opposite signs. The movable dislocation is blocked and becomes an immovable dislocation model. The immovable dislocation is transformed into a movable dislocation model. The cross-slip model for spiral dislocations. This model represents the reduction in dislocation density caused by the interaction between dislocations and immovable dislocations on grain boundaries. A model for the formation of dislocation dipoles. For dislocation density flux model; S3: Based on the change in dislocation density obtained from the dislocation density evolution model, update the slip system information and dislocation density information of the crystal plasticity model, thereby realizing the coupling of the dislocation density evolution model and the crystal plasticity model, and obtaining a multi-scale crystal plasticity model based on dislocation density.

2. The method for establishing a multi-scale crystal plasticity model based on dislocation density according to claim 1, characterized in that, Based on the dislocation density flux generated by dislocations flowing from one Fourier point to another, the dislocation density flux model formula is defined as follows: in, It is the distance between two adjacent Fourier points. The increase in dislocation density is due to dislocations moving from adjacent Fourier points into slip system s. The dislocation density decreases as a dislocation moves from the slip system s to the slip system at the adjacent Fourier point. To account for dislocation flux, the average dislocation velocity, When the Fourier point is located at the grain boundary = , It is the resistance that the grain boundaries themselves exert on the movement of dislocations; When the Fourier point is located within the crystal. = , The probability of activating the slip transfer is expressed as: It is a slip system The partial shear stress, It is a slip system that may translocate. It is a slip system The critical shear stress that needs to be overcome for dislocations to translocate through grains. Let be the shear stress of any slip system that may translocate at adjacent Fourier points. It represents the critical shear stress of any slip system that may translocate at adjacent Fourier points; The geometric condition under which transgranularity may occur between slip system s in two different grains and any slip system i is expressed as: For two target slip systems s and slip systems in two different grains The geometric conditions under which transgranular crossing may occur are expressed as: For the slip normal of the slip system s, For the slip system The slip normal, To determine the slip direction for entering the slip system s, For outflow slip system The direction of slippage, For the slip system The slip normal, For outflow slip system The direction of slippage; when When = 1, the Fourier point is located on the grain boundary. , These are the geometric eigenvalues ​​between two slip systems at different Fourier points; when When = 0, the Fourier point is located within the crystal. That is, dislocation flow does not consider the obstruction effect of grain boundaries.

3. The method for establishing a multi-scale crystal plasticity model based on dislocation density according to claim 2, characterized in that, 。

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