Method and system for constructing elastic-viscoplastic multi-scale constitutive model of polycrystalline materials

Abstract

The present invention discloses a method and system for constructing an elastic viscoplastic multi-scale constitutive model of a polycrystalline material. A single crystal scale constitutive model is established on the basis of a representative volume element model RVE of the polycrystalline material, and the relationship between the stress rate and the strain rate of a single grain is obtained. Then, the relationship between the stress rate and the strain rate of the RVE scale is obtained, and the relationship between the affine strain rate, the stress local tensor, and the strain local tensor is established; the initial single grain strain increment is set as the overall strain increment, and the stress increment of the RVE scale is obtained through iterative calculation of finite element analysis. The present invention is suitable for solving deformation problems under complex boundary conditions, and uses two quantities, the algorithm tangent operator and the affine strain increment, to define the relationship between the strain increment and the stress increment, thereby increasing the accuracy of the calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-scale simulation of polycrystalline materials, in particular to a method and system for constructing an elastic-viscoplastic multi-scale constitutive model of polycrystalline materials. Background Art

[0002] Polycrystalline materials are composed of many grains with different orientations, and each grain with different orientations is separated by grain boundaries. They are usually used as welding materials in electronic packaging structures. For example, sintered nanosilver, by sintering nano-scale silver particles at an appropriate temperature, forms a silver layer with high electrical conductivity and high thermal conductivity. It has excellent thermal conductivity and chemical stability and is an interconnection material for the third generation of semiconductor packaging. In electronic packaging structures, as a connecting material between different components, the failure of micro-solder joints may lead to the failure of the overall packaging structure, and then cause the failure of electronic equipment. Therefore, the study of the mechanical properties of welding materials is very necessary and meaningful.

[0003] As one of the effective tools to describe the deformation behavior of materials, constitutive models that can accurately reflect the stress-strain relationship of materials ensure the correctness of finite element simulation. Traditional macroscopic phenomenological constitutive models are mostly based on experimental data. Although they can better reflect the deformation response of materials, they cannot reflect the evolution of the microstructure of materials and their deformation mechanism. From a microscopic point of view, most polycrystalline materials are composed of grains with different orientations. The development of a multi-scale constitutive model that can link the single crystal scale deformation of materials with the macroscopic scale deformation has important engineering practice significance and scientific research value.

[0004] At present, for polycrystalline materials with elastic viscoplastic deformation, self-consistent models are mostly used to link their macro and micro deformation behaviors. However, most methods cannot be applied to finite element simulation, which limits their further application. Some methods are based on the Hill increment method and only use the tangent stiffness matrix to define the relationship between strain increment and stress increment, which may cause the calculation results to be too "rigid". Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a method and system for constructing an elastic-viscoplastic multi-scale constitutive model of polycrystalline materials, so as to solve the deformation problem under complex boundary conditions and improve the calculation accuracy.

[0006] Technical solution: The method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials described in the present invention comprises the following steps:

[0007] (1) Establish a representative volume element model (RVE) of polycrystalline materials;

[0008] (2) Based on the representative volume element model, a single crystal scale constitutive model is established based on the small deformation assumption, and the stress rate of grain r is obtained by linearization. and strain rate The relationship between: ,in is the algorithmic tangent operator of grain r, is the affine strain rate of grain r;

[0009] (3) According to the stress rate of grain r and strain rate , assuming that the stress rate of the RVE scale and strain rate The relationship between: , subscript 0 indicates RVE;

[0010] (4) Establishment , local stress tensor and , local strain tensor and and , , , and the affine strain rate at the representative volume element scale The relationship between: , , ;in, is the algorithmic flexibility operator of grain r, , The symbol represents the volume average of each grain;

[0011] (5) For the same time increment, the stress rate, strain rate and affine strain rate are converted into incremental stress increment, strain increment and affine strain increment, and the strain increment of each grain is iteratively calculated by finite element analysis. , the initial setting assumes that the strain increment of grain r is equal to the strain increment of RVE scale, that is, , the stress increment of the RVE scale is obtained according to the formula established in steps (2) to (4): .

[0012] Furthermore, step (5) includes the following steps:

[0013] (5.1), initial setting , the algorithm tangent operator of the grain is calculated through step (2) and the affine strain increment , respectively set the algorithmic tangent operator and affine strain increment of the RVE scale equal to the volume average of the algorithmic tangent operator and affine strain increment of each grain , , the superscript 0 indicates the initial value before the iteration starts;

[0014] (5.2) Through steps (3) and (4), and Calculate the stress local tensor , , the local strain tensor , , the algorithm tangent operator of RVE scale and the affine strain increment , ii is the number of iteration steps;

[0015] (5.3) Calculate the first tolerance and second tolerance of the algorithm tangent operator and affine strain increment of the RVE scale between the ii-th iteration and the ii-1-th iteration respectively, until the first tolerance or the second tolerance is less than the corresponding threshold, the calculation is terminated, otherwise let , Return to step (5.2);

[0016] (5.4) Calculate the stress increment of a single grain using the local strain tensor in step (4): , the superscript jj is the second iteration number, and the third tolerance of the grain stress increment between the jj-th iteration and the jj-1-th iteration is calculated until the third tolerance is less than the corresponding threshold value, and the calculation is terminated. Otherwise, let Return to step (5.1).

[0017] Furthermore, the strain rate of the grain , the stress rate of grain r ,in is the elastic modulus of grain r, is the elastic strain rate, and the viscoplastic strain rate Originated from the slip system.

[0018] Furthermore, in step (2), the viscoplastic strain rate , where the slip system Schmid factor , slip system Slip rate ;

[0019] is the unit vector of the sliding direction, is the unit vector in the normal direction of the slip surface, is the reference slip rate, It is a slip system The current intensity, n is the rate sensitivity parameter, It is a slip system The shear stress depends on the current stress and the Schmid factor. ;

[0020] Voce hardening law is used to describe the strain hardening behavior of grains. The intensity change rate is , where the threshold intensity for ,in, is the accumulated shear force within the grain, , and are the initial critical shear stress and the reverse critical shear stress, and It is a slip system The initial hardening rate and progressive hardening rate.

[0021] Furthermore, in step (2), the algorithm tangent operator ;

[0022] in ,

[0023] is the elastic modulus of grain r, and Slip system and The slip rate, and Slip system Slip system The Schmid factor, It is a slip system The shear stress, yes The reference slip rate of the slip system, is the Kronecker Delta function, is the integration parameter, is the time increment.

[0024] Furthermore, in step (2), the affine strain rate of grain r is , viscoplastic strain rate Originated from the slip system.

[0025] Furthermore, in step (4),

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] in, and is the RVE scale and grain r algorithm flexibility operator, , are the interaction flexibility tensor and the interaction stiffness tensor, respectively. , , , I is the identity matrix, S r is the Eshelby tensor with respect to grain r;

[0034] Using the above formula, we can calculate and , and calculate the stress increment of RVE scale through step (3); then, , calculated to obtain and , and calculate the stress increment of the polycrystalline matrix through step (3).

[0035] The system for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials of the present invention comprises:

[0036] The grain modeling unit is used to establish a representative volume element model RVE of polycrystalline materials; a single crystal scale constitutive model is established based on the representative volume element model and the small deformation assumption, and the stress rate of the grain r is obtained by linearization. and strain rate The relationship between: ,in is the algorithmic tangent operator of grain r, is the affine strain rate of grain r;

[0037] RVE scale modeling unit is used to calculate the stress rate according to the grain r and strain rate , assuming that the stress rate of the RVE scale and strain rate The relationship between: , subscript 0 indicates RVE; establish , local stress tensor and , local strain tensor and and , , , and the affine strain rate at the representative volume element scale The relationship between: , , ;in, is the algorithmic flexibility operator of grain r, , The symbol represents the volume average of each grain;

[0038] Iterative solution unit, for the same time increment, converts stress rate, strain rate and affine strain rate into incremental stress increment, strain increment and affine strain increment, and iteratively calculates the strain increment of each grain through finite element analysis , the initial setting assumes that the strain increment of grain r is equal to the strain increment of RVE scale, which is , the RVE scale stress increment is obtained based on the grain modeling unit and the RVE scale modeling unit .

[0039] The electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the method for constructing the elastic-viscoplastic multi-scale constitutive model of the polycrystalline material is implemented.

[0040] The computer-readable storage medium of the present invention stores a computer program, and when the computer program is executed by a processor, the method for constructing the elastic-viscoplastic multi-scale constitutive model of the polycrystalline material is implemented.

[0041] Beneficial effect: Compared with the prior art, the advantages of the present invention are: the present invention constructs a representative volume unit containing grains of different orientations, adopts crystal plasticity theory to characterize the deformation behavior of grains of different orientations, constructs a linearized equation between stress increment and strain increment on a single crystal and RVE scale, and establishes an improved elastic viscoplastic self-consistent model, which can be used to solve deformation problems under complex boundary conditions, improves the development efficiency of the model, and increases its applicability; and uses the algorithm tangent operator and affine strain increment to define the relationship between strain increment and stress increment, thereby increasing the accuracy of the calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The present invention is a flowchart of the method for constructing the multi-scale constitutive model.

[0043] Figure 2 The figure is a compilation logic flow chart of an embodiment of the present invention.

[0044] Figure 3 This is a comparison chart of Taylor coefficients calculated under uniaxial tensile load for embodiments of the present invention.

[0045] Figure 4It is a comparison diagram of Taylor coefficients calculated under uniaxial shear load of an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0047] like Figure 1 As shown, the method for constructing the elastic-viscoplastic multi-scale constitutive model of the polycrystalline material includes the following steps.

[0048] S1. Use SEM (scanning electron microscope) and TEM (transmission electron microscope) to characterize the microscopic information of polycrystalline materials, obtain structural morphology and grain orientation information, and establish a representative volume element model (RVE).

[0049] S2. A multi-scale constitutive model framework based on mesomechanics is constructed based on the representative volume element model of RVE.

[0050] S21. Determine the deformation behavior of a single grain and perform a linear solution of the single crystal scale constitutive model.

[0051] The single crystal scale constitutive model adopts the small strain assumption and assumes that the total strain rate of the grain r Equal to the elastic strain rate and viscoplastic strain rate The strain rate can be calculated by the following formula:

[0052] (1)

[0053] Among them C r is the elastic modulus of grain r, and the viscoplastic strain rate From the slip system:

[0054] (2)

[0055] Slip system Schmid factor :

[0056] (3)

[0057] is the unit vector of the sliding direction, is the unit vector in the normal direction of the slip plane. Assuming that the grain slip satisfies Schmid's law, the slip system The slip rate is :

[0058] (4)

[0059] in, is the reference slip rate, set to 0.001s -1 , It is a slip system The current intensity, n is the rate sensitivity parameter, is the shear stress, which depends on the current stress and Schmid factor :

[0060] (5)

[0061] At the same time, Voce's hardening law is used to describe the strain hardening behavior of grains:

[0062] (6)

[0063] Subscript , represent , Slip system, and Represents the slip system , The slip ratio, slip coefficient Current strength growth rate Threshold intensity Find:

[0064] (7)

[0065] in, is the accumulated shear force within a single grain:

[0066] (8)

[0067] and are the initial critical shear stress and the reverse critical shear stress, and It is a slip system The initial hardening rate and progressive hardening rate.

[0068] The deformation behavior of a single crystal can be determined from the above equations, and the stress rate can be characterized by the following linear equation: and strain rate The relationship between:

[0069] (9)

[0070] Calculation algorithm Tangent operator :

[0071] (10)

[0072] (11)

[0073] is the elastic modulus of a single grain r, and Represents the slip system and The slip rate, and Slip system Slip system The Schmid factor, It is a slip system The shear stress, for The reference slip rate of the slip system, is the Kronecker Delta function, is the integral parameter, which is taken as 0.5 in this embodiment. is the time increment.

[0074] Affine strain rate of a single grain r :

[0075] (12)

[0076] S22. Through the relationship between the single crystal scale strain rate and the RVE scale strain rate, the deformation behavior of multiple grains is obtained, and the linearization solution of the RVE scale constitutive model is performed using a self-consistent model.

[0077] The stress rate of a single grain can be calculated according to equation (9), so the stress rate of multiple grains is and strain rate The relationship between can be assumed as follows, with subscript 0 representing RVE:

[0078] (13)

[0079] The stress local tensor is derived , , the algorithm tangent operator of RVE scale , affine strain rate :

[0080] (14)

[0081] (15)

[0082] (16)

[0083] in, and is the flexibility operator of the polycrystalline matrix and the single grain r algorithm, that is, , I is the identity matrix. Interaction tensor as follows:

[0084] (17)

[0085] in, is the Eshelby tensor of a single grain r. Substituting equations (9) and (13) into equation (14), we can obtain the relationship between the single crystal scale strain rate and the RVE scale strain rate, and obtain the local strain tensor :

[0086] (18)

[0087] (19)

[0088] (20)

[0089] in, .

[0090] Algorithmic flexibility operator of RVE scale and the affine strain rate :

[0091] (twenty one)

[0092] (twenty two)

[0093] because , so the calculation algorithm of RVE scale is the tangent operator:

[0094] (twenty three)

[0095] The symbol represents the volume average of each grain. According to the above equation, the deformation behavior of multiple grains can be obtained, which is related to the local behavior of each single grain.

[0096] S3. The equations in steps S1 and S2 of the present invention are presented in rate form. For the same time increment, the equations can be converted into increment form. This allows the model to be applied in finite element analysis. Since the strain increment of the RVE scale It is known that the key variable that needs to be determined in the calculation is the strain increment of each grain , which can be determined by an iterative scheme. The multiscale constitutive model framework constructed in step S2 is compiled into a UMAT subroutine using Fortran language. The compilation logic flow chart is as follows: Figure 2shown.

[0097] S3.1. Assuming that the strain increment on each grain is equal to the macroscopic strain increment, the linearized equation of each grain is determined by using the crystal plasticity theory (Equation 9). It is worth noting that equation (9) is in rate form. The equation in increment form can be obtained by multiplying both sides of the equation by the time increment: ,in, , and are the stress increment, strain increment, and affine strain increment of grain r respectively.

[0098] S3.2. Determine and assume that the algorithmic tangent operator and affine strain increment of the RVE scale are equal to the volume average of the algorithmic tangent operator and affine strain increment of each grain; then, calculate the stress local tensor according to formulas (14)-(16): , , calculate the local strain tensor according to formulas (18)-(20) , , where the superscript ii is the number of first iteration steps.

[0099] S3.3. Calculate the algorithm flexibility operator and affine strain increment of the RVE scale by equations (21)-(22), and then obtain a new algorithm tangent operator based on the relationship between the algorithm flexibility operator and the algorithm tangent operator. Compare and calculate the tolerance between the algorithm tangent operator and affine strain increment of the RVE scale and the previous step. , If the condition is not met or , then the loop is entered, the number of iterations becomes ii+1, and the calculation returns to step S3.2, otherwise the calculation ends.

[0100] S3.4. Calculate the strain increment on each grain using formula (18), where the superscript jj is the number of iterations. And calculate the tolerance between the strain increment on each grain and the previous step If the condition is not met , enter the loop, the number of iteration steps becomes jj+1, and return to step S3.1, otherwise the calculation ends.

[0101] S3.5. Algorithmic tangent operator for calculating RVE scale using formula (23) , the affine strain increment of the RVE scale is calculated by formula (22) , and then the stress increment of the RVE scale is calculated by formula (13) to complete the calculation.

[0102] S4. In this embodiment, the UMAT subroutine is called in Abaqus to compare the Taylor coefficients obtained by simulation with those obtained in the four schemes to verify the validity of the developed model, which are:

[0103] Scheme 1: Hutchinson J W. Bounds and self-consistent estimates for creepof polycrystalline materials[J]. Proceedings of the Royal Society of London.A. Mathematical and Physical Sciences, 1976, 348(1652): 101-127.

[0104] Option 2: Yoshida K, Brenner R, Bacroix B, et al. Effect of regularization of Schmid law on self-consistent estimates for rate-independent plasticity of polycrystals[J]. European Journal of Mechanics-A / Solids, 2009, 28(5): 905-915.

[0105] Scheme 3: Zeng T, Shao JF, Xu W Y. Micromechanical modeling of theelasto-viscoplastic behavior of granite[J]. Comptes Rendus. Mécanique, 2015,343(2): 121-132.

[0106] Scheme 4: Liu L, Yao Y, Zeng T. A micromechanical analysis to the elasto-viscoplastic behavior of solder alloys[J]. International Journal of Solidsand Structures, 2019, 159: 211-220.

[0107] The calculation assumes that the Young's modulus E of each grain is 10000MPa and the Poisson's ratio is is 0.3333, and its critical decomposed shear stress is 10MPa, assuming that the material is a perfect plastic material, the rate sensitivity coefficient n is 100, and the initial hardening rate The value is 0. Taylor-Bishop-Hill bound and Self-consistent estimation are the Taylor coefficients under two uniaxial tensile loads in Scheme 1. The Taylor coefficient of Taylor-Bishop-Hill bound is 1.530, and the Taylor coefficient of Self-consistent estimation is 1.474; the Taylor coefficient under uniaxial tensile load in Scheme 4 is 1.413; the Taylor coefficient under uniaxial tensile load in Scheme 3 is 1.412; the Taylor coefficient under uniaxial tensile load in Scheme 2 is 1.410.

[0108] Figure 3 The curve between the normalized stress and the loading strain in the loading direction under uniaxial tensile load is shown. It can be seen that the normalized stress increases with the increase of strain until it stabilizes. This value is the Taylor coefficient. The parameter values ​​used to calculate the Taylor coefficient are shown in Table 1. In the present invention, if it is assumed that the RVE is composed of 50 grains, the Taylor coefficient under the uniaxial tensile load obtained by simulation is 1.437. If it is assumed that the RVE is composed of 500 grains, the Taylor coefficient under the uniaxial tensile load obtained by simulation is 1.452, which is close to the Taylor coefficients in Schemes 1, 2, 3 and 4, and does not exceed the Taylor-Bishop-Hill limit of 1.530, which proves the effectiveness of the model. At the same time, through Figure 3 By comparing the blue and black lines, we can see that the Taylor coefficients under uniaxial tensile loads simulated with 50 grains and 500 grains are very close. Therefore, 50 grains can be used to replace 500 grains for simulation under uniaxial tensile load to reduce the amount of calculation.

[0109] KBW model and Zeng et al. are the Taylor coefficients under uniaxial shear load in Scheme 3. The Taylor coefficient of KBW model is 1.658, and the Taylor coefficient of Zeng et al. is 1.578.

[0110] Figure 4The curve between the normalized stress and the loading strain in the loading direction under uniaxial shear load is shown. It can be seen that the normalized stress increases with the increase of strain until it stabilizes. This value is the Taylor coefficient. The parameter values ​​used to calculate the Taylor coefficient are shown in Table 1. In the present invention, if it is assumed that the RVE is composed of 50 grains, the Taylor coefficient under the uniaxial shear load obtained by simulation is 1.431. If it is assumed that the RVE is composed of 500 grains, the Taylor coefficient under the uniaxial shear load obtained by simulation is 1.442, which is close to the result in Scheme 3 and does not exceed the calculation result of the KBW model of 1.658, which proves the effectiveness of the model. At the same time, through Figure 4 By comparing the blue and black lines, we can see that the Taylor coefficients under uniaxial shear load simulated with 50 grains and 500 grains are very close. Therefore, 50 grains can be used to replace 500 grains for simulation under uniaxial shear load to reduce the amount of calculation.

[0111] Table 1 Parameters used to calculate Taylor coefficients

[0112]

[0113] The system for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials of the present invention comprises:

[0114] A single grain modeling unit is used to establish a representative volume element model RVE of a polycrystalline material; a single crystal scale constitutive model is established based on the representative volume element model and the small deformation assumption, and the stress rate of the grain r is obtained by linearization. and strain rate The relationship between: ,in is the algorithmic tangent operator of grain r, is the affine strain rate of grain r;

[0115] RVE scale modeling unit is used to calculate the stress rate according to the grain r and strain rate , assuming that the stress rate of the RVE scale and strain rate The relationship between: , subscript 0 indicates RVE; establish , local stress tensor and , local strain tensor and and , , , and the affine strain rate at the representative volume element scale The relationship between: , , ;in, is the algorithmic flexibility operator for a single grain r, , The symbol represents the volume average of each grain;

[0116] Iterative solution unit, for the same time increment, converts stress rate, strain rate and affine strain rate into incremental stress increment, strain increment and affine strain increment, and iteratively calculates the strain increment of each grain through finite element analysis , the initial setting assumes that the strain increment of grain r is equal to the strain increment of RVE scale, which is , the RVE scale stress increment is obtained based on the single grain modeling unit and the RVE scale modeling unit .

[0117] The electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the method for constructing the elastic-viscoplastic multi-scale constitutive model of the polycrystalline material is implemented.

[0118] The computer-readable storage medium of the present invention stores a computer program, and when the computer program is executed by a processor, the method for constructing the elastic-viscoplastic multi-scale constitutive model of the polycrystalline material is implemented.

[0119] The computer-readable storage media may include RAM, ROM, EEPROM, CDROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory, or any other media that can be used to store program code in the form of instructions or data structures and that can be accessed by a computer.

[0120] The processor is used to execute the computer program stored in the memory to implement each step of the method involved in the above embodiment.

Claims

1. A method for constructing an elastic-viscoplastic multi-scale constitutive model of a polycrystalline material, characterized in that: The steps include: (1) Establish a representative volume element model (RVE) of polycrystalline materials; (2) Based on the representative volume element model, a single crystal scale constitutive model is established based on the small deformation assumption, and the stress rate of grain r is obtained by linearization. and strain rate The relationship between: Where L r is the algorithmic tangent operator of grain r, is the affine strain rate of grain r; (3) According to the stress rate of grain r and strain rate , assuming that the stress rate of the RVE scale and strain rate The relationship between: Subscript 0 indicates RVE; (4) Establishment Stress local tensor B r and b r , local strain tensor A r and a r and and the affine strain rate at the representative volume element scale The relationship between: Among them, M r is the algorithmic flexibility operator of grain r, M r :L r =I, <> symbol represents the volume average of each grain; (5) For the same time increment, the stress rate, strain rate and affine strain rate are converted into incremental stress increment, strain increment and affine strain increment, and the strain increment Δε of each grain is iteratively calculated by finite element analysis. r , the initial setting assumes that the strain increment of grain r is equal to the strain increment of RVE scale, that is, Δε r =Δε0, and the stress increment Δσ0 of the RVE scale is obtained according to the formula established in steps (2) to (4); Step (5) comprises the following steps: (5.1), with the initial setting Δε r =Δε0, the algorithmic tangent operator L of the grain is calculated by step (2) r and the affine strain increment Set the algorithmic tangent operator and affine strain increment of the RVE scale to be equal to the volume average of the algorithmic tangent operator and affine strain increment of each grain. The superscript 0 indicates the initial value before the iteration starts; (5.2) Through steps (3) and (4) using and Calculate the stress local tensor Strain local tensor Algorithmic tangent operator for RVE scale and the affine strain increment ii is the number of iteration steps; (5.3) Calculate the first tolerance and second tolerance of the algorithm tangent operator and affine strain increment of the RVE scale between the ii-th iteration and the ii-1-th iteration respectively, until the first tolerance or the second tolerance is less than the corresponding threshold, the calculation is terminated, otherwise let Return to step (5.2); (5.4) Calculate the stress increment of the grain using the local strain tensor through step (4) The superscript jj is the second iteration number. The third tolerance of the grain stress increment between the jj-th iteration and the jj-1-th iteration is calculated until the third tolerance is less than the corresponding threshold value. The calculation is terminated. Otherwise, let Return to step (5.1).

2. The method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials according to claim 1, characterized in that: In step (2), the strain rate of the grain Stress rate of grain r Among them C r is the elastic modulus of grain r, is the elastic strain rate, and the viscoplastic strain rate Originated from the slip system.

3. The method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials according to claim 2, characterized in that: In step (2), the viscoplastic strain rate The Schmid factor of the slip system α Slip ratio of slip system α s α is the unit vector of the sliding direction, m α is the unit vector in the normal direction of the slip surface, is the reference slip rate, g α is the current strength of the slip system α, n is the rate sensitivity parameter, τ α is the shear stress of slip system α, which depends on the current stress magnitude and the Schmid factor, The Voce hardening law is used to describe the strain hardening behavior of grains. The strength change rate of the current slip system α is The threshold intensity for where Γ is the accumulated shear force within the grain, and are the initial critical shear stress and the reverse critical shear stress, and are the initial hardening rate and progressive hardening rate of slip system α.

4. The method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials according to claim 1, characterized in that: In step (2), the algorithm tangent operator in C r is the elastic modulus of grain r, and are the slip rates of slip systems α and β, and are the Schmid factors of slip system α and slip system β, τ α is the shear stress of slip system α, is the reference slip rate of the α slip system, δ αβ is the Kronecker Delta function, θ is the integration parameter, and Δt is the time increment.

5. The method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials according to claim 1, characterized in that: In step (2), the affine strain rate of grain r is Viscoplastic strain rate Originated from the slip system.

6. The method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials according to claim 1, characterized in that: In step (4), M0=<Μ r :B r > matrix ; Among them, M0 and M r is the RVE scale and grain r algorithm flexibility operator, are the interaction flexibility tensor and interaction stiffness tensor, M r :L r =I, M0:L0=I, I is the identity matrix, S r is the Eshelby tensor with respect to grain r; Calculate L0 and And calculate the stress increment of RVE scale through step (3).

7. A system for constructing an elastic-viscoplastic multi-scale constitutive model of polycrystalline materials, characterized in that: include: The grain modeling unit is used to establish a representative volume element model RVE of polycrystalline materials; a single crystal scale constitutive model is established based on the representative volume element model and the small deformation assumption, and the stress rate of the grain r is obtained by linearization. and strain rate The relationship between: Where L r is the algorithmic tangent operator of grain r, is the affine strain rate of grain r; RVE scale modeling unit is used to calculate the stress rate according to the grain r and strain rate , assuming that the stress rate of the RVE scale and strain rate The relationship between: Subscript 0 indicates RVE; establish Stress local tensor B r and b r , local strain tensor A r and a r and and the affine strain rate at the representative volume element scale The relationship between: Among them, M r is the algorithmic flexibility operator of grain r, M r :L r =I, <> symbol represents the volume average of each grain; Iterative solution unit, for the same time increment, converts stress rate, strain rate and affine strain rate into incremental stress increment, strain increment and affine strain increment, and iteratively calculates the strain increment Δε of each grain through finite element analysis r , the initial setting assumes that the strain increment of grain r is equal to the strain increment of RVE scale, that is, Δε r =Δε0, the RVE scale stress increment Δσ0 is obtained based on the grain modeling unit and the RVE scale modeling unit; The iterative solution unit includes the following steps: (a), initial setting Δε r =Δε0, the algorithmic tangent operator L of the grain is calculated by the grain modeling unit r and the affine strain increment Set the algorithmic tangent operator and affine strain increment of the RVE scale to be equal to the volume average of the algorithmic tangent operator and affine strain increment of each grain. The superscript 0 indicates the initial value before the iteration starts; (b) Utilization of RVE scale modeling units and Calculate the stress local tensor Strain local tensor Algorithmic tangent operator for RVE scale and the affine strain increment ii is the number of iteration steps; (c) Calculate the first tolerance and second tolerance of the algorithm tangent operator and affine strain increment of the RVE scale between the ii-th iteration and the ii-1-th iteration respectively, until the first tolerance or the second tolerance is less than the corresponding threshold, and then end the calculation. Otherwise, let Return to step (b); (d) Calculation of grain stress increment using strain local tensor through RVE scale modeling unit The superscript jj is the second iteration number. The third tolerance of the grain stress increment between the jj-th iteration and the jj-1-th iteration is calculated until the third tolerance is less than the corresponding threshold value. The calculation is terminated. Otherwise, let Return to step (a).

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into a processor, the method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for constructing the elastic-viscoplastic multi-scale constitutive model of polycrystalline materials according to any one of claims 1 to 6 is implemented.

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