Cellular automaton method for simulating static recrystallization of nickel-based superalloy

Abstract

Embodiments of the present disclosure provide a cellular automaton method for simulating static recrystallization of a nickel-based superalloy, comprising: establishing an initial microstructure geometric model on the basis of an initial microstructure metallographic picture; inputting static recrystallization conditions into the initial microstructure geometric model, wherein the static recrystallization conditions comprise a simulated temperature, a strain velocity, and a strain; determining a nucleation number in static recrystallization, wherein the nucleation number is determined by a nucleation rate; selecting a position for nucleation; calculating a driving force for growth of static recrystallization grains; and outputting a simulation result. In the embodiments of the present disclosure, by means of the above cellular automaton simulation method, preferential nucleation can be effectively performed at a high-energy position at a grain boundary triple junction, and recrystallization evolution is more in line with reality, thereby accurately reflecting the morphology characteristics and transformation dynamics of microstructure evolution inside the material under the combined action of thermal activation, grain boundary energy, etc., which cannot be realized by conventional cellular automaton simulation methods.

Description

A cellular automaton method for simulating static recrystallization of nickel-based superalloys Technical Field

[0001] The embodiments disclosed herein belong to the field of computational materials science and technology, specifically relating to a cellular automata method for simulating the static recrystallization of nickel-based superalloys. Background Technology

[0002] When the annealing temperature is high enough and the annealing time is long enough, new, strain-free grains—static recrystallization nuclei—are generated in the microstructure of deformed metals or alloys. These new grains grow continuously until the original deformed structure completely disappears, and the properties of the metal or alloy change significantly. This process is called static recrystallization. Static recrystallization, as a major mechanism for the evolution of metal microstructure, is considered an effective method for grain refinement. The new grains generated during static recrystallization and grain refinement are important factors affecting the load, microstructure, and product forming quality during hot working. Therefore, in-depth research into the kinetics and microstructure evolution during static recrystallization is crucial. Currently, the cellular automaton (CA) method has become a powerful tool for studying the evolution of material microstructure due to its significant advantages, such as not requiring interface tracking, high computational efficiency, and simplicity of implementation. Furthermore, the CA method has been widely applied and has a solid research foundation in predicting microstructure evolution, such as static recrystallization and grain growth.

[0003] However, when the current CA method model simulates the static recrystallization process, the nucleation process occurs randomly at the grain boundaries. In reality, the energy varies at different locations on the grain boundaries, and some locations have a clear nucleation advantage. This indicates that the existing model does not match the actual situation, so the original CA model still needs to be further improved and perfected.

[0004] Static recrystallization is a highly complex physical metallurgical process, and its actual evolution is influenced by numerous factors. For example, triple grain boundaries are typically areas of high density of crystal defects and localized high energy, which is conducive to the nucleation of static recrystallization during hot deformation. This phenomenon is widely recognized. However, traditional simulations using the Calibration and Coding (CA) method generally assume that static recrystallization nuclei form uniformly at grain boundaries, without considering the specific location of triple grain boundaries. Furthermore, the static recrystallization nucleation of the GH4169 alloy is primarily grain boundary bowing, requiring the acquisition of static recrystallized grains with large-angle grain boundaries. Generally, a grain orientation difference greater than 15° is considered a large-angle grain boundary. Therefore, during CA modeling, the orientation values ​​assigned to static recrystallized grains must ensure an orientation difference greater than 15° with surrounding grains to form large-angle grain boundaries. However, in traditional CA simulations, the orientation of static recrystallization nuclei is simply assigned randomly between 1 and 180, without considering the orientation difference between the static recrystallization nuclei and surrounding grains. Therefore, in order to solve this problem, it is necessary to develop a static recrystallization CA model that is more in line with reality.

[0005] Summary of the Invention

[0006] The embodiments disclosed herein aim to at least solve one of the technical problems existing in the prior art, and provide a cellular automata method for simulating static recrystallization of nickel-based superalloys.

[0007] Embodiments of this disclosure provide a cellular automaton method for simulating static recrystallization of nickel-based superalloys, comprising:

[0008] Step S1: Establish the initial microstructure geometric model based on the metallographic images of the initial microstructure of the nickel-based superalloy;

[0009] Step S2: Input static recrystallization conditions into the initial tissue geometry model; wherein, the static recrystallization conditions include simulation temperature, strain rate, and strain;

[0010] Step S3: Determine the number of nuclei formed during static recrystallization; wherein the number of nuclei is determined by the nucleation rate, and the model for the nucleation rate is shown in the following formula:

[0011] In the formula, For the model of the nucleation rate, C SRX E is a constant related to static recrystallization; E is the distortion energy accumulated within the material in the current state; E min Q is the minimum distortion energy required to initiate static recrystallization. SRX_nuc R is the activation energy required for static recrystallization nucleation; R is the gas constant; T in the formula is the current temperature (K);

[0012] Step S4: Select nucleation sites; at each computation time step, assign random numbers between 0 and 1 to the cells at nucleation sites, and correlate them with the nucleation probability P. nuc_SRX If the random number of the cell is less than P, then... nuc_SRX If the cell at that position forms a static recrystallization nucleus, then the cell at that position will not form a static recrystallization nucleus;

[0013] Step S5: Calculate the driving force for static recrystallization grain growth;

[0014] Step S6: Output the simulation results.

[0015] Optionally, the simulated temperature range is 1020℃~1060℃, and the strain rate is... The range is 0.005s. -1 ~0.015s -1 The strain ε ranges from 0.05 to 0.15.

[0016] Optionally, the simulated temperature is 1040℃, and the strain rate is... It is 0.01s -1 The strain ε is 0.1.

[0017] Optionally, before determining the number of static recrystallization nuclei in step S3, the method further includes: calculating the incubation period of the static recrystallization process;

[0018] The gestation period is calculated using the following formula:

[0019] In the formula, τ SRX The incubation period is defined as r0, which is the critical nucleation radius for static recrystallization; γ is the grain boundary energy at large angles; χ max M is the maximum radius of the subgrain; SRX is the static recrystallization grain boundary mobility, which is temperature-dependent; G is the accumulated storage energy of the material; M SRX G and G are respectively expressed as the following formulas:

[0020] In the formula, δD ob Q is a material constant; K is the Boltzmann constant; Q is a material constant. b_SRX σ is the activation energy for diffusion at grain boundaries during static recrystallization. m The stress at the end of pre-deformation; σ yield M is the yield stress of the material; Taylor α is the Taylor factor; μ is a constant; μ is the material shear modulus.

[0021] Optionally, the value of K ranges from 1.36 × 10⁻⁶. -23 J / K ~ 1.39 × 10 -23J / K; the value of α ranges from 0.3 to 0.7.

[0022] Optionally, the value of K is 1.38 × 10⁻⁶. -23 J / K; the value of α is 0.5.

[0023] Furthermore, the method also includes:

[0024] The nucleation probability model at triplet grain boundaries and ordinary grain boundaries is modified by introducing a nucleation probability location factor, where the nucleation probability is expressed as:

[0025] In the formula, P nuc_SRX β is the SRX kernel probability; nuc t is the nucleation probability location factor; step To calculate the time step; cell S represents the cell unit size; GB Calculate the total area of ​​grain boundaries within the domain.

[0026] Optionally, step S5 specifically includes:

[0027] The driving force for static recrystallization grain growth is calculated based on the following formula: P SRX =P dis -P gb ,

[0028] In the formula, P SRX P is the total driving force for the growth of static recrystallized grains. gb The driving force related to the grain boundary energy difference; P dis The driving force related to the dislocation density difference; P dis Represented as: P dis =αμb 2 Δρ,

[0029] In the formula, α is the material constant; b is the Burgers vector mode; Δρ is the dislocation density difference between adjacent grains; and P gb It can be represented as: P gb =κγ,

[0030] In the formula, κ is the grain boundary curvature; where the grain boundary curvature κ is expressed as:

[0031] In the formula, A is the topology parameter; l cell C is the cell unit size, and kink is the number of cells in the extended molar neighborhood assuming the grain boundary is straight; i To expand the number of cells belonging to the current grain within the Mohs neighborhood; N long_moore To expand the total number of cells within Moore's neighbors.

[0032] Optionally, α is 0.5; A is 1.28; kink is 15; N long_moore The value is 24.

[0033] Optionally, static recrystallization grain growth occurs via grain boundary migration, where the grain boundary mobility is the kinetic coefficient determining the grain boundary migration rate; the grain boundary migration rate is expressed as: v SRX =M SRX P SRX ,

[0034] In the formula, v SRX The grain boundary migration rate is the rate of static recrystallization of grains.

[0035] The beneficial effects of the embodiments disclosed herein are as follows:

[0036] Compared with the prior art, the embodiments of this disclosure can effectively promote preferential nucleation at higher energy locations such as the three-pointed grain boundary through the above-described cellular automata simulation method. The recrystallization evolution is more realistic and can accurately reflect the morphological characteristics and transformation dynamics of the internal microstructure of the material under the combined effects of thermal activation and grain boundary energy. This is something that traditional cellular automata simulation methods cannot achieve. Attached Figure Description

[0037] Figure 1 is a schematic flowchart of a cellular automaton method for simulating static recrystallization of nickel-based superalloys according to an embodiment of the present disclosure.

[0038] Figure 2 is a metallographic diagram of the static recrystallization of a nickel-based superalloy according to another embodiment of the present disclosure;

[0039] Figure 3 is a metallographic diagram of the static recrystallization of a nickel-based superalloy according to another embodiment of this disclosure;

[0040] Figure 4 is a schematic diagram of the microstructure evolution of SRX under two nucleation modes: preferential nucleation at the three-point grain boundary and random nucleation at the grain boundary, according to an embodiment of this disclosure. Detailed Implementation

[0041] To enable those skilled in the art to better understand the technical solutions of this disclosure, the disclosure will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] The embodiments of this application will be further described in detail below with reference to the accompanying drawings and examples. The detailed descriptions and accompanying drawings of the following embodiments are used to exemplarily illustrate the principles of this application, but should not be used to limit the scope of this application; that is, this application is not limited to the described embodiments. In the description of this application, it should be noted that, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," "outer," etc., indicating orientation or positional relationships are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. "Vertical" is not strictly vertical, but within the allowable error range. "Parallel" is not strictly parallel, but within the allowable error range.

[0043] In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application depending on the specific circumstances.

[0044] As shown in Figure 1, a cellular automaton method for simulating static recrystallization of nickel-based superalloys includes:

[0045] Step S1: Establish an initial microstructure geometric model based on the metallographic image of the initial microstructure of the nickel-based superalloy; wherein, the initial microstructure geometric model includes characteristics such as grain size and distribution of the grain structure.

[0046] Step S2: Input static recrystallization conditions into the initial tissue geometry model; wherein, the static recrystallization conditions include simulation temperature, strain rate and strain.

[0047] Step S3: Determine the number of static recrystallization nuclei; wherein the number of nuclei is determined by the nucleation rate.

[0048] Specifically, in this step, the static recrystallization process does not begin instantly upon heating; rather, it requires a certain incubation period. It only begins when the energy for static recrystallization accumulates to a certain level. The incubation period can be calculated using the following formula:

[0049] In the formula, r0 is the critical nucleation radius for static recrystallization; γ is the grain boundary energy of a large-angle grain boundary; and χ is the grain boundary energy of a large-angle grain boundary. max M is the maximum radius of the subgrain. SRXM represents the grain boundary mobility of static recrystallized grains, which is temperature-dependent, and G represents the accumulated stored energy of the material. SRX G can be expressed as equation (2) and equation (3) respectively:

[0050] In the formula, δD ob is a material constant; K is the Boltzmann constant, with a value ranging from 1.36 × 10⁻⁶. -23 J / K ~ 1.39 × 10 -23 J / , preferably 1.38 × 10 -23 J / K; Q b_SRX This is the activation energy for diffusion at grain boundaries during static recrystallization.

[0051] In the formula, σ m σ is the stress at the end of the pre-deformation process. yield M is the yield stress of the material. Taylor α is the Taylor factor, and in equation (3), α is a constant with a value ranging from 0.3 to 0.7. For most alloys, the value is 0.5. μ is the material shear modulus.

[0052] Once the incubation period is reached, the static recrystallization nucleation process begins, and the nucleation rate model is as follows:

[0053] In the formula, C SRX E is a constant related to static recrystallization, and E is the distortion energy accumulated within the material in the current state. min Q is the minimum distortion energy required for the initiation of static recrystallization. SRX_nuc R is the activation energy required for static recrystallization nucleation, R is the gas constant, and T in equation (4) is the current temperature in K).

[0054] Step S4: Select the nucleus location.

[0055] Specifically, in this step, during the static recrystallization simulation using the CA method, a random number between 0 and 1 is assigned to the nucleation site cell at each computation time step, and this value is compared with the nucleation probability P. nuc_SRX If the random number of the cell is less than P, then... nuc_SRX If the cell at that position does not form a static recrystallization nucleus, then the cell at that position will form a static recrystallization nucleus; otherwise, the cell at that position will not form a static recrystallization nucleus.

[0056] Furthermore, in order to distinguish the different nucleation probabilities at ordinary grain boundaries and triple grain boundaries, this embodiment of the present disclosure introduces a nucleation probability location factor to modify the nucleation probability model at triple grain boundaries and ordinary grain boundaries. The nucleation probability is expressed as:

[0057] In the formula, P nuc_SRXLet β be the SRX kernel probability. nuc t is the nucleation probability location factor. step To calculate the time step, l cell S is the cell unit size. GB Calculate the total area of ​​grain boundaries within the domain.

[0058] Step S5: Calculate the driving force for static recrystallization grain growth.

[0059] Specifically, in this step, the driving force for static recrystallization grain growth can be calculated according to the following formula (6): P SRX =P dis -P gb (6),

[0060] In the formula, P SRX P is the total driving force for static recrystallization grain growth. gb P is the driving force related to the grain boundary energy difference. dis P is the driving force related to the dislocation density difference. dis Represented as: P dis =αμb 2 Δρ(7),

[0061] In the formula, α is a material constant, which is 0.5 for most alloys, b is the Burgers vector modulus, and Δρ is the dislocation density difference between adjacent grains. In formula (7), P gb Represented as: P gb =κγ(8),

[0062] In the formula, κ represents the grain boundary curvature. The grain boundary curvature is expressed as:

[0063] In the formula, A is the topology parameter, and its value is taken as 1.28, l cell Where C is the cell unit size, kink is the number of cells in the extended molar neighborhood assuming the grain boundary is straight, with a value of 15, and C i To expand the number of cells belonging to the current grain within the mole neighborhood, N long_moore To expand the total number of cells within the Moore neighborhood, the value is 24.

[0064] Static recrystallization grain growth occurs via grain boundary migration, and the grain boundary mobility rate is the kinetic coefficient determining the grain boundary migration rate. Therefore, the growth process depends not only on the driving force but also on the grain boundary mobility rate. The classical grain boundary migration rate is expressed as: v SRX =M SRX P SRX (10),

[0065] In the formula, v SRX The grain boundary migration rate is the rate of static recrystallization of grains.

[0066] Step S6: Output the simulation results.

[0067] Specifically, the above method is implemented by a computer, including:

[0068] (1) The input austenitic uniform grain structure is used as the initial structure, and the average grain size is set after solution treatment.

[0069] (2) The actual time corresponding to the current calculation step is obtained based on the time step and the calculation step. The time step can be calculated using the following formula:

[0070] (3) Compare the current calculation time with the incubation period. If the current time has not reached the incubation period, no static recrystallization calculation will be performed in the calculation domain. If the current time has reached the incubation period, the subsequent steps will be performed.

[0071] (4) After the nucleation and incubation period conditions are met, a cell is randomly selected at the original grain boundary, and a random number r between 0 and 1 is assigned to the current calculation cell. rand The number of static recrystallization nuclei N at the current time step is calculated using the nucleation rate model (Equation (5)). SRX_tstep The nucleation probability P at the current time step is calculated. SRX_tstep Compare the random number of the current cell with the nucleation probability P. SRX_tstep The size of r rand <P SRX_tstep If the nucleation condition is met, the current cell transforms from a matrix structure into a static recrystallization nucleus, the recrystallization state of the cell changes to a static recrystallization state, and the state variable changes from 0 to 1. Conversely, if the nucleation condition is not met, the current cell does not satisfy the nucleation condition, and the recrystallization state variable of the cell remains unchanged.

[0072] (5) Traverse all cells in the current computational domain, and determine whether each cell satisfies the aforementioned cell transformation rules. For cells that simultaneously satisfy all cell transformation rules, perform cell state transformation, static recrystallization grain boundary migration, and realize static recrystallization grain growth.

[0073] (6) Compare whether the current calculation time has reached the set duration. If not, return to step (2) to continue the calculation. If the set duration has been reached, terminate the calculation and output the required simulation results.

[0074] Compared with the prior art, the embodiments of this disclosure have the following beneficial effects: the above-mentioned cellular automata simulation method can effectively promote preferential nucleation at the higher energy locations of the triple grain boundaries, and the recrystallization evolution is more in line with reality. It can accurately reflect the morphological characteristics and transformation dynamics of the internal microstructure of the material under the combined effects of thermal activation, grain boundary energy, etc., which is something that traditional cellular automata simulation methods cannot achieve.

[0075] The present disclosure will now be described in further detail with reference to the accompanying drawings and embodiments.

[0076] Example 1

[0077] A cellular automaton method for simulating static recrystallization of nickel-based superalloys includes:

[0078] Step S1: Establish an initial microstructure geometric model based on the metallographic images of the initial microstructure of GH4169 alloy. The initial microstructure geometric model includes characteristics such as grain size and distribution.

[0079] Step S2: Input static recrystallization conditions, including simulation temperature. T = 1040℃, strain ε = 0.1, strain rate

[0080] Step S3: Determine the number of nuclei for static recrystallization. The number of nuclei is determined by the nucleation rate.

[0081] Step S4: Select the nucleus location.

[0082] Step S5: Calculate the driving force for static recrystallization grain growth.

[0083] Step S6: Output the simulation results.

[0084] The metallographic structure of the nickel-based superalloy after static recrystallization under the static recrystallization conditions defined in this embodiment for 20 seconds is shown in Figure 2a.

[0085] Example 2

[0086] A cellular automaton method for simulating static recrystallization of nickel-based superalloys includes:

[0087] Step S1: Establish an initial microstructure geometric model based on the metallographic images of the initial microstructure of GH4169 alloy. The initial microstructure geometric model includes characteristics such as grain size and distribution.

[0088] Step S2: Input static recrystallization conditions, including simulation temperature T = 1040℃, strain ε = 0.1, and strain rate.

[0089] Step S3: Determine the number of nuclei for static recrystallization. The number of nuclei is determined by the nucleation rate.

[0090] Step S4: Select the nucleus location.

[0091] Step S5: Calculate the driving force for static recrystallization grain growth.

[0092] Step S6: Output the simulation results.

[0093] The metallographic structure of the nickel-based superalloy after static recrystallization under the static recrystallization conditions defined in this embodiment for 20 seconds is shown in Figure 2b.

[0094] Example 3

[0095] A cellular automaton method for simulating static recrystallization of nickel-based superalloys includes:

[0096] Step S1: Establish an initial microstructure geometric model based on the metallographic images of the initial microstructure of GH4169 alloy. The initial microstructure geometric model includes characteristics such as grain size and distribution.

[0097] Step S2: Input static recrystallization conditions, including simulation temperature T = 1040℃, strain ε = 0.1, and strain rate.

[0098] Step S3: Determine the number of nuclei for static recrystallization. The number of nuclei is determined by the nucleation rate.

[0099] Step S4: Select the nucleus location.

[0100] Step S5: Calculate the driving force for static recrystallization grain growth.

[0101] Step S6: Output the simulation results.

[0102] The metallographic structure of the nickel-based superalloy after static recrystallization under the static recrystallization conditions defined in this embodiment for 20 seconds is shown in Figure 2c.

[0103] Example 4

[0104] A cellular automaton method for simulating static recrystallization of nickel-based superalloys includes:

[0105] Step S1: Establish an initial microstructure geometric model based on the metallographic images of the initial microstructure of GH4169 alloy. The initial microstructure geometric model includes characteristics such as grain size and distribution.

[0106] Step S2: Input static recrystallization conditions, including simulation temperature T = 1040℃, strain ε = 0.1, and strain rate.

[0107] Step S3: Determine the number of nuclei for static recrystallization. The number of nuclei is determined by the nucleation rate.

[0108] Step S4: Select the nucleus location.

[0109] Step S5: Calculate the driving force for static recrystallization grain growth.

[0110] Step S6: Output the simulation results.

[0111] Figure 3 shows the metallographic structure of the nickel-based superalloy after static recrystallization under the static recrystallization conditions defined in this embodiment and after holding at the temperature for 200 s.

[0112] The evolution of the microstructure of two nucleation modes, preferential nucleation at the three grain boundaries and random nucleation at the grain boundaries, in the cellular automaton method for simulating static recrystallization of nickel-based superalloys according to the embodiments of this disclosure, will be explained below with reference to Figure 4.

[0113] As shown in Figure 4, Figure 4(a) shows the microstructure evolution of SRX after preferential nucleation at the three-way grain boundary for 50 s, Figure 4(b) shows the microstructure evolution of SRX after preferential nucleation at the three-way grain boundary for 100 s, Figure 4(c) shows the microstructure evolution of SRX after preferential nucleation at the three-way grain boundary for 200 s, Figure 4(d) shows the microstructure evolution of SRX after random nucleation at the grain boundary for 50 s, Figure 4(e) shows the microstructure evolution of SRX after random nucleation at the grain boundary for 100 s, and Figure 4(f) shows the microstructure evolution of SRX after random nucleation at the grain boundary for 200 s.

[0114] It is understood that the above embodiments are merely exemplary embodiments used to illustrate the principles of this disclosure, and this disclosure is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and substance of this disclosure, and these modifications and improvements are also considered to be within the scope of protection of this disclosure.

Claims

1. A cellular automaton method for simulating static recrystallization of nickel-based superalloys, characterized in that, The method includes: Step S1: Establish the initial microstructure geometric model based on the metallographic images of the initial microstructure of the nickel-based superalloy; Step S2: Input static recrystallization conditions into the initial tissue geometry model; wherein, the static recrystallization conditions include simulation temperature, strain rate, and strain; Step S3: Determine the number of nuclei formed during static recrystallization; wherein the number of nuclei is determined by the nucleation rate, and the model for the nucleation rate is shown in the following formula: In the formula, For the model of the nucleation rate, C SRX E is a constant related to static recrystallization; E is the distortion energy accumulated within the material in the current state; E min Q is the minimum distortion energy required to initiate static recrystallization. SRX_nuc R is the activation energy required for static recrystallization nucleation; R is the gas constant; T in the formula is the current temperature (K); Step S4: Select nucleation sites; at each computation time step, assign random numbers between 0 and 1 to the cells at nucleation sites, and correlate them with the nucleation probability P. nuc_SRX If the random number of the cell is less than P, then... nuc_SRX If the cell at that position forms a static recrystallization nucleus, then the cell at that position will not form a static recrystallization nucleus; Step S5: Calculate the driving force for static recrystallization grain growth; Step S6: Output the simulation results.

2. The cellular automaton method for simulating static recrystallization of nickel-based superalloys according to claim 1, characterized in that, The simulated temperature range is 1020℃~1060℃, and the strain rate is... The range is 0.005s. -1 ~0.015s -1 The strain ε ranges from 0.05 to 0.

15.

3. The cellular automaton method for simulating static recrystallization of nickel-based superalloys according to claim 2, characterized in that, The simulated temperature was 1040℃, and the strain rate was... It is 0.01s -1 The strain ε is 0.

1.

4. A cellular automaton method for simulating static recrystallization of nickel-based superalloys according to any one of claims 1 to 3, characterized in that, Before determining the number of static recrystallization nuclei in step S3, the method further includes: calculating the incubation period of the static recrystallization process; The gestation period is calculated using the following formula: In the formula, τ SRX The incubation period is defined as r0, which is the critical nucleation radius for static recrystallization; γ is the grain boundary energy at large angles; χ max M is the maximum radius of the subgrain; SRX is the static recrystallization grain boundary mobility, which is temperature-dependent; G is the accumulated storage energy of the material; M SRX G and G are respectively expressed as the following formulas: In the formula, δD ob Q is a material constant; K is the Boltzmann constant; Q is a material constant. b_SRX σ is the activation energy for diffusion at grain boundaries during static recrystallization. m The stress at the end of pre-deformation; σ yield M is the yield stress of the material; Taylor α is the Taylor factor; μ is a constant; μ is the material shear modulus.

5. The cellular automaton method for simulating static recrystallization of nickel-based superalloys according to claim 4, characterized in that, The value of K is in the range of 1.36 × 10⁻⁶. -23 J / K ~ 1.39 × 10 -23 J / K; the value of α ranges from 0.3 to 0.

7.

6. The cellular automaton method for simulating static recrystallization of nickel-based superalloys according to claim 5, characterized in that, The value of K is 1.38 × 10 -23 J / K; the value of α is 0.

5.

7. A cellular automaton method for simulating static recrystallization of nickel-based superalloys according to any one of claims 1 to 3, characterized in that, The method further includes: The nucleation probability model at triplet grain boundaries and ordinary grain boundaries is modified by introducing a nucleation probability location factor, where the nucleation probability is expressed as: In the formula, P nuc_SRX β is the SRX kernel probability; nuc t is the nucleation probability location factor; step To calculate the time step; cell S represents the cell unit size; GB Calculate the total area of ​​grain boundaries within the domain.

8. A cellular automaton method for simulating static recrystallization of nickel-based superalloys according to any one of claims 1 to 3, characterized in that, Step S5 specifically includes: The driving force for static recrystallization grain growth is calculated based on the following formula: P SRX =P dis -P gb , In the formula, P SRX P is the total driving force for the growth of static recrystallized grains. gb The driving force related to the grain boundary energy difference; P dis The driving force related to the dislocation density difference; P dis Represented as: P dis =amb 2 Dr. In the formula, α is the material constant; b is the Burgers vector mode; Δρ is the dislocation density difference between adjacent grains; and P gb It can be represented as: P gb =kg, In the formula, κ is the grain boundary curvature; where the grain boundary curvature κ is expressed as: In the formula, A is the topology parameter; l cell C is the cell unit size, and kink is the number of cells in the extended molar neighborhood assuming the grain boundary is straight; i To expand the number of cells belonging to the current grain within the Mohs neighborhood; N long_moore To expand the total number of cells within Moore's neighbors.

9. The cellular automaton method for simulating static recrystallization of nickel-based superalloys according to claim 8, characterized in that, The value of α is 0.5; the value of A is 1.28; the value of kink is 15; N long_moore The value is 24.

10. The cellular automaton method for simulating static recrystallization of nickel-based superalloys according to claim 4, characterized in that, Static recrystallization grain growth occurs via grain boundary migration, and the grain boundary migration rate is the kinetic coefficient that determines the grain boundary migration rate; the grain boundary migration rate is expressed as: v SRX =M SRX P SRX , In the formula, v SRX The grain boundary migration rate is the rate of static recrystallization of grains.

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