A cellular automaton method for simulating continuous dynamic recrystallization behavior of alloys

Abstract

The application discloses a cellular automaton method for simulating continuous dynamic recrystallization behavior of an alloy, and comprises the following steps: (1) generating an initial microstructure; (2) carrying out cellular topological deformation calculation, and updating a cellular state variable; (3) establishing a dislocation density evolution model, and generating subgrain nucleation in an original grain; (4) establishing a subgrain rotation and growth model, and calculating subgrain orientation change and small-angle grain boundary migration rate; (5) establishing a high-angle grain boundary migration model, and calculating a growth speed of newly generated recrystallization grains; and (6) outputting grain topological morphology, average subgrain / grain size, recrystallization fraction, and small-angle / high-angle grain boundary fraction. The cellular automaton method for simulating continuous dynamic recrystallization behavior of the alloy can accurately simulate the continuous dynamic recrystallization behavior of the alloy, and provides technical guidance for alloy process parameter setting and microstructure regulation.

Description

Technical Field

[0001] This invention belongs to the field of numerical calculation of alloy plastic forming, and relates to a cellular automata method for simulating the continuous dynamic recrystallization behavior of alloys. Background Technology

[0002] Large and complex alloy components are typically manufactured using multi-pass thermoplastic forming methods such as forging, rolling, and extrusion. During the forming process of these components, the microstructure of the alloy undergoes highly complex evolution. Dynamic recrystallization is a physical phenomenon that occurs in metals during hot working; recrystallization can refine grains and is a powerful way to improve material properties.

[0003] For high-fault-energy metals (Ti, α-Fe, Al, etc.), extended dislocations tend to cluster, while whole dislocations tend to climb and cross-slip. Dynamic recovery plays a dominant role. Insufficient dislocation accumulation makes it difficult to trigger discontinuous dynamic recrystallization, and continuous dynamic recrystallization is the main microstructure evolution mechanism. However, the microstructure evolution of high-fault-energy metals during continuous dynamic recrystallization is very complex, involving a series of microstructure changes such as subgrain nucleation, subgrain rotation and growth, high-angle grain boundary migration, and microstructure topological deformation. Currently, there is a lack of a method that can accurately, quantitatively, and visually simulate the microstructure evolution of alloys, and therefore, it is impossible to provide a reliable predictive means for optimizing the thermoplastic forming process and controlling the microstructure of parts.

[0004] The patent specification with publication number CN110929416A discloses a method for simulating the microstructure evolution process of Ni-Mn-In alloy based on cellular automata. The recrystallization mechanism involved in this method is discontinuous dynamic recrystallization, and recrystallization nucleation only occurs at grain boundaries. It cannot simulate the continuous dynamic recrystallization behavior of high fault energy metals.

[0005] The patent specification with publication number CN110706758B discloses a multi-level cellular automaton method for simulating dynamic recrystallization. This method discretizes potential grain boundary cell nuclei during the nucleation process in multiple levels to simulate the incubation period and nucleation rate of the actual nucleation process. However, the recrystallization mechanism is discontinuous dynamic recrystallization and cannot predict the continuous dynamic recrystallization behavior of the alloy.

[0006] The patent specification with publication number CN114417664A discloses an online simulation and visualization method for the microstructure evolution of hot-rolled steel based on cellular automata. The dislocation density evolution is based on the traditional KM equation, which does not involve high-angle grain boundary migration sweeping dislocations with volume absorption. Furthermore, the grain boundary is selected as a potential nucleation site, which cannot realize subcrystalline nucleation and growth inside the original grain, and cannot simulate the continuous dynamic recrystallization microstructure evolution of the alloy.

[0007] The patent specification with publication number CN105740513B discloses a method for simulating the dynamic recrystallization of GH4169 alloy during hot deformation. The method is based on the phenomenological theory of dynamic recrystallization, which does not have obvious physical meaning. Furthermore, recrystallization nucleation only occurs in grain boundary cells, and the recrystallization mechanism is described as discontinuous dynamic recrystallization. It cannot calculate and simulate the continuous dynamic recrystallization behavior of the alloy, nor can it predict the microstructure evolution during the deformation process of high-level fault energy metals.

[0008] The patent specification with publication number CN105653822B discloses a cellular automata method for simulating the static recrystallization behavior of GH4169 alloy. This method can accurately predict the microstructure evolution that occurs during the heat preservation process after alloy deformation. The described recrystallization mechanism is static recrystallization and cannot simulate the recrystallization behavior that occurs during the hot deformation process of the alloy.

[0009] The paper “Feng Rui, Wang Kelu, Lu Shiqiang, Li Xin, Ouyang Delai, Zhou Xuan, Zhong Mingjun. Cellular Automata Simulation of Dynamic Recrystallization Behavior of BT25 Titanium Alloy. Journal of Mechanical Engineering, 2020, pp. 66-73” discloses a cellular automata simulation method for simulating the dynamic recrystallization behavior of BT25 titanium alloy. This method is used to simulate the discontinuous dynamic recrystallization behavior of titanium alloy, where recrystallized grains nucleate only at grain boundaries, and the dislocation density evolution equation is the traditional KM equation. This method cannot realize the nucleation, rotation, and growth of subgrains within grains, and therefore cannot simulate continuous dynamic recrystallization behavior.

[0010] The literature “Lei Liu, Yun-Xing Wu, Abdulrahaman-Shuaibu Ahmad. A novel simulation of continuous dynamic recrystallization process for 2219 aluminum alloy using cellular automata technique. Materials Science and Engineering A. 2021, pp. 141-256” discloses a cellular automata method for simulating the continuous dynamic recrystallization behavior of aluminum alloys. The initial microstructure described in this method already contains a large number of subgrains, and the subsequent subgrain nucleation and growth occur at the subgrain boundaries. It cannot realize that subgrains nucleate only inside the original grains during deformation, and cannot simulate the microstructure evolution from the initial annealed state (without subgrains) to the end of deformation in its entirety. Therefore, it cannot guide the control of actual process parameters. Summary of the Invention

[0011] To address the shortcomings of existing technologies, the present invention aims to provide a cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys, comprising the following steps:

[0012] Step 1: Generate the initial microstructure;

[0013] Step 2: Perform cell topological deformation calculations and update cell state variables;

[0014] Step 3: Establish a dislocation density evolution model, and generate subcrystalline nuclei inside the original grain;

[0015] Step 4: Establish a subgrain rotation and growth model, and calculate the subgrain orientation change and small-angle grain boundary migration rate;

[0016] Step 5: Establish a high-angle grain boundary migration model and calculate the growth rate of newly generated recrystallized grains;

[0017] Step 6: Output grain topology, average subgrain / grain size, recrystallization fraction, and small-angle / high-angle grain boundary fraction;

[0018] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 1 includes the following steps:

[0019] (1) Set the initial simulation region and grain size, discretize the simulation region into a cell mesh, and set the cell size and neighbor type;

[0020] (2) Assign initial values ​​to the cell state variables, which include grain orientation variables, grain numbering variables and grain boundary variables;

[0021] (3) Perform the following calculations on all cells: The current cell is the central cell. Calculate the grain boundary curvature of the cell. If the grain boundary curvature is greater than 0, the cell will transform. If the grain boundary curvature is equal to 0, calculate the change in grain boundary energy before and after the transformation. If the energy decreases, the current cell will transform into a neighboring cell. Calculate the grain size and assign the cell grain number variable. Calculate and assign the cell grain boundary variable.

[0022] (4) Repeat sub-step (3) of step 1 until the set grain size is reached.

[0023] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 2 includes the following steps:

[0024] (1) Set the critical strain value ε for topological deformation. c Calculate whether the subsequent simulated strain value is greater than ε. c If it is greater than , then calculate the grain and cell shape after deformation;

[0025] (2) After the topological deformation is completed, update the corresponding state variables; if the subsequent simulated strain value is less than ε cIf so, skip this step and proceed to step 3.

[0026] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 3 includes the following steps:

[0027] (1) Calculate and update the dislocation density variable of the cell. The calculation model is as follows:

[0028]

[0029] In the formula: ρ(ε) is the dislocation density, and ε is the strain. v is the strain rate. H f is the high-angle grain boundary migration velocity, D is the equivalent grain size, and f is the high-angle grain boundary migration velocity. H K represents the percentage of high-angle grain boundaries, and k1, k2, and k3 are material constants.

[0030] (2) Determine whether the dislocation density of the cell is greater than the critical dislocation density; if it is greater than the critical dislocation density, calculate the continuous dynamic recrystallization nucleation rate.

[0031] (3) Calculate the nucleation probability of intragranular cells, compare the nucleation probability with a random number generated by the computer, if the nucleation probability is greater than the random number (0-1) generated by the computer, then the current cell is selected as a subgrain nucleus, and the dislocation density variable of the current cell is reset to ρ0, the recrystallization number variable is incremented by 1 and the grain boundary migration distance variable is reset to 0, and the cell orientation variable value is set to the small angle grain boundary critical value;

[0032] (4) Repeat sub-step (3) in step 3 until all cells are judged and all cell boundary variables are calculated.

[0033] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 4 includes the following steps:

[0034] (1) Calculate the rotation of the subcell due to absorbed dislocations. The calculation formula is as follows:

[0035]

[0036] In the formula: θ is the subcell orientation value, b is the Burgers vector, n is the number of dislocations forming grain boundaries, α is the percentage of dynamic recovery dislocation density used to form critical small-angle grain boundaries, and S is the grain boundary area contained in a unit volume.

[0037] (2) Traverse the newly generated small-angle grain boundary cells and calculate the subgrain boundary migration driving force P. i With migration speed v i ;

[0038] (3) Calculate the migration distance L of the subgrain boundary cell;

[0039] (4) If the migration distance L of the subgrain boundary cell is greater than the unit cell size, the current cell is transformed; if the migration distances of several cells around the central cell simultaneously meet the requirements, the cell with the largest orientation difference is transformed; update the other state variables of the cell.

[0040] Compared with the prior art, the innovation and beneficial effects of the technical solution of the present invention are as follows: (1) The dislocation density evolution model of the cell is increased by the dislocation part absorbed by the migration of high-angle grain boundaries, which can accurately describe the dislocation density evolution law of the continuous dynamic recrystallization process of the alloy; (2) Subcrystalline nucleation only occurs inside the original grain, and the subcrystalline rotation model considers the influencing factors such as grain boundary area and dislocation density. The calculation results can accurately describe the subcrystalline orientation change; (3) The calculation results of grain boundary mobility reflect the influence of the size of the grain boundary orientation difference, which is consistent with the physical nature of alloy grain boundary migration; (4) The present invention is a continuous dynamic recrystallization simulation method based on physical mechanism, which can accurately, quantitatively and visually simulate the continuous dynamic recrystallization behavior of alloys, and help to achieve precise control of the microstructure of alloy components. Attached Figure Description

[0041] Figure 1 This is a flowchart simulating the continuous dynamic recrystallization behavior of TC18 titanium alloy in the single-phase region during deformation in a preferred embodiment of the present invention.

[0042] Figure 2 This is the initial structure generation process of the cellular automaton in a preferred embodiment of the present invention; wherein, (a) the initial grain diagram of TC18 titanium alloy after 3000 steps of calculation; (b) the initial grain diagram of TC18 titanium alloy after 30000 steps of calculation; and (c) the initial grain diagram of TC18 titanium alloy after 60000 steps of calculation.

[0043] Figure 3 This is a schematic diagram showing the predicted microstructure of TC18 titanium alloy (d = 340 μm, T = 890 °C) under different deformation conditions in a preferred embodiment of the present invention; (a1, a2, a3, a4) strain rates 0.1s -1 Microstructures with strains of 0.2, 0.4, 0.6, and 0.9, respectively; strain rates (b1, b2, b3, b4) It is 0.01s -1 Microstructures with strains of 0.2, 0.4, 0.6, and 0.9, respectively;

[0044] Figure 4 This is a schematic diagram of the microstructure experimental results of TC18 titanium alloy (d = 340 μm, T = 890 °C) under different deformation conditions in a preferred embodiment of the present invention; (a) strain rate 0.1s -1 (a) Microstructure with strain 0.9; (b) Strain rate It is 0.01s -1 Microstructure with a strain of 0.9;

[0045] Figure 5 This is a comparison chart of the measured and predicted average subgrain size of TC18 titanium alloy (d = 340 μm, T = 890 °C) under different deformation conditions in a preferred embodiment of the present invention. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1 As shown, this invention is a cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys, comprising the following steps:

[0048] Step 1: Generate the initial microstructure;

[0049] Step 2: Perform cell topological deformation calculations and update cell state variables;

[0050] Step 3: Establish a dislocation density evolution model, and generate subcrystalline nuclei inside the original grain;

[0051] Step 4: Establish a subgrain rotation and growth model, and calculate the subgrain orientation change and small-angle grain boundary migration rate;

[0052] Step 5: Establish a high-angle grain boundary migration model and calculate the growth rate of newly generated recrystallized grains;

[0053] Step 6: Output grain topology, average subgrain / grain size, recrystallization fraction, and small-angle / high-angle grain boundary fraction;

[0054] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 1 includes the following steps:

[0055] (1) Set the initial simulation region size to 500×500μm 2 With a target grain size of 340 μm, the simulation region was discretized into a square cell grid, and the cell size was set to 2 μm and the molar neighbor type was set.

[0056] (2) Randomly assign grain orientation values ​​of 1-180° to all cells, with the initial grain number variable being 0 and the grain boundary variable being 0;

[0057] (3) Perform the following calculations on all cells: The current cell is the central cell. Calculate the grain boundary curvature of the cell. If the grain boundary curvature is greater than 0, the cell undergoes a transformation. If the grain boundary curvature is equal to 0, calculate the change in grain boundary energy before and after the transformation. If the energy decreases, the current cell transforms into a neighboring cell. Calculate the grain size and assign a grain number variable to the cell. Calculate and assign a grain boundary variable to the cell. The grain boundary variable includes intragranular 1, small-angle grain boundary 2, and large-angle grain boundary 3.

[0058] (4) Repeat sub-step (3) of step 1 until the set grain size of 340 μm is reached. The initial microstructure formation process is as follows: Figure 2 As shown, the grain growth process is continuous and uniform, the grain boundaries tend to be straight, and the morphology is equiaxed, which is an ideal normal growth.

[0059] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 2 includes the following steps:

[0060] (1) Set the critical strain value of topological deformation to 0.2, calculate whether the subsequent simulated strain value is greater than 0.2. If it is greater, calculate the grain and cell shape after deformation.

[0061] (2) After the topological deformation is completed, update the corresponding state variables; if the subsequent simulated strain value is less than 0.2, skip this step and proceed to step 3.

[0062] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 3 includes the following steps:

[0063] (1) Calculate and update the dislocation density variable of the cell. The calculation model is as follows:

[0064]

[0065] In the formula: ρ(ε) is the dislocation density, and ε is the strain. The strain rate is 0.001-1 s. -1 v H Here, f represents the high-angle grain boundary migration velocity, D represents the equivalent average grain size in the current calculation step, and f represents the high-angle grain boundary migration velocity. H The percentage represents the high-angle grain boundary content. k1, k2, and k3 are constants fitted based on rheological stress; in this embodiment, 0.1s is preferred. -1 The time was 7.09 × 10 8 m -1 15.83 and 2.41×10 11 Optimal 0.01s -1 The time was 2.51 × 10 8 m -1 18.5 and 9.62×1011 .

[0066] (2) Determine whether the cell dislocation density is greater than the critical dislocation density ρ. c If it is greater than the critical dislocation density, then calculate the continuous dynamic recrystallization nucleation rate. In this embodiment, 0.1s is preferred. -1 The critical dislocation density and recrystallization nucleation rate were taken as 1.63 × 10⁻⁶. 15 m -2 and 1.18×10 -3 s -1 ·μm -2 Optimal 0.01s -1 The time was 8.57 × 10 14 m -2 and 3.31×10 -4 s -1 ·μm -2 .

[0067] (3) Calculate the intracellular nucleation probability P n , S c Let Δt be the area of ​​a single cell, and Δt be the time step, assigned to the intracellular cell, and let the nucleation probability P be... n Compared with a computer-generated random number (0-1), if the nucleation probability P... n If the value is greater than the computer-generated random number, the current cell is selected as the subgrain nucleus, and the dislocation density variable of the current cell is reset to ρ0 = 10. 10 m -2 The recrystallization number variable is incremented by 1 and the grain boundary migration distance variable is reset to 0. The cell orientation variable value is set to the critical value of 2° for small-angle grain boundaries.

[0068] (4) Repeat sub-step (3) in step 3 until all cells are judged and all cell boundary variables are calculated.

[0069] Preferably, in the cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described above, step 4 includes the following steps:

[0070] (1) Calculate the rotation of the subcell due to absorbed dislocations. The orientation change model is as follows:

[0071]

[0072] In the formula: θ is the subcell orientation value, and b is the Burgers vector 2.86 × 10⁻⁶. -10 m and n are the number of dislocations forming grain boundaries (2), α is the percentage of dynamic recovery dislocation density used to form critical small-angle grain boundaries (0.45), and S is the grain boundary area contained in a unit volume.

[0073] (2) Traverse the newly generated small-angle grain boundary cells and calculate the subgrain boundary migration driving force P. i , In the formula, Δρ is the dislocation density difference, and τ is the dislocation line energy. γ L Small-angle grain boundary energy; calculate subgrain boundary migration velocity v. i v i =M L P i M L The small-angle grain boundary mobility is calculated using the following formula:

[0074]

[0075] In the formula: M0 is the large-angle grain boundary mobility, θ m The critical angle value is set to 15°, θ r The angle of cell orientation difference;

[0076] (3) Calculate the cell migration distance L, L = v i Δt;

[0077] (4) If the migration distance L of the subgrain boundary cell is greater than the unit cell size, the current cell is transformed; if the migration distances of several cells around the central cell simultaneously meet the requirements, the cell with the largest orientation difference is transformed; update the other state variables of the cell.

[0078] Using the above method, the continuous dynamic recrystallization behavior of TC18 titanium alloy under different deformation conditions was simulated. Figure 3 890℃, 0.1s -1 and 890℃, 0.01s -1 The changes in microstructure topology under deformation conditions with strains of 0.2, 0.4, 0.6, and 0.9 are described. Figure 4 890℃, 0.1s -1 and 890℃, 0.01s -1 The actual microstructure diagram when the strain is 0.9 under deformation conditions. Figure 5 This section compares the predicted and measured values ​​of the average subgrain size under the above conditions. Figure 3 , Figure 4 and Figure 5 The comparison results show that the present invention can accurately simulate the continuous dynamic recrystallization behavior of high-level fault energy alloys.

Claims

1. A cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys, characterized in that, The method specifically includes the following steps: Step 1: Generate the initial microstructure, which is divided into the following sub-steps: Step 1.1: Set the initial simulation region and grain size, and assign initial values ​​to the cell state variables; Step 1.2: Calculate the grain boundary curvature of the central cell. If the grain boundary curvature is greater than 0, the cell undergoes a transformation. If the grain boundary curvature is equal to 0, calculate the energy change of the grain boundary before and after the transformation. If the energy decreases, the current cell transforms into a neighboring cell. Step 1.3: Repeat step 1.2 until the set grain size is reached; calculate and assign cell grain number variables and grain boundary variables; Step 2: Perform cell topological deformation calculations and update cell state variables; Step 3: Establish a dislocation density evolution model, and generate subcrystalline nuclei inside the original grain; Step 4: Establish a subgrain rotation and growth model, and calculate the subgrain orientation change and small-angle grain boundary migration rate; Step 5: Establish a high-angle grain boundary migration model and calculate the growth rate of newly generated recrystallized grains; Step 6: Output grain topology, average subgrain / grain size, recrystallization fraction, and small-angle / high-angle grain boundary fraction; Step 3 can be implemented using the following sub-steps: Step 3.1: Calculate and update the dislocation density variable of the cell. The calculation model is as follows: In the formula: For dislocation density, In response, For strain rate, For high-angle grain boundary migration velocity, For equivalent grain size, This represents the percentage of high-angle grain boundary content. , and These are material constants; Step 3.2: Determine whether the dislocation density of the cell is greater than the critical dislocation density; if it is greater than the critical dislocation density, calculate the continuous dynamic recrystallization nucleation rate. Step 3.3: Calculate the nucleation probability of intragranular cells. If the nucleation probability is greater than the random number (0-1) generated by the computer, the current cell is selected as a subgrain nucleus. Continue until all cells have been determined, and then calculate the cell grain boundary variable.

2. The cellular automaton method for simulating the continuous dynamic recrystallization behavior of alloys as described in claim 1, characterized in that, Step 4 can be comprised of the following sub-steps: Step 4.1: Calculate the rotation of the subcell due to absorbed dislocations. The orientation change model is as follows: In the formula: For sub-cell orientation values, Burgers vector, The number of dislocations required to form grain boundaries, This represents the percentage of dynamic recovery dislocation density used to form critical small-angle grain boundaries. This refers to the area of ​​grain boundaries per unit volume; Step 4.2: Traverse the newly generated small-angle grain boundary cells and calculate the migration distance of the subgrain boundary cells; Step 4.3: If the migration distance of the subgrain boundary cell is greater than the unit cell size, the current cell will be transformed; if the migration distances of several cells around the central cell simultaneously meet the requirements, the cell with the largest orientation difference will be transformed.

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