A method for determining edge mixed crystal of high-temperature alloy bar in experiment and simulation double driving

CN122901401APending Publication Date: 2026-10-13西部超导材料科技股份有限公司
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Patent Information

Application Number
CN202611044855.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-07-14
Publication Date
2026-10-13

AI Technical Summary

Technical Problem

然而,针对热加工过程的数值模拟技术也面临结果无法有效验证,准确性有待提升的问题

Benefits of technology

1.该方法结合多批次实验数据与有限元模拟验证,解决了现有锻造模拟准确性难以验证、模拟结果精确度不足的问题。

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Abstract

The application discloses a method for determining edge mixed crystal of high-temperature alloy rod by experiment and simulation double driving, which comprises the following steps: S1, obtaining the peak stress of GH738 alloy under different deformation temperatures and strain rates, and establishing a constitutive model of hot working of the GH738 alloy; S2, performing macro corrosion analysis on batches of GH738 rods prepared by different forging processes; S3, performing numerical simulation on the corresponding forging process in S2, combining the simulation with the macro mixed crystal structure analysis data of the actual forged rods, and obtaining a critical mixed crystal factor epsilon p of the GH738 alloy rod; S4, simulating and optimizing the equivalent strain distribution epsilon of the rod prepared by the process, combining the critical mixed crystal factor epsilon p , and determining the feasibility of the process; S5, optimizing the forging scheme of the process in which the edge equivalent strain epsilon is greater than or equal to the critical mixed crystal factor epsilon p , preparing the GH738 rod, and obtaining the GH738 rod with no mixed crystal structure in the edge. The application can improve the accuracy of simulation, improve the structure uniformity of the GH738 rod, and reduce the experimental trial and error cost.
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Description

Technical Field

[0001] This invention belongs to the field of high-temperature alloy preparation technology, specifically relating to a method for determining edge mixed crystals in high-temperature alloy bars driven by both experiments and simulations. Background Technology

[0002] GH738 alloy, a typical precipitation-strengthened high-temperature alloy, is widely used in load-bearing components of aero-engines. Due to its narrow hot working window, the degree of recrystallization in GH738 alloy is highly sensitive to the matching relationship between deformation temperature, rate, and deformation amount. Mismatched process parameters can easily lead to localized non-recrystallization and mixed crystal problems, becoming a major bottleneck hindering the improvement of GH738 forged bar quality. Existing forging processes for GH738 bars are mainly based on experience-based trial and error methods, often requiring multiple iterations to obtain the optimal hot working process. This makes it difficult to guarantee cost and efficiency, and also fails to achieve real-time and accurate monitoring of microstructure changes in different regions of the bar.

[0003] Numerical simulation technology for material thermal processing is a rapidly developing and increasingly widely applied cutting-edge interdisciplinary field in recent years. Its core lies in leveraging the powerful computing capabilities of computers to solve the governing equations describing the complex multiphysics coupling during thermal processing, thereby achieving accurate prediction and in-depth analysis of the actual process in virtual space. This technological development has fundamentally changed the traditional process development model that relies on trial and error, ushering in a new paradigm of digital manufacturing: "theoretical prediction, simulation first, and experimental verification." However, numerical simulation technology for thermal processing also faces challenges such as the inability to effectively verify results and the need to improve accuracy.

[0004] Based on the above problems, this invention proposes a method for determining mixed crystals in GH738 that combines experiments and simulations. This method can improve the accuracy of simulations, accurately predict mixed crystals at the edges, and improve and optimize the forging process by combining simulations, thereby enhancing the microstructure uniformity of GH738 bars. Summary of the Invention

[0005] The purpose of this invention is to provide a method for determining edge mixed crystals in high-temperature alloy bars driven by both experiments and simulations. This method can improve the accuracy of simulations, accurately predict edge mixed crystals, and combine simulations to improve and optimize the forging process, thereby increasing the microstructure uniformity of GH738 bars and reducing experimental trial and error costs.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for determining edge mixed grains in high-temperature alloy bars, driven by both experimental and simulation methods, includes the following steps: S1. Obtain the peak stress of GH738 alloy at different deformation temperatures and strain rates. Based on the Arrhenius formula, establish a constitutive model for hot working of GH738 alloy. S2, Low-magnification corrosion analysis was performed on multiple batches of GH738 bars prepared by different forging processes. Combined with image recognition technology, the edge mixed crystal structure morphology and mixed crystal layer depth characteristics of GH738 bars under multiple batches and multiple process conditions were analyzed. S3. Numerical simulation of the forging process corresponding to S2 is performed. Combining the simulation data with the low-magnification mixed grain microstructure analysis data of the actual forged bars, the critical mixed grain factor ε of the GH738 alloy bars is obtained. p ; S4, combined with finite element simulation, performs simulation optimization design on forging deformation, single hammer reduction, and feed rate, simulates and optimizes the equivalent strain distribution ε of the bar material prepared by the process, and combines the critical mixed crystal factor ε. p To determine the feasibility of the process; S5, in the preferred simulation optimization process, the equivalent strain at the edge ε is greater than or equal to the critical mixed crystal factor ε. p The forging scheme was used to prepare GH738 bars, and GH738 bars without mixed grain structure at the edge were obtained.

[0007] Preferably, in step S2, the GH738 bars are all prepared using a high-speed forging machine, and the number of batches prepared is no less than 20.

[0008] Preferably, in S3, the critical mixed crystal factor ε of the GH738 alloy bar is... p It is the minimum equivalent variable value that characterizes the region when mixed crystals appear.

[0009] Preferably, in S3, the critical mixed crystal factor ε of the GH738 alloy bar is... p It is 0.8.

[0010] Preferably, in step S4, if the equivalent strain distribution ε of the bar prepared by the simulated optimized process is less than 0.8, the process is further optimized until the equivalent strain distribution ε of the bar prepared by the optimized process is greater than or equal to 0.8.

[0011] Compared with the prior art, the present invention has the following beneficial effects: 1. This method combines multiple batches of experimental data with finite element simulation verification, solving the problems of difficulty in verifying the accuracy of existing forging simulations and insufficient precision of simulation results.

[0012] 2. By introducing the critical mixed crystal factor ε p By combining experimental and simulation results, the forging deformation amount and process steps are optimized, significantly reducing the cost of process trial and error.

[0013] 3. This invention combines simulation to precisely control the reduction and rotation angle of each forging pass, optimizes the equivalent strain after deformation of each pass. Since the equivalent strain is related to the degree of recrystallization of the alloy, combined with experiments, the real-time temperature and recrystallization of each region of the bar can be accurately determined, effectively solving the problem of mixed crystals at the edges. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention.

[0015] Figure 2 These are typical characteristics of the lateral low-magnification edge mixed crystal structure morphology of GH738 prepared using different processes. Figure 2 (a) It exhibits four symmetrical mixed crystal arcs. Figure 2 (b) It exhibits two symmetrical mixed crystal arcs.

[0016] Figure 3 The equivalent strain distribution of GH738 bar at low magnification in the transverse direction was obtained through finite element simulation of the corresponding forging process. Figure 3 (a) is Figure 2 (b) Transverse equivalent strain distribution of bar stock simulated by forging process Figure 3 (b) is Figure 2 (a) Transverse equivalent strain distribution of bar stock simulated by forging process Figure 3 (c) is Figure 2 (b) Equivalent strain distribution on the overall surface of the bar stock as simulated by the forging process. Figure 3 (d) is Figure 2 (a) Equivalent strain distribution on the overall surface of the bar stock as simulated by the forging process.

[0017] Figure 4 This invention, in Example 1, simulates the equivalent strain distribution in the transverse direction of a GH738 alloy bar with a diameter of Φ230mm and the transverse microstructure of the prepared bar. Figure 4 (a) shows the simulated transverse equivalent strain distribution of the bar. Figure 4 (b) shows the transverse low-magnification structure of the bar. Figure 4 (c) shows the microstructure of the edge of the bar.

[0018] Figure 5 This invention, in Example 2, simulates the equivalent strain distribution in the transverse direction of a GH738 alloy bar with a diameter of Φ350mm and the transverse microstructure of the prepared bar. Figure 5 (a) shows the simulated transverse equivalent strain distribution of the bar. Figure 5 (b) shows the transverse low-magnification structure of the bar. Figure 5 (c) shows the microstructure of the edge of the bar.

[0019] Figure 6This invention, in Example 3, simulates the equivalent strain distribution in the transverse direction of a GH738 alloy bar with a diameter of Φ450mm and the transverse microstructure of the prepared bar. Figure 6 (a) shows the simulated transverse equivalent strain distribution of the bar. Figure 6 (b) shows the transverse low-magnification structure of the bar. Figure 6 (c) shows the microstructure of the edge of the bar.

[0020] Figure 7 The transverse microstructure of the GH738 alloy bar with a specification of Φ230mm prepared in Comparative Example 1 of this invention is shown below. Figure 7 (a) shows the transverse low-magnification structure of the bar. Figure 7 (b) shows the microstructure of the edge of the bar.

[0021] Figure 8 The transverse microstructure of the GH738 alloy bar with a diameter of Φ350mm prepared in Comparative Example 2 of this invention is shown below. Figure 8 (a) shows the transverse low-magnification structure of the bar. Figure 8 (b) shows the microstructure of the edge of the bar.

[0022] Figure 9 The transverse microstructure of the GH738 alloy bar with a diameter of Φ450mm prepared in Comparative Example 3 of this invention is shown below. Figure 9 (a) shows the transverse low-magnification structure of the bar. Figure 9 (b) shows the microstructure of the edge of the bar. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0024] like Figure 1 As shown, a method for determining edge mixed grains in high-temperature alloy bars driven by both experimental and simulation methods includes the following steps: S1. Obtain the peak stress of GH738 alloy at different deformation temperatures and strain rates. Based on the Arrhenius formula, establish a constitutive model for hot working of GH738 alloy.

[0025] S2. Low-magnification corrosion analysis was performed on multiple batches of GH738 bars prepared using different forging processes. Combined with image recognition technology, the edge mixed crystal structure morphology and mixed crystal layer depth characteristics of GH738 bars under multiple batches and various process conditions were analyzed.

[0026] All GH738 bars are prepared using a high-speed forging machine, with no fewer than 20 batches produced.

[0027] S3. Numerical simulation of the forging process corresponding to S2 is performed. Combining the simulation data with the low-magnification mixed grain microstructure analysis data of the actual forged bars, the critical mixed grain factor ε of the GH738 alloy bars is obtained. p .

[0028] A geometric model for bar forging was established, and boundary conditions were defined. Numerical simulations were performed on the forging process of multiple batches of GH738 corresponding to S2. Combining the simulation data with low-magnification mixed grain microstructure analysis data of actual forged bars, the critical mixed grain factor ε of GH738 alloy bars was obtained. p .

[0029] Critical mixed crystal factor ε of GH738 alloy bars p It is the minimum equivalent variable value that characterizes the region when mixed crystals appear.

[0030] Critical mixed crystal factor ε of GH738 alloy bars p It is 0.8.

[0031] S4, combined with finite element simulation, performs simulation optimization design on forging deformation, single hammer reduction, and feed rate, simulates and optimizes the equivalent strain distribution ε of the bar material prepared by the process, and combines the critical mixed crystal factor ε. p To determine the feasibility of the process.

[0032] If the equivalent strain distribution ε at the edge of the bar prepared by the simulation optimization process is less than 0.8, continue to optimize the process until the equivalent strain distribution ε of the bar prepared by the optimized process is greater than or equal to 0.8.

[0033] S5, the preferred simulation optimization process for edge equivalent strain ε≥ε p The forging scheme was used to prepare GH738 bars, and GH738 bars without mixed grain structure at the edge were obtained.

[0034] The simulation optimization process produces GH738 rods with an edge equivalent strain distribution ε≥0.8, outputs a process scheme, and completes the preparation of GH738 rods without mixed crystal structure at the edge.

[0035] The present invention will be further described in detail below with reference to specific embodiments.

[0036] Example 1 (Preparation of GH738 high-temperature alloy rods with a diameter of Φ230mm) S1. Using a thermal simulation compression testing machine, the strain rates of GH738 alloy at temperatures of 1160℃, 1130℃, 1100℃, 1070℃, 1040℃, 1010℃, 950℃, and 900℃ were obtained, with each strain rate being 1 s⁻¹. -1 0.1s -1 0.01s -1The stress-strain curves were obtained, and based on the Arrhenius formula, the relationship between peak stress, deformation temperature and strain rate was constructed to obtain the constitutive equation for hot working of GH738 alloy. S2, Low-magnification corrosion analysis was performed on multiple batches of GH738 bars prepared by different forging processes. Combined with image recognition technology, the edge mixed crystal structure morphology and mixed crystal layer depth characteristics of GH738 bars under multiple batches and multiple process conditions were analyzed. S3. Numerical simulation of the forging process corresponding to S2 is performed. Combining the simulation data with the low-magnification mixed grain microstructure analysis data of the actual forged bars, the critical mixed grain factor ε of the GH738 alloy bars is obtained. p =0.8; S4. Using finite element simulation, the forging deformation, single hammer reduction, and feed rate of GH738 high-temperature alloy bars with a specification of Φ230mm were simulated and optimized. The equivalent strain ε distribution of the bars was simulated and optimized in the process, combined with the critical mixed crystal factor ε. p To determine the feasibility of the process; S5, in the preferred simulation optimization process, the equivalent strain at the edge ε > ε p The forging scheme was adopted to prepare GH738 bars with a diameter of 230mm, resulting in GH738 bars without mixed grain structure at the edges. The preparation parameters are as follows: the GH738 ingot was subjected to five consecutive furnace forgings, with the forging temperature of the first two furnace forgings being 1130℃, the third furnace forging temperature being 1100℃, and the fourth and fifth furnace forging temperatures being 1070℃. The key parameters of the specific forging process are shown in Table 1 below: Table 1: Forging Process Parameters for Example 1

[0037] Example 2 (Preparation of GH738 high-temperature alloy rods with a diameter of Φ350mm) S1. Using a thermal simulation compression testing machine, the strain rates of GH738 alloy at temperatures of 1160℃, 1130℃, 1100℃, 1070℃, 1040℃, 1010℃, 950℃, and 900℃ were obtained, with each strain rate being 1 s⁻¹. -1 0.1s -1 0.01s -1 The stress-strain curves were obtained, and based on the Arrhenius formula, the relationship between peak stress, deformation temperature and strain rate was constructed to obtain the constitutive equation for hot working of GH738 alloy. S2, Low-magnification corrosion analysis was performed on multiple batches of GH738 bars prepared by different forging processes. Combined with image recognition technology, the edge mixed crystal structure morphology and mixed crystal layer depth characteristics of GH738 bars under multiple batches and multiple process conditions were analyzed. S3. Numerical simulation of the forging process corresponding to S2 is performed. Combining the simulation data with the low-magnification mixed grain microstructure analysis data of the actual forged bars, the critical mixed grain factor ε of the GH738 alloy bars is obtained. p =0.8; S4. Using finite element simulation, the forging deformation, single hammer reduction, and feed rate of GH738 high-temperature alloy bars with a specification of Φ350mm were simulated and optimized. The equivalent strain ε distribution of the bars was simulated and optimized in the process, combined with the critical mixed crystal factor ε. p To determine the feasibility of the process; S5, in the preferred simulation optimization process, the equivalent strain at the edge ε > ε p The forging scheme was adopted to prepare GH738 bars with a diameter of 350mm, resulting in GH738 bars without mixed grain structure at the edges. The preparation parameters are as follows: the GH738 ingot was subjected to 6 consecutive furnace forgings, with the forging temperature of the first 2 furnace forgings being 1130℃, the forging temperature of the third and fourth furnace forgings being 1100℃, and the forging temperature of the fifth and sixth furnace forgings being 1070℃. The key parameters of the specific forging process are shown in Table 2 below: Table 2: Forging Process Parameters for Example 2

[0038] Example 3 (Preparation of GH738 high-temperature alloy rods with a diameter of Φ450mm) S1. Using a thermal simulation compression testing machine, the strain rates of GH738 alloy at temperatures of 1160℃, 1130℃, 1100℃, 1070℃, 1040℃, 1010℃, 950℃, and 900℃ were obtained, with each strain rate being 1 s⁻¹. -1 0.1s -1 0.01s -1 The stress-strain curves were obtained, and based on the Arrhenius formula, the relationship between peak stress, deformation temperature and strain rate was constructed to obtain the constitutive equation for hot working of GH738 alloy. S2, Low-magnification corrosion analysis was performed on multiple batches of GH738 bars prepared by different forging processes. Combined with image recognition technology, the edge mixed crystal structure morphology and mixed crystal layer depth characteristics of GH738 bars under multiple batches and multiple process conditions were analyzed. S3. Numerical simulation of the forging process corresponding to S2 is performed. Combining the simulation data with the low-magnification mixed grain microstructure analysis data of the actual forged bars, the critical mixed grain factor ε of the GH738 alloy bars is obtained. p =0.8; S4. Using finite element simulation, the forging deformation, single hammer reduction, and feed rate of GH738 high-temperature alloy bars with a specification of Φ350mm were simulated and optimized. The equivalent strain ε distribution of the bars was simulated and optimized in the process, combined with the critical mixed crystal factor ε. pTo determine the feasibility of the process; S5, in the preferred simulation optimization process, the equivalent strain at the edge ε > ε p The forging scheme was adopted to prepare GH738 bars with a diameter of 350mm, resulting in GH738 bars without mixed grain structure at the edges. The preparation parameters are as follows: the GH738 ingot was subjected to 8 consecutive furnace forgings, with the forging temperature of 1130℃ for the first 3 furnace forgings, 1100℃ for the 4th to 6th furnace forgings, and 1070℃ for the 7th to 8th furnace forgings. The key parameters of the specific forging process are shown in Table 3 below: Table 3: Forging Process Parameters for Example 3

[0039] Comparative Example 1 (GH738 high-temperature alloy bar with a diameter of Φ230mm prepared by conventional process) The key parameters for the specific forging process are shown in Table 4 below: Table 4: Forging process parameters for Comparative Example 1

[0040] Comparative Example 2 (GH738 high-temperature alloy bars with a diameter of 350mm prepared using conventional processes) The key parameters for the specific forging process are shown in Table 5 below: Table 5: Forging process parameters for Comparative Example 2

[0041] Comparative Example 3 (GH738 high-temperature alloy bar with a diameter of Φ450mm prepared by conventional process) The key parameters for the specific forging process are shown in Table 6 below: Table 6: Forging process parameters for Comparative Example 3

[0042] Results analysis: Figure 2 These are typical batches of GH738 bars prepared using different processes, as compiled in the preliminary statistics, showing the mixed crystal morphology at the edge. Figure 2 (a) The low-magnification microstructure of the bar prepared by the corresponding forging process shows four symmetrical mixed crystal arcs with a depth of 16~21 mm. Figure 2 (b) The low-magnification microstructure of the bar prepared by the corresponding forging process shows two symmetrical mixed crystal arcs with mixed crystal arc depths of 20 mm and 24 mm, respectively.

[0043] Figure 3 (a) is a simulation Figure 2 (b) Transverse equivalent strain distribution of the process bar: the red area is without mixed crystal structure, the other colors are mixed crystal structure, and the edge presents 4 symmetrical mixed crystal arcs with a mixed crystal arc depth of 16~21mm. Figure 3 (b) is a simulation Figure 2 (a) The transverse equivalent strain distribution of the process bar has two symmetrical mixed crystal arcs at the edge, with mixed crystal arc depths of 20 mm and 24 mm, respectively. Figure 3 (c) and Figure 3 (d) are simulations Figure 2 (b) and Figure 2 (a) Equivalent strain distribution on the surface of the process rods: The mixed crystal range on the surface of the rods prepared by the two processes is large, and there are multiple mixed crystal structures.

[0044] Figure 4 (a) shows the simulated transverse equivalent strain distribution of the Φ230mm GH738 bar from Example 1, where the depth of the mixed-grain structure layer is significantly reduced to below 11.9mm. Figure 4 (b) and Figure 4 (c) are the transverse low magnification and edge high magnification structures of the rod prepared by this process. The depth of the mixed crystal layer of the prepared rod is reduced, the edge structure is uniform, and there is no mixed crystal residue on the edge after the rod is machined.

[0045] Figure 5 (a) shows the simulated transverse equivalent strain distribution of the Φ350mm GH738 bar from Example 2, where the depth of the mixed-grain structure layer is significantly reduced to below 12mm. Figure 5 (b) and Figure 5 (c) are the transverse low magnification and edge high magnification structures of the rod prepared by this process. The depth of the mixed crystal layer of the prepared rod is reduced, the edge structure is uniform, and there is no mixed crystal residue on the edge after the rod is machined.

[0046] Figure 6 (a) shows the simulated transverse equivalent strain distribution of the Φ450mm GH738 bar in Example 3, where the depth of the mixed crystal layer is significantly reduced to below 11.7mm. Figure 5 (b) and Figure 5 (c) are the transverse low magnification and edge high magnification structures of the rod prepared by this process. The depth of the mixed crystal layer of the prepared rod is reduced, the edge structure is uniform, and there is no mixed crystal residue on the edge after the rod is machined.

[0047] In contrast. Figure 7 (a) Figure 7 (b) are the low-magnification and high-magnification microstructures of the Φ230mm GH738 bar in Comparative Example 1, respectively. The mixed crystal layer depth of the prepared bar reached 23mm, the edge microstructure uniformity was poor, and obvious mixed crystal structure could be observed. Figure 8 (a) Figure 8 (b) are the low-magnification and high-magnification microstructures of the Φ350mm GH738 bar in Comparative Example 2, respectively. The mixed crystal layer depth of the prepared bar reached 23mm, the edge microstructure uniformity was poor, and obvious mixed crystal structure could be observed. Figure 9 (a) Figure 9 (b) are the low-magnification and high-magnification microstructures of the Φ450mm GH738 bar of Comparative Example 3, respectively. The mixed crystal layer depth of the prepared bar reached 30mm, and the microstructure uniformity at the edge was poor, with obvious mixed crystal structure observed. After the bar prepared in the above comparative examples was machined, mixed crystal residues still existed at the edge, which were inherited by the forgings and had an adverse effect on the performance of the relevant forgings.

Claims

1. A method for determining edge mixed crystals in high-temperature alloy bars driven by both experimental and simulation methods, characterized in that, Includes the following steps: S1. Obtain the peak stress of GH738 alloy at different deformation temperatures and strain rates. Based on the Arrhenius formula, establish a constitutive model for hot working of GH738 alloy. S2, Low-magnification corrosion analysis was performed on multiple batches of GH738 bars prepared by different forging processes. Combined with image recognition technology, the edge mixed crystal structure morphology and mixed crystal layer depth characteristics of GH738 bars under multiple batches and multiple process conditions were analyzed. S3. Numerical simulation of the forging process corresponding to S2 is performed. Combining the simulation data with the low-magnification mixed grain microstructure analysis data of the actual forged bars, the critical mixed grain factor ε of the GH738 alloy bars is obtained. p ; S4, combined with finite element simulation, performs simulation optimization design on forging deformation, single hammer reduction, and feed rate, simulates and optimizes the equivalent strain distribution ε of the bar material prepared by the process, and combines the critical mixed crystal factor ε. p To determine the feasibility of the process; S5, in the preferred simulation optimization process, the equivalent strain at the edge ε is greater than or equal to the critical mixed crystal factor ε. p The forging scheme was used to prepare GH738 bars, and GH738 bars without mixed grain structure at the edge were obtained.

2. The method for determining edge mixed crystals of high-temperature alloy bars under dual experimental and simulated driving as described in claim 1, characterized in that, In S2, the GH738 bars are all prepared using a high-speed forging machine, with no fewer than 20 batches prepared.

3. The method for determining edge mixed crystals in high-temperature alloy bars under dual experimental and simulated driving as described in claim 1, characterized in that, In S3, the critical mixed crystal factor ε of the GH738 alloy bar is... p It is the minimum equivalent variable value that characterizes the region when mixed crystals appear.

4. The method for determining edge mixed crystals of high-temperature alloy bars under dual experimental and simulated driving as described in claim 3, characterized in that, In S3, the critical mixed crystal factor ε of the GH738 alloy bar is... p It is 0.

8.

5. The method for determining edge mixed crystals of high-temperature alloy bars under dual experimental and simulated driving as described in claim 1, characterized in that, In step S4, if the equivalent strain distribution ε of the bar prepared by the simulated optimized process is less than 0.8, the process is further optimized until the equivalent strain distribution ε of the bar prepared by the optimized process is greater than or equal to 0.8.