A method and system for designing a solution heat treatment regime for a single crystal superalloy

Abstract

The application discloses a design method and system of a single-crystal high-temperature alloy solid solution heat treatment system, relates to the cross technical field of numerical simulation and material processing, and comprises the following steps: based on the relationship between element concentration and solidus temperature, determining the solidus temperature distribution of a cast single-crystal high-temperature alloy sample according to the element concentration distribution extracted from the cast single-crystal high-temperature alloy sample; adopting a phase field method to simulate solid solution heat treatment of the cast single-crystal high-temperature alloy sample, so as to obtain the element concentration distribution under the initial melting temperature and heat preservation for one simulation time step, and mark the element concentration distribution after treatment as the element concentration distribution, and determine the segregation coefficient of each element; when the segregation coefficients of all elements are within a preset range, marking all initial melting temperatures and corresponding current simulation times as heat treatment simulation results, and then determining the actual solid solution heat treatment system of the cast single-crystal high-temperature alloy sample. The application has the advantages of short time consumption, high efficiency and low cost.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of numerical simulation and materials processing, and in particular to a design method and system for a solution heat treatment regime for single-crystal high-temperature alloys. Background Technology

[0002] Single-crystal superalloys possess high strength and toughness, good oxidation and corrosion resistance, excellent machinability, and superior high-temperature comprehensive performance, making them the preferred material for manufacturing advanced aero-engine turbine blades. Single-crystal superalloys are typically prepared using directional solidification methods, resulting in a cast microstructure containing interdendritic phases and microsegregation (uneven element distribution), which is detrimental to high-temperature mechanical properties. To dissolve the interdendritic phases and reduce microsegregation to obtain a uniform single microstructure, solution heat treatment is necessary. The temperature selection during solution treatment is crucial. Low temperatures require a significant amount of time to reduce microsegregation, and secondary phases may not dissolve; while high temperatures, although able to dissolve secondary phases and reduce microsegregation in a shorter time, can cause initial melting, i.e., localized melting, forming solution pores, which severely weaken the alloy's high-temperature mechanical properties.

[0003] To improve heat treatment efficiency, it is necessary to ensure the highest possible solution heat treatment temperature without initial melting. Therefore, the solution heat treatment temperature needs to be lower than the initial melting temperature. However, the initial melting temperature is not a fixed value; as the solution heat treatment process progresses, microscopic segregation decreases, and the initial melting temperature continuously increases. The localization and variability of the initial melting temperature complicates the design of solution heat treatment regimes. The traditional method for designing solution heat treatment regimes is experimental. In experimental methods, the holding temperature and holding time are typically adjusted multiple times, and the occurrence of initial melting is observed through microstructural characterization in order to obtain an optimized solution heat treatment regime. For example, the literature “HTPang, LJZhang, RAHobbs, HJStone, CMFRAe. Solution heat treatment optimization of fourth-generation single-crystal nickel-base superalloys[J]. Metall. Mater. Trans. A., 2012, 43A: 3264-3282” uses experimental methods to optimize the solution heat treatment regime of fourth-generation nickel-based single-crystal superalloys LDSX-6B and LDSX-6C. However, the trial-and-error experimental method is time-consuming and labor-intensive, and the designed solution heat treatment regime is not universally applicable. Summary of the Invention

[0004] The purpose of this invention is to provide a design method and system for the solution heat treatment regime of single-crystal high-temperature alloys. The solution heat treatment regime of single-crystal high-temperature alloys is designed based on simulation results, which has the advantages of short time consumption, high efficiency and low cost.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] In a first aspect, the present invention provides a method for designing a solution heat treatment regime for single-crystal high-temperature alloys, comprising:

[0007] Extracting elemental concentration distribution from cast single-crystal superalloy samples;

[0008] Based on the relationship between element concentration and solidus temperature, the solidus temperature distribution of the cast single-crystal superalloy sample is determined according to the element concentration distribution.

[0009] The lowest solidus temperature in the solidus temperature distribution is marked as the initial melting temperature, and the current simulation time is determined at the same time.

[0010] Based on the initial melting temperature, the phase field method was used to simulate the solution heat treatment of the cast single crystal high-temperature alloy sample to obtain the element concentration distribution after holding at the initial melting temperature for one simulation time step, and marked as the element concentration distribution after treatment.

[0011] Based on the element concentration distribution after the treatment, the segregation coefficient of each element is determined;

[0012] When the segregation coefficient of any element is not within the preset range, the element concentration distribution is updated to the processed element concentration distribution, and the step of determining the solidus temperature distribution of the cast single crystal high-temperature alloy sample based on the relationship between element concentration and solidus temperature and the element concentration distribution is returned.

[0013] When the segregation coefficients of all elements are within the preset range, all the initial melting temperatures and the corresponding current simulation times are marked as heat treatment simulation results.

[0014] Based on the heat treatment simulation results, the actual solution heat treatment regime for the cast single-crystal high-temperature alloy sample was determined.

[0015] Secondly, the present invention provides a design system for a solution heat treatment process of single-crystal high-temperature alloys, comprising:

[0016] An element concentration distribution extraction module is used to extract element concentration distribution from cast single-crystal superalloy samples.

[0017] The solidus temperature distribution determination module is used to determine the solidus temperature distribution of the cast single-crystal superalloy sample based on the relationship between element concentration and solidus temperature, and according to the element concentration distribution.

[0018] The initial melting temperature determination module is used to mark the lowest solidus temperature in the solidus temperature distribution as the initial melting temperature, and at the same time determine the current simulation time;

[0019] The solution heat treatment simulation module is used to simulate the solution heat treatment of the cast single crystal high-temperature alloy sample based on the initial melting temperature using the phase field method, so as to obtain the element concentration distribution after holding at the initial melting temperature for one simulation time step, and mark it as the element concentration distribution after treatment.

[0020] The segregation coefficient determination module is used to determine the segregation coefficient of each element based on the processed element concentration distribution.

[0021] The solid solution simulation iteration module is used to update the element concentration distribution to the processed element concentration distribution when the segregation coefficient of any element is not within the preset range, and return the step of determining the solidus temperature distribution of the cast single crystal high-temperature alloy sample based on the relationship between element concentration and solidus temperature and the element concentration distribution.

[0022] The simulation result determination module is used to mark all the initial melting temperatures and the corresponding current simulation times as heat treatment simulation results when the segregation coefficients of all elements are within a preset range.

[0023] The solution heat treatment regime determination module is used to determine the actual solution heat treatment regime of the cast single crystal high-temperature alloy sample based on the heat treatment simulation results.

[0024] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0025] This invention discloses a design method and system for solution heat treatment regimes of single-crystal superalloys. The method involves extracting the element concentration distribution from a cast single-crystal superalloy sample to determine the solidus temperature distribution. The lowest solidus temperature in the solidus temperature distribution is marked as the initial melting temperature. Simultaneously, the current simulation time is determined, and then the phase-field method is used to simulate solution heat treatment. This allows for real-time observation of the element diffusion process during solution heat treatment, obtaining the element concentration distribution at the initial melting temperature for one simulation time step, and thus determining the segregation coefficient of each element. When the segregation coefficients of all elements are within a preset range, all initial melting temperatures and their corresponding current simulation times are marked as heat treatment simulation results. Finally, based on the heat treatment simulation results, the actual solution heat treatment regime for the cast single-crystal superalloy sample is determined. This invention, based on the relationship between element concentration and solidus temperature, achieves real-time updates of the solution temperature during solution heat treatment simulation. An optimized solution heat treatment regime can be obtained from a single complete simulation result. Compared to existing experimental methods, this method has the advantages of shorter time consumption, higher efficiency, and lower cost. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating the design method for the solution heat treatment regime of single-crystal high-temperature alloys according to the present invention.

[0028] Figure 2 A schematic diagram of the as-cast microstructure of a single-crystal superalloy prepared by directional solidification; Figure 2 (a) is a schematic diagram showing the dendritic morphology of a cast single-crystal superalloy due to uneven element distribution. Figure 2 (b) is a schematic diagram of the (γ+γ′) eutectic phase, (β+γ′) eutectic phase and coarsened γ′ phase existing between dendrites;

[0029] Figure 3 This is a schematic diagram showing the concentration distribution of the refractory element W during the heat treatment simulation process; Figure 3 (a) in the diagram is a simulation time of 3600s. Figure 3 (b) in the diagram is a simulation time of 18000s. Figure 3 (c) in the diagram is a simulation time of 72000s;

[0030] Figure 4 A schematic diagram of the isothermal solution heat treatment regime designed for Example 1;

[0031] Figure 5 A schematic diagram of the multi-step solution heat treatment regime designed for Example 2;

[0032] Figure 6 A schematic diagram of the slope solution heat treatment regime designed for Example 3;

[0033] Figure 7 A schematic diagram of the microstructure after solution heat treatment following an experiment based on three specific examples of solution heat treatment regimes designed. Figure 7 (a) is a schematic diagram of the microstructure after heat treatment according to the solution treatment regime designed in Example 1. Figure 7 (b) is a schematic diagram of the microstructure after heat treatment according to the solution treatment regime designed in Example 2. Figure 7 (c) is a schematic diagram of the microstructure after heat treatment according to the solution treatment regime designed in Example 3;

[0034] Figure 8 This is a schematic diagram of the design system for the solution heat treatment process of single-crystal high-temperature alloys according to the present invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] To make the objectives, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] Example 1

[0038] like Figure 1 As shown, this invention provides a method for designing a solution heat treatment regime for single-crystal superalloys, comprising:

[0039] Step 100: Extract the element concentration distribution from the cast single-crystal superalloy sample; specifically, the element concentration distribution of the cast single-crystal superalloy sample is measured using an electron probe microanalyzer (EPMA).

[0040] Furthermore, the pull-out rate of directional solidification ranges from 0.1 μm / s to 3000 μm / s, and the as-cast sample is a single-crystal alloy. The as-cast microstructure of the alloy exhibits a dendritic morphology and contains secondary phases. The element concentration distribution of the as-cast microstructure was obtained by EPMA measurement, which reflects not only microsegregation but also secondary phases.

[0041] The method of the present invention can be applied to single-crystal superalloys of any elemental composition. In one example, the elements extracted from the cast single-crystal superalloy sample include at least one of nickel, cobalt, chromium, molybdenum, tungsten, aluminum, tantalum, titanium, niobium, rhenium, ruthenium, and hafnium.

[0042] Step 200: Based on the relationship between element concentration and solidus temperature, determine the solidus temperature distribution of the cast single-crystal high-temperature alloy sample according to the element concentration distribution.

[0043] The relationship between element concentration and solidus temperature is established using thermodynamic software. The specific establishment process includes: using thermodynamic calculation software to calculate the solidus temperature of multiple sets (at least 500 sets) of alloy compositions with different element concentration distributions; and using nonlinear fitting to obtain the corresponding functional relationship between element concentration and solidus temperature.

[0044] That is, the relationship between element concentration and solidus temperature can be expressed by the following function:

[0045]

[0046] Among them, T s Represents the solidus temperature, i, j, k represent single-crystal high-temperature alloying elements, and c i c j c k Let P represent the concentrations of element i, element j, and element k in single-crystal high-temperature alloys, respectively. i p represents the interaction coefficient between single-crystal high-temperature alloying element i and single-crystal high-temperature alloying element i. ij p represents the interaction coefficient between single-crystal high-temperature alloying element i and single-crystal high-temperature alloying element j. ijk Let r represent the interaction coefficients between single-crystal high-temperature alloy elements i, j, and k, and m represent the order of the interaction between single-crystal high-temperature alloy elements i and j. m is at most 2, i.e., 0, 1, and 2 respectively, and r∈m.

[0047] By establishing the relationship between element concentration and solidus temperature, real-time tracking of the initial melting temperature was achieved during solution heat treatment simulation, providing a theoretical basis for the formulation of solution heat treatment regimes. Furthermore, based on the aforementioned function formula, the solidus temperature distribution of the as-cast sample can be solved from the as-cast element concentration distribution, or a new solidus temperature distribution can be solved from the element concentration distribution after one time step of the solution simulation.

[0048] Step 300: Mark the lowest solidus temperature in the solidus temperature distribution as the initial melting temperature, and determine the current simulation time; wherein, the initial melting temperature varies with the element concentration.

[0049] The process of determining the current simulation time specifically includes: 1) Obtaining the number of steps in the step of determining the solidus temperature distribution of the cast single-crystal superalloy sample based on the relationship between element concentration and solidus temperature, and marking it as the simulation step number. 2) Multiplying the simulation step number by the simulation time step to obtain the current simulation time.

[0050] Specifically, initially, the number of return steps cannot be obtained, meaning the simulation step count is 0, no simulation has been performed yet, and the current simulation time is also 0. If the number of return steps is 1, it indicates that the simulation step count is 1 (one simulation of steps 400-500 below has been completed). Multiplying the simulation step count by the simulation time step gives the current simulation time. Furthermore, the simulation time step value must ensure the stability of the solution heat treatment simulation calculation process; therefore, the simulation time step value in this invention ranges from 0.1s to 10s.

[0051] Step 400: Based on the initial melting temperature, the phase field method is used to simulate the solid solution heat treatment of the cast single crystal high-temperature alloy sample to obtain the element concentration distribution after holding at the initial melting temperature for one simulation time step, and it is marked as the element concentration distribution after treatment.

[0052] Specifically, the initial melting temperature is used as the simulation temperature for solution heat treatment. Element homogenization during the solution heat treatment process is simulated to obtain the element concentration distribution after holding at the simulation temperature for one simulation time step. The governing equation for the phase-field method is shown below; solving this equation yields the evolution of the element concentration distribution over time.

[0053] The governing equations for the phase-field method are:

[0054]

[0055] The system's thermodynamic free energy F is related to its Gibbs free energy G; therefore, F = G / V m G is solved using the phase diagram method, and the equation is:

[0056]

[0057] Dynamic mobility M ij Similarly, the phase diagram calculation method is used to solve the problem, and the equation is:

[0058]

[0059] M k With atomic activation energy Q k The relevant equation is:

[0060]

[0061] Among them, c i c j c k Let M represent the concentrations of element i, element j, and element k in single-crystal high-temperature alloys, respectively. ij V represents the kinetic mobility, F represents the thermodynamic free energy of the system, G represents the Gibbs free energy, and V represents the kinetic mobility. m Volume is the molar volume; and Obtained from a thermodynamic database, R is the gas constant; T is the absolute temperature, which is also the simulation temperature for solution heat treatment; m represents the order of the interaction between single-crystal high-temperature alloying element i and single-crystal high-temperature alloying element j; δ ik and δ jk M is the delta function. k Q represents atomic mobility. k This represents the atomic activation energy, obtained from a kinetics database.

[0062] According to a specific embodiment of the present invention, by running a solution heat treatment simulation for one simulation time step, a new element concentration distribution can be obtained after holding at the solution heat treatment simulation temperature for a time dt, that is, the element concentration distribution after treatment.

[0063] Step 500: Based on the element concentration distribution after processing, determine the segregation coefficient of each element. The segregation coefficient is the ratio of the dendritic core element concentration to the interdendritic element concentration. The closer the segregation coefficient is to 1, the higher the requirement for solution heat treatment. The preset range of the segregation coefficient in this invention is 0.9-1.1.

[0064] Step 600: When the segregation coefficient of any element is not within the preset range, update the element concentration distribution to the processed element concentration distribution and return to step 200.

[0065] Step 700: When the segregation coefficients of all elements are within the preset range, mark all the initial melting temperatures and the corresponding current simulation time as heat treatment simulation results; specifically, the element concentrations obtained from the phase field simulation can be used to calculate the initial melting temperature of the new element concentration distribution, and at the same time update the solution temperature (usually the new solution temperature is higher), thereby improving the solution heat treatment efficiency.

[0066] Step 800: Based on the heat treatment simulation results, determine the actual solution heat treatment regime for the cast single-crystal superalloy sample. The actual solution heat treatment regime is one in which the temperature and time of the solution heat treatment are variable.

[0067] Step 800 specifically includes:

[0068] 1) For any set of initial melting temperatures and corresponding current simulation times in the heat treatment simulation results, subtract a preset constant from the initial melting temperature to obtain the ideal temperature; the ideal temperature and the corresponding current simulation time constitute an ideal solution heat treatment result; multiple ideal solution heat treatment results constitute an ideal solution heat treatment regime; specifically, the preset constant can be determined according to the temperature control accuracy of the experimental heat treatment furnace, and is usually no greater than 5 degrees Celsius. Simultaneously, the solution temperature is set lower than the initial melting temperature to prevent initial melting.

[0069] Because the ideal solution treatment temperature exhibits a curved relationship with time, it is difficult to set this regime in commonly used heat treatment furnaces. Therefore, it is necessary to design an operable regime based on the ideal solution heat treatment temperature and time relationship, where operability refers to the temperature and time that the heat treatment furnace can be set. That is:

[0070] 2) Based on the principle that the temperature of solution heat treatment should not be higher than the range of the ideal temperature, the actual solution heat treatment regime is designed according to the ideal solution heat treatment regime. The actual solution heat treatment regime includes isothermal solution treatment (holding at a fixed temperature), multi-step solution treatment (holding at a low temperature for a period of time and then raising the temperature and holding), and slope solution treatment (temperature increases linearly with time).

[0071] The following are three specific examples based on the method of this invention, along with comparative analysis:

[0072] Example 1.

[0073] Taking a newly designed cobalt-based single-crystal superalloy as an example, its chemical composition (atomic percentage, %) is Ni 30, Al 11, W 5, Ta 1, Ti 4, Cr 5, Co balance. During the directionally solidified preparation of the single-crystal superalloy, the pulling rate was 100 μm / s, and the resulting as-cast sample microstructure is as follows. Figure 2 As shown. From Figure 2 As can be seen in (a), the cast single-crystal superalloy exhibits a dendritic morphology due to the uneven distribution of elements, and the (γ+γ′) eutectic phase and coarsened γ′ phase exist between the dendrites. Figure 2 (b) in the middle.

[0074] An EPMA measurement was performed on a region containing a complete dendrite to obtain the elemental concentration distribution of the as-cast sample. This elemental concentration distribution was converted into a matrix and used as the initial input for phase-field simulation. Based on the established relationship between elemental concentration and solidus temperature, the solidus temperature distribution of the as-cast sample was calculated, and its lowest value was taken as the initial melting temperature. A solution heat treatment simulation was performed at the initial melting temperature with a holding time step of 1 s to obtain the elemental concentration distribution after holding for 1 s. Based on the simulated elemental concentration distribution, the solidus temperature distribution and initial melting temperature were recalculated, and the holding process simulation was repeated until the segregation coefficients of all elements were within the range of 0.9–1.1.

[0075] Figure 3 This represents the homogenization process of W, the slowest diffusing element, during solution heat treatment simulation. Figure 3 Figures (a), (b), and (c) show schematic diagrams for simulation times of 3600 s, 18000 s, and 72000 s, respectively. The initial melting temperature change during the solid solution thermal care simulation process is shown below. Figure 4 As shown by the dashed line, lowering the initial melting temperature by 5°C yields the ideal solution heat treatment regime, as follows: Figure 4 As shown by the midpoint line, design based on this. Figure 4 The isothermal solution heat treatment regime is shown by the solid line in the middle.

[0076] Example 2 and Example 3.

[0077] The difference between Examples 2 and 3 and Example 1 lies in the design of a workable solution heat treatment regime based on an ideal solution regime. Example 2's solution heat treatment regime is a multi-step solution regime, as detailed in [link to example]. Figure 5 As shown by the solid line. Example 3 uses a slope solution treatment regime for the solution heat treatment; see details below. Figure 6 As shown by the solid line in the middle.

[0078] Based on the solution treatment regimes designed in Examples 1 to 3, corresponding solution heat treatment experiments were conducted. Specifically, the microstructures of the samples after solution heat treatment in Examples 1 to 3 were observed, and the results are as follows: Figure 7 As shown, Figure 7 In the diagram, (a) is a schematic diagram of the microstructure after heat treatment according to the solution treatment regime designed in Example 1; (b) is a schematic diagram of the microstructure after heat treatment according to the solution treatment regime designed in Example 2; and (c) is a schematic diagram of the microstructure after heat treatment according to the solution treatment regime designed in Example 3. Figure 7 It can be seen that the solution heat treatment regime for single-crystal high-temperature alloys designed using the method of the present invention will not cause initial melting of the sample during the experiment, and the multi-step solution treatment at higher temperatures has the best solution effect, that is, the dendritic structure has completely disappeared and there is no secondary phase between dendrites.

[0079] Example 2

[0080] like Figure 8 As shown, in order to implement the technical solution in Embodiment 1 and achieve the corresponding functions and technical effects, this embodiment also provides a design system for the solution heat treatment process of single-crystal high-temperature alloys, including:

[0081] The element concentration distribution extraction module is used to extract the element concentration distribution from cast single-crystal superalloy samples.

[0082] The solidus temperature distribution determination module is used to determine the solidus temperature distribution of the cast single-crystal superalloy sample based on the relationship between element concentration and solidus temperature, and according to the element concentration distribution.

[0083] The initial melting temperature determination module is used to mark the lowest solidus temperature in the solidus temperature distribution as the initial melting temperature, and at the same time determine the current simulation time.

[0084] The solution heat treatment simulation module is used to simulate the solution heat treatment of the cast single crystal high-temperature alloy sample based on the initial melting temperature using the phase field method, so as to obtain the element concentration distribution after holding at the initial melting temperature for one simulation time step, and mark it as the element concentration distribution after treatment.

[0085] The segregation coefficient determination module is used to determine the segregation coefficient of each element based on the processed element concentration distribution.

[0086] The solid solution simulation iteration module is used to update the element concentration distribution to the processed element concentration distribution when the segregation coefficient of any element is not within the preset range, and return the step of determining the solidus temperature distribution of the cast single crystal high-temperature alloy sample based on the relationship between element concentration and solidus temperature and the element concentration distribution.

[0087] The simulation result determination module is used to mark all the initial melting temperatures and the corresponding current simulation times as heat treatment simulation results when the segregation coefficients of all elements are within a preset range.

[0088] The solution heat treatment regime determination module is used to determine the actual solution heat treatment regime of the cast single crystal high-temperature alloy sample based on the heat treatment simulation results.

[0089] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0090] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for designing a solution heat treatment regime for single-crystal superalloys, characterized in that, The methods include: Extracting elemental concentration distribution from cast single-crystal superalloy samples; Based on the relationship between element concentration and solidus temperature, the solidus temperature distribution of the cast single-crystal superalloy sample is determined according to the element concentration distribution. The lowest solidus temperature in the solidus temperature distribution is marked as the initial melting temperature, and the current simulation time is determined at the same time. Based on the initial melting temperature, the phase field method was used to simulate the solution heat treatment of the cast single crystal high-temperature alloy sample to obtain the element concentration distribution after holding at the initial melting temperature for one simulation time step, and marked as the element concentration distribution after treatment. The initial melting temperature is used as the simulation temperature for solution heat treatment. Element homogenization simulation is performed during the solution heat treatment process to obtain the element concentration distribution after holding at the solution heat treatment simulation temperature for one simulation time step. The governing equation of the phase field method is shown below. Solving this governing equation yields the evolution of the element concentration distribution over time. The governing equations for the phase-field method are: ； F=G / V m ; G The equation is obtained by calculating the phase diagram: ； Dynamic mobility M ij Similarly, the phase diagram calculation method is used to solve the problem, and the equation is: ； With atomic activation energy The relevant equation is: ； in, c i 、c j 、c k They represent elements of single-crystal high-temperature alloys. i Concentration of single-crystal high-temperature alloying elements j Concentration of single-crystal high-temperature alloying elements k concentration, M ij Indicates kinetic mobility. F Represents the thermodynamic free energy of the system; G Gibbs free energy, V m Volume is the molar volume; , and Obtained from a thermodynamic database. R It is the gas constant; T This is both the absolute temperature and the simulated temperature for solution heat treatment. m Indicates single-crystal high-temperature alloying elements i With single-crystal high-temperature alloying elements j The order of the interaction between them; and For the delta function, It represents atomic mobility; Q k The atomic activation energy is obtained from a kinetics database. Based on the element concentration distribution after the treatment, the segregation coefficient of each element is determined; When the segregation coefficient of any element is not within the preset range, the element concentration distribution is updated to the processed element concentration distribution, and the step of determining the solidus temperature distribution of the cast single crystal high-temperature alloy sample based on the relationship between element concentration and solidus temperature and the element concentration distribution is returned. When the segregation coefficients of all elements are within the preset range, all the initial melting temperatures and the corresponding current simulation times are marked as heat treatment simulation results. Based on the heat treatment simulation results, the actual solution heat treatment regime for the cast single-crystal high-temperature alloy sample was determined.

2. The design method for the solution heat treatment regime of single-crystal high-temperature alloys according to claim 1, characterized in that, The elements extracted from the cast single-crystal superalloy sample include at least one of nickel, cobalt, chromium, molybdenum, tungsten, aluminum, tantalum, titanium, niobium, rhenium, ruthenium, and hafnium.

3. The design method for the solution heat treatment regime of single-crystal high-temperature alloys according to claim 1, characterized in that, The relationship between the element concentration and the solidus temperature is expressed by the following function: ； in, T s Represents the solidus temperature. i , j , k Represents single-crystal high-temperature alloy elements. c i 、c j 、c k They represent elements of single-crystal high-temperature alloys. i Concentration of single-crystal high-temperature alloying elements j Concentration of single-crystal high-temperature alloying elements k concentration, P i Indicates single-crystal high-temperature alloying elements i With single-crystal high-temperature alloying elements i The interaction coefficient, Indicates single-crystal high-temperature alloying elements i With single-crystal high-temperature alloying elements j The interaction coefficient, Indicates single-crystal high-temperature alloying elements i Single-crystal high-temperature alloying elements j With single-crystal high-temperature alloying elements k The interaction coefficient, m Indicates single-crystal high-temperature alloying elements i With single-crystal high-temperature alloying elements j The order of the interaction between them .

4. The design method for the solution heat treatment regime of single-crystal high-temperature alloys according to claim 1, characterized in that, Extracting elemental concentration distribution from cast single-crystal superalloy samples specifically includes: The elemental concentration distribution of the cast single-crystal superalloy sample was measured using an electron probe microanalyzer.

5. The design method for the solution heat treatment regime of single-crystal high-temperature alloys according to claim 1, characterized in that, The process of determining the current simulation time specifically includes: The number of steps to obtain the return value based on the relationship between element concentration and solidus temperature, and to determine the solidus temperature distribution of the cast single crystal superalloy sample according to the element concentration distribution, is marked as the simulation step number. Multiply the number of simulation steps by the simulation time step to obtain the current simulation time; The simulation time step ranges from 0.1s to 10s.

6. The method for designing the solution heat treatment regime for single-crystal high-temperature alloys according to claim 1, characterized in that, Based on the heat treatment simulation results, the actual solution heat treatment regime for the as-cast single-crystal superalloy sample was determined, specifically including: For any set of initial melting temperatures and corresponding current simulation times in the heat treatment simulation results, a preset constant is subtracted from the initial melting temperature to obtain the ideal temperature; the ideal temperature and the corresponding current simulation time constitute the ideal solution heat treatment result; multiple ideal solution heat treatment results constitute the ideal solution heat treatment regime. Based on the principle that the temperature of solution heat treatment should not exceed the range of the ideal temperature, the actual solution heat treatment regime is designed according to the ideal solution heat treatment regime.

7. The design method for the solution heat treatment regime of single-crystal high-temperature alloys according to claim 1, characterized in that, The actual solution heat treatment regime is a regime in which the temperature and time of solution heat treatment are variable; the actual solution heat treatment regime includes isothermal solution treatment, multi-step solution treatment and slope solution treatment.

8. The method for designing the solution heat treatment regime for single-crystal high-temperature alloys according to claim 1, characterized in that, The preset range of the segregation coefficient is 0.9-1.

1.

9. A design system for a solution heat treatment regime of a single-crystal superalloy, employing the design method for a solution heat treatment regime of a single-crystal superalloy as described in any one of claims 1-8, characterized in that, The system includes: An element concentration distribution extraction module is used to extract element concentration distribution from cast single-crystal superalloy samples. The solidus temperature distribution determination module is used to determine the solidus temperature distribution of the cast single-crystal superalloy sample based on the relationship between element concentration and solidus temperature, and according to the element concentration distribution. The initial melting temperature determination module is used to mark the lowest solidus temperature in the solidus temperature distribution as the initial melting temperature, and at the same time determine the current simulation time. The solution heat treatment simulation module is used to simulate the solution heat treatment of the cast single crystal high-temperature alloy sample based on the initial melting temperature using the phase field method, so as to obtain the element concentration distribution after holding at the initial melting temperature for one simulation time step, and mark it as the element concentration distribution after treatment. The segregation coefficient determination module is used to determine the segregation coefficient of each element based on the processed element concentration distribution. The solid solution simulation iteration module is used to update the element concentration distribution to the processed element concentration distribution when the segregation coefficient of any element is not within the preset range, and return the step of determining the solidus temperature distribution of the cast single crystal high-temperature alloy sample based on the relationship between element concentration and solidus temperature and the element concentration distribution. The simulation result determination module is used to mark all the initial melting temperatures and the corresponding current simulation time as heat treatment simulation results when the segregation coefficients of all elements are within the preset range. The solution heat treatment regime determination module is used to determine the actual solution heat treatment regime of the cast single crystal high-temperature alloy sample based on the heat treatment simulation results.

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