A method of predicting the propensity for freckle formation in a single crystal superalloy casting

Abstract

This invention belongs to the field of high-temperature alloy technology, specifically relating to a method for predicting the freckle formation tendency of single-crystal high-temperature alloy castings. The invention uses single-crystal high-temperature alloy castings as samples, obtaining the casting modulus and measuring the solidification temperature range. It uses either experimental or simulation methods to obtain the minimum value of the temperature gradient in the mushy region of the overall solidification area during the directional solidification process. Based on the criterion values ​​for freckle formation tendency under different casting moduli, different sample compositions, and different directional solidification process parameters, and the corresponding freckle lengths in the castings, the relationship between the criterion values ​​for freckle formation tendency and the freckle length is determined, which is used to predict the freckle formation tendency of different single-crystal high-temperature alloy castings under different process conditions. By considering the casting modulus of the single-crystal high-temperature alloy castings, the solidification temperature range of the mushy region in single-crystal high-temperature alloy castings with different compositions, the minimum value of the temperature gradient in the mushy region, and the directional solidification growth rate, the accuracy of freckle defect prediction results is improved.

Description

Technical Field

[0001] This invention belongs to the field of high-temperature alloy technology, and particularly to the field of directional solidification preparation technology of single-crystal high-temperature alloy castings. Specifically, it relates to a method for predicting the tendency of freckle formation in single-crystal high-temperature alloy castings. Background Technology

[0002] Nickel-based single-crystal superalloys possess excellent room-temperature and high-temperature mechanical properties, as well as superior fatigue and oxidation resistance, making them widely used in the manufacture of hot-end castings for aero-engines and ground-based gas turbines. Single-crystal superalloy castings are typically prepared using directional solidification, with the solidification direction being bottom-up. During the directional solidification process, negatively segregating elements W and Re generally accumulate in the dendrite trunks, while positively segregating elements Al and Ti accumulate in the interdendritic regions. As solidification progresses, the liquid density in the interdendritic or mushy regions decreases, resulting in a top-heavy, bottom-light liquid state. Under the influence of gravity, this easily generates strong convection currents, causing remelting and breakage of dendrite arms. These broken dendrites grow in a restricted manner in the interdendritic region, ultimately forming freckle defects. With the increasing demands for high-temperature resistance in superalloys, the content of W and Re in single-crystal superalloys is constantly increasing. This leads to more severe liquid convection between dendrites or in the pasty regions, significantly increasing the tendency for freckle defects to form in single-crystal superalloy castings during directional solidification. Freckle defects disrupt the single-crystal structure of hot-end castings, worsening the creep performance of the superalloy, posing certain safety hazards, and directly resulting in increased casting scrap rates and significantly higher manufacturing costs.

[0003] Therefore, in the design and fabrication of single-crystal superalloy castings, effectively predicting the tendency for freckle defects to form has received widespread attention. Currently, methods such as experimental methods, the density difference method between alloy solute and melt, and the Reynolds number criterion are commonly used to predict the tendency for freckle defects to form.

[0004] Patent application CN202211245648.6 discloses a method for evaluating the freckle formation tendency of single-crystal superalloys. This method only provides experimental results on the number of freckle chains in single-crystal superalloys of different compositions and stepped samples of specific sizes under different processes. It does not consider or count the total length of freckles, and ignores the restricted growth process of freckles. At the same time, it does not consider the combined effects of casting size and shape characteristics, equipment cooling capacity, and temperature characteristics of the alloy paste region, and has obvious limitations. Therefore, it cannot be used as an effective criterion for judging the freckle formation tendency of single-crystal superalloy castings.

[0005] Patent application CN202110994035.1 discloses a simple and effective method for predicting the freckle formation tendency of single-crystal superalloys, which can accurately predict the freckle defect formation tendency of single-crystal superalloys with different compositions. However, this method only focuses on the influence of alloy composition segregation on freckle formation, and does not consider the comprehensive influence of factors such as casting size characteristics, equipment cooling capacity, dynamic changes in solidification temperature gradient distribution, and solidification rate, making it difficult to evaluate the freckle formation tendency of actual single-crystal superalloy castings.

[0006] Patent application CN202510683731.9 discloses a method for predicting freckle defects in single-crystal blades based on large-module casting technology. This method directly uses parameter values ​​obtained from simulation or literature to calculate Rayleigh number. The process is complex and the accuracy is poor. Even with the improved Rayleigh number formula, it is still not possible to accurately predict the freckle formation tendency of single-crystal high-temperature alloys and lacks practicality.

[0007] In the existing technologies mentioned above, the relevant criteria do not fully consider the casting size and structural characteristics, the solidification paste-like region characteristic parameters of alloys with different compositions, the distribution characteristics and dynamic changes of temperature gradients during directional solidification, and the comprehensive influence of directional solidification process parameters. Furthermore, they neglect the specific formation location of freckle defects in the casting during directional solidification. Therefore, current methods for predicting freckle formation tendency are difficult to accurately predict the freckle formation tendency of single-crystal superalloys with different compositions, castings with different sizes and structures, and under different process parameters, resulting in low accuracy of prediction results. This problem severely restricts the process optimization and defect control capabilities of nickel-based single-crystal superalloys in actual production, thereby affecting the improvement of the yield rate and cost control of single-crystal superalloy castings in aero-engines and ground gas turbines. Summary of the Invention

[0008] To address the technical problem that current methods for predicting freckle formation tendencies are difficult to accurately predict under different compositions of single-crystal superalloys, castings of different sizes and structures, and different process parameters, resulting in low accuracy of prediction results, this invention provides a method for predicting freckle formation tendencies in single-crystal superalloy castings.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows.

[0010] This invention provides a method for predicting the tendency of freckle formation in single-crystal superalloy castings, comprising the following steps: Using single-crystal superalloy castings as samples, the casting modulus of the samples was obtained; the liquidus temperature and solidus temperature of the samples were measured to obtain the solidification temperature range of the mushy region; the minimum value of the temperature gradient of the mushy region in the overall solidification area during the directional solidification process of the samples was obtained by experimental or simulation methods; based on the first product of the casting modulus and the solidification temperature range of the mushy region, and the second product of the directional solidification growth rate and the minimum value of the temperature gradient of the mushy region, the quotient of the first product and the second product was used as the criterion value for freckle formation tendency; the corresponding directional solidification samples were etched, cleaned, and dried to obtain the freckle length of the castings; based on the criterion value for freckle formation tendency under different casting modulus, different sample compositions, and different directional solidification process parameters, and the corresponding freckle length of the castings, the relationship between the criterion value for freckle formation tendency and the freckle length of the castings was determined, in order to predict the freckle formation tendency of different single-crystal superalloy castings under different process conditions.

[0011] This invention comprehensively considers the casting modulus of single-crystal superalloy castings, the solidification temperature range of the mushy region in single-crystal superalloy castings with different compositions, the minimum value of the temperature gradient in the mushy region, and the directional solidification growth rate. Using these factors as key elements, it obtains criterion values ​​for freckle formation tendency under different casting modulus, sample compositions, and directional solidification process parameters, along with the corresponding actual freckle lengths in single-crystal superalloy castings. It then determines the relationship between the criterion value for freckle formation tendency and the freckle length, thereby enabling the prediction of freckle defect formation tendency using the criterion value for freckle formation tendency.

[0012] Preferably, the formula for calculating the criterion value for freckle formation tendency is as follows: C=M×△T / (G min ×V); where C is the criterion value for freckle formation tendency; M is the casting modulus of the sample; △T is the solidification temperature range of the pasty region of the sample; G min V represents the minimum value of the temperature gradient in the pasty region; V is the directional solidification growth rate.

[0013] The lowest value of the temperature gradient in the pasty region corresponds to the location where freckles are prone to form.

[0014] This invention first obtains the product of the casting modulus of the sample and the solidification temperature range of the mushy region, and the second product of the sample's directional solidification growth rate and the lowest value of the temperature gradient in the mushy region. The quotient of the first product and the second product is used as the criterion for freckle formation tendency. This invention improves the accuracy of prediction results by comprehensively considering the casting modulus of single-crystal superalloy castings, the solidification temperature range of the mushy region of single-crystal superalloy castings with different compositions, the lowest value of the temperature gradient in the mushy region, and the directional solidification growth rate.

[0015] In this invention, the minimum value of the temperature gradient of the pasty region in the overall solidification area of ​​the sample during directional solidification is obtained by simulation or actual measurement. When using simulation, actual measurement is required for correction, and the simulation result error is ≤5%.

[0016] Preferably, the relationship between the criterion value for freckle formation tendency and the length of freckles in the casting is as follows: y = -46.62141 × e (-C / 1317.35) +48.13318; where y represents the length of the freckles on the casting; C represents the criterion value for the tendency of freckle formation.

[0017] This invention determines the relationship between the criterion value of freckle formation tendency and the corresponding actual freckle length in the casting by obtaining the criterion value of freckle formation tendency under different casting moduli, sample compositions, and directional solidification process parameters. This allows for the accurate prediction of freckle defect length in single-crystal superalloy castings using the criterion value of freckle formation tendency. In this invention, a larger criterion value of freckle formation tendency indicates a greater freckle formation tendency in the sample, and vice versa.

[0018] Preferably, the method for obtaining the casting modulus of the sample is to use the quotient of the sample volume and the sample surface area as the casting modulus of the sample.

[0019] In this invention, the formula for calculating the casting modulus of the specimen is: M = V / S; where M is the casting modulus of the specimen; V is the volume of the specimen; and S is the surface area of ​​the specimen. The casting modulus in this invention can be calculated using the entire specimen or by dividing the specimen into segments along the directional solidification direction and calculating them separately.

[0020] Preferably, the method for obtaining the solidification temperature range of the paste region of the sample is as follows: under a protective atmosphere, the liquidus temperature and solidus temperature of the sample are determined by differential scanning calorimetry; based on the liquidus temperature and solidus temperature of the sample, the solidification temperature range of the paste region of the sample is obtained.

[0021] This invention uses a differential scanning calorimeter to measure the solidification temperature range of the mushy region in single-crystal superalloy castings. The solidification temperature range of the mushy region is denoted as ΔT. The protective atmosphere is argon. The heating rate is 5 K / min to 10 K / min. The sample size is Φ3 to 3.5 × (2 to 3 mm).

[0022] Preferably, the method for obtaining the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample using actual measurement is as follows: The sample is directionally solidified using a preset directional solidification pulling speed as the directional solidification growth rate. Based on the liquidus temperature and solidus temperature of the sample, the liquidus position and solidus position during the directional solidification process are obtained, and the minimum value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process is obtained.

[0023] Preferably, the parameters for directional solidification of the sample are as follows: The temperature of the holding furnace is 1480℃~1520℃, the pouring temperature is 1480℃~1520℃, and the pulling speed for directional solidification is 1mm / min~9mm / min.

[0024] In this invention, the specific operation for obtaining the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification process of the sample using the experimental method is as follows: A platinum-rhodium-platinum thermocouple is selected and rigorously calibrated before use; a small hole is pre-drilled along the axial direction of the ceramic mold used for directional solidification, i.e., the directional solidification direction, and then the measuring end of the thermocouple is precisely fixed in the pre-drilled hole; at least two or more thermocouples need to be arranged on the mold shell, and the distance between the two thermocouples is denoted as ΔZ, which must be accurately measured. Wherein, ΔZ = Z L -Z S Z L Indicates the position of the liquidus at the preset directional solidification pulling speed; Z S This indicates the position of the solidus line at the preset directional solidification pulling speed.

[0025] The ceramic mold is installed in the directional solidification furnace for normal directional solidification. The temperature change of each thermocouple over time is continuously recorded. Since the mold shell moves at a certain pulling speed, the thermocouple positions are relatively fixed, thus the temperature-time relationship can be converted into a temperature-position relationship. The formula for calculating the instantaneous height position of the thermocouple is Z = V × t, where Z is the instantaneous height position of the thermocouple, V is the preset directional solidification pulling speed, and t is time. Z is calculated using the formula for the instantaneous height position of the thermocouple. L and Z S Then, according to the formula ΔZ=Z L -Z S This allows us to obtain the distance between the two thermocouples.

[0026] Plot all the converted thermocouple data points into a curve of temperature versus the instantaneous height position of the thermocouple, thus obtaining the relationship curve between temperature and the instantaneous height position of the thermocouple.

[0027] Based on the results measured by the differential scanning calorimeter, the liquidus temperature and solidus temperature can be accurately determined. Then, the liquidus and solidus positions corresponding to the liquidus and solidus temperatures can be found on the relationship curve between temperature and the instantaneous height position of the thermocouple. The temperature gradient value of the mushy region can be obtained according to the calculation formula of the temperature gradient value of the mushy region.

[0028] Preferably, the formula for calculating the temperature gradient in the pasty region is as follows: G = (T) L -T S ) / (Z L -Z S ); where G represents the temperature gradient value of the mushy region; T L T represents the liquidus temperature; S Z represents the solidus temperature; L Indicates the position of the liquidus at the preset directional solidification pulling speed; Z S This indicates the position of the solidus line at the preset directional solidification pulling speed.

[0029] Preferably, the method for obtaining the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample using simulation is as follows: The directional solidification process of the sample was simulated to obtain the temperature gradient distribution curve of the pasty region at different locations of the sample, and the minimum value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process of the sample was obtained.

[0030] In this invention, the method for simulating the directional solidification process of the sample is as follows: ProCAST is used to simulate the solidification process of the casting to obtain the temperature gradient distribution of the pasty region at different positions of the sample during the directional solidification process, thereby obtaining the lowest value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process of the sample.

[0031] In this invention, the minimum value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process of the sample is obtained by simulation or actual measurement. When simulation is used, actual measurement is required for correction. The simulation result error is ≤5%.

[0032] Preferably, the material of the single-crystal high-temperature alloy casting is a nickel-based alloy; the casting modulus is 0.2mm to 20mm.

[0033] Preferably, the single-crystal superalloy casting is in the form of a plate, rod, or variable cross-section; the dimensional parameters of the plate-shaped single-crystal superalloy casting are: thickness 0.6mm to 20mm, width 10mm to 100mm, and length 30mm to 500mm; the dimensional parameters of the rod-shaped single-crystal superalloy casting are: diameter 5mm to 50mm and length 100mm to 300mm.

[0034] In this invention, the material of the single-crystal superalloy casting is a first-generation nickel-based alloy, a second-generation nickel-based alloy, or a third-generation nickel-based alloy; for example, the material of the single-crystal superalloy casting is DD413, DD6, DD33, PWA1483, CMSX-4, or CMSX-6. In this invention, the single-crystal superalloy casting is prepared using a spiral crystal selection method or a seed crystal method.

[0035] Preferably, the etching agent used for etching the corresponding directionally solidified samples is a mixture of hydrochloric acid and hydrogen peroxide at a volume ratio of 3–5:1, or a mixture of hydrochloric acid, hydrogen peroxide, and water at a volume ratio of 2–3:1:1–2, and the etching time is 1 min–10 min. The mass fraction of H2O2 in the hydrogen peroxide is 30%, and the mass fraction of HCl in the hydrochloric acid is 36%–38%.

[0036] In this invention, the number of single-crystal high-temperature alloy casting samples obtained by directional solidification with the same process parameters is at least 6. When calculating the freckle length of the casting, the average value of the freckle length of all samples is taken.

[0037] The beneficial effects of this invention are: This invention comprehensively considers the casting modulus of single-crystal superalloy castings, the solidification temperature range of the mushy region in single-crystal superalloy castings with different compositions, the minimum value of the temperature gradient in the mushy region, and the directional solidification growth rate. Using these factors as key elements, it obtains the criterion values ​​for freckle formation tendency under different casting modulus, different sample compositions, and different directional solidification process parameters, along with the corresponding actual freckle lengths of the single-crystal superalloy castings. It then determines the relationship between the criterion value for freckle formation tendency and the predicted freckle length, thereby enabling accurate prediction of freckle defect formation tendency in different castings of different single-crystal superalloys under different process conditions using the criterion value for freckle formation tendency.

[0038] This invention improves the accuracy of freckle formation tendency prediction by comprehensively considering the casting modulus of single-crystal superalloy castings, the solidification temperature range of the mushy region of single-crystal superalloy castings with different compositions, the minimum value of the temperature gradient of the mushy region, and the directional solidification growth rate, with an error of less than ±10%. Attached Figure Description

[0039] Figure 1 The graph shows the relationship between the criterion value for freckle formation tendency and the freckle length in single-crystal superalloy castings with different casting moduli, compositions, and solidification process parameters. Figure 1 The illustration shows the relationship between the criterion value for freckle formation tendency and the length of freckles on the casting.

[0040] Figure 2The differential scanning calorimetry curve is the cooling process of the single-crystal high-temperature alloy casting in Example 1.

[0041] Figure 3 The differential scanning calorimetry curve is the cooling process of the single-crystal high-temperature alloy casting in Example 5. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0043] 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.

[0044] A method for predicting the freckle formation tendency of single-crystal superalloy castings includes the following steps: S1. Using a single-crystal high-temperature alloy casting as a sample, obtain the casting modulus of the sample.

[0045] The method for obtaining the casting modulus of a specimen is as follows: the quotient of the specimen's volume and its surface area is used as the casting modulus. In this invention, the formula for calculating the casting modulus of a specimen is: M = V / S; where M is the casting modulus of the specimen; V is the volume of the specimen; and S is the surface area of ​​the specimen. The casting modulus in this invention can be calculated using the entire specimen or by dividing the specimen into segments along the direction of directional solidification and calculating them separately.

[0046] Single-crystal superalloy castings are in the form of plates, rods, or variable cross-sections. The dimensional parameters of plate-shaped single-crystal superalloy castings are: thickness 0.6mm to 20mm, width 10mm to 100mm, and length 30mm to 500mm. The dimensional parameters of rod-shaped single-crystal superalloy castings are: diameter 5mm to 50mm and length 100mm to 300mm.

[0047] The material of the single-crystal superalloy casting is a nickel-based superalloy; the casting modulus is 0.2 mm to 20 mm. Specifically, the material of the single-crystal superalloy casting is a first-generation, second-generation, or third-generation nickel-based superalloy; for example, the material of the single-crystal superalloy casting is DD413, DD6, DD33, PWA1483, CMSX-4, or CMSX-6. In this invention, the single-crystal superalloy casting is prepared using a spiral crystal selection method and a seed crystal method.

[0048] S2. Measure the liquidus temperature and solidus temperature of the sample to obtain the solidification temperature range of the pasty region of the sample.

[0049] The method for obtaining the solidification temperature range of the paste-like region of the sample is as follows: Under a protective atmosphere, the liquidus temperature and solidus temperature of the sample are determined by differential scanning calorimetry (DSC). Based on the liquidus temperature and solidus temperature of the sample, the solidification temperature range of the paste-like region is obtained. This invention uses a differential scanning calorimeter to measure the solidification temperature range of the paste-like region in single-crystal high-temperature alloy castings. The solidification temperature range of the paste-like region is denoted as ΔT. The protective atmosphere is argon. The heating rate is 5 K / min to 10 K / min. The sample size is Φ3 to 3.5 × (2 to 3 mm).

[0050] S3. Obtain the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification process of the sample using actual measurement or simulation methods.

[0051] In this invention, the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample can be obtained by either actual measurement or simulation. Specifically, the actual measurement method involves measuring the directional solidification of the sample, while the simulation method involves simulating the directional process of the sample.

[0052] The method for obtaining the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample using experimental measurement is as follows: The sample is directionally solidified using a preset directional solidification pulling speed as the directional solidification growth rate. Based on the liquidus temperature and solidus temperature of the sample, the liquidus position and solidus position during the directional solidification process are obtained, and the minimum value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process is obtained.

[0053] In this invention, the minimum temperature gradient value of the pasty region in the overall solidification area during directional solidification is obtained by actual measurement. Platinum-rhodium / platinum thermocouples are selected and rigorously calibrated before use. Small holes are pre-drilled along the axial direction of the ceramic mold used for directional solidification, i.e., the direction of directional solidification, and the measuring ends of the thermocouples are then precisely fixed within these holes. At least two or more thermocouples need to be arranged on the mold shell, and the distance between two thermocouples is denoted as ΔZ, which must be accurately measured. Wherein, ΔZ = Z L -Z S Z L Indicates the position of the liquidus at the preset directional solidification pulling speed; Z S This indicates the position of the solidus line at the preset directional solidification pulling speed.

[0054] The ceramic mold is installed in the directional solidification furnace for normal directional solidification. The temperature change of each thermocouple over time is continuously recorded. Since the mold shell moves at a certain pulling speed, the thermocouple positions are relatively fixed, thus the temperature-time relationship can be converted into a temperature-position relationship. The formula for calculating the instantaneous height position of the thermocouple is Z = V × t, where Z is the instantaneous height position of the thermocouple, V is the preset directional solidification pulling speed, and t is time. Z is calculated using the formula for the instantaneous height position of the thermocouple. L and Z S Then, according to the formula ΔZ=Z L -Z S This allows us to obtain the distance between the two thermocouples.

[0055] Plot all the converted thermocouple data points into a curve of temperature versus the instantaneous height position of the thermocouple, thus obtaining the relationship curve between temperature and the instantaneous height position of the thermocouple.

[0056] Based on the measurement results of the differential scanning calorimeter, the liquidus temperature and solidus temperature can be accurately determined. Then, the liquidus and solidus positions corresponding to the liquidus and solidus temperatures can be found on the relationship curve between temperature and the instantaneous height position of the thermocouple. The temperature gradient value of the mushy region can be obtained according to the calculation formula of the temperature gradient value of the mushy region.

[0057] Preferably, the formula for calculating the temperature gradient in the pasty region is as follows: G = (T) L -T S ) / (Z L -Z S ); where G represents the temperature gradient value of the mushy region; T L T represents the liquidus temperature; S Z represents the solidus temperature; L Indicates the position of the liquidus at the preset directional solidification pulling speed; Z S This indicates the position of the solidus line at the preset directional solidification pulling speed.

[0058] Preferably, the method for obtaining the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample using simulation is as follows: The directional solidification process of the sample was simulated to obtain the temperature gradient distribution curve of the pasty region at different locations of the sample, and the minimum value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process of the sample was obtained.

[0059] In this invention, the method for simulating the directional solidification process of the sample is as follows: ProCAST is used to simulate the solidification process of the casting, obtaining the temperature gradient distribution of the mushy region at different locations of the sample during directional solidification, thereby obtaining the minimum value of the temperature gradient of the mushy region in the overall solidification area during the directional solidification process. In this invention, the minimum value of the temperature gradient of the mushy region in the overall solidification area during the directional solidification process is obtained using either simulation or experimental methods. When using the simulation method, correction using experimental methods is required, and the simulation result error is ≤5%.

[0060] The parameters for directional solidification of the sample are as follows: The temperature of the holding furnace is 1480℃~1520℃, the pouring temperature is 1480℃~1520℃, and the pulling speed for directional solidification is 1mm / min~9mm / min.

[0061] In this invention, a preset directional solidification pulling speed is used as the directional solidification growth speed.

[0062] S4. Based on the first product of the casting modulus of the sample and the solidification temperature range of the mushy region, and the second product of the sample's directional solidification growth rate and the lowest value of the temperature gradient of the mushy region, the quotient of the first product and the second product is used as the criterion value for freckle formation tendency.

[0063] The formula for calculating the criterion value for freckle formation tendency is as follows: C=M×△T / (G min ×V); where C is the criterion value for freckle formation tendency; M is the casting modulus of the sample, in mm; △T is the solidification temperature range of the pasty region of the sample, in K; G min is the minimum value of the temperature gradient in the pasty region, in K / mm; V is the directional solidification growth rate, in mm / s.

[0064] The higher the criterion value for freckle formation tendency, the greater the freckle formation tendency of the sample, and vice versa.

[0065] S5. Corrosion treatment is performed on the corresponding directional solidification samples, followed by cleaning and drying to obtain the length of the freckles on the casting.

[0066] The etching reagents used for etching the corresponding directional solidification samples are a mixture of hydrochloric acid and hydrogen peroxide at a volume ratio of 3–5:1, or a mixture of hydrochloric acid, hydrogen peroxide, and water at a volume ratio of 2–3:1:1–2. The etching time is 1 min–10 min. The mass fraction of H2O2 in the hydrogen peroxide is 30%, and the mass fraction of HCl in the hydrochloric acid is 36%–38%.

[0067] In this invention, the number of single-crystal high-temperature alloy casting samples obtained by directional solidification with the same process parameters is at least 6. When calculating the freckle length of the casting, the average value of the freckle length of all samples is taken.

[0068] S6. Based on the criteria value of freckle formation tendency under different casting modulus, different sample composition and different directional solidification process parameters and the corresponding casting freckle length, determine the relationship between the criteria value of freckle formation tendency and the casting freckle length, so as to predict the freckle formation tendency of different single crystal high temperature alloy castings under different process conditions.

[0069] The present invention mainly obtains the criteria value of freckle formation tendency and the corresponding freckle length of the casting under different casting modulus, different sample composition and different directional solidification process parameters according to steps S1 to S5, and determines the relationship between the criteria value of freckle formation tendency and the freckle length of the casting.

[0070] The relationship between the criterion value for freckle formation tendency and the length of freckles in the casting is as follows: y = -46.62141 × e (-C / 1317.35) +48.13318; where y represents the length of the freckles on the casting; C represents the criterion value for the tendency of freckle formation.

[0071] In this invention, the higher the criterion value for freckle formation tendency, the greater the freckle formation tendency of the sample, and vice versa.

[0072] The technical solution of the present invention will be further described below through specific embodiments. Unless otherwise specified, the methods described in the following embodiments are conventional methods; the reagents and materials described are commercially available unless otherwise specified.

[0073] Example 1 A method for predicting the freckle formation tendency of single-crystal superalloy castings includes the following steps: A single-crystal superalloy casting was used as the sample. The sample had a thickness of 2 mm, a width of 40 mm, and a length of 35 mm. The casting modulus of the sample was obtained using the casting modulus calculation formula: M = V / S, where V is the casting volume and S is the casting surface area. The calculated casting modulus was 0.927 mm. The single-crystal superalloy was the third-generation nickel-based superalloy DD33. By mass percentage, the alloy composition was 2.5% Cr, 9% Co, 6% W, 1.5% Mo, 6% Al, 0.2% Ti, 8% Ta, 0.1% Hf, and 4.0% Re, with the balance being Ni, totaling 100%.

[0074] The solidification temperature range of the mushy region in single-crystal superalloy castings was measured using differential scanning calorimetry. The sample size was Φ3×2mm, the protective gas was argon, and the heating rate was 10K / min. The measured solidification temperature range of the mushy region was 1333.3℃~1401.9℃, and the width of the mushy region was 68.6℃. (See attached image.) Figure 2 Single-crystal high-temperature alloy castings were prepared using the spiral crystal selection method. The directional solidification process of the single-crystal high-temperature alloy was as follows: holding furnace temperature 1520℃, pouring temperature 1520℃, and pulling speed 1mm / min.

[0075] The minimum value of the temperature gradient in the mushy region of the overall solidification zone during the directional solidification of the sample was obtained by simulation method as G. min =2.4K / mm; The C value was calculated to be 1577.8 using the formula for calculating the criterion value of freckle formation tendency, with the unit being mms, and the predicted freckle length value was 34.05mm.

[0076] After the actual castings were directionally solidified, macroscopic etching was performed using a mixture of hydrochloric acid and hydrogen peroxide at a volume ratio of 3:1 for 1 minute. The castings were then rinsed with water and dried. Six samples were tested, and the average length of the freckles was 35 mm, with a predicted relative error of -2.7%. The results indicate that single-crystal castings of this composition have a greater tendency to form freckles under this directionally solidified process.

[0077] Example 2 A method for predicting the freckle formation tendency of single-crystal superalloy castings includes the following steps: A single-crystal superalloy casting was used as the sample. The sample had a thickness of 10 mm, a width of 40 mm, and a length of 35 mm. The casting modulus of the sample was obtained using the casting modulus calculation formula: M = V / S, where V is the casting volume and S is the casting surface area. The calculated casting modulus was 3.88 mm. The single-crystal superalloy was the second-generation nickel-based superalloy CMSX-4. By mass percentage, the alloy composition was 6.5% Cr, 9% Co, 6% W, 0.5% Mo, 6% Al, 0.8% Ti, 7.0% Ta, and 3% Re, with the balance being Ni, totaling 100%.

[0078] The solidification temperature range of the mushy region in single-crystal superalloy castings was measured using differential scanning calorimetry. The sample size was Φ3×2mm, the protective gas was argon, and the heating rate was 10K / min. The measured solidification temperature range of the mushy region was 1339.4℃~1408.4℃, and the width of the mushy region was 68.0℃. Single-crystal superalloy castings were prepared using the spiral crystal selection method. The directional solidification process of the single-crystal superalloy was as follows: holding furnace temperature 1500℃, pouring temperature 1500℃, and pulling speed 1mm / min.

[0079] The minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample was obtained by experimental measurement as G. min =2.6K / mm; The C value was calculated using the formula for calculating the criterion value of freckle formation tendency, which is 6088.6, in mms, and the predicted freckle length is 47.67mm.

[0080] After the actual castings were directionally solidified, macroscopic etching was performed using a mixture of hydrochloric acid and hydrogen peroxide at a volume ratio of 3:1 for 1 minute. The castings were then rinsed with water and dried. Six samples were tested, and the average length of the freckles was 50 mm, with a predicted relative error of -4.66%. The results indicate that single-crystal castings of this composition have a high tendency to form freckles under this directionally solidified process.

[0081] Example 3 A method for predicting the freckle formation tendency of single-crystal superalloy castings includes the following steps: A single-crystal superalloy casting was used as the sample. The sample had a thickness of 0.6 mm, a width of 40 mm, and a length of 35 mm. The casting modulus of the sample was obtained using the casting modulus calculation formula: M = V / S, where V is the casting volume and S is the casting surface area. The calculated casting modulus was 0.2937 mm. The single-crystal superalloy was the third-generation nickel-based superalloy DD33. By mass percentage, the alloy composition was 2.5% Cr, 9% Co, 6% W, 1.5% Mo, 6% Al, 0.2% Ti, 8% Ta, 0.1% Hf, and 4.0% Re, with the balance being Ni, totaling 100%.

[0082] The solidification temperature range of the mushy region in single-crystal superalloy castings was measured using differential scanning calorimetry. The sample size was Φ3×2mm, the protective gas was argon, and the heating rate was 10K / min. The measured solidification temperature range of the mushy region was 1334.8℃~1403.4℃, and the width of the mushy region was 68.6℃. Single-crystal superalloy castings were prepared using the seed crystal method, with the crystal orientation in the

[001] direction. The directional solidification process of the single-crystal superalloy was as follows: holding furnace temperature 1490℃, pouring temperature 1500℃, and pulling speed 6mm / min.

[0083] The minimum value of the temperature gradient in the mushy region of the overall solidification zone during the directional solidification of the sample was obtained by simulation method as G. min =10.0K / mm; The C value was calculated to be 20.15 using the formula for calculating the criterion value of freckle formation tendency, in mms, and the predicted freckle length value was 2.22mm.

[0084] After the actual castings were directionally solidified, macroscopic etching was performed using a mixture of hydrochloric acid and hydrogen peroxide at a volume ratio of 3:1 for 1 minute. The castings were then rinsed with water and dried. Six samples were tested, and the average freckle length was 2.0 mm, with a predicted relative error of -6.0%. The results indicate that the tendency for freckle formation in single-crystal superalloy castings of this composition is very small under this directionally solidified process.

[0085] Example 4 A method for predicting the freckle formation tendency of single-crystal superalloy castings includes the following steps: A single-crystal superalloy casting was used as the sample, with a diameter of 10 mm and a length of 300 mm. The casting modulus of the sample was obtained using the casting modulus calculation formula: M=V / S, where V is the casting volume and S is the casting surface area. The calculated casting modulus was 2.479 mm. The single-crystal superalloy was the third-generation nickel-based superalloy DD33, with the alloy composition by mass percentage as follows: 2.5%Cr, 9%Co, 6%W, 1.5%Mo, 6%Al, 0.2%Ti, 8%Ta, 0.1%Hf, and 4.0%Re, with the balance being Ni, totaling 100%.

[0086] The solidification temperature range of the mushy region in single-crystal superalloy castings was measured using differential scanning calorimetry. The sample size was Φ3×3mm, the protective gas was argon, and the heating rate was 10K / min. The measured solidification temperature range of the mushy region was 1334.8℃~1403.4℃, and the width of the mushy region was 68.6℃. Single-crystal superalloy castings were prepared using the spiral crystal selection method. The directional solidification process of the single-crystal superalloy was as follows: holding furnace temperature 1500℃, pouring temperature 1520℃, and pulling speed 6mm / min.

[0087] The lowest temperature gradient value of the pasty region in the overall solidification area during the directional solidification process of the sample was obtained by actual measurement method, which was 4.0 K / mm; the C value was calculated as 423.6 using the formula for calculating the criterion value of freckle formation tendency, in mms, and the predicted freckle length value was 14.33 mm.

[0088] After the actual castings were directionally solidified, macroscopic etching was performed using a mixture of hydrochloric acid and hydrogen peroxide at a volume ratio of 3:1 for 5 minutes. The castings were then rinsed with water and dried. Six samples were tested, and the average length of the freckles was 13.4 mm, with an error of 6.94%. The results indicate that single-crystal castings of this composition exhibit a certain tendency for freckle formation under this directionally solidified process.

[0089] Example 5 A method for predicting the freckle formation tendency of single-crystal superalloy castings includes the following steps: A single-crystal high-temperature alloy casting was used as the sample. The sample had a thickness of 10 mm, a width of 40 mm, and a length of 35 mm. The casting modulus of the sample was obtained using the casting modulus calculation formula: M = V / S, where V is the casting volume and S is the casting surface area. The casting modulus was 3.88 mm. The single-crystal high-temperature alloy was a first-generation single-crystal high-temperature alloy SX-1. By mass percentage, the alloy composition was 12% Cr, 9% Co, 2% Mo, 5% W, 5% Ta, and 5% Al, with the balance being Ni, totaling 100%.

[0090] The solidification temperature range of the mushy region in single-crystal superalloy castings was measured using differential scanning calorimetry. The sample size was Φ3×2mm, the protective gas was argon, and the heating rate was 10K / min. The measured solidification temperature range of the mushy region was 1340.91℃~1349.38℃, and the width of the mushy region was 8.47℃ (K). (See attached image.) Figure 3 The single-crystal high-temperature alloy castings were prepared using the spiral crystal selection method. The directional solidification process of the single-crystal high-temperature alloy was as follows: holding furnace temperature 1500℃, pouring temperature 1520℃, and pulling speed 3mm / min.

[0091] The lowest temperature gradient value of the pasty region in the overall solidification area during the directional solidification process of the sample was obtained by actual measurement method, which was 3.0 K / mm; the C value was calculated as 259.2 using the criterion formula for freckle formation tendency, in mms, and the predicted freckle length was 9.84 mm.

[0092] After the actual castings underwent directional solidification, macroscopic etching was performed using a mixture of hydrochloric acid, hydrogen peroxide, and water in a volume ratio of 2:1:1 for 2 minutes. The castings were then rinsed with clean water and dried. Six samples were tested, and the average length of the freckles was 10 mm, with a prediction error of -1.6%. The results indicate that single-crystal castings of this composition have a weak tendency to form freckles under this directional solidification process.

[0093] Example 6 A method for predicting the freckle formation tendency of single-crystal superalloy castings includes the following steps: A single-crystal superalloy casting was used as the sample. The single-crystal superalloy casting had a variable cross-section extended structure. The first segment had a thickness of 10 mm, a width of 10 mm, and a length of 35 mm; the second segment had a thickness of 10 mm, a width of 20 mm, and a length of 35 mm; and the third segment had a thickness of 10 mm, a width of 40 mm, and a length of 35 mm. The casting modulus of the sample was obtained using the casting modulus calculation formula: M = V / S, where V is the casting volume and S is the casting surface area. The casting modulus was 3.876 mm. The single-crystal superalloy was the third-generation nickel-based superalloy DD33. By mass percentage, the alloy composition was 2.5% Cr, 9% Co, 6% W, 1.5% Mo, 6% Al, 0.2% Ti, 8% Ta, 0.1% Hf, and 4.0% Re, with the balance being Ni, totaling 100%.

[0094] The solidification temperature range of the mushy region in single-crystal superalloy castings was measured using a differential scanning calorimeter. The sample size was Φ3.5×2mm, the protective gas was argon, and the heating rate was 10K / min. The measured solidification temperature range of the mushy region was 1334.8℃~1403.4℃, and the width of the mushy region was 68.6℃.

[0095] Single-crystal high-temperature alloy castings were prepared using the spiral crystal selection method. The directional solidification process of the single-crystal high-temperature alloy was as follows: holding furnace temperature 1500℃, pouring temperature 1520℃, and pulling speed 6mm / min.

[0096] The lowest temperature gradient value of the pasty region in the overall solidification area during the directional solidification process of the sample was obtained by actual measurement method, which was 7.0 K / mm; the C value was calculated as 379 (mms) using the formula for calculating the criterion value of freckle formation tendency, and the predicted freckle length value was 13.17 mm.

[0097] After directional solidification of the castings, macroscopic etching was performed using a mixture of hydrochloric acid, hydrogen peroxide, and water in a volume ratio of 2:1:1 for 2 minutes. The castings were then rinsed with clean water and dried. Six samples were tested, and the average length of the freckles was 12 mm, with a prediction error of 9.75%. The results indicate that single-crystal castings of this composition exhibit a certain tendency for freckle formation under this directional solidification process.

[0098] Based on the method for predicting the freckle formation tendency of single-crystal superalloy castings, a relationship curve between the criterion value of the freckle formation tendency and the freckle length of single-crystal superalloy castings under different casting moduli, compositions, and solidification process parameters is established. Figure 1 As shown, this criterion value is used to predict the freckle formation tendency of different single-crystal superalloys, different castings, and different process conditions. The larger the criterion value for freckle formation tendency, the greater the freckle formation tendency of the sample, and vice versa.

[0099] The relationship between the criterion value for freckle formation tendency and the length of freckles in the casting is as follows: y = -46.62141 × e (-C / 1317.35) +48.13318; where y represents the length of the freckles on the casting; C represents the criterion value for the tendency of freckle formation.

[0100] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the tendency of freckle formation in single-crystal superalloy castings, characterized in that, Includes the following steps: Using single-crystal high-temperature alloy castings as samples, the casting modulus of the samples was obtained; the liquidus temperature and solidus temperature of the samples were measured to obtain the solidification temperature range of the pasty region of the samples. The minimum value of the temperature gradient in the paste-like region of the overall solidification area during the directional solidification of the sample was obtained by means of actual measurement or simulation. The quotient of the first product of the casting modulus of the sample and the solidification temperature range of the mushy region, and the second product of the directional solidification growth rate of the sample and the lowest value of the temperature gradient of the mushy region, is used as the criterion value for the tendency of freckle formation. Corrosion treatment was performed on the corresponding directionally solidified samples, followed by cleaning and drying to obtain the length of the freckles on the castings. Based on the criteria values ​​for freckle formation tendency under different casting moduli, different sample compositions, and different directional solidification process parameters, and the corresponding casting freckle lengths, the relationship between the criteria values ​​for freckle formation tendency and the casting freckle lengths is determined, in order to predict the freckle formation tendency of different single-crystal high-temperature alloy castings under different process conditions.

2. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 1, characterized in that, The formula for calculating the criterion value for freckle formation tendency is as follows: C=M×△T / (G min ×V); Where C is the criterion value for freckle formation tendency; M is the casting modulus of the sample; ΔT is the solidification temperature range of the pasty region of the sample; G min V represents the minimum value of the temperature gradient in the pasty region; V is the directional solidification growth rate.

3. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 1, characterized in that, The relationship between the criterion value for freckle formation tendency and the length of freckles in the casting is as follows: y=-46.62141×e (-C / 1317.35) +48.13318; Where y represents the length of the freckles on the casting; C represents the criterion value for the tendency of freckle formation.

4. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 1, characterized in that, The method for obtaining the casting modulus of a sample is as follows: the quotient of the sample's volume and its surface area is used as the casting modulus of the sample. The method for obtaining the solidification temperature range of the pasty region of the sample is as follows: under a protective atmosphere, the liquidus temperature and solidus temperature of the sample are determined by differential scanning calorimetry; based on the liquidus temperature and solidus temperature of the sample, the solidification temperature range of the pasty region of the sample is obtained.

5. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 1, characterized in that, The method for obtaining the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample using experimental measurement is as follows: The sample is directionally solidified using a preset directional solidification pulling speed as the directional solidification growth rate. Based on the liquidus temperature and solidus temperature of the sample, the liquidus position and solidus position during the directional solidification process are obtained, and the minimum value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process is obtained.

6. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 5, characterized in that, The parameters for directional solidification of the sample are as follows: The temperature of the holding furnace is 1480℃~1520℃, the pouring temperature is 1480℃~1520℃, and the pulling speed for directional solidification is 1mm / min~9mm / min.

7. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 5, characterized in that, The formula for calculating the temperature gradient in the pasty region is as follows: G=(T L -T S ) / (Z L -Z S ); Where G represents the temperature gradient value of the mushy region; T L T represents the liquidus temperature; S Z represents the solidus temperature; L Indicates the position of the liquidus at the preset directional solidification pulling speed; Z S This indicates the position of the solidus line at the preset directional solidification pulling speed.

8. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 1, characterized in that, The method for obtaining the minimum value of the temperature gradient in the pasty region of the overall solidification area during the directional solidification of the sample using simulation is as follows: The directional solidification process of the sample was simulated to obtain the temperature gradient distribution curve of the pasty region at different locations of the sample, and the minimum value of the temperature gradient of the pasty region in the overall solidification area during the directional solidification process of the sample was obtained.

9. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 1, characterized in that, The material of the single-crystal high-temperature alloy casting is a nickel-based alloy; the casting module is 0.2mm to 20mm.

10. The method for predicting the freckle formation tendency of single-crystal superalloy castings according to claim 1, characterized in that, Single-crystal high-temperature alloy castings are in the form of plates, rods, or variable cross-sections; The dimensional parameters of the plate-shaped single-crystal high-temperature alloy castings are: thickness 0.6mm~20mm, width 10mm~100mm, and length 30mm~500mm; The dimensional parameters of the rod-shaped single-crystal high-temperature alloy castings are: diameter 5mm~50mm, length 100mm~300mm.

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