A method to quantify the relationship between stress rupture and γ′ phase rafting in directionally solidified superalloys

Abstract

The present invention provides a method for quantifying the relationship between the stress and rafting of the γ′ phase in a directionally solidified superalloy. This method is based on the γ′ phase morphology under a SEM electron microscope. The original image is used as the processing object. Given that the alloy's γ′ phase initially exhibits a generally cubic morphology, an equal number of cross-sections are made in the directions parallel and perpendicular to the stress. The number of intersections between the longitudinal and transverse cross-sections and the γ′ phase is counted, and the ratio is calculated to define the rafting threshold of the γ′ phase. The degree of rafting at failure at different stresses is then determined, and the relationship between the change in the rafted γ′ phase at the time of fracture and the stress is quantitatively reflected. The present method is capable of quantitatively characterizing the degree of rafting of the γ′ phase after fracture in a directionally solidified superalloy. By constructing a rafting prediction model, the degree of rafting of the γ′ phase after fracture at a certain temperature can be effectively predicted, the degradation state of the alloy structure can be judged, and the method provides guidance for evaluating the high-temperature stress and rafting properties of directionally solidified superalloys.

Description

Technical Field

[0001] The invention belongs to the field of nickel-based high-temperature alloys, and in particular relates to a method for quantifying the relationship between the endurance stress and the rafting of a γ′ phase in a directionally solidified high-temperature alloy. Background Art

[0002] Studying the degradation of the γ′ phase during stress-induced deformation in nickel-based superalloys is a crucial component of studying the stress-induced properties of superalloys. Under long-term stress-induced deformation, the γ′ phase undergoes various transformations, including coarsening, spheroidization, and rafting. These transformations can lead to varying degrees of degradation in alloy properties. For directionally solidified superalloys with a high volume fraction of the γ′ phase, rafting of the γ′ phase is often used to assess the extent of damage to the alloy structure. Prior art methods for studying γ′ phase rafting during stress-induced deformation tests rely on controlled variables. For example, under conditions of varying stresses and duration, the rafting process is reflected, and the quantitative calculations yield predictable results. However, since the time to fracture varies under stress-induced deformation, the degree of γ′ phase rafting at fracture is unpredictable. Therefore, a quantitative method is needed to address the lack of existing methods for understanding the relationship between stress-induced deformation and the degree of γ′ phase rafting at fracture. Summary of the Invention

[0003] The present invention discloses a method for quantifying the relationship between the stress of the endurance test of a directionally solidified high-temperature alloy and the rafting of the γ′ phase, so as to solve any of the above and other potential problems of the prior art.

[0004] In order to solve the above problems, the technical solution of the present invention is: a method for quantifying the relationship between the stress of the endurance test and the rafting of the γ′ phase in a directionally solidified high-temperature alloy, the method specifically comprising the following steps:

[0005] S1) acquiring image data of a quantitative directionally solidified superalloy sample to obtain a reference value of γ′ phase rafting;

[0006] S2) confirming the fully rafted region of the γ′ phase according to the rafted reference value of the γ′ phase obtained in S1);

[0007] S3) establishing a fitting curve based on the quantized value data within the fully rafted region of the γ′ phase obtained in S2) to obtain a rafting prediction model for the γ′ phase;

[0008] S4) using the endurance stress data of the sample to be tested as input to a γ′ phase rafting prediction model, and outputting a quantitative value of the rafting degree of the γ′ phase of the sample to be tested.

[0009] The quantitative directionally solidified high-temperature alloy sample is a nickel-based high-temperature alloy.

[0010] Furthermore, the quantified directionally solidified high-temperature alloy samples include samples that have not been subjected to deformation treatment and samples that have been subjected to permanent deformation treatment.

[0011] Furthermore, the specific steps in S1) are:

[0012] S1.1) Obtain a high-magnification γ′ phase image of the sample before deformation treatment;

[0013] S1.2) converting the high-magnification γ′ phase morphology image into a binary image by binarization processing;

[0014] S1.3) Process the binary image using the line-section method to obtain the number of intersections between all horizontal and vertical lines and the γ′ phase boundary;

[0015] S1.4) Calculate the number of intersections between the transverse and longitudinal sections obtained in S1.3) and the γ′ phase boundary to determine a quantitative reference value v0 of the initial γ′ phase morphology.

[0016] Further, the specific steps of S2) are:

[0017] S2.1) Obtain a high-magnification γ′ phase morphology image near the fracture of the specimen after sustained deformation treatment;

[0018] S2.2) converting the high-magnification γ′ phase morphology image into a binary image by binarization processing;

[0019] S2.3) Using the line-cut method to process the binary image, count the number of intersections between all horizontal and vertical lines and the γ′ phase boundary;

[0020] S2.4) Calculate the number of intersections between the transverse and longitudinal sections obtained in S2.3) and the γ′ phase boundary to determine the quantitative value v of the initial γ′ phase morphology;

[0021] S2.5) Subtract the quantized value v obtained in S2.4) from the quantized reference value v0 obtained in S1.4), and select the quantized value v with a difference greater than 0.2 as the fully oriented rafting interval of the γ′ phase.

[0022] Furthermore, the quantization reference value v0 is obtained by the following formula:

[0023]

[0024] Where T0 is the number of intersections between the transverse section of the sample without deformation treatment and the γ′ phase boundary, and P0 is the number of intersections between the longitudinal section of the sample without deformation treatment and the γ′ phase boundary.

[0025] Furthermore, the quantized value v is obtained by the following formula:

[0026]

[0027] Where T is the number of intersections between the transverse section of the deformed specimen and the γ′ phase boundary, and P is the number of intersections between the longitudinal section of the deformed specimen and the γ′ phase boundary.

[0028] Further, the specific steps of S3) are:

[0029] S3.2) Select all data points within the fully oriented rafted region of the γ′ phase and establish a fitting curve;

[0030] S3.3) The least squares method is used to construct a rafting prediction model for the γ′ phase.

[0031] Furthermore, the rafting prediction model of the γ′ phase is:

[0032] y=C0+C1x+C2x 2 +C3x 3 +…+C n x n ,

[0033] Where: x is the endurance stress data of the sample, y is the quantitative value of the rafting degree corresponding to a certain endurance stress, C0…C n is an undetermined coefficient, which is obtained from the endurance stress data and the quantitative value of statistics; the value range of n is a positive integer greater than 0.

[0034] Another object of the present invention is to provide a system for implementing the above method, the system comprising:

[0035] An acquisition module, used to obtain quantitative image data of directionally solidified high-temperature alloy samples;

[0036] A data processing module is used to analyze and process the image data of the quantitative directionally solidified high-temperature alloy sample to obtain a rafting reference value and a rafting quantification value, and finally confirm the complete rafting interval;

[0037] The prediction module is used to establish a fitting curve according to the complete rafting interval, obtain a rafting prediction model, and finally output a quantitative value of the rafting degree of the sample to be tested.

[0038] A readable storage medium includes a memory storing a program and a processor, wherein the processor executes the above-mentioned method for quantifying the relationship between the stress of the endurance test of a directionally solidified high-temperature alloy and the rafting of the γ′ phase.

[0039] The beneficial effects of the present invention are as follows: due to the adoption of the above technical solution, the method of the present invention has the ability to quantitatively characterize the degree of rafting of the γ′ phase after sustained fracture of a directionally solidified high-temperature alloy. By constructing a rafting prediction model, the degree of rafting of the γ′ phase after sustained fracture at a certain temperature can be effectively predicted, the degradation state of the alloy structure can be judged, and it has guiding significance for the evaluation of the high-temperature sustained performance of the directionally solidified high-temperature alloy. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The present invention is a flowchart of a method for quantifying the relationship between the stress of a directionally solidified high-temperature alloy and the rafting of the γ′ phase.

[0041] Figure 2 The present invention is a logic block diagram of a system for quantifying the relationship between the stress of the endurance test and the rafting of the γ′ phase in a directionally solidified high-temperature alloy.

[0042] Figure 3 Comparison diagram of the original image and binary image of an embodiment using the method of the present invention; (a) and (b) are the SEM original image and binary image under 900°C / 310 MPa endurance conditions in the embodiment, and (c) and (d) are statistical diagrams of the selected area after adding cut lines.

[0043] Figure 4 Schematic diagram of the rafting degree of the γ′ phase and the range of fully oriented rafting and the initial γ′ phase arrangement at different stresses at 850°C and 900°C according to an embodiment of the method of the present invention;

[0044] Figure 5 Schematic diagram of the fitting curve of P and T values ​​statistically obtained at 900° C. and changes with the endurance stress in an embodiment of the method of the present invention.

[0045] Figure 6 The following is a schematic diagram comparing the original SEM image and the adjusted image under 900°C / 170 MPa endurance conditions of an embodiment of the method of the present invention: (a) is the original SEM image; (b) is the SEM image after adjustment. DETAILED DESCRIPTION

[0046] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1 As shown, the present invention provides a method for quantifying the relationship between the stress of the endurance test of a directionally solidified high-temperature alloy and the rafting of the γ′ phase, the method specifically comprising the following steps:

[0048] S1) acquiring image data of a quantitative directionally solidified superalloy sample to obtain a reference value of γ′ phase rafting;

[0049] S2) confirming the fully rafted region of the γ′ phase according to the rafted reference value of the γ′ phase obtained in S1);

[0050] S3) establishing a fitting curve for the quantized value data within the complete rafting interval of the γ′ phase obtained in S2) to obtain a rafting prediction model for the γ′ phase;

[0051] S4) using the endurance stress data of the sample to be tested as input to a γ′ phase rafting prediction model, and outputting a quantitative value of the rafting degree of the γ′ phase of the sample to be tested.

[0052] The quantified directionally solidified high-temperature alloy specimens include those that have not been subjected to deformation treatment and those that have been subjected to permanent deformation treatment.

[0053] The specific steps in S1) are:

[0054] S1.1) Obtain a high-magnification γ′ phase image of the sample before deformation treatment;

[0055] S1.2) converting the high-magnification γ′ phase morphology image into a binary image by binarization processing;

[0056] S1.3) Process the binary image using the line-section method to obtain the number of intersections between all horizontal and vertical lines and the γ′ phase boundary;

[0057] S1.4) Calculate the number of intersections between the transverse and longitudinal sections obtained in S1.3) and the γ′ phase boundary to determine a quantitative reference value v0 of the initial γ′ phase morphology.

[0058] The specific steps of S2) are:

[0059] S2.1) Obtain a high-magnification γ′ phase morphology image near the fracture of the specimen after sustained deformation treatment;

[0060] S2.2) converting the high-magnification γ′ phase morphology image into a binary image by binarization processing;

[0061] S2.3) Using the line-cut method to process the binary image, count the number of intersections between all horizontal and vertical lines and the γ′ phase boundary;

[0062] S2.4) Calculate the number of intersections between the transverse and longitudinal sections obtained in S2.3) and the γ′ phase boundary to determine the quantitative value v of the initial γ′ phase morphology;

[0063] S2.5) Subtract the quantized value v obtained in S2.4) from the quantized reference value v0 obtained in S1.4), and select the quantized value v with a difference greater than 0.2 as the fully oriented rafting interval of the γ′ phase.

[0064] The quantization reference value v0 is calculated by the following formula:

[0065]

[0066] Where T0 is the number of intersections between the transverse section of the sample without deformation treatment and the γ′ phase boundary, and P0 is the number of intersections between the longitudinal section of the sample without deformation treatment and the γ′ phase boundary.

[0067] The quantized value v is obtained by the following formula:

[0068]

[0069] Where T is the number of intersections between the transverse section of the deformed specimen and the γ′ phase boundary, and P is the number of intersections between the longitudinal section of the deformed specimen and the γ′ phase boundary.

[0070] The specific steps of S3) are:

[0071] S3.2) Select all data points within the fully oriented rafted region of the γ′ phase and establish a fitting curve;

[0072] S3.3) The least squares method is used to construct a rafting prediction model for the γ′ phase.

[0073] The rafting prediction model of the γ′ phase is:

[0074] y=C0+C1x+C2x 2 +C3x 3 +…+C n x n ,

[0075] Where: x is the endurance stress data of the sample, y is the quantitative value of the rafting degree corresponding to a certain endurance stress, C0…C n is an undetermined coefficient, which is obtained from the endurance stress data and the quantitative value of statistics; the value range of n is a positive integer greater than 0.

[0076] like Figure 2 As shown, the system of the present invention for quantifying the relationship between the stress of the endurance test and the rafting of the γ′ phase in a directionally solidified high-temperature alloy comprises:

[0077] An acquisition module, used to obtain quantitative image data of directionally solidified high-temperature alloy samples;

[0078] The data processing module is used to analyze and process the image data of the quantitative directionally solidified high-temperature alloy sample to obtain the rafting reference value and rafting quantitative value of the γ′ phase, and finally confirm the complete rafting range of the γ′ phase;

[0079] The prediction module is used to establish a fitting curve according to the complete rafting interval of the γ′ phase, obtain a rafting prediction model of the γ′ phase, and finally output a quantitative value of the rafting degree of the sample to be tested.

[0080] A readable storage medium includes a memory storing a program and a processor, wherein the processor executes the above-mentioned method for quantifying the relationship between the stress of the endurance test of a directionally solidified high-temperature alloy and the rafting of the γ′ phase.

[0081] In nickel-based superalloys, the γ' phase is gradually connected into a raft by adjacent cubic γ' phases under long-term high temperature and low stress, forming a raft-like structure.

[0082] Example:

[0083] Directionally solidified DZ411 alloy was used as the research object. Endurance tensile tests were performed at 850°C and 900°C under various stresses (230MPa to 475MPa) until fracture. The longitudinal section near the fracture of the standard endurance specimen was used as the observation surface. The γ′ phase morphology of the observation surface was obtained by electropolishing in a concentrated H2SO4+methanol solution for 5 seconds, followed by electrolysis in an electrolytic etching solution of Cr2O3+H3PO4+concentrated H2SO4 for 2 seconds. The surface was then cleaned with alcohol and observed under a scanning electron microscope. Images of the γ′ phase morphology captured under the scanning electron microscope at 20,000X magnification were selected as statistical samples. The detailed implementation method is described below, using the γ′ phase morphology image obtained under a specific stress as an example.

[0084] exist Figure 3 (a) and (b) are the original image and the processed binary image of the γ′ phase morphology taken by SEM under the conditions of 900℃ / 310MPa rupture. Figure 3 In (a), the gray area is the rafted γ′ phase, and the black area is the γ matrix channel. A binary image that completely distinguishes the γ′ phase from the matrix channel was derived in ImageJ software based on the binarization algorithm. Figure 3 In (b), the black part represents the rafted γ′ phase, and the white part represents the γ matrix. Using the cross-section method in Photoshop, equidistant longitudinal and transverse cross-sections were created to extract the overall morphology of the layer after retaining the reference cross-section within the γ′ phase. Figure 3 (c) and (d). The number of intercepts in the γ′ phase is counted by the recording measurement tool in the software. The data is multiplied by 2 to obtain the P value and T value. The ratio v of the intersection of the longitudinal (P) and transverse (T) intercepts is used to define the degree of rafting achieved when the γ′ phase breaks. The v0 value of the regular γ′ phase morphology under SEM in the heat-treated state is defined as the initial quantization value, and the calculated result is v 0＝0.8. The v values ​​at different temperatures and stresses were calculated respectively, and it was determined that the v value is a growing process from regular arrangement to rafting, so we can continue to look for the critical value between coarsening and complete rafting. A scatter plot is formed in origin to observe the pattern of the obtained v value. According to the morphology of the γ′ phase under SEM and the calculated v value results, it was found that there was still no rafting when it was fractured under high stress at 850°C. When the difference between the v value and v0 is greater than 0.2, that is, the v value is greater than 1, and directional rafting occurs seriously. According to the morphology and quantitative results, v=1 is defined as the critical value between directional rafting and partial coarsening. By Figure 4 As shown in the figure, all the endurance stresses at 900℃ cause the rafting of the γ′ phase. Since the purpose is to establish the relationship between the rafting γ′ phase change and stress, the relationship between stress and rafting state is selected under the condition of 900℃. Figure 5 The figure shows a scatter plot of the P and T values ​​calculated at different stresses at 900°C versus stress changes. Since the DZ411 alloy undergoes "N"-type rafting (rafting perpendicular to the stress direction), no longitudinal γ′ phase connection is found in the observed morphology, resulting in a peak in the P value. However, the peak cannot be determined at the intersection of the transverse section and γ′ due to directional rafting at 900°C, so the dotted line portion is not taken into account.

[0085] The least squares method was used to fit the data in the origin software, and the P value and T value fitting curves were obtained as follows:

[0086] P(σ)=-0.03x 2 +2.59x-216.67

[0087] T(σ)=0.56x+62.60

[0088] The fitting curve shows that there is an intersection in the fitting data. When the stress is lower than 190 MPa, the T value is greater than the P value, indicating that the rafting form has changed significantly. Since rafting will inevitably occur under low stress for a long time, it is inferred that the γ′ phase parallel to the stress direction (longitudinal direction) will also be connected, causing a sharp drop in the P value. That is, when the stress is lower than about 190 MPa, the γ′ phase exhibits abnormal rafting behavior.

[0089] In order to verify the reliability of the fitting formula results, the same endurance test and sampling analysis methods were used to supplement the samples of DZ411 alloy after endurance fracture under low stress, with the endurance condition of 900℃ / 170MPa as a supplementary example. Figure 6Shown is a comparison of the original and adjusted SEM images under 900°C / 170 MPa stress-curing conditions. The results reveal a disordered arrangement of the γ′ phase, lacking the characteristic of directional rafting. The longitudinal γ′ phase is clearly connected. The statistical and calculation results from the PS software satisfy the fitted P and T value curves, indicating that the quantitative prediction of the rafting phenomenon in the DZ411 alloy with stress is consistent with the morphological observations. The P and T value relationship also satisfies the stress-dependent results, indicating that this method can predict the rafting of directionally solidified alloys.

[0090] The above describes in detail a method for quantifying the relationship between the stress-rupture behavior and rafting of the γ′ phase in directionally solidified superalloys. The above embodiments are intended only to facilitate understanding of the method and its core concept. Furthermore, those skilled in the art will appreciate that variations in the specific implementation and scope of application are possible based on the principles of this application. Therefore, this specification should not be construed as limiting this application.

[0091] For example, certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that hardware manufacturers may use different nouns to refer to the same component. This specification and claims do not use differences in names as a way to distinguish components, but use differences in the functions of components as the criteria for distinction. For example, "including" and "comprising" mentioned throughout the specification and claims are open-ended terms, so they should be interpreted as "including / including but not limited to". "Approximately" means that within an acceptable error range, those skilled in the art can solve the technical problems within a certain error range and basically achieve the technical effects. The subsequent description in the specification is a preferred embodiment of the present application, but the description is for the purpose of illustrating the general principles of the present application, and is not used to limit the scope of the present application. The scope of protection of the present application shall be as defined in the attached claims.

[0092] It should also be noted that the terms "include," "comprises," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a product or system comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such product or system. In the absence of further limitations, an element defined by the phrase "comprises a..." does not exclude the presence of other identical elements in the product or system comprising the element.

[0093] It should be understood that the term "and / or" as used herein is merely a description of the relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the associated objects are in an "or" relationship.

[0094] The above description shows and describes several preferred embodiments of the present application. However, as previously mentioned, it should be understood that the present application is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Instead, the present application can be used in various other combinations, modifications, and environments and can be modified within the scope of the application concept described herein through the above teachings or technology or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present application should be protected by the claims appended hereto.

Claims

1. A method for quantifying the relationship between the stress of the endurance test and the rafting of the γ′ phase in a directionally solidified superalloy, characterized in that: The method specifically comprises the following steps: S1) acquiring image data of a quantitative directionally solidified superalloy sample, and processing the image data to obtain a rafting reference value of the γ′ phase of the sample; The specific steps are: S1.1) Obtain a high-magnification γ′ phase image of the sample before deformation treatment; S1.2) converting the high-magnification γ′ phase morphology image into a binary image by binarization processing; S1.3) Process the binary image using the line-cut method to obtain the number of intersections between all horizontal and vertical lines and the γ′ phase boundary; S1.4) Calculate the number of intersections between the transverse and longitudinal sections obtained in S1.3) and the γ′ phase boundary to determine the quantitative reference value v0 of the initial γ′ phase morphology; S2) confirming the complete rafting range of the γ′ phase of the sample according to the rafting reference value of the γ′ phase of the sample obtained in S1); The specific steps are: S2.1) Obtain a high-magnification γ′ phase morphology near the fracture of the specimen after sustained deformation treatment; S2.2) converting the high-magnification γ′ phase morphology image into a binary image by binarization processing; S2.3) Using the line-cut method to process the binary image, count the number of intersections between all horizontal and vertical lines and the γ′ phase boundary; S2.4) Calculate the number of intersections between the transverse and longitudinal sections obtained in S2.3) and the γ′ phase boundary to determine the quantitative value v of the initial γ′ phase morphology; S2.5) Subtract the quantized value v obtained in S2.4) from the quantized reference value v0 obtained in S1.4), and select the quantized value v with a difference greater than 0.2 as the interval of complete directional rafting of the γ′ phase; S3) Based on the complete rafting interval of the γ′ phase of the sample obtained in S2), a fitting curve is established for the quantified value data within the interval to obtain a rafting prediction model for the γ′ phase; S4) using the endurance stress data of the directionally solidified high-temperature alloy sample to be measured as input to a γ′ phase rafting prediction model, and outputting a quantitative value of the rafting degree of the γ′ phase of the sample to be measured.

2. The method according to claim 1, characterized in that The quantitative directionally solidified high-temperature alloy samples are samples that have not been subjected to deformation treatment and samples that have been subjected to permanent deformation treatment.

3. The method according to claim 1, characterized in that The quantization reference value v0 is calculated by the following formula: ， Where T0 is the number of intersections between the transverse section of the sample without deformation treatment and the γ′ phase boundary, and P0 is the number of intersections between the longitudinal section of the sample without deformation treatment and the γ′ phase boundary.

4. The method according to claim 1, wherein The quantized value v is obtained by the following formula: ， Where T is the number of intersections between the transverse section of the deformed specimen and the γ′ phase boundary, and P is the number of intersections between the longitudinal section of the deformed specimen and the γ′ phase boundary.

5. The method according to claim 2, characterized in that The specific steps of S3) are: S3.2) Select all data points in the fully oriented rafted region of the γ′ phase and establish a fitting curve; S3.3) A least squares method is used to construct a rafting prediction model for the γ′ phase.

6. The method according to claim 4, characterized in that The rafting prediction model of the γ′ phase is: y=C0+C1x+C2x 2 +C3x 3 +…+C n x n , Where: x is the endurance stress data of the sample, y is the quantitative value of the rafting degree corresponding to a certain endurance stress, C0…C n is an undetermined coefficient, which is obtained from the endurance stress data and the quantitative value of statistics; the value range of n is a positive integer greater than 0.

7. A system for implementing the method according to any one of claims 1 to 6, characterized in that: The system comprises: A data acquisition module is used to obtain quantitative image data of directionally solidified high-temperature alloy samples; The data processing module is used to analyze and process the image data of the quantitative directionally solidified high-temperature alloy sample to obtain the rafting reference value and rafting quantitative value of the γ′ phase, and finally confirm the complete rafting range of the γ′ phase; The prediction module is used to establish a fitting curve according to the complete rafting interval of the γ′ phase, obtain a rafting prediction model of the γ′ phase, and finally output a quantitative value of the rafting degree of the γ′ phase of the test sample.

8. A readable storage medium comprising a memory and a processor, wherein the memory stores a program, wherein: The processor executes the method for quantifying the relationship between the stress rupture and the rafting of the γ′ phase in a directionally solidified high-temperature alloy according to claims 1 to 6.

Images