Process window screening method for nickel-based superalloy single crystal preparation

Abstract

The invention relates to a process window screening method for nickel-based high-temperature alloy single crystal preparation. According to the method, based on a double-ellipsoid molten pool analysis heat source model and solidification condition calculation, the geometrical morphology and solidification behavior of the molten pool caused by electron beam scanning can be simulated in a multi-parameter space in a high-flux mode. The grain orientation evolution trend of the material after the powder bed is molten can be accurately predicted by calculating parameters such as the penetration depth, the penetration width, the molten pool leading edge angle and the temperature gradient under different energy input conditions, and a single crystal forming window suitable for the nickel-based superalloy is constructed. By adopting the method, process parameters such as energy input, scanning speed, scanning strategy and the like can be screened and optimized, and a multi-dimensional process window is established so as to identify stable growth conditions required by single crystal preparation. According to the method, the internal relation between the geometric behavior of the molten pool and the preferred orientation of the crystal grains can be disclosed, and technical support is provided for realizing controllable forming of a single-crystal structure, reducing the defect generation risk and improving the structural integrity and performance of an additive manufacturing part.

Description

A method for screening the process window in the preparation of single crystals of nickel-based superalloys Technical Field

[0001] This invention relates to the field of nickel-based superalloy technology, and in particular to a method for screening the process window for preparing single crystals of nickel-based superalloys. Background Technology

[0002] Electron beam powder bed fusion (EB-PBF) is widely used in the manufacture of complex structures of nickel-based superalloys due to its advantages such as high preheating, low thermal gradient and residual stress. It is especially suitable for hot-end components such as single-crystal blades that require high microstructure stability.

[0003] Nickel-based single-crystal superalloys are widely used in hot-end components of aerospace engines, and their mechanical properties depend on strictly controlled crystal orientation and single-crystal microstructure. When preparing nickel-based single crystals using EB-PBF, it is necessary to control the energy input range to ensure that the solidification interface meets the solidification conditions suitable for single-crystal growth, thereby guaranteeing stable and preferential grain growth in the building direction and suppressing the generation of transverse competing crystals.

[0004] However, the molten pool of EB-PBF is affected by multiple factors such as energy density, scanning speed, and preheating temperature, exhibiting a strongly nonlinear relationship. Traditional empirical methods struggle to accurately determine the process window suitable for single crystal growth. Existing simulation methods largely rely on computational fluid dynamics, phase field, and cellular automata models, which, while capable of predicting local molten pool and grain behavior, are complex and computationally expensive, making them unsuitable for large-scale process window selection.

[0005] Currently, there is a lack of a method that, starting from a molten pool heat source model, can simultaneously obtain molten pool geometry parameters, solidification heat conditions, and grain growth-related process windows with relatively low computational cost. Particularly in the preparation of single crystals of nickel-based superalloys, there is no effective means to construct a comprehensive process window encompassing "energy density-molten pool geometry-defect formation-solidification conditions" for rapid screening of suitable process ranges for single crystals.

[0006] Therefore, there is an urgent need for a method that can quickly calculate the temperature field, molten pool morphology and solidification parameters based on an analytical heat source model, and further construct a multi-dimensional process window suitable for the preparation of nickel-based superalloy single crystals, so as to guide the optimization of the EB-PBF process, shorten the experimental cycle and improve the success rate of single crystal preparation. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a process window screening method for the preparation of nickel-based superalloy single crystals. This method can quickly obtain a large number of parameters such as the molten pool temperature field, geometric characteristics and solidification conditions with low computational load, and construct a multi-dimensional process window suitable for single crystal growth, thereby providing a reliable basis for process parameter optimization.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a method for screening the process window for preparing single crystals of nickel-based superalloys, comprising the following steps:

[0009] Step S1: Construct an analytical heat source integral model of the EB-PBF double ellipsoid based on MATLAB;

[0010] Step S2: Solve the transient temperature field based on MATLAB and the process parameter set, and store the historical dataset of molten pool temperature;

[0011] Step S3: Calculate the molten pool geometry, defect criteria, solidification angle, and interlayer growth parameters based on the dataset, and filter the available process ranges;

[0012] Step S4: Construct a multi-dimensional integrated process window based on each individual process window.

[0013] In a preferred embodiment, the specific process of step S1 is as follows:

[0014] Using a Cartesian coordinate system, with the positive x-axis as the electron beam scanning direction and the z-axis as the

[001] direction, the integral solution of the transient temperature field using an analytical heat source integral model is implemented based on MATLAB. The heat source integral model is as follows:

[0015]

[0016]

[0017]

[0018] in, Material density Specific heat capacity ; Integral step size thermal diffusivity ;

[0019] These represent the lengths of the ellipsoid in the Y and Z directions, respectively. and These represent the lengths of the first and second halves of the ellipsoid in the X direction, respectively.

[0020] and These are the distribution coefficients for the front and rear ellipsoids, respectively;

[0021] and These are the two amplitude coefficients of the ellipsoid. and The amplitude coefficient of the first half of the ellipsoid. and The amplitude coefficient of the rear hemispheric ellipsoid;

[0022] Scan speed , This indicates the relative distance to the current position of the electron beam in three directions.

[0023] In a preferred embodiment, step S2 is specifically described as follows:

[0024] Step S21: Based on the energy requirements of the target material in the EB-PBF process, construct a parameter set containing process parameters; this parameter set includes: beam power, scanning speed, layer thickness, scanning spacing, preheating temperature, and beam diameter;

[0025] Step S22: Based on the heat source movement characteristics during the electron beam scanning process, construct the cross-section YOZ, longitudinal section XOZ, and upper surface XOY as key data sections to characterize the spatial distribution of the molten pool depth, width, and thermal gradient; establish a corresponding data matrix for each calculation section to store temperature field data.

[0026] Step S23: Import the process parameter set into MATLAB item by item, initialize the data matrix, and call the double ellipsoidal analytical heat source model established in step S1 to perform iterative solution of the temperature field; save the calculation results of all parameter sets in the form of .mat file, which will be used to build the database for subsequent process window discrimination.

[0027] In a preferred embodiment, step S3 is specifically described as follows:

[0028] Step S31: Load the database obtained in step S2 into MATLAB and extract the temperature field distribution under the corresponding parameter combinations; extract the single-channel molten pool depth based on the temperature field data. , Single-channel molten pool width and temperature gradient G;

[0029] Step S32: Based on the requirement to avoid incomplete fusion defects, the minimum forming depth criterion is used to screen process parameters:

[0030]

[0031] in This refers to the powder layer thickness or the minimum required melt depth; when this condition is met, the process parameters are considered to avoid incomplete fusion defects.

[0032] Step S33: Further filter parameters based on the molten pool depth ratio

[0033]

[0034] in This refers to the morphological stability threshold obtained based on material properties and experimental calibration.

[0035] Step S34: Calculate the temperature gradient in each direction:

[0036] , , , , ,

[0037]

[0038] in Indicates the magnitude of the temperature gradient in different directions. This represents the xoy horizontal plane gradient. For solidification angle; based on the requirements of preferred crystal growth direction, selection is carried out to meet the following criteria. process parameters, The minimum and maximum allowable deviation angles;

[0039] Step S35: Screening based on the morphology of multiple molten pools:

[0040]

[0041] in A threshold that ensures continuous growth of grains between adjacent channels; a set of parameters that meets this condition can form a columnar crystal structure with stable interlayer structure.

[0042] In a preferred embodiment, step S4 is specifically described as follows:

[0043] Step S41: Map the parameter sets that meet the conditions of no defects, stable morphology, suitable solidification angle and stable growth in step S3 to the process diagram to form a visual distribution corresponding to each region;

[0044] Step S42: Overlay the aforementioned multiple process windows according to their corresponding coordinate regions to generate a complete single crystal preparation process diagram; the overlay process maintains the distinguishability of the boundaries of each window so as to select the priority window according to different needs;

[0045] Step S43: Extract the intersection region of all regions that meet the conditions in the overlay image; this intersection region is the screening window for the best comprehensive single crystal process conditions that simultaneously meet the requirements of no defects, stable morphology, suitable solidification angle, and stable interlayer growth.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) The computational model is simplified yet highly accurate, making it suitable for large-scale process screening. This invention, based on a double ellipsoidal analytical heat source and MATLAB numerical integration method, achieves rapid temperature field solution for the electron beam powder bed melting process. Compared with traditional complex models that rely on fluid dynamics and interface tracking, this method significantly reduces computational costs and can achieve rapid scanning and analysis of large parameter sets while ensuring the geometric accuracy of the molten pool, making it suitable for process optimization and high-throughput screening scenarios.

[0048] (2) It has good scalability and engineering applicability. The input parameters of the model constructed in this invention are all process physical quantities, which have good portability. This method is not only applicable to different EB-PBF forming conditions, but can also be extended to other additive manufacturing technologies such as laser powder bed melting, and can cover different material systems, different scanning strategies and different layer thickness settings. Attached Figure Description

[0049] Figure 1 is a schematic diagram of the shape of the double ellipsoidal heat source of the present invention;

[0050] Figure 2 is a schematic diagram of the technical route of a preferred embodiment of the present invention;

[0051] Figure 3 is a schematic diagram of four process windows obtained from simulation calculations in a preferred embodiment of the present invention;

[0052] Figure 4 shows the single-crystal process window obtained from simulation calculations and the microstructure obtained from experiments according to a preferred embodiment of the present invention. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0054] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0055] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0056] A method for screening the process window for preparing nickel-based superalloy single crystals, as shown in Figures 1-4, includes the following specific steps:

[0057] S1. Constructing an analytical heat source integral model of the EB-PBF double ellipsoid based on MATLAB;

[0058] S2. Solve the transient temperature field and store the historical dataset of molten pool temperature based on MATLAB and process parameter set;

[0059] S3. Calculate the molten pool geometry, defect criteria, solidification angle and interlayer growth parameters based on the dataset, and screen the available process range;

[0060] S4. Construct a multi-dimensional integrated process window based on each individual process window.

[0061] The software platform (including MATLAB), calculation model, material thermophysical parameters, and processing parameters used in the embodiments of this invention are not subject to any particular source restriction and can be obtained through conventional means or through publicly available methods that are accessible to those skilled in the art. The thermophysical parameters and electron beam process parameters of the CMSX-4 nickel-based superalloy involved are commonly used data in the industry and can also be adjusted according to specific equipment configurations.

[0062] The nickel-based superalloy CMSX-4 was used as the material in the example, and the transient temperature field simulation calculation of EB-PBF was performed.

[0063] The physical properties of CMSX-4 are as follows: material density Specific heat capacity Thermal diffusivity ;

[0064] Parameter set: Beam power The parameter range is 40-3000 W, and the electron beam scanning speed is... The range is 0.2-3 substrate preheating temperature Integral step size That is, the transient temperature field distribution at any time can be obtained through the aforementioned integral formula.

[0065] In the present invention, the first step is to analyze the heat source integral model based on the EB-PBF double ellipsoid according to step S1.

[0066] Using a Cartesian coordinate system, with the positive x-axis as the electron beam scanning direction and the z-axis as the

[001] direction, the integral solution of the transient temperature field using an analytical heat source integral model is implemented based on MATLAB. The heat source integral model is as follows:

[0067]

[0068]

[0069]

[0070] in, Material density Specific heat capacity

[0071] Integral step size thermal diffusivity ;

[0072] These represent the lengths of the ellipsoid in the Y and Z directions, respectively. and These represent the lengths of the first and second halves of the ellipsoid in the X direction, respectively.

[0073] and These are the distribution coefficients for the front and rear ellipsoids, respectively;

[0074] and These are the two amplitude coefficients of the ellipsoid. and The amplitude coefficient of the first half of the ellipsoid. and The amplitude coefficient of the rear hemispheric ellipsoid;

[0075] Scan speed , This indicates the relative distance to the current position of the electron beam in three directions.

[0076] The transient temperature field distribution at any given time can be obtained through the above integral formula. The temperature history of each point can be obtained by iterative calculation by constructing a data matrix.

[0077] Based on temperature history, the width and depth of the molten pool can be determined.

[0078] The nickel-based superalloy CMSX-4 was used as the verification material for the model. The heat source model was corrected by verifying the single-pass molten pool size data, and a correction model suitable for specific materials (such as CMSX-4) was obtained.

[0079] Secondly, according to step S2, the transient temperature field is solved using MATLAB and a parameter set, and the historical dataset of the molten pool temperature is stored. The specific process is as follows:

[0080] Step S21: Based on the forming stability requirements of the target material in the EB-PBF process, construct a set of process parameters covering a wide range of energy input combinations. This parameter set includes at least beam power, scanning speed, layer thickness, scanning spacing, preheating temperature, and beam diameter, enabling batch simulation of melt pool behavior under different energy densities and heat input conditions.

[0081] Step S22: Based on the thermal input characteristics of the electron beam moving at high speed along the scanning path, three key calculation sections—YOZ (cross section), XOZ (longitudinal section), and XOY (upper surface)—are constructed to characterize the spatial distribution of the molten pool depth, width, and thermal gradient. An independent data matrix structure is established for each section to record the evolution of the transient temperature field in both time and space, providing input data for subsequent molten pool geometry, solidification conditions, and defect identification.

[0082] Step S23: Input the process parameter set described in step S21 into the analytical model in batches, automatically initialize the corresponding data matrix, and call the double-ellipsoidal analytical heat source model constructed in step S1 to perform transient temperature field integral solution. The solution results of all process parameter sets are stored in structured .mat file format to form a temperature field database covering multiple energy conditions, providing a data foundation for subsequent process window selection and single crystal preparation window construction.

[0083] Subsequently, according to step S3, the melt pool geometry, defect criteria, solidification angle, and interlayer growth parameters are calculated based on the dataset, and the available process range is selected. The specific process is as follows:

[0084] Step S31: Load the dataset obtained in step S2 into MATLAB. After processing invalid data points, extract the temperature field distribution under the corresponding parameter combinations. Extract the single-channel molten pool depth based on the temperature field data. , Single-channel molten pool width And temperature gradient G. Initialize data judgment matrix. =0;

[0085] Step S32: Based on the requirement to avoid incomplete fusion defects, the minimum forming depth criterion is used to screen process parameters:

[0086]

[0087] Where d represents the powder layer thickness or the minimum required melt depth. When this condition is met, the process parameters are considered to avoid incomplete fusion defects, and this will be included in the data matrix. Set the corresponding position of the process parameter to 1;

[0088] Step S33: To avoid unstable heat flow caused by an excessively deep or narrow molten pool, further parameters are selected based on the molten pool depth ratio.

[0089]

[0090] in To determine the morphological stability threshold based on material properties and experimental calibration, the data matrix will be used... Set the corresponding position of the process parameter to 1;

[0091] Step S34: To obtain a suitable temperature gradient direction distribution for single crystal or directional solidification, calculate the temperature gradient in each direction:

[0092] , , , , ,

[0093]

[0094] in Indicates the magnitude of the temperature gradient in different directions. This represents the xoy horizontal plane gradient. For solidification angle; based on the requirements of preferred crystal growth direction, selection is carried out to meet the following criteria. process parameters, The minimum and maximum allowable deviation angles;

[0095] Based on the requirement of preferred crystal growth direction, screening is carried out to meet the following conditions. The process parameters are set to ensure stable growth of columnar crystals along the construction direction, which will be used in the data matrix. Set the corresponding position of the process parameter to 1.

[0096] Step S35: To ensure the continuity of grains across layers under multi-pass scanning conditions, selection is based on the morphology of the multi-pass molten pool:

[0097]

[0098] in A threshold is set to ensure continuous grain growth between adjacent channels. Parameter sets meeting this condition can form a stable columnar crystal structure, which will be displayed in the data matrix. Set the corresponding position of the process parameter to 1.

[0099] Based on the regions where each data matrix contains a value of 1, the parameter sets E1, E2, E3, and E4 can be extracted.

[0100] Finally, the single crystal preparation window is extracted according to step S4. The specific process is as follows:

[0101] Step S41: Map the parameter sets that meet the conditions of no defects, stable morphology, suitable solidification angle and stable growth in step S3 to the process diagram to form a visual distribution corresponding to each region.

[0102] Step S42: Overlay the aforementioned multiple process windows according to their corresponding coordinate regions to generate a complete single crystal fabrication process diagram. The overlay process maintains the distinguishability of the boundaries of each window so as to select the priority window according to different needs.

[0103] Step S43: Extract the intersection of all regions that meet the conditions in the overlay image. This intersection region is the screening window for the best comprehensive single crystal process conditions that simultaneously satisfy defects-free, morphologically stable, suitable solidification angle, and stable interlayer growth, as shown in Figure 3.

[0104] This invention proposes a method for constructing a single-crystal preparation process window for electron beam powder bed fusion additive manufacturing (EB-PBF). By constructing a double ellipsoidal analytical heat source, conducting parallel computation with a large parameter set, establishing a historical dataset of molten pool temperature, and filtering based on multidimensional criteria, it achieves a full-process numerical analysis from "heat source – temperature field – molten pool geometry – solidification direction – single crystal conditions". This invention can not only accurately capture the evolution characteristics of molten pool morphology, but also efficiently evaluate the influence of different process parameters on single crystal growth, thereby constructing a single-crystal additive manufacturing process window that can be directly used for production.

Claims

1. A method for screening the process window for preparing single crystals of nickel-based superalloys, characterized in that, Includes the following steps: Step S1: Construct an EB-PBF double ellipsoidal analytical heat source integral model based on MATLAB; Step S2: Solve the transient temperature field and store the historical dataset of molten pool temperature based on MATLAB and process parameter set; Step S3: Calculate molten pool geometry, defect criteria, solidification angle and interlayer growth parameters based on the dataset and filter available process intervals; Step S4: Construct a multi-dimensional integrated process window based on each individual process window.

2. The method for screening the process window for preparing single crystals of nickel-based superalloys according to claim 1, characterized in that, The specific process of step S1 is as follows: Using a Cartesian coordinate system, the positive x-axis is set as the electron beam scanning direction, and the z-axis is the [001] direction. The integral solution of the transient temperature field by the analytical heat source integral model is implemented based on MATLAB. The heat source integral model is as follows: in, Material density Specific heat capacity ； Integral step size thermal diffusivity ； These represent the lengths of the ellipsoid in the Y and Z directions, respectively. and These represent the lengths of the first and second halves of the ellipsoid in the X direction, respectively. and These are the distribution coefficients for the front and rear ellipsoids, respectively; and These are the two amplitude coefficients of the ellipsoid. and The amplitude coefficient of the first half of the ellipsoid. and The amplitude coefficient of the posterior hemispheric ellipsoid; scanning speed. ， This indicates the relative distance to the current position of the electron beam in three directions.

3. The method for screening the process window for preparing single crystals of nickel-based superalloys according to claim 1, characterized in that, The specific process of step S2 is as follows: Step S21: Based on the energy requirements of the target material in the EB-PBF process, construct a parameter set containing process parameters; this parameter set includes: beam power, scanning speed, layer thickness, scanning spacing, preheating temperature, and beam spot diameter; Step S22: Based on the heat source movement characteristics during the electron beam scanning process, construct the cross-section YOZ, longitudinal section XOZ, and upper surface XOY as key data sections to characterize the spatial distribution of melt pool depth, width, and thermal gradient; establish a corresponding data matrix for each calculation section to store temperature field data; Step S23: Import the process parameter set item by item into MATLAB, initialize the data matrix, and call the double ellipsoidal analytical heat source model established in step S1 to iteratively solve the temperature field; the calculation results of all parameter sets are saved in .mat file format to build a database for subsequent process window discrimination.

4. The method for screening the process window for preparing single crystals of nickel-based superalloys according to claim 1, characterized in that, The specific process of step S3 is as follows: Step S31: Load the database obtained in step S2 into MATLAB and extract the temperature field distribution under the corresponding parameter combination; extract the single-channel molten pool depth based on the temperature field data. 、 Single-channel molten pool width And temperature gradient G; Step S32: Based on the requirement to avoid incomplete fusion defects, the minimum forming depth criterion is used to screen process parameters: in The powder layer thickness or the minimum melt depth requirement is considered; when this condition is met, the process parameters are considered to avoid incomplete fusion defects; Step S33: Further screen parameters based on the melt pool depth ratio. in Based on the material properties and the morphological stability threshold obtained through experimental calibration; Step S34: Calculate the temperature gradient in each direction: ， ， ， ， ， in Indicates the magnitude of the temperature gradient in different directions. This represents the xoy horizontal plane gradient. For solidification angle; based on the requirements of preferred crystal growth direction, selection is carried out to meet the following criteria. process parameters, For the minimum and maximum allowable deviation angles; Step S35: Screening based on multi-channel melt pool morphology: in A threshold that ensures continuous growth of grains between adjacent channels; a set of parameters that meets this condition can form a columnar crystal structure with stable interlayer structure.

5. The method for screening the process window for preparing single crystals of nickel-based superalloys according to claim 1, characterized in that, The specific process of step S4 is as follows: Step S41: Map the parameter groups that meet the conditions of defect-free, morphological stability, suitable solidification angle and stable growth in step S3 to the process diagram to form a visual distribution corresponding to each region; Step S42: Overlay the aforementioned multiple process windows according to their corresponding coordinate regions to generate a complete single crystal preparation process diagram. The superposition process maintains the distinguishability of the boundaries of each window so as to select the priority window according to different needs; Step S43: Extract the intersection region of all regions that meet the conditions in the superposition map; This intersection region is the screening window for the comprehensive best single crystal process conditions that simultaneously meet the requirements of no defects, stable morphology, suitable solidification angle and stable interlayer growth.

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