Molten pool grain solidification analysis method and device based on continuous growth restriction factor

Abstract

The invention provides a molten pool grain solidification analysis method and device based on a continuous growth limiting factor, and belongs to the field of material processing. The method provided by the invention comprises the following steps: establishing a first relationship between a continuous growth limiting factor and a model for predicting the continuous growth rate of crystal grains; according to the first relationship, determining a second relationship between a model for predicting the continuous growth rate of the crystal grains and the solidification path, and along with the increase of the solidification path, exponentially increasing a growth curve corresponding to the second relationship; determining a demarcation point according to the correlation among the solute concentration, the welding speed and the solidification path; calculating the curvature radius of each point on the growth curve; and determining a demarcation point of plane growth and cellular growth according to the calculated curvature radius. According to the molten pool grain solidification analysis method and device based on the continuous growth limiting factor, provided by the invention, help can be provided for establishing a solidification mode conversion criterion near a melting boundary and mastering a grain size evolution rule.

Description

Technical Field

[0001] The present application relates to the technical field of material processing, and in particular to a method and device for analyzing molten pool grain solidification based on a continuous growth limiting factor. Background Art

[0002] In the field of material processing, especially in the application of alloy materials, accurate analysis and control of their solidification process is crucial. With the continuous development of industrial technology, the requirements for the performance of alloy materials are getting higher and higher, so it is necessary to deeply study the solidification behavior of alloy materials under various process conditions. Among them, the molten pool solidification process is a key link, which involves the growth of grains, the formation of organizational structure and the final determination of performance.

[0003] At present, the theoretical research on "solidification structure evolution near the melting boundary of the molten pool" mainly includes numerical calculation-based methods and analytical methods. Numerical calculation methods can effectively predict the dynamic evolution of the solid-liquid interface during solidification. Compared with numerical calculation methods, analytical methods have the advantages of low computational cost and high efficiency. However, these two methods are still insufficient in predicting high-speed solidification microstructures, and cannot reflect the evolution law of local solidification structure in the molten pool, which limits the depth of research on the transformation of molten pool solidification mode and grain size evolution. Summary of the invention

[0004] In view of this, the present application provides a molten pool grain solidification analysis method and device based on a continuous growth limiting factor, which can help establish a solidification mode transition criterion near the melting boundary and grasp the law of grain size evolution.

[0005] Specifically, the present application is implemented through the following technical solutions: In a first aspect, the present application provides a molten pool grain solidification analysis method based on a continuous growth restriction factor, the method comprising: Establishing a first relationship between the continuous growth limiting factor and a model for predicting the continuous growth rate of grains, wherein the first relationship is an inverse relationship; Determining a second relationship between the model for predicting the continuous growth rate of grains and the solidification path according to the first relationship, wherein as the solidification path increases, a growth curve corresponding to the second relationship increases exponentially; Determine a demarcation point according to the correlation between the solute concentration, the welding speed and the solidification path, the demarcation point being the point corresponding to the maximum growth rate in the growth curve; Calculating the radius of curvature of each point on the growth curve; The dividing point between planar growth and cellular growth is determined based on the calculated radius of curvature.

[0006] A second aspect of the present application provides a molten pool grain solidification analysis device based on a continuous growth restriction factor, the device comprising an establishment module, a determination module and a calculation module; Wherein, the establishing module is used to establish a first relationship between the continuous growth limiting factor and the model for predicting the continuous growth rate of grains, and the first relationship is an inverse relationship; The determining module is used to determine a second relationship between the model for predicting the continuous growth rate of grains and the solidification path according to the first relationship, and as the solidification path increases, a growth curve corresponding to the second relationship increases exponentially; The determination module is further used to determine a demarcation point according to the correlation between the solute concentration, the welding speed and the solidification path, the demarcation point being a point corresponding to the maximum growth rate in the growth curve; The calculation module is used to calculate the curvature radius of each point on the growth curve; The determination module is also used to determine the boundary point between planar growth and cellular growth according to the calculated radius of curvature.

[0007] The molten pool grain solidification analysis method and device based on the continuous growth limitation factor provided in the present application determine a curve reflecting the solidification behavior through the relationship between the solidification process and the continuous growth rate, and then determine the change point of the physical and chemical behavior according to the shape characteristics of the curve, that is, determine the change point of the physical and chemical behavior through the geometric turning point. On the one hand, it avoids tedious physical and chemical process analysis, avoids consideration of other physical and chemical characteristics, processes, and interference factors, and improves the efficiency of locating the solidification boundary point; on the other hand, it can accurately calculate the boundary point through geometric numerical calculations, without the need for estimation through other conditions, thereby improving the accuracy of locating the boundary point. First, by establishing an inverse relationship between the continuous growth restriction factor and the model used to predict the continuous growth rate of grains (the first relationship), we can more clearly understand the mechanism of the influence of the restriction factor on the grain growth rate during the solidification process of the molten pool grains, which helps researchers accurately grasp the restrictive factors of grain growth under different conditions and provide a theoretical basis for regulating the solidification process; secondly, the second relationship between the model used to predict the continuous growth rate of grains and the solidification path is determined, and it grows exponentially with the increase of the solidification path, and the growth rate continues to increase, which makes it possible to quantitatively analyze the law of the change of grain growth rate with the solidification path during the solidification process, providing a basis for accurately predicting the solidification behavior; further, according to the correlation between the solute concentration, welding speed and solidification path, the dividing point is determined, that is, the point corresponding to the maximum growth rate in the growth curve. This dividing point can clearly distinguish between the two different growth modes of planar growth and cellular growth, which is of great significance for studying the grain characteristics and solidification behavior under different growth modes; in addition, the radius of curvature of each point on the growth curve is calculated, and the dividing point between planar growth and cellular growth is determined again according to the radius of curvature, which further improves the accuracy and reliability of the dividing point. The method provided in this application comprehensively considers key factors such as the continuous growth limitation factor, the continuous grain growth rate, the solidification path, the solute concentration and the welding speed. It can comprehensively analyze the solidification process of the molten pool grains and reflect the evolution law of the local solidification structure of the molten pool, thereby providing assistance in establishing the solidification mode conversion criteria near the melting boundary and mastering the grain size evolution law. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 A flow chart of Example 1 of a molten pool grain solidification analysis method based on a continuous growth restriction factor provided in the present application; Figure 2 A schematic diagram of a second relationship shown in the present application; Figure 3 Schematic diagram of the actual plane growth distance and the distance change between the dividing point and the melting boundary under different liquid solute concentrations shown in this application; Figure 4 Schematic diagram of the evolution curve of the actual plane growth distance and the distance between the dividing point and the melting boundary at different welding speeds shown in this application; Figure 5 This is a schematic structural diagram of Example 2 of the molten pool grain solidification analysis device based on the continuous growth limitation factor provided in the present application. DETAILED DESCRIPTION

[0009] Here, exemplary embodiments are described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application.

[0010] The terms used in this application are only for the purpose of describing specific embodiments and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application are also intended to include plural forms, unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used in this article refers to and includes any or all possible combinations of one or more associated listed items.

[0011] It should be understood that although the terms first, second, third, etc. may be used in the present application to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0012] Specific embodiments are given below to introduce the technical solution of the present application in detail.

[0013] Figure 1 This is a flow chart of Example 1 of the molten pool grain solidification analysis method based on the continuous growth restriction factor provided by this application. Please refer to Figure 1 , the method provided in this embodiment may include: S101 . Establishing a first relationship between a continuous growth limiting factor and a model for predicting a continuous growth rate of grains, wherein the first relationship is an inverse relationship.

[0014] It should be noted that the continuous growth restriction factor is a parameter used to describe the degree of restriction on the continuous growth of grains during the solidification process of materials. During the solidification of molten pool grains, there are many factors that affect the growth of grains. The continuous growth restriction factor comprehensively considers the hindering effect of these factors on grain growth. It may be related to factors such as solute concentration, temperature gradient, and solidification rate. For example, a higher solute concentration may cause the continuous growth restriction factor to increase, thereby limiting the continuous growth rate of grains. Its role is to quantitatively measure the degree of constraint of various factors on grain growth, and provide important indicators for understanding and regulating the solidification process. The model used to predict the continuous growth rate of grains is a method to predict the continuous growth rate of grains during solidification through mathematical expressions or theoretical models. The model usually considers multiple variables, such as temperature, solute concentration, solidification path, continuous growth restriction factor, etc. It establishes the relationship between these variables and the continuous growth rate of grains so that the growth of grains can be predicted based on known process parameters and conditions. For example, the model may be expressed as a functional relationship between the continuous growth rate of grains and temperature, solute concentration, and continuous growth restriction factor. By measuring and analyzing these variables, the model can be used to predict the growth rate of grains under different conditions, providing a basis for optimizing the solidification process of the material and controlling the grain structure.

[0015] Specifically, establishing a first relationship between the continuous growth limiting factor and the model for predicting the continuous growth rate of grains includes: (1) Determining common parameters associated with a model for predicting the continuous growth rate of grains based on the continuous growth limiting factor.

[0016] It should be noted that when establishing a model of the continuous growth limiting factor and the continuous grain growth rate, it is necessary to determine the associated common parameters. The common parameters reflect the key variables that affect the interaction between the two, which usually include temperature and temperature gradient, solute concentration, liquidus slope, solidification path, distribution coefficient and diffusion coefficient.

[0017] Among them, temperature changes will affect the diffusion rate of atoms, thereby affecting the restriction factor. The temperature gradient determines the direction and speed of heat transfer and affects the rate of the solidification process. The solute concentration will affect the formation and growth of the crystal nucleus. A higher solute concentration will usually increase the value of the restriction factor. The liquidus slope reflects the effect of alloy composition changes on the melting point. During the solidification process, the size of the liquidus slope determines the rate at which the liquid phase composition changes with temperature. If the liquidus slope is large, it means that a slight change in temperature will cause a large change in the liquid phase composition, which will affect the distribution of the solute between the liquid and solid phases. Changing the composition and structure at the solid-liquid interface will affect the continuous growth limitation factor; the distribution coefficient indicates the distribution ratio of the solute between the solid phase and the liquid phase. When the distribution coefficient is small, it means that the solute is more inclined to remain in the liquid phase. During the solidification process, this will lead to the enrichment of the solute at the solid-liquid interface, thereby increasing the continuous growth limitation factor; the diffusion coefficient describes the diffusion ability of solute atoms in the liquid phase and the solid phase. If the diffusion coefficient is small, the diffusion of solute atoms near the solid-liquid interface will be relatively slow, which will lead to the accumulation of solute at the interface and increase the continuous growth limitation factor.

[0018] (2) Determining a growth limiting factor model based on solute concentration, liquidus slope and distribution coefficient, and optimizing the growth limiting factor model by combining other parameters in the associated common parameters except the common parameters to obtain a continuous growth limiting factor model.

[0019] Combining the common parameters determined above and the study of related theories, the model of the growth limiting factor can be determined based on the solute concentration, liquidus slope and distribution coefficient. Specifically, the model of the growth limiting factor is as follows: ; in, Q is the growth limiting factor, m L is the liquidus slope, C 0 is the solute concentration in the liquid, k is the distribution coefficient.

[0020] Furthermore, the model of the growth restriction factor is optimized by taking into account parameters such as the solidification path, welding speed, diffusion coefficient, and the angle between the welding speed direction at a point on the solid-liquid interface and the normal line of the fusion line to obtain a model of the continuous growth restriction factor. Specifically, the model of the continuous growth restriction factor is as follows: ; in, Q C is the continuous growth limiting factor, m L is the liquidus slope, C 0is the solute concentration in the liquid, k is the distribution coefficient, v is the welding speed, ξ is the solidification path, α It is the angle between the welding velocity direction at a point on the solid-liquid interface and the normal line of the fusion line. D is the diffusion coefficient of the solute in the liquid.

[0021] (3) Determine a model for predicting the continuous growth rate of grains by combining the KGT model, the common parameters, the model of the growth limiting factor, and the proportional relationship between the model for predicting the continuous growth rate of grains.

[0022] It should be noted that the KGT model is a commonly used method in the model for predicting the continuous growth rate of grains. It combines factors such as solute distribution, temperature gradient and crystal growth rate to describe and predict the growth behavior of grains. For the content of the KGT model, please refer to the description of the relevant technology, which will not be repeated here. By combining the KGT model and the determined growth limitation factor, and analyzing the proportional relationship between the model of the growth limitation factor and the model for predicting the continuous growth rate of grains, specifically, since the continuous growth rate of grains is inversely proportional to the growth limitation factor, that is, the larger the growth limitation factor, the smaller the continuous growth rate of grains, a prediction model for the continuous growth rate of grains can be further established. Specifically, the model for predicting the continuous growth rate of grains is as follows: ; in, v c is the continuous grain growth rate, D is the diffusion coefficient of the solute in the liquid, Γ is the Gibbs-Thomson coefficient, Q is the growth limiting factor, is the degree of supercooling.

[0023] (4) Establishing the first relationship based on the model for predicting the continuous growth rate of grains and the continuous growth limiting factor.

[0024] In combination with the above description, specifically, the continuous growth limiting factor is substituted for the growth limiting factor in the model for predicting the continuous growth rate of grains to obtain a first relationship, wherein the first relationship can be expressed as: ; in, v c is the continuous grain growth rate, m L is the liquidus slope, C 0 is the solute concentration in the liquid, k is the distribution coefficient,v is the welding speed, ξ is the solidification path, α It is the angle between the welding velocity direction at a point on the solid-liquid interface and the normal line of the fusion line. D is the diffusion coefficient of the solute in the liquid, Q C is the continuous growth limiting factor, Γ is the Gibbs-Thomson coefficient.

[0025] It should be noted that the first relationship characterizes the constraint and influence mechanism of the continuous growth restriction factor on the continuous growth rate of grains during the solidification of the molten pool; the output value of the model of the continuous growth rate of grains changes with the continuous growth restriction factor. During the solidification of the molten pool, the continuous growth restriction factor covers a variety of factors that affect the continuous growth of grains, and these factors are reflected in the constraint on the continuous growth rate of grains through the continuous growth restriction factor, a comprehensive indicator. For example, when the solute concentration involved in the continuous growth restriction factor increases, the solute atoms aggregate at the solid-liquid interface, changing the equilibrium state of the interface and increasing the resistance to grain growth. This resistance is expressed by the increase of the continuous growth restriction factor, which in turn constrains the continuous growth rate of grains and reduces it.

[0026] When the continuous growth restriction factor changes, it means that the conditions affecting grain growth have changed. If the continuous growth restriction factor increases, it means that the factors limiting grain growth have increased. For example, the slope of the liquidus line may increase, making the liquid phase composition change caused by temperature change more drastic, resulting in more serious segregation of solute at the interface, or the distribution coefficient may decrease, making the solute more inclined to remain in the liquid phase, aggravating the enrichment of solute at the interface. These changes will increase the continuous growth restriction factor, thereby reducing the value of the model used to predict the continuous growth rate of grains, that is, the continuous growth rate of grains decreases. Conversely, if the continuous growth restriction factor decreases, it means that the restriction on grain growth is weakened, and the continuous growth rate of grains will increase accordingly. This dynamic change relationship accurately reflects the influence of complex physical and chemical processes on grain growth during the solidification of the molten pool.

[0027] S102. Determine a second relationship between the model for predicting the continuous growth rate of grains and the solidification path according to the first relationship, and as the solidification path increases, a growth curve corresponding to the second relationship increases exponentially.

[0028] Combined with the above description, it is known that the first relationship is that the continuous growth rate of grains (represented by the model used to predict the continuous growth rate of grains) is inversely proportional to the continuous growth limiting factor. The continuous growth limiting factor itself is related to a variety of factors in the solidification process, and the solidification path is one of the key factors. During the solidification process, as the solidification path extends (which can be the advancement of time or the change of spatial position, such as the distance traveled by the molten pool from the initial solidification point to complete solidification, etc.), factors such as the distribution of solutes and temperature gradients will change, and these changes will directly affect the continuous growth limiting factor.

[0029] Figure 2 For a schematic diagram of the second relationship shown in this application, please refer to Figure 2 , as the solidification path increases, the growth curve corresponding to the second relationship grows exponentially, and the growth rate of the growth curve continues to increase. By changing the input and output variables of the first relationship, the second relationship can be obtained. Specifically, the input and output of the first relationship can be calibrated as Figure 2 The second relationship is obtained by using the content in , so there is no need to recalculate. Among them, Figure 2 PG in it means planar growth, CG means cellular growth, vc means growth velocity, rmin means minimum curvature radius, ξ S Represents the distance from the solidification boundary.

[0030] Please continue to refer to Figure 2 The second relationship between the model for predicting the continuous growth rate of grains and the solidification path shows that as the solidification path increases, the growth rate of the growth curve corresponding to the second relationship changes from small to large, and there is a turning point from slow to fast. The turning point of the growth rate change can be determined according to the change direction and change value of the growth rate. Specifically, Figure 2 The turning point is N, and the value of the continuous growth rate of the grains is relatively stable before point N. The growth rate of the grains in this stage is very small, that is, the solidification mode of the molten pool near the melting boundary can be assumed to be near-planar growth. When the solid-liquid interface gradually approaches point N, the value of the continuous growth rate of the grains begins to increase, and rises rapidly in the later stage, indicating that a transition from planar growth to cellular growth occurs at point N. Among them, planar growth is a growth mode in which the solid-liquid interface basically maintains a planar shape and moves forward during the solidification process. In this growth mode, the solidification front is relatively smooth, and the new crystal layer grows on the existing crystal layer in an approximately parallel manner. Cellular growth refers to a growth mode in which the solidification interface no longer maintains a planar state during the solidification process, but forms a series of cell-like protruding structures. These protruding cellular structures can be regular hexagons or other shapes, and they grow from the solidification front to the liquid phase.

[0031] In the method provided by the present invention, the second relationship is the relationship between the distance to the solidification boundary and the continuous growth rate of the grain, and the second relationship is an exponential growth curve, that is, the absolute value continues to rise, but the growth rate changes from small to large. Determining the demarcation point also includes determining the maximum circumscribed circle of each position point, obtaining the radius of the maximum circumscribed circle, and taking the position point corresponding to the minimum value of the radius of the maximum circumscribed circle as the demarcation point. As an optional embodiment, since the second relationship is a continuously changing curve, continuous calculation may result in a large amount of calculation. Determining the demarcation point may include: estimating a candidate region of the solidification boundary based on the solidification behavior, the candidate region is a region within a preset distance from the solidification boundary, estimating the solidification velocity distribution characteristics based on the solidification behavior, determining the demarcation point candidate region of the second relationship based on the candidate region and the distribution characteristics, and calculating the demarcation point in the demarcation point candidate region.

[0032] S103, determining a demarcation point according to the correlation between the solute concentration, the welding speed and the solidification path, the demarcation point being a point corresponding to the maximum growth rate in the growth curve.

[0033] It should be noted that in the solidification process of the molten pool, the solute concentration plays a key role. A higher solute concentration will cause the solute to segregate at the solid-liquid interface, thereby affecting the solidification path. As solidification proceeds, the redistribution of solute atoms will change the composition and temperature conditions at the solidification front, thereby affecting the growth pattern and solidification path of the grains. For example, when the solute concentration increases, the possibility of component supercooling increases, and the solidification path may deviate from the planar growth mode and transform to a more complex mode such as cellular growth. The welding speed is directly related to the heat input and cooling rate of the molten pool. A faster welding speed means that the molten pool receives relatively less heat input per unit time and the cooling rate is faster, which affects the solidification time and solidification path of the molten pool. For example, when welding quickly, the solidification path of the molten pool may be shortened, and the time for solute diffusion is correspondingly reduced, making the distribution of solute at the solid-liquid interface more uneven, thereby affecting grain growth and solidification pattern.

[0034] It should also be noted that the solidification path is the result of the combined effect of factors such as solute concentration and welding speed, which can be reflected by describing the change trajectory of parameters such as temperature and composition in the process of the molten pool from liquid to solid. Different combinations of solute concentration and welding speed will lead to different solidification paths, which may cause the grain growth to show planar growth, cellular growth or other more complex growth patterns.

[0035] Specifically, the demarcation point is determined according to the correlation between the solute concentration, the welding speed and the solidification path, including: (1) Obtain the grain growth at the alloy melting boundary under different liquid solute concentrations and welding speeds.

[0036] It should be noted that different liquid solute concentrations and welding speed conditions can be simulated by experimental means, such as setting different welding process parameters in the laboratory. For example, alloy materials with different compositions can be used to change the solute concentration, and the welding speed can be controlled by adjusting the parameters of the welding equipment (such as welding current, voltage, etc.).

[0037] During the welding process, high-speed cameras, microscopes and other observation equipment are used to observe the grain growth at the melting boundary of the alloy. High-speed cameras can capture the dynamic growth process of grains during solidification, while microscopes can provide more detailed information on the microstructure of grains, including the size, shape, orientation, etc. of the grains. For each combination of liquid solute concentration and welding speed, the growth state of the grains at different times is recorded in detail. For example, the time when the grains begin to form, the growth direction of the grains, and the growth rate of the grains in different directions are recorded.

[0038] (2) Based on the growth conditions, a curve showing the actual plane growth distance and the distance between the boundary point and the melting boundary at different liquid solute concentrations as a function of the liquid solute concentration is determined.

[0039] It should be noted that the range of the planar growth stage is determined based on the observed grain growth. The characteristic of the planar growth stage is that the solid-liquid interface basically maintains a planar shape and moves forward. At this time, the distance of the planar growth can be measured. At the same time, by observing the changes in the grain growth mode (such as the transition from planar growth to cellular growth), the position of the dividing point is determined, and then the distance between the dividing point and the melting boundary is measured.

[0040] The above measurement process is repeated as the concentration of the liquid solute changes. The actual plane growth distance and the distance between the dividing point and the melting boundary under different liquid solute concentrations are sorted out, and two curves are drawn with the liquid solute concentration as the horizontal axis and the plane growth distance and the distance between the dividing point and the melting boundary as the vertical axis. Figure 3 This is a schematic diagram of the actual plane growth distance and the distance change between the dividing point and the melting boundary under different liquid solute concentrations shown in this application. Please refer to Figure 3 The curve can intuitively reflect the influence of liquid solute concentration on plane growth and boundary point position.

[0041] (3) Determine, based on the growth conditions, an evolution curve of the actual plane growth distance and the distance between the dividing point and the melting boundary at different welding speeds.

[0042] Similar to the analysis of liquid solute concentration, for different welding speed conditions, the plane growth distance and the distance between the demarcation point and the melting boundary are determined based on the observed grain growth at the alloy melting boundary. Repeat the measurement and record as the welding speed changes. Draw two evolution curves with the welding speed as the horizontal axis and the plane growth distance and the distance between the demarcation point and the melting boundary as the vertical axis. Figure 4 This is a schematic diagram of the actual plane growth distance and the distance evolution curve between the dividing point and the melting boundary at different welding speeds shown in this application. Please refer to Figure 4 , the effect of welding speed on plane growth and boundary point position is shown through evolution curve.

[0043] (4) Determine the correlation and obtain the demarcation point based on the curve and the evolution curve.

[0044] Through the comprehensive analysis of the above liquid solute concentration correlation curve and welding speed evolution curve, the correlation between solute concentration, welding speed and solidification path can be determined. For example, it is observed that with the increase of liquid solute concentration and the decrease of welding speed, the plane growth distance may decrease, and the distance between the boundary point and the melting boundary may change (such as decrease or increase).

[0045] Based on these curves and evolution curves, the demarcation point can be obtained by finding the characteristic point where the planar growth ends and the growth mode changes (i.e., the demarcation point). This characteristic point may be the point where the slope of the curve changes suddenly, or the point that meets certain conditions (such as a specific proportional relationship between the planar growth distance and the distance between the demarcation point and the melting boundary). The demarcation point determined based on these analyses can be used to accurately distinguish different grain growth modes such as planar growth and cellular growth.

[0046] It should be noted that the determination of the dividing point based on the correlation between solute concentration, welding speed and solidification path is mainly based on the macroscopic process parameter perspective, taking into account the relationship between factors such as solute concentration and welding speed that have an important influence on the solidification process in actual production and the solidification path, so as to find a dividing point that can distinguish between planar growth and cellular growth. This dividing point more reflects the influence of external process conditions on the transformation of growth mode. Among them, this dividing point is the point corresponding to the maximum growth rate in the growth curve, which represents a key state in the solidification process. Before and after this point, the pattern and rate of grain growth will change significantly.

[0047] S104: Calculate the radius of curvature of each point on the growth curve.

[0048] It should be noted that by calculating the radius of curvature of each point on the growth curve, the dividing point between the two growth modes of planar growth and cellular growth can be determined more accurately. Specifically, in the planar growth stage, the growth curve is relatively flat and the radius of curvature is large; when the growth mode begins to change to cellular growth, the curvature of the curve changes and the radius of curvature becomes smaller. By analyzing the change in the radius of curvature, the change in this growth mode can be captured more keenly.

[0049] In a specific implementation, calculating the curvature radius of each point on the growth curve includes: (1) Determining a curve equation corresponding to the growth curve based on the growth curve.

[0050] It should be noted that data fitting technology can be used to determine the curve equation corresponding to the growth curve. For details, please refer to the description of related technologies, which will not be repeated here.

[0051] (2) Obtaining the coordinates of each point on the growth curve.

[0052] The coordinates of a series of points can be obtained by discretizing the independent variables (such as variables related to the solidification path) and then substituting these values ​​into the curve equation to calculate the corresponding dependent variables (such as grain growth rate).

[0053] (3) Based on the curve equation and the coordinates of each point, the first-order derivative and the second-order derivative corresponding to each point are calculated respectively.

[0054] Depending on the actual situation, you can choose the analytical derivation method (for simple function forms) or the numerical derivation method (for complex or discrete data) to calculate the first-order derivative and second-order derivative corresponding to each point respectively.

[0055] (4) Calculate the curvature corresponding to each point based on the curvature formula and the calculated first-order derivatives and second-order derivatives corresponding to each point.

[0056] It should be noted that for plane curves y = f(x) The curvature of a point on a curve k The expression is: ; in, is the first-order derivative at that point, is the second-order derivative at that point.

[0057] By substituting the first-order derivative and second-order derivative of each point calculated previously into this curvature formula, the curvature of each point can be calculated.

[0058] (5) Calculate the curvature radius corresponding to each point based on the curvature corresponding to each point.

[0059] It should be noted that the radius of curvature R and curvature k The relationship between (when k ≠0), therefore, the specific formula for the radius of curvature is as follows: ; in, is the first-order derivative of each point calculated, is the calculated second-order derivative of each point.

[0060] S105. Determine the boundary point between planar growth and cellular growth according to the calculated radius of curvature.

[0061] It should be noted that the point where the calculated minimum value of the radius of curvature is located is the dividing point between planar growth and cellular growth. In the growth curve, the curve in the planar growth stage is relatively flat. This is because during planar growth, the change in grain growth rate is relatively slow, the slope of the growth curve does not change much, and the corresponding curvature is small, so the radius of curvature is larger. When the growth mode changes from planar growth to cellular growth, the change in grain growth rate intensifies. This change is reflected in the growth curve as a sharp increase in the curvature of the curve, an increase in curvature, and a corresponding decrease in the radius of curvature. Therefore, the point with the smallest radius of curvature represents the position where the curve is most curved, that is, the position where the growth mode changes dramatically. This position can be reasonably considered to be the dividing point between planar growth and cellular growth.

[0062] It should be noted that the dividing point between planar growth and cellular growth is determined based on the calculated radius of curvature. This is determined from a microscopic geometric perspective by analyzing the change in the radius of curvature of the growth curve. This dividing point focuses more on distinguishing different growth modes from the perspective of the morphological characteristics of the curve. Combining the previous determination of the dividing point from the perspective of macroscopic process parameters and the determination of the dividing point from the perspective of microscopic geometry, determining the dividing point from different perspectives helps to more comprehensively and accurately understand and grasp the transformation process between planar growth and cellular growth, and provide a more reliable basis for the analysis and control of the solidification process of the molten pool grains.

[0063] Optionally, the dividing point between the planar growth and the cellular growth is determined according to the calculated curvature radius, and then, the method includes: (1) Obtain the grain growth rate data of the melting boundary of the alloy material under different process parameters.

[0064] It should be noted that changes in process parameters such as welding speed, solute concentration, and temperature gradient will affect the solidification process of the alloy material at the melting boundary. Experiments are conducted under a variety of different process parameter combinations to collect grain growth rate data of the alloy material at the melting boundary. Advanced measurement techniques such as high-speed photography combined with image analysis software can be used to measure grain growth rate to ensure the accuracy and reliability of the data.

[0065] (2) Based on the correlation between the data and the solidification path, a phase field model simulation is performed to obtain simulation results.

[0066] It should be noted that the phase field model is a microstructure evolution simulation method based on the continuum theory. It describes the transition region between different phases by introducing an order parameter (phase field variable). In the process of simulating grain growth, the phase field model can consider multiple physical factors such as solute diffusion, thermal diffusion, and interface energy. According to the collected grain growth rate data and their correlation with the solidification path, the parameters in the phase field model (such as interface energy coefficient, solute diffusion coefficient, etc.) are reasonably set. The setting of these parameters is based on experimental data and the physical properties of the material, so that the phase field model can accurately reflect the actual solidification process.

[0067] The phase field model is run to perform simulation calculations to simulate the solidification process of alloy materials under different process parameters. As the simulation time progresses, the phase field model can output microstructure information at different times, including the shape, size and growth rate of the grains. These simulation results can intuitively show the growth evolution of the grains during the solidification process.

[0068] (3) Based on the simulation results, determine the data points where the grain growth rate changes with the solidification path and the position of the transition point from planar growth to cellular growth.

[0069] Data on the change of grain growth rate with solidification path are extracted from the simulation results of the phase field model. These data form a series of data points, depicting the dynamic process of grain growth under simulation conditions. By observing the change in the growth morphology of the grains during the simulation, the transition point from planar growth to cellular growth is determined. In the phase field model, this transition point can be determined based on characteristics such as the flatness of the grain interface and the change in growth direction. For example, when the grain interface begins to bulge from a relatively smooth plane to form a cellular structure, it can be determined as a transition point.

[0070] (4) Comparing the position of the data point with the point corresponding to the maximum value of the growth curvature, and comparing the position of the transition point from planar growth to cellular growth with the position point on the solidification path corresponding to the point corresponding to the maximum value of the growth curvature, so as to determine the validity of the simulation results and the second relationship.

[0071] It should be noted that the point corresponding to the maximum growth curvature is the theoretical boundary point between planar growth and cellular growth obtained from the previous analysis of the growth curve. By comparing the data points and transition points obtained by the phase field model simulation with it, it can be verified whether the simulation results are consistent with the theoretical analysis. If the data points and transition points in the simulation results are close to the points corresponding to the theoretical maximum growth curvature, it means that the phase field model can accurately simulate the grain growth process, and it also proves that the second relationship (the relationship between grain growth rate and solidification path) obtained based on the growth curve analysis is valid.

[0072] In specific implementation, for data points, their positions on the solidification path coordinate axis and the value of the grain growth rate can be compared. If the simulated data point is near the same solidification path position as the point corresponding to the theoretical maximum growth curvature, and the growth rate change trend is also consistent, then it means that the simulation results are consistent with the theoretical analysis. For the transition point from planar growth to cellular growth, compare its position on the solidification path. If the position of the transition point obtained by simulation is close to the position of the point corresponding to the theoretical maximum growth curvature on the solidification path, it means that the phase field model has successfully captured the transition of the growth mode, further verifying the validity of the simulation results and the second relationship.

[0073] Optionally, the dividing point between the planar growth and the cellular growth is determined according to the calculated curvature radius, and then, the method includes: (1) The molten pool solidification process is divided into different stages based on the dividing point, and the stages include a planar growth stage and a cellular growth stage.

[0074] It should be noted that after determining the dividing point between planar growth and cellular growth by calculating the radius of curvature, the two main stages in the solidification process of the molten pool can be clearly distinguished. The interval from the beginning of solidification to the dividing point is the planar growth stage, which is characterized by the solid-liquid interface basically maintaining a planar shape and moving forward. From the dividing point onwards is the cellular growth stage, at which time a series of cell-like protrusions are formed on the solidification interface and grow into the liquid phase. This division helps to study the molten pool solidification process in more detail. Different growth stages are dominated by different factors and have different effects on the microstructure and properties of the final material. For example, the grain structure formed in the planar growth stage is relatively regular and smooth, while the cellular growth stage introduces complex microstructural changes.

[0075] (2) Determine the influence of liquid solute concentration and welding speed on solidification results at each stage.

[0076] It should be noted that in the planar growth stage, a lower liquid solute concentration is conducive to maintaining the planar growth mode, because the low solute concentration reduces the enrichment of the solute at the solid-liquid interface and avoids the supercooling of the components. If the solute concentration increases slightly, the planar growth may be maintained within a certain range, but the stability of the planar growth will be reduced. For example, when the solute concentration increases, the temperature gradient requirements at the solidification front may be more stringent to suppress the occurrence of component supercooling, otherwise it may enter the cellular growth stage in advance. At this time, a faster welding speed will accelerate the cooling of the molten pool, and the temperature gradient at the solidification front can be increased at this stage. A larger temperature gradient helps to maintain planar growth because it can more effectively conduct heat away from the solidification front and suppress local supercooling. However, if the welding speed is too fast, it may lead to insufficient solute diffusion and accumulation in local areas, which will also have an adverse effect on planar growth.

[0077] In the cellular growth stage, a higher liquid solute concentration is an important factor that promotes cellular growth. The enrichment of solutes at the solid-liquid interface changes the composition of the liquid phase at the interface, lowering the melting point of the liquid phase. This causes the liquid in the local area to begin to solidify at a temperature slightly higher than the equilibrium solidification temperature, forming cellular protrusions. As the solute concentration increases further, the cellular structure may become more complex, such as smaller cell size and more cellular branches. At this time, a slower welding speed will slow down the cooling rate of the molten pool in the cellular growth stage, providing more time for solute diffusion and the growth of cellular structures. At the same time, due to the slow cooling rate, the temperature gradient is relatively small, and the supercooling of the composition is easier to maintain, which is conducive to the continued growth of cellular growth. If the welding speed is increased, the cellular growth may be inhibited because the heat loss is too fast, which may cause the growing cellular structure to be surrounded by the rapidly solidifying liquid phase before it has time to fully develop.

[0078] (3) Based on the above influence, the relationship between the plane growth distance and the average grain size during the molten pool solidification process is determined.

[0079] It should be noted that in the planar growth stage, the length of the planar growth distance directly affects the initial size of the grains. A longer planar growth distance means that the grains have more growth time in the planar direction, which will increase the size of the grains in the planar growth stage. For example, under the same liquid solute concentration and welding speed conditions, the molten pool with a longer planar growth distance has a relatively larger grain size at the end of the planar growth stage.

[0080] It should also be noted that the cellular growth stage is carried out on the basis of the planar growth stage, and the planar growth distance will affect the initial state of cellular growth. If the planar growth distance is short, cellular growth may start earlier, and due to the small initial grain size, the development of the cellular structure may be limited to a certain extent, while a longer planar growth distance provides a better foundation for cellular growth, which may make the cellular structure more regular and developed. From the perspective of average grain size, the molten pool with a long planar growth distance and sufficient cellular growth may have a larger final average grain size, because the grains have sufficient growth space and time in both the planar growth stage and the cellular growth stage. At the same time, the interaction between the planar growth distance and the cellular growth stage will also affect the distribution of grain size.

[0081] Optionally, the dividing point between the planar growth and the cellular growth is determined according to the calculated curvature radius, and then, the method further includes: (1) Measure the grain size of the local area of ​​the molten pool at the melting boundary of the alloy and obtain the average grain size data.

[0082] It should be noted that an optical microscope or an electron microscope can be used to observe the microstructure of the molten pool at the melting boundary of the alloy, by taking pictures of the grains in the local area and then using image analysis software to measure the size of each grain.

[0083] (2) Analyze the average grain size data to form an average grain size evolution curve.

[0084] With solidification time or solidification path and other related parameters as the horizontal coordinate and average grain size as the vertical coordinate, the average grain size data measured at different times or different solidification stages are plotted in the coordinate system, and these data points are connected with a curve to form an average grain size evolution curve. This curve intuitively shows the trend of grain size change over time or solidification path during the entire molten pool solidification process. By observing the shape of the curve, the stage characteristics of grain growth can be preliminarily judged. For example, the stage with a larger slope of the curve may indicate a faster grain growth rate, while the stage with a smaller slope may indicate a slower growth rate or inhibited growth.

[0085] (3) Based on the evolution curve, the variation relationship of the average grain size under different solute concentrations and welding speeds is analyzed respectively.

[0086] It should be noted that when the solute concentration changes, the changes in the average grain size evolution curve are observed. At lower solute concentrations, the planar growth stage may be longer, and the average grain size may gradually and steadily grow during the planar growth stage, because low solute concentrations are conducive to planar growth, allowing grains to grow under relatively stable conditions. As the solute concentration increases, a transition in growth mode may occur earlier, transitioning from planar growth to cellular growth. During the cellular growth stage, due to solute segregation and complex growth patterns, the growth trend of the average grain size may change, and there may be a slowdown in growth, fluctuations, or grain refinement. This is because the enrichment of solute atoms at the solid-liquid interface changes the growth conditions and affects the driving force and growth direction of grain growth.

[0087] As for welding speed, faster welding speed will accelerate the cooling speed of the molten pool. In the average grain size evolution curve, it is shown that the plane growth stage may be shortened, and the size growth time of the grains in the plane growth stage is reduced, resulting in a relatively small average grain size at the end of the plane growth. In the cellular growth stage, rapid cooling may inhibit the full growth of the cellular structure, so that the growth of the average grain size is also limited. On the contrary, at a slower welding speed, the molten pool cools more slowly, and the plane growth stage may be extended, which is conducive to the growth of grains in the plane growth stage. Moreover, in the cellular growth stage, the slower cooling rate provides more favorable conditions for the growth of the cellular structure, which may cause a larger increase in the average grain size, but it may also lead to an increase in grain size non-uniformity. Through such analysis, the specific influence of welding speed on grain size change can be clarified, thereby providing a basis for controlling the welding process to obtain an ideal grain size.

[0088] The method provided in the present application, by determining the dividing point between planar growth and cellular growth, can, on the one hand, clearly divide the molten pool solidification process into different stages. This division helps to deeply understand the physical mechanism and growth characteristics of each stage. For example, the grain growth in the planar growth stage is relatively regular and stable, while the cellular growth stage presents complex cellular structure growth. This makes the analysis of the molten pool solidification process more accurate from the overall to the local. In the analysis process, the effects of factors such as solute concentration and welding speed on the solidification process are comprehensively considered. The effects of these factors in different growth stages are different. By studying their effects in detail, the evolution of the microstructure during the solidification process of the molten pool can be more comprehensively grasped. For example, the solute concentration affects the growth stability in the planar growth stage and affects the formation of cellular structure in the cellular growth stage; the welding speed affects the time and morphology of grain growth by changing the cooling rate of the molten pool.

[0089] Secondly, the first relationship between the continuous growth limiting factor and the model for predicting the continuous growth rate of grains (inverse relationship) and the second relationship between the model for predicting the continuous growth rate of grains and the solidification path (the growth curve is exponentially growing and the growth rate is increasing) were established. These relationships quantitatively describe the interaction between the grain growth rate and other factors through mathematical models, making the prediction of the grain growth rate more accurate.

[0090] Third, the validity of the model and simulation results is verified in a variety of ways. For example, after determining the demarcation point, the grain growth rate data under different process parameters is obtained, a phase field model simulation is performed, and the simulation results are compared with the point corresponding to the maximum growth curvature obtained based on theoretical analysis. This multi-dimensional verification method can ensure that the model and simulation results can accurately reflect the actual situation of the molten pool solidification process and improve the reliability of the analysis method.

[0091] Corresponding to the aforementioned embodiment of a molten pool grain solidification analysis method based on a continuous growth restriction factor, the present application also provides an embodiment of a molten pool grain solidification analysis device based on a continuous growth restriction factor.

[0092] Figure 5 This is a schematic diagram of the structure of the second embodiment of the molten pool grain solidification analysis device based on the continuous growth restriction factor provided by this application. Figure 5 , the device provided in this embodiment includes an establishing module 510, a determining module 520 and a calculating module 530; The establishing module 510 is used to establish a first relationship between the continuous growth limiting factor and the model for predicting the continuous growth rate of grains, wherein the first relationship is an inverse relationship; The determination module 520 is used to determine a second relationship between the model for predicting the continuous growth rate of grains and the solidification path according to the first relationship, and as the solidification path increases, the growth curve corresponding to the second relationship increases exponentially; The determination module 520 is further used to determine a demarcation point according to the correlation between the solute concentration, the welding speed and the solidification path, and the demarcation point is a point corresponding to the maximum growth rate in the growth curve; The calculation module 530 is used to calculate the curvature radius of each point on the growth curve; The determination module 520 is further used to determine the boundary point between planar growth and cellular growth according to the calculated radius of curvature.

[0093] The device of this embodiment can be used to perform Figure 1 The steps, specific implementation principles and implementation processes of the method embodiment shown are similar and will not be repeated here.

[0094] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0095] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present application scheme. A person of ordinary skill in the art can understand and implement it without paying any creative work.

[0096] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A method for analyzing molten pool grain solidification based on continuous growth limiting factor, characterized in that: The method comprises: Establishing a first relationship between the continuous growth limiting factor and a model for predicting the continuous growth rate of grains, wherein the first relationship is an inverse relationship; Determining a second relationship between the model for predicting the continuous growth rate of grains and the solidification path according to the first relationship, wherein as the solidification path increases, a growth curve corresponding to the second relationship increases exponentially; Determine a demarcation point according to the correlation between the solute concentration, the welding speed and the solidification path, the demarcation point being the point corresponding to the maximum growth rate in the growth curve; Calculating the radius of curvature of each point on the growth curve; The dividing point between planar growth and cellular growth is determined based on the calculated radius of curvature.

2. The method according to claim 1, characterized in that The input and output variables of the first relationship are changed to obtain the second relationship; as the solidification path increases, the growth rate of the growth curve corresponding to the second relationship changes from small to large, and the turning point of the growth rate change is determined according to the change direction and change value of the growth rate.

3. The method according to claim 1, characterized in that Calculating the curvature radius of each point on the growth curve includes: Determining a curve equation corresponding to the growth curve based on the growth curve; Obtaining coordinates of each point on the growth curve; Based on the curve equation and the coordinates of each point, respectively calculate the first-order derivative and the second-order derivative corresponding to each point; Calculate the curvature corresponding to each point based on the curvature formula and the calculated first-order derivative and second-order derivative corresponding to each point; The curvature radius corresponding to each point is calculated based on the curvature corresponding to each point.

4. The method according to claim 1, characterized in that: The step of establishing a first relationship between the continuous growth limiting factor and a model for predicting the continuous growth rate of grains comprises: determining a common parameter associated with a model for predicting a continuous growth rate of grains based on the continuous growth limiting factor; Determining a growth limiting factor model based on solute concentration, liquidus slope and partition coefficient, and optimizing the growth limiting factor model by combining other parameters in the associated common parameters except the common parameters to obtain a continuous growth limiting factor model; Determine a model for predicting the continuous growth rate of grains by combining the KGT model, the common parameters, and the proportional relationship between the model of the growth limiting factor and the model for predicting the continuous growth rate of grains; The first relationship is established based on the model for predicting the continuous growth rate of grains and the continuous growth limiting factor.

5. The method according to claim 1, characterized in that The first relationship represents the constraint and influence mechanism of the continuous growth limiting factor on the continuous growth rate of grains during the solidification of the molten pool; the output value of the model of the continuous growth rate of grains varies with the continuous growth limiting factor.

6. The method according to claim 1, characterized in that The dividing point between the planar growth and the cellular growth is determined according to the calculated curvature radius, and then, the method comprises: Obtain the grain growth rate data of the melting boundary of the alloy material under different process parameters; Perform phase field model simulation based on the correlation between the data and the solidification path and obtain simulation results; Determine, based on the simulation results, data points of grain growth rate changes with solidification path and the position of the transition point from planar growth to cellular growth; The data point is compared with the position of the point corresponding to the maximum value of the growth curvature, and the position of the transition point from planar growth to cellular growth is compared with the position point corresponding to the point corresponding to the maximum value of the growth curvature on the solidification path to determine the validity of the simulation results and the second relationship.

7. The method according to claim 1, characterized in that The step of determining the demarcation point according to the correlation between the solute concentration, the welding speed and the solidification path includes: Obtain the grain growth at the alloy melting boundary under different liquid solute concentrations and welding speeds; Based on the growth conditions, determining a curve showing the actual plane growth distance and the distance between the dividing point and the melting boundary changing with the liquid solute concentration at different liquid solute concentrations; Determine, based on the growth condition, an evolution curve of the actual plane growth distance and the distance between the dividing point and the melting boundary at different welding speeds; The correlation is determined based on the curve and the evolution curve and a demarcation point is obtained.

8. The method according to claim 1, characterized in that The dividing point between the planar growth and the cellular growth is determined according to the calculated curvature radius, and then, the method comprises: Dividing the molten pool solidification process into different stages based on the dividing point, the stages include a planar growth stage and a cellular growth stage; Determine the influence of liquid solute concentration and welding speed on solidification results at each stage; Based on the degree of influence, the relationship between the plane growth distance and the average grain size during the molten pool solidification process is determined.

9. The method according to claim 1, characterized in that: The dividing point between the planar growth and the cellular growth is determined according to the calculated curvature radius, and then, the method comprises: Measure the grain size of the local area of ​​the molten pool at the melting boundary of the alloy to obtain the average grain size data; Analyzing the average grain size data to form an average grain size evolution curve; Based on the evolution curve, the variation relationship of the average grain size under different solute concentrations and welding speeds is analyzed respectively.

10. A molten pool grain solidification analysis device based on continuous growth limiting factor, characterized in that: The device includes an establishment module, a determination module and a calculation module; Wherein, the establishing module is used to establish a first relationship between the continuous growth limiting factor and the model for predicting the continuous growth rate of grains, and the first relationship is an inverse relationship; The determining module is used to determine a second relationship between the model for predicting the continuous growth rate of grains and the solidification path according to the first relationship, and as the solidification path increases, a growth curve corresponding to the second relationship increases exponentially; The determination module is further used to determine a demarcation point according to the correlation between the solute concentration, the welding speed and the solidification path, the demarcation point being a point corresponding to the maximum growth rate in the growth curve; The calculation module is used to calculate the curvature radius of each point on the growth curve; The determination module is also used to determine the boundary point between planar growth and cellular growth according to the calculated radius of curvature.

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