Method and system for analyzing crystallographic behavior of tc4 titanium alloy during deformation process

Abstract

The application discloses a kind of TC4 titanium alloy deformation process crystallography behavior analysis method and system, belong to the field of computational materials science.The method is by analyzing the EBSD data collected in the deformation process of TC4 titanium alloy sample, extract the phase component and Euler angle of each pixel point from it;Again, spatial position analysis and crystallography connection judgment are carried out to all pixel points, extract all phase component same adjacent pixel point pair and then calculate the probability connection weight and record in adjacency matrix;Markov clustering is carried out based on adjacency matrix, then grain and grain boundary are identified;Finally, the slip trace direction of visual object under target slip system and schmidt factor are calculated, and visual output is carried out.The application can effectively distinguish the grains with similar orientation in texture region, and can also analyze and give all possible slip trace directions of selected grain under complex stress state and corresponding schmidt factor, so as to identify the slip system started in the deformation process.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of computational materials science, and particularly relates to a method and system for analyzing crystallographic behavior of TC4 titanium alloy in a deformation process. BACKGROUND

[0002] TC4 titanium alloy (Ti-6Al-4V) is widely used in aerospace, biomedical and high-end chemical industries due to its high specific strength, excellent corrosion resistance and good biocompatibility. In the plastic deformation of the alloy, dislocation slip is the main mechanism, which has a key influence on the mechanical properties such as strength, fatigue behavior and fracture toughness. Different slip systems will form slip traces in different directions on the sample surface, which can be characterized by scanning electron microscopy, thereby providing important basis for revealing the dislocation motion and microstructure evolution of the material in the plastic deformation process.

[0003] However, the existing analysis tools cannot automatically identify the specific slip system corresponding to the slip trace, and in the calculation of the Schmidt factor, they can only handle simple stress states such as uniaxial tension or compression, and are difficult to cope with complex stress conditions, thereby restricting the in-depth understanding of the deformation mechanism of TC4 titanium alloy under complex load. With OIM Analysis, AztecCrystal and other EBSD data analysis software, the software can automatically implement division when performing grain recognition and division, but it uses a hard threshold and cannot be modified, and the grain division may not be sufficient in the texture area; when analyzing the slip trace, it cannot automatically calculate the slip trace direction, and can only manually calculate one by one through the pole figure, which is low in efficiency; when calculating the Schmidt factor under complex stress, OIM Analysis can calculate the Schmidt factor under complex stress, while AztecCrystal can only calculate the Schmidt factor under uniaxial tension / compression, and only outputs the maximum value in the same slip system, and cannot obtain the Schmidt factor of the specific slip plane and slip direction.

[0004] As can be seen, the existing EBSD data analysis software cannot adjust the grain division result, and the grain division may not be sufficient in the texture area where the orientations are close; and the existing analysis method can only obtain the crystallographic information of a single pixel or a single grain, greatly reducing the data analysis efficiency; secondly, it cannot calculate the direction of the slip trace generated on the sample surface by dislocation slip; at the same time, its Schmidt factor calculation function is limited to simple stress states such as uniaxial tension or compression, and is difficult to adapt to the analysis requirements under complex stress conditions, and thus cannot determine the activation of the slip system under complex stress conditions. SUMMARY

[0005] The present application aims to solve the problems existing in the prior art, and provides a TC4 titanium alloy deformation process crystallographic behavior analysis method and system. The present application aims to identify the slip trace direction of all slip systems of a specific grain under a complex stress state and calculate the corresponding Schmidt factor, and further provides a Schmidt factor distribution diagram of a specific slip system of a sample as a whole.

[0006] The specific technical solutions adopted by the present application are as follows:

[0007] In a first aspect, the present application provides a TC4 titanium alloy deformation process crystallographic behavior analysis method, which comprises:

[0008] S1, analyzing the EBSD data collected in the deformation process of the TC4 titanium alloy sample, and extracting the phase composition and Euler angle of each pixel point therefrom;

[0009] S2, performing spatial position analysis and crystallographic connection judgment on all pixel points, extracting all adjacent pixel point pairs with the same phase composition and adding them to a potential connection pair set; for each adjacent pixel point pair in the potential connection pair set, calculating the orientation difference based on the Euler angles of the two pixel points, inputting the ratio of the orientation difference to a threshold value into an exponential decay function to obtain a probabilistic connection weight, and recording it in an adjacency matrix; based on the adjacency matrix, performing Markov clustering to obtain the transition probability matrix after iterative convergence as a connection weight matrix, regarding each connected component in the connection weight matrix as an independent grain, marking the pixel points contained in each grain in the pixel space to form a grain map; and marking all pixel point pairs corresponding to zero elements in the connection weight matrix as grain boundaries;

[0010] S3, taking a target grain and / or a target pixel point in the grain map as a visual object, converting the slip direction vector and the slip plane normal vector of a target slip system to the sample coordinate system, then calculating the slip trace direction and the Schmidt factor of the visual object under the target slip system, and performing visual output.

[0011] As a preferred embodiment of the first aspect, the EBSD data is collected by loading an external load on the TC4 titanium alloy sample to perform a deformation experiment, and then using the backscattered electron diffraction technology (EBSD) to obtain grain orientation information to obtain an EBSD data file.

[0012] As a preferred embodiment of the first aspect, in S2, the method for performing spatial position analysis and crystallographic connection judgment on all pixel points to obtain the potential connection pair set is as follows: for all pixel points in the pixel space of the EBSD data, extracting all pixel point pairs belonging to von Neumann neighbors, combining the phase composition information of each pixel point obtained by analysis, retaining the pixel point pairs belonging to von Neumann neighbors and having the same phase composition, and constructing them into a potential connection pair set.

[0013] As a preferred embodiment of the first aspect, the exponential decay function is an exponential function with natural base e, and the power of the exponential function is the negative of the square of the ratio of the misorientation and a threshold value.

[0014] As a preferred embodiment of the first aspect, in the adjacency matrix, the element value in the i-th row and the j-th column corresponds to the probabilistic connection weight of the pixel pair formed by the i-th pixel point and the j-th pixel point in the pixel space of the EBSD data, and if the pixel pair is not located in the set of potential connection pairs, the element value is directly set to zero.

[0015] As a preferred embodiment of the first aspect, the grain boundaries are further classified into sub-grain boundaries and real grain boundaries according to the grain division results, if the pixel pair corresponding to the grain boundary belongs to the same grain, the grain boundary is classified as a sub-grain boundary, otherwise, the grain boundary is classified as a real grain boundary.

[0016] As a preferred embodiment of the first aspect, in S3, the specific method for calculating the slip trace direction of the visualization object under the target slip system and the Schmidt factor is as follows:

[0017] Firstly, the slip direction vector and the slip plane normal vector of the TC4 titanium alloy sample under the target slip system are converted from the crystal coordinate system to the Cartesian coordinate system, and then a rotation matrix is constructed according to the Euler angles of the visualization object and is further converted to the sample coordinate system;

[0018] Then, the converted slip plane normal vector is multiplied by the matrix with the surface normal direction of the TC4 titanium alloy sample to obtain the slip trace direction of the visualization object under the target slip system;

[0019] Then, the converted slip direction vector and the slip plane normal vector are used to calculate the Schmidt tensor of the target slip system, and the external load applied during the deformation process of the TC4 titanium alloy sample is read in the form of a second-order tensor, and the Schmidt tensor and the external load tensor are subjected to double dot product operation;

[0020] Finally, the operation result is divided by the Mises stress equivalent to the external load tensor to obtain the Schmidt factor of the visualization object under the target slip system.

[0021] As a preferred embodiment of the first aspect, the Schmidt factor of the visualization object under the target slip system is further divided by a correction factor for critical shear stress correction, and the visualization is performed based on the corrected Schmidt factor; the correction factor is the ratio of the critical shear stress of the target slip system to the cylindrical The critical ratio of the shear stress of the slip system.

[0022] As the preferred embodiment of the first aspect, in the S3, the visualization object is a single target grain specified by the user for analysis, the target slip system covers all the optional slip systems, and the visualization output result is the morphology of the target grain and the slip trace direction and Schmid factor of each corresponding slip system in the target grain.

[0023] Alternatively, the visualization object is all the pixel points, the target slip system is a single slip system specified by the user, and the visualization output result is a Schmid factor distribution map of all the pixel points under the target slip system.

[0024] In a second aspect, the present application provides a system for analyzing the crystallographic behavior of a TC4 titanium alloy during deformation, comprising:

[0025] A data input module for inputting EBSD data collected during deformation of a TC4 titanium alloy sample;

[0026] A behavior analysis module for outputting the slip trace direction and Schmid factor of the visualization object under the target slip system according to the TC4 titanium alloy deformation process crystallographic behavior analysis method of any one of the first aspect.

[0027] Compared with the prior art, the present application has the following beneficial effects:

[0028] The present application realizes rapid and accurate grain identification of complex microstructure samples, effectively distinguishes grains with similar orientations in the texture region, and can analyze and give all possible slip trace directions and corresponding Schmid factors of selected grains under complex stress states, thereby identifying the slip system activated during deformation. The present application is beneficial for analyzing the dislocation slip process and deformation mechanism of TC4 titanium alloy under complex stress states after deformation, and has the advantages of rapid and accurate statistics, wide application, convenient use, etc. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 The steps of the method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation are shown in the schematic diagram;

[0030] Figure 2A schematic diagram of a module composition of a TC4 titanium alloy deformation process crystallographic behavior analysis system;

[0031] Figure 3 A pole figure of a TC4 titanium alloy sample after deformation;

[0032] Figure 4 A schematic diagram of a slip trace;

[0033] Figure 5 A slip trace and a Schmid factor diagram of a grain (429);

[0034] Figure 6 A Schmid factor cloud diagram of a <11-20> {01-10} slip system in x and y direction compression. DETAILED DESCRIPTION

[0035] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application are described in detail below with reference to the drawings. In the following description, a large number of specific details are set forth in order to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the spirit of the present application, so the present application is not limited to the specific embodiments disclosed below. The technical features in each embodiment of the present application can be combined accordingly without conflict.

[0036] In the description of the present application, it should be understood that when an element is considered to be "connected" to another element, it can be directly connected to the other element or indirectly connected to the other element with an intermediate element. In contrast, when an element is referred to as being "directly" connected to another element, there is no intermediate element.

[0037] In the description of the present application, it should be understood that the terms "first", "second" are only used for distinguishing purposes of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one of the features.

[0038] The present application provides a TC4 titanium alloy deformation process crystallographic behavior analysis method, which can be used to analyze all slip systems of grains in a TC4 titanium alloy sample after deformation under a complex stress state, the intersection direction of the sample surface, i.e. the slip trace direction, and the corresponding Schmid factor, and can give a Schmid factor cloud diagram of the sample as a whole under a complex stress state, thereby realizing efficient identification of activated slip systems in the deformation process.

[0039] As Figure 1As shown, in a preferred embodiment of the present application, the method for analyzing the crystallographic behavior of the TC4 titanium alloy during deformation includes steps S1-S3. The specific implementation of each step is described below.

[0040] S1, analyze the EBSD data collected during the deformation of the TC4 titanium alloy sample, and extract the phase composition and Euler angles of each pixel point therefrom.

[0041] It should be noted that the EBSD data is obtained by backscattered electron diffraction technology (EBSD), and the specific data format is determined by the export format of the actual EBSD data analysis software. In theory, as long as the EBSD data contains the phase composition and Euler angles of all EBSD pixel points of the TC4 titanium alloy sample. Since the present application needs to analyze the crystallographic behavior of the TC4 titanium alloy during deformation, the collection method of the EBSD data is as follows: perform a deformation experiment on the TC4 titanium alloy sample by loading an external load, then use backscattered electron diffraction technology (EBSD) to obtain grain orientation information, and obtain an EBSD data file. In the embodiments of the present application, the format of the EBSD data file is preferably.cpr file format. This file format records the complete context of obtaining EBSD data from the original deformed sample. It not only contains the original EBSD scan data, but also integrates various settings and results during data processing and analysis.

[0042] It should be noted that the.cpr file of the EBSD data records various information of each pixel in the form of an EBSD array, including pixel coordinates / phase composition and Euler angles, etc. When analyzing the.cpr file of the EBSD data, the phase composition and reference coordinate system need to be determined. Since the TC4 titanium alloy is a duplex titanium alloy, the phase composition is selected as "Titanium cubic" and "Ti-Hex", which respectively represent the alpha phase and the beta phase. The reference coordinate system is ensured to be consistent with the image coordinate system of the EBSD shooting, which facilitates comparative analysis of the results.

[0043] S2, analyze the spatial position and crystallographic connection of all pixel points, extract all adjacent pixel point pairs with the same phase composition and add them to the potential connection pair set; for each adjacent pixel point pair (which can be referred to as a potential connection pair) in the potential connection pair set, calculate the orientation difference based on the Euler angles of the two pixel points, input the ratio of the orientation difference to the threshold value into the exponential decay function, obtain the probabilistic connection weight, and record it in the adjacency matrix ; based on the adjacency matrix , perform Markov clustering to obtain the transition probability matrix after iterative convergence as the connection weight matrix ; and Each connected component in the graph is treated as an independent grain, and the pixels contained in each grain are marked in the pixel space to form a grain map; at the same time, the connection weight matrix is... All pixel pairs corresponding to zero elements are marked as grain boundaries.

[0044] In an embodiment of the present invention, the method for performing spatial location analysis and crystallographic connectivity determination on all pixels to obtain a set of potential connectivity pairs is as follows: for all pixels in the pixel space of the EBSD data, extract all pixel pairs belonging to von Neumann neighbors, and then combine the phase composition information of each pixel obtained by analysis to retain pixel pairs belonging to von Neumann neighbors and having the same phase composition, thus constructing a set of potential connectivity pairs.

[0045] It should be noted that determining whether a pixel belongs to a von Neumann neighbor can be based on the spatial relationship between pixels in the pixel space, which is existing technology and will not be elaborated further. To improve computational efficiency, an adjacency matrix can be constructed to record whether each pair of pixels belongs to a von Neumann neighbor. Specifically, assuming the number of pixels in the pixel space of the EBSD data is... Then a adjacency matrix If the i-th pixel and the j-th pixel are von Neumann neighbors, then the adjacency matrix will be... median coordinate The element value at position is updated to If the i-th pixel and the j-th pixel are not von Neumann neighbors, then the adjacency matrix will be... median coordinate The element value at position is updated to Therefore, by iterating through all pairs of pixels, the complete adjacency matrix can be obtained. The adjacency matrix Since it is a symmetric matrix, only the upper triangular portion is needed to obtain the binary classification information of whether all pixels belong to von Neumann neighbors. For all pairs of pixels belonging to von Neumann neighbors, this can be achieved using two pairs of pixels of length... array and To record the index of each pair of pixels, specifically, if the indices of the i-th pair of pixels belonging to von Neumann neighbors are respectively and Then Recorded in array The i-th position will Recorded in array The i-th position. Therefore, subsequent operations only need to be performed on the array. and By sequentially reading the array elements at the same position, a pair of pixels belonging to von Neumann neighbors can be determined.

[0046] Furthermore, the potential connectivity pair set is initially empty. Pixel pairs added to the potential connectivity pair set, besides being determined through spatial location analysis to satisfy the condition of belonging to von Neumann neighbors, should also undergo crystallographic connectivity checks to ensure that the pixel pairs have the same phase composition. If the array... and If two pixels in a pair of pixels belonging to von Neumann neighbors recorded in the dataset have different phase components, they need to be removed from the potential connection pair set. It should be noted that in actual implementation, the potential connection pair set can also be implemented using an array, for example, directly based on an array... and Delete pixel pairs that differ in phase group; the remaining pixel pairs can be considered as the set of potential connection pairs. Of course, the set of potential connection pairs can also be recorded in other forms besides arrays; there is no limitation on this.

[0047] For any i-th pair of pixels in the set of potential connected pairs, they satisfy the conditions of being von Neumann neighbors and having the same phase composition. Therefore, the orientation difference between the two EBSD pixels can be calculated based on the Euler angles between them. Based on this orientation difference A soft threshold can be used to calculate probabilistic connection weights. This exponential decay function uses an exponential function with the natural base e, and the power of the exponent is the difference. Threshold of orientation difference with softness The negative square of the ratio is expressed by the formula:

[0048]

[0049] In the formula: It is an adjacency matrix used to store the probabilistic connection weights of pixel pairs in the set of potential connection pairs. The matrix size is O(n). It should be noted that the actual calculation of this formula involves converting the array... and Orientation difference of all pixel pairs recorded in The input is batched as an array, and the probabilistic connection weights are output in batches. However, in practice, the probabilistic connection weights can also be calculated serially for each pair of pixels in the potential connection pair set; the principle is the same, only the computational efficiency is lower. For example, for a pixel pair consisting of the i-th pixel and the j-th pixel in the potential connection pair set, the orientation difference of this pixel pair can be calculated. After that, the probability connection weight in scalar form is obtained by exponential conversion according to the above exponential decay function formula, and recorded in the adjacency matrix . Position.

[0050] It should be noted that the matrix size of the adjacency matrix is , so some matrix elements in the adjacency matrix correspond to pixel pairs that are not actually in the set of potential connection pairs. Therefore, if the i-th pixel and the j-th pixel in the pixel space of the EBSD data form a pixel pair in the set of potential connection pairs, the probability connection weight of the pixel pair is calculated according to the above exponential decay function and recorded in the element value of the i-th row and the j-th column in the adjacency matrix . In the above, if the pixel pair is not in the set of potential connection pairs, the element value is directly set to zero.

[0051] In addition, after obtaining the adjacency matrix , Markov clustering can be performed. Markov clustering (MCL) algorithm is a graph-based clustering algorithm for dividing nodes in a graph into different clusters. The algorithm mainly uses the idea of random walk to enhance the connection within the cluster and weaken the connection between the clusters, so as to achieve the purpose of clustering. The input of the MCL algorithm is a graph (represented in the form of an adjacency matrix), and the adjacency matrix is normalized by column to become an initial transition probability matrix. The core of the algorithm is to perform expansion and inflation operations by iteration until the transition probability matrix reaches a stable state. Then, the clustering result is interpreted from the stable transition probability matrix. The specific process of the MCL algorithm is a prior art and will not be described here.

[0052] In addition, considering the calculation efficiency, before performing Markov clustering, the element values in the adjacency matrix that are less than a preset weight threshold can be set to zero, and it is verified whether the adjacency matrix after zero setting is a symmetric matrix and the element values on the diagonal are all 1. After passing the verification, it is input as the adjacency matrix for Markov clustering.

[0053] In the present application, the transition probability matrix obtained after the MCL iteration converges is used as the connection weight matrix , and the connection weight matrix In essence, it corresponds to the figure, so as to find the connected components in the figure, each connected component corresponds to an independent grain. In the pixel space of EBSD, mark the pixels contained in each grain, and form a grain map. In visualization, different grains in the grain map can be given index labels and rendered in different colors. In addition, in addition to grain recognition, the connection weight matrix The grain boundaries are identified. Specifically, the connection weight matrix The pixel pairs corresponding to the non-zero elements in the connection weight matrix are regarded as connections within the same grain, and all pixel pairs corresponding to zero elements are marked as grain boundaries.

[0054] In addition, in the embodiments of the present application, the grain boundaries can be further classified into sub-grain boundaries and real grain boundaries according to the grain division results, and the specific classification rule is: if the pixel pair corresponding to the grain boundary belongs to the same grain, the grain boundary is classified as a sub-grain boundary, otherwise the grain boundary is classified as a real grain boundary.

[0055] After all the grains and grain boundaries are identified, the slip trace direction and Schmid factor calculation and visualization output operation of step S3 are performed according to the analysis purpose or visualization output setting.

[0056] S3, taking the target grain and / or target pixel in the above grain map as the visualization object, converting the slip direction vector and slip plane normal vector of the target slip system to the sample coordinate system, then calculating the slip trace direction and Schmid factor of the visualization object under the target slip system, and performing visualization output.

[0057] In the embodiments of the present application, the specific method for calculating the slip trace direction and Schmid factor of the visualization object under the target slip system is:

[0058] First, after converting the slip direction vector and slip plane normal vector of the TC4 titanium alloy sample under the target slip system from the crystal coordinate system to the Cartesian coordinate system, a rotation matrix is constructed with the Euler angles of the visualization object and further converted to the sample coordinate system;

[0059] Then, the converted slip plane normal vector is multiplied by the matrix with the surface normal direction of the TC4 titanium alloy sample to obtain the slip trace direction of the visualization object under the target slip system;

[0060] Then, the converted slip direction vector and slip plane normal vector are used to calculate the Schmid tensor of the target slip system, and the second-order tensor form is read into the external load applied to the TC4 titanium alloy sample during deformation, and the Schmid tensor and the external load tensor are subjected to double dot product operation;

[0061] Finally, the double dot product operation result is divided by the Mises stress equivalent to the external load tensor to obtain the Schmid factor of the visualization object under the target slip system.

[0062] It should be noted that, considering that the forces required for the activation of each slip system of the TC4 titanium alloy are different in the actual deformation process, that is, the critical shear stress is different, so in the actual deformation process, the slip system with the maximum Schmid factor will not be activated first, and the influence of the critical shear stress needs to be considered. Therefore, in the embodiment of the present application, after the Schmid factor of the visualization object under the target slip system is calculated, a correction factor can be further divided to correct the critical shear stress, and the Schmid factor after correction is used for visualization; wherein the above-mentioned correction factor is the critical shear stress of the target slip system and the cylindrical Critical ratio of shear stress for slip systems. In TC4 titanium alloy, due to the influence of crystal structure, the ratio of shear stress for basal The critical resolved shear stress is the minimum, so its value is selected as the reference value for calculating the correction factor.

[0063] In addition, it should be noted that in performing specific crystallographic behavior analysis and visualized output, the present application can be provided with a plurality of different analysis and output modes.

[0064] The first mode is a grain analysis mode for a single grain, which can analyze all possible slip trace directions of the selected grain and the corresponding Schmidt factors, so as to identify the activated slip system in the deformation process. In this mode, the visualized object is a single target grain specified by the user, and the target slip system covers all selectable slip systems (including basal planes slip, basal slip, pyramidal The visualization output result is the morphology of the target grain and the slip trace direction and Schmid factor of each slip system in the target grain.

[0065] The second mode is a sample overall analysis mode, and a Schmid factor distribution diagram of a specified target slip system in the global range of the sample can be generated. In this mode, the visualization object is all pixel points, the target slip system is a single slip system specified by the user, and the visualization output result is a Schmid factor distribution diagram of all pixel points under the target slip system.

[0066] It should be noted that the method steps shown in S1-S3 can be essentially realized in the form of a computer program or a software functional module.

[0067] In addition, based on the same inventive concept, another embodiment of the present application also provides a TC4 titanium alloy deformation process crystallographic behavior analysis system, as shown in Figure 2 As shown in the figure, the system comprises:

[0068] A data input module for inputting the EBSD data collected in the deformation process of the TC4 titanium alloy sample;

[0069] A behavior analysis module for outputting the slip trace direction and Schmid factor of the visualization object under the target slip system according to the TC4 titanium alloy deformation process crystallographic behavior analysis method shown as S1-S3.

[0070] It should be noted that the above-mentioned data input module and behavior analysis module are software function modules realized by computer programs, and both can be interacted with the user through the GUI interface form, and of course, data input and result output can also be performed through the instruction form.

[0071] Since the TC4 titanium alloy deformation process crystallographic behavior analysis method shown as S1-S3 and the TC4 titanium alloy deformation process crystallographic behavior analysis system composed of modules can be essentially executed by a computer program, the method and the system can be run on a computer electronic device. The computer electronic device comprises a memory and a processor;

[0072] The memory is used to store a computer program;

[0073] The processor is used to execute the computer program to realize the TC4 titanium alloy deformation process crystallographic behavior analysis method as described above, or to realize the TC4 titanium alloy deformation process crystallographic behavior analysis system as described above.

[0074] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of a software function unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application.

[0075] In addition, based on the same inventive concept, the present application provides a computer readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the method for analyzing crystallographic behavior of TC4 titanium alloy in a deformation process or the system for analyzing crystallographic behavior of TC4 titanium alloy in a deformation process as described above can be implemented.

[0076] In addition, based on the same inventive concept, the present application provides a computer program product, comprising computer programs / instructions, which, when executed by a processor, can implement the method for analyzing crystallographic behavior of TC4 titanium alloy in a deformation process or the system for analyzing crystallographic behavior of TC4 titanium alloy in a deformation process as described above.

[0077] It can be understood that the above-mentioned storage medium / memory can include a random access memory (RAM) and can also include a non-volatile memory (NVM), for example, at least one disk memory. Meanwhile, the storage medium can also be a U disk, a mobile hard disk, a magnetic disk or an optical disk, and various media that can store program codes.

[0078] It can be understood that the above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0079] It should be noted that the skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system described above can refer to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the embodiments provided in the present application, the division of steps or modules in the system and method described above is only a logical functional division, and there can be another division mode in actual implementation, for example, a plurality of modules or steps can be combined or integrated together, or a module or step can be split.

[0080] The present application will be further illustrated by a specific embodiment below to show the detailed implementation process and technical effects of the analysis method of the crystallographic behavior of the TC4 titanium alloy deformation process shown in the steps S1-S3 on specific data, so as to understand the essence of the present application.

[0081] Embodiment

[0082] In the embodiment, the implementation process of the analysis method of the crystallographic behavior of the TC4 titanium alloy deformation process is shown in the steps S1-S3 above, and the specific process and results of each step will be further shown below on the basis thereof. Part of the explanation and definition in each step can refer to the steps S1-S3 above, and will not be repeated here.

[0083] Firstly, the TC4 titanium alloy sample is pre-deformed by external load, and then the grain orientation information is obtained by using the backscattered electron diffraction technology (EBSD), and the EBSD data output is.cpr file.

[0084] Secondly, the.cpr file is read, the read phase composition and reference coordinate system are determined, the external load is read , and the critical shear stress value of each slip system is read.

[0085] In the embodiment, the.cpr file read in the form of ebsd array stores phase composition information of each pixel point, pixel coordinates and Euler angle information , corresponding to in the standard Euler angle expression form , the phase composition information is divided into three kinds:

[0086]

[0087] Among them is the unanalyzed pixel point due to too large scanning step or the existence of non "Ti-Hex" and "Titanium cubic" phases in the sample.

[0088] Since the TC4 titanium alloy is a dual-phase titanium alloy, the phase composition is selected to represent Phase "Titanium cubic" and represents Phase "Ti-Hex"; read in.cpr file when the coordinate system needs to be consistent with the image coordinate system of EBSD shooting, easy to compare and analyze the results.

[0089] In addition, in order to facilitate the calculation of subsequent other steps, the second step also needs to read in external load , the external load is read in the form of second order tensor:

[0090]

[0091] Where , respectively , the normal stress in three directions, and the rest are the shear stress in the corresponding direction of the two subscripts, and the subscripts 1, 2 and 3 correspond to the direction of stress.

[0092] At the same time, the critical shear stress value of the slip system corresponding to the TC4 titanium alloy sample needs to be read in , wherein , , , , are the critical shear stress of basal slip, cylindrical slip, pyramidal slip, pyramidal I slip, pyramidal II slip, respectively. The critical shear stress value of each slip system belongs to the inherent property of the TC4 titanium alloy sample.

[0093] Step 3, according to the pixel point orientation information, divide the grains and label, establish the image containing the sample orientation information and divide different grains.

[0094] The Markov clustering method (Markov Clustering Algorithm, MCL) used in this embodiment is a graph-based clustering algorithm, which simulates random walk and expansion and contraction of flow, and divides the grains according to the Euler angle information of the pixel points. The specific grain and grain boundary recognition generation process includes the following substeps 1~substep 4:

[0095] Substep 1: spatial decomposition and basic adjacency relationship extraction

[0096] According to the read EBSD pixel point information, construct the basic adjacency matrix , which represents different EBSD pixel points, and the matrix size is , EBSD pixel number. Corresponding to the adjacency relationship between the i-th pixel point and the j-th pixel point. Since the EBSD data is acquired in the form of square pixel points during the acquisition process, all pixel points need to be traversed, and if the i-th pixel point and the j-th pixel point are von Neumann neighbors, then , otherwise the value is 0; then the upper triangular part of the base adjacency matrix is extracted to obtain the index list of all adjacent pixel point pairs, which are respectively stored in and Two arrays contain all potential connection pairs that need to be further evaluated.

[0097] Substep 2: Crystallographic connection judgment

[0098] Traverse all potential connection pairs recorded in and Based on the condition that the connection pair components are the same, that is , according to the ratio of the orientation difference of the connection pair to the orientation difference threshold, a probabilistic connection weight is given to the adjacent pair, and its expression is:

[0099]

[0100] Where is the adjacency matrix for storing the connection weight of the potential connection pair , the matrix size is , is the orientation difference of the potential connection pair, which is calculated from the Euler angle information of the two EBSD pixel points; is the pre-set orientation difference threshold. Based on the probabilistic connection model, when the orientation difference is close to 0, it almost belongs to the same grain, and at this time the weight ≈ 1; when the orientation difference is much larger than the threshold, it basically does not belong to the same grain, and at this time the weight ≈ 0; and when the orientation difference is near the threshold, the connection weight will be smoothly transitioned from 1 to 0 based on an exponential decay function. This soft threshold has obvious advantages for materials with texture regions after plastic deformation, and better reflects the gradual process of grain boundary formation in real materials, especially in the region of sub-grain boundaries to high-angle grain boundaries, which is in line with the physical reality.

[0101] Substep 3: Markov clustering

[0102] The Markov clustering process is performed as follows:

[0103] First, based on the adjacency matrix obtained in substep 2, three-step initialization is performed: 1. Remove edges with a weight lower than , if then , i.e. edges with too low connection weights are considered disconnected to improve computational efficiency and stability; 2. Ensure that the adjacency matrix is symmetric, i.e. Di and Dr are connected to each other, ensuring that the graph is undirected; 3. Ensure that the diagonal of the adjacency matrix is of value 1, ensuring self-connections (self-connections of the same pixel are considered to be in the same grain), allowing to stay at the current pixel in the random walk.

[0104] Secondly, the adjacency matrix is column-normalized to become the initial transition probability matrix, which enters the core iteration process. In each iteration, the following operations are sequentially performed:

[0105] 1. Extend the transition probability matrix This process simulates the multi-step transition of the random walk, allowing the connection between pixels to propagate to further neighbors, and allowing closely connected regions to emerge;

[0106] 2. Inflate the transition probability matrix , where p is the set inflation parameter, usually taking 1.5-3.0, which can be adjusted according to the grain division effect. This inflation process increases the weight of strong connections and reduces the weight of weak connections, thereby sharpening the boundaries of the grains. The value of parameter p is very critical, which can be adjusted by modifying the function call. The larger the value of p, the more the resulting grains tend to be smaller and more numerous; the smaller the value of p, the larger the grains and the fewer the number of grains.

[0107] 3. Remove the transition probability matrix with a weight lower than the preset threshold minval, and normalize the connection weight matrix to divide the value of each column by its column sum, ensuring that the sum of each column is 1, maintaining the randomness of the matrix. Through the above operations, the sum of each column of the connection weight matrix is ensured to be 1, making it a random matrix and maintaining the probability interpretation.

[0108] Each round of iteration needs to judge whether the convergence condition is met, and the iteration will continue until one of the following two conditions is met:

[0109] Termination condition 1: residual energy is less than the set maximum value , The calculation involves the row vector composed of the maximum values of the matrix columns, and the row vector composed of the sum of the squares of all column elements of the matrix, , which measures the stability of the matrix;

[0110] ​Termination condition 2: Reaching the maximum number of iterations .

[0111] After the above sub-steps converge, the transition probability matrix that has converged through clustering can be obtained. This transition probability matrix is ​​then used as the connection weight matrix. .

[0112] Sub-step 4: Grain boundary formation

[0113] Based on the connection weight matrix obtained after clustering Find the connected components in the graph, each connected component corresponds to an independent grain, and store the partitioning results in a two-dimensional array of connected components. , representing a pixel Belongs to the Each grain. In this embodiment, the inverse pole figure of the TC4 titanium alloy sample after deformation is as follows. Figure 3 As shown, a series of grains are divided into them, with different colors representing different crystal orientations, black solid lines representing grain boundaries, and numbers inside the grains representing grain numbers.

[0114] The size of the reconstructed matrix is Blocking connection matrix ,Will In the case of non-zero elements, the corresponding pixel pairs are considered as connections within the same grain, and in Middle Mark for ,and The pixel pairs corresponding to zero elements are considered as grain boundaries, and in Middle Mark for The grain boundaries defined at this point are divided into two types: subgrain boundaries and true grain boundaries. The classification principle is: if the pixel pair corresponding to the grain boundary belongs to the same grain, then the grain boundary is classified as a subgrain boundary; otherwise, the grain boundary is classified as a true grain boundary. Subgrain boundaries are boundaries formed within the same grain due to orientation differences, and are defined in the blocking connectivity matrix. This is reflected in the fact that adjacent pixel pairs are not connected, that is However, in the connected component array, adjacent pixel pairs appear to belong to the same grain, i.e. This allows us to identify all the grains and their boundaries.

[0115] The fourth step is to execute the grain analysis mode: Based on the image generated in the third step, select and extract the target grains to be analyzed, calculate the intersection directions of all slip systems with the sample surface and their corresponding Schmidt factors, and visualize the morphology of the target grains as well as the slip trace directions and Schmidt factors of each slip system in the target grains.

[0116] In this step, it is necessary to denote a two-dimensional array of connected components based on the grain diagram divided in step three. Select the grain to be analyzed, draw the grain morphology (i.e., grain boundary contour), and calculate the arithmetic mean of the orientations of all pixels in the grain as the grain orientation, i.e.:

[0117]

[0118] in The orientation of the i-th pixel within this grain. This represents the total number of EBSD pixels contained within the die.

[0119] In addition, to calculate the direction of the intersection line between the slip system and the sample surface (i.e., the slip trace direction) and the Schmidt factor, it is also necessary to obtain the slip surface normal vector and the slip direction vector of the TC4 titanium alloy sample. These two direction vectors are inherent property parameters of the TC4 titanium alloy sample. However, the slip surface and slip direction are usually represented using a crystal coordinate system, such as in the TC4 titanium alloy. A basal slip system of a phase The four-index representation is used in the crystal coordinate system, but the slip path direction and Schmidt factor are expressed in the sample coordinate system (Cartesian coordinate system). Therefore, a coordinate transformation is required for the slip surface and slip direction vector. The conversion from the four-index representation (hkil) in the crystal coordinate system to the three-coordinate representation (xyz) in the Cartesian coordinate system is existing technology, and its general formula can be expressed as:

[0120] For slip surfaces:

[0121]

[0122] Regarding the direction of slip:

[0123]

[0124] in, and These are the lattice constants in the basal plane and perpendicular to the basal plane, respectively. , , These are the coordinates in the four-exponential notation. .

[0125] Cartesian coordinates after this transformation For unnormalized dimensionless coordinates; then, through the rotation matrix... Transform this coordinate system from the crystal coordinate system to the sample coordinate system. Without loss of generality, the slip surface normal vector and slip direction vector of any slip system in Cartesian coordinates are assumed to be... The general formula is shown, and the rotation matrix The formula for converting to the sample coordinate system is:

[0126]

[0127] where the rotation matrix R is obtained from the orientation of the current grain

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138] So far, the conversion from the four-index notation coordinates (hkiI) in the crystal coordinate system to the three-coordinate notation (xyz) in the Cartesian coordinate system and further to the sample coordinate system has been completed.

[0139] In this embodiment, this step constructs five structures for storing the normal direction vectors and slip direction vectors of the slip planes of the five types of slip systems after coordinate transformation: , respectively represent the basal slip, prismatic slip, pyramidal slip, pyramidal I slip, and pyramidal II slip. Take the basal slip as an example, which contains and represent the normal direction vector and the slip direction vector of the slip plane, respectively.

[0140] Next, the calculation of the slip trace direction can be performed, and a schematic diagram of the slip trace is shown in Figure 4The formation principle of metal surface slip traces is shown in (a), and the slip traces on the surface of the deformed metal sample observed by scanning electron microscopy are shown in (b), and the yellow dashed line in the figure represents the slip traces in different grains. Slip traces are small steps or traces formed on the surface due to the movement of dislocations along a specific slip plane and slip direction to the sample surface, in the direction of the intersection line between the slip plane and the sample surface, i.e.:

[0141]

[0142] wherein represents the slip plane normal direction vector of a single slip system in the sample coordinate system, is the slip trace direction of the slip system, is the normal direction of the sample surface, and . is the general expression of the five slip systems.

[0143] All five slip systems are traversed, and the slip trace direction of each slip system is calculated and the results are plotted in the previously plotted grain.

[0144] Subsequently, the Schmidt factor of all slip systems is calculated, and in a complex stress state, the Schmidt factor of the corresponding slip system is calculated as follows:

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] wherein is the Schmidt tensor of the corresponding slip system , and and are the slip direction vector and the slip plane normal vector converted to the sample coordinate system, respectively, is the equivalent Mises stress of the stress tensor . Considering that the forces required for each slip system of TC4 titanium alloy to start in the actual deformation process are different, i.e. the critical shear stress is different, the slip system with the largest Schmidt factor will not start first in the actual deformation process, and the influence of the critical shear stress needs to be considered, so this embodiment can be a cylindrical slip For reference, all the critical interlamellar shear stresses of the slip systems are divided by the cylinder radiusCritical shear stress for slip The critical shear stress for slip is 0.2 GPa The critical shear stress of slip is minimum, so its value is chosen as the reference, i.e.:

[0151]

[0152] where, denotes the corresponding slip system with cylindrical The ratio of the critical resolved shear stress.

[0153] Finally, the Schmid factor of each slip system is divided by the critical resolved shear stress of that slip system to obtain the Schmid factor corrected by the critical resolved shear stress.

[0154] The corrected Schmid factor results are plotted on the corresponding slip trace to accurately calculate and plot the slip trace and corresponding Schmid factor in the selected grain. In this example, the grain (429) is used as an example, and its slip trace and Schmid factor diagram is as follows Figure 5 are shown, where different slip modes are distinguished by the color of the slip traces, but note that in this figure due to the picture size limitation only the basal planes slip, basal slip, pyramidal Slip trace direction and Schmid factor of slip.

[0155] Step 5, execute the sample overall analysis mode: re-traverse all pixel points, calculate the Schmid factor results of each pixel point under a specified target slip system in the global range of the sample and generate a distribution cloud map.

[0156] In this step, since the minimum unit of visualization is the pixel point, the process of calculating the Schmid factor is basically the same as that of calculating the Schmid factor of the grain in step 4, the only difference is that the grain orientation needs to be replaced by the pixel point orientation. Specifically, select the slip system to generate the Schmid factor cloud map, traverse all pixel points, refer to the method of step 4, for each pixel point, replace the grain orientation with the pixel point orientation, calculate the Schmid factor of each pixel point, and output in the form of a cloud map. In this embodiment, as shown in Figure 6 are shown, showing the Schmid factor cloud of the <11-20>{01-10} slip system in x and y direction compression.

[0157] In summary, the present application adopts the Markov clustering algorithm based on the probability threshold to divide the grains, the parameters can be adjusted according to the real metallography, and the grain division of the texture area can be ensured to be accurate; meanwhile, the present application can quickly generate all the slip trace directions of all the grains, which is convenient for comparison and analysis with SEM; and the present application can also calculate the Schmid factors of all the slip systems under any stress state.

[0158] The above-mentioned embodiments are only some preferable implementation schemes of the present application, but not intended to limit the present application. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application. Therefore, all the technical schemes obtained by equivalent replacement or equivalent transformation shall fall within the protection scope of the present application.

Claims

1. A method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation, characterized in that, include: S1. Analyze the EBSD data collected during the deformation process of the TC4 titanium alloy sample, and extract the phase composition and Euler angle of each pixel. S2. Perform spatial location analysis and crystallographic connectivity determination on all pixels, extract all adjacent pixel pairs with the same phase composition and add them to the potential connectivity pair set; For each pair of adjacent pixels in the potential connection pair set, the orientation difference is calculated based on the Euler angles of the two pixels, and the ratio of the orientation difference to the threshold is input into the exponential decay function to obtain the probabilistic connection weight, which is then recorded in the adjacency matrix. Markov clustering is performed based on the adjacency matrix. The transition probability matrix obtained after iterative convergence is used as the connection weight matrix. Each connected component in the connection weight matrix is ​​regarded as an independent grain. The pixels contained in each grain are marked in the pixel space to form a grain map. At the same time, all pixel pairs corresponding to zero elements in the connection weight matrix are marked as grain boundaries. S3. Using the target grain and / or target pixel in the grain diagram as the visualization object, transform the slip direction vector and slip surface normal vector of the target slip system to the sample coordinate system, then calculate the slip trace direction and Schmidt factor of the visualization object in the target slip system, and output the visualization.

2. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 1, characterized in that, The EBSD data was acquired by applying an external load to a TC4 titanium alloy sample to perform a deformation experiment, and then using backscattered electron diffraction technology to obtain grain orientation information and obtain an EBSD data file.

3. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 1, characterized in that, In step S2, the method for performing spatial location analysis and crystallographic connectivity judgment on all pixels to obtain a set of potential connectivity pairs is as follows: For all pixels in the pixel space of the EBSD data, extract all pixel pairs that belong to von Neumann neighbors, and then combine the phase composition information of each pixel obtained by analysis to retain pixel pairs that belong to von Neumann neighbors and have the same phase composition, thus constructing a set of potential connectivity pairs.

4. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 1, characterized in that, The exponential decay function is an exponential function with the natural base e as the base, and the power of the exponential function is the negative of the square of the ratio of the orientation difference to the threshold.

5. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 1, characterized in that, In the adjacency matrix, the element value in the i-th row and j-th column corresponds to the probabilistic connection weight of the pixel pair formed by the i-th pixel and the j-th pixel in the pixel space of the EBSD data, and if the pixel pair is not located in the set of potential connection pairs, the element value is directly set to zero.

6. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 1, characterized in that, The grain boundaries need to be further classified into subgrain boundaries and real grain boundaries based on the grain division results. If the pixel pair corresponding to the grain boundary belongs to the same grain, the grain boundary is classified as a subgrain boundary; otherwise, the grain boundary is classified as a real grain boundary.

7. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 1, characterized in that, In step S3, the specific method for calculating the slip trajectory direction and Schmidt factor of the visualized object in the target slip system is as follows: First, the slip direction vector and slip surface normal vector of the TC4 titanium alloy sample in the target slip system are transformed from the crystal coordinate system to the Cartesian coordinate system. Then, a rotation matrix is ​​constructed using the Euler angles of the visualized object and further transformed to the sample coordinate system. Then, the transformed slip surface normal vector is multiplied by the normal direction of the TC4 titanium alloy sample surface to obtain the slip trace direction of the visualized object in the target slip system. Next, the Schmidt tensor of the target slip system is calculated from the transformed slip direction vector and slip surface normal vector. The external load applied during the deformation process of the TC4 titanium alloy sample is read in as a second-order tensor. The Schmidt tensor and the external load tensor are then double-dot producted. Finally, the calculation result is divided by the Mises stress, which is equivalent to the external load tensor, to obtain the Schmidt factor of the visualized object in the target slip system.

8. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 7, characterized in that, The Schmidt factor of the visualized object in the target slip system needs to be further divided by a correction factor to correct for the critical shear stress. The corrected Schmidt factor is then used for visualization. The correction factor is the critical shear stress of the target slip system and the cylindrical surface. The ratio of the critical shear stresses of the slip system.

9. The method for analyzing the crystallographic behavior of TC4 titanium alloy during deformation as described in claim 1, characterized in that, In S3, the visualization object is a single target grain that the user specifies to be analyzed. The target slip system covers all selectable slip systems. The visualization output is the morphology of the target grain and the slip trace direction and Schmidt factor corresponding to each slip system in the target grain. Alternatively, the visualization object may be all pixels, the target glide system may be a single glide system specified by the user, and the visualization output may be a Schmidt factor distribution map of all pixels under the target glide system.

10. A crystallographic behavior analysis system for the deformation process of TC4 titanium alloy, characterized in that, include: The data input module is used to input EBSD data collected during the deformation process of the TC4 titanium alloy specimen; The behavior analysis module is used to output the slip trace direction and Schmidt factor of the visualized object in the target slip system according to the crystallographic behavior analysis method of the deformation process of TC4 titanium alloy as described in any one of claims 1 to 9.

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